Biomedical applications of light scattering

BiomedicalApplications of

Light Scattering

Biophotonics Series

Series Editors: Israel Gannot and Joseph Neev

Artificial Tactile Sensing in Biomedical Engineering by Siamak Najarian,Javad Dargahi, and Ali Abouei Mehrizi

Biomedical Applications of Light Scattering, edited by Adam Wax andVadim Backman

Optofluidics: Fundamentals, Devices, and Applications, edited byYeshaiahu Fainman, Luke P. Lee, Demetri Psaltis, and ChanghueiYang

Organic Electronics in Sensors and Biotechnology, edited by Ruth Shinarand Joseph Shinar

BiomedicalApplications of

Light ScatteringAdam Wax, Ph.D.

Vadim Backman, Ph.D.

New York Chicago San FranciscoLisbon London Madrid Mexico City

Milan New Delhi San JuanSeoul Singapore Sydney Toronto

Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved. Except as permittedunder the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the priorwritten permission of the publisher.

ISBN: 978-0-07-159881-1

MHID: 0-07-159881-2

The material in this eBook also appears in the print version of this title: ISBN: 978-0-07-159880-4,MHID: 0-07-159880-4.

All trademarks are trademarks of their respective owners. Rather than put a trademark symbol afterevery occurrence of a trademarked name, we use names in an editorial fashion only, and to the benefit of the trademark owner, with no intention of infringement of the trademark. Where such designations appear in this book, they have been printed with initial caps.

McGraw-Hill eBooks are available at special quantity discounts to use as premiums and sales promotions, or for use in corporate training programs. To contact a representative please e-mail us [email protected].

Information contained in this work has been obtained by The McGraw-Hill Companies, Inc.(“McGraw-Hill”) from sources believed to be reliable. However, neither McGraw-Hill nor its authorsguarantee the accuracy or completeness of any information published herein, and neither McGraw-Hill nor its authors shall be responsible for any errors, omissions, or damages arising outof use of this information. This work is published with the understanding that McGraw-Hill and itsauthors are supplying information but are not attempting to render engineering or other professionalservices. If such services are required, the assistance of an appropriate professional should be sought.

TERMS OF USE

This is a copyrighted work and The McGraw-Hill Companies, Inc. (“McGraw-Hill”) and its licen-sors reserve all rights in and to the work. Use of this work is subject to these terms. Except as per-mitted under the Copyright Act of 1976 and the right to store and retrieve one copy of the work, youmay not decompile, disassemble, reverse engineer, reproduce, modify, create derivative works basedupon, transmit, distribute, disseminate, sell, publish or sublicense the work or any part of it withoutMcGraw-Hill’s prior consent. You may use the work for your own noncommercial and personal use;any other use of the work is strictly prohibited. Your right to use the work may be terminated if youfail to comply with these terms.

THE WORK IS PROVIDED “AS IS.” McGRAW-HILL AND ITS LICENSORS MAKE NOGUARANTEES OR WARRANTIES AS TO THE ACCURACY, ADEQUACY OR COMPLETE-NESS OF OR RESULTS TO BE OBTAINED FROM USING THE WORK, INCLUDING ANY INFORMATION THAT CAN BE ACCESSED THROUGH THE WORK VIA HYPERLINK OROTHERWISE, AND EXPRESSLY DISCLAIM ANY WARRANTY, EXPRESS OR IMPLIED,INCLUDING BUT NOT LIMITED TO IMPLIED WARRANTIES OF MERCHANTABILITY ORFITNESS FOR A PARTICULAR PURPOSE. McGraw-Hill and its licensors do not warrant or guarantee that the functions contained in the work will meet your requirements or that its operationwill be uninterrupted or error free. Neither McGraw-Hill nor its licensors shall be liable to you oranyone else for any inaccuracy, error or omission, regardless of cause, in the work or for any dam-ages resulting therefrom. McGraw-Hill has no responsibility for the content of any informationaccessed through the work. Under no circumstances shall McGraw-Hill and/or its licensors be liablefor any indirect, incidental, special, punitive, consequential or similar damages that result from theuse of or inability to use the work, even if any of them has been advised of the possibility of suchdamages. This limitation of liability shall apply to any claim or cause whatsoever whether such claimor cause arises in contract, tort or otherwise.

Contents

Contributors . . . . . . . . . . . . . . . . . . . . . . . . . xiii

Part 1 Introduction to Light Scattering Models

1 Classical Light Scattering Models . . . . . . . . . . . . 31.1 Introduction to Light Scattering . . . . . . . . . 31.2 Structure and Organization of

Biological Tissue . . . . . . . . . . . . . . . . . . . 41.3 Basics of Light Scattering Theory . . . . . . . . 101.4 Approximate Solutions to Light Scattering . . 151.5 Review of Computational Light

Scattering Codes . . . . . . . . . . . . . . . . . . . 22Mie Theory Calculators . . . . . . . . . . . . . 23T-Matrix Calculations . . . . . . . . . . . . . . 25Discrete Dipole Approximation . . . . . . . . 26Time-Domain Codes . . . . . . . . . . . . . . . 26

1.6 Inverse Light Scattering Analysis . . . . . . . . 27Nonuniqueness Problem . . . . . . . . . . . . 27Ill-Conditioned Problem . . . . . . . . . . . . 28Summary . . . . . . . . . . . . . . . . . . . . . . 28

References . . . . . . . . . . . . . . . . . . . . . . . 29

2 Light Scattering from ContinuousRandom Media . . . . . . . . . . . . . . . . . . . . . . . . 31

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . 312.2 3D Continuous Random Media . . . . . . . . . 33

Mean Differential Scattering Cross Section . 33Scattering Coefficient andRelated Parameters . . . . . . . . . . . . . . . 37Simplifying Approximations . . . . . . . . . 40

2.3 2D Continuous Random Media . . . . . . . . . 42Mean Differential Scattering Cross Section . 42Scattering Coefficient and RelatedParameters . . . . . . . . . . . . . . . . . . . . . 43

2.4 1D Continuous Random Media . . . . . . . . . 442.5 Generation of Continuous Random

Media Samples . . . . . . . . . . . . . . . . . . . . 45References . . . . . . . . . . . . . . . . . . . . . . . 47

v

vi C o n t e n t s

3 Modeling of Light Scattering by BiologicalTissues Via Computational Solution ofMaxwell’s Equations . . . . . . . . . . . . . . . . . . . . 49

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . 493.2 Overview of FDTD Techniques for

Maxwell’s Equations . . . . . . . . . . . . . . . . 50Advantages of FDTD Solution Techniquesfor Maxwell’s Equations . . . . . . . . . . . . 51Characteristics of the Yee-AlgorithmFDTD Technique . . . . . . . . . . . . . . . . . 53

3.3 FDTD Modeling Applications . . . . . . . . . . 55Vertebrate Retinal Rod . . . . . . . . . . . . . 55Precancerous Cervical Cells . . . . . . . . . . 57Validation of the Born Approximationin 2D Weakly Scattering BiologicalRandom Media . . . . . . . . . . . . . . . . . . 60Sensitivity of Backscattering Signatures toNanometer-Scale Cellular Changes . . . . . 62

3.4 Overview of Liu’s Fourier-Basis PSTDTechnique for Maxwell’s Equations . . . . . . . 64

3.5 PSTD Modeling Applications . . . . . . . . . . . 65Total Scattering Cross Section of a RoundCluster of 2D Dielectric Cylinders . . . . . . 65Enhanced Backscattering of Light by aLarge Rectangular Cluster of 2D DielectricCylinders . . . . . . . . . . . . . . . . . . . . . . 65Optical Phase Conjugation for TurbiditySuppression . . . . . . . . . . . . . . . . . . . . 68Multiple Light Scattering in 3D RandomMedia . . . . . . . . . . . . . . . . . . . . . . . . 69

3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . 72References . . . . . . . . . . . . . . . . . . . . . . . 73

4 Interferometric Synthetic ApertureMicroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . 77

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . 774.2 Background . . . . . . . . . . . . . . . . . . . . . . 794.3 Theory . . . . . . . . . . . . . . . . . . . . . . . . . 81

Physics of Data Acquisition . . . . . . . . . . 81Compact Forward Model . . . . . . . . . . . . 83Rigorous Forward Model . . . . . . . . . . . . 87Inverse Scattering Procedure . . . . . . . . . 89Numerical Simulations for a SingleScatterer . . . . . . . . . . . . . . . . . . . . . . 90Alternate Acquisition Geometries . . . . . . 91

viiC o n t e n t s

4.4 Experimental Implementation and Validation 92Phase Stability and Data AcquisitionRequirements . . . . . . . . . . . . . . . . . . . 92Three-Dimensional ISAM of TissuePhantoms . . . . . . . . . . . . . . . . . . . . . 96Cross-Validation of ISAM and OCT . . . . . 97ISAM Processing and Real-TimeImplementation . . . . . . . . . . . . . . . . . . 98Practical Limitations . . . . . . . . . . . . . . . 100

4.5 Clinical and Biological Applications . . . . . . 101Optical Biopsy . . . . . . . . . . . . . . . . . . 102Surgical Guidance . . . . . . . . . . . . . . . . 102Imaging Tumor Development . . . . . . . . . 106

4.6 Conclusions and Future Directions . . . . . . . 106References . . . . . . . . . . . . . . . . . . . . . . . 107

Part 2 Application to In Vitro Cell Biology

5 Light Scattering as a Tool in Cell Biology . . . . . . . 1155.1 Introduction . . . . . . . . . . . . . . . . . . . . . 1155.2 Light Scattering Assessments of

Mitochondrial Morphology . . . . . . . . . . . . 1165.3 Light Scattering Assessments of Lysosomal

Morphology . . . . . . . . . . . . . . . . . . . . . 1215.4 Light Scattering Assessments of Nuclear

Morphology . . . . . . . . . . . . . . . . . . . . . 1275.5 Light Scattering Assessments of General

Subcellular Structure . . . . . . . . . . . . . . . . 1355.6 Future Perspectives . . . . . . . . . . . . . . . . . 137

References . . . . . . . . . . . . . . . . . . . . . . . 139

6 Light Absorption and Scattering SpectroscopicMicroscopies . . . . . . . . . . . . . . . . . . . . . . . . . 143

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . 1436.2 Absorption and Scattering in Microscopic

Applications . . . . . . . . . . . . . . . . . . . . . 1446.3 Physical Principles and Basic Parameters

of Elastic Light Scattering . . . . . . . . . . . . . 1476.4 Light Scattering from Cells and Subcellular

Structures . . . . . . . . . . . . . . . . . . . . . . . 1506.5 Confocal Light Absorption and Scattering

Spectroscopic (CLASS) Microscopy . . . . . . . 1536.6 Applications of CLASS Microscopy . . . . . . . 1596.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . 165

References . . . . . . . . . . . . . . . . . . . . . . . 166

viii C o n t e n t s

Part 3 Assessing Bulk Tissue Properties from ScatteringMeasurements

7 Light Scattering in Confocal ReflectanceMicroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . 171

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . 1717.2 The Basic Idea . . . . . . . . . . . . . . . . . . . . 173

Theory Mapping (�, � ) to (�s, g) . . . . . . . 177Experimental Data . . . . . . . . . . . . . . . . 178

7.3 Basic Instrument . . . . . . . . . . . . . . . . . . . 1807.4 Monte Carlo Simulations . . . . . . . . . . . . . 182

Current Ongoing Work . . . . . . . . . . . . . 1867.5 Literature Describing Confocal Reflectance

Measurements . . . . . . . . . . . . . . . . . . . . 188References . . . . . . . . . . . . . . . . . . . . . . . 190

8 Tissue Ultrastructure Scattering withNear-Infrared Spectroscopy: Ex Vivo and In VivoInterpretation . . . . . . . . . . . . . . . . . . . . . . . . . 193

8.1 Introduction . . . . . . . . . . . . . . . . . . . . . 1938.2 Understanding Light Scattering

Measurements in Tissue . . . . . . . . . . . . . . 1958.3 Ex Vivo Measurements: Analysis of Scatter

Signatures . . . . . . . . . . . . . . . . . . . . . . . 197Microsampling Reflectance Spectroscopy . . 199Phase-Contrast Microscopy . . . . . . . . . . 202Electron Microscopy: Understandingthe Submicroscopic Source of Scatter . . . . 204

8.4 Diagnostic Imaging: Approaches forIn Vivo Use . . . . . . . . . . . . . . . . . . . . . . 206

8.5 Therapeutic Imaging: Surgical Assist . . . . . . 2088.6 Acknowledgment . . . . . . . . . . . . . . . . . . 208

References . . . . . . . . . . . . . . . . . . . . . . . 208

Part 4 Dynamic Light Scattering Methods

9 Dynamic Light Scattering and Motility-ContrastImaging of Living Tissue . . . . . . . . . . . . . . . . . 213

9.1 Dynamic Light Scattering and Speckle . . . . . 213Single-Mode Scattering . . . . . . . . . . . . . 214Planar Scattering . . . . . . . . . . . . . . . . . 215Volumetric Scattering . . . . . . . . . . . . . . 216Spatial Homodyne and Heterodyne . . . . . 217Dynamic Scattering . . . . . . . . . . . . . . . 219

ixC o n t e n t s

9.2 Holographic Optical Coherence Imaging . . . 221Fourier-Domain Holography . . . . . . . . . 221Digital Holography . . . . . . . . . . . . . . . 223

9.3 Multicellular Tumor Spheroids . . . . . . . . . . 225Biology in Three Dimensions . . . . . . . . . 227Holographic Optical Coherence Imagingof Tumor Spheroids . . . . . . . . . . . . . . . 227

9.4 Subcellular Motility in Tissues . . . . . . . . . . 2309.5 Motility-Contrast Imaging . . . . . . . . . . . . 2309.6 Conclusions and Prospects . . . . . . . . . . . . 2349.7 Acknowledgment . . . . . . . . . . . . . . . . . . 236

References . . . . . . . . . . . . . . . . . . . . . . . 236

10 Laser Speckle Contrast Imaging of Blood Flow . . . 24110.1 Introduction . . . . . . . . . . . . . . . . . . . . . 24110.2 Single-Exposure Laser Speckle

Contrast Imaging . . . . . . . . . . . . . . . . . . 24210.3 Applications of LSCI to Brain Imaging . . . . . 247

Methodological Details for ImagingCBF Using LSCI . . . . . . . . . . . . . . . . . 247Functional Brain Activation . . . . . . . . . . 248Stroke . . . . . . . . . . . . . . . . . . . . . . . . 250

10.4 Multiexposure Laser Speckle ContrastImaging (MESI) . . . . . . . . . . . . . . . . . . . 253

MESI Theory . . . . . . . . . . . . . . . . . . . 254MESI Instrument . . . . . . . . . . . . . . . . . 255MESI Measurements in MicrofluidicsFlow Phantoms . . . . . . . . . . . . . . . . . . 256

10.5 Future Directions . . . . . . . . . . . . . . . . . . 258References . . . . . . . . . . . . . . . . . . . . . . . 258

Part 5 Clinical Applications

11 Elastic-Scattering Spectroscopy for OpticalBiopsy: Probe Designs and Analytical Methodsfor Clinical Applications . . . . . . . . . . . . . . . . . . 263

11.1 Introduction . . . . . . . . . . . . . . . . . . . . . 26311.2 Fiberoptic Probe Designs . . . . . . . . . . . . . 264

Single Optical Fiber Probes . . . . . . . . . . 265Differential Pathlength Spectroscopy . . . . 266Angled Probes . . . . . . . . . . . . . . . . . . 266Probes Incorporating Full andHalf-Ball Lenses . . . . . . . . . . . . . . . . . 267Side-Sensing Probes . . . . . . . . . . . . . . . 268

x C o n t e n t s

Diffusing-Tip Probes . . . . . . . . . . . . . . . 268Polarized Probes . . . . . . . . . . . . . . . . . 270

11.3 Models for the Reflectance Spectra . . . . . . . 270Methods for Analyzing Reflectance Spectra 270A Quantitative Analytical Model Well-Suitedto Superficial Tissues . . . . . . . . . . . . . . 272Influence of Blood Vessel Radius . . . . . . . 274

11.4 In Vivo Application in a Human Study . . . . . 27711.5 Influence of Probe Pressure . . . . . . . . . . . . 281

Influence of Probe Pressure on NormalColon Mucosa: A Preliminary ClinicalStudy . . . . . . . . . . . . . . . . . . . . . . . . 281Influence of Probe Pressure on ReflectanceMeasurements: A QuantitativeAnimal Study . . . . . . . . . . . . . . . . . . . 283Temporal Influence of Probe Pressureon Reflectance Measurements: An AnimalStudy . . . . . . . . . . . . . . . . . . . . . . . . 286

11.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . 287References . . . . . . . . . . . . . . . . . . . . . . . 288

12 Differential Pathlength Spectroscopy . . . . . . . . . 29312.1 Basic Concepts . . . . . . . . . . . . . . . . . . . . 293

Introduction . . . . . . . . . . . . . . . . . . . . 293Main Properties and Features . . . . . . . . . 294Pathlength . . . . . . . . . . . . . . . . . . . . . 295Basic Mathematical Analysis of Spectra . . . 297

12.2 DPS Measurements In Vivo . . . . . . . . . . . . 299Main Features . . . . . . . . . . . . . . . . . . . 299Additional Spectral Features . . . . . . . . . . 302Confidence Intervals . . . . . . . . . . . . . . . 303

12.3 Clinical Measurements . . . . . . . . . . . . . . . 30512.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . 309

References . . . . . . . . . . . . . . . . . . . . . . . 310

13 Angle-Resolved Low-Coherence Interferometry:Depth-Resolved Light Scattering forDetecting Neoplasia . . . . . . . . . . . . . . . . . . . . 313

13.1 Introduction . . . . . . . . . . . . . . . . . . . . . 31313.2 Instrumentation . . . . . . . . . . . . . . . . . . . 315

Early Implementations . . . . . . . . . . . . . 315Frequency-Domain Implementation . . . . . 319Portable System . . . . . . . . . . . . . . . . . . 321

xiC o n t e n t s

13.3 Processing of a/LCI Signals . . . . . . . . . . . . 322Data Processing for Phantoms . . . . . . . . . 323Data Processing for Cell Nuclei . . . . . . . . 323

13.4 Validation Studies . . . . . . . . . . . . . . . . . . 325Polystyrene Microspheres . . . . . . . . . . . 325In Vitro Cell Studies . . . . . . . . . . . . . . . 327

13.5 Tissue Studies . . . . . . . . . . . . . . . . . . . . 330Animal Studies . . . . . . . . . . . . . . . . . . 330Human Esophageal Epithelium . . . . . . . . 335

13.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . 33713.7 Acknowledgments . . . . . . . . . . . . . . . . . 337

References . . . . . . . . . . . . . . . . . . . . . . . 338

14 Enhanced Backscattering and Low-CoherenceEnhanced Backscattering Spectroscopy . . . . . . . . 341

14.1 Principles of Enhanced Backscattering . . . . . 341Overview and Further Reading . . . . . . . . 341Theory of EBS . . . . . . . . . . . . . . . . . . . 342Applications of EBS . . . . . . . . . . . . . . . 347

14.2 Low-Coherence Enhanced Backscattering . . . 347Enhanced Backscattering of PartiallyCoherent Light . . . . . . . . . . . . . . . . . . 348Observation of Low-Coherence EnhancedBackscattering . . . . . . . . . . . . . . . . . . . 349Characteristics of LEBS . . . . . . . . . . . . . 350Theory of LEBS in Tissue . . . . . . . . . . . . 352

14.3 Applications of Low-Coherence EnhancedBackscattering Spectroscopy . . . . . . . . . . . 353

Colorectal Cancer . . . . . . . . . . . . . . . . 353LEBS Detection of Early CancerousAlterations in Colon Carcinogenesis . . . . . 355

References . . . . . . . . . . . . . . . . . . . . . . . 358

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361

About the EditorsAdam Wax, Ph.D., is an associate professor of biomedi-cal engineering at Duke University with a research em-phasis on biophotonics.

Vadim Backman, Ph.D., is a professor of biomedical en-gineering at Northwestern University, where he spe-cializes in optical imaging.

Contributors

Steven G. Adie Beckman Institute for Advanced Science and Technology,University of Illinois at Urbana-Champaign, Urbana, Illinois (Chap. 4)J. G. J. V. Aerts Department of Respiratory Diseases, Amphia Hospital,Breda, The Netherlands (Chap. 12)Arjen Amelink Assistant Professor, Center for Optical Diagnostics andTherapy, Department of Radiation Oncology, Erasmus Medical Center,Rotterdam, The Netherlands (Chap. 12)Vadim Backman Professor, Biomedical Engineering Department,McCormick School of Engineering and Applied Sciences, NorthwesternUniversity, Evanston, Illinois (Chaps. 1, 2, 14)Irving J. Bigio Professor, Departments of Biomedical Engineering,Electrical and Computer Engineering, Physics, Medicine, BostonUniversity, Boston, Massachusetts (Chap. 11)Stephen A. Boppart Professor, Beckman Institute for Advanced Scienceand Technology, University of Illinois at Urbana-Champaign, Urbana,Illinois (Chap. 4)S. C. (Chad) Canick Center for Optical Diagnostics and Therapy,Erasmus Medical Center, Rotterdam, The Netherlands (Chap. 12)

Ilker R. Capoglu Postdoctoral Research Fellow, Biomedical EngineeringDepartment, Northwestern University, Evanston, Illinois (Chaps. 2, 3)

P. Scott Carney Associate Professor, Department of Electrical andComputer Engineering, University of Illinois at Urbana-Champaign,Urbana, Illinois (Chap. 4)Kevin J. Chalut Postdoctoral Research Associate, Department of Physics,University of Cambridge, Cambridge, United Kingdom (Chap. 5)

Niloy Choudhury Research Associate, Department of BiomedicalEngineering, Oregon Health & Science University, Portland, Oregon(Chap. 7)

Brynmor J. Davis Beckman Institute for Advanced Science and Technology,University of Illinois at Urbana-Champaign, Urbana, Illinois (Chap. 4)

Andrew K. Dunn University of Texas at Austin, Austin, Texas (Chap. 10)Thomas H. Foster Professor, The Institute of Optics and Department ofImaging Sciences, University of Rochester, Rochester, New York (Chap. 5)

Daniel S. Gareau Postdoctoral Fellow, Department of Dermatology andBiomedical Engineering, Oregon Health & Science University, Portland,Oregon (Chap. 7)

xiii

xiv C o n t r i b u t o r s

Irving Itzkan Lecturer, Biomedical Imaging and Spectroscopy Laboratory,BIDMC, Harvard University, Boston, Massachusetts (Chap. 6)

Steven L. Jacques Professor, Department of Dermatology and BiomedicalEngineering, Oregon Health & Science University, Portland, Oregon(Chap. 7)

Kwan Jeong Professor, Korean Military Institute, Seoul, Korea (Chap. 9)

Young Kim Assistant Professor, Department of Biomedical Engineering,Purdue University, West Lafayette, Indiana (Chap. 14)

Venkataramanan Krishnaswamy Research Associate, Thayer School ofEngineering, Dartmouth College, Hanover, New Hampshire (Chap. 8)

Ashley M. Laughney Graduate Research Assistant, Thayer School ofEngineering, Dartmouth College, Hanover, New Hampshire (Chap. 8)

David Levitz Graduate Student, Department of Biomedical Engineering,Oregon Health & Science University, Portland, Oregon (Chap. 7)

Daniel L. Marks Department of Electrical and Computer Engineering,Duke University, Durham, North Carolina (Chap. 4)

David D. Nolte Professor, Department of Physics and Department of BasicMedical Sciences, Purdue University, West Lafayette, Indiana (Chap. 9)

Lev T. Perelman Associate Professor and Director, Biomedical Imagingand Spectroscopy Laboratory, BIDMC, Harvard University, Boston,Massachusetts (Chap. 6)

Brian W. Pogue Professor, Thayer School of Engineering, DartmouthCollege, Hanover, New Hampshire (Chap. 8)

Le Qiu Postdoctoral Fellow, Biomedical Imaging and SpectroscopyLaboratory, BIDMC, Harvard University, Boston, Massachusetts(Chap. 6)

Tyler S. Ralston MIT Lincoln Laboratory, Lexington, Massachusetts(Chap. 4)

Roberto Reif Program Manager, Microsoft Corporation, Redmond,Washington (Chap. 11)

Jeremy D. Rogers Postdoctoral Fellow, Department of BiomedicalEngineering, Northwestern University, Evanston, Illinois (Chaps. 2, 14)

Ravikant Samatham Graduate Student, Department of BiomedicalEngineering, Oregon Health & Science University, Portland, Oregon(Chap. 7)

H. J. C. M. (Dick) Sterenborg Professor, Center for Optical Diagnosticsand Therapy, Erasmus Medical Center, Rotterdam, The Netherlands(Chap. 12)

Allen Taflove Professor, Department of Electrical Engineering andComputer Science, Northwestern University, Evanston, Illinois (Chap. 3)

xvC o n t r i b u t o r s

Neil Terry Graduate Student, Department of Biomedical Engineering,Duke University, Durham, North Carolina (Chaps. 1, 13)

Frederic Truffer Graduate Student, Department of BiomedicalEngineering, Oregon Health & Science University, Portland, Oregon(Chap. 7)

Snow H. Tseng Assistant Professor, Graduate Institute of Photonics andOptoelectronics, and Department of Electrical Engineering, NationalTaiwan University, Taipei, Taiwan (Chap. 3)

John Turek Department of Physics and Department of Basic MedicalSciences, Purdue University, West Lafayette, Indiana (Chap. 9)

Vladimir Turzhitsky Graduate Student, Biomedical EngineeringDepartment, McCormick School of Engineering and Applied Sciences,Northwestern University, Evanston, Illinois (Chap. 14)

C. van der Leest Department of Respiratory Diseases, Amphia Hospital,Breda, The Netherlands (Chap. 12)

Adam Wax Associate Professor, Department of Biomedical Engineering,Duke University, Durham, North Carolina (Chaps. 1, 13)

Yizheng Zhu Postdoctoral Associate, Department of BiomedicalEngineering, Duke University, Durham, North Carolina (Chap. 13)

This page intentionally left blank

P A R T 1Introduction to LightScattering Models

CHAPTER 1Classical Light Scattering Models

CHAPTER 2Light Scattering from ContinuousRandom Media

CHAPTER 3Modeling of Light Scattering byBiological Tissues viaComputational Solution ofMaxwell’s Equations

CHAPTER 4Interferometric Synthetic ApertureMicroscopy


C H A P T E R 1Classical Light

Scattering Models

V. Backman and A. Wax

1.1 Introduction to Light ScatteringLight scattering first captured the imagination of the ancients withobservations of variations of color in nature, including the blue sky,the rainbow, and the dramatic colors seen at dusk and dawn. The firstrecorded light scattering observations date back to the 11th centurywhen Alhasen of Basra attempted to explain the color of the blue sky.Many great scientific minds that followed pursued light scatteringexperiments, including Leonardo da Vinci and Sir Isaac Newton. LordRayleigh was the first to provide a quantitative treatment of lightscattering in the 19th century and the concept of Rayleigh scatteringsurvives to this day. While light scattering analysis is used in manyfields of study, it is only recently that light scattering has become usefulfor biomedical applications, which is the subject of this text.

In this text, we seek to provide a review of recent advances inthe use light scattering for biomedical applications. This introductorychapter provides a framework for the chapters that follow, includingan overview of biological scatterers and basic light scattering theories.The chapter then turns its attention to practical matters, providinga review of approximate solutions to the light scattering problemsand discussing various light scattering codes and the inverse lightscattering problem.

The remainder of this text is divided into five sections. The first sec-tion includes chapters on light scattering from continuous media anda review of time-domain simulations of light scattering for biologicalapplications. The section concludes with the introduction of a new in-verse light scattering method for optical coherence tomography. The

3

4 I n t r o d u c t i o n t o L i g h t S c a t t e r i n g M o d e l s

second section turns its attention toward using light scattering forexamining cell in vitro. Chapters in this section include a review oflight scattering analysis to identify particular subcellular features aswell as an overview of light scattering measurements using confocalmicroscopy.

The third section of this text focuses on characterizing biologicaltissues by measuring their bulk optical properties. Chapters in thissection examine the use of this approach with two different modal-ities, confocal microscopic imaging and diffuse optical tomography.The fourth section presents recent work on using dynamic light scat-tering for tissue imaging. Although dynamic light scattering has beenused for studying biomolecules in solution since the early days ofthe laser, the work covered here focuses on application for imag-ing tissues, including motility contrast imaging and speckle contrastimaging.

The final section of this text reviews recent clinical applicationsof light scattering. The chapters in this section include a review ofelastic scattering spectroscopy for optical biopsy and an overviewof differential path-length spectroscopy for characterizing bulk tis-sue properties in vivo. The last two chapters present angle-resolvedlow-coherence interferometry, which combines light scattering withinterferometry to execute depth-resolved nuclear morphology mea-surements as means of detecting precancerous lesions and enhancedbackscattering spectroscopy, which uses the coherent backscatteringphenomenon to obtain spectroscopic information from surface tissuelayers as a screening technique to risk stratify patients for colono-scopies.

1.2 Structure and Organization of Biological TissueElastic light scattering is the most dominant type of light–tissue inter-action. Static light scattering originates from spatial heterogeneity ofthe optical refractive index. In turn, refractive index depends on theconcentration and type of tissue constituencies. Various tissue struc-tures such as cellular organelles and extracellular matrix give rise tospatially heterogeneous distribution of refractive index and may affectlight propagation in tissue including the spectroscopic, polarization,or angular features of scattered light emerging from tissue. In princi-ple, a tissue structure of any size may result in light scattering. How-ever, it is structures comparable to the wavelength of light that aremostly responsible for light scattering. The term “comparable,” how-ever, should be used with caution because it covers a very broadlydefined range of sizes that, depending on the observable property ofscattered light, may range from a few tens of nanometers to tens ofmicrons. Therefore, in order for us to understand the origin of light

5C l a s s i c a l L i g h t S c a t t e r i n g M o d e l s

scattering in biological media, we first need to overview the basicprinciples of tissue micromorphology.

There are four basic tissue types: epithelium, connective tissueand blood as its specialized form, nervous tissue, and muscle. Tissuesof any organ are composed of a combination of these four basic tissuetypes. For example, esophageal wall contains layers of epithelial cellsthat line up its innermost surface, connective tissue underlying theepithelium, a number of layers of smooth muscle cells, nerve fibers,and blood vessels interspersed within the connective tissue and mus-cle. From a simplified perspective, any of these basic tissues can beviewed as a combination of cellular material and extracellular matrix(ECM). For example, on zooming in on the connective tissue of theepithelium, one will see white blood cells and connective tissue cells(generating and remodeling ECM) all within an ECM. In this chapter,we first review the basics of the cell structure followed by a discussionof ECM organization. This should not be viewed as a comprehensivediscussion of tissue morphology—a good book on histology wouldhave no less than 1000 pages!—instead, the goal of this section is tointroduce the absolute minimum of information necessary to under-stand the basic principles of elastic light scattering in tissue.

In a human body, at least 200 cell types can be identified. Despitethis diversity, many cells possess a number of key common features.A cell is bounded by a membrane, the plasmalemma. Plasmalemma is aphospholipid bilayer ∼10 nm thick with transmembrane and peripheralproteins embedded in it. The overall thickness of the plasmalemmaincluding membrane proteins may reach 30 nm. Little is known aboutthe mass density of essentially any cellular organelle including cellmembrane. Plasmalemma and intracellular membranes (see below),however, are frequently considered some of the most dense structuresin a cell with local density approaching 30–40% of solid mass (lipidsand proteins) by volume (i.e., membrane solids occupy 30–40% of theentire volume of the membrane).

Inside a cell, two major compartments are the nucleus and the cyto-plasm. Decades ago, a widely used representation of the cell was rathercartoonish and pictured cytoplasm as a liquid soup with organellesswimming around. We know now that this picture is highly inaccu-rate. Indeed, cytoplasm is a highly organized compartment wherethe location of organelles is tightly regulated. Various elements ofcytoskeleton and a complex network of intracellular membranes pro-vide integrity and mechanical stability to the cell. We start with a listof major organelles and inclusions and their properties.

Cell nucleus is the largest organelle in the cell. Frequently, it hasa spheroidal shape, although in some cases, it may be infolded orlobulated. Typical size of a cell nucleus is 5–10 �m, although it maysignificantly vary among different cell types. The nucleus is boundedby the nuclear envelope, two membranes separated by 30 nm. The major


part of the nucleus is the chromatin. Each nucleus typically containstwo forms of chromatin: the heterochromatin, which contains a non-transcribed portion of the genome, and the euchromatin, where thetranscription happens. This divide between heterochromatin and eu-chromatin is by no means fixed. DNA may move from euchromatinto heterochromatin in the process that is still poorly understood butin what appears to be controlled by hypermethylation. Heterochro-matin appears as a collection of irregularly shaped, interconnectedclumps that vary in size from 300 to 1000 nm. It is made up of closelyspaced 30 nm fibrils, which in turn are composed of even smallersubunits, the nucleosomes. Heterochromatin appears darker whenstained with basic dyes (e.g., H&E) and on electron microscopy im-ages. It is easy to assume that the heterochromatin is denser than theeuchromatin. This also agrees with the conceptual understanding oftheir functions: access of transcription factors to DNA is restricted inthe heterochromatin. On the other hand, density distribution in thenucleus remains a bit of a mystery, and it is entirely possible that newresearch will uncover potentially counterintuitive facts. Based on con-focal microscopy studies, it appears that at least the euchromatin por-tion of the nucleus (which frequently occupies most of the nucleus) isrelatively homogeneous with little density variations at length scalesabove 500 nm. Neutron scattering studies revealed that both nuclearproteins and DNA components have a mass fractal organization fromlength scales as small as 15 nm and up to the size of entire nuclei withmass fractal dimension between 2 and 3.1 (Although nuclear proteinsmay have the same mass fractal dimension for all length scales, DNAorganization appears to be biphasic with the mass fractal dimension∼2 at length scales under 400 nm and approaching 3 at the largerscales. Larger mass fractal dimension is indicative of a more globularorganization.)

An important nuclear inclusion is the nucleolus, which is respon-sible for the transcription of ribosomal RNA and ribosomal assembly.It has a size from 500 to 1000 nm and consists of a network of parsgranulose strands, which are made of 15 nm ribonucleoprotein particles.Intranucleolar fibrillar centers are ∼80 nm in size. According to somemicroscopy studies, nucleolus is denser than the rest of the nucleusand, in fact, may well be the most dense structure in a cell. Again,future studies will show if these conclusions are entirely correct.

Mitochondria typically have spheroidal shapes. A length of largeaxis of a mitochondrion may range anywhere from 1 to 2 �m, al-though some mitochondria may reach up to 5 �m (which is rare). Thelength of the small axis typically varies between 0.2 and 0.8 �m. Me-chanical flexibility of mitochondria ensures that in living tissue theyare constantly in motion and may easily change their shape. Becausethe metabolic requirements of different cells vary, the number of mi-tochondria in cells differs, depending dramatically on the cell type.


For example, membranous epithelial cells (e.g., epithelial lining ofgastrointestinal tract, bronchial tree, genitourinary tract, etc.) mayhave only a few mitochondria per cell. On the other hand, liver cells,hepatocytes, typically contain thousands of mitochondria, denselypacked within cells, which gives hepatic tissue its unique histologi-cal appearance. A mitochondrion is bounded by an outer membraneand has a folded inner membrane. Because of a high concentrationof membranes within mitochondria, they are typically expected tohave a relatively high refractive index and behave as powerful lightscatters.

Endoplasmic reticulum (ER) is composed of tubules and sheets ofmembranes with sizes ranging from 30 to 100 nm. ER comes in twovarieties: smooth endoplasmic reticulum (SER), which plays a role inmolecular transport and cholesterol and lipid synthesis, and rough en-doplasmic reticulum (RER), which is the main site of protein synthesis.RER received its name from the time of first electron microscopy stud-ies, as it appears denser on electron microphotographs. This is due to25 nm ribosomes that like fine beads embroider RER—these are thesites of protein assembly. RER is typically located close to the nucleus,while SER is farther at the cell periphery. Because of the dense mem-branous network, the refractive index of RER may spatially fluctuateat length scales as small as a few tens of nanometers.

Cytoskeleton is a network of filamentous proteins that includes mi-crotubules, intermediate filaments, and microfilaments, with diameters of25, 10, and 7 nm, respectively. The importance of the cytoskeletongoes far beyond the role that has been traditionally assigned to it,mechanical stability. It certainly participates in the signal transduc-tion, thus influencing gene transcription in response to extracellularfactors.

Other prominent organelles are Golgi apparatus with the overallthickness from 100 to 400 nm, lysosomes (250–800 nm structures of vari-ous shapes, sometimes spherical but sometimes resembling a randomsphere), and peroxisomes (200–1000 nm spheroidal structures of lowerinner density than lysosomes, more abundant in the metabolically ac-tive cells such as hepatocytes, which may contain as many as hundredsof lysosomes and peroxisomes in sharp contrast to less metabolicallyactive cells such as the ones found in membranous epithelia). Themass density inside these organelles has not been thoroughly stud-ies and we can only speculate. It is possible that these organelles areless dense than mitochondria, although one can argue that the oppo-site is also feasible. Future studies will hopefully shine some light onthis issue. Besides organelles, each cell contains numerous cytoplas-mic inclusions, such as secretory granules, lipid granules, and pigmentbodies. Most of these inclusions are nearly spherical (surface rough-ness under 40 nm) and have a huge variability in sizes from 20 to500 nm.


At this point, we can make a few conclusions regarding cell orga-nization:

1. The nucleus is by far the largest organelle in the cell. Thesize of most other cytoplasmic organelles is typically less than1 �m.

2. Organelles are not homogenous particles. Most organelleshave an intricate and complex internal organization withsmaller substructures typically identifiable. In turn, these sub-structures are assembled from fundamental macromolecularbuilding blocks (e.g., macromolecular complexes and mem-branes) with sizes in the order of a few tens of nanometers.These are ribosomes in the RER; membranes in the RER,SER, mitochondria; and Golgi apparatus and nucleosomes inthe nucleus, just to name a few. (Of course, macromolecularcomplexes themselves are composed of individual proteinsand/or lipid layers. However, because individual moleculesare negligibly small compared to the wavelength of visiblelight, we can usually ignore this level of organization.)

3. It is a matter of curious coincidence that the wavelength oflight in the optical range is essentially at the borderline be-tween the world of organelles with sizes 200–1000 nm andthe world of macromolecular complexes with sizes below100 nm.

Out of the four basic tissue types, epithelium has the highest celldensity. Indeed, it primarily consists of contiguous epithelial cells.Epithelia do not have either blood supply (these cells derive theirnutrients and satisfy their oxygen demand from the vasculature lo-cated in the underlying connective tissue) or nerve fibers. There arequite a few different types of epithelia. They are classified based onthe number of cell layers, shape of the cells, and the free surfacespecializations. Based on the number of cell layers, an epithelium isclassified as simple (one cell layer), stratified (multiple cell layers),pseudostratified (single layer of cells that appear to be stratified), ortransitional (multiple cell layers with larger cells on the surface andcolumnar-like cells at the bottom). Based on the shape of the cells,an epithelium is classified as squamous (flat cells), cuboidal (cells ofcuboidal shape), or columnar (tall cells). One can identify a particu-lar type of epithelial tissue through a combination of these two clas-sifications (e.g., simple columnar epithelium or squamous stratifiedepithelium). Some of the examples of epithelia are simple squamous(endothelium lining up blood vessels); squamous stratified (mucosallining of the esophagus, cervix, skin, and oral cavity); simple columnar(mucosa of the large and small intestines); pseudostratified (bronchial


mucosa); and transitional (bladder). Epithelial thickness varies widelydepending not only on its type but also on the location. The thinnestepithelium is simple squamous, which is only 1–2 �m thick. Squa-mous stratified epithelium, on the other hand, can be ∼1 mm thick.Other types fall in between, with simple columnar that is ∼20 �m tall(although simple columnar mucosae are usually not flat and ratherfolded into higher-order structures such as crypts in the colon or villiin the small intestine; these mucosal structures are a few hundredmicrons thick), transitional, and pseudostratified, that is, ∼500 �mthick.

Unfortunately, despite years of research, it is still difficult to unam-biguously talk about the optical properties of most tissue types. Thisis primarily due to experimental difficulties and multiple confound-ing factors that hinder rock-solid experimental measurements of thescattering properties of tissue. Factors such as hydration and tissuehandling may change tissue density and, thus, its scattering proper-ties. It is sometimes difficult to completely separate different tissuecompartments (connective vs. epithelium, mucosa vs. submucosa vs.muscularis mucosa, etc.). Furthermore, the accuracy of measurementsperformed using the most widely used and best trusted experimentaltechnique, an integrating sphere, is limited for tissues with a highlyforward pattern of light scattering (quantified by a large anisotropycoefficient g, as discussed in the following section). Although mostliving tissues have relatively high values of g, epithelium in partic-ular is likely to have one of the largest anisotropy coefficients. Moststudies do agree, however, that epithelium has a relatively long trans-port mean free path length l ′s (for definition of the transport mean freepath length and other scattering properties, see the following section),which is in the order of several millimeters. Scattering mean free pathlengths, l ′s, as short as ∼100 �m and as long as a few hundred micronshave been quoted. Further studies are necessary to fully understandthis issue. It is also possible that different types of epithelia have dis-tinctly different scattering properties. For instance, columnar epitheliaappear to be optically denser than squamous stratified epithelia and,in fact, may even have similar optical thickness (optical thickness ifthe product of mean free path lengths and the physical thickness) de-spite their dramatic differences in physical thickness. Finally, whenone considers light propagation in an epithelium, the question of theorigin of light scattering almost always comes up: Does the scatteringoriginate from cells that comprise the epithelium or from intracellu-lar structures discussed above? It is widely believed that because thecells are contiguous, there is no large refractive index mismatch amongneighboring cells and it is the refractive index variations due to the in-tracellular structure that give rise to light scattering. This justifies theimportance of understanding of intracellular structure as discussedabove.


We now turn our attention to the organization of connective tissue.At least eight types of connective tissue have been identified includ-ing loose (areolar), dense irregular, dense regular, adipose, reticular,cartilage, bone, and blood. As biomedical applications of light scat-tering are concerned, loose connective tissue found in the mucosaeand submucosae is the most relevant. Although extracellular matrixis prevalent in loose connective tissue, it is important to rememberthat connective tissue does have a cellular component. Connective tis-sue cells include white blood cells, fibroblasts, and occasionally othercells. Most connective tissues do not contain a large number of cells,which in part justifies a simplified view of connective tissue as beingprimarily composed of extracellular materials. The extracellular ma-terials include connective tissue fibers, amorphous ground substance, andtissue fluid. There are three types of fibers: collagen, elastin, and retic-ular fibers. The first are the best known and for a good reason—theyare the dominant type of ECM fibers. Collagen fibers are unbranching,∼500 nm in diameter, and consist of smaller fibrils, which are ∼70 nmin diameter, separated by about 100 nm. Collagen types I and II arethe two most dominant types of collagens in loose connective tissue.Collagen type IV is another important collagen and comprises base-ment membranes underlying essentially all types of epithelia, thusseparating an epithelial lining from the underlying connective tissue.Elastic fibers branch and are 10 nm in diameter and form a loose three-dimensional network. Reticular fibers are also ∼10 nm in diameter andbranching.

Collagen fiber network is believed to be randomly birefringent,i.e., its birefringent properties become apparent locally, e.g., within a100 �m-sized volume, but vary randomly from location to locationand, thus, may not be apparent at larger scales. This view, however,as many aspects of tissue optics, awaits its ultimate proof. Further-more, collagen fibers are believed to be quite optically dense becauseof their high mass density. This may explain higher scattering prop-erties of connective tissue when compared to cellular tissues such asmembranous epithelia. Again, we have to point out that the scatter-ing properties of many connective tissues are not fully understood.In many studies, transport mean free path length l ′s is cited as ∼500–1000 �m, mean free path length ls ∼ 50–100 �m, and anisotropy factorg ∼ 0.8–0.9.

1.3 Basics of Light Scattering TheoryWhen light interacts with biological tissue (or any other turbidmedium for this matter), elastic scattering is inevitable. Any spatialvariation in refractive index contributes to light scattering. This is thesame process that scatters sunlight in the atmosphere, thus resulting in


a blue appearance of the sky and the same process that gives cloudsand milk their white color. The only difference is that scattering intissue is a more complex process because of the complexity of tissuestructure. Indeed, tissue structure and refractive index are interlinked.A simple relationship expresses an optical refractive index n throughthe local molecular density:

n = n0 + �� (1.1)

where n0 is a refractive index of the liquid medium (i.e., water), �is the portion of tissue solids by volume, and � is a proportionalitycoefficient. Naturally, all these quantities are functions of the wave-length of light. � quantifies the portion of the local volume occupiedby tissue solids such as proteins, DNA, RNA, lipids, etc., and canvary from 0 to 1. For a completely dry particle, � = 1. If a mediumis devoid of any molecules except those of water, � = 0. It is diffi-cult to precisely measure coefficient �, and different values have beenreported. Most studies agree that � ∼ 0.17–0.2. It is tempting to as-sign a specific value of � for a particular macromolecular species.This, however, is not clear as different studies reported slightly dif-ferent values of � for the same types of molecules. At the same time,what is actually remarkable is not the uncertainty associated withthe range of � values but the fact that this range is fairly narrowfor a wide variety of biological molecules! Perhaps the best explana-tion is that, at the molecular level, tissue is composed of a limitednumber of basic molecular species including proteins, lipids, DNA,and RNA. Despite their dramatic chemical and biological differences,all these macromolecules are composed of optically similar carbon-based chemical units. Ensemble averaging within any relevant vol-ume, even as small as a few tens of nanometers, further homogenizesthe optical behavior of biological structures. At this point we have tovoice some caution. Although widely accepted and frequently used,this equation has been rigorously verified only for low concentra-tions. Despite this fact, it is most likely still quite useful for largevalues of �.

What does Eq. (1.1) tell us about the refractive index of biolog-ical structures? The refractive index of a structure containing pureprotein or lipids and no water would be around 1.53. This is rea-sonable as this value is not far from what we know about the re-fractive index of oil. Denser structures such as collagen fibers andcell membranes are expected to have a higher refractive index. Cy-tosole (with no organelles) has � ∼ 10%, which translates into n∼ 1.35.In a cell organelle, on the other hand, � ∼ 30% and n∼ 1.39. Somecell compartments such as nucleolus and heterochromatin probablyhave as much as 50% of their volume occupied by macromoleculeswith n∼ 1.42. Of course, all these values are approximate because


we do not know with certainty the mass density of most intracellu-lar and extracellular structures. However, these estimates are close tothe experimental values measurable using techniques such as phasemicroscopy, low-coherence interference, and differential interferencecontrast.

We are now ready to define basic physical characteristics thatdescribe the process of light scattering. Consider an electromagneticwave with unit amplitude propagating in direction s0 impinging upona region of refractive-index variations. In the far field, at a point r lo-cated at a distance r = |r| from the location of the scatter, the process ofscattering generates a spherical wave E(s)(r) propagating in directions = r/r :

E(s)(r) = f(s, s0)eikr

r(1.2)

where f(s, s0) is the scattering amplitude. Despite its name, generallyf(s, s0) is a complex vector. Scattering amplitude has a dimension ofinverse length.

A related (and by all means equivalent) description of the scat-tered field is based on the concept of the scattering matrix. The scatter-ing matrix relates the components of the incident wave Ei2 and Ei1,which are parallel and perpendicular to the plane of scattering (s, s0),respectively, to those of the scattered wave Es2 and Es1:

(Es2

Es1

)= e−i(kr−kz)

ikr

(S2 S3

S4 S1

)(Ei2

Ei1

)(1.3)

Here s0 is chosen along z direction; r = r (� ,�), with � and � being thepolar angles in the spherical system of reference associated with theparticle; and Sj (�,�), j = 1, . . . , 4, are complex functions. Angle � =cos−1 (s · s0) is called the scattering angle. If a particle is cylindricallysymmetrical in respect to the direction of propagation of the incidentlight, S3 = S4 = 0, and S1 and S2 are functions of scattering angle � onlyand do not depend on �. In this case, the intensities of the componentsof the scattered field that are polarized along and orthogonally tothe scattering plane, I||s and I⊥s, are proportional to the respectivecomponents of the incident light I||i and I⊥i:

I||s = |S2(�)|2k2r2 I||i, I⊥s = |S1(�)|2

k2r2 I⊥i (1.4)

Scattering cross section (sometimes referred to as the total scatteringcross section) is perhaps the most widely used property characteriz-ing a scattering event. It is the geometrical cross section of a particle,which would produce an amount of scattering equal to the observed


scattered power in all directions of a solid angle � and is given by

�s =∫

(4�)| f (s, s0)|2 d� = 1

2k2

∫ 2�

0

∫ 0

�

(|S1+S4|2+|S2+S3|2)

d cos �d�

(1.5)A related quantity, the total cross section is the sum of the scattering

and absorption cross sections:

�t = �s + �a (1.6)

The ratio �s/�t is called the albedo. Scattering efficiency is definedas Q = �s/G, where G is the geometrical cross section of a scatteringobject.

While scattering cross section quantifies the total scattering powerof a scattering object, it does not tell us about the angular distributionof the scattered field. The differential cross section �s(s, s0) and the phasefunction p(s, s0) do just that:

�s(s, s0) = | f (s, s0)|2 , p(s, s0) ∝ |f(s, s0)|2�t

(1.7)

There are two means to normalize the phase function. Accordingto one notation, the phase function is normalized such that the integralover all angles of scattering equals the albedo:∫

(4�)p(s, s0) d� = �s

�t(1.8)

Alternatively, it can be normalized such that the integral equalsthe total solid angle 4�: ∫(4�) p(s, s0) d� = 4�(�s/�t). Both notationsare used. It is important to remember that although both the phasefunction and the scattering cross section are expressed through thescattering amplitude, they do not convey the same information. Onecan envision an object with a large scattering cross section and a highlyforward-peaked scattering pattern and vice versa. Typically, largerscattering particles (relative to the wavelength) have more forward-peaked phase function, while smaller scatters scatter more isotropi-cally.

There are two approaches to calculate �t: one by integrating thedifferential cross section over solid angle and the other by using theforward scattering theorem that states that

�t = 4�

kIm f (s0, s0) (1.9)

where Im stands for the imaginary part. This remarkable and a priorinot so intuitive result will be used later on to derive the total scatteringcross section of large soft particles.


In tissue optics, light propagation is conveniently quantified bythree parameters: scattering coefficient �s, absorption coefficient �a, andanisotropy coefficient (also known as anisotropy factor) g, as well astheir derivatives. For a particulate medium with scattering particleslocated in the far field of each other

�s = �s�N (1.10)

where �N is the number density of scattering particles. Absorptioncoefficient is defined in a similar way through the absorption crosssection of individual absorbing particles. �s has units of length. Alongwith the reduced scattering coefficient (see below), it is one of the twomost widely used measures of how strong the scattering tissue is. Analternate and equivalent definition of �s is as follows:

�s = �s,V

V(1.11)

where �s,V is the scattering cross section of a volume V. This def-inition is particularly useful when considering a medium where theconcept of isolated scattering particles is poorly defined such as amedium with spatially continuous refractive index fluctuations (seebelow). Naturally, these two definitions agree in case of a particulatemedium.

Mean free path length is defined as the inverse of the scatteringcoefficient: ls = 1/�s. Conceptually, ls is the mean distance betweentwo scattering events. In tissue, ls is in the order of few tens of mi-crons in highly scattering tissues and can be as long as a few hundredmicrons.

Anisotropy coefficient

g =

∫(4�)

p(s, s0)(s · s0) d�∫(4�)

p(s, s0) d�

(1.12)

is the average cosine of the phase function. g approaches 1 for highlyforward scattering (thus large scattering particles). In tissue, typicalvalues of g range from 0.8 to 0.95.

Another very popular measure of scattering is the reduced scat-tering coefficient

�′s = �s (1 − g) (1.13)

and the corresponding transport mean free path length l ′s = 1/�′s. If �s

is a property of a single scattering event, then �′ contains informationabout multiple scattering. A reason �′

s is such an important parameteris that ls tells only a part of the whole story. In a tissue with g ∼1, a large


value of �s may not necessarily be indicative of how strongly light isdeviated from its original direction through scattering. Conceptually,l ′s is the distance over which light is being randomized in directiondue to multiple scattering.

1.4 Approximate Solutions to Light ScatteringOur objective now is to gain an insight into how the scattering pa-rameters introduced above relate to the refractive index variations intissue. For this, we have to return to the definition of the scatteringamplitude. The scattering amplitude can be expressed through thefield inside the scattering region V:2

f(s, s0) = − k2

4�

∫V

s × (s × E(r′)

) (n′2(r′) − 1

)e−iksr′

dr′ (1.14)

where k is the wave number and n′ = n/n0 is the relative refractiveindex within the scattering volume V. (Without the loss of generality,we assume the medium surrounding a scattering particle to be water.)The problem, of course, is that this integration requires knowledge ofthe field inside the scattering volume, and in order to calculate thisfield one would need to solve Maxwell’s equations. This becomes acatch 22. As we will see shortly, a way out of this predicament is toapproximate the field inside a scattering particle by making certainassumptions.

We first consider the case when scattering particles can be approx-imated as independent scatters. For better or worse, this is perhapsthe most popular approximation in tissue optics. Depending on a pri-ori information about the scattering particles, Eq. (1.14) can be greatlysimplified and, in some cases, its closed form solution exists.

The first approximation that we consider here is the first-orderBorn approximation. The Born approximation has been exceedinglyuseful to address a great variety of scattering problems, from quantummechanics to tissue scattering. The allure is in its simplicity. Strictlyspeaking, this approximation is valid for relatively small scatters, al-though in practice the range of applicability of the Born approximationmay go beyond this. In the Born approximation, the field inside a scat-tering particle is assumed to be the same as the incident field. In thiscase, Eq. (14) can be rewritten as follows:

f(s, s0) = − k2

4�

(s × (

s × e(i)(r)))

VR(s, s0) (1.15)

where

R(s, s0) = 1V

∫V

(n′2(r′) − 1

)e−ik(s−s0)r′

dr′ (1.16)


and e(i) is the unit vector along the incident field E(i). Thus, scatteringamplitude is a Fourier transform of the scattering potential n′2(r) − 1and, because

n′2(r) − 1 ≈ 2�

n0� (r)

it is a Fourier transform of the spatial distribution of tissue mass den-sity. This is an important relationship between scattering and tissuearchitecture.

The scattering matrix can be simplified as follows:

(S2 S3

S4 S1

)=(

cos � 00 1

)ik3

4�VR(�, �) (1.17)

where z is chosen parallel to s0 and s = s(�, �). The main requirementfor this approximation to be valid is that the phase gained by thefield propagating inside the particle be small. In other words, the fieldperturbation due to the interaction with the particle is negligible.

The Born approximation can be further simplified if not just thephase gain but also the scattering particle itself is small comparedto the wavelength. Consider a particle of radius a such that ka � 1.(Although we use the term radius, we do not necessarily assume theparticle to be spherical or spheroidal; instead a is half of the linear di-ameter of a particle of arbitrary shape.) Equation (1.16) can be furthersimplified and the Born approximation is reduced to the approxima-tion of Rayleigh scattering3:

R(s, s0) = 1V

∫V

(n′2(r′) − 1

)dr′ (1.18)

and, thus

I (s) = 1 + cos2 �

2k2

r2 �2 I0 (1.19)

where the total electric susceptibility � = (V/4�)R and I0 is the inten-sity of the incident light. The scattering cross section equals

�s = 83

�k4�2 ∝ a6

4 (1.20)

This scattering pattern is that of a dipole (1 + cos2 � dependence).Other notable feature of Rayleigh scattering is that its spectral behav-ior is essentially independent of the particle shape and internal struc-ture: it is an inverse 4th power dependence on wavelength . This fact


is a consequence of Ewald’s sphere principle: the Fourier transform inEq. (1.16) is evaluated for a range of spatial frequencies with the high-est frequency being 2k (backscattering, s = −s0).2 Thus, the sensitivityof scattering pattern to spatial frequencies above this cut off is dimin-ishing. This observation, however, is sometimes misinterpreted. It isincorrectly assumed that the sensitivity of scattering to spatial lengthscales of refractive index variations is limited by (or /2), whichseems to agree with the diffraction limit of the resolution of an opti-cal microscope. In reality, in the visible wavelength range, ka = 1 isachieved for a ∼ 50 nm, and Rayleigh regime does not start until theparticle is so small that a < /20 ∼ 20 nm!

For particles larger than 1/k, we can use the Rayleigh–Gans–Debye(RGD) approximation, which is essentially renamed the first-order Bornapproximation. It is valid when ka (n′ − 1) � 1. For a spherical homo-geneous particle

R = 3k3

s a3

(n′2 − 1

)(sin ksa − ksa cos ksa ) (1.21)

with ks = k|s − s0| = 2k sin �/2. As can be seen from Eq. (1.21), thephase function is getting more complicated as the particle size in-creases. Anisotropy coefficient g increases with a . Scattering in theforward direction predominates. The spectral and angular patternsexhibit characteristic oscillations in wavelength. The wavelength fre-quency of these oscillations is proportional to a . It is important torealize that these conclusions are not limited to spherical particles.Although the exact scattering pattern does depend on the internalstructure of a particle as well as its shape, the Fourier transform rela-tionship between the scattering potential and the scattering amplitudeensures that the main frequency of the spectral or angular oscillatorypattern is primarily determined by the dimension of the particle (or,to be more precise, the maximum phase shift gained by wave propa-gating through the particle).

When does the RGD approximation break down? For the rangeof refractive index variations existing in tissue (n′ − 1 ≈ 0.01 − 0.1),the cut off a should be in the order of a micron. This covers mostorganelles within a cell and collagen fibers. In reality, the validity rangeis probably greater than that and the RGD approximation is valid evenfor larger structures. Interestingly, this approximation works betterfor backscattering rather than forward scattering, and in backwarddirections, it probably greatly exceeds its strictly defined range ofvalidity.

If a particle is much larger than the wavelength, the Born ap-proximation is no longer valid. This is the case when we considerscattering by large scatters such as individual cells or large organellessuch as nuclei. In these circumstances, the scattering cross section


can be estimated using the Wentzel–Kramers–Brillouin approximation(WKB), which is also known in optics as the Van de Hulst or theanomalous diffraction approximation. It is used when two conditionsare satisfied: ka (n′ − 1) > 1 and (n′ − 1) � 1. In this approximation,the wave inside the particle is approximated as a propagating wave(which is the essence of WKB approximation). The scattering crosssection can be estimated by applying the forward scattering theorem[Eq. (1.9)]:

R(s, z) = 1V

∫V

(n′2(r′) − 1

)exp

(ikz1 + ikn′(z − z1) − ikr′s

)dr′

(1.22)

�s = k Im∫

V

(n′2(r′) − 1

)exp(ik(n(r′) − 1(z − z1))dr′, (1.23)

where axis z is chosen along s0 and z1 = z1(x,y) is the z-coordinate ofan entry point of the incident light ray into the particle.

For a spherical homogeneous particle,

�s = 2�a2

{1 − sin 2y

y+ sin2 y

y2

}(1.24)

with y = ka�n and �n ≡ n′ − 1. A more accurate equation can beobtained by taking into account surface effects and the elongation ofthe light path inside the particle due to refraction4:

�s = 2�a2

(1 +

(�ny

)2/3

− n′ sin 2yy

+ n′ sin2 yy2

)(1.25)

For Eq. (1.25) to be valid, �n does not have to be much smallerthan 1.

Elements of the scattering matrix (or scattering amplitude) canalso be found. For small scattering angles,5

S1 = S2 = k2

2�

∫∫A

(1 − exp (−i�(r))

)exp

(−i(r′, �))

d2r (1.26)

where r is a vector in plane A orthogonal to the direction of propa-gation of the incident light, � is a phase difference between a wavethat enters the particle at a position given by r and passes through theparticle along a straight trajectory and a wave that propagates outsidethe particle, and is the phase difference between the rays scatteredby different parts of the particle. The integration is performed overthe geometrical cross section of the particle A that is orthogonal to


the direction of the propagation of the incident light. For a sphericalparticle,

|f(�)|2 ≈ a2x2

(

J1(x�)x�

−√

�

2J1/2(� (�))√

� (�)

)2

+(

2y� 2(�)

)2 (cos � (�) − sin � (�)

� (�)

)2}

(1.27)

where size parameter x = ka and � =√

x2�2 + 4y2. In the limit y →∞ and �n → 0, scattering amplitude [Eq. (1.26)] approaches that ofFraunhofer diffraction on a disk, as expected:

|f(�)|2 ≈ a2 J 21 (x�)�2

The WKB approximation works quite well in the forward directionand provides a good estimate of the scattering cross section. However,this approximation is frequently not sufficient to describe backscatter-ing and needs to be modified for these purposes. Because the WKBmethod lacks accuracy for backscattering, attempts have been madeto merge it with the Born approximation–based analyses. For exam-ple, the WKB approximation or Mie theory (see below) was used tomodel forward scattering from cells and cell nuclei, while Born ap-proximation was used to model backscattering under the assumptionthat the nuclear structure is fractal.6

As seen from Eq. (1.24), the spectrum of the scattering crosssection exhibits characteristic oscillations in wavelength with fre-quency proportional to a�n. This is the interference structure. It is aresult of the far-field interference of two waves: a wave propagat-ing along the longest diameter of the particle and another wave thatdoes not interact with the particle. For a few micron particle with�n ∼ 0.05, we count several oscillations within the visible range. In re-ality, the spectrum is more complicated and shows at least three typesof spectral features with the interference structure being of the lowestfrequency.

Ripple structure has a much higher frequency, which is proportionalto a . Its origin has not been fully understood. It cannot be describedby the WKB approximation. It appears that when the forward scat-tering is considered (including the total scattering cross section), theripple structure is a result of the interference of surface waves (thus, nostrong dependence on �n). In backscattering, the ripple structure hasa different frequency and can be modeled by the Born approximation.This may sound surprising but, in fact, agrees with the understandingthat, as we discussed above, in case of backscattering the validity of theBorn approximation greatly exceeds the range given by ka�n � 1.The frequency of the ripple structure in backscattering is primarilydetermined by the overall size of the particle. Of course, when scat-tering from an ensemble of particles is measured rather than scattering


by an isolated particle such as a single cell, size distribution tends towash out some of these oscillations. The spectral feature of the high-est frequency is due to the whispering-gallery-mode (WGM) resonances.These are extremely narrow peaks with full width of half maximumwell under 1 nm. Although observable in experiments with nonbio-logical perfectly spherical structures, they are not likely to be relevantto scattering from biological objects.

The popularity of the WKB approximation in optics (where it isbetter known under an alternate name, anomalous diffraction approx-imation) is in part because it can be used to describe light scatter-ing by nonspherical and inhomogeneous particles. A scattering crosssection of a heterogeneous and/or nonspherical particle is actuallyquite similar to that of the equiphase sphere (EPS), i.e., a sphere thatwould produce the same maximal phase shift as the nonsphericalor inhomogeneous particle.7 If d is the diameter of a particle in thedirection of propagation, the maximal phase shift is kdn. Thus, thesphere of diameter d and refractive index equal to the average re-fractive index of the nonspherical particle is the equiphase sphere.The total scattering cross section of a nonspherical and inhomoge-neous particle can then be described by Eq. (1.25). The validity con-dition of the EPS approximation for an inhomogeneous particle isgiven by7

n = 4√

LCd

n < 1 (1.28)

where n is the standard deviation of refractive index variations insidethe particle and LC is the refractive index correlation length. A similarvalidity condition for a nonspherical (e.g., irregularly shaped) particleis

r = 2

√2�

(n′ − 1

) �

√� < 1, (1.29)

where � is the radial standard deviation from its best-fitting sphereand � is the radial-angular correlation angle. We see that the EPS ap-proximation and the scattering cross section given by the anomalousdiffraction approximation [Eq. (1.25)] work best for particles with finegrains of either refractive index (small LC) or surface perturbation(small �). It is large clumps of refractive index and highly elongatedshapes that make the EPS approximation break down.

An obvious advantage of the approximate methods discussedabove is that they are applicable to problems that otherwise cannotbe solved from the first principles. There is a class of particles, how-ever, for which the equation of scattering can be solved exactly. Theseare homogeneous spheres and the solution is known as Mie theory.


Consider a spherical particle of radius a .

S1(�) =∞∑

n=1

2n + 1n(n + 1)

(an�n(cos �) + bn�n(cos �)) (1.30)

S2(�) =∞∑

n=1

2n + 1n(n + 1)

(an�n(cos �) + bn�n(cos �))

�s = 2�a2

�

∞∑n=1

(2n + 1)(|an|2 + |bn|2

)(1.31)

where

an = �n(�)� ′n( ) − n′�n( )� ′

n(�)ζn(�)� ′

n( ) − n′�n( )ζ ′n(�)

, bn = n′�n(�)� ′n( ) − �n( )� ′

n(�)n′ζn(�)� ′

n( ) − �n( )ζ ′n(�)

,

�n(cos �) = P1n (cos �)sin �

, �n(cos �) = dd�

P1n (cos �),

�n(x) =√

�x2

Jn+(1/2)(x), ζn(x) =√

�x2

Hn+(1/2)(x),

� = ka , = k�na ,

Jn+(1/2) and Hn+(1/2) are Bessel and Hunkel functions, respectively,P1

n (cos �) is the associate Legendre polynomial, and � is the scatteringangle.

It is arguable that Mie theory does not allow one to gain physicalinsights into scattering. Although it does present a solution, it is in theform of an infinite series, which can only be estimated numerically.The solution, however, is widely available enabled by well-tested soft-ware (see section “Review of Computational Light Scattering Codes”).For better or worse, Mie theory has been widely used by many inves-tigators to model light scattering in tissue. In particular, it has beenused to determine size distributions of tissue scatterers based on an-gular or spectral scattering patterns. There are potential drawbacks tothis approach. Indeed, as discussed above, tissue structures are nei-ther spherical nor homogeneous. Furthermore, Mie theory is, strictlyspeaking, valid only for isolated scatters. This would assume thatscattering particles in tissue are in the far field of each other, which isclearly incorrect.

Given all its limitations, why is Mie theory so popular then? Atruthful answer is that we simply do not have many good alternatives.A more rigorous solution of the scattering problem would requiretaking into account heterogeneous distribution of refractive index in-cluding length scales as small as a few tens of nanometers and as largeas tens of microns. We would have to take into account interactionsamong particles in the near field of each other. If we want to be serious


about this, the only way to approach this is by numerically solvingMaxwell’s equations. Recently, new powerful numerical approachessuch as finite-difference time-domain (FDTD) calculations have be-come available (see Chap. 3 on FDTD). Although the use of thesecomputational methods is currently limited by computer resources,one can expect that as more powerful computers are made availablein the future we should be able to develop more robust understand-ing of tissue scattering. Another approach, of course, is to developapproximate but robust methods. Until that time, we will most likelycontinue using Mie theory.

On the positive side, if we pose the question: Are we missingan important physical picture by interpreting scattering signals us-ing Mie theory? The answer most likely would be no. Although wemay indeed be missing potentially interesting but subtle effects inlight scattering, it is quite possible that the main conclusions drawnfrom Mie theory are still correct, i.e., we ask the right question andinterpret a Mie theory–based answer in the correct context. Indirectevidence is that the approximations such as the RGD and the WKBare applicable to nonspherical and heterogeneous structures, and themain conclusions we draw from these approximations show (at leastqualitatively) that the main scattering features (e.g., the angular extentof the forward-scattering peak, the spectrum of scattering) can indeedbe approximated by the use of Mie theory for an equivalent parti-cle size. So perhaps if we view the size distribution recovered usingMie theory in the context of length scales of refractive index variationsrather than real scattering particles, we may not be getting such anincorrect picture after all. Although these questions await answers,we are hopeful that the answers will be available in the near future.

In summary, light scattering depends on the spatial refractive in-dex distribution, which in turn depends on the spatial distribution oflocal mass density. Light scattering depends on a wide range of lengthscales of tissue structures. On the low end, the limit of sensitivity isapproached when Rayleigh scattering regime ensures. This happensfor length scales a such that ka � 1, which corresponds to a few tens ofnanometers. On the upper end, refractive index correlation eventuallyvanishes, which sets the upper limit of light scattering sensitivity. Itis this broadband sensitivity of light scattering to tissue architectureat length scales as small as a few tens of nanometers and as large astens of microns that makes this contrast mechanism so unique and socomplex at the same time.

1.5 Review of Computational Light Scattering CodesThere are many good light scattering software routines available freelyon the World Wide Web. These include routines written in FORTRAN


and C, routines written for mathematical calculation environmentssuch as Matlab (Mathworks, Natick, MA) and Mathematica (Wolfram,Inc., Champaign, IL), as well as stand alone software packages writtenas executables for the Windows environment. Software routines arealso available for a variety of light scattering formalisms, includingMie theory, T-Matrix, FDTD, and multipole/dipole simulations. Here,we review these various codes, discuss their optimal usage, and givelinks on the Web for easy access. A summary of this review with htmllinks is given in Table 1.1.

Mie Theory CalculatorsThe most widely used calculation software for Mie theory scatter-ing is the BHMIE routine, originally published as an appendix in theclassic light scattering book, Absorption and Scattering of Light by SmallParticles, by C. F. Bohren and D. Huffman (Wiley, 1983). The originalroutines were written in FORTRAN, the most popular computationallanguage at that time. Since then, many packages have adapted theBHMIE routine to other languages and environments. For example,the SCATTERLIB light scattering codes library (http://atol.ucsd.edu/scatlib/index.htm) maintained by Piotr J. Flatau at the Scripps Insti-tution of Oceanography, lists several versions of the BHMIE routine,including FORTRAN, C, and idl programming language adaptations,as well as a BHMIE routine for Matlab. In addition, the SCATTER-LIB site gives an extension of the BHMIE routine for coated spheres(BHCOAT).

As an alternative to compiling and executing the BHMIE rou-tine, MiePlot is a popular software package that provides a graphi-cal user interface. The MiePlot software, written and maintained asfreeware by Philip Laven (http://philiplaven.com/MiePlot.htm), isbased on a visual basic adaptation of the BHMIE routine. This pack-age offers a significant benefit in that it can allow a novice to beginplotting Mie theory scattering distributions after a brief installationand a few mouse clicks. In addition, the software is fairly flexible, al-lowing comparisons across scattering angle or wavelength, a varietyof plotting options, including linear, logarithmic, and polar plots, andincludes several built-in refractive index choices for the scatterer andsurroundings, plus the option for user-defined distributions. The mostrecent version, MiePlot v4, also includes the ability to model scatteringof Gaussian beams, distributions of scatterer sizes, and new graph-ing options such as scattering and absorption cross-sections versusdiameter.

Although installation and setup of light scattering codes is notparticularly arduous, there are software routines that are available asonline calculators in which the user enters data into a browser inter-face and is provided graphical or numerical scattering data. A basic

http://atol.ucsd.edu/scatlib/index.htm


http://philiplaven.com/MiePlot.htm

Calculation Type Software Type Web Address

Mie theory FORTRAN, C SCATTERLIB: http://atol.ucsd.edu/scatlib/index.htmWindows http://philiplaven.com/MiePlot.htmOnline http://omlc.ogi.edu/calc/mie calc.html

MieCalc http://www.lightscattering.de/MieCalc/eindex.htmCell Phone SCATTPORT: http://www.scattport.org

T -matrix FORTRAN http://www.giss.nasa.gov/∼crmim/t matrix.htmlSCATTERLIB: http://atol.ucsd.edu/scatlib/index.htmSCATTPORT: http://www.scattport.org

Matlab http://www.physics.uq.edu.au/people/nieminen/software.htmlDiscrete dipole

approximation (DDA)FORTRAN C http://www.astro.princeton.edu/∼draine/DDSCAT.7.0.html

http://www.science.uva.nl/research/scs/Software/adda/Multipole expansion FORTRAN, Windows http://alphard.ethz.ch/FDTD C++ http://ab-initio.mit.edu/wiki/index.php/Meep

Java http://www.thecomputationalphysicist.com/jfdtd.htmlGPU http://www.emphotonics.com/products/fastfdtd

http://smadasam.googlepages.com/gpufdtdcode

TABLE 1.1 Summary of Review of Light Scattering Software

24


http://philiplaven.com/MiePlot.htm

http://omlc.ogi.edu/calc/mie_calc.html

http://www.lightscattering.de/MieCalc/eindex.htm

http://www.scattport.org

http://www.giss.nasa.gov/~crmim/t_matrix.html



http://www.physics.uq.edu.au/people/nieminen/software.html

http://www.astro.princeton.edu/~draine/DDSCAT.7.0.html

http://www.science.uva.nl/research/scs/Software/adda/

http://alphard.ethz.ch/

http://ab-initio.mit.edu/wiki/index.php/Meep

http://www.thecomputationalphysicist.com/jfdtd.html

http://www.emphotonics.com/products/fastfdtd



calculator, written by Scott Prahl, is available at the Oregon Medi-cal Laser Center Web site (http://omlc.ogi.edu/calc/mie calc.html).This calculator provides basic information such as scattering efficiencyand cross section, as well as a few graphical representations, includingpolar, linear, and log scattering distributions. Numerical data can alsobe retrieved and then imported into analysis or spreadsheet softwarefor further processing. A more advanced online Mie calculator canbe found at the MieCalc Web site (http://www.lightscattering.de/MieCalc/eindex.html). This online calculator is based on a Java ap-plet, which implements the BHMIE code. This software offers a bitmore flexibility, including the ability to compare multiple distribu-tions on the same plot. However, this flexibility comes with an increasein complexity that results in a slightly longer learning curve to fullytake advantage of all of the software options.

As a final note, in honor of the 100th anniversary of the original1908 Mie paper on scattering by dielectric spheres, Thomas Wreindthas implemented a Mie calculator for the mobile phone, available onhis SCATTPORT Web site (http://www.scattport.org). Although thecomputational times are rather long by today’s standards for desktopcomputers, reaching several (2–20) minutes for moderate size param-eters, there is simply no substitute for light scattering calculations onthe run.

T-Matrix CalculationsT-matrix calculations offer an advantage over Mie theory in thatspheroidal geometries and a variety of orientations can be considered.The primary resource for T-matrix calculations can be found on theweb pages of Michael I. Mischenko at the Goddard Institute for SpaceStudies (NASA) Web site. FORTRAN codes are available at http://www.giss.nasa.gov/∼crmim/t matrix.html with variations of calcu-lation precision (extended and double) and scattering geometries.

Another resource for T-matrix calculations can be found on theSCATTLIB Web site where Fortran codes for specific scattering ge-ometries are given, including oriented spheroids and 2D and 3D ran-dom orientations. These routines are based on codes given in the book,Light Scattering by Particles: Computational Methods, by P. W. Barber andS. C. Hill from the Advanced Series in Applied Physics Vol. 2 (WorldScientific Pub. Co., Inc., 1990).

The SCATTPORT Web site gives several additional T-matrixcodes from various sources which have been adapted for specificscattering geometries such as randomly oriented spheroids and ab-sorbing spheroids. While most of the T-matrix codes found on thissite are written in the FORTRAN language, codes for Matlab canbe found as well. For example, the Optical Tweezer Toolbox 1.0,http://www.physics.uq.edu.au/people/nieminen/software.html is

http://www.lightscattering.de/MieCalc/eindex.html

http://www.lightscattering.de/MieCalc/eindex.html




http://www.physics.uq.edu.au/people/nieminen/software.html

http://omlc.ogi.edu/calc/mie_calc.html


a Matlab implementation of T-matrix codes specifically designed forthe optical trapping geometry.

Discrete Dipole ApproximationThe discrete dipole approximation (DDA) method provides even moreflexibility than the T-matrix method in that light scattered by arbitraryobjects can be calculated. In this approach, the scatterer is approxi-mated by a discrete array of polarizable points that acquire dipolemoments due to an incident field. The most well-known light scatter-ing code for DDA calculations is the DDSCAT software package byB. T. Draine and P. J. Flatau. The most recent version, DDSCAT 7.0, isa FORTRAN-based calculator and is available at Draine’s Web site,http://www.astro.princeton.edu/∼draine/DDSCAT.7.0.html. Thislatest version offers optimized calculations and can handle periodicstructures in one or two dimensions in addition to discrete scatterers. AC software routine for DDA calculations has been developed by M. A.Yurkin and A. G. Hoekstra at the University of Amsterdam, availableat http://www.science.uva.nl/research/scs/Software/adda/. Thissoftware is reported to offer advantages in computation time but mayhave limitations in calculations of orientation averaged scatterers.

An extension of the DDA method can be realized by generalizingthe approach to include higher order moments. In particular, inclusionof the electric quadrupole can improve light scattering calculations. Apopular multipole light scattering program can be found at the Website of Christian Hafner http://alphard.ethz.ch/. A review of multi-pole techniques can be found in Generalized Multipole Techniques forElectromagnetic and Light Scattering, Thomas Wriedt, editor (Amster-dam: Elsevier, 1999).

Time-Domain CodesTime-domain methods for calculating light scattering include thefinite-difference time-domain (FDTD) and pseudospectral time-domain (PSTD) methods. The application of these two methods tobiological problems is reviewed in Chap. 3. There are not only manycommercially available FDTD software packages with various fea-tures but also many good free simulators available on the World WideWeb.

Freeware FDTD simulators are available in several native lan-guages. The MEEP software package is an open source basedon C++ that supports parallel simulations. It is available on theserver at MIT, http://ab-initio.mit.edu/wiki/index.php/Meep. An-other free FDTD solver is the JFDTD package, available at http://www.thecomputationalphysicist.com/jfdtd.html and written in Java.Although FDTD code has been written for Matlab, the intensive com-putation required by this computational approach limits the utility

http://www.astro.princeton.edu/~draine/DDSCAT.7.0.html

http://www.science.uva.nl/research/scs/Software/adda/



http://alphard.ethz.ch/

http://ab-initio.mit.edu/wiki/index.php/Meep


of such packages. In an effort to improve computation times, re-cent efforts have turned to exploiting the graphics processing unit(GPU) to accelerate the calculations. Commercial software manu-facturer, EM Photonics, offers a GPU-based FDTD solver for freeat http://www.emphotonics.com/products/fastfdtd, while opensource developer, Sam Adams, offers a GPU FDTD code that is still un-der development http://smadasam.googlepages.com/gpufdtdcode.

1.6 Inverse Light Scattering AnalysisThe analysis of light scattering for use in biomedical applications canbe divided into two parts, the forward problem and the inverse prob-lem. This chapter so far has largely focused on the forward problem,i.e., determining the scattered electromagnetic field for a given scatter-ing geometry, defined by the refractive-index distribution of a struc-ture. However, for diagnostic applications, one is typically trying tosolve the inverse problems where the refractive-index distribution ofbiological structures is sought based on the measurements of the scat-tered electromagnetic field. Typically, the inverse problem can only besolved analytically for a few geometries, which offers only a limitedutility for biomedical applications. Instead, inverse light scatteringanalysis is executed to gain information about biological structuresbased on the scattered field.

The main concern in solving the inverse problem in light scatteringis that the problem is ill-posed: meaning that there may be multiplesolutions for the same data or that there may be small errors (noise) inthe data that result in widely diverging inversion. The first problemis the issue of nonuniqueness, while the second problem is the issue ofan ill-conditioned problem.

Nonuniqueness ProblemThe structure and density (refractive index) of biological objects canhave a practically infinite number of degrees of freedom. Thus, it isnot possible to obtain complete knowledge of that structure througha finite number of light scattering measurements. This eventuality iscalled the nonuniqueness problem. In light scattering for biomedicalapplications, the most useful method to deal with this problem is toemploy a priori knowledge to limit the set of possible solutions to theinverse problem. For example, if one seeks to identify the light scat-tering signature of a particular biological structure or a modulation ofthat structure because of a pathological condition, the range of possi-ble conformations that exist can be assessed by using a direct imagingtool such as microscopy.

Upon defining a suitable range of parameters for the structures,solutions to the forward problem can be constructed as estimated

http://www.emphotonics.com/products/fastfdtd



models that may have produced the light scattering signature. In gen-eral, estimated models from the forward problem must make certainassumptions about the scattering structure, based on the calculationmethod or limitations of the prior knowledge that may be imposed.For example, if light microscopy is used to assess possible conforma-tions of biological structures, the diffraction limit will impose a lowerbound on the dimensions of light scattering structures that contributein the model.

Ill-Conditioned ProblemThe ill-conditioned problem arises from the fact that all measurementsystems have an inherent uncertainty due to noise in the measurementprocess. As these noise processes are by definition unaccounted for, itis not possible to accurately include them within the range of possiblemodels. However, there are several approaches to mitigate the effectof measurement noise in the inverse analysis.

The main strategy in working with an ill-conditioned problem isto engage in some form of regularization. With this approach, practi-cal constraints are introduced, which ameliorate noisy features in thedata that may influence the inversion. A simple form of regulariza-tion would be using a smoothing function to eliminate high-frequencycomponents in the data set, which are not present in the range of struc-tures considered in the forward light scattering model. Another ap-proach would be to include a practical constraint in the analysis. Whencomparing measured data to possible forward models, a penalty canbe introduced that will prevent unrealistic solutions to the forwardproblem from contributing to the overall outcome.

A different approach to overcome the ill-conditioned nature of theinverse light scattering problem is to rely on a statistical view instead ofa deterministic one. In the deterministic picture, each individual set oflight scattering data is uniquely identified with a particular scatteringgeometry. By moving to the statistical picture, repeated measurementsof the sample are analyzed to assess an overall figure of merit thatcharacterizes the sample. This figure, such as an average structuresize, density, or correlation length, can then be compared to a similarfigure obtained by ensemble averaging several components producedby the forward model.

SummaryIn practice, inverse light scattering analysis is executed with a particu-lar goal in mind. Typically, in biomedical applications, light scatteringis used to try and detect pathological abnormality with a simple non-invasive measurement. At the most basic level, an empirical approachcan be taken where light scattering data is simply sorted by the patho-logical classification and used as a learning set for a discrimination


algorithm such as principle component analysis. This approach hasbeen effective but often sheds little light on the underlying processthat has caused the change in light scattering.

At a more advanced level, comparison of the light scattering datato a physical model can provide more information about biologicalstructures. However, this approach can suffer from the limitations oftrying to solve the ill-posed inverse light scattering problem. By in-cluding some of the basic strategies outlined above, namely, usinga priori knowledge, restricting the parameter space of the forwardmodel, employing signal conditioning, and extracting statistical fig-ures of merit, the light scattering methods for biomedical applicationsdescribed throughout this book have begun to realize the promise ofnoninvasive optical diagnostic methods.

References1. D. V. Lebedev, M. V. Filatov, A. I. Kuklin, A. K. Islamov, E. Kentzinger, R. Pantina,

B. P. Toperverg, and V. V. Isaev-Ivanov, “Fractal nature of chromatin organizationin interphase chicken erythrocyte nuclei: DNA structure exhibits biphasic fractalproperties,” FEBS Lett 579, 1465–1468 (2005).

2. M. Born and E. Wolf, “Principles of Optics,” Cambridge University Press, Cam-bridge U.K. (1999).

3. Ishimaru, “Wave Propagation and Scattering in Random Media,” IEEE Press, NewYork and Oxford University Press, Oxford (1997).

4. Z. Chen, A. Taflove, and V. Backman, “Equivalent volume-averaged light scat-tering behavior of randomly inhomogeneous dielectric spheres in the resonantrange,” Opt Lett 28(10), 765–767 (2003).

5. R. G. Newton, “Scattering Theory of Waves and Particles,” McGraw-Hill BookCompany, New York (1969).

6. T. T. Wu, J. Y. Qu, and M. Xu, “Unified Mie and fractal scattering by biologicalcells and subcellular structures,” Opt Lett 32(16), 2324–2326 (2007).

7. X. Li, A. Taflove, and V. Backman, “Recent Progress in Exact and Reduced-OrderModeling of Light-Scattering Properties of Complex Structures,” IEEE J SelectedTop Quant Elect 11(4), 759–765 (2005).


C H A P T E R 2Light Scatteringfrom Continuous

Random Media

Ilker R. Capoglu, Jeremy D. Rogers, and Vadim Backman

2.1 IntroductionOne of the complicating factors in the analysis of light scattering fromcomplex continuous media is the fact that there are theoretically aninfinite number of scattering events taking place inside the scatter-ing medium. Although the resulting total wave is usually nontrivial,the underlying mechanism of these scattering events follows a simplepattern: the incident wave creates a primary scattered wave within themedium, which in turn gets scattered in the same medium and createsa secondary scattered wave. This process continues indefinitely, inex-tricably linking every part of the medium to each other with a bondof mutual scattering. Therefore, a rigorous mathematical descriptionof light scattering from a known distribution of refractive index (RI)inevitably involves an integral equation, the solution of which canrarely be obtained analytically [1, 2].

In many biomedical applications, the biological medium can beregarded as a weakly scattering medium. This implies that the primaryscattered wave created by the incident wave is the most prominent,and subsequent scattered waves resulting from the primary scatteredwave can be neglected. A necessary condition for the validity of thisapproximation is that the RI fluctuations are very weak throughoutthe medium. This principle, expressed in an informal manner hereinand made more precise in what follows, is commonly known as theBorn or single-scattering approximation. This approximation was first

31


introduced by the German physicist Max Born (1882–1970) in the con-text of atomic particle scattering; however, it is equally applicableto light scattering, as both processes are governed by similar waveequations.

Without going into much rigorous detail, it is instructive to explainin a few words the mathematical principle used in the Born approxi-mation. As mentioned above, each point in the scattering medium actsas a scatterer to any wave that is incident upon it, which is a superposi-tion of scattered waves that have propagated to that point from everyother point. If the amplitude of the wave was known precisely at eachpoint in the medium, the scattered wave could be calculated using thevolume equivalence principle [1, 3], which is the mathematical expres-sion of the total scattered wave calculated as a summation of all thescattered waves created by every point in the medium. The difficultyhere is that the total wave amplitude inside the medium is not knownin advance, so the formulation reduces to an integral equation withthe total wave amplitude as unknown, as mentioned above. How-ever, the power of the Born approximation comes to the rescue at thispoint. In the Born approximation, the total wave amplitude at a pointis assumed to be equal to the amplitude of the incident wave, whichis known in advance. This is the mathematical expression of the as-sumption that only the primary scattered wave created by the incidentwave is of importance, and every other scattering event is neglected.

Although the foregoing definition of the Born approximation isgiven for a deterministic scattering medium, this version of the the-ory is not particularly useful for biological media, owing to the generallack of knowledge regarding their exact properties. In such cases, oneoften resorts to statistical analysis, in which only certain average prop-erties of the biological medium are known. These properties, such asthe average correlation length of the material fluctuations, are used tobuild a statistical model for the medium and are usually inferred fromother measurements or theory. As a result of the randomness of thescattering medium, the properties of the scattered light should also beconsidered in a statistical manner. In this respect, the Born approxi-mation offers a tremendous simplification and allows the statistics ofthe scattering parameters to be expressed in terms of the statistics ofthe material properties of the medium, as discussed in the followingsections.

In this chapter, we will be chiefly concerned with several scatter-ing parameters of wide interest in light scattering. These parametersare the mean differential cross section per unit volume 〈�〉, the scat-tering coefficient 〈�s〉 (which is equal to the total scattering cross sec-tion per unit volume), the mean free path ls = 1/ 〈�s〉, the anisotropyfactor g, the reduced scattering coefficient

⟨�′

s

⟩ = 〈�s〉 (1 − g), and thetransport mean free path l ′s = ls/(1 − g). The detailed definitions ofthese parameters will be provided, when necessary, in the followingsections.

33L i g h t S c a t t e r i n g f r o m C o n t i n u o u s R a n d o m M e d i a

In the following text, we will assume that the random mediumis statistically homogeneous, or, in mathematical terms, stationary. Thismeans that the covariance 〈x(r1)x(r2)〉 of any material property x(r ),where 〈·〉 denotes ensemble average, depends only on the distance�r = r1 − r2 between the two points r1 and r2. Another commonassumption that we will adopt is that the statistics of the randommedium is jointly Gaussian. Apart from being the most frequently en-countered statistical distribution in nature, this distribution has theadditional advantage that the entire statistics of the medium is de-termined by the mean and covariance. In more specific examples, wewill also make the traditional assumption of isotropy, which states thatthe statistics are independent of orientation; namely, the covarianceonly depends on the absolute distance |�r |. The material property ofmain interest in light scattering applications is naturally the RI distri-bution of the medium, n (r ). A somewhat more convenient parameteris the normalized RI fluctuation, �n (r ) = (n(r ) − n0)/n0, where n0 is theRI of the outside medium. In accordance with the weak RI fluctuationrequirement implicit in the definition of the Born approximation, wewill assume that the normalized RI fluctuation �n (r ) has zero mean,namely, 〈�n (r )〉 = 0. A simple condition for the applicability of theBorn approximation can be given as [2]

kL�n(r ) � 1 (2.1)

where k is the wave number in the surrounding medium and L is theaverage size of the sample. This condition ensures that the extra phaseaccumulated by the incident wave due to the RI inhomogeneities isminimal, and the primary scattered wave is much weaker than theincident wave.

We will first present our analysis of light scattering in the Bornapproximation for the full three-dimensional (3D) case, and subse-quently consider the simpler cases of two-dimensional (2D) and one-dimensional (1D) media in somewhat lesser detail. In all cases, we willstart by outlining the general theory of the Born approximation in therespective geometry, and subsequently focus on a specific correlationfunction suited to that geometry to demonstrate the potential use ofthe formulation.

2.2 3D Continuous Random Media

Mean Differential Scattering Cross SectionFor representing the normalized RI of a 3D random medium, we em-ploy a 3D stationary Gaussian random process �n (r ) with correlation

E{�n (r ) �n(r + �r )} = Bn(�r ) (2.2)


θ

ki

eiko

φ

Incidentplane wave

χ

FIGURE 2.1 The geometry of plane-wave scattering from the random medium.The unit polarization vector e i; incidence and observation directions ki and k0,respectively; and the scattering angles �, � , � are defined as shown.

It is assumed that the random medium is illuminated by amonochromatic plane wave with wave number k = �(ε0�0)1/2, direc-tion ki, and polarization ei, and the radiated scattered wave is observedin the far-field region at direction k0 (Fig. 2.1). The mean differential scat-tering cross section per unit volume 〈�〉 (k0, ki) is defined as the averagepower per unit solid angle at direction k0 scattered by unit volumeof the random medium. Here, scattered power should be understoodas the absolute square of the electric field amplitude at the far fielddirection k0. It can be shown [1] that the Born approximation yieldsthe following simple formula for the mean differential scattering crosssection per unit volume:

〈�〉 (k0, ki) = 2�k4 sin2 ��n(ks) (2.3)

where ks = k(ki − k0) and � is the angle between the incident electricpolarization ei and the far field observation angle k0 (Fig. 2.1), and�n(�) is the power-spectral density of the normalized RI fluctuationgiven by

�n(�) = 1(2�)3

∫∫ ∫ ∞

−∞Bn(r ) exp(−i� · r ) dr (2.4)

If the RI correlation function Bn(r ) were known in tissue, we couldcalculate the differential cross section and, thus, all other scattering pa-rameters of the medium. Unfortunately, this function is not known.A number of hypotheses have been proposed. Commonly used mod-els for the correlation function Bn(r ) include an exponential corre-lation (resulting in the Booker-Gordon formula for the differential


scattering cross section), the Gaussian model, and the Kolmogorovspectrum (von Karman spectrum) [1]. Recently, attention has beengiven to a fractal model for index distributions [4, 5]. On the otherhand, other investigators argued that stretched-exponential correla-tion function is physically more sound. Furthermore, for a coupleof decades Henyey–Greenstein phase function has been a householdname in tissue optics and is arguably the most widely used phase func-tion in modeling of light propagation in tissue. Henyey–Greensteinphase function corresponds to a limiting case of the RI correlation fora mass fractal medium with mass fractal dimension approaching 3.Thus, the argument over which form of the correlation function is themost relevant in tissue will most likely continue.

Luckily for us, there is a general family of functions that cov-ers all these reasonable possibilities including Gaussian, exponential,stretched exponential, and mass fractal types of correlation functions.This is the Whittle–Matern family of correlations [6, 7]. This functionis defined by a three-parameter model with parameters lc, �2

n , andm, discussed below in greater detail. The Whittle–Matern family ofcorrelations is defined as follows:

Bn(r ) = �2n

25/2−m(r/ lc)m−3/2

|�(m − 3/2)| Km−3/2

(rlc

)(2.5)

where K�(·) denotes the modified Bessel function of the second kindand �(·) denotes the gamma function. The parameter lc describes theindex correlation distance or turbulence scale and the parameter �2

n isthe variance of the RI, sometimes written as

⟨n2

1

⟩. The third parameter

m is related to the mass fractal dimension by dmf = dE − 2m, wheredE is the Euclidean dimension. Equation (2.5) is normalized such thatBn(0) = �2

n for m > 3/2. The model reduces to several important spe-cific functions for certain values of m: As m → ∞, the function ap-proaches a Gaussian (or normal) distribution. When m = 2, the func-tion is a decaying exponential. Values of m between 2 and 3/2 resultin a stretched exponential for r < lc. A singularity exists at m = 3/2,and the function collapses to zero because of the normalization fac-tor of �(m − 3/2). However, the unnormalized Bn(r ) becomes a deltafunction for m = 3/2 and the corresponding power-spectral density isthe often used Henyey–Greenstein function. This can be interpretedas describing pointlike scatterers or a discrete rather than continuousmedium. Values of m < 3/2 correspond to a mass fractal index distri-bution with correlation function described by a power law. Figure 2.2shows Bn(r ) for several representative values of m. When m < 3/2, thefunction Bn(r ) is infinite at r = 0 and as a consequence the functioncannot be normalized. This is not physical and in reality the correlationmust roll off to a finite value below some minimum length scale rmin.This is represented by a truncated version of the function such that


0 0.5 1 1.5 2 2.5 30

0.2

0.4

0.6

0.8

1

r/lc

Bn/σ

n 2m = 3

m = 2

m = 1.6

m = 1.52

m = 1.4

FIGURE 2.2 Example index correlation functions for several values of m.

Bn(r ) = Bn(rmin) for r < rmin. When rmin � lc, the error in the meanscattering parameters between the full model and truncated versionis minimal, as discussed later. For r > lc, the function drops quicklyto zero. The model can be thought of as a fractal over the range rmin tolc, where rmin is the inner length scale and lc is the outer scale as withthe Kolmogorov spectrum.

The mean differential scattering cross section per unit volume fol-lows from Eq. (2.3), for which the power-spectral density �n for thismodel is of the form of the Pearson distribution type VII:

�n(ks) = �2n l3

n�(m)�3/2 |�(m − 3/2)|

1(1 + k2

s l2c

)m (2.6)

where ks = |ks| = 2k sin(�/2). Substituting this equation in Eq. (2.3),we obtain the following expression for the mean differential scatteringcross section per unit volume:

〈�〉 (k0, ki) = 2�k4 sin2 ��n(ks)

= 2�2n k4l3

c �(m)√� |�(m − 3/2)|

(1 − sin2(�) cos2(�))(1 + [2klc sin(�/2)]2)m (2.7)

in which the identity sin2 � = 1 − sin2(�) cos2(�) is used, where � and� are defined as shown in Fig. 2.1. The term sin2 � represents theeffect of the polarization orientation � of the incident light and is re-ferred to as the dipole factor. This name reminds us that for klc � 1,


FIGURE 2.3 An example mean differential scattering cross section per unitvolume plotted in spherical coordinates. The incident wave is oriented topropagate from left to right and the polarization is such that electric field is inthe vertical plane. The dimple is located at the origin.

this factor becomes dominant and results in the dipole radiation pat-tern. Figure 2.3 shows an example 〈�〉 (k0, ki) with slightly forwarddirected scattering.

The relationship in Eq. (2.7) constitutes an important link betweenthe statistical model parameters lc, �2

n , m, and a scattering parameter,〈�〉 (k0, ki). In the following sections, we will use this relationship toderive direct expressions for other measurable optical properties interms of the same statistical model parameters.

Scattering Coefficient and Related ParametersThe scattering coefficient 〈�s〉 is defined as the total average powerscattered by unit volume of the random medium and is obtained byintegrating 〈�〉 (k0, ki) in Eq. (2.7) over all angles. It is convenient tonormalize 〈�s〉 by the wave number k so that the relationship dependsonly on klc:

〈�s〉k

=

∫∫�

〈�〉 (k0, ki) d�

k

= �2n√

��(m − 3)2k3l3

c |�(m − 3/2)|[(

1 + 2k2l2c

(2k2l2

c (m − 2) − 1)(m − 3)

)(2.8)

−(1 + 4k2l2c

)1−m(1 + 2k2l2

c (m + 1) + 4k4l4c (4 + (m − 3)m)

)].

The mean free path ls is the inverse of the scattering coefficient〈�s〉. When all length scales are normalized by the wavelength, therelationships depend only on klc and kls (or 〈�s〉 /k).

Equation (2.8) is not easy to interpret, so some insight can begained by considering the equation for either very small or very


large klc. In the limit of klc � 1 or klc � 1, and m > 1, the relationshipsimplifies dramatically:

〈�s〉k

=

16�2n√

��(m)3 |�(m − 3/2)| (klc)3, if klc � 1

2�2n√

��(m − 1)|�(m − 3/2)| klc, if klc � 1 and m > 1

(2.9)

The anisotropy factor g is used in many cases to describe the degreeof forward directed scattering and is defined as the average cosine ofthe scattering angle over all directions:

g =

∫∫�

cos(�) 〈�〉 (k0, ki) d�∫∫�

〈�〉 (k0, ki) d�

, (2.10)

which, for our model, can be written explicitly as

g = [(1 + 4k2l2c

)m(3 + 2k2l2

c (m − 4)(− 3 − 4k2l2

c

×(k2l2c (m − 2) − 1)(m − 3)

))− (1 + 4k2l2

c

)×(3 + 6k2l2

c (2 + m) + 8k6l6c m(10 + (m − 5)m

)(2.11)

+ 8k4l4c (6 + (m − 1)m)

)]/[2k2l2

c (m − 4)((1 + 4k2l2

c

)m

×(− 1 − 2k2l2c

(2k2l2

c (m − 2) − 1)(m − 3)

)+ (1 + 4k2l2

c

)×(1 + 2k2l2

c (1 + m) + 4k4l4c (4 + (m − 3)m)

))].

The asymptotic forms of g for small and large klc are as follows:

g =

45

m(klc)2 if klc � 1

1 − 23−2m(m − 1)(8 + m(m − 5))(4 − m)(6 + m(3 − m))

(klc)2−2m if klc � 1 and 1 < m < 2

1 − 12(m − 2)

(klc)−2 if klc � 1 and m > 2(2.12)

Another useful optical parameter is the reduced scattering coef-ficient

⟨�′

s

⟩ = (1 − g) 〈�s〉. Figures 2.4 and 2.5 show the dependenceof the normalized scattering coefficient 〈�s〉 /k and the normalizedreduced scattering coefficient

⟨�′

s

⟩/k on klc for �n = 1. A key fea-

ture of⟨�′

s

⟩is the wavelength dependence. Note that for small klc,

g → 0 and⟨�′

s

⟩ = 〈�s〉. In this case, 〈�s〉 = −4, which is consistentwith Rayleigh scattering. In most biological tissues, measurementsindicate that g is large, implying that klc is large [8]. When klc is large


10−2

100

102

104

10−6

10−3

100

103

< µ

s >

/ k

klc

m = 1.51m = 1.99m = 1.1

10−2

100

102

104

10−5

101

107

kls

FIGURE 2.4 Scattering coefficient 〈�s〉 as a function of index correlationlength lc (both normalized by wavelength). Inset: mean free path klsdependence.

10−2

100

102

104

10−4

10−2

100

102

klc

< µ

s > /

k

1.3

1.5

1.7

1.9

2.1

FIGURE 2.5 Reduced scattering coefficient⟨�′

s

⟩as a function of index

correlation length lc (both normalized by wavelength.)


and m > 2,⟨�′

s

⟩does not depend on wavelength at all. When klc is

large and 1 < m < 2,⟨�′

s

⟩ = 2m−4. This provides a critical link betweenspectral dependence of scattering and shape of the index correlationfunction, parameterized by m in this model. This spectral dependence,combined with the previous relationships, provides the link betweenmeasurable optical properties and the statistical model parameters lc,�2

n , and m.

Simplifying ApproximationsThere are two major approximations that can be made to simplifythe scattering parameters found in the previous sections. The first isneeded for values of m < 3/2, where Bn(r ) approaches infinity as r →∞. As this situation cannot exist in reality, the actual correlation func-tion must level off. However, this would complicate the model signif-icantly, so, provided that the error is small, the simple model can legit-imately be used even for values of m that result in infinite correlation.To verify this, the normalized error is calculated numerically by com-puting the difference in ls from the model and a truncated version ofBn, where B(r ) = Bn(rmin) for r < rmin. This approximation can be usedfor values of rmin much less than lc and the result is shown in Fig. 2.6.

The second approximation that is often used is to assume scalarwave incidence and neglect the dipole factor sin2 � (dependence on �),

0.05 0.1 0.15 0.2 0.250

0.01

0.02

0.03

0.04

0.05

0.06

krmin

1 −

µs_

trun

c / µ

s

klc = 0.5 | m = 1.01

klc = 1.0 | m = 1.01

klc = 2.0 | m = 1.01

klc = 1.0 | m = 1.2

FIGURE 2.6 Normalized error in the scattering coefficient 〈�s〉 when the massfractal index correlation function is truncated at rmin. The error is maximumwhen m → 1 and gets smaller for larger values of m. The error also increaseswith smaller values of klc. The error is small and the model works well,however, for all values of m and klc provided krmin is sufficiently small.


FIGURE 2.7 Plots comparing the rotationally averaged mean differential crosssection per unit volume

⟨�up⟩(inner) and the scalar wave approximation 〈�sw〉

(outer) for klc = 0.1 (isotropic scattering) shown at the left and klc = 1(forward scattering) shown at the right.

which results in an axially symmetric 〈�sw〉 (without dimples). In thecase of unpolarized illumination, 〈�〉 (k0, ki) is sampled at all orien-tations of � and the result can be expressed by averaging over � toproduce a rotationally symmetric

⟨�up⟩. Figure 2.7 shows the difference

between the scalar wave approximation and the result of averagingover polarization orientations. To quantify the error in this approxi-mation, the normalized error in the scattering coefficient 〈�s〉 is cal-culated and is maximum for the case of isotropic scattering where(〈�s〉sw − 〈�s〉)/〈�s〉 → 1/3. The error in neglecting the dipole factoralso affects the anisotropy factor g and hence the reduced scattering co-efficient

⟨�′

s

⟩, as shown in Fig. 2.8. Because this second approximation

introduces significant error and the complexity of the relationships is

0 5 10 15 200

0.2

0.4

0.6

0.8

1

< µ

s >

/ k

klc

Dipole m = 1.9Scalar m = 1.9Dipole m = 1.6Scalar m = 1.6Dipole m = 1.4Scalar m = 1.4

FIGURE 2.8 Plots of⟨�′

s

⟩/k versus klc with and without the dipole factor.


not significantly reduced, it is concluded that inclusion of the dipolefactor is advisable.

2.3 2D Continuous Random Media

Mean Differential Scattering Cross SectionA 2D medium is characterized by the invariance of the geometry andthe illumination along a particular axis called the axis of invariance. Asin the previous section, we will model the statistics of the normalizedRI fluctuation of the 2D random medium by a 2D stationary Gaussianrandom process with correlation

E{�n(� )�n(� + �� )} = Bn(�� ). (2.13)

It is assumed that the random medium is illuminated by a planewave with direction ki, and the radiated scattered wave is observed atdirection k0. If the magnetic field of the plane wave is perpendicular tothe axis of invariance, the excitation is said to be transverse magnetic(TM), or scalar. Otherwise, the excitation is transverse electric (TE),or vector. For simplicity, the results are derived for TM excitation andextended trivially to TE. Using a method similar to that in Ref. [1] for3D media, it can be shown that the mean differential scattering crosssection per unit area is given by the following simple formula in theBorn approximation:

〈�TM〉 (k0, ki) = 2�k3�n(ks), (2.14)

in which ks = k(ki − k0), and �n(�) is the power-spectral density of thenormalized RI fluctuation, given by

�n(�) = 1(2�)2

∫ ∫ ∞

−∞Bn(� ) exp(−i� · � ) d� . (2.15)

Now, let us assume an isotropic spatial correlation function of theform

Bn(�� ) = �2n

(��

lc

)K1

(��

lc

), (2.16)

where �n is the fluctuation strength, lc is the correlation length, andK1(·) is the modified Bessel function of second kind and order 1. Itcan be argued that this correlation is one of the “natural” choices in2D because it corresponds to the solution of a stochastic differentialequation of Laplace type [6]. With this correlation function, the mean


differential scattering cross section 〈�TM〉 becomes

〈�TM〉 (k0, ki) = 2�2n k3l2

c

(1 + (kslc)2)2 = 2�2n k3l2

c(1 + 4k2l2

c sin2 (�/2))2 , (2.17)

in which ks = |ks| = 2k sin(�/2), where � is the angle between ki andk0.

Although the above results have been derived for TM excitation,they can be easily extended to TE excitation by multiplying Eq. (2.14)by a dipole factor sin2 � , where � = (�/2) − � is the angle between thepolarization direction of the electric field and the observation directionk0. For the specific correlation function in Eq. (2.16):

〈�TM〉 (k0, ki) = 2�2n k3l2

c sin2 �

(1 + (kslc)2)2 = 2�2n k3l2

c cos2(�)(1 + 4k2l2

c sin2 (�/2))2 . (2.18)

Scattering Coefficient and Related ParametersThe scattering coefficient, 〈�s〉, is found by integrating Eqs. (2.17) and(2.18) over 0 < � < 2�:

⟨�sTM

⟩ = 4�2n k3l2

c

(1 + 2k2l2

c

)�(

1 + 4k2l2c

)3/2 , (2.19)

⟨�sTE

⟩ = �2n

(−1 − 4k4l4

c + 8k6l6c +

√1 + 4k2l2

c + 2k2l2c

(−3 + 2

√1 + 4k2l2

c

))�

kl2c

(1 + 4k2l2

c

)3/2

(2.20)

It is again convenient to normalize the mean free path ls = 1/ 〈�s〉by the wave number k. For klc � 1 and klc � 1, the mean free pathassumes the following asymptotic forms:

kls =

(klc)−2

4�2n �

if klc � 1

(klc)−1

�2n �

if klc � 1(TM)

kls =

(klc)−2

2�2n �

if klc � 1

(klc)−1

�2n �

if klc � 1

(TE)

(2.21)


The anisotropy factor g, defined as the average cosine of the scat-tering angle over all directions, can also be obtained analytically. ForTM incidence

gTM =

∫�

cos(�) 〈�TM〉 (k0, ki)

d�∫�

〈�TM〉 (k0, ki)

d�

= 1 − 11 + 2k2l2

c

=

2 (klc)2 if klc � 1

1 − 1

2 (klc)2 if klc � 1(2.22)

For TE incidence, the exact expression g is quite unwieldy. Here,we only provide the asymptotic forms for small and large klc:

gTE =

3 (klc)2 if klc � 1

1 − 1

2 (klc)2 if klc � 1(2.23)

2.4 1D Continuous Random MediaA 1D medium is characterized by the invariance of the geometry andthe illumination in every plane perpendicular to a certain axis calledthe axis of symmetry. Because of this extensive symmetry, the scatteringparameters for 1D media reduce to exceedingly simple forms.

The normalized RI fluctuation of the 1D random medium is rep-resented by a 1D stationary Gaussian random process, �n(z), withspatial correlation Bn(�z):

E{�n(z)�n(z + �z)} = Bn(�z). (2.24)

In the 1D case, there is no difference between the differential crosssection and the scattering coefficient, because there are only two di-rections (up or down) in the geometry, and angular dependence is notan issue. In the Born approximation, the scattering coefficient of the1D random medium is given simply by [1, 9]

〈�s〉 = 2�k2�n(2k), (2.25)

in which �n(�) = (1/2�)∫∞−∞ Bn(z′) exp(−ikz′) dz′ is the power-

spectral density of the normalized RI fluctuation. For exponentialcorrelation Bn (�z) = �2

n exp (−|�z/ lc|), in which �n is the fluctua-tion strength and lc is the correlation length, the scattering coefficient


becomes

〈�s〉 = 2�2n k2lc

1 + 4k2l2c. (2.26)

The normalized mean free path kls = k/ 〈�s〉 is therefore given by

kls = 1 + 4k2l2c

2�2n klc

=

(klc)−1

2�2n

if klc � 1

2 (klc)�2

nif klc � 1

(2.27)

2.5 Generation of Continuous Random Media SamplesIn some situations, one might require independent normalized RI fluc-tuation samples with known statistical properties. One such situation,described in more detail in the chapter on Finite-Difference Time-Domain (FDTD) simulations, is the statistical finite-difference time-domain (FDTD) electromagnetic modeling of light scattering from arandom medium. Generation of independent normalized RI fluctua-tion samples greatly facilitates the application of deterministic meth-ods such as FDTD modeling to statistical problems, a good exampleof which is the main subject of this chapter. In this section, we willdiscuss one of the methods for generating these independent sam-ples: The spatial-Fourier-spectrum method, in which the spatial Fourierspectrum of the normalized RI fluctuation is generated first, and in-verse Fourier transformed to spatial domain for the final result. Thismethod is based on a straightforward generalization of the principlethat the Fourier spectrum of a stationary random process is nonsta-tionary white noise with variance proportional to the power-spectraldensity of the random process [10]. This principle is utilized in the gen-eration of independent normalized RI fluctuation samples as follows:First, the spatial Fourier spectrum of the normalized RI fluctuationis constructed with independent Gaussian-distributed values at eachspatial frequency (because of the white noise property), and weightedthe values by the power-spectral density of the normalized RI fluctu-ation. Finally, inverse Fourier transform yields the desired sample.

The continuous-domain principle described above stays validwhen the medium is spatially discretized for computational purposes(e.g., the grid structure in FDTD modeling), provided that the spatialdiscretization step is much smaller than the correlation length of themedium. Let us consider a d-dimensional discrete Gaussian station-ary random function n(r ) of dimensions N1 × N2 · · · Nd , with correla-tion Bn(r ) and power-spectral density �n(�) = F {Bn}. It can easily be


shown that the spatial discrete Fourier transform (DFT) [11] of n(r ),N(�), is Gaussian white noise (meaning that its values at different �are independent) and has variance equal to N1 N2 . . . Nd�(�). Usingthis principle, the discrete spectrum N(�) can be easily constructed byassigning independent values with variances N1 N2 . . . Nd�(�) to eachspatial frequency �. Finally, the desired correlated discrete randomsample is obtained via inverse DFT.

In the following, a MATLAB function generate corr 3D is pro-vided as a reference for producing 3D random samples of a mediumwith correlation given by Eq. (2.5) in the section “Mean DifferentialScattering Cross Section.”

% *** generate corr 3D. m ***%% by Ilker R. Capoglu & Jeremy D. Rogers (c)2009%% Generates a three-dimensional (3D)% zero-mean real correlated array x[a,b,c].% sigma n is the variance of the random array : E{x∧2}% nc is the correlation length in grid cells : nc = lc/dx,% where dx is the spatial increment and lc is the% continuous-domain correlation length.% A,B,C are the extents of the array x[a,b,c].% The correlation function is given by% Bn[a,b,c] = Bn[r] = 2∧(5/2-m)(sigma n∧2)*(r/nc)∧(m-3/2)*% BesselK(m-3/2,r/nc)/Gamma(m-3/2)% where r = (a2+b2+c2)1/2.% For m = 2, this becomes the exponential correlation function:% Bn[r,m = 2] = sigma n∧2*exp(-r/nc)% To avoid aliasing in the spatial-frequency domain, nc�(1/pi)% must be satisfied, so that 1/(1+(K*nc).∧2)∧m decays% sufficiently at K = pi.% To avoid aliasing in the spatial domain,% (A/nc)�1, (B/nc)�1, and (C/nc)�1 must be satisfied% separately, so that the correlation decays sufficiently% at a = A and b = B and c = C.

function corr 3D = generate corr 3D(sigma n,nc,A,B,C,m)ka = -pi:2*pi/A:(pi-2*pi/A);kb = -pi:2*pi/B:(pi-2*pi/B);kc = -pi:2*pi/C:(pi-2*pi/C);[Ka, Kb, Kc] = ndgrid(ka, kb, kc);K = sqrt(Ka.∧2+Kb.∧2+Kc.∧2); clear Ka Kb Kc;power spec = sigma n∧2*nc∧3*gamma(m)./ . . .(pi (3/2)*gamma(m-3/2)*(1+K.∧2*nc∧2).∧m);


% each frequency point is independent with% power (A*B*C*power spec(a,b,c)):spec ampl = sqrt(A*B*C*power spec);% randomly selected frequency points with Gaussian distribution:sample spec = randn(size(power spec)).*spec ampl;% 3D inverse FFT of the randomly selected frequency array:sample waveform = ifftn(fftshift(sample spec));% The real part of sample waveform is symmetric, and% the imaginary part is anti-symmetric.% Add real and imaginary parts to get nonsymmetric array:corr 3D = real(sample waveform) + imag(sample waveform);%% *** end of function generate corr 3D.m ***

Although the above code is given for 3D media, it can easily bemodified to produce 2D and 1D media by following the same inverseFourier transform principle described in this section. For a visualiza-tion of the random samples generated using a 2D version of the abovecode, the reader can refer to Fig. 3.4 in the chapter on FDTD.

References1. A. Ishimaru, Wave Propagation and Scattering in Random Media. New York: Wiley-

IEEE Press, 1999.2. W. C. Chew, Waves and Fields in Inhomogeneous Media. New York: Van Nostrand

Reinhold, 1990.3. C. A. Balanis, Advanced Engineering Electromagnetics. New York: Wiley, 1989.4. J. M. Schmitt and J. M. Kumar, “Turbulent nature of refractive-index variations

in biological tissue,” Opt Lett 21, 1310 (1996).5. M. Xu and R. R. Alfano, “Fractal mechanisms of light scattering in biological

tissue and cells,” Opt Lett 30, 3051 (2005).6. P. Guttorp and T. Gneiting, “On the Whittle-Matern Correlation Family,” NRCSE,

Seattle, WA: Tech. Rep. 080, 2005.7. C. J. R. Sheppard, “Fractal model of light scattering in biological tissue and

cells,” Opt Lett 32, 142 (2007).8. J. F. Beek, P. Blokland, P. Posthumus, M. Aalders, J. W. Pickering, H. J. C.

M. Sterenborg, and M. J. C. van Gemert, “In vitro double-integrating-sphereoptical properties of tissues between 630 and 1064 nm,” Phys Med Biol 42, 2255(1997).

9. I. R. Capoglu, V. Backman, and A. Taflove, “Theory and FDTD Simulation ofWave Propagation in 1-D Random Media,” USNC-URSI National Radio ScienceMeeting, San Diego, CA, 2008.

10. A. Papoulis, Probability, Random Variables, and Stochastic Processes. New York:McGraw-Hill, 1991.

11. A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-Time Signal Processing,2nd ed. Upper Saddle River, NJ: Prentice Hall, 1999.


C H A P T E R 3Modeling of Light

Scattering byBiological Tissues

via ComputationalSolution of

Maxwell’s Equations

Snow H. Tseng, Ilker R. Capoglu, Allen Taflove, and Vadim Backman

3.1 IntroductionBiophotonics is an exciting emerging discipline that involves theory,computational simulations, laboratory experiments, and clinical stud-ies of optical interactions with biological tissues. A primary potentialapplication of biophotonics is the diagnosis of human disease, espe-cially cancer, using relatively noninvasive means.

This chapter reviews recent biophotonics research involving com-putational modeling of linear (“elastic”) light scattering by tissues viadirect solution of Maxwell’s equations, the fundamental set of partialdifferential equations of Nature, which form the basis of all classicalelectromagnetic wave interactions with materials. We focus on twospecific computational techniques for Maxwell’s equations implemen-ted on Cartesian space grids: the Yee-algorithm finite-difference time-domain (FDTD) method [1, 2] and the Liu-algorithm pseudospectraltime-domain (PSTD) method [3]. To date, these two techniques have

49


shown the best promise for rigorously modeling optical waveinteractions with inhomogeneous cellular structures over largethree-dimensional (3D) volumes of space while providing uniformlyfine-grained spatial resolution in the order of 0.1 wavelength (0.1).

Why are rigorous FDTD and PSTD solutions to Maxwell’s equa-tions important in biophotonics? First, FDTD and PSTD can accountfor how the shape and internal inhomogeneities of each individualbiological cell generates its own local optical electromagnetic fieldstructure, which can involve both propagating and evanescentmultivector-component electric fields. Second, PSTD (and to a lesserdegree FDTD) can account for the simultaneous interaction of thelocal optical electromagnetic field structures of many closely spacedbiological cells to obtain what is best described as the composite emer-gent macroscopic optical properties of the tissue. The comprehensivenature of such rigorous Maxwell’s equations modeling over an ap-proximate 1,000:1 range of distance scales from order (50 nm) to order(50 �m) yields a rich set of electromagnetic wave phenomena, whichcannot be calculated by previous approximate techniques employingheuristic simplifications based upon radiative transfer theory [4]. Suchapproximate techniques omit the electromagnetic wave characteristicsof light and treat light propagation as an energy-transport problem.This omission can yield research findings of potentially questionableaccuracy and validity [5, 6].

In the following sections, we shall review recent work in FDTDand PSTD computational Maxwell’s equations modeling of light scat-tering by biological tissues. Topics include (1) summary of the basicprinciples underlying FDTD and PSTD computational solutions ofMaxwell’s equations; (2) FDTD modeling results showing how opti-cal interactions can be sensitive to submicron and even nanometer-scale features embedded within micron-scale models of living cells;and (3) PSTD modeling results showing promise for studies of op-tical interactions with random arrangements of hundreds and eventhousands of living cells, spanning in aggregate macroscopic tissueregions. Overall, our goal is to demonstrate that FDTD and PSTDsolution techniques for Maxwell’s equations are providing means tostrengthen the science base for cellular-level and tissue-level biopho-tonics, as well as to accelerate the development of corresponding novelclinical technologies.

3.2 Overview of FDTD Techniques forMaxwell’s Equations∗Before 1990, computational modeling of electromagnetic wave prop-agation and interaction was almost exclusively implemented using

∗Adapted with permission from Sections 1.3, 1.4, and 1.6 of Ref. [2].

51M o d e l i n g o f L i g h t S c a t t e r i n g b y B i o l o g i c a l T i s s u e s

solution techniques for the sinusoidal steady-state Maxwell’s equa-tions, i.e., in the frequency domain. Principal approaches for com-plex geometries involved high-frequency asymptotic techniques forconducting structures spanning many wavelengths [7, 8] and in-tegral equation/method-of-moment techniques for material struc-tures of dimensions comparable to or smaller than one wavelength[9, 10].

However, these frequency-domain techniques have difficultiesand trade-offs. For example, although asymptotic analyses are wellsuited for modeling the scattering properties of electrically large com-plex shapes, such analyses have difficulty treating nonmetallic mate-rial composition and volumetric complexity of a structure. Althoughintegral equation methods can deal with material and structural com-plexity, their need to construct and solve systems of linear algebraicequations limits the electrical size of possible models, especially thoserequiring detailed treatment of geometric details within a volume, asopposed to just the surface shape.

Although significant progress has been made in solving the ultra-large systems of equations generated by frequency-domain integralequations [11], the capabilities of even the latest such technologiesare exhausted by many volumetrically complex structures of engi-neering interest. This also holds for frequency-domain finite-elementtechniques, which generate sparse rather than dense matrices.

Advantages of FDTD Solution Techniques forMaxwell’s EquationsDuring the 1970s and 1980s, various defense agencies working inradar technologies and nuclear weapons effects realized the limita-tions of frequency-domain integral-equation solutions of Maxwell’sequations. This led to early explorations of a novel alternative ap-proach: direct time-domain solutions of Maxwell’s differential (curl)equations on spatial grids or lattices. The FDTD method, introducedby Yee in 1966 [1], was the first technique in this class and has remainedthe subject of continuous development. Since 1990, when engineers inthe general electromagnetics community became aware of the model-ing capabilities afforded by FDTD and related techniques, the interestin this area has expanded well beyond defense technologies.

There are seven primary reasons for the expansion of interest inFDTD solution techniques for Maxwell’s equations:

1. FDTD uses no linear algebra: Being a fully explicit computation,FDTD avoids the difficulties with linear algebra that limitthe size of frequency-domain integral-equation and finite-element electromagnetics models to generally fewer than 106

electromagnetic field unknowns. FDTD models with as many


as 109 field unknowns have been run; there is no intrinsicupper bound to this number.

2. FDTD is accurate and robust: The sources of error in FDTD cal-culations are well understood and can be bounded to permitaccurate models for a very large variety of electromagneticwave interaction problems.

3. FDTD treats impulsive behavior naturally: Being a time-domaintechnique, FDTD directly calculates the impulse response ofan electromagnetic system. Therefore, a single FDTD sim-ulation can provide either ultra-wideband temporal wave-forms or the sinusoidal steady-state response at any frequencywithin the excitation spectrum.

4. FDTD treats nonlinear behavior naturally: Being a time-domaintechnique, FDTD directly calculates the nonlinear responseof an electromagnetic system. This allows natural hybridingof FDTD with sets of auxiliary differential equations that de-scribe nonlinearities from either the classical or semi-classicalstandpoint.

5. FDTD is a systematic approach: With FDTD, specifying a newstructure to be modeled is reduced to a problem of grid gen-eration rather than the potentially complex reformulation ofan integral equation. For example, FDTD requires no calcu-lation of structure-dependent Green functions. Furthermore,FDTD permits the systematic and straightforward calculationof the complete radiated or scattered far fields of any struc-ture being modeled in its computation grid, regardless of thepotentially irregular shape or complex material compositionof the structure.

6. Parallel-processing computer architectures have come to dominatesupercomputing: FDTD scales with very high efficiency onparallel-processing (cluster-type) computers.

7. Computer visualization capabilities are increasing rapidly: Whilethis trend positively influences all numerical techniques, itis of particular advantage to FDTD methods, which gener-ate time-marched arrays of field quantities suitable for use incolor videos to illustrate the field dynamics.

An indication of the expanding level of interest in FDTD Maxwell’sequations’ solvers is the tremendous increase in the number of FDTD-related journal papers published worldwide each year, from fewerthan 10 papers in 1985 [12] to approximately 2000 papers in 2006 [13].This expansion continues as engineers and scientists in nontraditionalelectromagnetics-related areas such as biophotonics become aware ofthe power of FDTD modeling. It is possible that FDTD will emerge


as the dominant computational modeling technique for mid-21st cen-tury electrodynamics problems of surpassing volumetric complexityand/or multiphysics.

Characteristics of the Yee-Algorithm FDTD TechniqueThe Yee-algorithm FDTD technique is a direct solution of the time-dependent Maxwell’s curl equations on a Cartesian space lattice. Itemploys no potentials, rather is based upon volumetric sampling ofthe unknown electric field vector E and magnetic field vector H withinand surrounding the structure of interest, and over a period of time.The sampling in space is at subwavelength resolution set by the user toproperly sample the highest near-field spatial frequencies thought tobe important in the physics of the problem. Typically, 10–20 samplesper wavelength are needed. Sampling in time is selected to ensurenumerical stability of the algorithm.

Overall, FDTD is a marching-in-time procedure that simulatesthe continuous actual electromagnetic waves in a finite spatial regionby sampled-data numerical analogs propagating in a computer dataspace. Time-stepping continues as the numerical wave analogs propa-gate in the space lattice to causally connect the physics of the modeledregion. For simulations where the modeled region must extend to in-finity, absorbing boundary conditions (ABCs) are employed at the outerlattice truncation planes. ABCs ideally permit all outgoing numericalwave analogs to exit the computation space with negligible reflec-tion. Phenomena such as induction of surface currents, scattering andmultiple scattering, aperture penetration, and cavity excitation aremodeled time-step by time-step by the action of the numerical analogto the curl equations. Self-consistency of these modeled phenomenais generally assured if their spatial and temporal variations are wellresolved by the space and time sampling process. In fact, the goal isto provide a self-consistent model of the mutual coupling of all of theelectrically small volume cells constituting the structure and its nearfield, even if the structure spans tens of wavelengths in 3D and thereare hundreds of millions of space cells.

Time-stepping is continued until the desired late-time pulse re-sponse is observed at the field points of interest. For linear wave in-teraction problems, the sinusoidal response at these field points can beobtained over a wide band of frequencies by discrete Fourier transfor-mation of the computed field versus time waveforms at these points.Prolonged “ringing” of the computed field waveforms due to a highQ-factor or large electrical size of the structure being modeled requiresa combination of extending the computational window in time andextrapolation of the windowed data before Fourier transformation.

For FDTD computational modeling of electromagnetic wave in-teractions, it is useful to consider the concept of predictive dynamic


range, defined as follows. Let the power density of the incident wave inthe space grid be P0. Further, let the minimum observable power den-sity of a scattered wave be PS, where “minimum observable” meansthat the accuracy of the field computation degrades due to numericalartifacts to poorer than 1 dB at lower levels than PS. Then, we candefine the predictive dynamic range as 10 log(P0/PS) dB.

In the 1980s, researchers demonstrated a predictive dynamic rangeon the order of 40–50 dB for FDTD models, limited principally bythe imperfect analytical ABCs of this era, which provided grid outer-boundary reflection coefficients ranging from about 3% (−30 dB)down to 0.3% (−50 dB). The 1990s saw the emergence of a power-ful new class of perfectly matched layer (PML) ABCs [14–17] hav-ing grid outer-boundary reflection coefficients of better than -80 dBfor impinging pulsed electromagnetic waves having ultra-widebandspectra. Excellent capabilities were demonstrated in terminating free-space lattices, multimode and dispersive waveguiding structures, andlossy and dispersive materials.

Consequently, the predictive dynamic range of present-day Yee-algorithm FDTD simulations is not limited by imperfect ABCs. Rather,the dynamic range is limited primarily because of the “staircasing”of smoothly curved material surfaces mapped onto the Cartesian Yeespace lattice, and because of accumulating numerical dispersion arti-facts within the computation lattice. A rule of thumb is that, in com-parison to the Mie solution for the far-field differential scattering crosssection of a homogeneous dielectric sphere, a spatially well-resolvedYee-algorithm FDTD model can yield a predictive dynamic range onthe order of 60 dB over the full range of scattering angles.

Finally, we consider the computational burden for the Yee-algorithm FDTD technique. The following factors are involved:

1. Number of space lattice cells, N: The six vector electromagneticfield components located at each lattice cell must be updatedat every time step. This yields by itself an order (N) scaling.

2. Number of time steps, nmax: A self-consistent solution in the timedomain mandates that the numerical wave analogs propagateover time scales sufficient to causally connect each portionof the structure of interest. Therefore, nmax must increase asthe maximum electrical size of the structure. In 3D, it can beargued that nmax is a fractional power function of N, such asN1/3. Further, nmax must be adequate to step through “ring-up” and “ring-down” times of energy storage features suchas cavities. These features vary from problem to problem andcannot be ascribed a functional dependence relative to N.

3. Cumulative propagation errors: Additional computational bur-dens may arise due to the need for either mesh refinement or


the use of a higher-accuracy algorithm to bound cumulativeerrors for propagating numerical modes in enlarged meshes.Any need for mesh refinement would feed back to factor 1.

For most problems, factors 2 and 3 are weaker functions of thesize of the modeled structure than factor 1. This is because geometri-cal features at increasing electrical distances from each other becomedecoupled due to radiative losses by the electromagnetic waves prop-agating between these features. Furthermore, it can be shown thatreplacing Yee’s second-order accurate algorithms by higher-order-accuracy versions such as PSTD sufficiently reduces numerical dis-persion errors to avoid the need for mesh refinement for object sizesup to the order of 100. Overall, the computational burden of FDTDscales as order (N · nmax) = order (N4/3) for large models. This scalingmatches very well with the capabilities of current parallel-processingcomputer clusters, which can apply FDTD to solve for more than 109

electromagnetic field unknowns.

3.3 FDTD Modeling Applications

Vertebrate Retinal Rod†

Arguably the first application of FDTD to cellular-level biophotonicswas reported in Ref. [18], wherein visible light interactions with a reti-nal photoreceptor were modeled for the two-dimensional (2D) TMz

and TEz polarization cases. The working hypothesis was that the de-tailed physical structure of a photoreceptor impacts the physics of itsoptical absorption and thereby, vision. One such photoreceptor wasstudied: the vertebrate retinal rod. The bulk structure of the retinal rodexhibits the physics of an optical waveguide, while the periodic inter-nal disk-stack structure adds the physics of an optical interferometer.These effects combine to generate a complex optical standing wavewithin the rod, thereby creating a pattern of local intensifications ofthe optical field.

The FDTD model of the rod reported in Ref. [18] had the cross-section dimensions of 2 × 20 �m, corresponding to (3.8d − 5.7d)×(38d−57d) over the range of wavelengths considered, where d de-notes the optical wavelength within the rod’s dielectric media. A uni-form Cartesian space grid having 5.0 nm2 unit cells was utilized. Thispermitted resolution of the 15-nm-thick outer wall membrane of therod and the 15-nm-thick internal disk membranes. There was a total of799 disks distributed uniformly along the length of the rod, separatedfrom each other by 10 nm of fluid, and separated from the outer wall

†Adapted with permission from Section 16.26 of Ref. [2].


FIGURE 3.1 Visualizations of the FDTD-computed optical E -field standingwave within the retinal rod model for TMz illumination at free-spacewavelengths 0 = 714, 505, and 475 nm. (Source: Piket-May et al. [18].)See also color insert.

membrane by 5 nm of fluid. The index of refraction of the membranewas chosen to be 1.43, and the index of refraction of the fluid waschosen to be 1.36, in accordance with generally accepted physiologi-cal data. These parameters implied a resolution within the dielectricmedia of d/70 to d/105, depending on the incident wavelength.

As reported in Ref. [18], Fig. 3.1 provides visualizations of theFDTD-computed magnitude of the normalized electric field valuesof the optical standing wave within the retinal rod model for TMz

illumination at the free-space wavelengths 0 = 714, 505, and 475nm. Similar visualizations were obtained for the TEz illuminationcase.


To assist in understanding the physics of the retinal rod as anoptical structure, the standing-wave magnitude data at each 0 werereduced as follows. First, at each transverse plane located at a giveny0 in the rod, the electric field values, E(x,y0), of the optical standingwave were integrated over the x-coordinate to obtain a single num-ber, Eint(y0). Second, a discrete spatial Fourier transform of the set ofEint(y0) values was performed over the y-coordinate. With the excep-tion of isolated peaks unique to each 0, the spatial-frequency spectrafor each polarization were found to be essentially independent of theillumination wavelength. It was concluded that the retinal rod exhibitsa type of frequency-independent electrodynamic behavior.

The agreement of the spatial-frequency spectra for the three in-cident wavelengths for each polarization was so remarkable that theoverall procedure was tested for computational artifacts. The test in-volved perturbing the indices of refraction of the membrane and fluidfrom those of the vertebrate rod to those of glass and air, while leav-ing the geometry unchanged. It was found that the glass–air spectrumexhibited little correlation (i.e., numerous sharp high-amplitude os-cillations) over the entire spatial-frequency range considered. On theother hand, the normalized membrane–fluid spectrum varied in atight range near unity through spatial frequencies of 3.6 �m−1. It wasconcluded that the agreement of the spatial-frequency spectra for thevertebrate retinal rod indicates a real physical effect that is dependentupon the proper definition of the indices of refraction of the compo-nents of the rod structure.

From an electrical engineering standpoint, frequency-independent structures have found major usages in broadbandtransmission and reception of radio frequency and microwave sig-nals. There is a limited set of such structures, and it is always excitingto find a new one. Reference [18] concluded by speculating thatsome engineering usage of wavelength-independent retinal-rod-likestructures may eventually result for optical signal processing.

Precancerous Cervical CellsIn a series of papers (Refs. [19, 20] being most relevant to the presentdiscussion), the Richards-Kortum group pioneered FDTD modeling oflight scattering from cervical cells during their earliest stages of cancerdevelopment. This group investigated how the light-scattering prop-erties of cervical cells are affected by changes in nuclear morphology,DNA content, and chromatin texture that occur during neoplastic pro-gression. FDTD was applied to calculate the magnitude and angulardistribution of scattered light as a function of pathologic grade.

We now consider work by the Richards-Kortum group on 2DFDTD models of cellular scattering, as illustrated in Fig. 3.2 [19]. Inthis example, the cell cytoplasm, when present, had a diameter of


(a)

(a) Nucleus only

(c) Nucleus and cytoplasm (d) Cell with organelles

Scattering angleScattering angle

(b) Cytoplasm only1000

Wav

elen

gth

(nm

)

900

800

700

6000°

1000

900

800

700

6000°50° 100° 150°

1000

900

800

700

6000° 50° 100° 150°

50° 100° 150°

1000

900

800

700

6000° 50° 100° 150°

–6

–5

–4

–3

–2

–1

0

1

–6

–5

–4

–3

–2

–1

0

1

–6

–5

–4

–3

–2

–1

0

1

–6

–5

–4

–3

–2

–1

0

1

(b) (c) (d)

FIGURE 3.2 Visualizations of the FDTD-computed optical scattering of fourmodels of a cell: (a) nucleus only, (b) cytoplasm only, (c) nucleus andcytoplasm, and (d) nucleus and cytoplasm containing organelles. The scalecorresponds to the log of the scattered intensity. (Source: Drezek et al. [19].)See also color insert.

8 �m, and the nucleus had a diameter of 4 �m. Refractive index val-ues for the cytoplasm and the nucleus were 1.37 and 1.40, respectively.Organelle refractive indices ranged from 1.38 to 1.42, and organellesizes ranged from 0.1 to 1 �m. Approximately 25% of the availablespace within the cell (i.e., space not already occupied by the nucleus)was filled with organelles. Wavelengths spanned from 600 to 1000 nmin 5-nm increments.

From Fig. 3.2, we note how the introduction of heterogeneitiesin the form of small organelles impacts scattering. Closely followingthe discussion of Ref. [19], the addition of cytoplasmic organelles be-gins to obscure the interference peaks visible in the simulations usinghomogeneous geometries. The effects of the heterogeneities are mostnoticeable at angles over 90◦, partially because the scattered intensity


Normal cell

Scattering angle

Wavelength (nm)

Wav

elen

gth

(nm

)

1000 0

–0

–2

–3

–4

–5

–6

–7

900

800

700

600

102

100

10–2

10–4

600

Inte

grat

ed in

tens

ity

Inte

grat

ed in

tens

ity0 – 20°

160 – 180°

80 – 100°

0 – 20°

160 – 180°

80 – 100°

700 800 900 1000Wavelength (nm)

102

100

10–2

10–4

600 700 800 900 1000

0° 50° 100° 150°

Normal cell

Scattering angle

1000 0

–0

–2

–3

–4

–5

–6

–7

900

800

700

6000° 50° 100° 150°

FIGURE 3.3 (Top) Visualizations of the FDTD-computed optical scattering frommodels of normal (left) and dysplastic (right) cervical cells. The scalecorresponds to the log of the scattered intensity. (Bottom) Integratedscattered intensities over three angular ranges for normal (left) and dysplastic(right) cervical cells. (Source: Drezek et al. [19].) See also color insert.

values in this region are 5–6 orders of magnitude smaller than thescattered intensity values at low angles.

Reference [19] then proceeded to consider more complicated 2Ddescriptions of cellular morphology. In the example illustrated inFig. 3.3, two cells containing multiple sizes and shapes of organellesand heterogeneous nuclei were considered. In the first cell, the mor-phology was defined using histological features of normal cervicalcells. In the second cell, the morphology was defined based on thefeatures of cervical cells staged as high-grade dysplasia. In order toemphasize differences due to the internal contents, both cells wereassumed to be circular with 9-�m diameters. The most significant dif-ferences between the dysplastic cell relative to the normal cell includedincreased nuclear size and nuclear-to-cytoplasmic ratio (normal 0.2,dysplastic 0.67), asymmetric nuclear shape, increased DNA content,and hyperchromatic nucleus with areas of coarse chromatin clumpingand clearing.

For the normal cell considered in Fig. 3.3, nuclear refractive-indexvariations were assumed to be uniformly distributed in the rangen = 1.40 ± 0.02 at spatial frequencies ranging from 10 to 30 �m−1,


thereby simulating a fine, heterogeneous chromatin structure. In thedysplastic cell, nuclear refractive-index variations were distributedin the range n = 1.42 ± 0.04 at spatial frequencies ranging from 3 to30 �m−1, thereby simulating a coarser, more heterogeneous chromatinstructure. Both normal and dysplastic cells contained several hun-dred organelles (radii: from 50 to 500 nm; n = 1.38–1.40) randomlydistributed throughout the cytoplasm.

From Fig. 3.3, the results of the FDTD modeling study indicatethat the dysplastic cell exhibits elevated scattering. There is increasedscattering at small angles due to the larger nucleus, and increasedscattering at larger angles due to alterations in the chromatin structure,which results in increased heterogeneity of the refractive index [19].Because the dysplastic cell contains a large heterogeneous nucleus thatis comprised of an assortment of scatterer sizes and refractive indexes,distinct interference peaks are not present. Although heterogeneitiesare present in the structure of a normal cell, they are not significantenough to disrupt the peaks resulting from the cytoplasm and nuclearboundaries [19].

The bottom half of Fig. 3.3 displays the integrated scattered in-tensity as a function of wavelength for three angular ranges: 0–20◦,80–100◦, and 160–180◦. Closely following the discussion of Ref. [19],these results show that the integrated intensity is a function of bothangle and cellular structure. Here, changes in the wavelength de-pendence of the scattering between the normal and dysplastic cellsare especially evident at large angles. To develop optimized opticalprobes and measurement techniques that can discriminate betweennormal and dysplastic tissues based on differences in the wavelengthdependence of cellular scattering, it is important to be aware of whichangular regions offer the greatest potential for differential diagnosis.

Validation of the Born Approximation in 2D Weakly ScatteringBiological Random MediaBy comparison with detailed FDTD computational modeling results,Ref. [21] investigated the validity of the Born (or single-scattering)approximation [22] to analyze light scattering by 2D weakly scat-tering biological random media. It was not apparent from the exist-ing literature that such a rigorous comparison had been previouslyreported.

Reference [21] first constructed a statistical model for the normal-ized refractive-index fluctuations of a representative biological ran-dom medium. Using literature values of refractive-index data corre-sponding to biological cells [23, 24], the statistical model was a 2Dstationary Gaussian random process having a defined spatial corre-lation length lc. Then, applying the Born approximation, analyticalformulas were derived for the expected value of the total scattering


cross section (TSCS) of the random medium for both scalar transversemagnetic (TM) and vector transverse electric (TE) polarizations of theincident plane wave.

To obtain comparative statistical FDTD results for the mean TSCSof the biological random medium, averaging was performed over 200FDTD runs for each of eight different lc values ranging from 11 to560 nm. The realization of the Gaussian random medium for eachFDTD run was assigned a mean refractive index n0 = 1.38 and a fluc-tuation strength �n = 0.02, and implemented on a 7.45 × 7.45 �mPML-terminated grid with a uniform square grid cell size of 13.3 nm.Using a broadband illuminating pulse for each FDTD run, the normal-ized scattered far field was calculated for 10 log-spaced frequenciesfrom 400 to 700 nm. (Hence, defining k as the wave number, the FDTDmodeling runs spanned a klc range of approximately 0.1–10.) At eachfrequency, the far-field values at 360 equally spaced angles were nu-merically integrated to yield the TSCS.

Figure 3.4a and b provides grayscale visualizations of therefractive-index fluctuations of two sample realizations of the Gaus-sian random medium [21]. The sample in Fig. 3.1a has a spatial corre-lation length lc = 100 nm, whereas lc = 300 nm for the sample shownin Fig. 3.1b.

Figure 3.5a and b plots, for the TM and TE cases, respectively,the mean TSCS (normalized by k) as a function of klc [21]. In thesefigures, the dashed lines denote the theoretical values predicted bythe Born approximation, while the solid lines denote the results ob-tained using the statistical FDTD analysis. The results are within 1 dBof each other over the entire klc range. This confirms the validity of theBorn approximation within the range of refractive-index fluctuations(�n = 0.02) considered in Ref. [21], which were based on values re-ported previously in the literature.

x (µm) x (µm)

y (µ

m)

y (µ

m)

FIGURE 3.4 Grayscale images of the refractive-index fluctuations of twoGaussian random medium samples: (a) spatial correlation length lc = 100 nmand (b)lc = 300 nm. (Source: Capoglu and Backman [21].)


FIGURE 3.5 Mean total scattering cross section normalized by the wavenumber k for 2D random media: (a) TM (scalar) illumination and (b) TE(vector) illumination. (Source: Capoglu and Backman [21].)

In summary, using statistical FDTD computational modeling, Ref.[21] validated the Born approximation for 2D weakly scattering bio-logical random media. These results should be valuable for researchersseeking to utilize the simplicity and analytical power of the Born ap-proximation in the analysis of weakly scattering biological media, animportant example of which is the single biological cell. Although theresults of Ref. [21] are for 2D random media, they lend a strong sup-port to the validity of the Born approximation in a general 3D setting,which remains to be investigated in a future study.

Sensitivity of Backscattering Signatures to Nanometer-ScaleCellular Changes∗

Recent experimental evidence indicates that light-scattering signalscan provide means for ultra-early-stage detection of colon cancer [25]before any other biomarker that is currently known. In combinationwith the findings reported by the Richards-Kortum group, it is nowquite clear that light scattering is very sensitive to minute differencesin tissue and cellular structures. An important question then arises forresearchers investigating optical tissue diagnostic techniques: Whichlight-scattering parameters provide the best sensitivity to detect cellu-lar changes that are at the nanometer scale (i.e., those that may indicatecancer)?

Figure 3.6 illustrates the application of FDTD to evaluate the sen-sitivity of optical backscattering and forward-scattering signatures torefractive-index fluctuations spanning nanometer length scales [26].Here, the spectral and angular distributions of scattered light from

∗Adapted with permission from Section 16.26 of Ref. [2].


FIGURE 3.6 Visualizations of the FDTD-computed optical scattering signaturesof a 4-�m-diameter particle with a volume-averaged refractive index navg =1.1. (a) Homogeneous particle; (b) inhomogeneous particle with refractiveindex fluctuations �n = ± 0.03 spanning distance scales of approximately50 nm; and (c) inhomogeneous particle with refractive index fluctuations�n = ± 0.03 spanning distance scales of approximately 100 nm. (Source:X. Li et al. [26].) See also color insert.

inhomogeneous dielectric particles with identical sizes and volume-averaged refractive indices are compared with corresponding datacalculated for their homogeneous counterparts.

The optical backscattering signatures (shown in the center pan-els of Fig. 3.6) are of particular interest. These are visualizations ofthe FDTD-calculated backscattering intensity distributions as func-tions of wavelength and scattering angle within a ±20◦ range of directbackscatter. Relative to the homogeneous case of Fig. 3.6a , we observedistinctive features of the backscattering signatures for the randomlyinhomogeneous cases of Fig. 3.6b and c. This is despite the fact thatthe inhomogeneities for these cases have characteristic sizes of only50 and 100 nm, respectively, which are much smaller than the illu-mination wavelength of 750 nm. In contrast, the forward-scatteringsignatures shown in the right-hand panels exhibit no distinctivefeatures.

These FDTD calculations strongly support the hypothesis thatthere exist signatures in backscattered light that are sufficiently


sensitive to detect alterations in the cellular architecture at thenanometer scale. Importantly, this sensitivity is not bound by the diffrac-tion limit. Potentially, backscattering signatures can serve as biomark-ers to detect and characterize slight alterations in tissue structure,which may be precursors of cancer [25].

3.4 Overview of Liu’s Fourier-Basis PSTD Technique forMaxwell’s EquationsIn principle, FDTD techniques can be used to model arbitrarily largecollections of biological cells, and thereby attack the tissue-optics prob-lem at its most fundamental basis, Maxwell’s equations. However, inpractice, the size of problems amenable to FDTD modeling is limited,especially in 3D. Here, the database of electromagnetic field vectorcomponents used by Yee-algorithm FDTD rapidly exceeds availablecomputer resources because of the fine-grained spatial resolution (10–20 or more samples per optical wavelength in each direction) requiredto achieve an acceptable predictive dynamic range.

In order to model large-scale electromagnetic wave interactionproblems while retaining all of the advantages of FDTD, researchershave proposed replacing Yee’s second-order accurate numerical spa-tial derivative approximations with ones of higher accuracy. A promis-ing class of such techniques for general partial differential equationsis spectral collocation [27, 28], of which PSTD is a realization specifi-cally aimed to solve the time-domain Maxwell’s equations. Originallyproposed by Liu [3], the Fourier-basis PSTD method permits in prin-ciple relaxing the spatial-resolution requirement to the Nyquist limitof two samples per wavelength. Liu has shown that, for large mod-els in D dimensions that do not have geometrical details or materialinhomogeneities smaller than one-half wavelength, the Fourier-basisPSTD method reduces computer-resource requirements by approxi-mately 8D:1 relative to Yee-algorithm FDTD while achieving compa-rable accuracy [3]. This is the key to modeling large-scale biophotonicsproblems directly from Maxwell’s equations.

Section 4.9.4 and Chapter 17 of Ref. [2] provide a comprehensivediscussion of the technical basis of PSTD techniques. A few addi-tional details apply to the PSTD biophotonics models discussed inthe following sections. (1) The wraparound caused by periodicity inthe discrete Fourier transforms employed to implement PSTD is elim-inated by bounding the computation space with PML. (2) Incidentwave excitation is provided by the scattered-field technique [2]. (3)Surfaces of scattering shapes are approximated by staircasing at thegrid resolution. (4) PSTD results for plane-wave scattering by dielec-tric spheres exhibit an accuracy of better than ±1 dB at all angles,including backscattering, over predictive dynamic ranges exceeding50 dB.


3.5 PSTD Modeling Applications

Total Scattering Cross Section of a Round Cluster of 2DDielectric CylindersWe first consider the application of PSTD to calculate the total scatter-ing cross section (TSCS) of a round cluster of 2D dielectric cylinders[29, 30]. The principal finding of this study, shown in Fig. 3.7, is thatwhen the average dielectric coverage of the cluster increases beyonda certain threshold, the TSCS of the cluster becomes independent ofits internal geometrical details such as the size, position, and numberof its constituent cylinders. In this regime, the frequency dependence(spectrum) of the TSCS of the cluster represents essentially the averagebehavior of the TSCS spectrum of the volume-averaged homogeneouscylinder of the same diameter. The primary difference is that the ho-mogeneous cylinder exhibits ripples of its TSCS spectrum as a resultof coherent internal wave-interference effects that are suppressed byscattering events within the random clusters.

Enhanced Backscattering of Light by a Large RectangularCluster of 2D Dielectric CylindersWe next consider PSTD modeling of optical enhanced backscatter-ing (EBS), a phenomenon that has recently elicited attention as a

FIGURE 3.7 PSTD-computed total scattering cross section of (a) 160-�moverall-diameter cylindrical bundle of 120 randomly positioned, noncontactingdielectric cylinders of individual diameter d = 10 �m and refractive index n =1.2; (b) as in part (a), but for 480 cylinders of individual diameter d = 5 �m;and (c) single cylinder of n = 1.0938, the volume-average refractive index ofthe random bundles of parts (a) and (b). (Source: S. H. Tseng et al. [30].)


FIGURE 3.8 PSTD simulation of enhanced backscattering (EBS) in twodimensions. The 800 �m × 400 �m rectangular cluster of noncontacting,1.2 �m diameter, n = 1.25 dielectric cylinders is illuminated by a coherentplane wave incident at 15◦ relative to the normal. Both the incident light andthe backscattered light are polarized perpendicular to the plane of incidence,equivalent to collinear detection in EBS experiments. (Source: S. H. Tsenget al. [34].)

potential means for clinical diagnosis of disease [31–33]. EmployingPSTD, Ref. [34] reported the first simulation of EBS by numericallysolving Maxwell’s equations without heuristic approximations.

Figure 3.8 illustrates the geometry of the PSTD model: an 800 �m× 400 �m rectangular cluster of 20,000 randomly positioned, noncon-tacting, infinitely long, dielectric cylinders [34]. Each cylinder is 1.2�m in diameter with a refractive index n = 1.25. There is an averagesurface-to-surface spacing of 2.8 �m between adjacent cylinders. Therectangular cluster is illuminated by a coherent plane wave at f0 =300 THz (0 = 1 �m) that is incident at 15◦ relative to the normal. Boththe incident light and the backscattered light are polarized perpen-dicular to the plane of incidence, equivalent to collinear detection inEBS experiments. The PSTD grid has a uniform spatial resolution of0.33 �m, equivalent to 0.42d at the illumination wavelength. At thiswavelength, the transport mean free path, l ′s, is 5.59 �m.

In order to suppress speckle due to coherent interference effectsof the random medium, the computed scattered light intensity isensemble-averaged over 40 PSTD simulations, each correspondingto a different random arrangement of cylinders within the rectangu-lar cluster [34]. Speckle can be further suppressed by averaging over50 different incident frequencies evenly spaced between 0.95 f0 and1.05 f0 [34]. (This is similar to experimental observations of EBS usingnonmonochromatic illumination with a temporal coherence length of10 �m.) An estimated 16 modes are averaged in the process.


(a) λ = 2 µm, N = 100002

1.5

1

–1 0backscattering angle (deg) backscattering angle (deg) backscattering angle (deg)

I s = 65 µm

10.5

(d) λ = 2 µm, N = 200002

1.5

Sca

ttere

d in

tens

ityS

catte

red

inte

nsity

1

–1 0backscattering angle (deg)

I s = 32.5 µm

10.5

(e) λ = 1.52 µm, N = 200002

1.5

1


I s = 20.7 µm

10.5

(f) λ = 1 µm, N = 200002

1.5

1


I s = 18.9 µm

10.5

(b) λ = 1.52 µm, N = 100002

1.5

1

–1 0

I s = 41.5 µm

10.5

(c) λ = 1 µm, N = 100002

1.5

1

–1 0

I s = 37.7 µm

10.5

FIGURE 3.9 Comparison of PSTD-computed EBS peaks (solid lines) for threewavelengths, with theoretical benchmark results (dash-dotted lines) forrectangular clusters consisting of N cylinders. Parts (a–c) correspond to N =10,000 cylinders with l ′s = 65.0, 41.5, and 37.7 �m, respectively; and parts(d–e) correspond to N = 20,000 cylinders with l ′s = 32.5, 20.7, and18.9 �m, respectively. (Source: S. H. Tseng et al. [34].)

We note that the PSTD model can include only a finite randommedium region. However, the finite size of the random region can beefficiently accounted. We need only to implement a convolution ofthe comparative benchmark analytical results for an infinite randomregion with an appropriate windowing function that represents theeffective aperture of the finite random region in the PSTD model.

Figure 3.9 compares the angular distribution of the PSTD-computed EBS peak with that obtained using standard EBS theorybased on the diffusion approximation [35]. The PSTD calculations arein good agreement with the benchmark theory.

Recently, the phenomenon of low-coherence EBS has been demon-strated to be promising for clinical diagnosis [33]. In order to sim-ulate this phenomenon using PSTD, the frequency-averaging tech-nique mentioned above can be modified. Leveraging the robustnessof PSTD, it appears that low-coherence EBS can be studied for ran-dom media of arbitrary geometry not amenable by other simulationmethods.


Optical Phase Conjugation for Turbidity SuppressionTissue turbidity has been a formidable obstacle for optical tissue imag-ing and related applications. Multiply scattered photons are conven-tionally regarded as being random and stochastic in their trajectories.However, recent research indicates that such scattering is actually acausal and time-reversible process.

Recently, optical phase conjugation (OPC) has been experimen-tally demonstrated as a means to suppress tissue turbidity [36]. Be-cause several aspects of the physical basis and application of OPC arenot yet well understood, rigorous simulations are required to revealinformation that cannot be easily obtained via laboratory experiments.PSTD is well suited for such simulations because it is based upon thefundamental Maxwell’s equations and furthermore can accommodatethe macroscopic light-interaction regions, which are involved in OPC.

The initial application of PSTD to simulate OPC has been reported[37]. Figure 3.10 illustrates the geometry of this 2D PSTD simula-tion, which employs a uniform spatial resolution of 0.3 �m. Here, the

FIGURE 3.10 OPC simulation geometry. A rectangular (560 �m × 260 �m)cluster of 2500 randomly positioned, 2.5-�m diameter dielectric cylinders(n = 1.2) is illuminated on the left by a pulsed light beam. The light is multiplyscattered, as it propagates through the cluster before reaching aphase-conjugate mirror. Then, the phase and propagation direction of the lightis inverted, causing the light to propagate in the reverse direction and traceback to its origination point. (Source: S. H. Tseng and C. Yang [37].)


FIGURE 3.11 PSTD simulation of the OPC phenomenon. The physicaldimension of the simulation region is 320 �m × 600 �m. The electric fieldsat various time-steps throughout the evolution are shown: (a) 200 fs, (b)1000 fs, and (c) 2400 fs. As light scatters through the cluster of dielectriccylinders, the wavefront gradually spreads out due to diffraction. After theOPC effect of the PCM, light back-traces and refocuses back to the originallocation where it first emerged. (Source: S. H. Tseng and C. Yang [37].)See also color insert.

incident light is a pulsed Gaussian beam with a cross-sectional widthof 13.4 �m and a temporal duration of 4.472 fs. This beam undergoesmultiple scattering within a rectangular (560 �m × 260 �m) cluster of2500 randomly positioned dielectric cylinders before reaching a phase-conjugate mirror. Each cylinder within the cluster has a diameter of2.5 �m and a refractive index of 1.2.

Figure 3.11 visualizes the PSTD-computed evolution of the opticalelectric field for this model. From this figure, we see that the wavefrontof the incident light spreads out due to diffraction, as it propagatesthrough the random cluster of dielectric cylinders. After reaching thephase-conjugate mirror, the phase and propagation direction of theimpinging light is inverted, causing the light to propagate in the re-verse direction and trace back to its origination point, where refocus-ing occurs. This refocusing effect is imperfect, however, because somelight is lost due to scattering out of the computation grid. This resultsin a wider and reverberant refocused wavefront profile than the orig-inal. Nevertheless, the basic principle of turbidity compensation byemploying a phase-conjugate mirror is well demonstrated.

Multiple Light Scattering in 3D Random MediaReference [38] reported the initial application of PSTD to model full-vector 3D scattering of light by macroscopic random clusters of dielec-tric spheres. A primary finding of this work is that multiply scattered


FIGURE 3.12 Validations of the 3D PSTD modeling tool. (a) Differentialscattering cross section of a single 8-�m-diameter dielectric sphere (n = 1.2)in free space for an incident wavelength 0 = 0.75 �m. (b) Total scatteringcross section of a 20-�m-diameter cluster of 19 randomly positioned,noncontacting, 6-�m-diameter dielectric spheres (n = 1.2) in free space.(Source: S. H. Tseng et al. [38].)

light contains information indicative of the size of the spheres com-prising the cluster, even for closely packed spheres.

Reference [38] first reported two validations of its 3D PSTD mod-eling tool. The first validation is illustrated in Fig. 3.12a . Here, thePSTD-computed differential scattering cross section versus angle of asingle 8-�m-diameter dielectric sphere (n = 1.2) in free space is com-pared with the analytical Mie expansion for an incident wavelength0 = 0.75 �m. Here, each cubic PSTD space cell (and hence, eachstaircasing step of the sphere’s surface) has a uniform size of 0.0833�m (0.133d). From Fig. 3.12a , we see that the PSTD and Mie resultsagree very well over ∼5 orders of magnitude for the complete rangeof scattering angles.

The second validation is illustrated in Fig. 3.12b. Here, the PSTD-computed total scattering cross section (TSCS) versus frequency of a20-�m-diameter cluster of 19 randomly positioned, noncontacting, d0

= 6 �m diameter dielectric spheres (n = 1.2) in free space is comparedwith a generalized multisphere Mie expansion. Here, each cubic PSTDspace cell (and hence, each staircasing step of each sphere’s surface)has a uniform size of 0.167 �m. From Fig. 3.12b, we see that the PSTD


FIGURE 3.13 PSTD-computed TSCS spectra of three different 25-�m-diameterclusters of N randomly positioned, closely packed, noncontacting, dielectricspheres (n = 1.2) of diameter d0 in free space. (a)N = 192, d0 = 3 �m,optical thickness ∼26; (b)N = 56, d0 = 5 �m, optical thickness ∼21; (c)N =14, d0 = 7 �m, optical thickness ∼10. (Source: S. H. Tseng et al. [38].)

and the multisphere Mie results agree very well for the complete rangeof frequencies investigated.

Having validated its PSTD modeling tool, Ref. [38] then reporteda PSTD study of the TSCS spectra of three different 25-�m-diameterspherical clusters of N randomly positioned, closely packed, noncon-tacting, dielectric spheres (n = 1.2) of diameter d0 in free space. Auniform PSTD space lattice resolution of 0.167 �m was employed.The three cluster geometries are illustrated in Fig. 3.13: (a )N = 192, d0

= 3 �m, optical thickness ∼26; (b)N = 56, d0 = 5 �m, optical thickness∼21; and (c)N = 14, d0 = 7 �m, optical thickness ∼10. (Here, the opti-cal thickness is equal to the cluster diameter divided by the scatteringmean free path.)

From Fig. 3.13, we observe that all three TSCS spectra are sim-ilar at wavelengths longer than ∼3 �m. This suggests that for longwavelengths, incident light cannot discern microscopic structural dif-ferences between the three cluster geometries. However, for wave-lengths shorter than ∼1.5 �m, the TSCS spectra exhibit distinctiveoscillatory features. Reference [38] offered the hypothesis that theseoscillatory features could yield information regarding the diameter d0

of the individual dielectric spheres comprising each cluster, despitethe close packing and mutual interaction of these spheres.


FIGURE 3.14 Cross-correlation analyses of the TSCS spectra shown in Fig.3.13. In each case, the peak of the cross-correlation occurs at a trial spherediameter dp that is approximately equal to the actual diameter d0 of thespheres comprising the cluster. (Source: S. H. Tseng et al. [38].)

To test this hypothesis, Ref. [38] conducted a cross-correlationstudy of each TSCS spectrum in Fig. 3.13. Specifically, each TSCSspectrum in Fig. 3.13 was cross-correlated with the TSCS spectrumof a single isolated dielectric sphere of trial diameter d. This cross-correlation was performed for several hundred trial values of d in therange 2–10 �m, and the set of results was plotted as a function of d.The hypothesis would be strongly supported if the cross-correlationdata were to peak exactly at d ≡ dp = d0, the actual diameter of theconstituent spheres of the cluster. Figure 3.14 illustrates the results ofthis study.

From Fig. 3.14, we observe that, despite the close packing of eachcluster, the peak of its cross-correlation occurs at approximately the ac-tual diameter of its constituent spheres: dp = 3.25 �m versus d0 = 3 �mfor cluster (a ); dp = 4.70 �m versus d0 = 5 �m for cluster (b); and dp =6.83 �m versus d0 = 7 �m for cluster (c). This supports the hypothe-sis that significant information regarding cluster constituent particlesis embedded within the oscillatory features of the TSCS spectrum–even for optically thick clusters where the surface-to-surface spacingbetween adjacent constituent particles is less than the illuminatingwavelength.

3.6 SummaryThis chapter reviewed qualitatively the technical basis and represen-tative applications of FDTD and PSTD computational solutions ofMaxwell’s equations to biophotonics. The four FDTD applications thatwere highlighted in this chapter reveal the potential utility of FDTD toprovide high-resolution models of optical interactions with individual


biological cells and corresponding microscopic sections of tissue: (1)demonstration of the response of a 2D model of the vertebrate retinalrod to impinging visible light, (2) calculation of the optical scatteringproperties of models of precancerous cervical cells, (3) validation ofthe Born approximation in 2D weakly scattering biological randommedia, and (4) demonstration of the sensitivity of optical backscatter-ing spectral signatures of randomly inhomogeneous dielectric spheresto weak refractive-index fluctuations having correlation lengths thatare much smaller than the illuminating wavelength.

The four PSTD applications that were highlighted in this chap-ter indicate the potential utility of PSTD to model optical interactionswith clusters of many biological cells and corresponding macroscopicsections of tissue: (1) analysis of the total scattering cross section ofa large random cluster of 2D dielectric cylinders, (2) analysis of en-hanced backscattering of light by a large random cluster of 2D dielec-tric cylinders, (3) demonstration of the use of OPC to suppress turbid-ity within a very large random cluster of 2D dielectric cylinders, and(4) demonstration that multiple light scattering from a random clusterof uniformly sized dielectric spheres can be analyzed to deduce thediameter of the constituent spheres.

In all this, a key goal has been to alert and inform readers howFDTD and PSTD can put Maxwell’s equations to work in the analysisand design of a wide range of biophotonics technologies. The range ofapplications of these computational techniques to biophotonics willcertainly grow, as more researchers become aware of these powerfultools, and furthermore as computer capabilities continue to improve.

References1. K. S. Yee, “Numerical solution of initial boundary value problems involving

Maxwell’s equations in isotropic media,” IEEE Trans Antennas Propagation 14,302–307 (1966).

2. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. Norwood, MA: Artech (2005).

3. Q. H. Liu, “The PSTD algorithm: A time-domain method requiring only twocells per wavelength,” Microw Opt Technol Lett 15(3), 158–165 (1997).

4. S. Chandrasekhar, Radiative Transfer. New York: Dover (1960).5. S. H. Tseng and B. Huang, “Comparing Monte Carlo simulation and pseu-

dospectral time-domain numerical solutions of Maxwell’s equations of lightscattering by a macroscopic random medium,” Appl Phy Lett 91, 051114(2007).

6. L. Marti-Lopez, J. Bouza-Dominguez, J. C. Hebden, S. R. Arridge, and R. A.Martinez-Celorio, “Validity conditions for the radiative transfer equation,”J Opt Soc Am A 20(11), 2046–2056 (2003).

7. J. B. Keller, “Geometrical theory of diffraction,” J Opt Soc Am 52, 116–130(1962).

8. R. G. Kouyoumjian and P. H. Pathak, “A uniform geometrical theory of diffrac-tion for an edge in a perfectly conducting surface,” Proc IEEE 62, 1448–1461(1974).


9. R. F. Harrington, Field Computation by Moment Methods. New York: Macmillan(1968).

10. K. R. Umashankar, “Numerical analysis of electromagnetic wave scatteringand interaction based on frequency-domain integral equation and method ofmoments techniques,” Wave Motion 10, 493–525 (1988).

11. J. Song and W. C. Chew, “The fast Illinois solver code: Requirements and scalingproperties,” IEEE Comput Sci Eng 5, 19–23 (July-Sept. 1998).

12. K. L. Shlager and J. B. Schneider, “A Survey of the Finite-Difference Time-Domain Literature,” Chap. 1 in Advances in Computational Electrodynamics: TheFinite-Difference Time-Domain Method, A. Taflove, ed. Norwood, MA: Artech(1998).

13. http://en.wikipedia.org/wiki/Finite-difference time-domain methodPage: 1.Accessed February 9, 2009.

14. J. P. Berenger, “A perfectly matched layer for the absorption of electromagneticwaves,” J Comput Phy 114, 185–200 (1994).

15. Z. S. Sacks, D. M. Kingsland, R. Lee, and J. F. Lee, “A perfectly matchedanisotropic absorber for use as an absorbing boundary condition,” IEEE TransAntennas Propagation 43, 1460–1463 (1995).

16. S. D. Gedney, “An anisotropic perfectly matched layer absorbing media for thetruncation of FDTD lattices,” IEEE Trans Antennas Propagation 44, 1630–1639(1996).

17. J. A. Roden and S. D. Gedney, “Convolutional PML (CPML): An efficient FDTDimplementation of the CFS-PML for arbitrary media,” Microw Opt Tech Lett 27,334–339 (2000).

18. M. J. Piket-May, A. Taflove, and J. B. Troy, “Electrodynamics of visiblelight interactions with the vertebrate retinal rod,” Opt Lett 18, 568–570(1993).

19. R. Drezek, A. Dunn, and R. Richards-Kortum, “A pulsed finite-difference time-domain (FDTD) method for calculating light scattering from biological cellsover broad wavelength ranges,” Opt Express 6, 147–157 (2000).

20. R. Drezek, M. Guillaud, T. Collier, I. Boiko, A. Malpica, C. Macaulay, M. Follen,and R. Richards-Kortum, “Light scattering from cervical cells throughout neo-plastic progression: Influence of nuclear morphology, DNA content, and chro-matin texture,” J Biomed Opt 8, 7–16 (2003).

21. I. R. Capoglu and V. Backman, “Validation of the Born approximation in 2-Dweakly-scattering biological random media using the FDTD Method,” IEEEInternational Symposium on Antennas and Propagation, Charleston, S.C., June2009.

22. A. Ishimaru, Wave Propagation and Scattering in Random Media. New York: Wiley-IEEE Press (1999).

23. N. Lue, G. Popescu, T. Ikeda, R. R. Dasari, K. Badizadegan, and M. S. Feld,“Live cell refractometry using microfluidic devices,” Opt Lett 31(18), 2759–2761(2006).

24. F. Charriere, A. Marian, F. Montfort, J. Kuehn, T. Colomb, E. Cuche, P. Marquet,and C. Depeursinge, “Cell refractive index tomography by digital holographicmicroscopy,” Opt Lett 31(2), 178–180 (2006).

25. H. K. Roy, Y. Liu, R. K. Wali, Y. L. Kim, A. K. Kromin, M. J. Goldberg, andV. Backman, “Four-dimensional elastic light-scattering fingerprints as preneo-plastic markers in the rat model of colon carcinogenesis,” Gastroenterology 126,1071–1081 (2004).

26. X. Li, A. Taflove, and V. Backman, “Recent progress in exact and reduced-ordermodeling of light-scattering properties of complex structures,” IEEE J SelectedTopics Quantum Electron 11, 759–765 (2005).

27. H. O. Kreiss and J. Oliger, “Comparison of accurate methods for integration ofhyperbolic equations,” Tellus 24(3), 199 (1972).

28. S. A. Orszag, “Comparison of pseudospectral and spectral approximation,”Stud Appl Math 51(3), 253 (1972).

http://en.wikipedia.org/wiki/Finite-difference_time-domain_methodPage:1


29. S. H. Tseng, J. H. Greene, A. Taflove, D. Maitland, V. Backman, and J. Walsh,“Exact solution of Maxwell’s equations for optical interactions with a macro-scopic random medium,” Opt Lett 29(12), 1393–1395 (2004).

30. S. H. Tseng, J. H. Greene, A. Taflove, D. Maitland, V. Backman, and J. T. Walsh,“Exact solution of Maxwell’s equations for optical interactions with a macro-scopic random medium: addendum,” Opt Lett 30(1), 56–57 (2005).

31. H. K. Roy, V. Turzhitsky, A. Gomes, M. J. Goldberg, J. D. Rogers, Y. L. Kim, T. K.Tsang, D. Shah, M. S. Borkar, M. Jameel, N. Hasabou, R. Brand, Z. Bogojevic,and V. Backman, “Prediction of colonic neoplasia through spectral markeranalysis from the endoscopically normal rectum: An ex vivo and in vivo study,”Gastroenterology 134(4), A109–A109 (2008).

32. H. Subramanian, P. Pradhan, Y. L. Kim, and V. Backman, “Penetration depth oflow-coherence enhanced backscattered light in subdiffusion regime,” Phy RevE Stat Nonlin Soft Matter Phys 75(4), 4194–4203 (2007).

33. Y. L. Kim, V. M. Turzhitsky, Y. Liu, H. K. Roy, R. K. Wali, H. Subramanian,P. Pradhan, and V. Backman, “Low-coherence enhanced backscattering: Re-view of principles and applications for colon cancer screening,” J Biomed Opt11(4), 41125–41135 (2006).

34. S. H. Tseng, A. Taflove, D. Maitland, V. Backman, and J. T. Walsh, “Simulationof enhanced backscattering of light by numerically solving Maxwell’s equa-tions without heuristic approximations,” Opt Express 13(10), 3666–3672 (2005).

35. E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent backscattering of light bydisordered media: Analysis of the peak line-shape,” Phy Rev Lett 56, 1471–1474(1986).

36. Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation forturbidity suppression in biological samples,” Nat Photonics 2, 110–115 (2008).

37. S. H. Tseng and C. Yang, “2-D PSTD simulation of optical phase conjugationfor turbidity suppression,” Opt Express 15(24), 16005–16016 (2007).

38. S. H. Tseng, A. Taflove, D. Maitland, and V. Backman, “Pseudospectral time do-main simulations of multiple light scattering in three-dimensional macroscopicrandom media,” Radio Sci 41, RS4009, doi:10.1029/2005RS003408 (2006).


C H A P T E R 4Interferometric

Synthetic ApertureMicroscopy

Steven G. Adie, Brynmor J. Davis, Tyler S. Ralston, Daniel L. Marks,P. Scott Carney, and Stephen A. Boppart

4.1 IntroductionIn the history of imaging there are many examples of the develop-ment of data acquisition systems followed later by the mathematicaland computational infrastructure necessary to turn the acquired datainto quantitatively meaningful and more practically useful images.For example, while Roentgen discovered a means to record x-ray in-tensities on film at the turn of the 20th century, more than half a centuryelapsed before the computational power was available to turn a seriesof x-ray shadowgrams into a computed tomogram. In 1991, the evolu-tion of optical coherence tomography (OCT) [1] from low-coherenceinterferometry (LCI) [2] was followed by many years of technologydevelopment and application, most prolifically in the medical and bi-ological fields. Despite this rapid development, little was done to con-nect the acquired data to the underlying sample structure as describedby the spatially varying scattering potential, until the development ofinterferometric synthetic aperture microscopy (ISAM) in 2006 [3]. Thedelay between the development of OCT instrumentation and a so-lution and implementation of the associated inverse problem mightbe attributed, at least in part, to the success of OCT as a direct imag-ing method. The use of OCT as an instrument for data acquisition isapparent in the so-called trade-off between transverse resolution and

77


depth of imaging. The apparent degradation of OCT images associ-ated with regions far from focus was not a pressing concern, largelybecause low-numerical-aperture (NA) optics were used to focus lightinto tissue, thereby offering a large confocal parameter (depth-of-field)for cross-sectional imaging at the expense of reduced (worse) trans-verse imaging resolution. Higher (better) transverse resolutions wereachieved by using higher-NA focusing optics and performing opti-cal coherence microscopy (OCM) [4]. OCM captures images in the enface plane in a manner similar to confocal or multiphoton microscopy,rather than in cross section using OCT. The development of spectral-domain OCT (SD-OCT) [5–8] provided a number of distinct advan-tages for ISAM. However, using early time-domain OCT (TD-OCT)systems or SD-OCT systems, it was practical only to acquire data fromthe in-focus region. Absent a solution of the inverse problem, it wascommon (especially when higher NA optics are employed) to discardthe acquired data associated with regions out of the focus. With ISAM,the data are quantitatively and meaningfully connected to the samplestructure, and the entire sample is reconstructed at arbitrary distancesfrom the focus, thus the supposed trade-off between depth of imagingand resolution is eliminated. With ISAM, depth of imaging is limitedonly by the signal-to-noise ratio (SNR) and the advent of multiplescattering.

A brief overview of OCT instrumentation and applications is pre-sented in the following section. The physics of the data acquisitionsystem, i.e., the mathematical forward model relating the data to thesample, is then described in the section “Theory.” This forward modelis inverted to find an inverse scattering algorithm, i.e., a means to ob-tain quantitative estimate of the sample scattering potential from thedata. It is seen that the mathematical structure of the inverse problemis similar to that encountered in a broad class of applications where thesolution of the inverse problem can be reduced to Fourier-domain re-sampling. This class of applications includes computed tomography,diffraction tomography, and magnetic resonance imaging. In fact, fora particular ISAM modality the Fourier resampling scheme is iden-tical to that used in synthetic aperture radar (SAR). In the section“Experimental Implementation and Validation,” experimental imple-mentation and validation of ISAM are described. Material dispersionand phase instability corrections are described before a controlledsynthetic sample is used to demonstrate ISAM. Furthermore, ISAMimages computed from out-of-focus data are compared to in-focusOCT images taken in the same volume and are shown to be in goodagreement. Fast implementation of the ISAM software is describedbefore the limitations of ISAM are discussed. In the section “Clinicaland Biological Applications,” clinical and biological applications thattake advantage of the unique capabilities of ISAM are discussed. Thesection “Conclusions and Future Directions” summarizes the main

79I n t e r f e r o m e t r i c S y n t h e t i c A p e r t u r e M i c r o s c o p y

theoretical, experimental, and application aspects of ISAM, and con-cludes with an outlook on future directions.

4.2 BackgroundOptical coherence tomography instrumentation is illustrated in Fig.4.1. A sample is probed using a broadband optical source. The illu-minating light is focused into the sample and the backscattered lightis collected through the same objective lens. The two transverse (x, y)dimensions are probed by either physically translating the sample orscanning the focal spot. The scattering potential is resolved in the ax-ial z-dimension through LCI, i.e., the backscattered light is combinedwith a reference field in order to produce interference. In time-domainOCT, interference effects are only observed when the roundtrip pathlengths in the sample and reference arms are within the coherencelength of the source. Interference fringes that constitute the desired in-terference signal can be easily isolated from the constant background,with the result that only the scattering potential at a given axial depth

Fiber-basedbeam splitter

50

50

Sample

Objectivelens

x

zy

Source

Time-domaindetectionphotodiode

Grating Collimator

Lenses

Fourier-domaindetectionspectrometer

Line-scancamera

x–y galvos

x–y stage

Delay

Referencemirror

FIGURE 4.1 Schematic of time-domain and spectral-domain OCT systems.Light in one arm of a fiber-based Michelson interferometer is focused into thesample, while the other arm is used as a reference. In TD-OCT, the length ofthe reference path is adjusted and an interferogram is measured with aphotodiode. In SD-OCT, the reference arm is fixed and the spectralinterference measured with a spectrometer. (Source: This figure is adaptedfrom Ref. [3].)


affects the acquired signal. The probed depth is where the sample armpath length is equal to that given in the reference arm. Thus, a depthprofile is obtained by scanning the reference arm path length. Equiva-lent data are collected using a spectral-domain OCT system [9]. In thiscase, the reference mirror is fixed and a spectrometer replaces the sin-gle broadband detector employed in time-domain systems. Raw dataacquired in SD-OCT are the Fourier transform of the time-domaindata (with respect to delay). For this reason, SD-OCT is also referredto as Fourier-domain OCT (FD-OCT). The use of SD-OCT enablesboth high-speed data acquisition and high sensitivity [7, 10, 11], andthe use of a static reference arm, with superior phase stability, presentsan additional advantage for ISAM data acquisition.

For biological applications, OCT is typically implemented usingnear-infrared wavelengths, because in this region, the optical responseof tissue is typically dominated by scattering rather than absorption[12]. OCT therefore allows good depth of penetration, while the co-herence gating used for detection has the effect of rejecting some of themultiply scattered light that renders standard optical microscopes im-practical. OCT offers micron-scale resolution enabling image contrastbased on intrinsic sample properties, i.e., the scattering potential. Thishas led to extensive use of OCT in retinal imaging [13]. OCT has alsobeen applied with good success to the detection of vulnerable arterialplaques in vivo [14], and for long-scan-range in vivo monitoring ofupper airway profiles in the study of sleep apnea [15]. Other applica-tion areas are cancer detection in various parts of the body includingthe breast [16], gastrointestinal tract [17], bladder [18], skin [19], oralcavity [20], cervix [21], lung [22], and brain [23].

Transverse localization is achieved in OCT data through the focus-ing of the illuminating light and the focused detection of the backscat-tered light. The power of this focusing is in turn determined by theobjective lens used. The larger the NA of the lens, the tighter the result-ing focus. This effect can be seen in Fig. 4.2, where focused beams areillustrated for a number of NAs. The relationship between the trans-verse resolution and the depth of field is also illustrated in Fig. 4.2. Atightly focused beam diverges faster than a beam with a wider focus.Quantitatively, the focal width scales with 1/NA, while the depth offocus scales as 1/NA2. Thus, the raw data in OCT appear to sufferfrom a trade-off between transverse resolution and depth-of-field.

Axial discrimination in OCT images is provided by coherence gat-ing, with the axial resolution determined, with an inverse relationship,by the bandwidth of the optical source. Volumes of the sample thatfall within the beam focus are well imaged, but those that lie outof the focus are subject to transverse blurring and the generation ofcoherent artifacts sometimes referred to as speckle. The fundamentalrelationship between depth-of-focus and minimum beam-width illus-trated in Fig. 4.2 has lead to the idea that depth-of-field and transverse


FIGURE 4.2 Scale drawings of focused fields, based on a Gaussian beammodel [24], where all spatial dimensions are in units of wavelength. Thebeam edge is defined as the loci at which the field reaches 1/e of themaximum value and is illustrated with a heavy line. Every second oscillationof the phase is illustrated by a dotted line showing a wavefront. The NA is thesine of the angle the beam edge makes with the optical axis far from thefocus, w0 is a measure of the narrowest point of the beam, and 2zR is theconfocal parameter quantifying the depth-of-field.

resolution are competing constraints in OCT. As will be discussed,computational image reconstruction can be used to obviate this ap-parent trade-off.

4.3 Theory

Physics of Data AcquisitionThe sample to be imaged is described by a function, �, of three Carte-sian coordinates (x, y, z). The spectral-domain data are collected as afunction of transverse scan position (u, v) and the temporal frequency� of the optical field. The relationship between the spatial variables isillustrated in Fig. 4.3.

It will be convenient to exchange the temporal frequency � for anequivalent variable more directly related to the spatial structure of theoptical field. The wave number k = 2�/, where is the wavelength,in free space can be expressed as

k = �

c, (4.1)


FIGURE 4.3 Illustration of the system geometry and the behavior of theincident optical field. The geometrical focus lies in the x–y plane within thesample and the focal position is scanned through these two transversedimensions. A heavy dashed line indicates the optical axis of the beam,which has a position specified by the variables u and v. Away from focus thefield diverges and, for a fixed frequency �, has approximately spherical phasefronts.

where c is the speed of light. More complex, nonlinear dispersion re-lationships between � and k can account for propagation in materialswhere the index of refraction varies with the temporal frequency ofthe field [25, 26].

After extracting the analytic interferometric term from the col-lected data, and by ensuring that the reference plane lies outside theregion of the sample, the signal is described by the product [9]

S (u, v, k) = E∗r (k) Es (u, v, k) , (4.2)

where Es(u, v, k) is the backscattered field at the detector, Er(k) is thereference field, and a superscript ∗ denotes the complex conjugate.

The optical properties of the sample are described by the scat-tering potential �(x, y, z), which can also be identified, in terms offundamental material properties, as the susceptibility. An accurate re-construction of �(x, y, z) is the goal in ISAM. The sample is illuminatedby an electric field proportional to Er(k)g(x − u, y − v, z, k), where thereference field Er(k) is proportional to the source field and hence also


to the amplitude of illumination. Scattering produces optical sourceswith density k2 Er(k)g(x − u, y − v, z, k)�(x, y, z), where it can be seenthat the amplitude of the scattered light is proportional to both theilluminating field and the scattering potential.

Reciprocity [27] requires that coupling the light back into the op-tical system that produced the illuminating field will introduce intothe signal another factor of the beam pattern, g(x − u, y − v, z, k) [41].Integrating over all scattering locations results in the expression

Es (u, v, k) = k2 Er (k)∫∫∫

g2(x − u, y − v, z, k) �(x, y, z) dx dy dz,

(4.3)

for the backscattered field. Here, it can be seen that the scattered field islinearly related to the sample scattering potential through an integralequation. The kernel of this equation depends on the square of thefocused field produced by the objective lens. Scattering from sampleareas at the focus contribute more signal than scattering from areasout of focus. For the purposes of OCT, g2(x − u, y − v, z, k) is ideally anarrow, well-collimated beam, giving high transverse resolution andgood depth-of-field. Depth (axial) resolution is achieved using thespectral diversity of the data. However, as demonstrated in Fig. 4.2,a Gaussian optical beam cannot be simultaneously narrow and wellcollimated.

The results obtained with ISAM are achieved by inverting Eq. (4.3)to obtain an accurate estimate for �(x, y, z) both at and away from fo-cus, i.e., ISAM is accomplished by implementing inverse scattering.In the section “Compact Forward Model” below, we derive a simpli-fied forward model for ISAM based on a spherical beam model forthe focused field, while the section “Rigorous Forward Model” belowemploys a general description of the focused field to obtain a rigorousforward model. The section “Inverse Scattering Procedure” followswith a method to invert the forward model and obtain an estimate for�(x, y, z).

Compact Forward ModelBefore presenting a detailed picture of the theory of ISAM, it is instruc-tive to give a simplified explanation that captures the essential physicsof the system while simplifying the mathematics. The derivation pre-sented in this section is valid when the wavefronts in the incidentfield are spherical and at small angles from the optical axis, i.e., wellbeyond the depth-of-focus, as well as for low NA. The principal prob-lem addressed by ISAM is manifest outside the depth-of-focus in thedivergent-beam regions, as illustrated in Figs. 4.2 and 4.3. In these ar-eas, the beam broadens and the phase fronts (which are well definedfor a given value of k) become spherical. Consider, as a simplified


model of the focused field, a spherical wave propagating in the down-ward (+z) direction, i.e.,

g (x, y, z, k) =exp

[i�k

√x2 + y2 + z2

]√

x2 + y2 + z2, (4.4)

where � = sgn (z). This model does not account for the beam pro-file (e.g., the NA of the objective lens does not appear in thismodel) but, as will be verified in the section “Rigorous ForwardModel,” it captures the basic phase behavior and features of the ISAMalgorithm.

Combining Eqs. (4.2), (4.3), and (4.4) results in the model

S (u, v, k) = k2 |Er (k)|2∫∫∫ exp

[i�2k

√(x − u)2 + (y − v)2 + z2

](x − u)2 + (y − v)2 + z2

× �(x, y, z) dx dy dz. (4.5)

Here, the phase of the data is referenced to the focal point. The signalfrom each scattering location acquires a phase delay correspondingto the round-trip path from the focus to the scattering site and back.The signal is linearly attenuated by spreading losses in each prop-agation direction and all contributions are summed to produce thedata.

Simply restating Eq. (4.5) in a more convenient form yields theforward model used in ISAM. The simplification is achieved by usingthe Weyl identity [28, 29], where a spherical wave is constructed as asum of plane waves, i.e.,

exp[i��

√x2 + y2 + z2

]√

x2 + y2 + z2= i

2�

∫∫ exp[i(

qx x + qy y +√

�2 − q 2x − q 2

y z)]

√�2 − q 2

x − q 2y

dqx dqy,

(4.6)

where(

qx, qy,√

�2 − q 2x − q 2

y

)is the wavevector of the constituent

plane waves. Comparing this with Eq. (4.5), it can be seen that thechoice � = 2k is appropriate, so that

S (u, v, k) = ik2

2�|Er (k)|2

∫∫1√

4k2 − q 2x − q 2

y

exp[i(qxu + qyv

)]

×∫∫∫ �(x, y, z)√

(x − u)2 + (y − v)2 + z2exp

[−i(

qx x + qy y −√

4k2 − q 2x − q 2

y z)]

dx dy dz

dqx dqy.

(4.7)


The quotient in the inner integral will be approximated as

�(x, y, z)√(x − u)2 + (y − v)2 + z2

≈ �(x, y, z)z

. (4.8)

This approximation can be justified for low NA, as outside ofz2 � (x − u)2 + (y − v)2, the limited extent of the focused beam willtypically give low signal, and in high-signal areas, the unapproxi-mated denominator will be slowly varying. For high-NA systems,this approximation will be less accurate, and the detailed derivationof ISAM presented in the section “Rigorous Forward Model” must beused.

Returning to Eq. (4.7), a three-dimensional (3D) Fourier transformand a two-dimensional (2D) inverse Fourier transform can be recog-nized. The transverse Fourier transform of the data will be denotedby S(qx, qy, k), and the 3D Fourier transform of �(x, y, z)/z will bedenoted by ˜�′(qx, qy, ). Rewriting Eq. (4.7) using these definitionsgives

S(qx, qy, k

) = i�k2

kz(qx/2, qy/2

) |Er (k)|2 ˜�′[qx, qy, −2kz

(qx

2,

qy

2

)],

(4.9)where kz is the function:

kz(qx, qy) =√

k2 − q 2x − q 2

y. (4.10)

It should be noted that kz(qx, qy) is a function of k, but for brevity thisdependence is taken to be implied.

The multiplex spatial-domain relationship of Eq. (4.5) is reducedto a one-to-one Fourier-domain relationship in Eq. (4.9). Each pointin the 2D Fourier transform of the k-domain data is proportional toa point in the 3D Fourier transform of the sample (with a factor z−1

included). Inherent in the forward model presented here is the axialmapping between the Fourier space of the data and the Fourier spaceof the object, given by

= −2kz

(qx

2,

qy

2

)= −

√4k2 − q 2

x − q 2y. (4.11)

This mapping, illustrated in Fig. 4.4, suggests a simple inverse scat-tering method based on the remapping of data Fourier space to theobject Fourier space. Further details are presented in the section “In-verse Scattering Procedure.”

Image reconstruction in standard OCT processing usually consistsof scaling the axial dimension according to the elementary model that


FIGURE 4.4 Illustration of the ISAM remapping for a cross-sectionalplane—the three-dimensional contours are cylindrically symmetric about thevertical axis. In general, Fourier-domain data are a function of transversespatial frequencies (qx , qy ) and wave number k. These coordinates aremapped to the three spatial-frequency coordinates (qx , qy , ) in theFourier-domain representation of the sample. This mapping is such thatq2

x + q2y + 2 = 4k2.

a scatterer at depth z acquires an offset of twice its depth, so that

= −2k. (4.12)

This approach may be justified near focus as a coarse approximationof the ISAM result in Eq. (4.11). However, as will be discussed below,the ISAM method corrects out-of-focus blur, while the standard OCTmethod does not.

The coordinate relation given in Eq. (4.11) is known as the Stoltmapping [30, 31]. This coordinate change was originally derived forapplication in the field of geophysical imaging and has since foundwide application in synthetic aperture radar (SAR). Like ISAM, SAR isa coherent imaging technique that employs transverse scanning anda spectral or time-of-flight measurement to gather range information.In fact, SAR and ISAM can be cast in the same mathematical frame-work [32], with standard radar being the direct analog of OCT. More


broadly, the idea of computational imaging through Fourier-domaincoordinate mappings can be found in fields including x-ray computedtomography [33, 34], diffraction tomography [35–37], and magneticresonance imaging [38].

Rigorous Forward ModelIn this section, a rigorous description of the physics of data acquisi-tion is used to derive an accurate forward model that is valid for ar-bitrary NA and distance from focus. Specifically, the forward modelis formulated for both near and far-from-focus cases using a generaldescription for the focused field. This description of the focused fieldis incorporated into the general statement of the forward model inEq. (4.3).

An arbitrary propagating scalar field can be represented as anangular spectrum of plane waves [39]. With the plane wave coefficientsG(qx, qy

), the field can be synthesized as

g (x, y, z, k) = i2�

∫∫G(qx, qy, k

)exp

{i[qx x + qy y + kz

(qx, qy

)z]}

dqx dqy.

(4.13)

This equation is a more general expression for the focused field thanEq. (4.4). The Weyl identity from Eq. (4.6) is a specific case of theangular spectrum representation of Eq. (4.13), for a spherical wave.Equation (4.13) shows that for a fixed value of k the 3D field is definedby a 2D set of plane wave coefficients. The field in any 2D plane thusdefines the entire propagating field.

Focused beams can be described in the framework given in Eq.(4.13), e.g., for a Gaussian beam, G(qx, qy) is Gaussian. The relationshipto Fourier optics is also clear, as the transverse Fourier transform atany (x, y) plane is

g(qx, qy, z, k

) = i2�G(qx, qy, k

)exp

[ikz(qx, qy

)z]. (4.14)

In addition to describing the angular spectrum of the field, the functionG(qx, qy) gives the form of the field on the exit pupil of the objectivelens [40]. In this manner, the objective lens determines the structureof the focused beam.

As suggested by the simplified derivation in the section “CompactForward Model,” it is useful to take the forward model into the Fourierdomain. Returning to Eq. (4.3), it can be seen that the backscatteredfield is expressed as a correlation of the scattering potential with thesquare of the focused field. Using basic properties of the Fourier trans-form (in particular for correlation, convolution, and multiplication in


each domain), Eqs. (4.2) and (4.3) can be combined as

S(qx, qy, k

) = k2 |Er (k)|24�2

∫[g ∗ g]

(−qx, −qy, z, k)

�(qx, qy, z

)dz,

(4.15)

where ∗ is the convolution operator over the transverse coordinatesonly.

The Fourier-domain data and the Fourier-domain sample are nowrelated by a one-dimensional (1D) linear integral equation, rather thanby the 3D integral equation seen in the spatial domain. However, itis still necessary to specify the integral kernel [g ∗ g](−qx, −qy, z, k).Explicitly,

[g∗ g](qx, qy, z, k

)= −4�2∫∫

G(q ′

x, q ′y

)G(qx −q ′

x, qy−q ′y

)× exp

{i[kz(q ′

x, q ′y

)+kz(qx −q ′

x, qy−q ′y

)]z}

dq ′x dq ′

y.

(4.16)

This expression simplifies considerably in certain asymptotic limits.Unsurprisingly, these asymptotic limits differ depending on whetherin-focus or far-from-focus regions are considered.

For the in-focus case, the magnitude of z is small and the productG(q ′

x, q ′y)G(qx − q ′

x, qy − q ′y) dominates the convolution integral. For

an unobscured objective, the field at the exit pupil is singly peakedand continuous so that G(q ′

x, q ′y) is also singly peaked and continu-

ous. Consequently, the product G(q ′x, q ′

y)G(qx − q ′x, qy − q ′

y) is peakedaround (q ′

x, q ′y) = (qx/2, qy/2). Expanding the integrand of Eq. (4.16)

as a Taylor series about this point and retaining the first term resultsin the approximation:

[g ∗ g](−qx, −qy, z, k

) ≈ −4�2 HN(q x, qy, k

)exp

[i2kz

(qx

2,

qy

2

)z],

(4.17)

where HN(q x, qy, k) is a function describing the in-focus transfer func-tion of the instrument. Full details of this approximation and an ex-pression for HN(q x, qy, k) can be found in Ref. [41].

Far from the focus, the magnitude of z is large and the exponentialfactor in Eq. (4.16) becomes highly oscillatory and the integrals can beevaluated using the method of stationary phase [29]. This method rec-ognizes that the rapid oscillations will result in the integral cancellingto zero over the domain of integration, except at stationary pointsof the oscillation phase. Using Eq. (4.10) it can be shown that station-ary points of the phase function kz

(q ′

x, q ′y

)+ kz(qx − q ′

x, qy − q ′y

)occur

when (q ′x, q ′

y) = (qx/2, qy/2). As a result, for regions far from the focus,


Eq. (4.16) becomes

[g ∗ g](−qx, −qy, z, k

) ≈ −4�2 HF(q x, qy, k

)kz

exp[i2kz

(qx

2,

qy

2

)z],

(4.18)

where HF(q x, qy, k) is a function describing the out-of-focus transferfunction of the instrument. As in the compact derivation from thesection “Compact Forward Model,” the signal falls off as 1/z.

A simplified forward model incorporating both the in-focus andout-of-focus cases can be obtained by combining Eqs. (4.17) and (4.18)with the exact forward model of Eq. (4.15) to give

S(qx, qy, k

) ≈ k2 |Er (k)|2∫

H(qx, qy, k

)R (z)

�(qx, qy, z

)exp

[i2kz

(qx

2,

qy

2

)z]

dz

= k2 |Er (k)|2 H(qx, qy, k

)˜�′(qx, qy, −2kz

(qx

2,

qy

2

)), (4.19)

where H(qx, qy, k) = HN(qx, qy, k) and R(z) = 1 for near-focus regions,and H(qx, qy, k) = HF(qx, qy, k) and R(z) = kz for far-from-focus re-gions. It has been shown [41] that the transition between thesetwo regimes occurs at approximately one Rayleigh range, i.e., when|z| = /(�NA2).

As shown previously in Eq. (4.9), the effect of the imagingsystem is reduced to a one-to-one relationship between the Fourier-domain data and the Fourier-domain object, although the Fourier-domain object ˜�′(qx, qy, ) is defined here as the 3D Fourier trans-form of �(x, y, z)/R(z). The spherical-wave model used in the section“Compact Forward Model” only modeled low-NA out-of-focus re-gions accurately, and so did not address the near-focus or high-NAcases. However, it can be seen from the coordinate relationship inEq. (4.19) that the same Stolt mapping also applies for both in-focusregions and at high NA.

Inverse Scattering ProcedureThe Stolt mapping present in the forward model gives a one-to-one,Fourier-domain relationship between the data and the object. Thissuggests a simple algorithmic procedure for inverse scattering. Thealgorithm can be summarized as

1. Beginning with the complex interferometric signal S(u, v, k),take the transverse Fourier transform to get the Fourier-domain data S(qx, qy, k).

2. Apply a linear filter, i.e., Fourier-domain multiplication ofS(qx, qy, k) and a transfer function, in order to compensatefor the transfer function of the instrument H(qx, qy, k). Note


that the transfer function, and hence the filtering, dependson whether the scattering of interest is in the near- or far-from-focus zone. The instrument transfer function is usuallyrelatively smooth, meaning that this step can often be omittedwithout significant detriment to the resulting image.

3. Remap the coordinate space of S(qx, qy, k) according to theStolt mapping of Eq. (4.11) and Fig. 4.4. For computationalconvenience, resampling, i.e., interpolating the remappeddata to a regular grid, can be employed.

4. Take the inverse Fourier transform to recover �(x, y, z)/R(z),the attenuated object.

5. If required, the scattering potential �(x, y, z) can be computedby multiplying by R(z) to compensate for signal loss awayfrom the focus.

Note that it may also be necessary to add preprocessing steps toaccount for material dispersion and compensate for phase instabili-ties in the instrument. Further details of ISAM processing, includingits real-time implementation, are found in the section “ExperimentalImplementation and Validation.”

Numerical Simulations for a Single ScattererNumerical simulations provide a first step in validating the ISAMmethods derived above. In the simulations presented here, a high-NA system is modeled using a vectorial model of high-angle focusing[40]. Although not addressed in this work, it should be noted thatvectorial fields have also been investigated in ISAM [41], with similarresults to those shown here.

Results for the imaging of an out-of-focus on-axis point scattererare shown in Fig. 4.5. In these simulations, a NA of 0.75 was usedand light was collected between wavelengths of 660 and 1000 nm.Further explanation of this type of simulation can be found in Ref. [41].The ISAM processing consisted only of the Fourier-domain mappingshown in Fig. 4.4 and did not account for the transfer function of theinstrument (see step 2 of the inverse scattering algorithm in the section“Inverse Scattering Procedure”).

In Fig. 4.5, it is shown that out-of-focus blurring produces sig-nificant distortions in the OCT data. The point scatterer is extendedlaterally and has a curvature due to the curvature of the prob-ing wavefronts. In the Fourier space of the object, an on-axis pointshould become a complex exponential with phase fronts perpendic-ular to the z axis. However, in the measured OCT data, these Fourierphase fronts are curved. After ISAM processing is applied, straight


(a) OCT data (b) ISAM reconstruction

(c) OCT, Fourier-domain (d) ISAM, Fourier-domain

20 0.030.80.60.40.2

0.02

0.0110

0–20

–10–12–14–16–18

–15 –10 –5 0 5 10

0.5

0

–0.5

15

–10 0x (µm)

qx (µm–1)

x (µm)

z (µ

m)

–2k

( µm

–1)

–10–12–14–16–18

–15 –10 –5 0 5 10

0.5

0

–0.5

15qx (µm–1)

β (µ

m–1

)

20

10

0–20 –10 0 10 20

z (µ

m)

10 20

FIGURE 4.5 A simulated OCT image (a) of a point scatterer located at(0,0,10) �m and the real part of the three-dimensional Fourier transform ofthe image (c). ISAM processing takes the function seen in part (c) to thereconstruction with real part plotted in part (d). Taking the inverse Fouriertransform of part (d) results in the ISAM image seen in part (b). Note that thetwo-dimensional plots shown are cross sections of three-dimensionalfunctions, and the parts (a) and (b) display the magnitude of complex images.(Source: This figure is adapted from Ref. [32].)

parallel phase fronts are produced, as expected. The resulting in-phasesuperposition over all spatial frequencies produces a sharp image ofthe point scatterer in the spatial domain, with the effects of defocusingremoved.

Alternate Acquisition GeometriesThe results presented in the previous sections are derived for the stan-dard confocal implementation of OCT and ISAM, with Cartesian lat-eral beam scanning in the x–y plane. However, other modalities canbe addressed using a similar Fourier space resampling procedure. Forexample, in full-field ISAM [42], the sample is illuminated with anaxial plane wave exp(ikz) and the scattered light is focused onto anarray detector, leading to the detection model g(x − u, y − v, z, k). Inthis case, a one-to-one Fourier-domain forward model can be derivedwithout approximation and the mapping

= −k − kz(qx, qy

), (4.20)

applies. This coordinate mapping also appears in diffraction tomogra-phy. The solution of the inverse scattering problem via Fourier spaceresampling has also been described for full-field ISAM with partiallyspatially coherent illumination [43] and for a catheter-based, rotation-ally scanned geometry [44].


4.4 Experimental Implementation and Validation

Phase Stability and Data Acquisition RequirementsPhase stability is a primary requirement to perform ISAM on an OCTsystem. Although phase variations may be nearly imperceptible ina magnitude OCT image, phase stability is important to many OCTstudies that depend on the measurement of complex signals. For in-stance, phase stable measurements are required for Doppler OCT[45], phase microscopy [46–49], polarization sensitive OCT [50], co-herent averaging [51], and spectroscopic OCT [52, 53]. In ISAM, the3D Fourier transform of the object, ˜�(qx, qy, ), is obtained throughresampling of the experimentally derived complex array S(qx, qy, k).Implicit to the resampling scheme is the assumption of a precise andpredictable relationship between the components of S(qx, qy, k). Pre-cise recovery of the spatial-frequency profile for scatterers locatedaway from the beam focus is disrupted by random phase fluctuationsduring data acquisition.

Phase stability requirements on the instrument can be elucidatedby consideration of the data acquisition. Typically, 2D raster scan-ning of a Gaussian beam interrogates each scattering location withinthe object. As described in the section “Background,” lateral beamscanning across a point scatterer situated away from focus results incontributions to the data at many scan points (u, v). Image reconstruc-tion from these data therefore requires phase-stable acquisition duringthe “interrogation time” corresponding to the length of the syntheticaperture for any given scatterer. The interrogation time at any givenlocation (x0, y0, z0) depends on its distance from focus and the NA ofthe beam (Fig. 4.2). When beyond about one Rayleigh range, the in-terrogation time scales linearly with both distance from the focus andthe beam NA. The desired NA and depth-of-field determine the max-imum interrogation time, and thus place requirements on the phasenoise spectrum of the instrument.

Two main sources of phase noise can be identified in the instru-ment. First, environmental vibrations and thermal drifts produce axialfluctuations in the differential path length between the reference andsample arms. Second, imprecise lateral scanning due to mechanicaljitter can cause deviations from the expected iso-phase contours inS(qx, qy, k). For the first case, phase noise is spread uniformly overall q , whereas in the second case, instabilities in lateral beam scan-ning are more significant at higher NA and near the beam boundarywhere the phase slope ∂�/∂x|k is the greatest (Fig. 4.2). Mechani-cal instabilities during lateral scanning thus limit the bandwidth thatproduces predictable interference during reconstruction. As a generalrule of thumb, given that random phase shifts of �� = ±� producea maximal change in interference, it is desirable to maintain phase


fluctuations below /4 over the length of the depth-dependent syn-thetic aperture.

To date, ISAM has been performed on spectral-domain OCTsystems. Simultaneous acquisition of S(x, k) on the spectrometer fa-cilitates phase registration over k, while TD-OCT, acquired throughreference arm scanning, is prone to the effects of mechanical jitter.In addition, spectral-domain acquisition enables A-scan acquisitionrates on the order of tens of kilohertz, thus minimizing scatterer inter-rogation time during lateral scanning. At NAs around 0.1, the scan-ning and detection hardware for Fourier-domain OCT will producerelatively phase-stable 2D imagery. However, when performing 3Dimaging, the acquisition time generally increases to a point wherephase noise can again become an issue. Recent developments in swept-source technology, such the high-speed Fourier-domain mode-lockedlaser, can perform phase-sensitive imaging at speeds unattainable byspectrometer-based systems [54].

Hardware Solutions for Phase RegistrationPhase stable data acquisition can be achieved via a number of meth-ods. In general, phase noise can be mitigated by instrument design-incorporating higher speed acquisition, vibration isolation, and min-imizing fiber lengths to reduce thermal drifts. However, the optimalsolution largely depends upon the practical feasibility for the specificexperimental geometry or application, and cost of its implementation.For example, obtaining the level of vibration isolation required forhigh-NA systems may be cost prohibitive. Several alternative hard-ware solutions may be considered, such as the use of a phase refer-ence, a free-space or common path design, or a feedback control loopto compensate for phase fluctuations in real time.

A phase reference directly coupled to the sample has been shownto mitigate the ill effects of differential phase fluctuations between ref-erence and sample arms [48], enabling the observation of cell mem-brane dynamics. By referencing the heterodyne phase of the sample tothat of a coverslip, upon which the cells were mounted, displacementand velocity sensitivities of 3.6 nm and 1 nm/s were achieved. Forbulk samples, a coverslip can be placed upon the sample, and whenappropriately aligned, can also reduce strong surface reflections fromthe sample. This hardware solution is used in conjunction with algo-rithms to compensate for phase fluctuations in the system. The section“Postprocessing Methods for Phase Registration” describes a digitalalgorithm utilizing the response from such a phase reference to correctphase fluctuations.

Free-space or common-path interferometer designs are often em-ployed when low differential path length variations are required [46,47, 55]. Placing a beamsplitter in the free-space optical section of thesample arm essentially forms a free-space Michelson interferometer


within the sample arm probe. A common-path design may be ob-tained by utilizing the phase reference coverslip mentioned above asthe “reference arm reflection.” Virtually all phase noise in the systemis common mode between the reference and sample optical fields,resulting in subnanometer displacement sensitivities [47].

Other sophisticated hardware solutions exist, such as the use of afeedback control loop in conjunction with a fiber stretcher or piezoelec-tric modulator [56, 57]. In these setups, fringes are counted or trackedand the reference path length is adjusted to compensate. However,these physical compensators may only be moved with limited speedand accuracy, and may be most useful in the context of large driftsover a few microns.

Postprocessing Methods for Phase RegistrationPostprocessing techniques compensate for phase noise during data ac-quisition through alignment of the complex A-scans in time domain.This alignment can be carried out by using the phase reference men-tioned in the section “Hardware Solutions for Phase Registration,” orvia direct cross correlation of the complex A-scans based on scatteringsignals from the sample.

Phase Reference Technique In the phase reference technique, phaseand group delay values are calculated for each A-scan to compen-sate for the differential variations in optical path length. Because thecoverslip signal Sc(k) corresponds to a single reflection, it can be mod-eled as Sc(k) = A(k)ei�(k), where the phase function �(k) = �0 + kd,where �0 is an arbitrary phase and d is the true position of the surfacewhere the reference reflection occurs. Because of the relative motionof the sample, the actual phase will differ from this model givingarg[Sc(k)] = �′(k). By multiplying the axial scan data S(k) by the cor-rection factor ei[�(k)−�′(k)], the phase of the axial scan can be adjustedto place the reflection at its true known position d.

The phase �′(k) is modeled as a Taylor series around a centerfrequency k0:

�′(k) = �′(k0) + (k − k0)∂�′

∂k

∣∣∣∣k=k0

+ · · · , (4.21)

To utilize this model, the value of ∂�′/∂k∣∣k=k0

from the data function�′(k) must be estimated. Because the function �′(k) is wrapped to therange −� to �, any 2� discontinuities need to be removed beforecalculating the derivative. Utilizing the unwrapped function �w(k),the estimate then becomes

∂�′

∂k

∣∣∣∣k=k0

≈ �w(k2) − �w(k1)k2 − k1

, (4.22)


φ'(k0)∂φ'(k0)/∂k

k = k0

(a) Original coverslip (b) Corrected coverslip

Position(d)

Position(c)

FIGURE 4.6 Real part of the complex OCT signal for a single reflector for (a)the OCT data and (b) the phase-corrected OCT data. The correction factorcalculated from the original data for the (c) phase drift and (d) group delaydrift. (Source: This figure is adapted from Ref. [58].)

where k1 < k0 < k2, with the frequencies k1 and k2 chosen to span theillumination spectrum (typically with k1 and k2 corresponding to thefrequencies at which the power spectral density is half of that at thepeak).

Once �′(k0) and ∂�′/∂k∣∣k=k0

are known, the empirical �′(k) canbe computed, and the corrected axial scan spectrum S′(k) = S(k)ei[�(k)−�(k ′)] found. This corrected axial scan data will be modified suchthat the position of the reference reflection is always at the same loca-tion on the axial scan, thus removing differential path length fluctua-tions between the reference and sample arm.

Figure 4.6a shows the real part of the complex analytic OCT signalfrom a single reflection of a coverslip where there is a phase drift.Figure 4.6b shows the same data after running the phase correctionalgorithm. Figure 4.6c and d show plots of the phase and group delaycorrection factors calculated from the original data. Refinements tothis method could utilize higher order terms of the series for �′(k),which would account for instrument dispersion as well as motion.

The impact of this phase correction algorithm on the quality ofISAM reconstruction can be evaluated through imaging of a gel-basedtissue phantom containing TiO2 scatterers. Three-dimensional imag-ing was performed over 800 �m × 800 �m (transverse) × 2000 �m(axial) at 4 frames/s, on a system with 800 nm central wavelengthand 100 nm bandwidth, and a sample arm NA of 0.05. Cross-sectionalimages (400 × 1024 pixels) oriented along the slow y-axis scan (250 ms


FIGURE 4.7 Cross-sectional OCT and ISAM images of a gel-based tissuephantom containing scattering TiO2 particles, processed (a) without phasecorrection and (b) with phase correction. The images are extracted from a 3Ddataset, where the transverse dimension shown is oriented along the slowy -axis scan. Phase correction was applied to the entire 3D dataset. Imagedimensions are 800 �m (transverse) × 2000 �m (depth).

between A-scans) are shown in Fig. 4.7. It can be seen that the OCT im-ages are not noticeably different after the phase correction procedure.However, the ISAM image in Fig. 4.7b shows a dramatic improvementin away-from-focus resolution after phase correction.

Cross-Correlation Technique The cross-correlation technique, based onscattering signals within A-scans, may be employed when it is im-practical or undesirable to use a phase reference coverslip, or to cor-rect residual phase fluctuations due to motion between the coverslipand sample. Cross-correlation can be utilized when there is adequateoverlap between adjacent A-scans and when the phase fluctuationsare slow compared to the A-scan rate. Cross-correlation methods havepreviously enabled coherent spectral averaging, leading to improvedOCT system sensitivity [51].

The algorithm finds the cross-correlation of a pair of time-domainscans by multiplying their real-valued spectra in the Fourier domain.This operation results in a dataset that has a maximum peak at an offsetcorresponding to the drift between the A-scans. The correspondingphase correction can then be applied to the complex time-domainsignal.

Three-Dimensional ISAM of Tissue PhantomsIn order to test the performance of ISAM reconstruction, it is usefulto work with a sample in which the density and complexity of thestructure can be regulated, and the point-spread function of the sys-tem can be tracked. Tissue phantoms consisting of discrete point scat-terers represent an ideal sample for such investigations because the


FIGURE 4.8 Three-dimensional OCT (left) and ISAM (right) images of TiO2phantoms. The three en face planes in each dataset correspond to (1) z =1100 �m, (2) z = 475 �m, and (3) z = −240 �m, where z = 0 �m is thefocal plane. (Source: Figure reprinted with permission from Ref. [3].)

density and particle size can be controlled to study different regimesof operation. Three-dimensional imaging was performed on tissuephantoms consisting of TiO2 scatterers with a mean diameter of 1 �msuspended in silicone. Imaging was conducted on a system with800 nm central wavelength and 100 nm bandwidth. The sample armNA of 0.05 provided a confocal parameter (depth-of-focus equal totwice the Rayleigh range) of 239 �m. Figure 4.8 presents side-by-sidevisualization of the OCT and ISAM datasets. It can be seen that theOCT dataset begins to show blurring at a distance of 240 �m from fo-cus, with increased blurring further from focus. In contrast, the ISAMreconstruction provides spatially invariant resolution over a depthexceeding nine Rayleigh ranges.

Cross-Validation of ISAM and OCTWhile a good agreement is obtained between en face OCT and ISAMimages near the beam focal plane, it is of interest to determine whetherISAM reconstructed en face planes far from focus provide equivalentimages to those acquired with OCT after physically moving the beamfocus to that plane.

Cross-validation of ISAM and OCT was achieved by performingISAM and OCT imaging in a TiO2-doped tissue phantom at two sep-arate focal plane depths (Fig. 4.9). Three-dimensional ISAM and OCTdatasets were obtained with the focus fixed 450 �m below the en faceimages shown in Fig. 4a and b. The sample was then moved 450 �m


(a) (b) (c)

FIGURE 4.9 (a) En face OCT of a plane 450 �m above the focal plane. (b)ISAM reconstruction of the same en face plane. (c) En face OCT with the focalplane moved to the plane of interest in part (a). The field-of-view in each panelis 360 �m × 360 �m.

so that 3D OCT could be captured again, with the same en face planenow at focus. Accounting for the index of refraction in silicone, thein-focus OCT image was co-registered with the corresponding com-putationally reconstructed ISAM image (Fig. 4.9b and c).

The out-of-focus OCT image in Fig. 4.9a shows fringe patternsresulting from simultaneous illumination of two (or more) point scat-terers and the resulting interference of their scattered optical fields.The ISAM reconstruction of this plane in Fig. 4.9b shows that theseinterference fringes are correctly resolved as multiple point scatter-ers, and a good agreement is observed with the in-focus OCT im-age in Fig. 4.9c. While the resolution observed in the ISAM and in-focus OCT images are comparable, the SNR of the ISAM image is re-duced. This degradation of SNR away from the focal plane is discussedfurther in the section “Practical Limitations.”

ISAM Processing and Real-Time ImplementationReal-time imaging is important for clinical applications that requireimmediate feedback, as well as for monitoring transient dynamics ofbiological systems [59–62]. OCT acquisition speed has increased dra-matically with the development of new spectral-domain and swept-source imaging systems [54, 63], and in order to fully utilize theseacquisition speeds, computations need to be streamlined and paral-lelized. Commercialization of the technology for medical and researchapplications has accelerated the development of real-time OCT pro-cessing and visualization software. Although ISAM reconstruction ismore computationally intensive than SD-OCT processing, real-time2D ISAM reconstruction has been demonstrated on a personal com-puter with two 3.0 GHz Intel Xeon processors at frame rates of 2.25frames/s for 512 × 1024 pixel images [64]. The general processingsteps for offline 2D ISAM reconstruction are summarized below, alongwith the modifications made to achieve real-time processing. At this


(a)

(b)

FIGURE 4.10 (a) General processing steps for 2D reconstruction and (b)modified processing steps for real-time 2D reconstruction [64].

stage, the reader is cautioned that while 2D ISAM reconstruction mayproduce significant apparent resolution improvements away from fo-cus, it remains prone to blurring artifacts from out-of-plane scatterers,and that full 3D processing is required for accurate object reconstruc-tion. That is, 2D ISAM sharpens the features in the image, but featuresfrom adjacent planes contribute and those contributions increase withdistance from focus.

The general processing steps for reconstructing 2D images arepresented in Fig. 4.10a . The prime variables �′, k ′, and z′ denote up-sampled arrays of optical frequency, optical wave number, and time,and the double prime z′′ denotes an extra, upsampling step. The hatS is used to denote phase-corrected data. Modifications to the gen-eral algorithm for real-time implementation [64] are summarized inFig. 4.10b.

ISAM reconstruction requires two primary resampling operationsand Fourier transforms to switch between the time and frequencydomains. First is the resampling of �′ → k ′, which also corrects mis-matched dispersion between the sample and reference arms, i.e., dis-persion relations more complex than Eq. (4.1) can be accounted for.The reindexing array in for this step is given by

in = n + 2

( nN

− �ctr

)2+ 3

( nN

− �ctr

)3, (4.23)

where N is the array size, �ctr is the center frequency, and n is aninteger between 0 and N−1 [25, 26]. Equation (4.23) is a coordinateremapping, accounting for dispersion up to third order. Second isthe ISAM Fourier space resampling from k → , which transformsfrom optical wave number k to longitudinal spatial-frequency . Typ-ical SD-OCT processing is completed after computing |Sxz|, whereasISAM processing requires two extra 2D FFTs and a further resamplingstep.

Upsampling plays an important role to minimize noise introducedby resampling in the final OCT and ISAM datasets. The two resam-pling (interpolation) steps have the effect of increasing the apparent


bandwidth of the data, which in turn manifests as noise in Sxk ′ andSqk , if the resampled grid is not sufficiently dense. Periodic-sinc inter-polation of Sx� by a factor of 2 is often sufficient; however, reconstruc-tion quality may benefit from higher factors depending on the noiseperformance of the chosen interpolator. Similarly, upsampling of Sqk

(zero padding of Sxz′ ) can be performed to increase phase precisionduring ISAM resampling, or omitted to optimize processing speed. Anearest neighbor interpolation requires a minimal amount of compu-tation, while a weighted sinc interpolation requires O(N) operationsper sample [65]. The cubic B-spline interpolator has a reasonable fre-quency response and uses only four multiply operations and threeadd operations to compute each interpolated point [64]. Other band-limited interpolators that could be used include prolate-spheroidal,hamming, and raised cosine. The phase correction step mitigates theeffects of phase noise during data acquisition. Details of the algorithmsused can be found in the section “Postprocessing Methods for PhaseRegistration.”

For real-time implementation, the two main dispersion and ISAMresampling steps can be performed using precomputed tables of in-dices, where speed is further optimized by using the integer part ofthe computed indices, effectively employing nearest neighbor inter-polation. Phase correction can be neglected for 2D ISAM images, ifthe acquisition speed and lateral scanning repeatability of the systemare sufficient to maintain phase stability over the extent of the depth-dependent synthetic aperture. Upsampling of the data can be omittedto maximize speed, albeit with lower SNR in the reconstruction.

Most of the operations in ISAM reconstruction can be imple-mented using parallel processing code and hardware architectures.Therefore, additional computational hardware, such as multicoreCPUs or graphic processing units (GPUs), may be used to speed upthe computations further and bring real-time 3D ISAM reconstructionwithin reach. This will also address bleed-through artifacts present in2D reconstruction caused by out-of-plane scatterers.

Practical LimitationsISAM shares many of the practical limitations present in OCT, such asthe assumption of single scattering, reduction of signal-to-noise ratio(SNR) away from focus, and light extinction within the sample. Vi-gnetting occurs in both ISAM and OCT, although its effects are nottypically discernable in OCT images. Phase noise in the instrumentcan impose additional limitations on the quality of the ISAM recon-struction, particularly at high NA.

The assumption of single scattering, i.e., the first Born approx-imation, is used to linearize the inverse scattering problem. Whenthis assumption breaks down, the accuracy of both ISAM and OCT is


degraded. Indeed, the penetration depth in OCT is often limited by thecollection of multiple scattering, which can dominate over the singlyscattered component at large depths [9, 66, 67].

Reduction of SNR with distance from focus is governed by thebeam and confocal acquisition geometry. At out-of-focus depth z, theSNR is reduced by a factor of 1/R(z), where R(z) is proportional tothe number of Rayleigh ranges from focus [32]. Although ISAM doesnot require longitudinal scanning of the focus to achieve uniform res-olution, it may be possible to combine measurements from a varietyof focal depths to improve SNR. As the method provides a quantita-tive reconstruction uniform in the object space from data acquired ateach fixed depth, multiple scans, even those with foci many Rayleighranges away from each other, may be combined, for example, with aleast squares or maximum likelihood approach.

Vignetting is more apparent further away from focus and near theedge of the lateral field-of-view. It occurs for scatterers near the edgeof the field because they are probed by a truncated synthetic aperture.This results in a reduction of signal amplitude and an attenuation ofhigh lateral spatial frequency components. Higher NA and distancefrom focus increase the synthetic aperture length and therefore theeffects of vignetting.

Phase noise of the instrument can reduce the degree of coherentinterference obtained during resampling, and therefore the SNR ofthe reconstructed data. As discussed in the section “Phase Stabilityand Data Acquisition Requirements,” the phase noise of the instru-ment impacts on the maximum interrogation time (corresponding tothe extent of the synthetic aperture) and therefore the imaging NAand required depth-of-field cannot be chosen arbitrarily. In addition,at high NA, the effects of lateral scanning instabilities produce greaterphase noise for the acquisition of high lateral spatial frequencies. Thismay disrupt the coherent superposition of these high-frequency com-ponents during reconstruction, degrading the performance away fromfocus.

4.5 Clinical and Biological ApplicationsMany biological and clinical application areas of OCT could benefitfrom ISAM imaging, in particular when higher resolution and field-of-view increases the diagnostic value of images. Several studies investi-gating the impact of axial and lateral resolution have found that higherresolution provided enhanced diagnostic information, but that highlateral resolution did not permit clear visualization of important struc-tures away from focus [68–70]. Spatially invariant ISAM reconstruc-tion of the sample, offering both high lateral resolution and extendeddepth-of-field, could significantly enhance the diagnostic capabilities


of OCT. Important biological and clinical application areas, and howthey may benefit from ISAM, are discussed below.

Optical BiopsyExcisional biopsy and subsequent histopathological analysis is cur-rently the gold standard for diagnosing neoplasia. The main drawbackof this technique is sampling errors, which can occur from inaccurateselection of neoplastic tissue during excision, or during analysis of asample with both normal and neoplastic tissue in the pathology labo-ratory. Inaccurate excision is the result of imperfect methods for detect-ing and excising neoplastic areas of tissue, while the time-consumingnature of histopathology limits the number of tissue sections that areanalyzed routinely. Both can increase the false-negative rate of diag-nosis. One of the key areas that OCT is being applied to is performingan “optical biopsy” or for optical biopsy guidance [71, 72]. Opticalbiopsy refers to the detection of disease in vivo, while the capabilityof identifying suspicious areas can be used to guide physical exci-sion of tissue. Three-dimensional, high-resolution imaging combinedwith a large depth-of-field could significantly increase the diagnosticinformation available for optical biopsy. Visualization and analysis of3D volumetric data with spatially invariant resolution could furtherreduce sampling errors.

Three-dimensional imaging of resected human breast tissue wasperformed and compared with histology images, demonstrating theextended depth-of-field provided by ISAM. Imaging was performedon a system with 800 nm central wavelength and 100 nm bandwidth,with a focused beam NA of 0.05. Figure 4.11 presents the volumetricISAM rendering and selected en face sections from near and far fromfocus. The en face ISAM sections are compared with correspondingOCT and histological sections. While the ISAM and OCT sections in-focus show similar information to histology images, the away-from-focus resolution improvements of ISAM are evident, providing a moreaccurate representation of the tissue structure.

The combination of ultrahigh axial resolution [73] with ISAMpresents an opportunity for unprecedented 3D visualization of turbidtissue, bringing cellular-level resolution over a large depth-of-fieldwithin reach. As a result, significantly more information regardingthe tissue may be extracted without increasing the measurement timeor scanning the focal plane. Further study is required to investigatethe capability of ISAM to distinguish between normal and pathologictissues, and to assess its in vivo diagnostic capabilities.

Surgical GuidanceThe detection of tumor margins is important for the complete re-moval of tumor tissue. For example, positive or undetermined


Section A Section Ba

b

c

d

e

f

A

B

Beam

Focus

Raster scan

FIGURE 4.11 Resected human breast tissue imaged with spectral-domaindetection. The beam is scanned in the geometry shown at the top. En faceimages are shown for depths located at 591 �m (Section A) and 643 �m(Section B) above the focal plane. (a,d) Histological sections showcomparable features with respect to the (b,e) OCT data and (c, f ) the ISAMreconstructions. The ISAM reconstructions resolve features in the tissue,which are not decipherable from the OCT data. (Source: This figure is adaptedfrom Ref. [3].) See also color insert.

margins in excised breast tissue samples are correlated with signif-icantly higher rates of residual cancer [74]. The evaluation of mar-gin status during surgery motivates research on intraoperative OCTimaging of resected tissue [75], as well as direct imaging of the sur-gical field [18]. The sample arm of such systems can be implementedas a handheld or endoscopic probe, or incorporated into a surgicalmicroscope. Handheld or endoscopic probes can include an opticalwindow for contact with the tissue, allowing precise placement of thefocus, which can also act as a phase reference for ISAM. During opensurgery it is desirable for the surgeon to have access to the surgicalfield, suggesting a noncontact imaging geometry. For this geometry,precise placement of the focus relative to the sample surface is of-ten difficult to obtain due to surface topography of the tissue. Withthe extended depth-of-field obtained with ISAM, only coarse place-ment of the focus is required. This advantage is demonstrated through


1

1.5

2

3

4–1 –0.5 0 0.5 1

–1 –0.5 0 0.5 1

2.5

3.5

mm

1

1.5

2

3

4

2.5

3.5

mm

mm

mm

2×

2×(a)

(b)

FIGURE 4.12 Intraoperative imaging of human tissue excised during athyroidectomy procedure. (a) OCT image and (b) real-time 2D ISAMreconstruction.

intraoperative imaging, performed on a portable OCT system, with a1310-nm central wavelength and an 80-nm bandwidth, and a focusedbeam NA of 0.1.

Figure 4.12 presents real-time intraoperative imaging of tissue ex-cised during a thyroidectomy procedure. Follicular structure that istypical of the thyroid is seen in both the OCT and ISAM images. How-ever, because of the orientation (tilt) of the tissue surface, only a subsetof the OCT image (about the strong surface signals) is in focus, whilethe real-time 2D ISAM reconstruction is able to resolve tissue morphol-ogy throughout the image. In particular boundaries between high andlow scattering regions are resolved.

Imaging of the margins of excised human breast tissue was per-formed during a lumpectomy procedure (Fig. 4.13). Because of theirregular tissue topography and time constraints inherent with intra-operative imaging, precise positioning of the focus was not achieved.The current form of the real-time algorithm does not permit dynamicadjustment of the focus depth during image acquisition, and as aconsequence, the real-time 2D ISAM image (not shown here) did not


1.5

2.5

3.5

2

3

4–0.8 –0.6 –0.4 –0.2 0 0.2 0.4 0.6 0.8

mm

1.5

2.5

3.5

2

3

4–0.8 –0.6 –0.4–0.2 0 0.2 0.4 0.6 0.8

mm

mm

mm

2x

2x

(a)

(b)

FIGURE 4.13 Intraoperative imaging of human breast tissue excised during alumpectomy procedure. (a) OCT image and (b) postprocessed 2D ISAMreconstruction.

provide significantly better resolution. However, the postprocessedimage, shown in Fig. 4.13b, demonstrates that the tissue structure canbe brought into focus by adjustment of the focus depth used by the al-gorithm. With further work, the real-time algorithm can be adapted todynamically compensate for imprecise focus placement and provideautomated computational focusing.

Tolerance to surface topography and imprecise placement of thefocus provide flexibility for use during open surgery, or assessment ofmargin status of resected tissue. This could enable the surgeon to re-move a higher percentage of cancerous tissue, and thereby reduce therate of residual cancer. Another related procedure for which ISAMcould be employed is the intraoperative screening and detection ofabnormalities in sentinel lymph nodes [76]. This has the potential toreduce the number of nodes removed and thereby reduce the inci-dence of lymphedema, a lifelong complication associated with thedisruption of normal lymphatic drainage. For all of these proposedapplication areas, further work is required to investigate the sensitiv-ity and specificity of cancer detection with ISAM.


Imaging Tumor DevelopmentTraditional diagnosis of neoplastic changes is based on cellular fea-tures such as atypia of cell nuclei, accelerated rate of growth, and localinvasion. Thus, the pursuit of cellular imaging is motivating new de-velopments in optical sources for ultrahigh resolution OCT, with axialresolutions on the order of 1 �m [73, 77]. In contrast, lateral resolutioncan be up to an order of magnitude larger to maintain a reasonabledepth-of-field in cross-sectional images. The combination of ultrahighaxial resolution with high-NA ISAM has the potential to significantlyincrease the available diagnostic information by enabling isotropic,ultrahigh resolution.

Evaluation of the diagnostic capabilities of ultrahigh resolutionISAM can be conducted in the laboratory using tissue scaffolds. Thiscould also suggest new ways that ISAM could be used in the clinicalsetting, as well as provide valuable data addressing the fundamen-tal question of how tumors grow and spread. These studies could beextended to in vivo monitoring of tumor development in animal mod-els. Induction of tumors in the dorsal skin-flap window of a rodent[78] represents a methodology that may be well suited to ultrahighresolution ISAM imaging. In contrast to histopathology, where tis-sue excision provides a “snapshot” of tissue, ISAM could be used tomonitor tumor development over time within the same animal.

4.6 Conclusions and Future DirectionsISAM is a computed imaging technique that quantitatively recon-structs the 3D scattering object using broadband coherent microscopy.The solution of the inverse problem, implemented via Fourier spaceresampling, allows reconstruction of areas typically regarded as out offocus in OCT. The Fourier-domain resampling employed in ISAM isphysically motivated by the forward model for data acquisition andresults in a quantitative estimate of the scattering potential. WhileISAM shares many of the advantages and limitations present in OCT,its spatially invariant resolution obviates the perceived trade-off be-tween transverse resolution and depth-of-focus present in OCT.

It is worth addressing a common misconception. ISAM is inversescattering, where a reconstruction of the entire 3D sample is obtained.ISAM is not refocusing. In refocusing, the focal plane is moved com-putationally, causing some features to be defocused while others arefocused. Refocusing may be accomplished from a simple 2D hologramand the result is still 2D, while reconstruction such as ISAM requiresa 3D (or higher dimensional) dataset to obtain a 3D reconstruction.

Experimental implementation of ISAM has been achieved throughhigh-speed spectral-domain acquisition, and techniques for obtain-ing phase-registered 3D datasets. Imaging of tissue phantoms has


demonstrated spatially invariant resolution up to nine Rayleighranges from the focus, and cross-validation of ISAM with OCT wassuccessfully performed. The discussion of ISAM processing empha-sized the impact of key steps on reconstruction quality, such as phasecorrection, material dispersion correction, and upsampling. Modifica-tions for real-time 2D processing achieved frame rates of 2.25 frames/sfor 512 × 1024 pixel images.

Imaging of human tissue demonstrated extended depth-of-fieldimaging, providing more accurate representation of tissue morphol-ogy. Clinical applications where ISAM imaging could add significantvalue include optical biopsy and surgical guidance. Intraoperativeimaging was demonstrated with a portable OCT system incorporat-ing ISAM. The computational focusing capability of ISAM relaxes therequirement of precise focus placement within the tissue, providinggreater flexibility when imaging tissue with irregular topography.

Future work on ISAM spans the range from theoretical modeling,to development of optical instrumentation and software processing,to clinical and fundamental biological studies. For example, model-ing of light scattering within the sample is feasible when the structureof the sample is known. Thus, reconstruction of the object structurewith ISAM could allow extended modeling of scattering beyond thefirst Born approximation. Development of high-NA instrumentationfor high isotropic resolution, presents challenges and opportunities,such as computational compensation for optical aberrations. High-NAISAM combined with ultrahigh resolution sources promises cellular-level resolution, suggesting the application to fundamental laboratorystudies on tumor development. Parallelization of 3D ISAM algorithmsfor hardware architectures such as a GPU could add significant clinicaldiagnostic value by enabling high-resolution, real-time 3D visualiza-tion of tissue. Finally, clinical studies on the sensitivity and specificityof ISAM to diagnose diseases such as cancer will ultimately determinewhat role ISAM plays in the future of health care.

References1. Huang, D., et al., Optical coherence tomography. Science, 1991. 254(5035):

pp. 1178–1181.2. Youngquist, R. C., S. Carr, and D. E. N. Davies, Optical coherence-domain

reflectometry—a new optical evaluation technique. Opt Lett, 1987. 12(3):pp. 158–160.

3. Ralston, T. S., et al., Interferometric synthetic aperture microscopy. Nat Phy,2007. 3(2): pp. 129–134.

4. Izatt, J. A., et al., Optical coherence microscopy in scattering media. Opt Lett,1994. 19(8): pp. 590–592.

5. Fercher, A. F., et al., Measurement of intraocular distances by backscatteringspectral interferometry. Opt Commun, 1995. 117(1–2): pp. 43–48.

6. Hausler, G. and M. W. Lindner, “Coherence radar” and “spectral radar”—newtools for dermatological diagnosis. J Biomed Opt, 1998. 3(21): pp. 21–31.


7. Leitgeb, R., C. K. Hitzenberger, and A.F. Fercher, Performance of fourier do-main vs. time domain optical coherence tomography. Opt Express, 2003. 11(8):pp. 889–894.

8. Wojtkowski, M., et al., Ultrahigh-resolution, high-speed, Fourier domain op-tical coherence tomography and methods for dispersion compensation. OptExpress, 2004. 12(11): pp. 2404–2422.

9. Fercher, A. F., et al., Optical coherence tomography—principles and applica-tions. Rep Prog Phys, 2003. 66(2): pp. 239–303.

10. de Boer, J. F., et al., Improved signal-to-noise ratio in spectral-domain comparedwith time-domain optical coherence tomography. Opt Lett, 2003. 28(21): pp.2067–2069.

11. Choma, M. A., et al., Sensitivity advantage of swept source and Fourier domainoptical coherence tomography. Opt Express, 2003. 11(18): pp. 2183–2189.

12. Boulnois, Photophysical processes in recent medical laser developments: AReview. Lasers Med Sci, 1985. 1: pp. 47–66.

13. Schuman, J. S., C. A. Puliafito, and J.G. Fujimoto, Optical Coherence Tomographyof Ocular Diseases. 2004: SLACK Inc., Thorofare, NJ.

14. Bouma, B. E., et al., Evaluation of intracoronary stenting by intravascular op-tical coherence tomography. Heart, 2003. 89(3): pp. 317–320.

15. Armstrong, J. J., et al., Quantitative upper airway imaging with anatomicoptical coherence tomography. Am J Respir Crit Care Med, 2006. 173(2):pp. 226–233.

16. Boppart, S. A., et al., Optical coherence tomography: feasibility for basic re-search and image-guided surgery of breast cancer. Breast Cancer Res Treat, 2004.84(2): pp. 85–97.

17. Pitris, C., et al., Feasibility of optical coherence tomography for high-resolutionimaging of human gastrointestinal tract malignancies. J Gastroenterol, 2000.35(2): pp. 87–92.

18. Zagaynova, E., et al., A multicenter study of optical coherence tomographyfor diagnosis and guided surgery of bladder cancer. J Clin Oncol, 2004. 22(14):pp. 391S-391S.

19. Gambichler, T., et al., Characterization of benign and malignant melanocyticskin lesions using optical coherence tomography in vivo. J Am Acad Dermatol,2007. 57(4): pp. 629–637.

20. Kawakami-Wong, H., et al., In vivo optical coherence tomography-based scor-ing of oral mucositis in human subjects: a pilot study. J Biomed Opt, 2007. 12(5):pp. 051702.

21. Escobar, P. F., et al., Optical coherence tomography as a diagnostic aid to visualinspection and colposcopy for preinvasive and invasive cancer of the uterinecervix. Int J Gynecol Cancer, 2006. 16(5): pp. 1815–1822.

22. Whiteman, S. C., et al., Optical coherence tomography: real-time imaging ofbronchial airways microstructure and detection of inflammatory/neoplasticmorphologic changes. Clin Cancer Res, 2006. 12(3): pp. 813–818.

23. Bohringer, H. J., et al., Time-domain and spectral-domain optical coherencetomography in the analysis of brain tumor tissue. Las Surg Med, 2006. 38(6):pp. 588–597.

24. Saleh, B. E. A. and M. C. Teich, Fundamentals of Photonics. Wiley Series in Pureand Applied Optics. 1991, New York: Wiley.

25. Marks, D. L., et al., Autofocus algorithm for dispersion correction in opticalcoherence tomography. Appl Opt, 2003. 42(16): pp. 3038–3046.

26. Marks, D. L., et al., Digital algorithm for dispersion correction in optical co-herence tomography for homogeneous and stratified media. Appl Opt, 2003.42(2): pp. 204–217.

27. Potton, R. J., Reciprocity in optics. Rep Prog Phys, 2004. 67(5): pp. 717–754.28. Weyl, Expansion of electro magnetic waves on an even conductor. Annalen der

Physik, 1919. 60: pp. 481–500.29. Mandel, L. and E. Wolf, Optical Coherence and Quantum Optics. 1996: Cambridge

University Press, Cambridge, MA.


30. Gazdag, J. and P. Sguazzero, Migration of seismic data. Proc IEEE, 1984. 72(10):pp. 1302–1315.

31. Stolt, R. H., Migration by Fourier-transform. Geophysics, 1978. 43(1): pp. 23–48.

32. Davis, B. J., et al., Interferometric synthetic aperture microscopy: computedimaging for scanned coherent microscopy. Sensors, 2008. 8(6): pp. 3903–3931.

33. Cormack, A. M., Representation of a function by its line integrals, with someradiological applications. J Appl Phys, 1963. 34: pp. 2722–2727.

34. Hounsfield, G. N., Computerized transverse axial scanning (tomography).1. Description of system. Br J Radiol, 1973. 46(552): pp. 1016–1022.

35. Devaney, A. J., Reconstructive tomography with diffracting wavefields. InverseProblems, 1986. 2: pp. 161–183.

36. Pan, S. X. and A. C. Kak, A Computational study of reconstruction algorithmsfor diffraction tomography - interpolation versus filtered backpropagation.IEEE Trans Acoust Speech Signal Processing, 1983. 31(5): pp. 1262–1275.

37. Wolf, E., Three-dimensional structure determination of semi-transparent ob-jects from holographic data. Opt Commun, 1969. 1: pp. 153–156.

38. Lauterbur, P. C., Image formation by induced local interactions—examples employing nuclear magnetic-resonance. Nature, 1973. 242(5394):pp. 190–191.

39. Born, M. and E. Wolf, Principles of Optics: Electromagnetic Theory of Propaga-tion, Interference and Diffraction of Light. 7th ed. 1999, New York: CambridgeUniversity Press.

40. Richards, B. and E. Wolf, Electromagnetic diffraction in optical systems. II.Structure of the image field in an aplanatic system. Proc R Soc Lond A, 1959.253: pp. 358–379.

41. Davis, B. J., et al., Nonparaxial vector-field modeling of optical coherence to-mography and interferometric synthetic aperture microscopy. J Opt Soc Am A,2007. 24(9): pp. 2527–2542.

42. Marks, D. L., et al., Inverse scattering for frequency-scanned full-field opticalcoherence tomography. J Opt Soc Am A, 2007. 24(4): pp. 1034–1041.

43. Marks, D. L., et al., Partially coherent illumination in full-field interferometricsynthetic aperture microscopy. J Opt Soc Am A, 2009. 26(2): pp. 376–386.

44. Marks, D. L., et al., Inverse scattering for rotationally scanned optical coherencetomography. J Opt Soc Am A, 2006. 23(10): pp. 2433–2439.

45. Zhao, Y. H., et al., Phase-resolved optical coherence tomography and opticalDoppler tomography for imaging blood flow in human skin with fast scanningspeed and high velocity sensitivity. Opt Lett, 2000. 25(2): pp. 114–116.

46. Choma, M. A., et al., Spectral-domain phase microscopy. Opt Lett, 2005. 30(10):pp. 1162–1164.

47. Joo, C., et al., Spectral-domain optical coherence phase microscopy for quanti-tative phase-contrast imaging. Opt Lett, 2005. 30(16): pp. 2131–2133.

48. Yang, C., et al., Phase-referenced interferometer with subwavelength and sub-hertz sensitivity applied to the study of cell membrane dynamics. Opt Lett,2001. 26(16): pp. 1271–1273.

49. Rylander, C. G., et al., Quantitative phase-contrast imaging of cells withphase-sensitive optical coherence microscopy. Opt Lett, 2004. 29(13): pp. 1509–1511.

50. de Boer, J. F., et al., Two-dimensional birefringence imaging in biological tissueby polarization-sensitive optical coherence tomography. Opt Lett, 1997. 22(12):pp. 934–936.

51. Tomlins, P. H. and R.K. Wang, Digital phase stabilization to improve detectionsensitivity for optical coherence tomography. Meas Sci Technol, 2007. 18(11):pp. 3365–3372.

52. Adler, D. C., et al., Optical coherence tomography contrast enhancement usingspectroscopic analysis with spectral autocorrelation. Opt Express, 2004. 12(22):pp. 5487–5501.


53. Xu, C. Y., et al., Spectroscopic spectral-domain optical coherence microscopy.Opt Lett, 2006. 31(8): pp. 1079–1081.

54. Adler, D. C., R. Huber, and J.G. Fujimoto, Phase-sensitive optical coherencetomography at up to 370,000 lines per second using buffered Fourier domainmode-locked lasers. Opt Lett, 2007. 32(6): pp. 626–628.

55. Vakhtin, A. B., et al., Common-path interferometer for frequency-domain op-tical coherence tomography. Appl Opt, 2003. 42(34): pp. 6953–6958.

56. Jackson, D. A., et al., Elimination of drift in a single-mode optical fiber interfer-ometer using a piezoelectrically stretched coiled fiber. Appl Opt, 1980. 19(17):pp. 2926–2929.

57. Lin, D., et al., High stability multiplexed fiber interferometer and its applicationon absolute displacement measurement and on-line surface metrology. OptExpress, 2004. 12(23): pp. 5729–5734.

58. Ralston, T. S., et al., Phase stability technique for inverse scattering in opti-cal coherence tomography, In: Proceeding of IEEE International Symposium onBiomedical Imaging. April 6–9, 2006: Arlington, VA.

59. Leitgeb, R. A., et al., Real-time measurement of in vitro flow by Fourier-domain color Doppler optical coherence tomography. Opt Lett, 2004. 29(2):pp. 171–173.

60. Lerner, S. P., et al., Optical coherence tomography as an adjunct to white lightcystoscopy for intravesical real-time imaging and staging of bladder cancer.Urology, 2008. 72(1): pp. 133–137.

61. Park, B. H., et al., Real-time multi-functional optical coherence tomography.Opt Express, 2003. 11(7): pp. 782–793.

62. Wojtkowski, M., et al., Real-time in vivo imaging by high-speed spectral opticalcoherence tomography. Opt Lett, 2003. 28(19): pp. 1745–1747.

63. Yun, S. H., et al., High-speed spectral-domain optical coherence tomographyat 1.3 �m wavelength. Opt Express, 2003. 11(26): pp. 3598–3604.

64. Ralston, T. S., et al., Real-time interferometric synthetic aperture microscopy.Opt Express, 2008. 16(4): pp. 2555–2569.

65. Yaroslavsky, L., Boundary effect free and adaptive discrete signal sinc-interpolation algorithms for signal and image resampling. Appl Opt, 2003.42(20): pp. 4166–4175.

66. Pan, Y. T., R. Birngruber, and R. Engelhardt, Contrast limits of coherence-gatedimaging in scattering media. Appl Opt, 1997. 36(13): pp. 2979–2983.

67. Yadlowsky, M. J., J. M. Schmitt, and R. F. Bonner, Multiple-scattering in opticalcoherence microscopy. Appl Opt, 1995. 34(25): pp. 5699–5707.

68. Chen, Y., et al., Ultrahigh resolution optical coherence tomography of Barrett’sesophagus: preliminary descriptive clinical study correlating images with his-tology. Endoscopy, 2007. 39(7): pp. 599–605.

69. Wang, Z. G., et al., In vivo bladder imaging with microelectromechanicalsystems-based endoscopic spectral domain optical coherence tomography. JBiomed Opt, 2007. 12(3): pp. 034009.

70. Hsiung, P. L., et al., Ultrahigh-resolution and 3-dimensional optical coherencetomography ex vivo imaging of the large and small intestines. GastrointestEndosc, 2005. 62(4): pp. 561–574.

71. Fujimoto, J. G., Optical coherence tomography for ultrahigh resolution in vivoimaging. Nat Biotechnol, 2003. 21(11): pp. 1361–1367.

72. Fujimoto, J. G., et al., Optical coherence tomography: an emerging technologyfor biomedical imaging and optical biopsy. Neoplasia, 2000. 2(1–2): pp. 9–25.

73. Drexler, W., Ultrahigh-resolution optical coherence tomography. J Biomed Opt,2004. 9(1): pp. 47–74.

74. Cellini, C., et al., Factors associated with residual breast cancer after re-excisionfor close or positive margins. Ann Surg Oncol, 2004. 11(10): pp. 915–920.

75. Nguyen, F. T., et al. Portable real-time optical coherence tomography system forintraoperative imaging and staging of breast cancer. 2007. In: Proceedings ofSPIE, San Jose, CA, International Society for Optical Engineering, Bellingham,WA.


76. Luo, W., et al., Optical biopsy of lymph node morphology using optical coher-ence tomography. Technol Can Res Treat, 2005. 4(5): pp. 539–547.

77. Povazay, B., et al., Submicrometer axial resolution optical coherence tomogra-phy. Opt Lett, 2002. 27(20): pp. 1800–1802.

78. Huang, Q., et al., Noninvasive visualization of tumors in rodent dorsal skinwindow chambers—a novel model for evaluating anti-cancer therapies. NatBiotechnol, 1999. 17(10): pp. 1033–1035.


P A R T 2Application to In VitroCell Biology

CHAPTER 5Light Scattering as a Tool inCell Biology

CHAPTER 6Light Absorption andScattering SpectroscopicMicroscopies


C H A P T E R 5Light Scattering as

a Tool in Cell Biology

Kevin J. Chalut and Thomas H. Foster

5.1 IntroductionWhen light scatters from a sample, the amplitude and angular distri-bution of the scattered radiation depend on the size, shape, organiza-tion, and electromagnetic properties of the sample. Hence, the scat-tered light is a signature of the sample’s structure, and the detectedscattering signal can be analyzed to deduce the sample composition. Inthe present chapter, we consider scattering from biological cells, witha specific focus on how light scattering is used as a tool to measurestructure and function in cell biology.

Most light scattering techniques in biology, including the tech-niques discussed presently, consist of at least two steps. The first stepis to detect the light scattered from the sample, usually in the far field.The detected scattering signal is typically wavelength and/or angleresolved. The second step is to invert the signal: A light scatteringmodel is used to develop an algorithm by which the light scatteringsignal is compared to the light scattering model to deduce the mostprobable scattering configuration. This step will be referred to in thischapter as inverse light scattering analysis (ILSA). An intermediatestep, occasionally necessary when the scattered light includes contri-butions from a very large distribution of structures, may involve pre-processing the signal to isolate the contribution to the signal from thestructure of interest, for example, the cell nucleus. We refer the readerto other chapters in which these steps are discussed in greater detail;we will discuss details of these steps in subsequent sections only asthey pertain to the particular methods or experiments we highlight inthis chapter.

115

116 A p p l i c a t i o n t o I n V i t r o C e l l B i o l o g y

Mourant et al. published an influential paper in 1998 [1] in whichthey emphasized that most of the scattering due to the whole cell isat small angles in the extreme forward direction; therefore, the lightscattered outside of this angular range contains the relevant informa-tion about cellular organelles. They further showed that mitochondriaand lysosomes are primarily responsible for scattering at larger angles.In particular, at visible wavelengths, optical scattering measurementsrevealed a distribution of intracellular scatterers with volumes equiv-alent to spheres with diameters in the range 0.2–1.0 �m. Researchfrom the laboratory of one of the authors (Foster), which will be dis-cussed in greater detail shortly, lends support to and extends this lastobservation. Additionally, work from the laboratories of the editorsof this text (Wax and Backman) has shown that backscattering is verysensitive to nuclear structure. We conclude then, that an importantelement for studying a certain structure or organelle within the cell isthe geometry of the light scattering detection scheme.

The emphasis of this chapter will be the light scattering modelsand methods researchers have used to investigate the structure andorganization of organelles within the cell. Furthermore, we place em-phasis on detection schemes that evaluate the angular dependence,as opposed to the spectral dependence, of light scattered from bi-ological cells. The reason for this choice is that there is a relation-ship between the density fluctuations (inhomogeneities) in the sam-ple and the spatial fluctuations in the scattered field [2], making thespatial distribution of scattered light particularly sensitive to struc-ture and structural changes within the sample. The present chapter isdivided into four sections. The first three will present methods andresults of investigations of the structure of three different organelles—mitochondria, lysosomes, and nuclei, respectively—and their contri-bution to scattering from intact cells. All three sections will presentbiomedical/biological applications of these studies, where applica-ble. The fourth section will include conclusions and prospects for lightscattering applications in cell biology.

5.2 Light Scattering Assessments of MitochondrialMorphologyMitochondria perform a variety of essential functions in cell biology.In addition to ATP synthesis, which is vital for cell energetics, mito-chondria participate in regulating intracellular calcium concentrationand lipid biosynthesis and perform critical roles in mediating apop-totic and nonapoptotic cell death pathways [3]. Changes in cellularmetabolism [4] and apoptosis [5] have been associated with changesin mitochondrial morphology; therefore, monitoring mitochondrialmorphology can be a key to study changes in cellular function. Several

117L i g h t S c a t t e r i n g a s a T o o l i n C e l l B i o l o g y

groups have done extensive work using light scattering to monitor mi-tochondrial morphology; furthermore, these groups have linked thesemorphological changes to commensurate alterations in function, par-ticularly apoptosis. We will discuss some of these results and theirimplications in turn.

Boustany et al. used optical scattering imaging (OSI) to monitorcalcium-induced alterations in mitochondrial morphology [6]. OSIuses an inverted microscope setup to monitor the ratio of wide-to-narrow angle scattering. The detection of this ratio is achieved byplacing a variable iris with a center stop in the focal plane of the objec-tive to control the angular spread of the field detected in the imagingplane. The authors showed that the measured optical scatter imageratio (OSIR) decreases monotonically with the diameter of the scatter-ing particles. This relationship arises because larger particles possessa more forward-scattered peak. The authors used calcium injury toinduce the mitochondria from their native ellipsoidal shape into arounded sphere. This transition was verified by electron microscopy,but most importantly, it correlated with a 14% increase in OSIR (Fig.5.1). An increase in OSIR corresponds to an increase in wide-angle

−200.8

0.9

1

1.1

1.2

−15 −10 −5 0 5 10 15 20 25 30

TIME (min)

lonomycin

Ca2+

Ca2+ (1.6 mM)

No

rmal

ized

OS

IR

Ca2+ (1.6 mM) + CsA (25 µM)

FIGURE 5.1 Average optical scatter imaging ratio (OSIR) as a function of time.( �) Represents cells subjected to calcium injury, and (�) represents cellssubjected to calcium injury in the presence of cyclosporin A (CsA), amitochondrial permeability inhibitor [6]. Error bars represent the 95%confidence interval of the mean. These results indicate that the change inOSIR is due to a change in mitochondrial morphology.


scattering and/or a decrease in narrow-angle scattering: the increasein OSIR is indicative of smaller, or more rounded particles. The au-thors then applied CsA (cyclosporin A), a mitochondrial permeabilitytransition inhibitor, to the cells along with calcium injury. Because cal-cium could not cross the membrane, no change in OSIR was observed(Fig. 5.1), indicating that the change in OSIR was due only to thechange in mitochondrial morphology. The authors further verified us-ing finite-difference time-domain (FDTD) simulations that the changein OSIR was also not due to a change in refractive index in the mito-chondria.

Boustany et al. continued their study of mitochondrial morphol-ogy by investigating the effect of apoptosis resistance on the OSIR viaoverexpression of BCL-xL. BCL-xL is important in the study of apop-tosis because of its inhibitory effect on the release of cytochrome c [7].Cytochrome c, after initiation of apoptosis, is released from the mito-chondrial intermembrane space into the cytoplasm, where it results inthe activation of caspases. Caspases induce nuclear fragmentation andthe breakdown of subcellular structure. The authors treated a controlgroup of CSM14.1 cells and a group of CSM14.1 cells overexpressingBCL-xL with staurosporine (STS), which induces apoptosis. There wasa large decrease (∼25%) in the OSIR within 1 h in the control group,as well as a control group stably transfected with YFP, while in theYFP-BCL-xL variant, a much smaller increase (∼10%) was observed.However, the YFP-BCL-xL variant manifested a statistically significantlower (∼25%) OSIR in YFP-BCL-xL variant than its YFP counterpart.Because the baseline of the OSIR in the YFP-BCL-xL variant is almostexactly equal to the OSIR to which the CSM14.1 cells decrease duringapoptosis, the authors speculate that the BCL-xL may itself be respon-sible for the subcellular changes leading to changes in OSIR duringapoptosis. This could be caused by a translocation of BCL-xL to themitochondria after induction of apoptosis, but this has not yet beenshown.

The previous study highlights one of the most important advancesmade using light scattering as a tool for cell biology: early, noninvasivedetection of apoptosis, which is potentially important for monitoringcancer treatment. Further, this study represents an early attempt tolink changes in subcellular structure, observable by light scattering,to changes in cell function. This is an emerging theme in studies ofsubcellular light scattering for applications to cell biology.

Wilson et al. further pursued the idea that light scattering couldbe a very effective tool for monitoring mitochondrial morphology asa response to an environmental stimulus [8]. Using a goniometer thatmonitors the angular scattering between 3◦ and 90◦, the authors in-vestigated the effect of oxidative stress on mitochondrial swelling inEMT6 cells. The EMT6 cells were either left untreated or were sub-jected to photodynamic stress sensitized with aminolevulinic acid


Angle (deg)0

10−3

10−2

10−1

100

10 20 30

Treated cellsControl cells

Sca

tter

ed li

gh

t in

ten

sity

(A

DU

)

FIGURE 5.2 Angularly resolved light scattering from untreated EMT6 cells (�)and photodynamically insulted EMT6 cells (�) [8]. The treated cells scatterless light at small angles and have a more pronounced forward peak.

(ALA), which causes an accumulation of the endogenous photosen-sitizer protoporphyrin IX in mitochondria. As seen in Fig. 5.2, thereis a significant difference between the photodynamically treated andcontrol cells, particularly at low angles. The authors used an ILSAalgorithm that incorporates the following treatment.

Mie theory scattering angular distributions S(�, r ) were calculatedfor linearly polarized light scattered from particles with radius rranging from rmin = 0.005 �m to rmax = 8.0 �m, which correspondto expected possible values. The refractive indices of the scatteringcenter and surrounding medium were assumed to be 1.40 and 1.38,respectively. These values were chosen on the basis of previous work.Test functions, T(�), were built from Mie theory by integrating over aproduct of the scattering angular distributions with a size distribution� (r ):

T(�) =∫

�(r ) S(r, �) dr , (5.1)

where � (r ) is a sum of log-normal size distributions of the form

� (r ) =∑

j

aj lj (r ). (5.2)

T(�) are functions of the means, standard deviations, and relativeamplitudes of the log-normal particle size distributions. The measured


scattering data, I (�), is considered on both a log and linear scale toaccount for an overestimation of the forward scattering on the linearscale and an underestimation on the log scale. The fit was carried outby minimizing the function

F =∫ (

1 (I − T)2 + 2(log (I ) − log (T)

)2)

d� + 3

∑j

Rj . (5.3)

The j ’s were chosen to weight each term approximately equally(1 = 1.0, 2 = 7.0, 3 = 1010), and the minimization was carried outusing the simple downhill simplex of Nedler and Mead [9].

It was found using this ILSA algorithm that the best fit corre-sponded to a bimodal log-normal population of scatterers with meandiameters centered about 0.22 ± 0.057 �m and 1.15 ± 0.54 �m. Over65% of the scatterers fell within the size range 1.0–3.0 �m. The fact thatthe forward-scattered light (3◦–80◦) was dominated by mitochondriawas supported by angular scattering data from mitochondria isolatedfrom rabbit liver.

A theory based on Mie-type scattering from two log-normal sizedistributions provided a poor fit to angle-resolved scattering datameasured from the photodynamically insulted EMT6 cells; therefore,the authors modified the ILSA algorithm informed by results obtainedfrom electron microscopy. Based upon the observation that the mito-chondria swelled after photodynamic insult, the authors explored fitsusing three different models: uniformly expanding mitochondria withan initial refractive index of 1.4 diluted homogeneously by cytosol, acoated sphere model assuming a water-filling mitochondria interior(index of refraction 1.33), and a coated sphere model with a cytosol-filling mitochondria interior (index of refraction 1.38). The first twowere completely incompatible with the data; however, assuming thatthe mitochondria expanded with a cytosol-filling interior yielded anexcellent fit to the experimental data (Fig. 5.3). Furthermore, the ILSAalgorithm assuming a mitochondrial sphere surrounding a cytosoliccore predicts a 13% increase in mitochondrial diameter, which is con-sistent with the results of electron microscopy. The fact that the successof the ILSA algorithm is so sensitive to assumptions concerning themitochondrial morphology is a testament to two conclusions: First,the amount of light scattered at these wavelengths and in this angularrange is highly sensitive to mitochondria, and second, the scatteringprofile is highly sensitive to mitochondrial morphology.

The previous results are potentially important. Mitochondria arean extremely dynamic organelle in cellular activity, and pathwaysthat lead to changes in cellular function often start within them. Theability to attain high-throughput, noninvasive measurements of mito-chondrial structure could provide new windows through which cellbiologists can observe changes in cellular activity.


Angle (deg)0

10−5

10−4

10−3

10−2

10−1

100

20 40 60 80

Sca

tter

ed li

gh

t in

ten

sity

FIGURE 5.3 Scattering data (�) from cells subjected to photodynamic insultcompared with a coated sphere fit that accounts for cytosolic filling of theinner mitochondria [8].

5.3 Light Scattering Assessments ofLysosomal MorphologyLysosomes are cellular organelles that contain enzymes essential fordigestion of engulfed viruses or bacteria, as well as organelles that areno longer needed by the cell (authophagy). The role of lysosomes inapoptotic signaling is established [10]. Research in the area of photody-namic therapy (PDT) has shown that lysosomal photodamage can ini-tiate a downstream release of cytochrome c from mitochondria priorto the loss of membrane potential, thereby initiating mitochondrial-mediated apoptosis. Reiners et al. [11] have hypothesized that, in thecourse of PDT, lysosomal enzymes are released, causing the cleavageof the proapoptotic Bcl-2 protein Bid. In three separate papers, Fos-ter’s laboratory has investigated, using light scattering and techniquesdeveloped in PDT to photosensitized lysosomes, the lysosomal contri-bution to light scattering and the potential for using this informationfor detection of apoptosis. These three papers will now be discussedin turn.

The ILSA algorithm described above can be generalized: Whenmeasurements are made from an ensemble of particles such as or-ganelles within cells, it has been shown that the observed signal is aproduct of the number density of particles in a particular size range,� (r ), and their scattering cross section, �(r ). Furthermore, a sampled


phase function P(�) measured from a collection of particles followsthe form:

Ptotal (�) =∫

�(r )� (r )P(r, �)dr∫�(r )� (r )dr

. (5.4)

Importantly, although ability to size intracellular scatterers de-pends highly on the choice of the functional form of � (r ), the product�� extracts the dominant light scatterers regardless of this choice [12].Using this generalization, the scattering distribution S(r ,�) is writtenas

S(r, �) = �(r )P(r, �) (5.5)

and the test functions are written as

T(�) =∫

�(r )� (r )P(r, �)dr. (5.6)

T(�) are functions of six parameters, the means, the standard de-viations, and the relative amplitudes for two populations. The pa-rameters were adjusted by an iterative, nonlinear fit to minimize thefunction

� 2 =∑

n

(Dn − Tn)2

vn(5.7)

where Dn represents the nth data point, Tn represents the correspond-ing value of the test function, and vn represents the correspondingvariance.

In the first study, Wilson et al. [13] utilized high-extinctionlysosomal- and mitochondrial-localizing dyes, NPe6 and HPPH, re-spectively, to determine the effects of each organelle on the light scat-tering signature from intact cells. Following incubation with NPe6,the authors measured light scattering from EMT6 cells at 488, 633, and658 nm, corresponding to low, medium, and high absorption for thedye, respectively, and evaluated the effects on the light scattering ofeach versus untreated cells (no NPe6 dye). Although there was novisible change in the light scattering profile at 488 nm, there was adramatic change at 633 and 658 nm, particularly at a scattering an-gle around 30◦. Meanwhile, the light scattering profile did not changesubstantially at angles below 15◦ and above 60◦. These results differfrom the changes seen in Fig. 5.2, in which scattering changes are dueto morphological changes in mitochondria, and manifest primarily atangles less than 15◦. Moreover, because of the chromatic dependenceof the changes, which coincides with the absorption spectrum of the


dye, the changes indicate that these changes are lysosome dependent.This was an important finding because it was the first convincingevidence that light scattering is sensitive to lysosomes in intact cells.

The authors also found that, using HPPH localized to mitochon-dria, there was no change to the light scattering profile. This findingwas superficially surprising, because it would be expected that localiz-ing an absorbing dye to mitochondria, which have been shown to con-tribute significantly to light scattering, should change the light scat-tering profile. The authors investigated this apparent inconsistencyby incorporating absorption effects into their Mie theory model. Theyfound that the changes to the light scattering profile due to absorp-tion are highly dependent on the real part of the index of refraction,nr. For instance, at nr = 1.4, the addition of an imaginary compo-nent to the index of refraction, ni, results in a negligible change in thelight scattering profile, both in an angularly resolved and integratedsense. As mitochondria are known to have nr ∼ 1.4, these modelingresults explain why the light scattering profile does not change withthe addition of HPPH. However, at nr = 1.6, there was a decrease inscattering cross section for ni between ∼10−3 and 0.2, correspondingto an absorbing, but nonmetallic medium.

The authors then used the Mie theory ILSA algorithm describedabove, except they assumed a trimodal distribution [Eqs. (5.2 and 5.6)]for two test functions, one accounting for an absorbing sphere:

T control (�) =∫

� (r ) P(r, �) × [a1l1 + a2l2 + a3l3] dr

TNPe6 (�) = Ccell

∫� (r ) P(r, �) × [a1l1 + a2l2 + C�a3l3] dr

(5.8)

where C� is a model for the ratio of the scattering cross section of thestained population to its corresponding unstained population. Ccell

is an additional constant to account for errors in the counting of celldensities during measurement. This model is used to determine thecharacteristic particle sizes contributing to the light scattering signal.The result of this analysis is summarized in Table 5.1. These results

Population MeanNumber (l) Organelle (�m) SD (�m) R (%)

1 Mitochondria 1.3 0.6 80

2 Secretory granules 0.2 0.05 5

3 Lysosomes 0.6 0.3 15

TABLE 5.1 Summary of Typical Diameters of Three Populations of LightScattering Centers Returned from Simultaneous Fits to Angularly ResolvedLight Scattering from NPe6-Treated and Control Cells


should be compared to earlier results from Wilson et al. [8], in whicha nonabsorbing Mie theory model assuming a bimodal distributionyielded characteristic sizes of 0.22 ± 0.057 �m and 1.15 ± 0.54 �m. Theprevious results were most likely influenced by the grouping of mito-chondria and lysosome contributions together, thereby decreasing themean size of the larger measurement from ∼1.3 to ∼1.15 �m. In theprevious studies, in which no absorbing dyes were used, the assump-tion of a trimodal distribution yielded poor fits to the data. However,the trimodal absorbing sphere model yielded good fits to the datawhen NPe6 was used as an absorbing lysosomal dye. Moreover, theILSA algorithm yielded a new distribution with a diameter of 0.6 �m± 0.3 �m, which corresponds to the known size of lysosomes. Addi-tionally, with an absorption term included in the model, the refractiveindex of the lysosomes can be deduced from the ILSA algorithm. Thedetermined refractive index of lysosomes was nr ∼ 1.6. As discussedpreviously, absorbing spheres with a refractive index of 1.6 presenta reduced scattering cross section, which explains why the scatteringprofile is largely affected by adding an absorbing dye to lysosomes.

The previous study demonstrated primarily that lysosomes con-tribute significantly to light scattering from cells, and also that theirrefractive index was approximately 1.6. The size distribution extractedin the study was 0.6 �m ± 0.3 �m; however, the study was not specifi-cally designed to extract this information. Therefore, Wilson and Fos-ter set out to determine the size of lysosomes by photodynamicallyablating them and examining the effect on the angularly resolved lightscattering signature [14]. In the experimental procedure, lysosomeswere photosensitized with NPe6 and then ablated using a fluence of20 J/cm2 at 662 nm. The lysosomes presented morphological indi-cations of ablation in fluorescence images of cells subjected to thistreatment. The light scattering profile of the treated cells was thencompared to that of untreated cells (Fig. 5.4). It is clear in Fig. 5.4 that,again, changes in scattering from lysosomes (via ablation or addingan absorbing dye) presents at angles greater than 15◦, while there areno visible changes at more forward angles. Compared with the find-ings of Fig. 5.2, within a Mie theory model, these results indicate thatthe changes in light scattering are due to perturbations to particlessmaller than mitochondria.

As in the mitochondria studies, a bimodal distribution was as-sumed in the Mie theory model for both untreated and PDT-treatedcells. In the previously discussed study, a trimodal distribution wasemployed in the Mie theory model; however, in this study, the as-sumption of a trimodal distribution yielded poor fits to the data.Nonetheless, the bimodal distribution Mie theory model, althoughit yielded good fits to the data, did not account for changes in scat-tering due to lysosomes. The Mie theory model was then revised toassume a trimodal distribution of sizes in the form of Eq. (5.1), but


Angle (deg)

0

10−4

10−3

10−2

10−1

20 40 60 80

Sca

tter

ed li

gh

t in

ten

sity

No drug controlNPe6 + 20 J/cm2

FIGURE 5.4 Angularly resolved scattering data from control EMT6 cells (�)and cells treated with 20 J/cm2 NPe6-PDT treatment (◦) [14]. Bothpopulations have similar scattering distributions in the forward direction,while the PDT-treated cells scatter less light beyond 15◦, characteristic ofablated light scattering centers.

it was further assumed that one of the log-normal distributions wascompletely ablated after PDT. The particle size distributions were thenwritten

�PDT = a1l1 + a2l2, �control = �PDT + a3l3 (5.9)

and the datasets were fit simultaneously. Three distinct populationswere recovered, and l3, which were assumed to be lysosomes, returneda size of 0.8 �m ± 0.4 �m. Its contribution to the light scattering signalwas 14%. The population l1 returned a mean diameter of 1.3 ± 0.65 �m,comprising 77% of the signal; while the population l2 returned a meandiameter of 0.14 ± 0.08 �m, comprising 9% of the signal. These results,summarized in Fig. 5.5, are consistent with the conclusions from thepreviously discussed study, which were reached in an independentmanner. As this study was specifically designed to deduce lysosomalsize, this should be regarded as a more accurate assessment of sizethan the previous study.

Much of the work that has been discussed leads in a direct line tothe possibility of using light scattering as a tool for monitoring apop-tosis. An example of one such study was contributed by Wilson et al.[15], in which the PDT model using NPe6 was used to photosensitizelysosomes. In the work described above, after treating EMT6 cells withNPe6, the cells were irradiated with 20 J/cm2 of 662 nm light, causing


Particle diameter (µm)0 2

1.0

0.8

0.6

0.4

0.2

0.04 6 8 10

Tota

l lig

ht

scat

tere

d (

σρ)

No drug control

50 µg/ml NPe6 + 20 J/cm2

FIGURE 5.5 Cross-section–weighted particle size distributions resulting fromfitting to angularly resolved light scattering data from control and PDT-treatedcells [14]. Analysis of these plots indicates that lysosomes are between 0.5and 1.0 �m in size and contribute approximately 14% of the total scatteringsignal at 633 nm.

significant changes almost immediately in the light scattering profilebetween 15◦ and 60◦. In this study, the same procedure was followedexcept that the cells were irradiated at 662 nm with 1 J/cm2. Therewere no observed changes until 60 min after irradiation, at whichpoint significant changes were observed in the light scattering profile.However, the changes were observed in the forward-scattering direc-tion (<15◦), reminiscent not of the changes observed with alterationsin lysosomal morphology (Fig. 5.4), but of mitochondrial morphology(Fig. 5.2). The coated sphere model was applied as discussed above,and significant mitochondrial swelling, in which the mitochondriaswells and fills with cytosol on the inside, was observed at 60 min(Fig. 5.6). Using a fluorophore-conjugated antibody against cy-tochrome c in permeabilized cells, fluorescence imaging showed thatat the 60 min time point, where mitochondrial swelling is observedby light scattering, there is also a significant release of cytochromec. This study leads to seemingly counterintuitive conclusions. Lyso-somes were photodynamically insulted; yet no changes in lysosomalmorphology were observed in the light scattering profile. However,changes (swelling) are observed in mitochondrial morphology via thelight scattering profile, and these changes are linked to a release of cy-tochrome c. Lysosomal PDT has been previously observed to initiatethe release of cytochrome c and, as discussed above, mechanisms un-derlying this behavior have been hypothesized. The conclusions ofthis study enrich the investigation of this phenomenon in that thisprocess is linked to changes in mitochondrial morphology, and alsothis was a first example of a connection between changes in light scat-tering and intracellular signaling.


(a) (b)

(d)(c)

p < 0.01

p > 0.99

p > 0.99

NPe6 drug controlNPe6 + 1 J/cm2 + 60 min

NPe6 drug control

NPe6 + 1 J/cm2 + 60 min

NPe6 drug control

NPe6 + 0.5 J/cm2 + 60 min

NPe6 drug control

NPe6 + 1 J/cm2

Sca

tter

ed li

gh

t in

ten

sity

Sw

ellin

g p

aram

eter

(%

)

Time post-PDT (min)

Sca

tter

ed li

gh

t in

ten

sity

Sca

tter

ed li

gh

t in

ten

sity−1

−2

−3

−1

−2

−4

−3

−1

−2

−3

FIGURE 5.6 Angularly resolved light scattering data [15]. (a–c) Representscattering data from cells sensitized with NPe6 vs. cells that were sensitizedand irradiated with either 0.5 or 1.0 J/cm2 at two time points. P values(calculated by � 2 test) show that scattering data from cells 1 h after 1 J/cm2

was significantly different from control. (d) A representative time course in themitochondrial swelling parameter, �, for NPe6 control and 1 J/cm2

NPe6-PDT–treated cells.

5.4 Light Scattering Assessments of Nuclear MorphologyAll eukaryotic cells contain a nucleus, which is central to cell functionin addition to being an essential part of the cell structure. The nucleuscontains a membrane, a lamin scaffold, and chromatin; the chromatininteraction with the lamin network [16] and membrane largely definesnuclear architecture. Chromatin contains long molecules of DNA incomplex with histomes (chief among an assortment of other proteins)to form chromatin. Chromatin contains the genes that comprise thegenome of the cells. Chromatins are charged and mechanically inte-grated with the cellular cytoskeleton through lamins; therefore, theyare highly sensitive to the osmotic environment [17] as well as forces


transduced from the environment [18]. The cell nucleus–its mechan-ical properties and response to external forces–is important. The me-chanical properties of the cell nucleus have been associated withcancer [19], apoptosis [20], and stem cell differentiation [21], and theresponse of the nucleus to environmental stimuli is an active area ofresearch [22–25]. Changes in nuclear shape leading to conformationaladaptation in chromatin structure and organization affect transcrip-tional regulation [26]. The relative position of chromosomes is gen-erally consistent [27] and is likely compartmentalized into discreteterritories [28]. The location of a gene within a chromosome terri-tory affects its access to mechanisms responsible for specific cellularfunctions; therefore, changes in position affect genome regulation. Forthese reasons, techniques that could monitor the shape of the nucleusin response to external cues would be very powerful. There are in-dications that this monitoring could be provided accurately by lightscattering techniques.

It was first demonstrated using light scattering spectroscopy (LSS)that light scattering is sensitive to the cell nucleus and its structure [29].LSS was subsequently used to detect abnormalities in epithelial cellnuclei associated with neoplasia, a precancerous state [30]. Backmanet al. further extended the capabilities of LSS by assessing the spec-trum of scattered light at various angles to obtain information aboutcell nuclei and smaller structures [31]. Wax et al. subsequently de-veloped angle-resolved low-coherence interferometry (a/LCI), whichenabled depth-resolved assessment of the average nuclear size in bi-ological samples. By incorporating coherence gating into light scat-tering, a/LCI detects only singly scattered light from cell samples,thereby reducing detection noise caused by multiply scattered light.Additionally, a/LCI uses a backscattering detection geometry, whichhas been demonstrated to be particularly sensitive to light scatteredfrom the cell nucleus [32, 33]. While the a/LCI technique has beenused primarily for detecting neoplasia in tissue epithelial layers [34–36] (see also Chap. 13), the current section will focus on new effortsto use a/LCI to deduce nuclear morphology and deformation in cellbiology studies, which could provide a means for monitoring nuclearshape changes in response to environmental stimuli.

A/LCI, like most light scattering techniques, has typically useda Mie theory–based ILSA algorithm. The ILSA algorithm is similarto the algorithm discussed in previous sections, in that test functionsT(�) calculated from Mie theory are coalesced into a database rangingover a wide parameter space spanning size, standard deviation of sizedistribution, refractive index of medium (cytoplasm), and refractiveindex of scatterer (cell nucleus). The measured and processed scatter-ing signal I (�) is then compared to the elements of the database, andthe most probable scattering configuration is deduced based uponminimizing Eq. (5.7).


One factor that complicates deduction of nuclear size from theangle-resolved backscattered signal is that the signal includes con-tributions from structures other than the cell nucleus. Included in thebackscattered signal is scattering from the cell itself, smaller organellessuch as mitochondria, the cell nucleus, and higher order correlationsfrom the cell nucleus [33]. Furthermore, the spatial variations in theelectric field arise from interactions with a material comprising an in-homogeneous distribution of refractive indices. The component of thescattered field for each spatial frequency can be related to variationsin the dielectric constant of the inhomogeneous medium, such as abiological cell, which scattered the light:

E(�k⊥ ≈ k��

)∝ ∂ε

(�k⊥)

(5.10)

where �k⊥ represents the transverse component of the optical fieldwave vector [37]. The Fourier transform of the spatial variations inthe dielectric constant of the medium is

∂ε(�k⊥)

=∫

d2�r⊥di�k⊥·�r⊥∂ε (�r⊥). (5.11)

It is assumed that variations in the dielectric constant arise fromfluctuations in the density of the medium, ∂� (�r⊥):

�E (r ) =⟨E(�r ′

⊥)

E∗(�r ′⊥ + r ��

)⟩∝⟨∂�(�r ′

⊥)∂�(�r ′⊥ + r ��

)⟩≡ �� (r ).

(5.12)

Therefore, the Fourier transform of the scattering signal, whichis the two-point correlation function of the optical field, �E(r ), can berelated to the two-point correlation function of the density fluctuationsalong the direction defined by the angle �[2].

The direct relationship between scatterer size and the spatial fre-quencies of the scattered field can be exploited in the processing of thescattering signal. The signal can be low-pass filtered to remove higherorder correlations and the scattering from the cell itself, which is, bydefinition, larger than the nucleus and therefore contributes higherfrequencies to the signal. Moreover, organelles that are smaller thanthe nucleus contribute a slowly varying background, a variation thatdoes not contribute oscillations in the observed angular range (180◦

to ∼150◦). Scattering contributions from organelles smaller than thenucleus are removed by fitting a second-order polynomial to the low-pass filtered signal and subtracting the best-fit second-order polyno-mial [32]. This subtraction also removes the zeroth-order diffractionfrom the signal; therefore, a second-order polynomial (representingthe zeroth-order diffraction of the modeled signal) must be similarly


removed from the test functions T(�) in the database before the ILSAalgorithm is performed.

Chalut et al. applied the a/LCI technique using the Mie theory–based ILSA algorithm to assess the size of chondrocyte cell nuclei[23]. The native morphology of chondrocyte cell nuclei is known to behighly spherical; therefore, this experiment provided a solid frame-work for demonstrating the ability of light scattering techniques em-ploying Mie theory to deduce nuclear size. Osmotically stressed chon-drocyte cells were used as a model system to induce small changesin nuclear volume: The volume of chondrocyte cells is sensitive toextracellular osmolarity [38, 39], and small changes in the volume ofchondrocyte cells induce changes in the volume of their nuclei, in-dependent of the cytoskeleton [17]. The osmolarity of the media waschanged to induce small changes in nucleus volume, and then the un-stained sample was measured immediately after the change of mediawith the a/LCI system in order to demonstrate its ability to measurenuclear size. Independent measurements were performed using im-age analysis of fluorescently labeled, unfixed cells in correspondingsalinity to verify the accuracy of the a/LCI technique.

Chondrocyte cells were seeded at high density and equilibratedwith 500, 400, and 330 mOsm saline solution, in that order, for thea/LCI experiments. The nuclear diameters were measured as 6.45 ±0.30 �m, 6.60 ± 0.19 �m, 6.96 ± 0.27 �m, respectively, in the formof mean ± SD. There were statistically significant differences at a95% confidence level for all pairwise comparisons between differ-ent osmolarities for the a/LCI results. In the separate image analy-sis experiments at the same osmolarities, the measured nuclear di-ameter were 6.57 ± 0.33 �m, 6.78 ± 0.30 �m, 6.96 ± 0.29 �m. Theresults are summarized in Fig. 5.7. The a/LCI measurements of nu-clear volume are within 3% accuracy of the measurements obtained byimage analysis, indicating the potential of this technique for studiesof nuclear deformation in cell biology studies. It is noteworthy that, atlower osmolarities, the nucleus is larger and presents a more roundedmorphology. However, at 500 mOsm, the nucleus presents a muchmore complex morphology, which could explain why the accuracy ofthe a/LCI results decreases with increasing osmolarity.

A complicating factor for using light scattering to assess nuclearmorphology is that, unlike forward-scattered light [1], backscatteredlight is sensitive to scatterer shape. Mie theory calculates the light scat-tered from spherical objects; however, this is not necessarily a realisticmodel for cell nuclei, which can be more generally described as ellip-soidal. The geometric incompatibility does not obviate the use of Mietheory–based ILSA algorithms for deducing the size of nonsphericalscatterers, however. The a/LCI algorithm has been used to deducestructural changes in the nucleus morphology of cuboidal and colum-nar epithelial tissues [34, 35], in which the ellipsoidal nuclei present


Image analysisa/LCI technique

Image analysis measurements

a/LCI measurements

0.01.02.03.04.0

7.0

5.06.0

8.0S

ize

(µm

)

330 mOsm

330 mOsm

400 mOsm

400 mOsm

500 mOsm

500 mOsm

size6.966.96

S.D.0.290.27

S.E.M0.060.07

size6.786.60

S.D.0.30.19

S.E.M0.070.05

size6.576.45

S.D.0.330.30

S.E.M0.070.08

Osmolarity

FIGURE 5.7 Results of measurements of chondrocyte cell nuclei using QIAand the a/LCI technique [38]. Chondrocyte cell nuclei change volume with achanging media osmolarity. Each error bar corresponds to the standard errorof the mean in the 95% confidence interval. Both experiments demonstrate asignificant (p < 0.05) increase in nuclear size with decreasing osmolarity, aspredicted by previous results [17].

their axis of symmetry parallel to the axis of light propagation. Thisorientation of ellipsoidal nuclei, defined here as axially symmetric,was explored by Keener et al. [40]. In this study, simulated data foraxially symmetric ellipsoidal nuclei were modeled using a T-matrixlight scattering theory [41]. The T-matrix light scattering theory, whichwill be described in more detail later, calculates light scattered fromellipsoidal dielectric scatterers. These simulated data were input intothe Mie theory–based ILSA algorithm described above. The conclu-sion was that the size deduced by the ILSA algorithm correspondedto the equatorial axis of the ellipsoid. Therefore, it was concluded thatthe equatorial axis was the size measured in studies possessing an axi-ally symmetric scattering geometry, including cuboidal and columnarepithelial tissues.

An additional study was performed by Chalut et al. [42] to inves-tigate the efficacy of Mie theory–based ILSA algorithms in deducingthe structure of ellipsoidal scatterers in the axially transverse scat-tering geometry, which is defined as ellipsoids oriented with theiraxis of symmetry orthogonal to the axis of light propagation. Themethodology in this study was similar to the Keener et al. study de-scribed previously, which studied axially symmetric scattering ge-ometries. While Keener’s study was interested in a geometry withparticular relevance to clinical applications, in particular geometriesencountered in epithelial layers important to cancer studies, Chalutet al.’s study explored geometries particularly relevant to cell biol-ogy studies, in which cells adhere to a substrate and spread, form-ing ellipsoidal shapes with symmetry axes orthogonal to the axis oflight propagation. A T-matrix light scattering model was again usedto simulate data from axially transverse geometries in a range of


scattering sizes and refractive indices. Several conclusions werereached in this study. First, across the sizes, refractive indices, andaspect ratios of the ellipsoidal scattering geometries that were inves-tigated, the size determined by the Mie theory–based ILSA algorithmwas almost universally proximate to either the equatorial axis or polaraxis of the scattering ellipsoid. However, the best-fit size determina-tion was not an evident function of scattering orientation or incidentlight polarization. Another conclusion was that the signal condition-ing step in which the best-fit second-order polynomial was subtractedfrom both the simulated data and the test functions was essential forthe success of this method. If this step was not used, there was nocorrelation between the characteristic sizes of the scattering ellipsoidand the best-fit size determination of the Mie theory–based ILSA al-gorithm. This very likely indicates that, while there are similarities inthe frequency of oscillations between ellipsoidal and spherical scat-tering data for similar objects, there is no corresponding relationshipbetween the general trends of the data.

The conclusions of the previously described study were testedin biological samples. Chalut et al. [23] used substrate topographyto deform cells and their nuclei in preferred orientations in order todemonstrate the ability of light scattering to deduce the shape of thecell nuclei. The substrate used for this study employed a grating witha periodicity in the submicron range, which has been shown to orientand elongate smooth muscle cells [43] and human mesenchymal stemcells [44] with a corresponding orientation and elongation of the cellnucleus. Those studies also demonstrated phenotypic changes in pro-liferation, motility, and gene expression. In this study, macrophageswere cultured on the microgratings. Image analysis indicated that thecells and their nuclei oriented and elongated in the direction of thegrating. A/LCI measurements were performed on these samples incombinations of two different orientations–the grating transverse tothe electric field of the incident light and the grating transverse to themagnetic field of the incident light–and two different incident lightpolarizations, S22 and S11. Similar to the predictions of the previouslydiscussed study, the size determination was not an evident functionof orientation or polarization; however, when pooled, the best-fit sizedeterminations represented a bimodal size distribution separated bythree standard deviations. The smaller size determination was 6.50 ±0.50 �m (mean ± SD) and the larger size determination was 10.53 ±1.16 �m. Image analysis of the nuclei of similarly prepared samplesindicated that the macrophage cell nuclei were well oriented alongthe direction of the grating and that the minor axis of the nucleus was6.39 ± 1.30 �m while the major axis of the nucleus was 10.30 ± 2.18�m, yielding an aspect ratio of 0.62. Remarkably, these results corre-spond almost identically to the smaller and larger size determinationyielded, respectively, by the a/LCI technique. In fact, if the smaller


Image analysis measurements a/LCI measurements

Image analysisa/LCI technique

0.0

2.0

4.0

6.0

8.0

10.0

12.0

(a) (b)

0.0

2.0

4.0

6.0

8.0

10.0

12.0

Siz

e (µ

m)

Siz

e (µ

m)

Long shortPlanar controls

Planar controls Short Long Aspect ratio

PDMS gratingLong short

Planar controls PDMS grating

size5.896.46

size6.396.50

S.D.0.960.61

S.E.M0.220.38

size10.3010.53

S.D.1.780.50

S.E.M0.340.23

mean0.620.62

S.D.2.181.16

S.E.M0.420.47

S.E.M0.020.04

FIGURE 5.8 Results of measurements of macrophage cell nuclei using (a) QIAusing DAPI and (b) a/LCI technique [38]. These results were obtained using aMie theory–based ILSA technique described in the text. The samples arecultured on poly(dimethyl siloxane) (PDMS) microgratings and were orientedand elongated along the direction of the grating, while the control sampleswere cultured on planar glass surfaces. Error bars are standard error at 95%confidence interval. Nucleus elongation is statistically significant (p < 0.01)for both a/LCI and image analysis measurements.

and larger size determinations yielded by the a/LCI technique areconsidered a measurement of the minor and major axis of the nuclei,the aspect ratio is 0.62, in exact agreement with the results of imageanalysis. These results are summarized in Fig. 5.8.

The conclusions of this study are in good agreement with the mod-eling study performed by Chalut et al. There are several conclusionsto be drawn from these studies. First, a Mie theory–based ILSA algo-rithm can produce highly useful results of nuclear morphology evenin the case of ellipsoidal nuclei. Clearly, if one wants only a reasonableestimate of nuclear morphology in a study, this technique could pro-vide that. Also, it is worth noting at this time that Mie theory is veryeasy to implement and can be calculated over the entire biologicallyrelevant parameter space. Therefore, if a sample contains scattererswith large size parameters and/or extreme aspect ratios, this tech-nique may be desirable compared to alternatives such as FDTD ora T-matrix method, which break down when computing scatteringfrom extreme geometries. However, both studies point to a flaw inthis technique: There is no way of predicting whether the size deter-mination resulting from a study of these axially transverse ellipsoidalnuclei yields the major or the minor axis in a given measurement.Because of this, many measurements must be made to compile suffi-cient statistics, and the possibility of determining the shape of nearlycircular nuclei is elided. There is a need, therefore, to explore lightscattering models that account for more realistic nucleus shapes.


Giacomelli et al. investigated the use of a T-matrix–based ILSA al-gorithm, which is capable of calculating the scattered fields from morecomplicated geometries, including spheroids, ellipsoids, Chebyshevparticles, and cylinders [45]. The motivation of this exploration wasto discern if nuclear size and aspect ratio could be simultaneously as-sessed. There is a host of literature on the T-matrix method (the readercan start with Refs. [41, 46]). The T-matrix method, briefly, expandsthe incident and scattered waves in regular and outgoing vector spher-ical wave functions (VSWFs), respectively, and then relates the wavesto a transfer operator. The transfer operator is the T matrix, which isdefined as Esca = T(E inc). The incident and scattered fields are relatedto the surface field coefficients to form the matrix Q and RgQ, re-spectively, and the T matrix is obtained from T = −RgQ(Q)−1. Q andRgQ comprise surface integrals of products of VSWFs; they are explic-itly dependent on size, shape, and refractive index. The mathematicalrecipes necessary for implementing the T-matrix method are coveredin Mischenko’s book and Tsang’s book. It is important to note, how-ever, that a matrix conversion is required; therefore, rounding errorcan prevent convergence for particles much larger than a wavelength.

For the purposes of assessing nucleus size and aspect ratio, a T-matrix database was generated using public domain extended (128bit) precision FORTRAN codes provided by Mischenko. Modifica-tions were made so that parallel processing could be used. As a testof the T matrix–based ILSA algorithm, two identically prepared sam-ples of MCF-7 cells were used in two different experiments. In thefirst, N = 43 measurements of the sample were recorded using thea/LCI system; in the second, the cells were stained and fixed usingDAPI, a nuclear dye, and N = 50 cell nuclei were analyzed for sizeand aspect ratio. The T-matrix database simulated scatterers using830 nm illumination, with equivalent volume diameters ranging from7.5 to 12.5 �m and an aspect ratio ranging from 0.56 to 1.0. The re-fractive index of the cytoplasm ranged from 1.35 to 1.36, while therefractive index of the nucleus ranged from 1.42 to 1.43. The MCF-7cell nuclei were assumed to be randomly oriented with respect to theoptical axis. This database was plugged into the Mie theory–based al-gorithm described above to deduce equivalent volume diameter andaspect ratio.

The results are shown in Fig. 5.9: the a/LCI technique reached is inalmost exact agreement with QIA. Several conclusions can be drawnfrom these results. First, a T-matrix–based ILSA algorithm showsgreat promise for simultaneously measuring the size and shape of cellnuclei. Simultaneous measurement of these two parameters elimi-nates the need for trying to deduce them separately in a Mie theory–based ILSA algorithm by changing incident light polarization andsample orientation. Additionally, the uncertainty arising due to thelack of an evident causal relationship between sample orientation/


0.0

4.0

8.0

2.0

6.0

10.0

0.0

0.2

0.4

0.6

0.8

1.0

Equal volume diameter

Equ

al v

olum

e di

amet

er (

µm)

Aspect ratio

Asp

ect r

atio

Quantitative image analysis

a/LCI

FIGURE 5.9 Measurements of the average equal volume diameter and aspectratio of MCF-7 cell nuclei by QIA using DAPI stain and a/LCI technique [45].Error bars are standard error at 95% confidence interval.

incident light polarization and size determination is avoided. How-ever, these advantages are counterweighted by a significant computa-tional cost. Computation of a T-matrix database can take hours or daysusing parallel processing, while it is completely intractable withoutparallel processing. Nevertheless, the T matrix must only be calcu-lated once for a given geometry and set of refractive indices; it canthen be freely rotated.

The work discussed here establishes a solid foundation for us-ing light scattering to accurately deduce nuclear deformation, whichcould be very important for studies of cell biology. It is becomingclear that the shape of the nucleus is an indication of its function, andobserving how the nucleus changes shape is important in understand-ing the link between external stimuli and function. However, muchremains to be understood about the connection between nucleus de-formation and function, and tools must be developed to investigatechanges in nuclear shape. Light scattering is a promising tool for in-vestigating this connection, because it is nonperturbative and highthroughput and is displaying a promising level of accuracy in assess-ing nuclear deformation.

5.5 Light Scattering Assessments of GeneralSubcellular StructurePrevious sections describe significant advances in accurately connect-ing a specific organelle within the cell to its light scattering signature.


This connection facilitates investigations of more general subcellularstructure, which can considerably impact studies of cell biology. Arecent study of cellular apoptosis by Chalut et al. [47] explored thepossibility of assessing subcellular structure and its capabilities formonitoring cell function. In this study, the authors employed a fractaldimension formalism to detect changes in the light scattering profileof cells undergoing chemotherapy-induced apoptosis. The fractal di-mension of a biological sample is discerned in the following way. First,the predicted nuclear scattering is subtracted from the measured nu-clear scattering (which is low-pass filtered as discussed previously) toyield the residual scattering, which is due to small organelles (∼2 �m).Second, the residual is Fourier transformed to yield the two-point den-sity correlation function of small organelles, which generally exhibitsan inverse power-law function [2]. Inverse power laws in density cor-relation functions indicate self-similarity in a sample, which signifies afractal nature in the packing of subcellular structures [2]. The exponentof the power law can be used to deduce the mass fractal dimension ofthe sample in three dimensions.

In the apoptosis study, the authors administered two differentchemotherapy drugs, Doxurubicin and Paclitaxel, to MCF-7 breastcancer cells. Highly significant increases were observed in the fractaldimension of the samples as soon as 90 min after treatment (Fig. 5.10).An increasing fractal dimension is indicative of an increasing granu-larization, or increasingly punctate nature, in the sample. Intriguingly,in both treatments, the fractal dimension recovered slightly at the6 h time point, and then increased again at 12 h and beyond. Afteranalyzing images of labeled mitochondria and nuclei in the treatedcells, the authors concluded that there were two different structuralchanges responsible for the change in fractal dimension at two dif-ferent times. The early changes in fractal dimension were caused atleast in part by structural changes in mitochondria, while the laterchanges were caused at least in part by the fragmentation of the nu-cleus. Although the authors were not able to exclude the possibil-ity that other structural changes in the cells were responsible for achange in fractal dimension, this finding indicates that light scatter-ing is sensitive to structural changes in multiple locations within thecell.

One important finding in this study was that the fractal dimen-sion exhibited highly significant changes, and specifically, the highlevel of significance was achieved due to the use of the T-matrixformalism for modeling scattering from the cell nucleus. When Mietheory was used, no consistent changes in fractal dimension wereobserved. This investigation emphasizes the importance of continu-ing to search for accurate light scattering models for studies of cellbiology.


FIGURE 5.10 Paclitaxel and doxorubicin induce a significant change in themass FD of MCF-7 cells. Summary of mass FD results for MCF-7 cells treatedwith (a) 5 nM Paclitaxel and (b) 5 �M Doxorubicin at t = 3, 6, 12, and 24 hposttreatment. (c) Comparison of cells treated with 5 nM Paclitaxel andcontrols at t = 1.5 h. ∗Indicates statistical significance (p < 0.05).∗∗Indicates high statistical significance (p < 0.001). (Source: Taken fromRef. [48].)

5.6 Future PerspectivesIn contrast to techniques based on biochemical or molecular bio-logical approaches, light scattering is label-free, and measurementsare performed on cells that have not been perturbed even slightly.


To this point, light scattering techniques have shown great poten-tial for accurately monitoring the morphological changes in mito-chondria, lysosomes, and nuclei. Morphological changes in thesethree organelles play a role, either directly or indirectly, in apopto-sis, metabolic activity, proliferation, mitosis, and differentiation. Ad-ditionally, Wax et al. showed that light scattering is sensitive to thespatial correlations over small lengths scales in a cell sample. Theyfurther showed that these correlations take the form of an inversepower law, indicating a fractal nature in the packing of subcellularstructures. One of the authors (Chalut) has obtained considerable,unpublished evidence that exploiting the sensitivity of light scatter-ing to subcellular organization can be used to give clues to stem celldifferentiation. Clearly, light scattering techniques can play an impor-tant role in studies of cell biology, particularly in monitoring struc-tural changes that are associated with alterations in the function ofa cell.

There are three important perspectives for the future of light scat-tering techniques in cell biology. The first is to continue exploring whatstructural and compositional changes light scattering is sensitive to.The second is to link these structural changes to changes in cell func-tion. This is more difficult, because it will involve intense collaborationwith biologists and biophysicists, but it is arguably more important,because these collaborations will result in more widespread use oflight scattering in cell biology. The hope is that these collaborationswill enable discoveries that may not be possible with currently avail-able biochemical methods. Third, light scattering techniques must beimplemented in ways that are accessible to cell biologists. Cottrell et al.have made inroads here [48], in which the authors developed a micro-scope that is a multifunctional imaging and scattering spectroscopysystem built around a commercial inverted microscope platform. Es-sentially, this technique measures the light scattered from a cell samplewith the simultaneous capability of using fluorescence-based tech-niques. This microscope could have important implications for boththe second and third future perspective.

Given these future perspectives, although there is much work to bedone to more widely establish light scattering as a tool for cell biology,we hope that the research summarized in this chapter demonstratesthat it is certainly worthwhile to pursue scattering in this context.There are few tools available that offer such exquisite sensitivity tobiological structure and none that can assess this structure nonin-vasively and with such a high detection speed. We expect that theadvances reviewed in this chapter will empower important future in-vestigations of functional relationships in cell biology that will securea place for light scattering as an invaluable tool for the study of livingsystems.


References1. Mourant, J. R., J. P. Freyer, A. H. Hielscher, A. A. Eick, D. Shen, and T. M.

Johnson, Mechanisms of light scattering from biological cells relevant to non-invasive optical-tissue diagnostics. Appl Opt, 1998. 37(16): pp. 3586–3593.

2. Wax, A., C. H. Yang, V. Backman, K. Badizadegan, C. W. Boone, R. R. Dasari,and M. S. Feld, Cellular organization and substructure measured using angle-resolved low-coherence interferometry. Biophys J, 2002. 82(4): pp. 2256–2264.

3. Green, D. R. and J. C. Reed, Mitochondria and apoptosis. Science, 1998.281(5381): pp. 1309–1312.

4. Hackenbrock, C. R., Ultrastructural bases for metabolically linked mechanicalactivity in mitochondria. I. Reversible ultrastructural changes with change inmetabolic steady state in isolated liver mitochondria. J Cell Biol, 1966. 30(2): pp.269–297.

5. Petit, P. X., M. Goubern, P. Diolez, S. A. Susin, N. Zamzami, and G. Kroemer,Disruption of the outer mitochondrial membrane as a result of large amplitudeswelling: the impact of irreversible permeability transition. FEBS Lett, 1998.426(1): pp. 111–116.

6. Boustany, N. N., R. Drezek, and N. V. Thakor, Calcium-induced alterationsin mitochondrial morphology quantified in situ with optical scatter imaging.Biophys J, 2002. 83(3): pp. 1691–1700.

7. Boustany, N. N., Y. C. Tsai, B. Pfister, W. M. Joiner, G. A. Oyler, and N. V. Thakor,BCL-xL-dependent light scattering by apoptotic cells. Biophys J, 2004. 87(6):pp. 4163–4171.

8. Wilson, J. D., C. E. Bigelow, D. J. Calkins, and T. H. Foster, Light scattering fromintact cells reports oxidative-stress-induced mitochondrial swelling. Biophys J,2005. 88(4): pp. 2929–2938.

9. Press, W. H., B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, NumericalRecipes in C: The Art of Scientific Computing. 1992, New York: Cambridge Uni-versity Press.

10. Boya, P. and G. Kroemer, Lysosomal membrane permeabilization in cell death.Oncogene, 2008. 27(50): pp. 6434–6451.

11. Reiners, J. J., Jr., J. A. Caruso, P. Mathieu, B. Chelladurai, X. M. Yin, and D. Kessel,Release of cytochrome c and activation of pro-caspase-9 following lysosomalphotodamage involves Bid cleavage. Cell Death Differ, 2002. 9(9): pp. 934–944.

12. Wilson, J. D. and T. H. Foster, Mie theory interpretations of light scatteringfrom intact cells. Opt Lett, 2005. 30(18): pp. 2442–2444.

13. Wilson, J. D., W. J. Cottrell, and T. H. Foster, Index-of-refraction-dependentsubcellular light scattering observed with organelle-specific dyes. J Biomed Opt,2007. 12(1): p. 014010.

14. Wilson, J. D. and T. H. Foster, Characterization of lysosomal contribution towhole-cell light scattering by organelle ablation. J Biomed Opt, 2007. 12(3):p. 030503.

15. Wilson, J. D., B. R. Giesselman, S. Mitra, and T. H. Foster, Lysosome-damage-induced scattering changes coincide with release of cytochrome c. Opt Lett,2007. 32(17): pp. 2517–2519.

16. Goldman, R. D., Y. Gruenbaum, R. D. Moir, D. K. Shumaker, and T. P. Spann,Nuclear lamins: building blocks of nuclear architecture. Genes Dev, 2002. 16(5):pp. 533–547.

17. Guilak, F., Compression-induced changes in the shape and volume of the chon-drocyte nucleus. J Biomech, 1995. 28(12): pp. 1529–1541.

18. Dalby, M. J., M. J. Biggs, N. Gadegaard, G. Kalna, C. D. Wilkinson, and A. S.Curtis, Nanotopographical stimulation of mechanotransduction and changesin interphase centromere positioning. J Cell Biochem, 2007. 100(2): pp. 326–338.

19. Backman, V., M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Muller,Q. Zhang, G. Zonios, E. Kline, J. A. McGilligan, S. Shapshay, T. Valdez, K.Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler,


R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, Detection of preinvasivecancer cells. Nature, 2000. 406(6791): pp. 35–36.

20. Kerr, J. F., A. H. Wyllie, and A. R. Currie, Apoptosis: a basic biological phe-nomenon with wide-ranging implications in tissue kinetics. Br J Cancer, 1972.26(4): pp. 239–257.

21. Constantinescu, D., H. L. Gray, P. J. Sammak, G. P. Schatten, and A. B. Csoka,Lamin A/C expression is a marker of mouse and human embryonic stem celldifferentiation. Stem Cells, 2006. 24(1): pp. 177–185.

22. Dahl, K. N., A. J. Engler, J. D. Pajerowski, and D. E. Discher, Power-law rheologyof isolated nuclei with deformation mapping of nuclear substructures. BiophysJ, 2005. 89(4): pp. 2855–2864.

23. Chalut, K. J., S. Chen, J. D. Finan, M. G. Giacomelli, F. Guilak, K. W. Leong,and A. Wax, Label-free, high-throughput measurements of dynamic changes incell nuclei using angle-resolved low coherence interferometry. Biophys J, 2008.94(12): pp. 4948–4956.

24. Dahl, K. N., P. Scaffidi, M. F. Islam, A. G. Yodh, K. L. Wilson, and T. Mis-teli, Distinct structural and mechanical properties of the nuclear lamina inHutchinson-Gilford progeria syndrome. Proc Natl Acad Sci U S A, 2006. 103(27):pp. 10271–10276.

25. Cui, Y. and C. Bustamante, Pulling a single chromatin fiber reveals the forcesthat maintain its higher-order structure. Proc Natl Acad Sci U S A, 2000. 97(1):pp. 127–132.

26. Dahl, K. N., A. J. Ribeiro, and J. Lammerding, Nuclear shape, mechanics, andmechanotransduction. Circ Res, 2008. 102(11): pp. 1307–1318.

27. Heslop-Harrison, J. S., Comparative genome organization in plants: from se-quence and markers to chromatin and chromosomes. Plant Cell, 2000. 12(5):pp. 617–636.

28. Cremer, T. and C. Cremer, Chromosome territories, nuclear architecture andgene regulation in mammalian cells. Nat Rev Genet, 2001. 2(4): pp. 292–301.

29. Perelman, L. T., V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S.Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, andM. S. Feld, Observation of periodic fine structure in reflectance from biologicaltissue: A new technique for measuring nuclear size distribution. Phys Rev Lett,1998. 80(3): pp. 627–630.

30. Backman, V. and J. A. McGilligan, Detection of preinvasive cancer cells (vol406, pg 35, 2000). Nature, 2000. 408(6811): pp. 428–428.

31. Backman, V., V. Gopal, M. Kalashnikov, K. Badizadegan, R. Gurjar, A. Wax, I.Georgakoudi, M. Mueller, C. W. Boone, R. R. Dasari, and M. S. Feld, Measuringcellular structure at submicrometer scale with light scattering spectroscopy.IEEE J Select Top Q Electron, 2001. 7(6): pp. 887–893.

32. Pyhtila, J. W., R. N. Graf, and A. Wax, Determining nuclear morphology usingan improved angle-resolved low coherence interferometry system. Opt Express,2003. 11(25): pp. 3473–3484.

33. Pyhtila, J. W. and A. Wax, Coherent light scattering by in vitro cell arrays ob-served with angle-resolved low coherence interferometry. In: Coherence DomainOptical Methods and Optical Coherence Tomography in Biomedicine IX, Proc. SPIE2005. 5690: pp. 334–341.

34. Chalut, K. J., L. A. Kresty, J. W. Pyhtila, R. Nines, M. Baird, V. E. Steele, andA. Wax, In situ assessment of intraepithelial neoplasia in hamster trachea ep-ithelium using angle-resolved low-coherence interferometry. Cancer EpidemiolBiomarkers Prev, 2007. 16(2): pp. 223–227.

35. Pyhtila, J. W., K. J. Chalut, J. D. Boyer, J. Keener, T. D’Amico, M. Gottfried, F.Gress, and A. Wax, In situ detection of nuclear atypia in Barrett’s esophagus byusing angle-resolved low-coherence interferometry. Gastrointest Endosc, 2007.65(3): pp. 487–491.

36. Wax, A., C. H. Yang, M. G. Muller, R. Nines, C. W. Boone, V. E. Steele, G.D. Stoner, R. R. Dasari, and M. S. Feld, In situ detection of neoplastic trans-formation and chemopreventive effects in rat esophagus epithelium using


angle-resolved low-coherence interferometry. Cancer Res, 2003. 63(13): pp.3556–3559.

37. Landau, L. D. and E. M. Lifshitz, Electrodynamics of Continuous Media. 1960,Reading, MA: Cambridge University Press.

38. Bush, P. G. and A. C. Hall, The osmotic sensitivity of isolated and in situ bovinearticular chondrocytes. J Orthop Res, 2001. 19(5): pp. 768–778.

39. Guilak, F., G. R. Erickson, and H. P. Ting-Beall, The effects of osmotic stresson the viscoelastic and physical properties of articular chondrocytes. BiophysJ, 2002. 82(2): pp. 720–727.

40. Keener, J. D., K. J. Chalut, J. W. Pyhtila, and A. Wax, Application of Mie theoryto determine the structure of spheroidal scatterers in biological materials. OptLett, 2007. 32(10): pp. 1326–1328.

41. Mishchenko, M. I., L. D. Travis, and J. W. Hovenier, Light Scattering by Non-spherical Particles: Theory, Measurements, and Applications. 2000: Academic Press,London.

42. Chalut, K. J., M. G. Giacomelli, and A. Wax, Application of Mie theory to assessstructure of spheroidal scattering in backscattering geometries. J Opt Soc AmA Opt Image Sci Vis, 2008. 25(8): pp. 1866–1874.

43. Yim, E. K., R. M. Reano, S. W. Pang, A. F. Yee, C. S. Chen, and K. W. Leong,Nanopattern-induced changes in morphology and motility of smooth musclecells. Biomaterials, 2005. 26(26): pp. 5405–5413.

44. Yim, E. K., S. W. Pang, and K. W. Leong, Synthetic nanostructures inducingdifferentiation of human mesenchymal stem cells into neuronal lineage. ExpCell Res, 2007. 313(9): pp. 1820–1829.

45. Giacomelli, M. G., K. J. Chalut, J. H. Ostrander, and A. Wax, Application ofthe T-matrix method to determine the structure of spheroidal cell nuclei withangle-resolved light scattering. Opt Lett, 2008. 33(21): pp. 2452–2454.

46. Tsang, L., J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing. 1985:Wiley, New York.

47. Chalut, K. J., J. H. Ostrander, M. G. Giacomelli, and A. Wax, Light scatteringmeasurements of subcellular structure provide noninvasive early detection ofchemotherapy-induced apoptosis. Cancer Res, 2009. 69(3): pp. 1199–1204.

48. Cottrell, W. J., J. D. Wilson, and T. H. Foster, Microscope enabling multimodal-ity imaging, angle-resolved scattering, and scattering spectroscopy. Opt Lett,2007. 32(16): pp. 2348–2350.


C H A P T E R 6Light Absorption

and ScatteringSpectroscopicMicroscopies

Le Qiu, Irving Itzkan, and Lev T. Perelman

6.1 IntroductionThis chapter reviews biomedical applications of light absorption andscattering spectroscopic microscopies, which are optical imaging tech-niques that use light scattering spectra as a source of highly specificnative contrast of internal cell structures. Light absorption and scatter-ing spectroscopic microscopies combine the principles of microscopywith light scattering spectroscopy (LSS) [1–4], an optical techniquethat relates the spectroscopic properties of light that has been elasti-cally scattered by small particles to their size, refractive index, andshape. The multispectral nature of LSS enables it to measure internalcell structures much smaller than the diffraction limit without dam-aging the cell or requiring exogenous markers, which could affect cellfunction [5]. The confocal modality of light absorption and scatteringspectroscopic microscopies, called CLASS, approaches the accuracyof electron microscopy but is nondestructive and does not requirethe contrast agents common to optical microscopy [6]. Here, we dis-cuss the basic physical principles of LSS and CLASS microscopy. Wealso devote a significant amount of space to the discussion of applica-tions of light absorption and scattering spectroscopic microscopiesin such diverse areas as obstetrics, neuroscience, ophthalmology,

143


cellular and tissue imaging with nanoparticulate markers, and drugdiscovery.

There is a significant need for a tool that can monitor cells andsubcellular organelles on a submicrometer scale without causing celldamage or requiring exogenous markers that could affect cell function.The electron microscope (EM) can resolve subcellular structure withvery high resolution, but it can only work with nonviable cells andrequires considerable sample preparation. Thus, because of its non-destructive nature, researchers are studying various modifications ofoptical microscopy that can accomplish some of the same tasks as thoseof electron microscopy. However, standard optical microscopy lackscontrast in cells and thus requires the introduction of fluorophoresor other exogenous compounds to visualize subcellular structures.Optical microscopy is also diffraction limited and cannot resolve ob-jects much smaller than a wavelength, without employing complexsubdiffraction microscopy approaches.

Recently, Fang et al. [5] demonstrated experimentally that lightscattering spectra of various subcellular organelles can be used touniquely identify specific types of those organelles. Indeed, a veryimportant capability of LSS is that it provides an excellent and highlyspecific native contrast of internal cell structures by using a physicalparameter different from that used by other microscopy techniques.Here, light scattering spectra are the source of contrast. Another im-portant aspect of LSS is its ability to detect and characterize particleswell beyond the diffraction limit, as recently demonstrated by Itzkanet al. [6], Schuele et al. [7], Backman et al. [8], Wax et al. [9], and Fanget al. [10].

6.2 Absorption and Scattering inMicroscopic ApplicationsLight propagates through vacuum without change of direction, inten-sity, polarization, or wavelength. However, if light encounters matter,such as a biological particle, any of the above properties of light canchange. The particle could convert some of the light energy into otherforms of energy, such as heat or acoustic waves, or the particle mightredistribute all or part of the energy of the incoming light into lightpropagating in various directions. These phenomena are called ab-sorption and scattering, respectively.

In the case of absorption, the incoming photon excites a moleculewithin the particle to a higher energy state and disappears. The mech-anism of absorption depends strongly on the specific molecule andthe energy of the incident photon. Biological samples are frequentlycomposed of complex molecules and it is often a particular groupwithin a molecule that is responsible for the absorption. These groups

145L i g h t A b s o r p t i o n a n d L S S M i c r o s c o p i e s

are called chromospheres. Examples of biological chromospheres are[11] (1) peptide bonds in amino acids that have a strong absorptionband in the far-ultraviolet range (FUV); (2) purine and pyramidinebases and their derivatives in nucleic acids (DNA, RNA, NADH) thatabsorb energy in the middle to near UV (250–350 nm); (3) highly conju-gated systems such as porphyrin in red blood cells, which have strongabsorptions in the UV and visible regions; (4) transitions in metal com-plexes that cover the whole visible and part of the near-infrared range;(5) heme proteins that exhibit charge transfer.

When light propagates through a homogeneous absorbingmedium, it can be described using the Beer–Lambert–Bouguer law orsimply Beer’s law, which states that the intensity of light, I , traversingthe medium is

I = I0 e−�al (6.1)

where I0 is the intensity of the incoming light; l is the thickness of themedium; and �a is the absorption coefficient, which depends on theproperties of the medium. The absorption coefficient is proportional tothe sum of the molar concentrations of various chromophores presentin the medium ci multiplied by the chromophores’ molar extinctioncoefficients εi :

�a =∑

i

ci εi (6.2)

The exponential factor �al [Eq. (6.1)] is also often referred to as theoptical density (O.D.).

In microscopy, absorption is used either in a transmission geom-etry, which is also called bright-field microscopy, or in combinationwith reflection in a backreflection geometry. Absorption is one of themost basic and longest used sources of contrast in microscopy [12].However, live cells do not usually exhibits prominent chromospheres.Thus, to be able to image cells using absorption mechanisms, they areusually stained, which requires killing and fixing the cells. This is themajor limitation of absorption when used as the sole source of contrast.Another problem of absorption-based microscopy is artifacts due tothe above processing, which can significantly change the appearanceof the cell.

If, in addition to absorption, the medium also scatters light, thesituation becomes significantly more complex. Light scattering pro-cesses can be grouped into inelastic scattering and elastic scattering.The energy diagrams shown in Fig. 6.1 schematically show variouspossible scattering relaxation mechanisms.

In the case of elastic scattering, photon energy (and thus wave-length) is conserved. The electrons in the scattering medium are first


FIGURE 6.1 Energy diagram showing excitation and various possible physicalrelaxation mechanisms for (a) Rayleigh scattering, (b) fluorescencescattering, (c) two photon scattering, (d) phosphorescence scattering,(e) Raman scattering, ( f ) CARS scattering. See also color insert.

excited to a virtual state and then come back to the ground state (Fig.6.1a ). This type of molecular scattering is known as Rayleigh scat-tering and is the most common scattering process in the visible andnear-infrared spectral regions. We will discuss elastic scattering pro-cesses and their application to microscopy in the next section.

There are a variety of inelastic processes, where the energy (andwavelength) of the photon is not conserved. A frequently usedmicroscopy technique employs fluorescence scattering (Fig. 6.1b).Fluorescence is a three-step process, and the emission happens at awavelength longer than the excitation wavelength due to the photontransferring part of its energy to heat the medium via molecular ro-tations and vibrations. The time scale for excitation is femtoseconds,and the relaxation to heat happens on a picosecond to nanosecondtime scale. Fluorescent scattering–based microscopy is currently oneof the most popular approaches for specific high-resolution imagingof cells and tissues [13]. However, because native fluorescence of cellsand subcellular structures is often very weak or nonexistent, and lim-ited mainly to NADH and FAD, fluorescence microscopy is primarilyused in combination with exogenous fluorescence labels. As these la-bels can affect cell function and may exhibit staining artifacts, similarto those observed in absorption-based microscopy, there is a need fortechniques that use native sources of contrast in cells.

Another fluorescence-based technique is multiphoton fluores-cence scattering. In the case of multiphoton fluorescence (Fig. 6.1c),


several photons are involved, and thus the frequency of the excitationphotons is approximately one-half, one-third, etc., of the frequency ofthe emitted photon. Here, two or more photons with the same energyare required to reach the same molecule in the medium within approx-imately a femtosecond time interval. This can happen only at high-photon-density levels, such as at the focus of a laser beam, and thusthis technique offers an advantage for confocal microscopy by elim-inating need for a collection pinhole. Another important advantageof multiphoton fluorescence microscopy is the potential for imagingdeeper into a sample, as longer excitation wavelength photons usu-ally suffer less scattering and thus can penetrate deeper [14]. Theseclear advantages of multiphoton fluorescence microscopy come withcertain disadvantages such as the potential for thermal damage in thesample, but the main disadvantage comes from the fluorescence na-ture of this technique, as it also requires exogenous fluorescence labels.

Raman scattering is another interesting example of inelastic scat-tering, which is now used in microscopy [15]. In the case of nonres-onant Raman scattering (Fig. 6.1e), a molecule is excited to a virtualstate and has a small but nonzero probability to relax to a differentvibrational level in the ground state. The emission photon for this pro-cess has either less energy (Stokes line) or more energy (anti-Stokesline) than that of the excitation photon. The probability for such a pro-cess, that is, the Raman scattering cross section, is usually quite small,many orders of magnitude smaller than elastic or even fluorescencescattering cross sections in the majority of biological media [11]. On theother hand, Raman scattering is quite specific and exhibits very nar-row spectral lines, making it a good candidate for various microscopyapplications.

Finally, coherent anti-Stokes Raman scattering or CARS is a non-linear Raman-based scattering process, which is related to Ramanscattering in a way that is similar to the relationship of multipho-ton fluorescence and fluorescence scattering. CARS is a four-wavemixing process, which enhances significantly the anti-Stokes signal,providing the vibrational contrast of CARS microscopy [16].

While the above techniques each offer advantages and disadvan-tages, in this chapter, we will mainly discuss a different source ofmicroscopic contrast that is based on the spectral features of elasticlight scattering. This technique, called light scattering spectroscopy orLSS, is the main topic of the following sections.

6.3 Physical Principles and Basic Parametersof Elastic Light ScatteringFor the purposes of this chapter, which deals mainly with biomed-ical implications of elastic light scattering, we will make several


assumptions that will simplify the description of the light scatter-ing processes. First, we assume that the incident light is quasi-monochromatic and its amplitude fluctuates significantly slower thanthe frequency of the incident light. Second, we will only consider thescattering processes in the far-field zone. These concepts have beenintroduced and discussed in more detail in Chap. 1, section “Basicsof Light Scattering Theory,” and are reviewed here with slightly al-tered notation to agree with the literature on the subject matter in thischapter.

We will describe the field of the incoming light in the followingform:

Einc = E0 ei(�k·�r−�t) (6.3)

where E0 is a constant amplitude of the incoming field, k is the wavevector, and � is the frequency of incoming wave. If this field is scatteredby a particle, the distance to the point in space, r , where the scatteringis observed is always much larger than the particle’s characteristicsize and the wavelength . The scattering field can then be expressedusing the so-called scattering matrix S as (Fig. 6.2)

[Esca(�sca)Esca(�sca)

]= ei(kr−�t)

ikrS(nsca, ninc)

[Einc(�inc)Einc(�inc)

](6.4)

nsca = θsca × ϕsca

Scatter position

Scatter position

x

y

a

z

r

^ ^ ^

ninc = θinc × ϕinc^ ^ ^

θsca

→

^

θinc^

ϕsca^

ϕinc^

FIGURE 6.2Scatteringgeometry.


The scattering matrix S depends on the directions of incident andscattered waves as well as on the scatter’s size, shape, composition,and orientation. It can be further simplified by projecting both theincident and scattered fields on the axes parallel and perpendicular tothe scattering plane formed by the incident and outgoing wave vectordirections. In this case Eq. (6.4) becomes:

[Esca

E⊥sca

]= ei(kr−�t)

ikr

[S2S3

S4S1

] [Einc|E |

E⊥inc

](6.5)

The scattering matrix S provides the fundamental characteristicsof the scattering event. Any parameter describing various propertiesof scattering such as scattering cross section, scattering coefficient,phase function, etc., can be derived from S. The parameters mentionedabove, on the other hand, have clear physical meaning and are quiteconvenient in describing elastic light scattering.

For example, the differential scattering cross section [see also Eq.(1.7)] is used to describe the angular scattering intensity distribution.The probability for a photon to be scattered into direction nscawithincident direction ninc could be expressed as

d�(ninc, nsca)dnsca

= r2 Isca(nsca)Iinc(ninc)

(6.6)

where d�(ninc, nsca) is the differential scattering cross section, dnsca isthe scattering angle sin(�)d� d� (Fig. 6.2), r is distance from the scat-terer to the observer, Isca(nsca) is the scattering intensity, and Iinc(ninc)is the incident light intensity. Sometimes it is more convenient to useanother function—called the phase function—related to the differen-tial scattering cross section. The phase function f (ninc, nsca) is relatedto the differential scattering cross section via the following expression:

f (ninc, nsca) = 1�s

d�(ninc, nsca) (6.7)

By integrating d�(ninc, nsca) over full angle we can calculate thetotal scattering cross section [see also Eq. (1.5)] describing the totalscattered energy:

�sca =∫

4�

(d�

dnsca

)dnsca (6.8)

Another convenient parameter is the ratio of the total cross sectionto the geometrical cross section of the particle, which is called theq -factor (to avoid confusion with the second element of the Stokes


vector, which is also called Q-factor, we use lower case q ). It is definedas q = �sca/�a2, where a is the characteristic radius of the scatterer.

Using the total scattering cross section, we can introduce the scat-tering coefficient [see Eq. (1.10)], which is used to describe the like-lihood of a photon to be scattered while it is traveling through thescattering medium. For a medium consisting of a single type of parti-cles with number density N, the scattering coefficient is

�sca = N�sca (6.9)

The scattering coefficient has dimensions of inverse length andindeed is inversely proportional to the mean free path of the scatter-ing xmean = ∫∞

0 −x dP(x)dx dx = 1/�s, where P(d) = exp(−�s · d) is the

probability to find an unscattered photon in a scattering mediumafter it travels distance d. Interestingly, this behavior is identical tothe Beer–Lambert–Bouguer law for absorption from Eq. (6.1) with theonly difference that absorption coefficient here is replaced with thescattering coefficient.

For a medium consisting of a multiple types of scatters, the scat-tering coefficient becomes

�sca =∑

i

Ni �isca (6.10)

and the phase function is replaced by a mean phase function used toevaluate the effective angular scattering intensity distribution for agroup of particles. It is defined as

fmean(ninc, nsca) =∑

i Ni �isca · f (ninc, nsca)i∑

i Ni �isca

(6.11)

Finally, one more parameter used to describe scattering in cells andtissue is called the g-factor or average cosine of the scattering effect[see Eq. (1.12)]. Because in the majority of cases relevant to biomedicaloptics scattering depends only on the zenith angle �, the g-factor maybe defined as g = 2�

∫ �

0 cos(�) f (�)d cos(�). This parameter providesinformation on the asymmetry of the scattering phase function andthe relative contributions of forward scattering and backscattering.

6.4 Light Scattering from Cells andSubcellular StructuresAs explained in the previous section, all the above parameters of thescattered light could be derived from the amplitude scattering matrixS. Unfortunately, the exact solution for the wave equation that canprovide a scattering matrix is known only in a very limited number


of cases, and thus one would have to use various approximations ornumerical methods to calculate the scattering matrix. Here we brieflydescribe several of these approaches mainly concentrating on thosethat are used to describe light scattering from cells and subcellularstructures.

First, let us discuss characteristic scales and optical properties ofcompartments present in a cell (see also Chap. 1, section “Structureand Organization of Biological Tissue”). Although there are hundredsof cell types, the subcellular compartments in different cells are rathersimilar and are limited in number [4]. Any cell is bounded by a mem-brane, a phospholipid bilayer approximately 10 nm in thickness. Twomajor cell compartments are the nucleus, which has a size of 7–10�m, and the surrounding cytoplasm. The cytoplasm contains variousother organelles and inclusions. One of the most common organelles(and the largest after the nucleus) is a mitochondrion, which has theshape of a prolate spheroid. The large dimension of a mitochondrionmay range from 1 to 5 �m and the diameter typically varies between0.2 and 0.8 �m. Other smaller organelles include lysosomes, which are250–800 nm in size and of various shapes, and peroxisomes, which are200 nm to 1.0 �m spheroidal bodies of lower densities than the lyso-somes. Peroxisomes are more abundant in metabolically active cellssuch as hepatocytes where they are counted in hundreds.

Sizes and refractive indices of major cellular and subcellular struc-tures are presented in Fig. 6.3. In this figure, we also provide theinformation on the relevant approximations that can be used to de-scribe light scattering from these objects.

Hierarchy of scales inside of a cell

Shape:10 µm

1 µm

0.1 µm

0.01 µm

Membranes

Macromolecular aggregates

Miescattering

Rayleighscattering

Cells

• Nucleus:

Refractive indes• Cytoplasm, n ~ 1.36• Organelles, n ~ 1.42

ellipsoid• Mitochondria: spheroid

• Peroxisome: sphere• Lysosome: sphere

Nucleus, nucleolus

Lysosomes, peroxisomesmicrosomes

Mitochondria

FIGURE 6.3 Optical properties of cellular and subcellular structures andrelevant approximations that can be used to describe light scattering fromthose objects.


P

QO

B

A

b

nsca

r→

^

ninc^

θ

FIGURE 6.4Geometry of theRayleigh–Gansscatteringapproximation.

The first approximation we discuss here is the Rayleigh–Gans ap-proximation, which is very important for describing subcellular scat-tering [17]. It can be used if two important conditions are satisfied:(1) the relative refractive index of a particle is close to unity and (2)the light wave propagating through a scatterer undergoes only smallphase shifts. These conditions are usually satisfied for the majority ofsmall organelles (Fig. 6.3). Then the scatterer (organelle) can be treatedas a linear array of noninteracting dipoles and the scattering matrixin the Rayleigh–Gans approximation becomes (Fig. 6.4):

[S2S3

S4S1

]= ik3(m − 1)V

2�R(�, �)

[cos� 1

0 1

](6.12)

where R(�, �) = (1/V)∫

ei dV, and the phase shift is = kb · 2 sin( 12 �).

For the case of unpolarized light, the intensity of the scattered lightcan be then written as [see also Eq. (1.21)]

Isca = k4V2

2r2

(m − 1

2�

)2

|R(�, �)|2 (1 + cos2 �)Iinc (6.13)

If we disregard the phase term R(�, �), the scattering intensity [Eq.(6.13)] exhibits the well-known Rayleigh 1/4 wavelength behaviorand is proportional to square of the organelle’s volume and the squareof the difference of its relative refractive index from unity.


For the simplest case of a sphere, R(�, �) = (3/u3)(sin u − u cos u),where u = 2ka sin (�/2). For scattering sizes comparable to the wave-length, the Rayleigh–Gans approximation predicts a certain combina-tion of Rayleigh and oscillatory behavior for the spectrum.

The Rayleigh–Gans approximation provides quite an accurate de-scription of the scattering from the majority of subcellular organelles,except for one case, the nucleus. Since the size of a nucleus is severalmicrometers, the second condition (small phase shifts) is not satisfied.

However, since we can approximate the nucleus as a sphericalscatterer, one can take advantage of the existing rigorous solutionof Maxwell equations for a case of a sphere. This theory was intro-duced by Gustav Mie in 1908 [18]. Recently, Mie theory has also beenfound useful to evaluate light scattering from spheroidal objects [19].A good description of Mie theory is provided in many books, for ex-ample, in Refs. [17, 20] and reviewed briefly in Chap. 1 [see Eqs. (1.30)and (1.31)]. Mie theory though rigorous is not particularly physicallytransparent and requires numerical calculations to find light scatteringintensities.

In addition, there are several other numerically intense approachesthat can be used if the scatterer does not satisfy the conditions ofthe Rayleigh–Gans approximation nor has a spherical shape. In thiscase T-matrix [21, 22], finite-difference time-domain (FDTD) method[23] and discrete dipole approximation (DDA) [24] are often used.A review of widely available light scattering codes can be found inthe section “Review of Computational Light Scattering Codes,” inChap. 1 while Chap. 3 contains a thorough review of application ofFDTD methods. The use of T-matrix code for light scattering analysisis discussed in Chap. 5.

We can see now that elastic light scattering exhibits a very interest-ing feature. By using the methods described above, we can relate bothphysical and biochemical characteristics of a scatterer, such as subcel-lular organelles, to its light scattering spectrum. Thus, the light scatter-ing spectrum could, in principle, serve as a unique native biomarkercapable of differentiating organelles inside a cell and even monitorchanges in those organelles noninvasively and in real time. Thus, whatis needed is to combine the LSS methods described above with the mi-croscopy approach capable of high-resolution imaging of cells.

6.5 Confocal Light Absorption and ScatteringSpectroscopic (CLASS) MicroscopyRecently, a new type of microscopy that employs the intrinsic opticalproperties of tissue as a source of contrast has been developed [6].This technique, called confocal light absorption and scattering spec-troscopic (CLASS) microscopy, combines light scattering spectroscopy


FIGURE 6.5 Schematic of the prototype CLASS/fluorescence microscope.See also color insert.

(LSS) previously developed for tissue characterization [1–4] with con-focal microscopy. In CLASS microscopy, light scattering spectra arethe source of contrast. Another important aspect of LSS is its abilityto detect and characterize particles well beyond the diffraction limit.A schematic of the CLASS microscope is shown in Fig. 6.5.

Light from the broadband source is delivered through an opticalfiber onto a pinhole. The delivery fiber is mounted in a fiber positioner,which allows precise alignment of the fiber relative to the pinhole withthe aid of an alignment laser. An iris diaphragm positioned beyond thepinhole is used to limit the beam to match the acceptance angle of thereflective objective. The light beam from the delivery pinhole is par-tially transmitted through the beam splitter to the sample and partiallyreflected to the reference fiber. The reflected light is coupled into thereference fiber by the reference collector lens and delivered to the spec-trometer. The transmitted light is delivered through an achromatic re-flective objective to the sample. Light backscattered from the sample iscollected by the same objective and is reflected by the beamsplitter to-ward the collection pinhole. The collection pinhole blocks most of thelight coming from regions above and below the focal plane, allowingonly the light scattered from a small focal volume to pass through. The


light that passes through the pinhole is collected by a second opticalfiber for delivery to an imaging spectrograph with a thermoelectricallycooled CCD detector, which is coupled to a computer.

The experimentally measured CLASS spectrum of a cell is a linearcombination of the CLASS spectra of various subcellular organelleswith different sizes and refractive indices within the cell. In order toextract these parameters, one can express the experimental spectrumas a sum over organelles’ diameters and refractive indices. It is con-venient to write this in a matrix form S = I · F + E , where S is theexperimental spectrum measured at discrete wavelength points, F isa discrete size distribution, I is the CLASS spectrum of a single scat-terer with diameter d and relative refractive index n, and E is theexperimental noise [10]. Using the scalar wave model similar to theone developed by Weise et al. [25] and Aguilar et al. [26], it is possibleto calculate the CLASS spectrum of a single scatterer I . In this model,the incident and scattering waves are expanded into the set of planewaves with directions limited by the numerical aperture of the objec-tive. The amplitude of the signal detected at the center of the focusthrough the confocal pinhole is expressed as:

A(, , n, NA)

=∫ ∫ +∞

−∞

∫ ∫ +∞

−∞P(−kX, −kY)P(k ′

X, k ′Y) f

( �kk,

�k ′

k ′

)dkX dkY dk ′

X dk ′Y

(6.14)

where is the wavelength of both the incident and the scattered light, is the diameter of the scatterer, n is the relative refractive index, NAis the numerical aperture of the objective, k ′ is the wavevector of theincident light, kis the wavevector of the scattered light, P is the ob-jective pupil function, and f (�k/k, �k ′/k ′) is the far-field Mie scatteringamplitude of the wave scattered in direction �k created by the incidentwave coming from the �k ′ direction.

To calculate the CLASS spectrum of a single scatterer, one calcu-lates the scattering intensity, which is just the square of the amplitude,and relates it to the intensity of the incident light at each wavelength.This gives the following spectral dependence of the CLASS signal:

I (, , n, NA) = [A(, , n, NA)]2

I0

={∫ ∫ +∞

−∞∫ ∫ +∞

−∞ P(−kX, −kY)P(k ′X, k ′

Y) f( �k

k ,�k ′k ′

)dkX dkY dk ′

X dk ′y

}2

{∫ ∫ +∞−∞

∫ ∫ +∞−∞ P(−kX, −kY)P(k ′

X, k ′Y) dkX dkY dk ′

X dk ′y

}2

(6.15)


Because the CLASS spectrum I is a highly singular matrix anda certain amount of noise E is present in the experimental spectrumS, it is not feasible to calculate the size distribution F by directly in-verting the matrix I . Instead one multiplies both sides of the equationS = I · F + E by the transpose matrix I T and introduces the matrixC = I T · I [10]. Then one computes the eigenvalues �1, �2, . . . of thematrix C and sequences them from large to small. This can be donebecause C is a square symmetric matrix. Then, one uses a linear leastsquares algorithm with non-negativity constraints [27] to solve the setof equations

I T S − (C + �k H)F → minF ≥ 0

(6.16)

where �k H F is the regularization term and matrix H represents thesecond derivative of the spectrum. The use of the non-negativity con-straint and the regularization procedure is critical in finding the correctdistribution F . This reconstructs the size and refractive index distri-butions of the scattering particles present in the focal volume of theCLASS microscope [6].

Depth sectioning characteristics of the CLASS microscope can bedetermined by translating a mirror located near the focal point andaligned normal to the optical axis of the objective using five wave-lengths spanning the principal spectral range of the instrument (Fig.6.6). The half-width of the detected signal is approximately 2 �m,

FIGURE 6.6 Depth sectioning of CLASS microscope along vertical axis at fivedifferent wavelengths (500, 550, 600, 650, and 700 nm). The almostidentical nature of the spectra demonstrates the very good chromaticcharacteristics of the instrument.


which is close to the theoretical value for the 30-�m pinhole and 36×objective used [28–30]. In addition, the shapes of all five spectra shownin Fig. 6.6 are almost identical (500, 550, 600, 650, and 700 nm), whichdemonstrate the excellent chromatic characteristics of the instrument.Small maxima and minima on either side on the main peak are dueto diffraction from the pinhole. The asymmetry is due to sphericalaberration in the reflective objective [31].

To check the characteristics of the microscope, calibrate it, and testthe size extraction algorithms, several experiments using polystyrenebeads in suspensions were performed. The samples were created bymixing beads of two different sizes in water and in glycerol in orderto establish that the technique can separate particles of multiple sizes.Glycerol was used in addition to water because the relative refractiveindex of the polystyrene beads in water (1.194 at 600 nm) is substan-tially higher than that of subcellular organelles in cytoplasm, which isin the range of 1.03–1.1 at the visible wavelengths. By suspending thebeads in the glycerol, one can decrease the relative refractive indexto 1.07–1.1 in the visible range, a closer approximation to the biolog-ical range. (The refractive index of polystyrene in the working rangecan be accurately described by the expression n = 1.5607 + 10002/2,where is in nanometers [32].)

Beads with a nominal mean size of = 175 nm and a standarddeviation of size distribution of 10 nm were mixed with the beadswith a mean size of = 356 nm and a standard deviation of 14 nm.Figure 6.7a shows the CLASS spectra of polystyrene bead mixtures inwater and glycerol and a comparison with the theoretical fit. In theseexperiments, Brownian motion moved the beads in and out of themicroscope focus. Therefore the data were taken by averaging over alarge number of beads. This was necessary to improve the statistics ofthe measurements. The difference between the experimental measure-ments and the manufacturer’s labeling is less than 1% for both cases.

Figure 6.7b shows the extracted size distributions. The parametersof the extracted size distributions are very close to the parametersprovided by the manufacturer (Table 6.1). For example, the extractedmean sizes of the 175-nm beads are within 15 nm of the manufacturer’ssizes, and the mean sizes of the 356-nm beads are even better, within4 nm of the manufacturer’s sizes.

Another test involving beads (or microspheres) was performedto establish imaging capabilities of the CLASS microscope. To ensurethat CLASS microscopy detects and correctly identifies objects in thefield of view, it was modified by adding a wide-field fluorescencemicroscopy arm, which shares a major part of the CLASS optical train.The instrument was tested on suspensions of carboxylate-modifiedInvitrogen microspheres, which exhibit red fluorescence emission ata wavelength of 605 nm with excitation at 580 nm. The microsphereswere effectively constrained to a single-layer geometry by two thin


FIGURE 6.7 CLASS spectra (a) and extracted size distributions (b) forpolystyrene beads in water and glycerol. In part (a), the dots are forexperimental data points and solid curves are for the spectra reconstructedfrom the theoretical model; for part (b), the points are calculated values withsolid curves as a guide for the eye.

microscope slides coated with a refractive index matching optical gel.Figure 6.8 shows (from left to right) the fluorescence image of the layerof 1.9-�m diameter microspheres, the image reconstructed from theCLASS data, and the overlay of the images.


CLASS Measurement

Manufacturer’s Beads in Beads inPolystyrene Beads Data Water Glycerol

Size 1 Mean size (nm) 175 185 190

Standard deviation(nm)

10 40 40

Size 2 Mean size (nm) 356 360 360

Standard deviation(nm)

14 30 30

TABLE 6.1 Size Distribution Parameters for Polystyrene Beads

Figure 6.9 shows a mixture of three sizes of fluorescent beads withsizes 0.5, 1.1, and 1.9 �m mixed in a ratio of 4:2:1. Note the misleadingsize information evident in the conventional fluorescence images.

A 0.5-�m microsphere which is either located close to the focalplane of the fluorescence microscope or carries a high load of fluo-rescent label produces a spot that is significantly larger than the mi-crosphere’s actual size. The CLASS image of the same spot (middleof Fig. 6.9), on the other hand, does not make this error and correctlyreconstructs the real size of the microsphere. We also can see that priorfluorescence labeling does not affect the determination of the objectswith CLASS measurements.

6.6 Applications of CLASS MicroscopyTo confirm the ability of CLASS to detect and identify specific or-ganelles in a live cell, simultaneous CLASS and fluorescence imagingof live 16HBE14o- human bronchial epithelial cells, with the lysosomes

FIGURE 6.8 Fluorescence image of the suspensions of carboxylate-modified1.9 �m diameter microspheres exhibiting red fluorescence (left side), theimage reconstructed from the CLASS data (middle), and the overlay of theimages (right side). See also color insert.


FIGURE 6.9 Fluorescence image of the mixture of three sizes of fluorescentbeads with sizes 0.5 , 1.1, and 1.9 �m mixed in a ratio of 4:2:1 (left side),the image reconstructed from the CLASS data (middle), and the overlay of theimages (right side). See also color insert.

stained with a lysosome-specific fluorescent dye, was performed us-ing combined CLASS/fluorescence instrument. The fluorescence im-age of the bronchial epithelial cell, the CLASS reconstructed imageof the lysosomes, and the overlay of two images are provided in Fig.6.10.

The overall agreement is very good; however, as expected, there isnot always a precise, one-to-one correspondence between organellesappearing in the CLASS image and the fluorescence image. This isbecause the CLASS image comes from a single, well-defined confocalimage plane within the cell, whereas the fluorescence image comesfrom several focal “planes” within the cell, throughout the thickerdepth of field produced by the conventional fluorescence microscope.Thus, in the fluorescence image, one observes the superposition ofseveral focal “planes” and therefore additional organelles above andbelow those in the single, well-defined confocal image plane of theCLASS microscope.

Another interesting experiment is to check the ability of CLASSmicroscopy to do time sequencing on a single cell. The cell was

FIGURE 6.10 Image of live 16HBE14o- human bronchial epithelial cells withlysosomes stained with lysosome-specific fluorescence dye (left side), theimage reconstructed from the CLASS data (middle), and the overlay of theimages (right side). See also color insert.


FIGURE 6.11 The time sequence of CLASS microscope reconstructed imagesof a single cell. The cells were treated with DHA and incubated for 21 h. Thetime indicated in each image is the time elapsed after the cell was removedfrom the incubator. See also color insert.

incubated with DHA, a substance that induces apoptosis, for 21 h.The time indicated in each image is the time elapsed after the cell wasremoved from the incubator.

In Fig. 6.11, the nucleus, which appears as the large blue organelle,has its actual shape and density reconstructed from the CLASS spec-tra obtained using point-by-point scanning. The remaining individualorganelles reconstructed from the CLASS spectra are represented sim-ply as spheroids whose size, elongation, and color indicate differentorganelles. The small red spheres are peroxisomes, and the interme-diate size green spheres are lysosomes. Organelles with sizes in the1000–1300 nm range are mitochondria, and are shown as large yellowspheroids. The shape of the nucleus has changed dramatically by thethird hour, and the nuclear density, indicated by color depth, has de-creased with time. The organelles have almost completely vanishedby 4 h.

Recently, significant attention has been directed toward the ap-plications of metal nanoparticles such as gold nanorods to medicalproblems primarily as extremely bright molecular marker labels forfluorescence, absorption, or scattering imaging of living tissue [33].Nanoparticles with sizes small compared to the wavelength of lightmade from metals with a specific complex index of refraction, such asgold and silver, have absorption and scattering resonance lines in thevisible part of the spectrum. These lines are due to in-phase oscillationof free electrons and are called surface plasmon resonances.


However, samples containing a large number of gold nanorodsusually exhibit relatively broad spectral lines. This observed linewidthdoes not agree with theoretical calculations, which predict signifi-cantly narrower absorption and scattering lines. As shown in Ref. [34],the spectral peak of nanorods is dependent on their aspect ratio, andthis discrepancy is explained by the inhomogeneous line broadeningcaused by the contribution of nanorods with various aspect ratios.

This broadened linewidth limits the use of nanorods with uncon-trolled aspect ratios as effective molecular labels, because it would berather difficult to image several types of nanorod markers simultane-ously. However, this suggests that nanorod-based molecular markersselected for a narrow aspect ratio and, to a lesser degree, size distri-bution, should provide spectral lines sufficiently narrow for effectivebiomedical imaging.

In Ref. [34], the researchers performed optical transmission mea-surements of gold nanorod spectra in aqueous solutions using astandard transmission arrangement for extinction measurements de-scribed in Ref. [19]. Concentrations of the solutions were chosen tobe close to 1010 nanoparticles per milliliter of the solvent to eliminateoptical interference. The measured longitudinal plasmon mode of thenanorods is presented as a dotted curve in Fig. 6.12. It shows that mul-tiple nanorods in aqueous solution have width at half maximum ofapproximately 90 nm. This line is significantly wider than the line onewould get from either T-matrix calculations or the dipole approxi-mation. The solid line in Fig. 6.12 shows the plasmon spectral line

FIGURE 6.12 Optical properties of an ensemble of gold nanorods. Normalizedextinction of the same sample of gold nanorods in aqueous solution as in theTEM image. Dots, experiment; dashed line, T -matrix calculation for asingle-size nanorod with length and width of 48.9 and 16.4 nm, respectively[34].


calculated using the T-matrix for nanorods with a length and widthof 48.9 and 16.4 nm, respectively. These are the mean values of thesizes of the multiple nanorods in the aqueous solution. The theoret-ical line is also centered at 700 nm but has width of approximately30 nm. The ensemble spectrum is three times broader than the singleparticle spectrum.

The CLASS microscope with the supercontinuum broadband lasersource described above is capable of performing single nanoparti-cle measurements. To determine experimentally that individual goldnanorods indeed exhibit narrow spectral lines, single gold nanorodswere selected and their scattering spectra measured using the CLASSmicroscope.

The nanorods were synthesized in a two-step procedure adaptedfrom Jana et al. [35]. A portion of one of the transmission electronmicroscope (TEM) images of a sample of gold nanorods synthesizedusing the above procedure is shown in Fig. 6.13. Researchers mea-sured the sizes of 404 nanorods from six different TEM images. Theyevaluated the average length and width of the nanorods and standarddeviations and obtained 48.9 ± 5.0 nm and 16.4 ± 2.1 nm, respectively,with an average aspect ratio of 3.0 ± 0.4.

The concentration of gold nanorods used was approximately onenanorod per 100 �m3 of solvent. The dimensions of the confocal vol-ume have weak wavelength dependence and were measured to be0.5 �m in the lateral direction and 2 �m in the longitudinal directionat 700 nm, which gives a probability of about 0.5% to find a particle inthe confocal volume. Thus, it is unlikely that more than one nanorodis present in the confocal volume. To locate individual nanorods, re-searchers performed a 64 × 64 raster scan with 0.5 �m steps. Theintegrated spectral signal was monitored from 650 to 750 nm, and

FIGURE 6.13 TEMimage of a sampleof gold nanorodswith an averagelength andstandard deviationof 48.9 ± 5.0 nmand an averagediameter andstandard deviationof 16.4 ± 2.1 nm.


FIGURE 6.14 Normalized scattering spectrum for a single gold nanorod. Dots,CLASS measurements. Other lines are T -matrix calculations for a nanorodwith an aspect ratio of 3.25 and a diameter of 16.2 nm and various A values.Solid line is for the natural linewidth, A = 0. Also included are lines for A =0.5 and A = 1. The curve for A = 0.13 is the best fit for measurementsmade on eight different nanorods.

when a sudden jump in the magnitude of a signal was observed, itwas clear that a nanorod is present in the confocal volume. Then acomplete spectrum for this particle was collected.

Scattering spectra from nine individual gold nanorods, all ofwhich had a linewidth of approximately 30 nm was measured [37].The experimental data from one of these spectra is shown in Fig. 6.14.These measurements were compared with numerical calculations thatuse the complex refractive index of gold [36] and various values of thephenomenological A-parameter correction [38] used to account for fi-nite size and interface effects. The curve for A = 0.13 is the best fitfor measurements made on eight different nanorods. This agrees verywell with an A-parameter calculated using a quantum mechanicaljellium model.

Thus, using the CLASS microscope, researchers [34, 37] havedetected the plasmon scattering spectra of single gold nanorods.From these measurements, one can draw the conclusion that singlegold nanorods exhibit a scattering line significantly narrower thanthe lines routinely observed in experiments that involve multiplenanorods. Narrow, easily tunable spectra would allow several bio-chemical species to be imaged simultaneously with molecular markersthat employ gold nanorods of several different controlled aspect ra-tios as labels. These markers could be used for cellular microscopic


imaging where even a single nanorod could be detected. Minimizingthe number of nanoparticles should reduce possible damage to a liv-ing cell. For optical imaging of tumors, multiple gold nanorods with anarrow aspect ratio distribution might be used. A possible techniquefor obtaining a narrow aspect ratio distribution might employ devicesalready developed for cell sorting. These would use the wavelengthof the narrow plasmon spectral line for particle discrimination.

6.7 ConclusionThe results presented here show that light absorption and scatter-ing spectroscopic microscopies are capable of reconstructing im-ages of living cells with submicrometer resolution without using ex-ogenous markers. Fluorescence microscopy of living cells requiresapplication of molecular markers that can affect normal cell func-tioning. In some situations, such as studying embryo development,phototoxicity caused by fluorescent-tagged molecular markers is notonly undesirable but also unacceptable. Another potential problemwith fluorescence labeling is related to the fact that multiple flu-orescent labels might have overlapping lineshapes and this limitsnumber of species that can be imaged simultaneously in a singlecell.

Light absorption and scattering spectroscopic microscopies arenot affected by these problems. They require no exogenous labels andare capable of imaging and continuously monitoring individual vi-able cells, enabling the observation of cell and organelle functioningat scales on the order of 100 nm. For example, one of the modali-ties of light absorption and scattering spectroscopic microscopies, theCLASS microscope, can provide not only size information but alsoinformation about the biochemical and physical properties of the cellbecause light scattering spectra are very sensitive to absorption coef-ficients and the refractive indices, which in turn are directly relatedto the organelle’s biochemical and physical composition (such as thechromatin concentration in nuclei or the hemoglobin concentrationand oxygen saturation in red blood cells).

CLASS microscopy can also characterize individual nanoparticlesthat have been used recently for high-resolution specific imaging ofcancer and other diseases. Studies with CLASS microscope demon-strated that individual gold nanoparticles indeed exhibit narrow spec-tral lines usually not observed in experiments involving ensemblesof nanorods. Those studies also reveal that gold-nanorod-scattering-based biomedical labels with a single, well-defined aspect ratio mightprovide important advantages over the standard available absorptionnanorod labels.


References1. Perelman L. T., Backman V., Wallace M., Zonios G., Manoharan R., Nusrat A.,

Shields S., Seiler M., Lima C., Hamano T., et al. (1998), Phys Rev Lett 80: 627–630.2. Backman V., Wallace M. B., Perelman L. T., Arendt J. T., Gurjar R., Muller M.

G., Zhang Q., Zonios G., Kline E., McGillican T., et al. (2000), Nature 406: 35–36.3. Gurjar R. S., Backman V., Perelman L. T., Georgakoudi I., Badizadegan K.,

Itzkan I., Dasari R. R., and Feld M. S. (2001), Nat Med 7: 1245–1248.4. Perelman L. T. and Backman V. (2002), In: V. Tuchin, ed. Handbook on Optical

Biomedical Diagnostics SPIE Press, Bellingham, WA, pp. 675–724.5. Fang H., Ollero M., Vitkin E., Kimerer L. M., Cipolloni P. B, Zaman M. M.,

Freedman S. D., Bigio I. J., Itzkan I., Hanlon E. B., and Perelman L. T. (2003),IEEE J Sel Top Quant Elect 9: 267–276.

6. Itzkan I., Qiu L., Fang H., Zaman M. M., Vitkin E., Ghiran L. C., Salahuddin S.,Modell M., Andersson C., Kimerer L. M., Cipolloni P. B., Lim K.-H., FreedmanS. D., Bigio I., Sachs B. P., Hanlon E. B., and Perelman L. T. (2007), Proc NatlAcad Sci U S A 104: 17255.

7. Schuele G., Vitkin E., Huie P., Palanker D., and Perelman L. T. (2005), J BiomedOpt 10: 051404-1–051404-8.

8. Backman V., Gopal V., Kalashnikov M., Badizadegan K., Gurjar R., Wax A.,Georgakoudi I., Mueller M., Boone C. W., Dasari R. R., and Feld M. S. (2001),IEEE J Sel Top Quant Elect 7: 887–894.

9. Wax A., Yang C., and Izatt J. A. (2003), Opt Lett 28: 1230–1232.10. Fang H., Qiu L., Zaman M. M., Vitkin E., Salahuddin S., Andersson C., Kimerer

L. M., Cipolloni P. B., Modell M. D., Turner B. S., Keates S. E., Bigio I. J., ItzkanI., Freedman S. D., Bansil R., Hanlon E. B., and Perelman L. T. (2007), Appl Opt46: 1760–1769.

11. Campbell I. D. and Dwek R. A. (1984), Biological Spectroscopy, Benjamin/Cummings Pub. Co., Menlo Park, CA.

12. Bradbury S. and Bracegirdle B. (1998), Introduction to Light Microscopy, BIOSScientific Publishers.

13. Rost F. and Oldfield R. (2000), Fluorescence microscopy, Photography with a Mi-croscope, Cambridge University Press, Cambridge, U.K.

14. Denk W., Strickler J., and Webb W. (1990), Science 248: 73–76.15. Smith Z. J. and Berger A. J. (2008), Opt Lett 33: 714–716.16. Zumbusch A., Holtom G. R., and Xie X. S. (1999), Phys Rev Lett 82: 4142–4145.17. van de Hulst H. C. (1957), Light Scattering by Small Particles, Wiley, New York.18. Mie G. (1908), Ann Phys 330: 377–445.19. Chalut K. J., Giacomelli M. G., and Wax A. (2008), J Opt Soc Am A 25: 1866–1874.20. Bohren C. F. and Huffman D. R. (1983), Absorption and Scattering of Light by

Small Particles, Wiley, New York.21. Waterman P. C. (1965), Pr Inst Electr Elect 53: 805.22. Mishchenko M. I. and Travis L. D. (1998), J Quant Spectrosc Ra 60: 309–324.23. Yang P., Liou K. N., Mishchenko M. I., and Gao B. C. (2000), Appl Opt 39:

3727–3737.24. Morgan M. A. and Mei K. K. (1979), IEEE T Antenn Propag 27: 202–214.25. Weise W., Zinin P., Wilson T., Briggs A., and Boseck A. (1996), Opt Lett 21:

1800–1802.26. Aguilar J. F., Lera M., and Sheppard C. J. R. (2000), Appl Opt 39: 4621–4628.27. Craig I. J. D., Brown J. C., Inverse Problems in Astronomy: A Guide to Inversion

Strategies for Remotely Sensed Data (A. Hilger, 1986).28. Webb R. H. (1996), Rep Prog Phy 59: 427–471.29. Wilson T. and Carlini A. R. (1987), Opt Lett 12, 227–229.30. Drazic V. (1992). J Opt Soc Am A 9, 725–731.31. Scalettar B. A., Swedlow J. R., Sedat J. W., and Agard D. A. (1996), J Microsc

182: 50–60.32. Marx E. and Mulholland G. W. (1983), J Res Nat Bur Stand 88: 321–338.


33. Durr N. J., Larson T., Smith D. K., Korgel B. A., Sokolov K., and Ben-Yakar A.(2007), Nano Lett 941–945.

34. Qiu L., Larson T. A., Smith D. K., Vitkin E., Zhang S., Modell M. D., Itzkan I.,Hanlon E. B., Korgel B. A., Sokolov K. V., and Perelman L. T. (2007), IEEE J SelTop Quant Elect 13: 1730–1738.

35. Jana N. R., Gearheart L., and Murphy C. J. (2001), J Phys Chem B 105: 4065.36. Johnson P. B. and Christy R. W. (1972), Phys Rev B 6: 4370.37. Qiu L., Larson T. A., Smith D. K., Vitkin E., Modell M. D., Korgel B. A., Sokolov

K. V., Hanlon E. B., Itzkan I., and Perelman L. T. (2008), Appl Phys Lett 93:153106-1–4.

38. Kreibig U. and Vollmer M. (1995), Optical Properties of Metal Clusters, Springer-Verlag, Berlin, New York.


P A R T 3Assessing Bulk TissueProperties fromScatteringMeasurements

CHAPTER 7Light Scattering in ConfocalReflectance Microscopy

CHAPTER 8Tissue UltrastructureScattering with Near-InfraredSpectroscopy: Ex Vivo and InVivo Interpretation


C H A P T E R 7Light Scattering in

ConfocalReflectanceMicroscopy

Steven L. Jacques, David Levitz, Ravikant Samatham, Daniel S. Gareau,Niloy Choudhury, and Frederic Truffer

7.1 IntroductionThe optical measurement of light transport in a tissue can yield theabsorption and scattering properties of a tissue. Such measurementsof the tissue optical properties have two major purposes.

First, the measurement of tissue optical properties allows sepa-ration of the variables of absorption and scattering that specify lighttransport in a tissue. This separation of variables enables chemomet-ric analysis of the absorption spectrum, without interference from thescattering, to specify the absorbing chromophores in a tissue, whichlinearly add to yield the total absorption spectrum. This is the mostcommon motivation for measuring optical properties. Tissue bloodcontent and oxygen saturation, hydration, fat content, and cutaneousbilirubin levels are examples of parameters deduced from absorptionspectra that are of strong interest in medical research and clinical care.

Second, the use of optical scattering as a contrast agent in an im-age offers an alternative to the use of absorption or fluorescence as thecontrast mechanism. The scattering properties of a tissue are relatedto the ultrastructure of a tissue, that is, its cellular nuclei, mitochon-dria, cytoskeleton, and lipid membranes, as well as extracellular fibers

171

172 A s s e s s i n g B u l k T i s s u e P r o p e r t i e s

like collagen and actin–myosin. These structures present local spatialfluctuations in mass density and hence fluctuations in the numberdensity of polarizable dipoles, which determine the optical refractiveindex (n) of the tissue. Such refractive index fluctuations scatter light.One can discuss the fluctuations in terms of a continuum of fluctuat-ing refractive index with an associated spatial frequency spectrum, orin terms of a distribution of “particles,” each with a unique size andparticle refractive index that differs from the surrounding mediumrefractive index. Either way, the effect of this nonuniform refractiveindex is to scatter light with a strength and angular dependence that en-codes the amplitude and spatial frequency content of the continuumof fluctuations, or in the cross-sectional area, number density and re-fractive index of particles. This description of the source of scatteringmaps into the apparent size distribution and refractive index mis-match of the ultrastructure of a cell or tissue. Hence, scattering mea-surements can provide a characterization of cellular or tissue ultra-structure.

This chapter discusses how to measure the strength and angulardependence of photon scatter by tissues in vivo, so as to map into thefactors that depend on the ultrastructure of a tissue. The theoreticalmapping between observed scatter and the ultrastructure remains illdefined. If tissue was a collection of isolated microspheres embeddedin an aqueous medium, then we would be on firm footing. But tissueis a complex condensed phase material where scatterers cannot beaccurately defined. Our initial hope is simply to describe a “finger-print” based on observed scattering properties that characterizes theultrastructure of a tissue.

The optical measurements used to measure tissues very often in-volve measurement of light transport through a tissue in which thephotons are multiply scattered by the tissue. The transport is inter-preted in terms of the absorption coefficient, �a (cm−1), and the re-duced scattering coefficient, �′

s = �s(1 − g) (cm−1), where �s is thescattering coefficient and g is the anisotropy of scattering [g equalsthe average value 〈cos�〉, where � is the photon polar deflection angleof a scattering event; see also Chap. 1, section “Basics of Light Scat-tering Theory,” Eqs. (1.10) to (1.13)]. The �s encodes the strength ofscattering and g encodes the angular dependence of scattering. Hence,�s and g can characterize the ultrastructure of a tissue. It is usuallydifficult to optically measure a tissue in a manner that can separate�′

s into �s and g. An in vivo tissue site on a human patient presents avery thick tissue. One does not have the option of cutting a thin tissuelayer for bench-top transmission measurements to characterize singlescattering events within the thin tissue, so as to separately measure �s

and g. Yet the parameters �s and g are each uniquely affected by thesize and spatial distribution of “particles” in the tissue ultrastructure.Our goal is to measure the �s and g of tissue noninvasively in vivo

173L i g h t S c a t t e r i n g i n C o n f o c a l R e f l e c t a n c e M i c r o s c o p y

and learn if there is sufficient variation among tissues to justify using�s and g as a fingerprint for characterizing a tissue.

This chapter is devoted to a special type of optical measurementthat strives to separately measure the �s and g of a tissue usinga noninvasive in vivo measurement. This type of optical measure-ment is called confocal reflectance. Two examples are in common use:(1) reflectance-mode confocal microscopy (rCM) and (2) optical co-herence tomography (OCT), when operating in focus-tracking mode(discussed in the section “Basic Instrument”).

It should be noted that polarized light offers another approachtoward the goal of specifying a fingerprint for the ultrastructure of atissue. If the refractive index of a tissue structure is anisotropic, such asa birefringent collagen fiber bundle with a different n in the directionalong the length of the fiber than the n in the direction perpendicular tothe fiber, then polarization properties become an important aspect ofscattering and offer an additional parameter for optical contrast. Thischapter does not discuss polarized light, although the angular depen-dence of scatter for polarized light is an important contrast mechanismfor imaging to characterize tissue ultrastructure.

7.2 The Basic IdeaThe basic idea of rCM involves three steps: (1) the transmission of lightto the focus, (2) the interaction of light within the confocal volume atthe focus, and (3) the return of light from the focus, out of the tissue,and to a pinhole for detection. Steps 1 and 3 involve the attenuationof light by the tissue. Step 2 involves the process of scattering withinthe confocal volume. The term confocal volume refers to the region inthe tissue at the focus such that photons, which originate from thisregion but do not undergo further scatter by the tissue, can enter theobjective lens, be recollimated, and refocused into a pinhole to reacha detector.

Figure 7.1 schematically depicts how tissue can scatter photonseither isotropically or in a forward-directed manner. If scattering isisotropic, it will optimally prevent photons from reaching the focus.If scattering is forward directed, then photons can propagate to thefocus despite multiple scattering. Hence, the ability to reach a focus isdependent on both the frequency of scattering, described by �s, andthe angular dependence of scattering, described by g.

Figure 7.2 shows how photons that are backscattered from thefocus can reenter the lens and become recollimated for eventual col-lection by a lens that refocuses the photons into a pinhole or opticalfiber to guide the light to a detector. Only photons scattered from thefocus can be properly recollimated and eventually detected. Photonsscattered from other regions of the tissue will not be detected except at


Isotropicscatter Objective lens

3 Photon scatterings

FocusForwardscatter

(a) (b)

FIGURE 7.1 The penetration of light into a tissue toward a focus. (a) Photonsare scattered by tissue such that their trajectory is redirected according to ascattering function. The figure schematically illustrates a forward-directedscatter function (g = 0.90) and an isotropic scattering function (g = 0). (b) Alens directs photons toward a focus within a tissue. Despite multiplescatterings, if the scattering function is forward directed, then photons stillhave a significant probability of reaching the focus.

a very low efficiency. This selective collection of photons is the essenceof confocal imaging.

Figure 7.3 shows the basic experimental setup discussed in thischapter. A beam of light is focused into a tissue using a lens witha specific focal length (FL). The focus is moved up/down withinthe tissue along the z-axis by moving either the lens assembly orthe tissue. The numerical aperture (NA) of a lens is defined asNA = n1 sin(�max), where n1 is the refractive index of the medium

Objective lens

Tissue surface

Focus

FIGURE 7.2 The backscatter of light from the focus. The photonsbackscattered by the tissue within the focus return within the solid angle ofcollection by the lens and are recollimated. The recollimated photons arethen refocused into a pinhole or optical fiber for detection (not shown).


FIGURE 7.3 The measurement geometry involves focusing light to a focus atdepth zf, using a lens with a focal length (FL) at a height (h) above the tissue.The half-angle of photon delivery is �max. The half-angle of photon entry intothe tissue is �max. An apparent numerical aperture is used in this chapter,NAeff = sin(�max). (Schematic drawing exaggerates angles.) The tissue or lensis moved to vary h and hence vary the position of the focus, zf, within thetissue. Backscattered photons from the focus, which reenter the lens andproperly recollimate, are refocused into a pinhole or optical fiber (not shown)to reach a detector.

contacting the lens (in our experiments, water couples the lens tothe tissue, n1 ≈ 1.33). The angle � is the angle of photon delivery tothe tissue surface. At the medium/tissue interface, there is anotherrefraction, such that n1 sin(�) = n2 sin(�), where � is the angle of pho-ton entry into the tissue and n2 is the n for tissue (n2 ≈ 1.37–1.4). Themaximum half-angles of delivery and entry are �max and �max, re-spectively [�max = arcsin(n1 sin(�max)/n2)]. The depth position of thefocus, zf, is a function of the height of the lens above the tissue (h):zf = (FL − h) tan(�max)/ tan(�max). Hence, the value of zf is always a lit-tle more (typically 3–5% more) than the distance that the lens movesrelative to the tissue (FL–h).

In this chapter, the index mismatch between the tissue, externalmedium, and the lens is ignored to concentrate on the issues of scat-tering uncomplicated by the issue of refraction at the surface. In thischapter, we will use the term NAeff = sin(�max) to describe the half-angle of entry into the tissue. The change in the position of the focuszf is cited, but not the change in the lens/tissue distance (h). Hence,the issue of refraction is avoided.

As light is delivered into the tissue, the detector records a col-lected signal [S (W)]. If one delivers a laser power P (W) and de-tects a signal S, the value S/P is the fraction of delivered light that is


reflected and detected. The value of S/P depends on the choice of thesize of the pinhole (or optical fiber serving as a pinhole) that collectslight for detection. A larger pinhole will collect more light and yielda larger signal. Typically, the pinhole is a little larger than the lateralAiry radius of the focus, and often one sacrifices lateral resolution byenlarging the pinhole even further to achieve a better signal-to-noiseratio in the acquired signal. This chapter assumes that the pinhole issmall, only slightly larger than the lateral Airy radius of the focus. Thesignal is normalized by a factor NORM, R = (S/P)/NORM, such thata mirror placed in the focus will return all the delivered light, and thedetected reflectance signal (R) will be 1.0.

As the position of the focus (zf) is moved axially within the tissue,the reflectance R varies in the following manner:

R(zf) = �e−�zf + Bbkgd(zf) (7.1)

where � (dimensionless) is the reflectivity of the tissue and � (cm−1) isan attenuation coefficient. The factor Bbkgd(zf) is a background noisefloor due to a small amount of escaping diffuse reflectance that reachesthe pinhole. This chapter considers the relationship between the ex-perimentally observable parameters, � and �, and the tissue opticalproperties, �a, �s, and g. Figure 7.4 illustrates the behavior of R as thefocus is scanned into the tissue. The observed R falls exponentiallyas the focus at depth zf moves deeper into the tissue. This chapterdiscusses the relationship between the pair of observables � , � and

ρ = Local reflectivity (−)

µ = Attenuation (cm−1)

ρe−µzf

ρ

zf

Rµs = Scattering coefficient (cm−1)

g = Anisotropy of scattering (−)

FIGURE 7.4 The exponential decay of confocal reflectance (R) as the focus isscanned down into the tissue to a depth zf. The two observable parameters �and � are related to the tissue optical scattering properties �s and g.


the pair of optical scattering properties �s, g. The role of �a is alsomentioned.

Theory Mapping (�, �) to (�s, g)The experimental determination of � and � can be mapped into theoptical properties �s and g. The absorption coefficient �a also has arole, but it is usually much smaller than �s and is a minor playerin typical tissue measurements. Our model is based on analyticallydescribing the behavior of Monte Carlo simulations of confocal mea-surements. We have been investigating the relationship between �and � and the optical properties, and this work continues. Our latestwork is presented in the section “Monte Carlo Simulations.” But tointroduce the concept, we begin with our current model with all itsshortcomings.

The expression for the experimental R is

R(zf) = � e−(a�s+�a)G2zf + B e−Czf (7.2)

where comparison of Eqs. (7.1) and (7.2) indicates:

� = (a�s + �a)2G (7.3)

and

� = �s �zb (7.4)

In Eqs. (7.2) and (7.3), a is a factor between 0 and 1 that multipliesthe value �s, thereby decreasing the effectiveness of scattering to pre-vent photons reaching the focus at zf, as well as to prevent photonsbackscattered from the focus reaching the pinhole of the detector. Theability to prevent penetration of scattered photons to the focus is equalto the ability to prevent escape from the focus and collection by a pin-hole (results from Monte Carlo simulations, not shown here). Hence,there is a factor 2 in Eq. (7.3). The factor a was found to depend on theanisotropy of scattering, g, and this relationship has been determinedby Monte Carlo simulations. The section “Monte Carlo Simulations”revisits the behavior of a (g) in more detail.

The factor G describes the extra photon pathlength in the tissue asphotons are focused obliquely to reach the focus. G is always greaterthan 1.0. G is close to 1.0 for low–numerical aperture objective lensesas in OCT, and higher for high–numerical aperture lenses as in rCM.The section “Monte Carlo Simulations” revisits the behavior of G inmore detail.

The factor B exp(−Czf) refers to the noise floor due to a small por-tion of escaping multiply scattered photons, which enter the pinhole.


The factor C is related to the factor �eff in optical diffusion theory. Thefactors B and C can be predicted by diffusion theory (not shown here)and are not of interest to the discussion of this chapter.

In Eqs. (7.2) and (7.4), �z is the apparent axial extent of the confo-cal volume, which is assumed to be �z = 1.4/NA2

eff, where is thewavelength. At this point in our studies, we tentatively find this as-sumed value for �z to be operationally correct. In Eq. (7.4), the product�s �z is the fraction of photons reaching the focus that are scatteredby the confocal volume. The factor b is the fraction of these scatteredphotons that are backscattered toward the objective lens within thesolid angle of collection of the lens and detected.

In summary, the factor exp(−�zf) in Eq. (7.1) describes the atten-uation of photons by the scattering and absorption properties of thetissue as photons propagate from the source/lens to the confocal vol-ume and back to the lens/pinhole/detector. The factor � describes thefraction of photons scattered by the confocal volume that would reachthe pinhole if there were no attenuation by the tissue.

Equations (7.2) to (7.4) allow the scan measurement R(zf) to specifythe optical properties �s and g of a tissue, where �a is assumed tohave some low constant value. Hence, a noninvasive measurementcan separately specify the �s and g of a tissue.

Experimental DataTo illustrate the measurements, rCM measurements were made onfreshly excised mouse tissues: white matter brain, gray matter brain,liver, skin, and muscle. The wavelength of measurement was = 0.488�m from an argon-ion laser. The lens was a water-immersion lensoverfilled by the laser beam (NA = 0.90, NAeff ≈ 0.77–0.80 for n2 =1.4–1.37). The function R(zf) was measured as zf was varied over thefirst 100 �m of tissue. The signal decayed exponentially and specifiedthe values of � and � . Figure 7.5 shows these preliminary values of� and � for the mouse tissues. A grid of iso-�s and iso-g contours isincluded based on Eqs. (7.2) to (7.4). Also, measurements of a solutionof 0.1-�m-diameter polystyrene microspheres are shown. The grid isadjusted so that the predictions of Mie theory for microspheres andthe experimental measurements for microspheres agree. This adjust-ment accounts for the particular pinhole used in the experiment, aswell as for errors in our calibration using reflectance from an oil/glassinterface. Although there is close but not perfect agreement with theexperiment and theory for the microspheres, the calibration is suffi-cient to illustrate the concept of the measurement. The grid incorpo-rates the analysis of the section “Monte Carlo Simulations.” The tissuedata were from 8 mice, with 10 measurements on each of 3 tissue siteson each tissue type from each mouse. The large circles indicate the


FIGURE 7.5 Experimental data on the � and � of tissue from mice, whichwere specified by rCM as R(zf) was scanned down into freshly excised tissuesusing an argon-ion laser ( = 0.488 �m, NA = 0.90, NAeff ≈ 0.78). The grid isa set of iso-�s and iso-g contours generated by Eqs. (7.2) to (7.4). The tissueproperties range over �s = 100–1000 cm−1 and g = 0.6–0.9. The largecircles are the mean values of the � and � for each tissue type. Calibrationwas based on measurements on 0.1-�m-diameter microspheres and thecorresponding Mie theory predictions for microsphere measurements.

mean values for the five tissue types. Based on the calibration grid,the tissues had mean �s values ranging from 100 to 1000 cm−1 andmean g values of 0.6–0.9, although there was significant intratissuevariation.

The interested reader can see an application of this model to thestudy of mouse skin optics for a wild-type mouse and mutant mouse[1]. The mutation was a single gene defect causing osteogenesis imper-fecta, which affects the ability of collagen fibrils to assemble into largercollagen fiber bundles. This single gene defect influenced the valuesof �s and g for the skin, decreasing g due to smaller mean collagenfiber bundle size.

Now what were the shortcomings of this model? We had initiallyestimated G by using the mean value of the length of photon pathsduring delivery of light to the focus in the case of no absorption orscattering. For example, G = 1.009 for NAeff = 0.25, and G = 1.070 forNAeff = 0.65. The section “Monte Carlo Simulations” will refine ourunderstanding of G, but our initial estimates of G were rather closeto our latest estimates. We have also worked on the effect that thesingle scattering phase function, p(�), of the tissue within the confocalvolume has on the value G. When light scatters in the focus, the range


of angles of backscatter (or transmission) is altered, and hence thevalue of G is affected. This effect is a 5–10% effect, not discussed inthis chapter, but will eventually be incorporated in the analysis model.

We initially estimated a (g) based on Monte Carlo simulations,similar to the method outlined in the section “Monte Carlo Simula-tions.” This chapter refines our understanding of a (g), but our initialestimates of a (g) were rather close to our latest estimates.

We also need to incorporate the effect of the refraction at thewater/tissue surface, which affects the value of zf. This is anothersmall 3–5% effect, but must be incorporated in the analysis model.

We have also investigated the role of spherical aberration (andother Seidel aberrations) as the focused beam penetrates into a tissue.Objective lens are usually designed to focus at a single plane, some-times accounting for an intervening glass coverslip and sometimesnot. In either case, the lens is not designed for axial scanning througha variable thickness of tissue. As the focus is scanned down into thetissue, the aberration causes a broadening of the focus and a drop inthe value R(zf). This effect must also be incorporated in the analysismodel.

Despite these shortcomings, the analysis model has provided aninitial understanding of how R(zf) encodes the optical properties ofa tissue. With refinement, this method should provide a noninvasiveassessment of tissue optical properties in a superficial layer of an intactin vivo tissue.

7.3 Basic InstrumentThe basic confocal reflectance measurement involves an objective lensfocusing a beam into a tissue such that the light converges at the focuswithin the tissue. The light reflected from the focus is returned back toa pinhole (or optical fiber) for collection and routed to a detector. Thispinhole or fiber is aligned to preferentially accept the light scatteredback from the confocal volume at the focus.

A standard commercial fluorescence confocal microscope (fCM)often offers the option to create an image using the backscattered ex-citation light, rather than the generated fluorescence. Operating themicroscope in this manner is here called a reflectance-mode confo-cal microscope (rCM). Such an rCM image is an example of a confo-cal reflectance measurement. Hence, any commercial confocal micro-scope can be used for rCM imaging. It is also possible to transmit lightthrough a thin tissue such that the collected transmitted light is refo-cused to enter a pinhole and reach the detector. Such a measurement isa transmission-mode confocal microscope (tCM), not discussed in thischapter. Figure 7.6 illustrates the basic experimental setup of an rCM.The scanning optics change the angle at which collimated light enters


Laser Beam expander Beamsplitter

Scanningoptics

Objectivelens

Focus scannedalong z-axis bymoving tissue

Pinhole

Detector

Tissue

FIGURE 7.6 A reflectance-mode confocal microscope (rCM). Light is deliveredto a focus and light that is scattered by the focus (rCM) and enters a pinholeto reach a detector contributes to the signal. The scanning optics areenclosed in a box, and the details are not shown. The scanning opticsmodulate the angle of collimated light entry into the objective lens, whichmoves the focus laterally within the tissue, achieving x , y scanning. Onegalvo mirror moves the focus in x , and a second galvo mirror moves the focusin y. The scanning optics that collect transmitted light similarly recollimatethe light from a focus at x , y such that it enters the detector pinhole. Thefocus is scanned along the z-axis within the tissue by moving either the tissueor the objective lenses.

the objective lens, which causes the focus to move laterally withinthe tissue. The backscattered light again passes through the scanningoptics to recollimate, is reflected by the beam splitter, and refocusedonto a pinhole to reach the detector.

A standard commercial time-domain optical coherence tomogra-phy (OCT) system often delivers and collects light from a single modeoptical fiber. This optical fiber serves as the pinhole of a reflectance-mode confocal measurement. Usually, an OCT system uses a low–numerical aperture objective lens, and the focus extends over a largeaxial range within the tissue. The coherence gate of the OCT systemcan be scanned within this axially extended focus. However, if a high–numerical aperture objective lens is used, the focus is restricted axiallyto a foreshortened range. In this case, it is common to keep the fo-cus and the coherence gate aligned during scanning, a method called“focus tracking.” For this chapter, we assume that the OCT systemis operated in focus-tracking mode. In this case, OCT and rCM areessentially identical in their collection of backscattered photons. OCTstill has an advantage over rCM in rejecting the background of multi-ply scattered photons due to its coherence gate. The axial extent of thecoherence gate of an OCT system (�zOCT = 0.442/�) is typically2–10 �m. For OCT, the �z in Eq. (7.4) is the smaller of the two factors:


�zOCT due to the confocal gate and 1.4/NA2eff due to the focusing

power of the lens.

7.4 Monte Carlo SimulationsThis section describes our studies with Monte Carlo computer simu-lations that mimic the behavior of confocal measurements seen exper-imentally, using a program adapted from the well-known program,Monte Carlo Multi-Layered (MCML) [2]. These studies yield an ap-preciation of the role of anisotropy (g) of scattering in rCM and OCT,which is summarized by the factor a (g) that modifies the effectivenessof the scattering coefficient �s. The factor G describes the effectivephoton pathlength in the tissue.

Using MCML, photons were delivered as a uniform circular beamthat was focused toward a focal volume at depth zf within the tissue.The NAeff of the photon entry into the tissue was 0.65, as shown in Fig.7.7. The tissue was a 1-mm-thick slab, which was sufficiently thick tomodel the rCM, but allowed for multiply scattered light that passedbeyond zf to escape the tissue. The absorption coefficient, �a, was1 cm−1. Using a slab and having this �a allowed the long-lived mul-tiply scattered photons to be terminated in a timely fashion. The scat-tering coefficient, �s, was 250 cm−1. The anisotropy of scattering, g,was varied from 0 to 0.99. The depth zf was varied from 0 to 0.0900 cm.Figure 7.7 illustrates a typical Monte Carlo simulation for zf = 0.0400cm and g = 0.90, showing the spatial distribution of the relative flu-ence rate � (W/cm2 per W delivered) or (1/cm2). Figure 7.7b showsiso-� contours, and the asterisk (*) indicates � = 1 (1/cm2).

The model launched photons as if a uniform collimated beamilluminated an ideal objective lens, focusing the beam toward the focusat x = 0, z = zf. The position of photon launch, for each of the 107

photons propagated, was x = RADIUS√

RND, y = 0, z = 0, where

0

0.02

0.04

0.06

0.08

−0.05 0 0.05

x (cm)

z (c

m)

0

0.02(a) (b)

0.04

0.06

0.08

−0.05 0 0.05

x (cm)

z (c

m)

FIGURE 7.7 The geometry of the Monte Carlo simulations. A uniformcollimated beam is focused into a 1-mm-thick slab of tissue with matchedrefractive index at front (z = 0) and rear (z = 0.1 cm) boundaries. The focusis at z = 0.0400 cm. The numerical aperture of entry into the tissue isNAeff = 0.65. (a) Relative fluence rate of light within tissue, � (W/cm2 per W)or (1/cm2). (b) Iso-� contours. Asterisk (*) indicates � = 1 (1/cm2).


FIGURE 7.8 The Monte Carlo specification of confocal collection of escapingphotons. As photons escape, their escape trajectory is backprojected to thefocal plane at z = zf. The radial distribution of photon collection at thepinhole plane is the same as the radial position in the focal plane specifiedby the backprojection of each photon’s escaping trajectory to the focal plane.

RND was a random number between 0 and 1, and the radius of thebeam at the tissue surface was RADIUS = zf tan(arcsin(NAeff)). Theangle of photon delivery was �, where sin(�) = −x/sqrt(x2 + z2

f ) andcos(�) = zf/sqrt(x2 + z2

f ). The trajectory of the launch was expressedas the projections (ux, uy, uz) of the trajectory onto the x, y, and z axes:ux = sin(�), uy = 0, uz = cos(�).

To mimic the rCM measurement, the photons escaping at the sur-face were backprojected, reversing their escape trajectory, to the focalplane at z = zf. Figure 7.8 illustrates the method. The focal plane is con-jugate with the pinhole plane at the detector. Hence, when an escapingphoton reflects off the beamsplitter and reaches the pinhole plane, itsradial position in the pinhole plane is equivalent to its radial posi-tion in the focal plane within the tissue after backprojecting its escapetrajectory. Hence, the spatial distribution of escaped photons at thepinhole can be determined. One can assess the response to pinholesof varying size. Figure 7.9 illustrates the spatial distribution of pho-tons on the pinhole plane, expresses as the fraction of delivered lightper unit area, Rc (cm−2), at a radial position r from the center of thepinhole. Results for g = 0, 0.5, 0.90, and 0.99 are shown. In this study,we used the photons collected in the central pixel of this Rc(r ) function,


FIGURE 7.9 Examples of the radial distribution of photons on the pinholeplane. Results shown as fraction of delivered light returning to the pinholeplane per unit area (1/cm2). Results for g = 0, 0.5, 0.90, and 0.99 areshown. Each family of curves shows the results for each position of the focusat zf.

Rc.pinhole = Rc(r = 10 �m), where the area of the 20-�m-diameter pin-hole is Apinhole. The confocal reflectance R = Rc.pinhole × Apinhole isequivalent to the factor S/P mentioned earlier.

Figure 7.10 shows the behavior of the confocal measurement R asthe focus is moved to increasing depth in the tissue. Each curve is for adifferent value of g. In all cases, after zf exceeds an initial depth of justa few 10–100 �m (higher g requires more initial depth), an exponentialdecay versus increasing zf is established. Eventually, a noise floor isreached due to multiply scattered photons escaping the tissue with aLambertian angular pattern and some of these photons reaching thepinhole. Ignoring the initial behavior near the surface, the depth scanis well described by Eq. (7.1), with the background term adopted fromEq. (7.2):

R(zf) = � e−�zf + B e−Czf (7.5)

where �, � , B, and C are the fitting parameters. The first exponentialdescribes the initial decay of transmission, indicated by dashed linesin Fig. 7.10. The second exponential describes the background signalas multiply scattered light reaches the detector. We are concerned withthe factors � and � , and ignore the factors B and C except when usingEq. (7.5) to fit experimental or simulated data. For a given pair of gand NAeff, the function R(zf) yields a unique pair of values for � and


FIGURE 7.10 The confocal reflectance R versus the position of the focus zf.The value of R is Rc for the 20-�m pinhole times the area of a 20-�mpinhole, which yields the dimensionless fraction of photons delivered to thetissue that reach the pinhole. The results for different g from 0 to 0.99 areshown. Thin-dashed lines indicate the initial exponential decay that specifies�. The single thick-dashed line is simple attenuation exp(−2�szf) for g = 0,which is very close to the thin-dashed line for the g = 0 data.

� . The factor � will be equated with the factor (a�s + �a)G in Eq. (7.2)to specify the factors a and G.

Figure 7.11 shows the values of � and � as functions of theanisotropy g. Both � and � drop toward zero as g approaches 1. Inother words, with every forward-directed scattering, the effectivenessof attenuation as well as the ability to backscatter light to the pinholedetector is diminished.

10−8

10−9

10−10

10−11

0 0.5g

100

20

40

60

80

100

120 (a) (b)

µ (c

m−1

)

ρ (−

)

0.5g

1

FIGURE 7.11 The parameters � and � versus the anisotropy g. As gapproaches 0, the scattering is maximally effective and both attenuation andbackscatter are maximal. As g approaches 1, scattering becomes lesseffective, and both attenuation and backscatter drop.


The results in Fig. 7.11 are the key lesson of this chapter. The fac-tor � is not a constant but decreases with increasing g. As will bementioned in the section “Literature Describing Confocal ReflectanceMeasurements,” various investigators have reported the ability of Eq.(7.1) to describe the behavior of R(zf). But the value of � in this equa-tion has usually been assigned of the value 2�s. This chapter illustratesthat the value � is dependent on the tissue anisotropy g.

Current Ongoing WorkWe are currently engaged in the next step of the analysis, which is toparse the value � into the two parameters a and G. First, we must con-sider the factor G. The factor 2Gzf is the apparent average pathlength ofphotons in the tissue that reaches the pinhole detector. Again, we usethe observation that the ability of launched photons to reach the fo-cus is the same as the ability of photons backscattered by the confocalvolume to reach the pinhole.

The Gzf is not strictly a mean of all the photon pathlengths foreach angle of launch entry, as we had assumed in our early estimatesof G. The pathlength from surface to focus for each angle (�) off thecentral z-axis is zf/ cos �. The round-trip pathlength is assumed to be2zf/ cos �, ignoring for now the effect of g of scattering within the con-focal volume on the selection of escaping paths. Longer pathlengthsare attenuated more than shorter pathlengths. Let T be the total trans-port of light to the focus and back to the pinhole, using simple expo-nential attenuation and ignoring multiple scattering. Then, the con-tribution to the total T from an incremental angle d� at each angle �is exp(−(a�s + �a)zf/ cos �)2� sin� d�, and the total T is

T =∫ arcsin(NAtissue)

�=0exp

(−(a�s + �a)zf

cos �

)2�r sin� d� (7.6)

At larger angles �, the photon pathlength 2zf/ cos � is greater andthere is more attenuation. The photons entering at smaller � suffer lessattenuation and hence contribute more to T . Comparing Eqs. (7.5) and(7.6), the value of G is

G = −ln (T)(a�s + �a)2zf

=−ln

(∫ arcsin(NA/n)�=0 exp(−(a�s + �a)2zf/ cos �)2�r sin� d�

)(a�s + �a)2zf

(7.7)

The value of G is influenced by the parameters NAeff, a , �s, �a,and zf. For a choice of a , the value of G can be determined by Eq. (7.7)


for each choice of the optical properties �s and g, for each choice ofNAeff, and for the particular zf.

In turn, the value a can be determined for each specified G. Com-paring the factor � with the term (a�s + �a)2G, the value of a is

a = (�/2G) − �a

�s(7.8)

The protocol for determining a and G is to first determine � (Fig.7.11), then iteratively apply Eqs. (7.6) and (7.7) to specify G, and thenapply Eq. (7.8) to specify a . After at least three iterations, the valuesa and G stabilize to yield values that satisfy Eqs. (7.6) to (7.8) and thevalue �. This protocol can be repeated for each choice of �s, g, andNAeff. The results are shown in Fig. 7.12.

The values of a start at a value just below 1 and drop toward zeroat very high g values close to 1. At high g, the effectiveness of �s inattenuating R is diminished and the factor a�s drops toward zero. Thedata for a follow the expression:

a = u(

1 − exp(−(1 − g)v

w

))(7.9)

where u = 1.017, v = 0.351, w = 0.489. In this example, the value ofa at g = 0 is 0.904. Apparently, even when scattering is maximallyeffective, that is, g = 0, there are some multiply scattered photons thatstill reach the focus. Hence, the a is less than unity, even for g = 0.

The values of G start at 1.11 for g = 0 and rise to 1.13 at high gvalues. At high g, the ability of photons launched from more obliqueangles to reach the focus is enhanced. Hence, the pathlengths from

FIGURE 7.12 The parameters a and G versus the anisotropy g. At low g,scattering is maximally effective and a is close to 1. At high g, scattering isless effective and a drops toward zero. At high g, the more obliquely launchedphotons can reach the focus, so the factor G increases.


these oblique angles contribute more to the R. The value of G increasesslightly. This effect is greater for larger NAeff.

Why do we bother with all this analysis? The motivation is tocreate an algorithm, getmurho (mua, mus, g, NAeff), that will predictthe experimental values of � and � in Eq. (7.1) for a given choice oftissue properties (�a, �s, g) and NAeff. Such an algorithm would allowthe rCM measurements, R(zf), to specify the �s and g of a tissue. The�a is either known or is much smaller than �s and well approximatedby the expected value for a tissue with particular absorbers (water,blood, melanin, etc.). The goal is to use the optical parameters �s andg to characterize the ultrastructure of a tissue, providing a fingerprintfor classification of the tissue’s structural status.

7.5 Literature Describing Confocal ReflectanceMeasurementsThere have been several reports that have strived to use the attenu-ation coefficient, �, in Eq. (7.1) to characterize a tissue. This sectionpresents a short review of those papers.

The idea of extracting information about the optical scatteringproperties of an imaged sample was first proposed for OCT by Schmittet al. [3] based on similar efforts in lidar [4] and ultrasound [5].Originally, Schmitt based his model on a first-order approximationto multiple-scattering theory, namely, that I (z) = �b exp(−2�tz), inwhich �t is the total attenuation coefficient, approximately equal tothe scattering coefficient when the absorption coefficient is very low(�t ≈ �s when �a << �s), and �b is the backscattering coefficient whoseunits are dimensionless and not comparable to �a, �s, or �t (cm−1).Their �b is the same as the factor � in this chapter. Their model as-sumed that for point source illumination, the light contributing to thesignal was scattered once, while multiple small-angle scattering wasneglected. In a follow-up effort, Schmitt et al. [6] included focusingin their model and extracted �t from different arterial layers usingdifferent NA lenses under different illumination wavelengths. In thiswork, they outlined some of the complex relationships between focus-ing, wavelength, the OCT signal, and the evaluated optical properties.However, both experiments ignored the effect that anisotropy of scat-tering had on an OCT signal, either through the magnitude of thebackreflected light or through multiple small-angle scattering to andfrom the backscattering event.

Since these early studies over a decade ago, there have been severalpapers that attempted to extract optical properties from confocal andOCT images. These efforts can be categorized into two groups: thosethat use the single-scattering model to extract only �s [7–10], and thosethat use multiple-scattering models in an attempt to extract both �s


and g [11–13]. The first group of papers has the advantage that inboth confocal and OCT, there is an exact solution to fitting the single-scattering model and, up to a limited optical depth their fitted �s

values are rather stable and accurate. The second group of papers(OCT only) chose to extract additional information about anisotropyfrom data at all depths, but with poorer accuracy.

Thus far, theoretical models that describe the effects of multiplescattering and focusing have been limited to OCT, as have attemptsto extract both �s and g from images. Thrane et al. [14] developed amodel that made use of the extended Huygens–Fresnel principle [15]and the shower curtain effect [16] to explain the complex relationshipbetween the OCT signal, focusing and defocusing, and multiple scat-tering by the medium. With its proper accounting of the free spacebetween the objective lens and the tissue, the multiple small-anglescattering to and from the probing depth, and the backscattering off arough surface embedded in the imaged scattering medium, Thrane’smodel [14] represents the most complete effort at modeling OCT sig-nals to date. This model has been used by Levitz et al. [11] to char-acterize normal and atherosclerotic arteries ex vivo, and by Knuttelet al. [12] to monitor skin treatments. However, the Thrane model isquite complex and runs into computational problems during fitting inhighly anisotropic media (g ≥ 0.99). Moreover, it is not valid outsidethe paraxial approximation (g < 0.866), and thus assumes particlesthat dominate the scattering fall within a narrow range of sizes.

Another model that describes multiple scattering and focusing inOCT was developed by Dolin [17] based on the small-angle approxi-mation to the radiative transport equation. The underlying principlesbehind the Dolin model are similar to those in the Thrane model (in-cluding the restriction on g); however, in Dolin’s model, the final equa-tions are not in closed form. As a result, a genetic algorithm is neededto extract optical properties from tissues. Dolin’s model requires thatthe objective lens be in contact with the tissue. The efforts by Turchinet al. [13] to extract optical properties using the Dolin model havebeen quite fruitful, and their algorithm has been used in clinics inboth Russia and the United States to identify cervical cancer.

It is worth noting that modeling the effects of multiple scatteringon OCT and confocal imaging has not been without controversy. Onehotly debated topic is at what optical depth the signal no longer canbe described by a single exponential. According to both Thrane’s andDolin’s OCT models, this depth is quite superficial, near a round-tripoptical depth of OD = 2�szf = 1. However, the studies that extractedoptical properties using the single-scatter model [6–9] have claimedthat multiple scattering begins to reduce the attenuation (i.e., the sig-nal “turns the corner”) only at larger optical depths. Three of the fourstudies [6–8] restricted the maximum depth of fitting pixels to an op-tical depth of approximately 2, while the other [10] claimed that their


results were still accurate even at total round-trip optical depth of12. Furthermore, other confocal modeling papers [18–20] (geared atdetermining the maximum optical depth at which one can resolve areflecting structure) also attempted to characterize the exponential de-cay of confocal signals. These analyses showed that a single exponen-tial could still describe the attenuation up to total round-trip opticaldepths ranging between OD = 6 [18] and OD = 12 [19], depending onthe pinhole size, wavelength, and NA [18–20].

In our experience with OCT using a 1310-nm wavelength (notshown here), we find the signal begins turning the corner aroundround-trip OD = 6. The Monte Carlo simulations in Fig. 7.9 showthe signal turning the corner at zf = 0.0400 cm, or at a round-trip OD= 20. The initial data at OD < 2 is not reliable for fitting the initialexponential decay. Fitting with two exponentials, as in Eq. (7.5), al-lows the information from OD ≈ 0.2 to OD ≈ 20 to contribute to thespecification of the initial exponential.

References1. R. Samatham, S. L. Jacques, and P. Campagnola, “Optical properties of mutant

vs wildtype mouse skin measured by reflectance-mode confocal scanning lasermicroscopy (rCSLM),” J Biomed Opt 13, 041309 (2008).

2. L. -H. Wang, S. L. Jacques, and L. -Q. Zheng, “MCML—Monte Carlo modelingof photon transport in multi-layered tissues.” Comput Methods Progr Biomed 47,131–146 (1995).

3. J. M. Schmitt, A. Knuttel, and R. F. Bonner, “Measurement of optical propertiesof biological tissues by low-coherence reflectometry,” Appl Opt 32, 6032–6042(1993).

4. R. C. Anderson and E. V. Browell, “First- and second-order backscattering fromclouds illuminated by finite beams,” Appl Opt 11, 1345–1351 (1972).

5. R. A. Sigelmann and J. M. Reid, “Analysis and measurement of ultrasoundbackscattering from an ensemble of scatterers excited by sine-wave bursts,”J Acoust Soc Am 53, 1351–1355 (1973).

6. J. M. Schmitt, A. Knuttel, M. Yadlowsky, and M. A. Eckhaus, “Optical-coherencetomography of a dense tissue: statistics of attenuation and backscattering,” PhysMed Biol 39, 1705–1720 (1994).

7. T. Collier, D. Arifler, A. Malpica, M. Follen, and R. Richards-Kortum, “Determi-nation of the epithelial tissue scattering coefficient using confocal microscopy,”Sel Top Quantum Electron 9, 307–313 (2003).

8. T. Collier, M. Follen, A. Malpica, and R. Richards-Kortum, “Sources of scat-tering in cervical tissue: determination of the scattering coefficient by confocalmicroscopy,” Appl Opt 44, 2072–2081 (2005).

9. R. O. Esenaliev, K. V. Larin, I. V. Larina, and M. Motamedi, “Noninvasivemonitoring of glucose concentration with optical coherence tomography,”Opt Lett 26, 992–994 (2001).

10. D. Faber, F. van der Meer, M. Aalders, and T. van Leeuwen, “Quantitative mea-surement of attenuation coefficients of weakly scattering media using opticalcoherence tomography,” Opt Express 12, 4353–4365 (2004).

11. D. Levitz, L. Thrane, M. H. Frosz, P. E. Andersen, C. B. Andersen, J. Valanci-unaite, J. Swartling, S. Andersson-Engels, and P. R. Hansen, “Determinationof optical scattering properties of highly-scattering media in optical coherencetomography images,” Opt Express 12, 249–259 (2004).


12. A. Knuttel, S. Bonev, W. Knaak, “New method for evaluation of in vivo scatter-ing and refractive index properties obtained with optical coherence tomogra-phy,” J Biomed Opt 9, 232–273 (2004).

13. I. V. Turchin, E. A. Sergeeva, L. S. Dolin, V. A. Kamensky, N. M. Shakhova, and R.Richards-Kortum “Novel algorithm of processing Optical Coherence Tomog-raphy images for differentiation of biological tissue pathologies,” J Biomed Opt10, 064024 (2005).

14. L. Thrane, H. T. Yura, and P. E. Andersen, “Analysis of optical coherencetomography systems based on the extended Huygens–Fresnel principle,”J Opt Soc Am A 17, 484–490 (2000).

15. R. F. Lutomirski and H. T. Yura, “Propagation of a finite optical beam in aninhomogeneous medium,” Appl Opt 10, 1652–1658 (1971).

16. I. Dror, A. Sandrov, and N. S. Kopeika, “Experimental investigation of the influ-ence of the relative position of the scattering layer on image quality: the showercurtain effect,” Appl Opt 37, 6495–6499 (1998).

17. L. S. Dolin, “A theory of optical coherence tomography,” Radiophys QuantumElectron 41, 850–873 (1998).

18. J. M. Schmitt, A. Knuttel, and M. Yadlowsky, “Confocal microscopy in turbidmedia,” J Opt Soc Am A 11, 2226 (1994).

19. M. Kempe, W. Rudolph, and E. Welsch, “Comparative study of confocal andheterodyne microscopy for imaging through scattering media,” J Opt Soc Am A13, 46 (1996).

20. C. L. Smithpeter, A. K. Dunn, A. J. Welch, and R. Richards-Kortum, “Penetrationdepth limits of in vivo confocal reflectance imaging,” Appl Opt 37, 2749–2754(1998).


C H A P T E R 8Tissue

UltrastructureScattering with

Near-InfraredSpectroscopy:

Ex Vivo and In VivoInterpretation

Brian W. Pogue, Venkataramanan Krishnaswamy, and Ashley M. Laughney

8.1 IntroductionElastic scattering that dominates most of the visible and near-infraredlight interaction with tissue has a complex origin, but analysis of thissignal holds promise for insight into tissue ultrastructural morphol-ogy characterization. Scatter originates from refractive index changesin the features of the tissue that are between the size scale of nanome-ters and micrometers, and the measurement of this scatter signal canbe achieved readily with the range of wavelengths from visible up tonear infrared. Near-infrared propagation has been of particular inter-est because of the exceptionally low absorption at these same wave-lengths, and the combination of high scatter and low absorption leads

193


to an interesting transport regime, which is translucent over short dis-tances and diffuse over longer distances. This transport has been usedto take measurements through bulk tissue, with distances up to 12–14cm being feasible in the breast. Much focus has been devoted to mod-eling the scattering and absorption separately as a way to extract andinterpret the quantitative absorption due to the molecular absorbingchromophores present in tissue. Yet extraction of the scattering spec-trum has only recently been realized and analyzed in sufficient detailto understand what this can provide in terms of tissue structure andfunction. The benefit of understanding this signal is outlined here,and the tools to quantify it are demonstrated and discussed. It is notobvious that the elastic scattering spectrum can be uniquely exploitedfor diagnostic medical benefit, but it is certain that the origin of thisspectrum provides fundamentally new information about the tissueitself, on a distance scale that cannot be reasonably imaged with anyother diagnostic tool.

The elastic scatter in tissue is often described as resulting fromthe submicroscopic and microscopic fluctuations in the local indexof refraction, which are disordered by the high submicroscopic com-plexity of all tissues. Primary sources of scatter include the bi-lipidmembranes around other features such as cellular organelles andthe structural elements composed of molecules such as collagen andelastin.1−5 This scatter does not have a characterizable pattern whenmeasured at sub millimeter resolution, because of extreme variabilityobserved in tissue morphology at these size scales, but highly av-eraged regions of tissue, as measured over millimeters, have beenfound to have scattering patterns, which can be characterized by ana-lytic functions and polynomial expressions. In particular, the angularspread of scatter from a millimeter-sized tissue surface or through athin slice of tissue has a scatter phase function that appears to matchthose predicted by Henyey and Greenstein (H–G), among others.6,7

Many other phase functions have been proposed to better character-ize angular redistribution of light by different scattering centers intissue; but because these measures are highly averaged at millimetersize scales, it is not clear that they would be superior to the H-G func-tion, a priori. The elastic scatter coefficient, �s, as a function of wave-length, , is therefore complicated to measure because of the highlyanisotropic angular spread, with values of the average cosine of thescattering angle (g) near 0.8–0.99 having been directly measured.8 Thereduced scattering coefficient is defined as �s′ = �s(1 − g), which al-lows interpretation of scatter spectra over long distances where theanisotropic effects of the individual scattering event are not mea-surable. In distances beyond 3–5 scatter lengths,9 the field appearsdiffuse with an elastic scatter interaction coefficient, which is “re-duced” by the factor (1 − g). The spectrum of �s′() can be estimated

195T i s s u e U l t r a s t r u c t u r e S c a t t e r i n g

with diffusion theory–based interpretation of measured transmissiondata.10,11

The breast parenchyma can be broken down into the dominantmacroscopic subtypes of epithelium, stroma, and adipose tissue. Thescattering spectra and phase functions are different in each of thesetissues because the origin of the tissue composition is different. Each ofthese is examined in detail, at the nanoscopic and microscopic levelsin the following sections. In order to fully understand the measur-able scattering features from breast tissue and the exact value it canhave for diagnosis, we must analyze the signatures themselves frombasic measurements, and then translate these measurements into thetype of signals that can be measured in a clinically useful situation.Two potential uses are discussed at the end of this chapter, namely:(1) noninvasive tomographic imaging for diagnostic applications and(2) intrasurgical surface scanning for identification of tumor bound-aries and tissue pathology. The challenges in each of these practicalapplications are different, yet a fundamental understanding of whatthe scattering spectrum is from tissues is central to determining theutility of these approaches.

8.2 Understanding Light ScatteringMeasurements in TissueIn a sufficiently macroscopic sense, biological tissue can be seen asan ensemble of particle-like scattering centers (epithelial cells, fibrob-lasts, macrophages, adipocytes, etc.) embedded in a highly hetero-geneous supporting medium containing gel-like polysaccharides, fi-brous proteins, and other interstitial fluids that make up the rest of theextra-cellular matrix (ECM). The refractive index fluctuations in thiscomplex medium, with size scales ranging from a few nanometers toa few millimeters, are thought to be the source of light scattering. Ina broad sense, the scattering mechanism falls under a combination ofthe Rayleigh and Lorenz–Mie regimes, with the latter dominating theinteraction. But analytical modeling is not feasible, understandablydue to extreme variability in shape, size scale, and distribution of thescatterers.

The redistribution of the incident light in tissue is influenced bythe morphology of scattering features and their spatial distributionwithin the probed volume. This signal is characterized by an effectivephase function and its wavelength dependency, both of which couldbe measured experimentally. Neoplastic processes, from early dyspla-sia to the most advanced stage of infiltrating tumors, perturb the tissueultrastructure, thereby altering the local light scattering response. Boththe phase function and the wavelength dependency of the scattering


Tissue Tissue

(a) (b)

Wavelength

Irra

dian

ce

Detection cone

FIGURE 8.1 (a) A tomographic measurement scheme showing point sourceand point detectors used to measure diffusely scattered light in a tissueblock. (b) An illustration of microsampling imaging technique where highlylocalized illumination and detection scheme is used to measure the localscatter spectrum directly. See also color insert.

response are affected providing intrinsic spatial and spectral signa-tures that could be measured using suitable optical techniques. Strongmultiple scattering and absorption of light by the tissue chromophoresare often the major confounding factors in such measurements, the ef-fects of which should be minimized or accounted for in order to relatethe measured signal to the underlying tissue ultrastructure.

The extent to which the incident and scattered signals are localizedby the measurement system plays a crucial role in determining thetype of information obtained. Two contrasting measurement schemesare illustrated in Fig. 8.1, a tomographic scheme to measure diffusescatter signals and a weakly confocal scheme to measure localizedscatter signals from superficial tissue surfaces. Both these schemeswill be discussed in detail in the following sections.

In order to understand how changes in tissue ultrastructure atnanoscopic and submicroscopic levels influence macroscopic scattersignatures, and what causes these changes at the biological level, anintegrated approach is required, where the measured scatter data iscompared to other diagnostic schemes that provide complimentaryinformation. An example of such an approach is illustrated in Fig. 8.2,where scatter images obtained from the microsampling imaging sys-tem are compared with standard histopathology images to relate thescatter signatures to their corresponding tissue types. Phase-contrastimaging is used to assess the local refractive index fluctuations in thesample. Electron microscopy is used to analyze the orientation andpacking of collagen fibers, one of the main sources of scattering in tis-sue, in regions associated with malignant epithelia. A portion of thetissue sample, within a region-of-interest, is sampled using laser cap-ture microdissection (LCM) technique, and a low-density microarray


Micro sampling imaging White light image H &E

Phase contrast

(a) (b)Gene expression Electron microscopy

FIGURE 8.2 (a) A schematic of the microsampling imaging system, whereconfined illumination and confocal detection are used to sample the localscatter spectrum in bulk tissue. (b) An illustration showing data from othercomplementary modalities obtained along with the optical imaging data tohelp understand the origins of light scatter signatures in tissue. See alsocolor insert.

analysis is performed to identify gene expressions specific to the ma-nipulation of ECM and adhesion molecules.

8.3 Ex Vivo Measurements: Analysisof Scatter SignaturesThree laboratory methods of ex-vivo analysis have been used to eval-uate how macroscopic subtypes of tissue affect the distribution ofscatter, particularly in the breast. These three methods include

1. Characterization of backscattered light using microsamplingreflectance spectroscopy;

2. Characterization of microscopic and submicroscopic refrac-tive index fluctuations using phase-contrast microscopy;and

3. Analysis of the packing density and angular distribution oforganelles within a tissue subtype using transmission electronmicroscopy.

A different transport regime applies to each system; this in turngoverns the system’s spatial resolution and ultimately the level ofdiscrimination that can be achieved between tissue subtypes.


Breast tissue in the broadest sense has two primary subdivisions:parenchyma and stroma. Parenchyma consists of the functional tis-sues; in the breast this includes the milk ducts and lobules. These unitsare composed of epithelial cells and abnormal proliferation of such iswhat defines a breast cancer. Stroma refers to the structural tissues ofan organ. It predominantly consists of the extra-cellular matrix (ECM),as well as a compilation of cells including fibroblasts, myofibroblasts,fat, immune, vascular and smooth muscle cells. The ECM is a noncellu-lar, solid-state, structural component of the tumor microenvironment.Collagen fibers present in the ECM are the largest source of scatter inthe stroma because they are both fibrous and have a high refractiveindex (RI = 1.47). Pathologists easily distinguish between epithelium,stroma, and adipose, so we adopt this classification of macroscopicsubtypes with an understanding of each feature’s constituents. Stro-mal tissue scatters significantly more light than the epithelial cells em-bedded in its ECM, further adipose tissue scatters much less. Hence,scatter is an excellent mechanism of discrimination between these sub-types. Further, the intensity of the scatter signature in stroma couldrender cytological and architectural features of this supportive struc-ture particularly differentiating in terms of a diagnosis.

The effective resolution at which scatter features could be im-aged in tissue primarily depends on the applicable photon transportregime. In the case of deep tissue tomographic imaging, where photondiffusion dominates the transport, millimeter scale resolution is typ-ically achieved. However, for surface scanning applications, higherresolution is possible through spatial confinement of the signal usingweakly confocal optical schemes.

Microsampling reflectance spectroscopy, a surface scanning tech-nique described later in this section, uses a similar scheme to samplescatter measures at a lateral resolution of approximately 100 micronson tissue surface. The choice of this spot size is crucial in that it is smallenough to keep light transport modeling simpler and yet large enoughto allow scanning large areas of tissue surface in less time. In addition,scanning at this resolution yields average scatter measures that helpnormalize within patient variability, which is usually an impedingfactor in most tissue characterization measurements. Figure 8.3 com-pares the typical resolution levels obtained in other common opticalimaging modalities to size scales of various biological constituentsthat make up tissue.

In addition to low resolution ex vivo imaging of scatter featuresusing microsampling reflectance spectroscopy, high-resolution imag-ing using phase-contrast microscopy and electron microscopy couldbe utilized to investigate the origins of scatter contrast in tissue atsubmicron scales and how it relates to tissue pathology.

Phase-contrast measures are not directly related to scatter, ratherthey detect changes in optical path length. This will be discussed in


Resolution limit

Humaneye

Lightmicroscope

*Phase contrast

Electronmicroscops

Infrared

Visible

0.1nm

1nm

10nm

100nm

1µm

10µm

100µm

1mm

Adipocytes

Epithelial cells

Collagen (length)

Viruses

Proteins

Collagen (diameter)Amino acids

Atoms

Ultra violet

γ-Raysand x-rays

*Microsamplingreflectancespectroscopy

Radio

EM spectrum Biological reference

FIGURE 8.3 Resolution limits. (1) The resolution of microsampling reflectancespectroscopy is limited by its illumination and detection spot size (100 �m).(2) For standard phase-contrast illumination, the smallest resolvable phasedifference is approximately /100 to /3012; this translates to ∼50 nmresolution. (3) Electron microscopy is able to resolve specimens on thenanometer scale.

more detail shortly, but for now it is important to recognize that quan-tification of phase-contrast data requires great care. Meaningful in-terpretation of information provided by scatter-imaging modalities islargely dependent on correlates with histology. This presents a uniqueopportunity to directly associate imaging signals with characteristicsof cellular morphology and even genetic expression.

In the following sections, data acquisition and analysis of the scat-ter signatures provided by microsampling reflectance spectroscopyand phase-contrast microscopy are discussed in detail. In addition,biophysical origins of scatter contrast will be investigated using ge-nomic analysis and transmission electron microscopy.

Microsampling Reflectance SpectroscopyMicrosampling reflectance spectroscopy uses a weakly confocal sys-tem with a linear translation stage to provide a highly localizedmeasure of scatter in the backward direction. The scatter signal, as


measured by this system, is an ensemble averaged response of a local-ized region on tissue surface, approximately 100 �m in diameter anda few hundred microns in the depth co-ordinate. The signal is alsoaveraged in terms of the phase function of the backscattered light toan extent permitted by the field of view of the optics. Fresh breast tis-sue from biopsy or reduction is mounted on glass slides. The signal isnormalized to background reflection from the glass and to a referencespectrum that accounts for the instrumental spectral response. Opticsare constrained so that the illumination and detection spot sizes areless than one scattering length in diameter (approximately 100 �m intissue). This limits detected photons primarily to those experiencing asingle elastic collision. The axis of the glass–sample interface is tiltedto remove specularly (mirror-like) reflected photons, which are notinfluenced by the tissue ultrastructure, from the detection path.

The goal of microsampling reflectance spectroscopy is to extractscatter parameters related to tissue ultrastructure. Careful considera-tion must be taken to ensure the signal does in fact reflect structuralfeatures. While backscatter is primarily an effect of tissue constituents,surface artifacts on the specimen could also generate reflected pho-tons that are not suggestive of tissue structures and ultimately distortour signal as illustrated in Fig. 8.4. Therefore, it is very important toensure tissue specimens are mounted in a flat manner on the glassslide. This is generally not an issue because breast biopsy specimensare quite deformable and surface tension favorably pulls the moistspecimen toward the glass slide. Tissue storage and handling furtherinfluences scatter features. Tissue will dehydrate and become increas-ingly stiff and proteins will denature with time. It is imperative toimage the tissue when it is fresh and to maintain its moisture witha neutral phosphate buffer during the imaging process. Immediatelyupon completion of a scan, tissue should be placed in 10% formalin

Confocal MRS scan

a b c

a

b

c

Position

Sig

nal

FIGURE 8.4 An illustration of how changes in tissue ultrastructure (a, b) andsample artifacts (c) can influence the measured scatter signal.


to begin the fixation process. This will preserve the histology of thesection for future analysis.

Characterization of the scatter signature is achieved by fitting theacquired spectra to an empirical model. In the absence of significant lo-cal absorption, the relationship between the measured irradiance andwavelength would be approximated by a power law–type empiricalrelation:

IR=A−b (8.1)

where A is the scattering amplitude and b is the scattering power.However, in the presence of significant local absorption, for very smallsource–detector separations, an empirical relationship can be used toestimate the spectral reflectance:

IR=A−b exp (−k.c (d.HbO2 () + (1 − d) Hb ())) (8.2)

if scattering and absorption coefficients are within the typical rangefound in tissue. Parameter c is proportional to the concentration ofwhole blood, k is the path length, and d is the hemoglobin oxygensaturation fraction. The spatial extent of illumination is less than 1mean free-path length of interaction (typically 100 �m), so that thedetected photons are thought to be predominantly singly scatteredand the effect of the exponential term in the modified power law is thennegligible. In regions where high local concentration of chromophoresare encountered, like regions with blood pooling or high vascularity,the exponential term is needed as a correction factor to accuratelydescribe the scatter spectrum.13

Characterization of a tissue’s scatter signature is achieved by fit-ting spectra to the power law model for scattered amplitude (A) andscattering power (b), and the signal may be integrated for a quickmeasure of average scattered irradiance. Figure 8.5 is an example ofthe distribution of these parameters in normal and malignant breasttissue. Further, the gross effect of these parameters is effectually illus-trated through concatenation of parameters into the RGB channels ofan image.

Pathologists identify disease through interpretation of gross tissuespecimens and Hematoxylin and Eosin (H&E) stained sections of thetissue of interest. Histology is the gold standard in disease recognition,and the most valuable interpretation of the scatter signature can beachieved through correlation with histology. Immediately followingan image scan, biopsied samples may be fixed, sectioned, and stainedwith H&E. The stain permits visualization of individual epithelialcells embedded in the ECM. Association between scatter measuresand the morphology and distribution of cellular features explains thegradient in the scatter signature. Epithelial cells scatter significantly


Normal tissue from breast biopsy

Average irradiance Average irradianceNormal breast tissue

Invasive breast carcinoma

Combination of all three pa-rameters in RGB channel

log(rel. scatter ampl.) log(rel. scatter ampl.)

Rel. scatter power Rel. scatter power

200

20406080

20 1020406080

20 40 60 80100120100

5

-5

0

406080

20406080

10050 100 150

2 20406080

10020 40 60 80

2

10

5

0

-5

1

0

100120

1

0

10050 100 150

10050 100 150

20 20

100200300400

200 400 600

20

20605040302010

605040302010

10

040 60 80 120100

406080

100

10

0

400

600

800200400600800 12001000

Invasive carcinoma from breast biopsy

FIGURE 8.5 Spatial distribution of scatter parameters, with white light imagesat top and three types of derived scatter parametric data below, for a normalbreast tissue sample (left column) and an invasive carcinoma sample (middlecolumn). Compound images of the parameters are shown at the right. Seealso color insert.

less than the fibrous stroma, and fat scatters minimally. Malignancy ischaracterized by epithelial cell proliferation and abnormal nuclei size.The spatial gradient illustrated in the scatter parameters has diagnos-tic potential because it shows significant changes in cell size and theratio of stroma to epithelium.

Phase-Contrast MicroscopyPhase-contrast microscopy works by converting small phase shifts inlight passing through a transparent specimen (unobservable by thehuman eye) to amplitude shifts in the projected image. Small phaseshifts are produced by slight variations in the refractive index of tissuefeatures. In a bright-field light microscope, light from highly refractivestructures bends away from the center of the lens more so than lightfrom less-refractive structures, typically producing an approximatephase lag of /4. A phase-contrast microscope is an inverted micro-scope with a phase plate mounted near the objective rear focal plane.A positive phase plate retards light passing through the center of thelens by /4. This interferes constructively with the delayed light at


the edge of the lens (that which was diffracted). The positive phaseplate puts these two waves in phase, and brightness is enhanced whenfocused. For a more robust treatment of phase-contrast microscopy,please refer to Bennett et al.14 or Murphy.15

It is important to reiterate that phase-contrast enhancement re-flects variations in the optical path of light—not just variation in refrac-tive index. The optical path length is proportional to both the refractiveindex and thickness of the tissue specimen, so while refractive indexvariations illustrate scatter features, thickness of the tissue specimenis a product of how the tissue was cut. To ensure fairness in detectingrefractive index changes, the tissue specimen must be uniformly cut.This may be feasible using a microtome for thin slices (4–10 �m). It isbest to keep the thickness of the slide no greater than the size of anindividual cell. Phase-contrast measures are performed on frozen sec-tions as compared to paraffin-embedded sections because the fixationprocess will influence scatter mechanisms. Further, if sections are toothick, images will be distorted by the halo effect. Figure 8.6 illustratestypical artifacts found in phase-contrast images.

An example of phase-contrast image from normal breast tissue isshown in Fig. 8.7. Because the sample thickness is reasonably uniform,the phase-contrast images are a direct measure of local refractive indexfluctuations. Analysis of phase-contrast images is achieved throughcorrelation with histology. Following imaging, sections should bequick fixed and stained using H&E. High-resolution digital imagesof the H&E slide may be acquired using an automated scanning andimaging microscope that creates mosaic images of the slide. Resolutionof the imaging should be set to the resolution of the phase-contrastmicroscope. Various computer programs may be used to coregisterthe phase-contrast image with its corresponding H&E slide. Highly

(a) (b)

OP

DIr

radi

ance

OP

DIr

radi

ance

FIGURE 8.6 An illustration of typical artifacts in phase-contrast images:(a) the halo-effect and (b) reversal of contrast due to phase wrap around.


Phase contrast + H&E Overlay and selectROI based on H&E

Isolate pixels andexport toMATLAB

Phase contrastanalysis

Analyze distributionof pixel values

20×

FIGURE 8.7 An illustration of data extraction procedures from thephase-contrast images obtained from an unstained section of a breastcarcinoma specimen. See also color insert.

specific regions of interest may be selected, such as the stroma nearepithelial cells (illustrated in Fig. 8.7) and pixel values then exportedfor analysis.

A correlation between scatter spectra and histology facilitates in-vestigation of genetic expression in distinct features of the scatter spec-tra. Laser capture microdissection (LCM) permits extraction of tissueon the order of 5–7 �m (essentially the size of a single cell). A lasermounted on an inverted microscope provides enough energy to tran-siently melt a thermoplastic film mounted above the tissue specimenin a precise location, binding it to the targeted cell. Cells are lifted fromthe specimen and RNA is extracted, amplified, and probed using low-density genetic arrays. The preparation of tissue for phase-contrastmeasures (4-�m-thick sections of frozen breast tissue, mounted onuncharged slides) is ideal for LCM extraction following a quick H&Estain for visualization of individual cells. Therefore, we can directlycorrelate the phase-contrast scatter signature with genetic expressionin distinct regions of interest.

Electron Microscopy: Understanding the SubmicroscopicSource of ScatterMorphological changes at the protein level may be visualized usingelectron microscopy. Collagen fibers are the main source of scatter inthe stroma. Elastic scatter in stromal tissue originates from microscopicfluctuations in RI that occur between the cytosol and distribution of


organelles such as collagen. Although it is likely impossible to im-age the RI directly through collagen fibers, it is possible to consideralternative imaging systems to visualize these features. Electron mi-croscopy is considered one of the highest resolution systems availablefor such imaging and has been used in several studies to at least vi-sualize the substructure of the tissue and infer that if these featureshad changes in refractive index, then the scatter signature could bepredicted.16

The images provided by electron microscopy allow for quantifi-cation of the packing density and orientation of collagen fibers, one ofthe strongest scatterers in breast tissue, across diagnostic categories,as are seen in the Fig. 8.8. The interpretation of these images is thento assess the orientation variance, such as packing density, angularspread of the fibers, etc. Some of these features were assessed in theimages below to illustrate how this can be achieved. In this type ofimaging, it is fairly easy to assess that collagen density and orientation

FIGURE 8.8 Transmission electron microscopy analysis of collagen fiberorientation and packing density, with representative images at left and anexample of how density and orientation can be displayed in a histogram dataset for interpretation of the collagen organization.


changes dramatically with change in response to the presence of grow-ing tumor epithelium nearby. The magnitude of these changes are stillan ongoing subject of study, and the large variance in these parame-ters is the critical issue to assess, as this would point to how reliablethis signature would be as a tool to detect all tumor tissues.

8.4 Diagnostic Imaging: Approaches for In Vivo UseTomography of tissue with diffuse spectroscopy can be used to re-cover scatter spectra and thereby provide noninvasive measurements.Breast tissue imaging has been done with NIR tomography for a fewdecades, and, while still largely in research phases, has been usedmoderately in large single center trials in

1. breast cancer risk screening17,18;

2. screening as an adjunct to mammography,19 differential diag-nosis as combined with US and MRI 20−23;

3. prognostic trials to track response to neoadjuvant therapy.24

All these approaches have slightly different technological solu-tions being used, as the optimization of the technology is ongoingas clinical studies are outlined. However, all have used spectroscopicapproaches that allow recovery of the reduced scatter coefficient spec-trum from the tissue.19,25,26 Conversion of this spectrum to scatteringparticle size and number density has been demonstrated by a fewgroups, and pilot data presented from healthy and diseased tissuesbeing imaged.

Although there are reasonable approaches to derive scatter parti-cle size and density from the scatter spectrum, this can only be donewith some basic assumptions, which are outlined here. The processoutlined by Wang et al. used the following assumptions:

1. The scattering medium was the transition from cytoplasm orinterstitial fluid and the bi-lipid layer membrane (using theratio n2/n1 = 1.09 for fitting).

2. The phase functions could be linearly summed for particledistributions in tissue, using Mie theory calculations:

�′s() = N0

p∑i=1

f (ai )(�a2i )Qscat(m, ai , )[1 − g(m, ai , )]

(8.3)

where Qscat is calculated from Mie theory and N0 is the totalnumber density.


3. The normalized particle number density, f (a ), is well fit byan exponential decay with respect to the size of the scatterers,a , such that

f (ai ) = e−ai /〈a〉

〈a〉 (8.4)

where 〈a〉 is the average of the distribution.22,27

Given these assumptions, it was found that the measured value ofthe reduced scattering spectrum could be fit to the Mie theory estimate,and the effective values of average particle size 〈a〉 and number den-sity, N0, can be estimated. Clearly, these assumptions are not withoutpotential error, and it is feasible that errors in these could lead to er-roneous results; however, each assumption was analyzed for its effectupon the resulting estimates and it is likely that the value of particlesize is most reliable in this estimation process, while the value of num-ber density is subject to the most variation from any systematic errors.

The mapping from scattering amplitude and power into a pairof “effective” scatterer size and density was determined by Wanget al.22,27,28 to be feasible for the tomography images. These are called“effective” values because of the significant assumptions going intotheir creation, as denoted above. An example of the type of images isshown in Fig. 8.9. In these cases, the scatter amplitude and power areshown, as well as the effective scatter size and density values.

Num. density

HbT Oxy Wat

Scatt. ampl. Mean sizeScatt.

FIGURE 8.9 Reconstructed NIR images of a 73-yr-old female subject with a3.5-cm IDC in her left breast. Images showing the plane of the tumor in thebreast, sliced in a coronal view. The panel of images shows total hemoglobinconcentration (HbT), oxygen saturation (Oxy), water fraction (Wat), scatterpower (Scatt. Power), and amplitude (Scatt. Ampl.), as well as effective <a>(Mean Size) and N (Num. Density) images.27 See also color insert.


8.5 Therapeutic Imaging: Surgical AssistThe potential for using scatter signatures to enhance imaging duringsurgical resection of a tumor is clearly pressing. The pathway to ad-vance this methodology would be to develop an imaging system thatis easy to use and integrates into the surgical work flow in a seamlessmanner. Then the display of the information must be chosen to allowthe surgeon to interpret the images in real time to allow judgmentsabout when to carry out further resection. Prior to this happeningthough, studies would be carried out on resected tissues to validatethe accuracy of the system at identifying involved tissue margins dur-ing the surgical procedure. Thus, comparing in vivo data to ex vivomeasurements is a critical part of developing this method into a usefulclinical or biological tool.

8.6 AcknowledgmentThis work was funded by National Institutes of Health grantsPO1CA80139 and U54CA105480.

References1. J. R. Mourant, M. Canpolat, C. Brocker, O. Esponda-Ramos, T. M. Johnson, A.

Matanock, K. Stetter, and J. P. Freyer, ”Light scattering from cells: the contri-bution of the nucleus and the effects of proliferative status,” J Biomed Opt 5(2),131–137 (2000).

2. J. R. Mourant, T. J. Bocklage, T. M. Powers, H. M. Greene, K. L. Bullock, L. R.Marr-Lyon, M. H. Dorin, A. G. Waxman, M. M. Zsemlye, and H. O. Smith, ”Invivo light scattering measurements for detection of precancerous conditionsof the cervix,” Gynecol Oncol 105(2), 439–445 (2007).

3. T. Collier, M. Follen, A. Malpica, and R. Richards-Kortum, ”Sources of scat-tering in cervical tissue: determination of the scattering coefficient by confocalmicroscopy,” Appl Opt 44(11), 2072–2081 (2005).

4. R. Drezek, M. Guillaud, T. Collier, I. Boiko, A. Malpica, C. Macaulay, M. Follen,and R. Richards-Kortum, ”Light scattering from cervical cells throughout neo-plastic progression: influence of nuclear morphology, DNA content, and chro-matin texture,” J Biomed Opt 8(1), 7–16 (2003).

5. D. Arifler, M. Guillaud, A. Carraro, A. Malpica, M. Follen, and R. Richards-Kortum, ”Light scattering from normal and dysplastic cervical cells atdifferent epithelial depths: finite-difference time-domain modeling with aperfectly matched layer boundary condition,” J Biomed Opt 8(3), 484–494(2003).

6. A. Kienle, F. K. Forster, and R. Hibst, ”Influence of the phase function on de-termination of the optical properties of biological tissue by spatially resolvedreflectance,” Opt Lett 26(20), 1571–1573 (2001).

7. A. Kienle and M. S. Patterson, ”Determination of the optical properties of semi-infinite turbid media from frequency-domain reflectance close to the source,”Phys Med Biol. 42(9), 1801–1819 (1997).

8. L. H. Wang, S. L. Jacques, and L.-Q. Zheng, ”MCML—Monte-Carlo modelingof light transport in multilayered tissues,” Comput Methods Programs Biomed47(2), 131–146 (1995).


9. T. J. Farrell, Patterson, M. S., Wilson, B. C., ”A diffusion theory model of spa-tially resolved, steady-state diffuse reflectance for the noninvasive determina-tion of tissue optical properties,” Med Phys 19(4), 879–888 (1992).

10. M. S. Patterson, B. Chance, and B. C. Wilson, ”Time resolved reflectance andtransmittance for the noninvasive measurement of tissue optical-properties,”Appl Opt 28(12), 2331–2336 (1989).

11. D. T. Delpy and M. Cope, ”Quantification in tissue near-infrared spectroscopy,”Phil Trans R Soc Lond B 352, 649–659 (1997).

12. C. Van Duijn Jr., ”Visibility and resolution of microscopic detail,” Microscope11, 196–208 (1957).

13. V. Krishnaswamy, P. J. Hoopes, K. Samkoe, J. A. O’Hara, T. Hasan, and B. W.Pogue, ”Quantitative imaging of scattering changes associated with epithelialproliferation, necrosis and fibrosis in tumors using microsampling reflectancespectroscopy,” J Biomed Opt 14(1), 014004 (2009).

14. A. H. Bennet, H. Jupnik, H. Osterberg, and O. W. Richards, ”Phase MicroscopyPrinciples and Applications,” Am J Phys 20(5), 318–319 (1952).

15. D. B. Murphy, Fundamentals of Light Microscopy and Electronic Imaging, 1st ed.(Wiley-Liss, 2001).

16. M. Bartek, X. Wang, W. Wells, K. D. Paulsen, and B. W. Pogue, ”Estimation ofsubcellular particle size histograms with electron microscopy for prediction ofoptical scattering in breast tissue,” J Biomed Opt 11(6), 064007 (2006).

17. M. K. Simick and L. Lilge, ”Optical transillumination spectroscopy to quantifyparenchymal tissue density: an indicator for breast cancer risk,” Br J Radiol78(935), 1009–1017 (2005).

18. M. K. Simick, R. Jong, B. Wilson, and L. Lilge, ”Non-ionizing near-infrared radi-ation transillumination spectroscopy for breast tissue density and assessmentof breast cancer risk,” J Biomed Opt 9(4), 794–803 (2004).

19. S. P. Poplack, K. D. Paulsen, A. Hartov, P. M. Meaney, B. W. Pogue, T. D.Tosteson, S. K. Soho, and W. A. Wells, ”Electromagnetic breast imaging—pilotresults in women with abnormal mammography,” Radiology 243(2), 350–359(2007).

20. V. Ntziachristos, A. G. Yodh, M. Schnall, and B. Chance, ”Concurrent MRI anddiffuse optical tomography of breast after indocyanine green enhancement,”Proc Natl Acad Sci U S A 97(6), 2767–2772 (2000).

21. Q. Zhu, E. B. Cronin, A. A. Currier, H. S. Vine, M. Huang, N. Chen, andC. Xu, ”Benign versus malignant breast masses: optical differentiation withUS-guided optical imaging reconstruction.[Erratum appears in Radiology 2006May; 239(2):613],” Radiology 237(1), 57–66 (2005).

22. C. M. Carpenter, B. W. Pogue, S. Jiang, H. Dehghani, X. Wang, K. D. Paulsen,W. A. Wells, J. Forero, C. Kogel, J. B. Weaver, S. P. Poplack, and P. A. Kaufman,”Image-guided optical spectroscopy provides molecular-specific informationin vivo: MRI-guided spectroscopy of breast cancer hemoglobin, water, andscatterer size,” Opt Lett 32(8), 933–935 (2007).

23. C. M. Carpenter, S. Srinivasan, S. Jiang, B. W. Pogue, and K. D. Paulsen,“Methodology development for three-dimensional MR-guided near infraredspectroscopy of breast tumors,” Opt. Express 16, 17903–17914 (2008).

24. A. Cerussi, D. Hsiang, N. Shah, R. Mehta, A. Durkin, J. Butler, and B. J.Tromberg, ”Predicting response to breast cancer neoadjuvant chemotherapyusing diffuse optical spectroscopy,” Proc Natl Acad Sci U S A 104(10), 4014–4019(2007).

25. S. P. Poplack, K. D. Paulsen, A. Hartov, P. M. Meaney, B. W. Pogue, T. D. Toste-son, M. R. Grove, S. K. Soho, and W. A. Wells, ”Electromagnetic breast imaging:average tissue property values in women with negative clinical findings,” Ra-diology 231(2), 571–580 (2004).

26. B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman,U. L. Osterberg, and K. D. Paulsen, ”Quantitative hemoglobin tomographywith diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology218(1), 261–266 (2001).


27. X. Wang, B. W. Pogue, S. Jiang, H. Dehghani, X. Song, S. Srinivasan, B. A.Brooksby, K. D. Paulsen, C. Kogel, S. P. Poplack, and W. A. Wells, ”Imagereconstruction of effective Mie scattering parameters of breast tissue in vivowith near-infrared tomography,” J Biomed Opt 11(4), 041106 (2006).

28. X. Wang, B. W. Pogue, S. Jiang, X. Song, K. D. Paulsen, C. Kogel, S. P. Poplack,and W. A. Wells, ”Approximation of Mie scattering parameters in near-infraredtomography of normal breast tissue in vivo,” J Biomed Opt 10(5), 051704 (2005).

P A R T 4Dynamic LightScattering Methods

CHAPTER 9Dynamic Light Scattering andMotility-Contrast Imaging ofLiving Tissue

CHAPTER 10Laser Speckle ContrastImaging of Blood Flow


C H A P T E R 9Dynamic LightScattering and

Motility-ContrastImaging of

Living Tissue

David D. Nolte, Kwan Jeong, and John Turek

9.1 Dynamic Light Scattering and SpeckleDepth resolution in coherent imaging of tissue is achieved by coher-ence gating with interferometric detection using short-coherence light[1], most commonly in the form of optical coherence tomography [2–4]. High spatial resolution and deep penetration have been achievedwith point-by-point scanning [5]. More direct approaches that capturefull frames at depth have typically relied on interferometric imaging[6, 7] or off-axis holography [8–11]. Off-axis holography detectssignals from selected depths through the spatial interference betweencoherent backscattered light and a reference wave. If the light sourcehas a restricted coherence length (typically less than 30 microns), theninformation from a selected depth is encoded as a spatial heterodynesignal (holographic fringes). This spatial heterodyne signal is mostnaturally detected with a spatial detector like a CCD camera [12].

The illumination and imaging of living tissue by partially coher-ent light is characterized by dramatic dynamic speckle. The speckleis usually fully formed, with a contrast near unity, signifying that it

213

214 D y n a m i c L i g h t S c a t t e r i n g M e t h o d s

contains little spatially resolved information [13]. The speckle tends tobe highly dynamic, with intensity fluctuations spanning broad timescales, reflecting the wide range of physical rates taking place insideliving tissues and cells. The coherent imaging of living structures seeksto extract important biological and physical properties of the tissueand cells, with sufficient spatial and temporal resolution to distin-guish functional contributions from heterogeneous regions. The fluc-tuating strong speckle presents challenges for structural imaging, andmany coherence-gating approaches use speckle mitigation techniquesto reduce its effects [14–24], although dynamic speckle has been usedfor blood flow monitoring [25–30]. In our approach, we preserve thespeckle, using its statistical fluctuations in space and time to studydynamic processes within avascular tissue, measuring motion suchas organelle transport by molecular motors on the cytoskeleton [31].Because of our reliance on speckle, a solid understanding of the originof speckle is essential, starting from dilute limits where simple inter-pretations of dynamic speckle can be made, and then extending theseprinciples qualitatively to the dense-scattering limit appropriate forscattering in tissue.

Single-Mode ScatteringIn the dilute limit, speckle arises from the interference of multiplepoint sources, such as point scatterers at different depths reflectingincident light back to a detector. If the illumination has a single spatialmode (such as the focal waist of a Gaussian beam), then the scatteringconfiguration is idealized to a large depth of focus, as shown in Fig.9.1a . If, in addition, the light has a finite coherence length, then scat-terers located within a coherence length interfere coherently (fieldssum), while scatterers outside a coherence length add incoherently(intensities sum). Discrete coherence slabs (to keep the model simple)contribute to the interfering intensity in Fig. 9.1a as

IHom =∑

i

∣∣∣∣∣∑

j

εij exp

(ii

j

)∣∣∣∣∣2

=∑

i

I i

(9.1)

where the sum over i is over the discrete coherence slabs contributingintensities I i , while the sum over j is over the scatterers within theith coherence slab. The field amplitudes are εi

j and the phases are ij .

The homodyne intensity in Eq. (9.1) describes the intensity of a singlespeckle.

215M o t i l i t y - C o n t r a s t I m a g i n g

FIGURE 9.1 Idealized dilute scattering geometries in a sphere. In part (a) asingle optical mode illuminates scatterers on the optic axis. Thebackscattered fields sum with phase dependent on the positions of thescatterers. The total backscattered intensity is the incoherent sum over theindependent coherence volumes of the coherent sums from within eachcoherence volume. In part (b) a single plane is illuminated. The scatteredfields are transformed by the Fourier lens to k-vectors. The interfering partialwaves at the detector plane produces spatial speckle.

Planar ScatteringThe starting point for describing the spatial structure of speckle is toconsider scatterers randomly distributed on a plane within the fieldof view of an objective lens, as shown in Fig. 9.1b. In this case, thetransverse spatial coherence is larger than the field of view, althoughspeckle mitigation techniques (vibrating or rotating diffusers) can re-duce the transverse spatial coherence. Because we emphasize Fourier-domain holography in this chapter, we consider a 1f-1f Fourier opticalconfiguration that converts point sources to plane waves at a Fourierplane. For this situation, the intensity at the Fourier plane is

I =∑

j

ε j exp(

i�k j · �r)

=∑

j

ε j exp(

ikxj x + iky

j y) (9.2)

where r is the position vector on the Fourier plane, and where thetransverse components of the k-vector are

kxj = k

x′j

f

k yj ≈ k

y′j

f

(9.3)


where f is the lens focal length. The primes are for the scatterer loca-tion, and the sum is restricted by the numerical aperture of the lens.The aperture diameter D sets the size of the speckle at the Fourierplane to be approximately

aspek ≈ 1.22f

D(9.4)

From the scatterers on the single plane, assuming large transversecoherence length, the intensity distribution is Poissonian, for whichthe standard deviation of the spatially varying intensity is equal tothe mean value of the intensity, and the speckle contrast is unity. ThePoisson probability distribution is

P (I ) = 1〈I 〉 exp

(−I〈I 〉)

(9.5)

where 〈I 〉 is the mean intensity. The contrast of a speckle pattern sub-ject to stationary statistics is defined as

C =(⟨

I 2⟩− ⟨

I⟩2)1/2

〈I 〉 ≡ stdmean

(9.6)

which can also take on spatial values for slowly varying nonstationarystatistics through

C (x) =(⟨

I 2⟩�x − ⟨

I⟩2�x

)1/2

⟨I⟩�x

(9.7)

where the average is carried out over a spatial area defined by the size�x. For the Fourier plane, the averages are taken over annular regionscentered on the optic axis.

Volumetric ScatteringWe simplify volumetric scattering by assuming that the scatteringvolume has a thickness that is smaller than the depth-of-focus of theoptical system, which is appropriate for a telescopic optical configu-ration. In this case, all the scatterers can be viewed as approximatelylocated on the conjugate plane of the lens, and the total homodynespeckle intensity at the Fourier plane is

IHom =∑

i

∣∣∣∣∣∣∑

j

εij exp

(ii

j

)exp

ik

(x′

j x + iy′j y)

f

∣∣∣∣∣∣2

(9.8)


This equation describes an incoherent background on top ofwhich a speckle pattern is superposed. The contrast is by ne-cessity much less than unity, but if the background can be re-moved, then the residual speckle would again obey fully devel-oped speckle statistics. Indeed, the suppression of the backgroundis the main function of dynamic photorefractive holography [10, 32].Even in the case of digital holography, the background is subtractedusing coherence-gating methods to retain only the speckle com-ponent.

Spatial Homodyne and HeterodyneThe speckle field reflected from living tissue when illuminated bya partially coherent source represents a homodyne field. Each scat-tered field interferes with all the other scattered fields originating fromwithin the local coherence volume, representing a “self” interference.On the other hand, in off-axis holography a reference field is added,usually as a plane wave incident at an angle �ref, which interferes withthe speckle field to produce interference fringes inside the individualspeckles of the speckle pattern. This is called a heterodyne condition,resulting in spatial interference fringes that have spatial periodicity.The heterodyne, or off-axis holography, configuration is shown in Fig.9.2. For the case of a dilute suspension, and considering only a single

FIGURE 9.2 A plane of scatterers produces a spectrum of k-vectors at thedetector plane with a bandwidth set by the numerical aperture of the imaginglens. Superposed on the spatial spectrum is the reference wave k-vector. Inaddition to these optical periodicities, there is also the periodicity of thepixels on the CCD detector plane that set the upper limit to the spatialresolution of the holograms.


speckle on the optic axis originating from the kth coherence volume,the heterodyne intensity is

IHet =∣∣∣∣∣E0 exp

(i�k · �r

)+∑

j

εkj exp

(ik

j

)∣∣∣∣∣2

= I0 + E0

[exp (iKx)

∑j

εkj exp

(−ikj

)

+ exp (−iKx)∑

j

εkj exp

(ik

j

)]+ I k

= I0 + E0

[∑J

εkj exp

(iKx − ik

j

)+∑

j

εkj exp

(−iKx + ikj

)]+ I k

= I0 + 2E0

∑j

εkj cos

(iKx − ik

j

)+ I k

(9.9)

where the grating vector of the fringes that arise within each speckleis

K = ksin �ref (9.10)

In Eq. (9.9), only scatterers from the kth coherence slab are in-cluded, because the reference wave has a finite coherent length andonly interferes with scatterers from within the coherence slab of thetarget. This selection of the coherence slab is the “coherence gate” ofcoherence-gated holography, and is easily adjusted simply by movinga mirror position in the reference arm of the optical setup (describedbelow) to shallower or deeper positions within the target volume.

For scatterers outside the coherence slab, the homodyne intensityis again

IHom =∑i �=k

∣∣∣∣∣∑

j

εij exp

(ii

j

)∣∣∣∣∣2

=∑i �=k

I i

(9.11)

in which the sum skips the scatterers from the gated coherence slab.The total (of the single speckle) on the Fourier plane is then

ITot = IHet + IHom

=∣∣∣∣∣E0 exp

(i�k · �r

)+∑

j

εkj exp

(ik

j

)∣∣∣∣∣2

+∑i �=k

∣∣∣∣∣∑

j

εij exp

(ii

j

)∣∣∣∣∣2

= I0 +∑

i

I i + 2E0

∑j

εkj cos

(iKx − ik

j

)(9.12)


If each scatterer contributes an rms field ε to the detected intensity,then the Fourier component at spatial frequency K is

ITot (K ) = 2E0√

Nε (9.13)

where N is the number of scatterers within the coherence length. Therelative modulation is

m = 2E0√

NεI0 + IHom

(9.14)

The modulation depth has the deepest modulation for the condi-tion when IHom = I0 (when the reference intensity is set equal to thetotal incoherent background reflected intensity at the Fourier plane)at which the contrast equals

m = εE0

√N, (9.15)

which can be used to estimate effective tissue properties.It is important to reemphasize that these equations are only valid

for the case of dilute suspension of single scatterers distributed withthe depth of focus of the optical system. These conditions are violatedby real living tissue that is optically dense and has strong multiplescattering. However, these dilute-suspension equations can still pro-vide general behavior that, when fit to experimental data, can leadto effective parameters of the tissue system that can be interpretedsemiquantitatively.

Dynamic ScatteringDynamic scattering brings in the time dimension to the speckle pat-tern. When the discrete scatterers are time dependent, primarilythrough their spatial motion, then the multimode speckle patternsfluctuate over characteristic times related to the motion of the scatter-ers. The time autocorrelation of a spatiotemporal speckle field S (x, t)is defined by

A(x, � ) =⟨S (x, t) S (x, t − � )

⟩t⟨

S (x, t)2⟩t

(9.16)

where x refers to the pixel position and the averages are over time.When the scatterers undergo Brownian motion with diffusion co-

efficient D, then under heterodyne conditions, the autocorrelation


function takes the form:

A(� ) = exp(−q 2 D |� |) (9.17)

where the q -vector is the scattering vector, which for backscatteringis q = 2k = 4�/. Therefore, the autocorrelation function has a char-acteristic scattering time:

�q = 1/Dq 2 =

4�D(9.18)

By measuring the autocorrelation time, an estimate of the diffusioncoefficient can be obtained, in principle. It is important to rememberthat these equations are derived in the dilute scattering limit. Althoughdense scattering media also show exponential autocorrelation func-tions with characteristic times, the times must be viewed as effectivetimes and the corresponding diffusion coefficients as effective valuesthat may not relate directly to the actual diffusion.

For living tissue from which images are averaged over time scaleson the order of seconds, a random drift model is more appropriate thana diffusion model. The active functions of the cell drive the cytoskele-ton, and molecular motors move organelles along the cytoskeleton.These processes are directed rather than diffusive, especially at longtimes, and thermal motion is not a large contributor at these timescales. Under these conditions, the autocorrelation function is inte-grated over the velocity distribution P(v):

A(�q , � ) =∫

P (�v) exp (−�q · �v� ) d3�v (9.19)

which is isotropic in velocity, and hence

A(� ) = 4�

∫ ∞

0v2 P (v)

(sin qv�

qvt

)dv

=∫ ∞

0W (v)

(sin qv�

qvt

)dv (9.20)

where W(v) is the speed distribution. The speed distribution is ob-tained by the transform:

W (v) = 2vq 2

�

∫ ∞

0� A(� ) sin

(qv�

)d� (9.21)


When A(� ) has a single exponential form A(� ) = exp(− |� | /�q ),then the speed distribution is

W (v) = 2vq 2� 2q

�

sin(2 tan−1

(qv�q

))1 + (

qv�q)2 (9.22)

which has a maximum value that is approximately

vmax ≈ 1q�q

(9.23)

Therefore, the autocorrelation time �q provides an estimate of theaverage speed of the moving scatterers when they are drift dominatedrather than diffusion limited. This final simple equation is applied inthe section “Motility-Contrast Imaging” on dynamic light scatteringfrom living tissue.

9.2 Holographic Optical Coherence ImagingHolographic optical coherence imaging is based on the principle ofspatial periodicity induced by off-axis holography. The spatial peri-odicity of the interference fringes represents a carrier frequency that ismodulated by optical information from the object. Because demodula-tion is performed most naturally as a Fourier transform, the most nat-ural domain for the holographic recording is the Fourier domain. Byrecording Fourier holograms, the demodulation of the image and thereconstruction of the image are the same step. In addition, by recordingon the Fourier plane, highly efficient transforms, such as the FFT, canbe used, instead of more cumbersome Fresnel reconstructions [33, 34].By using an imaging system with a depth of focus comparable tothe thickness of the object, the Fourier approach remains approxi-mately valid across the gated depths. Because our interest is in tumorspheroids, which are typically thinner than a millimeter, the Fourierreconstruction is sufficient and fast.

Fourier-Domain HolographyThe optical configuration for Fourier-domain holography is shownschematically in Fig. 9.3, although not to scale. The object plane (x, y)is conjugate to the Fourier plane that is near the output face of thecube beam splitter. The focal distance between the lens and the Fourierplane is adjusted for the optical path through the glass beam splitter.The reference plane wave is directed by the beam splitter to intersectwith the object wave with a crossing angle �. The interference patternis recorded on the CCD chip that resides on the Fourier plane (FP).The numerical reconstruction of the image using an FFT is represented


FIGURE 9.3 Schematic of digital holographic imaging. The CCD is on theFourier plane that is conjugate to the object plane. The reference wave isincident off-axis, providing a spatial heterodyne signal that modulates thespeckle pattern from the object. (Source: Reprinted from Ref. [12].)

as the read-out lens transforming the field back to the space-domain(�,�).

An example of a Fourier-domain hologram is shown in Fig. 9.4a ,with an expanded view of one small section in Fig. 9.4b. This hologramis of lettering on diffusing white paper. The diffuse nature of the target(light scattered into wide angles) ensures that there is a wide recordingrange on the Fourier plane. The fringe patterns are visible in part (b),with a clear periodicity modulated by amplitude and phase across thespeckles.

The one-dimensional (1D) Fourier transform of the section de-noted by the dashed line in Fig. 9.4a is shown in Fig. 9.5. The

(a) (b)

FIGURE 9.4 The full-field holographic data (a) and a magnified portion (b). Thespatial interference fringes modulate the speckle pattern with approximately2–3 fringes within a speckle size. (Source: Reprinted from Ref. [12].)


FIGURE 9.5 Fourier transform of the data along the dashed line in Fig. 9.4.The two broad sidebands represent the imaging information. (Source:Reprinted from Ref. [12].)

zero-order diffraction is the wide base at the center of the graph, in-cluding a DC spike at zero spatial frequency. The two broad peaks atopposite symmetric spatial frequencies are the image. The width ofthese first-order peaks is

kmax = kD

2 f(9.24)

which is determined by the numerical aperture ( f/#) of the imagingoptics. An example of a two-dimensional (2D) Fourier transform isshown in Fig. 9.6 for an Air Force test chart as the target. The powerspectrum reconstruction produces an image and its conjugate. Phaseinformation can be retrieved by comparing the real and imaginaryparts of the image and its conjugate.

Digital HolographyThe digital holograms (containing N × N = 800 × 800 pixels) are en-coded on our CCD chip with 4096 gray levels (12 bits). The pixelsize is �x′ = �y′ = 6.8 �m and the area of the CCD chip is L × L =5.44 × 5.44 mm2. The FFT reconstruction of the digital hologram pro-duces an image with N × N pixels, with a pixel size �� (�� = ��)given by

�� = �� = f �vx′ = f �vy′ = fL

(9.25)

where �vx′ (�vx′ = �vy′ = 1/L) is the sampling spatial frequency.


FIGURE 9.6 The demodulated and transformed images showing the directimage and its conjugate (left). The image (right) is a magnified version of thelower-left reconstruction. (Source: Reprinted from Ref. [12].)

To record interference fringes in the digital hologram, the fringespacing should range from twice the pixel size (minimum) to the CCDchip size (in-line holography). The spatial frequency corresponding tothe maximum fringe spacing is �vx′ = 1/L , and the spatial frequencyfor the minimum fringe spacing is 1/(2�x′) = (N�vx′ )/2, which isthe spatial frequency limit. Four times the pixel size (4�x′) is thebest fringe spacing at which the sideband is located at half of thespatial frequency limit. When the fringe spacing is 4�x′, the maximumfield of view for the holographic image is achieved with N��/2 = f/(2�x′). The fringe spacing for Fig. 9.4 was 3�x′ with the center ofthe sideband located at the spatial frequency of 1/(3�x′) = 49 mm−1

in Fig. 9.5.The transverse resolution in Fourier-domain digital holographic

optical coherence imaging (FD-DHOCI) depends on the area of theCCD chip. If the object beam at the Fourier plane covers the full spanof the CCD, then the transverse resolution at the Rayleigh criterion is

Rs = 1.22 fL

= 1.22�� (9.26)

The longitudinal resolution depends on the coherence length of theshort-coherence source and is

�z = ln(2)2�

2

�(9.27)

where � is the wavelength bandwidth of the source intensity coher-ence envelope. Our 12-bit CCD camera has �x′ = 6.8 �m, N = 800,


= 840 nm, and f = 4.8 cm, and the bandwidth of the source is 17nm. The transverse and the longitudinal resolutions for this systemare 9 and 18 �m, respectively.

In FD-DHOCI, the CCD camera is placed at the Fourier planeconjugate to the target plane in the object. The depth of focus is [27]

�z =

2 · NA2 (9.28)

where is the wavelength and NA is the numerical aperture. Thedepth of focus for the system with the transverse resolution of 9 �m is131 �m. Our volumetric targets (tumor spheroids) are typically thickerthan the depth of focus. The spheroids range in size from 300 micronsto 1 mm. To minimize out-of-focus in the numerical reconstruction,we place the object plane about 1/3 of the way into the tumor fromthe incident face. In this way, the tumor images remain in focus, ex-cept for the back face of the tumor, where multiple scattering and the“showerglass effect” already limit the imaging resolution.

9.3 Multicellular Tumor SpheroidsMulticellular spheroids of normal cells or neoplastic cells (tumorspheroids) are balls of cells that may be easily cultured up to 1 mmin size in vitro [35–40]. The spheroids can be used to simulate theoptical properties of a variety of tissues such as the epidermis andvarious epithelial tissues and may be used to simulate the histologicaland metabolic features of small nodular tumors in the early avascularstages of growth [40]. The multicellular tumor spheroids have been areliable model for the systematic study of tumor response to therapy[38, 41] as three-dimensional (3D) aggregates of permanent cell lines.

Beyond a critical size (about 100 microns) most spheroids developa necrotic core surrounded by a shell of viable, proliferating cells, witha thickness varying from 100 to 300 �m. The development of necrosishas been linked to deficiencies in the metabolites related to energygeneration and transfer. The limiting factor for necrosis developmentis oxygen—the oxygen consumption and oxygen transport reflectingthe status of the spheroid [36, 42]. Early work [43] studied therapeuticstrategies for cancer, and especially the spheroid response to differentdrugs. The response to drug therapy was quantified by spheroid vol-ume growth delay, increase in the necrotic area, and change in survivalcapacity. This work focused on hypoxia and its induction by chemicalagents [44].

To create tumor spheroids for our studies, two different cell lineswere used: rat osteogenic sarcoma UMR-106 cells and human livercarcinoma Hep G2 cells. These were cultured in a rotating bioreactor(Synthecon, Houston, TX) where they were maintained in suspension.The spheroids may be grown up to several millimeters in diameter.


FIGURE 9.7 Two types of tumor spheroid. Human liver (left) and ratosteogenic (right) have different shapes and texture, but both have outerproliferating shells 100–200 microns thick encapsulating a necrotic core. Thelower images are magnified portions of the full spheroid images.

An advantage to using this continuous culture model is that freshspheroids of varying size are easily prepared on a daily basis. Overall,the tumor spheroids provide a reasonable tissue model that does notrequire special handling of animal subjects.

Electron microscopy sections of the two types of tumor embeddedin Toluidine-blue-stained epoxy resin and sectioned at 1 �m thicknessare shown in Fig. 9.7. The tumors are nearly a millimeter in diameterand share a common morphology. The outermost layers of the tumorshave healthy, proliferating cells that form a shell from 100 to 200 mi-crons thick. These cells are in close proximity to the nutrients and oxy-gen of the growth medium. This layer is structurally homogeneousand may be expected to be optically homogeneous as well. Deeperinside the tumors, the cells become apoptotic because of nutrient de-privation and oxidative stress caused by the difficulty for nutrient andoxygen diffusion into these avascular spheroids. The apoptotic cellsgive way, deeper in the tumor spheroids, to necrotic regions character-ized by voids of extracellular debris or by microcalcifications, whichare especially pronounced in the osteogenic spheroids. The core isstructurally heterogeneous and may be expected to be optically het-erogeneous as well. Therefore the tumor spheroids have the generalmorphology of a healthy outer shell that tends to be homogeneous,surrounding a necrotic core that is spatially heterogeneous. Opticalstudies of the spheroids would be expected to correspond with thisoverall structure.


The experimentally measured reduced scattering coefficient �′ ofrat osteogenic tumor spheroids is on the order of 8–15 mm−1 withdecreasing extinction with increasing tumor size. A tumor with a di-ameter of 416 microns was fit best with an anisotropy factor of g = 0.9,while a slightly larger tumor with a diameter of 484 microns was fitwith a smaller factor of g = 0.85. Overall, the rat osteogenic tumorspheroids are relatively translucent tumors with strong forward scat-tering.

Biology in Three DimensionsMicroscopic imaging of cellular motility and motility-related gene ex-pression is well established in 2D [45]. However, cells in contact withflat hard surfaces do not behave the same as cells embedded in the ex-tracellular matrix [46, 47]. Recent work has raised the dimensionalityof cellular motility imaging from 2D to 3D, including microscopiessuch as confocal fluorescence [48, 49], two-photon tissue imaging[50, 51], optical projection tomography (OPT) [52], and single-planeillumination projection (SPIM) [53]. Lateral resolution in these casesis diffraction-limited at the surface of the 3D matrix but degradesdeeper into the target sample. Although structured illumination [54]and stimulated emission [55] approaches can beat that limit underspecial circumstances, these too suffer significant degradation in res-olution with increasing probe depth, limiting access to motility in-formation from deep inside the sample where it is far from theartificial influence of surfaces. For these reasons, motility-contrastimaging is applied to 3D tissues that retain the relevant molecu-lar signaling of in vivo tissue, but with the advantages of workingin vitro.

Holographic Optical Coherence Imaging of Tumor SpheroidsThe scattering geometry of the tumor spheroids is shown in Fig. 9.8.Light is incident from the top, uniformly illuminating the full tumor.The coherence gate set by the reference pulse defines the section depth,and the coherence length of the laser sets the section thickness. Becauseof the off-axis holography configuration in the recording, the actualsection is tilted by half the crossing angle at the CCD between thesignal arm and the reference arm. Data are acquired in a mode calleda “fly through” in which the section depth is swept through the fullvolume of the tumor spheroid from top to bottom. (In inverted con-figurations, the light is incident from the bottom of the tumor and thesection sweeps from bottom to top.) The step size between sectionsis 10 microns (approximately half of the coherence length), and theexposure time per section is approximately 1 s.

A stack of selected sections in shown in Fig. 9.9a . In this case,the light was incident from the bottom (frame 24). The midsection is


FIGURE 9.8 Schematic of the tumor spheroid morphology and the coherenceslab defined by the reference wave.

FIGURE 9.9 (a) Selected en-face sections of an 800-micron-diameter tumorspheroid. (b) Reconstructed volume showing reflectance (darker stands formore intense reflections). The shades are on a logarithmic scale that spanapproximately 40 dB within the tissue. (Source: Reprinted from Ref. [12].)


approximately at frame 60, and the top of the tumor is at frame 114.These stacks are combined into a data volume representing the tumor,shown with volume cuts in Fig. 9.9b. The grayscale is on a logarith-mic scale spanning about 40 dB from the brightest to the darkest.The brightest reflections (the darkest pixels) are near the center, corre-sponding to the necrotic core. The outer healthy shell has noticeablyweaker reflections.

The section images and the volume representation in Fig. 9.9 showstrong speckle character. Histograms of the reconstructed intensitiesare shown in Fig. 9.10 at different depths through the tumor. The his-togram at a depth of 140 microns (near the transition from the healthyshell to the necrotic core) shows a nearly perfect exponential decay(inset) typical of fully developed speckle. Deeper in the core, there is adistinct peak to the intensity histograms, likely caused by the presenceof strongly localized scattering regions. Therefore, the global struc-ture of the tumor spheroid, delineating the healthy outer shell and thenecrotic core, is captured by the statistical properties of the speckle.However, specific structures inside the tumor spheroids are difficultto identify. This is mainly because the tumor spheroids are highlyhomogeneous, consisting of undifferentiated cellular tissue. But thisis also because of the strongly speckled character of the holographicreconstructions. This strong speckle becomes an important feature ofdynamic imaging.

FIGURE 9.10 Histograms of speckle intensities from a 560-micron-diametertumor spheroid at several depths. The speckle data from a depth of 140microns (near the transition from the healthy shell to the necrotic core) shownearly perfect Poisson statistics.


9.4 Subcellular Motility in TissuesMotion is the overarching characteristic that distinguishes living frominanimate matter. The cellular machinery that drives motion consistsof molecular motors [56, 57] and their molecular tracks [58–60] knownas the cytoskeleton. The cytoskeleton is composed of three types of fil-aments: microtubules, actin, and intermediate filaments. Of these, thebest studied and understood are the microtubules and actin. Micro-tubules form interconnected pathways that span the cytosol that pro-vide molecular highways for organelles carried by molecular motorslike kinesin and dynein. The smaller actin filaments form a tight meshcalled the cell cortex concentrated mostly near the cell membrane, butwith lower densities throughout the cytosol. The actin skeleton lendsmechanical stability to the cell membrane and allows its motion, in-cluding the crawling of metastatic cancer cells through tissue.

The most active use of the cytoskeletal machinery occurs duringmitosis in which the entire cellular structure is reorganized prior toand during division. During mitosis, the microtubules form the mi-totic spindle, which is an organized mechanical structure that helpsdivide the intracellular contents for cell division. Actin plays an impor-tant role in cytokinesis at the end of mitosis when the cell membranepinches off, and the cell physically divides. For these reasons, drugsthat inhibit the motors and their tracks are common anticancer agents,arresting the cell cycle by arresting motion [61, 62].

The largest class of anticancer therapeutic agents are known asantimitotic drugs (AMD), also called cytoskeletal drugs. These drugsaffect the cellular cytoskeleton and prevent cells from entering themitosis phase of the cell cycle. Some of the best-known anticancerdrugs fall in this class, such as Taxol and Colchicine. Although effica-cious, these drugs have serious toxic side effects because their actionis nonspecific as they affect the cytoskeleton of healthy and cancercells alike. Morbidity and death from the side effects of chemotherapyrival the death rate from the disease itself. Therefore, a modern gener-ation of antimitotic agents is being investigated that specifically targetactively dividing cells, while leaving interphase cells alone. Some ofthese drugs act on certain myosin molecular motors that only functionduring mitosis and are quiescent otherwise [63]. Others act on proteinsof the signaling pathways that constitute the mitotic checkpoints ofthe cell cycle. By turning off selected molecular signals with thesedrugs, the cell cycle is arrested and cancer cells do not proliferate.

9.5 Motility-Contrast ImagingMotility-contrast imaging relies on dynamic light scattering com-bined with coherence gating. Digital holography fulfills the functionof the coherence detection and hence the depth discrimination, while


FIGURE 9.11 Constant-depth one-dimensional sections of a healthy tumor(left) and a tumor cross-linked with glutaraldehyde (right). The vertical axis isframe number at a rate of one frame per second. (Source: Reprinted fromRef. [31].) See also color insert.

consecutive images fulfill the function of dynamic speckle recording.The data acquisition process consists of setting the optical path of thereference arm (and hence the depth inside the tissue) and recordingconsecutive holograms on the CCD chip, followed by numerical re-construction. Data from a fixed depth of about 300 microns inside twotumors are shown in Fig. 9.11. The data are the reconstructed pixel in-tensities plotted on a dB reflectance scale. One tumor was “healthy,”while the other had been cross-linked with glutaraldehyde. The recon-structed data are displayed as a 1D cut in space with distance along thehorizontal axis and time along the vertical axis. The time step betweenrows in the data is 1 s. The healthy tumor displays strongly dynamicspeckle fluctuations, with individual speckles blinking on and off, in-dicative of living tissue. The cross-linked tumor, on the other hand,displays constant speckle.

One goal of our data analysis is to extract the statistical proper-ties of the speckle and to relate them to structure and function. Theaverage autocorrelation graphs of a healthy tumor at selected depthsare shown in Fig. 9.12a . The most dynamic tissue (shortest correla-tion time and lowest long-time correlation value) is near the surfaceof the tumor within the healthy shell of proliferating cells. The leastdynamic tissue, by contrast, was the deepest section (in this figure at180 microns). This depth is near the transition from the proliferatingcells to the necrotic core. These correlation data show the clear differ-ence between the highly motile outer shell and the quiescent necroticlayers deeper inside.

Tumors under different physiological conditions (healthy,metabolically poisoned, and cross-linked) also show clear differencesin the dynamic speckle. The autocorrelation graphs for the three


FIGURE 9.12 Autocorrelation graphs of fixed-depth time-sequence data for ahealthy tumor at selected depths (left) and for tumors at a fixed depth butdifferent metabolic conditions (right). See also color insert.

physiological states are shown in Fig. 9.12b. The cross-linked tumorshows nearly constant correlation as a function of delay. The healthytumor shows the most dramatic decrease, while the metabolically poi-soned tumor falls in between these two extremes. These autocorrela-tion data can be used to estimate the speed distribution in the tissueusing Eq. (9.23) for motile scatterers dominated by drift. The speedsfor the three tissue conditions are 3 , 1 , and 0.1 nm/s for healthy, poi-soned, and cross-linked tumors, respectively. These speeds are con-sistent with the fairly broad range of velocities for movements of thecell membrane. However, selecting autocorrelation times to differen-tiate healthy from necrotic tissue is not robust. There are other choicesfor a motility metric that can reliably differentiate between healthyand necrotic tissue, and these become the basis of motility-contrastimaging.

Among the several possible ways to define a motility metric, oneparticularly robust approach simply calculates the coefficient of vari-ance (known as the CV or as the normalized standard deviation) of apixel value (after background subtraction) as a property related to thecellular and subcellular motions. This motility metric for individualpixels is plotted in Fig. 9.13 at nine selected depths inside the tumor.The first frame is near the top of the tumor, while the central frame isnear the center plane of the tumor. In the central plane, there is a strongcontrast between the healthy shell and necrotic core. The healthy shellappears highly motile, while the necrotic core shows low dynamiclight scattering. These images correlate with the known structure ofthe tumor spheroids with a healthy outer shell and a necrotic core.In these images, the internal motions of the cells themselves haveprovided the imaging contrast agent. This is a truly endogenous func-tional imaging approach.

Armed with the motility metric and the maps of cellular function-ing, we take the next step to image the effects of AMDs on the motility


FIGURE 9.13 Color-coded motility metric of a healthy tumor at selecteddepths. The healthy outer shell shows strong cellular or subcellular motion,while the necrotic core is quiet. (Source: Reprinted from Ref. [31].) See alsocolor insert.

images. A time series at a fixed depth is shown in Fig. 9.14 for Noco-dazole, which is an AMD that inhibits the polymerization of tubulininto microtubules. The first frame is the initial state of the tumor. By3 min after the application of 2 �g/ml of Nocodazole, the outer shellhas increased its activity by a small amount. However, by 21 min laterthe motion is partially suppressed, and by 119 min after applicationof the drug, the motility in the outer shell has been significantly re-duced. Nocodazole inhibits the polymerization of the microtubules,while treadmilling dissolves the microtubules from the other end, re-sulting in a significant reduction in the microtubule density withinthe cells. Without the microtubule cytoskeleton, organelle transport issuppressed, which is captured by the dynamic light scattering. Timeevolution under different doses is shown in Fig. 9.15a for Nocodazole,for Colchicine in Fig. 9.15b, and for Taxol in Fig. 9.15c. Nocodazole is asynthetic variant to the natural Colchicine with higher potency. Taxol,


FIGURE 9.14 Motility maps of a tumor responding to 2 �g/ml of theantimitotic drug, Nocodazole, as a function of time from the initial state(first frame) to 119 min after the dose. (Source: Reprinted from Ref. [31].)See also color insert.

on the other hand, operates by inhibiting depolymerization of the mi-crotubules back into tubulin. This stabilizes the microtubules, keepingthem available for organelle transport, but shutting down the cell cycleby preventing mitosis. For this reason, Taxol has less chemotherapeu-tic side effects. This is observed in the significantly smaller suppressionof the motility in response to the Taxol. The dose–response curves forthe three drugs are shown in Fig. 9.15d . Taxol shows the weakest effect,consistent with the stabilization of the microtubules, while Nocoda-zole shows the strongest suppression of cellular motion at the lowesteffective concentrations. The results of Figs. 9.14 and 9.15 show thespecific sensitivity of motility-contrast imaging to the cytoskeleton.

9.6 Conclusions and ProspectsThis chapter has outlined the operation and performance of digitaloptical coherence imaging of living tissue. The off-axis holographygeometry produces spatial heterodyne signals (holographic interfer-ence fringes) that are analogous to the time-domain heterodyne de-tection used in time-domain optical coherence tomography. On theother hand, as opposed to the single-mode operation of OCT, theholographic approach uses full-field illumination of many simulta-neous modes, creating fully developed speckle in the holographic im-ages. Rather than attempting to suppress the speckle, we rely on it to


FIGURE 9.15 Time course of tumor responses as a function of dose for(a) Nocodazole, (b) Colchicine, and (c) Taxol (Paclitaxel). The dose responsesare plotted as a reaction velocity in part (d). (Source: Reprinted fromRef. [31].)

provide the motility metric that defines a truly endogenous imagingcontrast for internal motion within the tissue and cells.

The dynamic light scattering from moving cell membranes andinternal organelles provides a strong signature of the internal mo-tion. The importance of the cytoskeleton to internal motion, in turn,makes motility-contrast imaging a highly sensitive probe of the func-tioning of the cytoskeleton. Our main focus in this chapter was on theAMDs. These are cytoskeletal drugs that inhibit the cell cycle, usuallyby arresting it at the G2M boundary. By preventing mitosis, the pro-liferation of cancer cells can be suppressed, which is why the AMDsare among the most common cancer chemotherapies. However, toxicside effects, especially in the loss of the cytoskeleton that is essentialto healthy and cancer cells alike, would be an important characteristicto screen for among the many cancer therapeutic drug candidates.Motility-contrast imaging has high sensitivity to precisely this aspectof the AMDs and provides a potential image-based screening assay for


AMD toxicity. One of the challenges for the future is the developmentof high-throughput screening platforms based on this technique thatcan screen for many drugs simultaneously. The 3D tissue constructionand the easy growth of numerous tumor spheroids are expected to aidin the high-throughput platform development.

9.7 AcknowledgmentThis work was performed under the support of the NSF grant CBET-0756005.

References1. C. Dunsby and P. M. W. French, “Techniques for depth-resolved imaging

through turbid media including coherence-gated imaging,” J Phys D Appl Phys,vol. 36, pp. R207–R227, 2003.

2. J. M. Schmitt, “Optical Coherence Tomography (OCT): A Review,” IEEE J SelTop Quant Elect, vol. 5, p. 1205, 1999.

3. J. G. Fujimoto, “Optical coherence tomography for ultrahigh resolution in vivoimaging,” Nat Biotechnol, vol. 21, pp. 1361–1367, 2003.

4. A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherencetomography—principles and applications,” Rep Prog Phys, vol. 66, pp. 239–303,2003.

5. W. Drexler, U. Morgner, R. K. Ghanta, F. X. Kartner, J. S. Schuman, and J. G.Fujimoto, “Ultrahigh-resolution ophthalmic optical coherence tomography,”Nat Med, vol. 7, pp. 502–507, 2001.

6. L. Vabre, A. Dubois, and A. C. Boccara, “Thermal-light full-field optical coher-ence tomography,” Opt Lett, vol. 27, pp. 530–532, 2002.

7. E. Beaurepaire, A. C. Boccara, M. Lebec, L. Blanchot, and H. Saint-Jalmes,“Full-field optical coherence microscopy,” Opt Lett, vol. 23, p. 244, 1998.

8. R. Jones, N. P. Barry, S. C. W. Hyde, M. Tziraki, J. C. Dainty, P. M. W. French,D. D. Nolte, K. M. Kwolek, and M. R. Melloch, “Real-time 3-D holographicimaging using photorefractive media including multiple-quantum-well de-vices,” IEEE J Sel Top Quant Electron, vol. 4, pp. 360–369, 1998.

9. S. C. W. Hyde, R. Jones, N. P. Barry, J. C. Dainty, P. M. W. French, K. M. Kwolek,D. D. Nolte, and M. R. Melloch, “Depth-resolved holography through turbidmedia using photorefraction,” IEEE J Sel Top Quant Electron, vol. 2, p. 965,1996.

10. K. Jeong, L. Peng, J. J. Turek, M. R. Melloch, and D. D. Nolte, “Fourier-domainholographic optical coherence imaging of tumor spheroids and mouse eye,”Appl Opt, vol. 44, pp. 1798–1806, 2005.

11. P. Yu, M. Mustata, L. L. Peng, J. J. Turek, M. R. Melloch, P. M. W. French, andD. D. Nolte, “Holographic optical coherence imaging of rat osteogenic sarcomatumor spheroids,” Appl Opt, vol. 43, pp. 4862–4873, 2004.

12. K. Jeong, J. J. Turek, and D. D. Nolte, “Fourier-domain digital holographicoptical coherence imaging of living tissue,” Appl Opt, vol. 46, pp. 4999–5008,2007.

13. J. W. Goodman, Speckle Phenomena in Optics. Englewood, CO: Roberts, 2006.14. Y. T. Pan, R. Birngruber, and R. Engelhardt, “Contrast limits of coherence-gated

imaging in scattering media,” Appl Opt, vol. 36, pp. 2979–2983, 1997.15. J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in optical coherence to-

mography,” J Biomed Opt, vol. 4, pp. 95–105, 1999.16. M. Bashkansky and J. Reintjes, “Statistics and reduction of speckle in optical

coherence tomography,” Opt Lett, vol. 25, pp. 545–547, 2000.


17. N. Iftimia, B. E. Bouma, and G. J. Tearney, “Speckle reduction in optical coher-ence tomography by “path length encoded” angular compounding,” J BiomedOpt, vol. 8, pp. 260–263, 2003.

18. M. Pircher, E. Gotzinger, R. Leitgeb, A. F. Fercher, and C. K. Hitzenberger,“Speckle reduction in optical coherence tomography by frequency compound-ing,” J Biomed Opt, vol. 8, pp. 565–569, 2003.

19. J. Kim, D. T. Miller, E. Kim, S. Oh, J. Oh, and T. E. Milner, “Optical coherence to-mography speckle reduction by a partially spatially coherent source,” J BiomedOpt, vol. 10, 2005.

20. A. E. Desjardins, B. J. Vakoc, G. J. Tearney, and B. E. Bouma, “Speckle reductionin OCT using massively-parallel detection and frequency-domain ranging,”Opt Express, vol. 14, pp. 4736–4745, 2006.

21. A. E. Desjardins, B. J. Vakoc, W. Y. Oh, S. M. R. Motaghiannezam, G. J. Tear-ney, and B. E. Bouma, “Angle-resolved optical coherence tomography withsequential angular selectivity for speckle reduction,” Opt Express, vol. 15,pp. 6200–6209, 2007.

22. A. Ozcan, A. Bilenca, A. E. Desjardins, B. E. Bouma, and G. J. Tearney, “Specklereduction in optical coherence tomography images using digital filtering,”J Opt Soc Am A Opt Image Sci Vis, vol. 24, pp. 1901–1910, 2007.

23. D. P. Popescu, M. D. Hewko, and M. G. Sowa, “Speckle noise attenuation inoptical coherence tomography by compounding images acquired at differentpositions of the sample,” Opt Commu, vol. 269, pp. 247–251, 2007.

24. P. Puvanathasan and K. Bizheva, “Speckle noise reduction algorithm for opticalcoherence tomography based on interval type II fuzzy set,” Opt Express, vol.15, pp. 15747–15758, 2007.

25. A. K. Dunn, T. Bolay, M. A. Moskowitz, and D. A. Boas, “Dynamic imagingof cerebral blood flow using laser speckle,” J Cereb Blood Flow Metab, vol. 21,pp. 195–201, 2001.

26. S. Yuan, A. Devor, D. A. Boas, and A. K. Dunn, “Determination of optimalexposure time for imaging of blood flow changes with laser speckle contrastimaging,” Appl Opt, vol. 44, pp. 1823–1830, 2005.

27. J. D. Briers, “Laser speckle contrast imaging for measuring blood flow,” OptAppl, vol. 37, pp. 139–152, 2007.

28. V. Kalchenko, D. Preise, M. Bayewitch, I. Fine, K. Burd, and A. Harmelin, “Invivo dynamic light scattering microscopy of tumour blood vessels,” J Microsc,vol. 228, pp. 118–122, 2007.

29. H. Y. Cheng, Y. M. Yan, and T. Q. Duong, “Temporal statistical analysis of laserspeckle images and its application to retinal blood-flow imaging,” Opt Express,vol. 16, pp. 10214–10219, 2008.

30. A. B. Parthasarathy, W. J. Tom, A. Gopal, X. J. Zhang, and A. K. Dunn, “Ro-bust flow measurement with multi-exposure speckle imaging,” Opt Express,vol. 16, pp. 1975–1989, 2008.

31. K. Jeong, J. J. Turek, and D. D. Nolte, “Imaging motility contrast in digitalholography of tissue response to cytoskeletal anti-cancer drugs,” Opt Express,vol. 15, p. 14057, 2007.

32. K. Jeong, L. L. Peng, D. D. Nolte, and M. R. Melloch, “Fourier-domain hologra-phy in photorefractive quantum-well films,” Appl Opt, vol. 43, pp. 3802–3811,2004.

33. T. C. Poon, T. Yatagai, and W. Juptner, “Digital holography—coherent opticsof the 21st century: introduction,” Appl Opt, vol. 45, pp. 821–821, 2006.

34. U. Schnars and W. Jueptner, Digital Holography, Berlin, Heidelberg, Springer,2004.

35. L. de Ridder, “Autologous confrontation of brain tumor derived spheroidswith human dermal spheroids,” Anticancer Res, vol. 17, pp. 4119–4120,1997.

36. K. Groebe and W. Mueller-Klieser, “On the relation between size of necro-sis and diameter of tumor spheroids,” Int J Radiat Oncol Biol Phys, vol. 34,pp. 395–401, 1996.


37. R. Hamamoto, K. Yamada, M. Kamihira, and S. Iijima, “Differentiation and pro-liferation of primary rat hepatocytes cultured as spheroids,” J Biochem (Tokyo),vol. 124, pp. 972–979, 1998.

38. G. Hamilton, “Multicellular spheroids as an in vitro tumor model,” Cancer Lett,vol. 131, pp. 29–34, 1998.

39. P. Hargrave, P. W. Nicholson, D. T. Delpy, and M. Firbank, “Optical propertiesof multicellular tumour spheroids,” Phys Med Biol, vol. 41, pp. 1067–1072, 1996.

40. L. A. Kunz-Schughart, M. Kreutz, and R. Knuechel, “Multicellular spheroids:a three-dimensional in vitro culture system to study tumour biology,” Int J ExpPathol, vol. 79, pp. 1–23, 1998.

41. L. A. Kunz-Schughart, “Multicellular tumor spheroids: intermediates betweenmonolayer culture and in vivo tumor,” Cell Biol Int, vol. 23, pp. 157–161, 1999.

42. W. Mueller-Klieser, “Method for the determination of oxygen consumptionrates and diffusion coefficients in multicellular spheroids,” Biophys J, vol. 46,pp. 343–348, 1984.

43. P. Freyer, P. L. Schor, K. A. Jarrett, M. Neeman, and L. O. Sillerud, “Cellu-lar energetics measured by phosphorous nuclear magnetic resonance spec-troscopy are not correlated with chronic nutrient deficiency in multicellulartumor spheroids,” Can Res, vol. 51, pp. 3831–3837, 1991.

44. W. Mueller-Klieser, “Three-dimensional cell cultures: from molecular mecha-nisms to clinical applications,” Am J Physiol, vol. 273, pp. 1109–1123, 1997.

45. T. D. Pollard and G. G. Borisy, “Cellular motility driven by assembly and dis-assembly of actin filaments,” Cell, vol. 112, pp. 453–465, 2003.

46. E. Cukierman, R. Pankov, D. R. Stevens, and K. M. Yamada, “Taking cell-matrixadhesions to the third dimension,” Science, vol. 294, pp. 1708–1712, 2001.

47. D. J. Webb and A. F. Horwitz, “New dimensions in cell migration,” Nat CellBiol, vol. 5, p. 690, 2003.

48. W. E. Moerner and D. P. Fromm, “Methods of single-molecule fluorescencespectroscopy and microscopy,” Rev Sci Instrum, vol. 74, pp. 3597–3619, 2003.

49. R. H. Webb, “Confocal optical microscopy,” Rep Prog Phys, vol. 59, pp. 427–471,1996.

50. M. D. Cahalan, I. Parker, S. H. Wei, and M. J. Miller, “Two-photon tissue imag-ing: seeing the immune system in a fresh light,” Nat Rev Immunol, vol. 2,pp. 872–880, 2002.

51. K. Konig, “Multiphoton microscopy in life sciences,” J Microsc, vol. 200,pp. 83–104, 2000.

52. J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sorensen, R. Bal-dock, and D. Davidson, “Optical projection tomography as a tool for 3D mi-croscopy and gene expression studies,” Science, vol. 296, pp. 541–545, 2002.

53. J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. K. Stelzer, “Optical sec-tioning deep inside live embryos by selective plane illumination microscopy,”Science, vol. 305, pp. 1007–1009, 2004.

54. M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” Proc NatlAcad Sci U S A, vol. 102, pp. 13081–13086, 2005.

55. T. A. Klar, S. Jakobs, M. Dyba, A. Egner, and S. W. Hell, “Fluorescence mi-croscopy with diffraction resolution barrier broken by stimulated emission,”Proc Natl Acad Sci U S A, vol. 97, pp. 8206–8210, 2000.

56. R. D. Vale, “The molecular motor toolbox for intracellular transport,” Cell,vol. 112, pp. 467–480, 2003.

57. R. D. Vale and R. A. Milligan, “The way things move: looking under the hoodof molecular motor proteins,” Science, vol. 288, pp. 88–95, 2000.

58. E. Karsenti and I. Vernos, “Cell cycle—the mitotic spindle: a self-made ma-chine,” Science, vol. 294, pp. 543–547, 2001.

59. N. Hirokawa, “Kinesin and dynein superfamily proteins and the mechanismof organelle transport,” Science, vol. 279, pp. 519–526, 1998.

60. A. Desai and T. J. Mitchison, “Microtubule polymerization dynamics,” AnnRev Cell DevBiol, vol. 13, pp. 83–117, 1997.


61. J. R. Peterson and T. J. Mitchison, “Small molecules, big impact: a history ofchemical inhibitors and the cytoskeleton,” Chem Biol, vol. 9, pp. 1275–1285,2002.

62. M. A. Jordan and L. Wilson, “Microtubules and actin filaments: dynamictargets for cancer chemotherapy,” Curr Opin Cell Biol, vol. 10, pp. 123–130,1998.

63. J. R. Jackson, D. R. Patrick, M. M. Dar, and P. S. Huang, “Targeted anti-mitotic therapies: can we improve on tubulin agents?” Nat Rev Cancer, vol. 7,pp. 107–117, 2007.


C H A P T E R 10Laser Speckle

Contrast Imaging ofBlood Flow

Andrew K. Dunn

10.1 IntroductionAs blood flow is one of the most important physiological indicators,methods for dynamic monitoring of blood flow are of great interest ina wide range of applications and diseases. Optical techniques basedon dynamic light scattering comprise a large number of the availablemethods for blood flow monitoring such as laser Doppler, specklecontrast imaging, and photon correlation spectroscopy. Although allthese techniques differ in their measurement geometry and analysis,each is based on dynamic light scattering. Laser Doppler flowmetryis a well-established technique for measuring blood flow, although itis usually limited to measurements at single spatial locations. Morerecently, laser speckle contrast imaging (LSCI) has become widelyused to image blood flow in a variety of tissues. Because LSCI enablesfull-field imaging of surface blood flow using simple instrumenta-tion, it has distinct advantages over techniques such as laser Dopplerflowmetry. Although the instrumentation for LSCI is simple, obtain-ing quantitative measures of blood flow is very challenging due to thecomplex physics that relate the measured quantities to the underlyingblood flow. This chapter will review the physics of LSCI and illustrateits use in vivo with particular emphasis on imaging blood flow in thebrain. In addition, a new extension to traditional LSCI is described,which is based on a multiple exposure technique that improves thequantitative accuracy of speckle imaging of blood flow.

241


10.2 Single-Exposure Laser Speckle Contrast ImagingWhen an object is illuminated with coherent laser light, a specklepattern, or random interference pattern, is produced at the camerabecause the laser light reaching each pixel has traveled slightly dif-ferent pathlengths and adds coherently, both constructively and de-structively. In many imaging systems, speckle is a significant source ofnoise, and considerable effort has been spent in eliminating speckle.However, the dynamics of the speckle pattern contains informationabout the motion of the scattering particles in the sample. When someof the scattering particles are in motion (i.e., blood cells), the specklepattern fluctuates in time. When the exposure time of the camera islonger than the time scale of the speckle intensity fluctuations (typi-cally less than 1 ms for biological tissues), the camera integrates theintensity variations, resulting in blurring of the speckle pattern. Inareas of increased motion, there is more blurring of the speckles dur-ing the camera exposure, resulting in a lower spatial contrast of thespeckles in these areas.

Full-field imaging of blood flow based on laser speckle was firstdemonstrated by Fercher and Briers in 1981 [1], and this method wasgiven the name LASCA (laser speckle contrast analysis). LASCA pro-duced full field images of motion by quantifying the spatial contrastof a time-integrated speckle pattern. A significant limitation of earlyLASCA instruments, however, was the need to record images on filmand then process these images later, which resulted in low temporalresolution and large uncertainties in the speckle contrast values. Withthe advent of CCD cameras and modern computers in the 1990s, ac-quisition and processing of speckle images improved drastically, andimaging of blood flow in tissues such as the skin and retina becamepossible.

Techniques based on the concept of time-integrated speckle relyon the fact that the motion of the scattering particles (i.e., blood flow)is encoded in the dynamics of the speckle pattern, and blood flowcan be measured by quantifying the spatial blurring of the specklepattern over the exposure time of the camera. The spatial blurring ismeasured by calculating the speckle contrast, K , defined as the ratioof the standard deviation, �s, to the mean intensity of pixel values, 〈I 〉,in a small region of the image [2]:

K (T) = �s(T)〈I 〉 (10.1)

where T is the exposure time of the camera. The speckle contrast istherefore a measure of the local spatial contrast in the speckle pattern.A spatially resolved map of local speckle contrast can be calculatedfrom a raw speckle image by computing this ratio at each point in

243L a s e r S p e c k l e C o n t r a s t I m a g i n g o f B l o o d F l o w

Laser

CCD

0

0.05

0.1

(a)

(c)

(b)

FIGURE 10.1 Illustration of single-exposure laser speckle contrast imaging(LSCI). A typical experimental setup (a) consists of a diode laser, whosebeam is expanded to fill the area of interest, and a camera to image thescattered laser light from the sample surface. The raw speckle images(b) exhibit the typical grainy appearance, while the speckle contrast images(c) reveal areas of motion. The image in part (c) was calculated from the rawimage in part (b) using a 5 × 5 window, and 30 speckle contrast images wereaveraged together.

the image from the pixels in a surrounding N × N region (typicallyN = 7). The speckle contrast has values between 0 and 1. A specklecontrast of 1 indicates that there is no blurring of the speckle pat-tern and therefore, no motion, while a speckle contrast of 0 meansthat the scatterers are moving fast enough to average out all of thespeckles.

One of the reasons that LSCI has become a widely adopted methodfor imaging blood flow is the relative simplicity of the instrumentation,as illustrated in Fig. 10.1a . The basic configuration consists of a laserdiode whose beam is expanded and adjusted to illuminate the area ofinterest, which can vary from a few millimeters to several centimeters.The angle of the incident light ranges from near normal incidence toas much as 45◦. The second main component is the camera. Light scat-tered from the sample is imaged onto the camera to enable recordingof the speckle pattern. The specifications of the cameras used for LSCIvary widely, but inexpensive 8-bit cameras have been demonstratedto provide excellent images of blood flow and enable detailed physio-logical studies to be performed [3–5]. In general, high dynamic rangecooled cameras are not required for LSCI, because the light levelsreaching the camera are usually high enough that the majority of noisearises from shot noise. In addition, the speckle pattern is inherently


high in contrast, so that 8-bit cameras have sufficient dynamic rangeto accurately quantify speckle contrast.

A typical example of a raw speckle image of the rat brain, takenthrough a thinned skull, and the computed speckle contrast are shownin Fig. 10.1b and c under normal conditions. The raw speckle imageillustrates the grainy appearance of the speckle pattern. The specklecontrast image, computed directly from the raw speckle image usingthe Eq. (10.1), represents a two-dimensional map of motion in thetissue, which is due primarily to blood flow. Areas of higher baselineflow, such as large vessels, have lower speckle contrast values andappear darker in the speckle contrast images.

The speckle contrast values are a function of the camera exposuretime, T , as indicated in Eq. (10.1). For very long exposure times, thespeckle intensity fluctuations will have sufficient time to blur com-pletely, and therefore speckle contrast values will approach 0, whileat very short exposure times, the speckles will be frozen and contrastvalues will be high (in theory close to 1). Figure 10.2 illustrates the ef-fect of changing exposure time on the speckle contrast recorded fromthe brain. At short exposure times (∼0.5 ms), only those areas withhigh flow (i.e., large vessels) appear in the speckle contrast image be-cause only these areas have speckle intensity fluctuations that are fastenough to cause appreciable averaging during the relatively short ex-posure times. Areas with lower flow result in speckle fluctuations thatare slow compared to the exposure times, and therefore no apprecia-ble blurring takes place. As the exposure time is increased, areas withlower flow, such as small vessels, appear in the speckle contrast image.Therefore, there is a close relationship between the exposure time andflow (or speed), as illustrated in Fig. 10.2, and optimal sensitivity todifferent flow rates can be achieved by proper selection of exposuretime [6].

T = 0.5 ms T = 1 ms T = 5 ms T = 10 ms

FIGURE 10.2 The speckle contrast values, K (T ), are the function of thecamera exposure time. Each image shows the speckle contrast recordedfrom a rat through a thinned skull at different exposure times ranging from0.5 to 10 ms.


Although speckle contrast values are indicative of the level of mo-tion in the sample, they are not directly proportional to speed or flow.In fact the exact quantitative relationship between speckle contrastand the underlying blood flow or speed is a complex function that isnot completely understood for complex biological tissues [7]. In theearly work of Fercher and Briers, a simplified model was proposed thatrelated the speckle contrast values to the speckle decorrelation time,�c [Eq. (10.3)], and speed of the scattering particles [1]. The intent ofthis model was not to establish a quantitative relationship betweenspeckle contrast and speed, but to illustrate the relationship betweentime-integrated speckle and traditional techniques based on dynamiclight scattering such as laser Doppler [8]. This simplified model hasbeen demonstrated to be fairly accurate in its ability to predict rel-ative changes in blood flow and has been used in a wide range ofapplications, particularly over the past 5 years.

Obtaining quantitative blood flow measurements from specklecontrast values involve two steps. The first is to accurately relate thespeckle contrast values, which are obtained from a time-integratedmeasure of the speckle intensity fluctuations, to a quantity commonlyused in dynamic light scattering such as the speckle correlation timeor a measure of the width of the Doppler power spectrum. The sec-ond step is to relate this quantity to the underlying flow or speed.The first step is unique to time-integrated speckle measurements andhas been the subject of several recent studies [7, 9, 10], while the sec-ond step is common to all dynamic light scattering techniques includ-ing laser Doppler, photon correlation spectroscopy, and speckle tech-niques.

The relationship between the speckle contrast values, K (T), andthe speckle correlation decay time, �c, is rooted in the field of dy-namic light scattering. The temporal fluctuations of the speckles canbe quantified through the electric field autocorrelation function, g1(� ).Typical dynamic light scattering measurements involve measurementof the intensity autocorrelation function, g2(� ). Using the Siegert re-lation, the field autocorrelation can be determined from the intensityautocorrelation:

g2(� ) = 1 + ∣∣g1(� )

∣∣2 (10.2)

where is a normalization factor that accounts for speckle averagingdue to the mismatch between speckle size and pixel size, as well aspolarization effects and the finite coherence of the light source. Thespeckle correlation decay time, �c, is a measure of the decay time ofthe field autocorrelation function. The original relationship between


K (T) and �c formulated by Briers was

K (T, �c) =(

1 − e−2x

2x

)1/2

(10.3)

where x = T/�c. Although this relationship has been widely used inthe literature, a more accurate expression that relates the measuredspeckle contrast to correlation decay time has been proposed [9]:

K (T, �c) =(

e−2x − 1 + 2x

2x2

)1/2

(10.4)

Generally, LSCI measurements involve direct measurement of thespeckle contrast at a single exposure time, and then conversion of themeasured contrast to correlation decay time using either Eq. (10.3) or(10.4). Blood flow is then assumed to be inversely related to �c, andrelative blood flow changes are determined by computing the changesin �c from some baseline state [4]. The assumption that blood flow isinversely proportional to �c is based on a number of simplifying as-sumptions and is rooted in the laser Doppler literature [11]. Therefore,depending on the sample optical properties and flow conditions, thisassumption may become highly inaccurate. However, a number ofreports have demonstrated a close agreement between speckle-basedmeasures of blood flow changes and laser Doppler flowmetry [4, 12].

Because of the large number of simplifying assumptions involvedin Eqs. (10.3) and (10.4), the quantitative accuracy of the measuredblood flow changes may be low in some cases. Some groups havetaken a different approach and do not attempt to relate the specklecontrast to correlation decay time. Instead, a calibration process isperformed directly on the measured speckle contrast values [13, 14],and a quantity such as a perfusion index is reported. This procedurehas the advantage that it does not rely on the assumptions that are builtinto Eqs. (10.3) and (10.4), but has the disadvantage that the valuesthat are reported are not quantitative.

Even though the measurement geometries differ experimentally,laser Doppler and speckle contrast imaging are based on the same un-derlying principle of dynamic light scattering. In laser Doppler mea-surements, the power spectrum of the temporal intensity fluctuations,S(�), is analyzed, and the first moment of S(�) is proportional to theRMS speed of the blood cells [11]. In laser speckle imaging and othertechniques based on photon correlation spectroscopy, the intensityfluctuations are analyzed in the time domain through either the tem-poral electric field autocorrelation function, g1(� ), or the autocorrela-tion function of the intensity fluctuations, g2(� ). The autocorrelationfunction and the power spectrum, S(�), are Fourier transform pairs,


and therefore each can be calculated from the other. This equivalencebetween the time- and frequency-domain quantities of the intensityvariations forms the underlying connection between laser Dopplerand LSCI [15]. Therefore, quantitative imaging of cerebral blood flow(CBF) requires full-field imaging of either the autocorrelation functionor the power spectrum of the intensity fluctuations because blood flowcan be quantified from the decay characteristics of either parameter[11]. Although the decay characteristics of either parameter are lin-early related to CBF, it remains difficult to determine CBF values inabsolute calibrated units from these measurements. Laser Dopplerflowmetry methods determine the power spectrum at only a singlepoint, while LSCI is based on a time-integrated measure of the auto-correlation function. As neither method is able to image these quan-tities directly, neither technique can be reliably used for quantitative,chronic imaging of blood flow.

10.3 Applications of LSCI to Brain ImagingLSCI and related techniques have been used for a large number ofblood flow imaging applications. Since 2001, however, LSCI has be-come one of the most widely used methods for in vivo imaging ofblood flow in the brain, particularly in small animal models of bothnormal and diseased brain [4]. Prior to its application to cerebral bloodflow studies, the standard method for in vivo blood flow determi-nation in animal models was laser Doppler flowmetry, which typi-cally consists of a fiber optic probe that provides relative blood flowmeasurements at a single spatial location. Although scanning laserDoppler instruments exist, their temporal resolution is limited by theneed to scan the beam. LSCI instruments, on the other hand, enablenoncontact full-field imaging of blood flow without the need for anyscanning. In addition, the relatively simple instrumentation makesLSCI instruments easy to construct and use. In this section, severalapplications of LSCI in the brain are illustrated.

Methodological Details for Imaging CBF Using LSCIOne of the reasons that LSCI has been so effective in imaging CBF isthat the cortical blood flow of interest is primarily on the surface ofthe brain in many applications such as stroke, functional activation,Alzheimer’s disease, and epilepsy. LSCI imaging of CBF is effective inany region of the brain where the vasculature is visible to the nakedeye. The first uses of LSCI in the brain were in rats where the skullwas thinned to transparency [4]. The images in Figs. 10.1 and 10.2illustrate the ability of LSCI to sense blood flow in a thinned skullpreparation, where the thickness of the remaining skull is approxi-mately 100 �m. Imaging of CBF through a thinned skull is usually


performed by applying a liquid such as saline or mineral oil to thesurface of the remaining skull. The liquid improves the image qual-ity by creating a smooth interface and also by reducing scattering inthe skull because the liquid acts as an index of refraction matchingmedium.

Imaging of cerebral blood flow in rats with LSCI requires either athinned skull or full craniotomy. However, in mice it has been shownthat imaging can be performed through the intact skull [12] becausethe thickness of the mouse skull is significantly less than that of rats.Provided that the skin is reflected, several studies have shown thatimaging of CBF in mice can be performed through the intact skullwhen mineral oil is applied to the skull surface [12, 16, 17]. By eliminat-ing the surgery involved with either thinning or removing the skull,the likelihood of damage to the cortical surface is greatly reduced. Inaddition, studies involving chronic blood flow are considerably easierwhen the skull is left intact. Although a number of studies have usedLSCI through an intact skull in mice, the effects of scattering from theskull on the accuracy of the CBF changes have not been thoroughlyinvestigated. Light scattering by the skull will result in a contributionof a static component to the otherwise dynamic speckle intensity fluc-tuations, which will add an offset to the speckle contrast values. Liet al. demonstrated that this offset can be suppressed by analyzingthe temporal contrast rather than the traditional spatial contrast [18].However, difficulties arise in relating the temporal contrast values tospeckle decorrelation times because ergodicity is violated in the casewhere temporal sampling and spatial sampling of the speckle pat-tern are not equivalent. To overcome this limitation, a new approachbased on multiexposure speckle imaging (described in detail below)has been proposed [10].

Functional Brain ActivationOver the past two decades, functional MRI (fMRI) has become thestandard technique for investigating how the brain responds to vari-ous types of stimuli. fMRI studies have been widely used in humansas well as in animals for both clinical applications and basic researchstudies. The majority of fMRI studies use BOLD (blood oxygen leveldependent) fMRI, whereby the changes in blood oxygenation, in par-ticular deoxyhemoglobin, are detected. Therefore, BOLD fMRI mea-surements sense the hemodynamic response to brain activation. Inmany situations, the parameter of most interest is the underlyingneuronal activity. However, traditional fMRI is only sensitive to thesecondary hemodynamic response to this neuronal activity. There-fore, there is great interest in developing improved understandingof the detailed relationship between the neuronal and hemodynamicresponses to brain activation in both the normal and diseased brain.


This neurovascular coupling has been investigated with a wide vari-ety of methods in animal models.

Optical techniques are widely used to image the hemodynamic re-sponse to various stimuli. In particular, optical imaging of intrinsic sig-nals is commonly used. This method has provided numerous insightsinto the functional organization of the cortex [19–22] by mapping thechanges in cortical reflectance arising from the hemodynamic changesthat accompany functional stimulation. The majority of these studieshave been based on qualitative mapping at a single wavelength, andwhile they have provided valuable insight into many aspects of cor-tical function, the techniques used in these studies have been unableto reveal quantitative spatial information about the individual hemo-dynamic (hemoglobin oxygenation and volume and blood flow) andmetabolic components that underlie the measured signals.

The blood flow changes that accompany brain activation are par-ticularly important in estimating the oxygen consumption of the brain.Laser Doppler flowmetry has been used extensively to quantify theblood flow changes in the somatosensory cortex in response to stimu-lation in animal models. However, laser Doppler measurements of theblood flow response are limited to single spatial locations due to therelatively fast temporal dynamics of the blood flow response (typicallya few seconds). Because LSCI does not require any scanning, full-fieldimaging is possible with high temporal resolution that is sufficient toresolve the blood flow dynamics due to functional activation in thenormal brain [23–26].

An illustration of the ability of LSCI to image the spatiotemporalchanges in CBF following functional activation is given in Fig. 10.3. A5 × 5 mm area of cortex was imaged in a rat through a thinned skullas the forepaw of the rat was stimulated with electrical pulses. Thestimulus was applied for 10 s (0.5 mA) and 20 trials were repeatedand the speckle contrast images at each time, relative to the stimulus,were averaged. Speckle contrast values were converted to specklecorrelation decay times (�c) at each pixel in all images using Eq. (10.3),and ratios of the inverse of the decay times were used as a measure ofthe relative changes in CBF.

Figure 10.3 highlights the strength of LSCI in revealing both thespatial and the temporal blood flow dynamics. A series of imagesare shown at 0.5-s intervals, and illustrate a localized increase inCBF beginning approximately 1 s after stimulation onset. The relativechanges in CBF are shown superimposed on the vasculature (derivedfrom the speckle contrast image) and the changes in CBF are displayedfor all pixels with an increase in CBF greater than 5%. The time courseof the CBF changes averaged over a region of interest centered onthe activated area illustrates a peak increase in CBF of approximately12% occurring 3 s after stimulus onset. The initial peak in CBF thendecreases to approximately half of its maximum amplitude to a value


0.0 sec 0.5 sec 1.0 sec 1.5 sec 2.0 sec





0 0.05 0.1 0.15 0.2

0 2 4 6 8 10 12

1

1.05

1.1

Time (s)R

elat

ive

CB

F

(a)

(b)

FIGURE 10.3 LSCI can be used to quantify both the spatial and temporal dynamicsof stimulus-induced brain activation. The sequence of images in part (a) illustratesareas of the brain where blood flow is increased due to electrical forepawstimulation in a rat. The color bar indicates the fractional increase in blood flow. Theplot in part (b) demonstrates the temporal dynamics of the blood flow changes withinthe center of activation. See also color insert.

of approximately 6%, where it remains until the end of the stimulus,in a manner consistent with previous laser Doppler measurements ofCBF during extended forepaw stimulation [27]. This time course alsoreveals the very high signal-to-noise ratio of LSCI for relative CBFmeasurements.

StrokeAnimal models of stroke are widely used to investigate the basicpathophysiology of stroke and to evaluate new stroke therapies. Acritical aspect of these studies is monitoring of blood flow dynam-ics in the brain. Laser Doppler flowmetry has been used for manyyears in such studies and is widely considered to be the gold standardfor quantifying blood flow changes in the brain in animal modelsof stroke. Although magnetic resonance imaging and positron emis-sion tomography have also been used in animal models of stroke, thespatial and temporal resolution of these techniques is usually not suf-ficient to permit detailed studies of blood flow dynamics. LSCI hasemerged as a powerful technique for quantifying both the spatial andtemporal blood flow changes during stroke due to its high spatial andtemporal resolution [4, 5, 16, 28, 29].


During ischemic stroke, blood flow is reduced in the localized re-gion of the brain leading to a cascade of cellular and molecular eventsthat ultimately results in tissue damage. Blood flow in the area closestto the affected region (ischemic core) is typically reduced to less than20% of its baseline value, and as a result neurons depolarize and dierapidly. In the region between the ischemic core and the normal tissue(penumbra), neurons preserve the ability to maintain ion homeostasisbut are considered to be electrically silent because evoked potentialsand spontaneous electrical activity cease [30]. The reduction in bloodflow in the penumbra is not as severe as in the core, because collateralblood supply to the area is maintained. This reduction in flow in thepenumbra can lead to secondary effects such as peri-infarct spread-ing depolarizations, inflammation, and ultimately cell death [31]. Thepenumbra has been a primary target of treatment strategies becausemembrane function is preserved in cells in the penumbra. Restora-tion of blood flow to the penumbra therefore, may provide a meansof salvaging tissue without loss of function.

As the ischemic penumbra varies both spatially and temporally,LSCI is one of the few techniques that can provide a dynamic viewof the penumbra, as well as the ischemic core and nonischemic areas.LSCI has been used to visualize the CBF changes throughout the is-chemic territory in stroke models in mice, rats, and cats [4, 16, 32, 33].Figure 10.4a shows an example of the spatial gradient in blood flowfollowing occlusion of the middle cerebral artery in a rat. Closest to theocclusion site, blood flow is reduced to less than 20% of preischemicvalues and the blood flow deficit gradually improves with distanceaway from the site of occlusion due to collateral blood flow.

One of the mechanisms that may lead to cell death in the penumbrais the presence of peri-infarct depolarizations (PID), which resemblethe spreading depressions of Leao [34]. Because of increased extra-cellular levels of K+ and glutamate in the penumbra, cells depolarize.These cells are able to repolarize, but at the expense of ATP. Because theK+ and glutamate levels remain elevated, successive depolarizationsoccur resulting in spreading depression-like waves of depolarization.Gradually, the cells in the penumbra lose the ability to repolarize dueto the depletion of energy, leading to cell death [35]. As the frequencyof PIDs increases, the extent of the ischemic injury has been foundto increase as well [31]. Because of the increased metabolic demand,hemodynamic changes occur during PIDs, and LSCI has been used toquantify the CBF changes during PIDs.

Recently, the importance of PIDs in human stroke and brain in-jury has been demonstrated [36]. Although PIDs have been observedin animal models of stroke and brain injury for many years, evidencefor the existence of PIDs in the human brain has been lacking until re-cently. Recordings from subdural electrodes in humans have revealedspreading waves of electrical depolarization whose propagation


0

0.5

1

1.5

2

Time (m)

0

0.5

1

1.5

Time (m)

0 10 20 30 40 50 600

0.5

1

1.5

0

Time (m)

HbOHbRHbTCBFCMRO2

Scat

isch

emic

cor

epe

num

bra

non-

isch

emic

0 20 40 60 80 100

Laser

CCD

QTHlamp

filterwheel

filter wheelfront view

DCmotor

fibersensor

CCD

long passfilter

short passfilter

(a) (c)

(b)

FIGURE 10.4 Application of LSCI to cerebral ischemia. (a) The spatial bloodflow gradient following occlusion of an artery can be visualized using LSCI.The middle cerebral artery was occluded just outside the top region of theimage and the color map shows the relative blood flow, expressed as apercentage of preischemic flow. (b) LSCI and multispectral reflectanceimaging can be performed simultaneously to image multiple hemodynamicparameters. (c) Time courses of changes in oxyhemoglobin (HbO),deoxyhemoglobin (HbR), total hemoglobin (HbT), blood flow (CBF), oxygenconsumption (CMRO2), and scattering during a stroke. The three graphsdemonstrate the changes in each of these parameters in three spatial regions(ischemic core, penumbra, and nonischemic cortex). See also color insert.

characteristics closely resemble recordings in animals during stroke.Furthermore, the presence of delayed neurological deficits was foundto be highly correlated with the occurrence of spreading depolariza-tions in patients with subarachnoid hemorrhage [37]. These resultsfurther underscore the need for improved methods for quantifyingthe role of PIDs in ischemic brain injury.

Recently, several groups have used LSCI to investigate the role ofPIDs in the evolution of the ischemic infarct [16, 17, 33]. The functionaloptical imaging laboratory at University of Texas at Austin (A. Dunn,principal investigator) has also extended the capabilities of LSCIby combining the LSCI instrument with a multispectral reflectance-imaging (MSRI) device that enables full-field imaging of hemoglobinconcentration and volume changes [23]. By adding a second cameraand light source to the experimental setup, LSCI and MSRI can be per-formed simultaneously [17]. A schematic of the instrument is shownin Fig. 10.4b. For MSRI, light of six different wavelengths (560–610 nm,


in 10 nm increments) sequentially illuminates the cortex via a continu-ously rotating filter wheel, and a low noise, high dynamic range CCDcamera, which is synchronized with the filter wheel, records the re-flectance images. Each set of six wavelengths can then be convertedto changes in oxyhemoglobin (HbO) and deoxyhemoglobin (HbR) ateach pixel to yield maps of hemoglobin changes.

We have begun to use this instrument to image the CBF andhemoglobin concentration changes during ischemia in rats and mice.Figure 10.4c illustrates the time course of the hemodynamic changesin a mouse stroke model (at t = 0). Average changes in each hemody-namic parameter within the core (top plot), penumbra (middle plot),and nonischemic cortex (bottom plot) reveal a complex pattern ofhemodynamic changes that varies considerably between each hemo-dynamic parameter and across areas of the cortex. The spatial het-erogeneity of these changes highlights the need for full-field imagingof each of the hemodynamic parameters. Spontaneous and repetitivePIDs are observed altering the hemodynamic parameters and oxygenconsumption (CMRO2), which can be calculated from the changes inCBF and hemoglobin concentrations [26]. The vertical dashed linesindicate the presence of PIDs. In the nonischemic cortex and penum-bra, each PID is accompanied by a drop in all parameters except HbR,followed by a transient overshoot. In the ischemic core, a decreaseis observed with no discernable overshoot, suggesting that a smallamount of metabolism is taking place even in the most severely is-chemic core as evidenced by a further reduction of CMRO2 duringa PID. These results illustrate the great potential for imaging of thecomplex hemodynamic changes that occur during ischemia.

10.4 Multiexposure Laser Speckle ContrastImaging (MESI)

Despite the tremendous utility of LSCI for imaging blood flow invivo, the method has some significant limitations. As described above,single-exposure LSCI is not able to quantify baseline, or absoluteblood flow, and although LSCI is widely used to measure blood flowchanges, the quantitative accuracy of these changes may be limited bythe assumptions made in converting the measured speckle contrastvalues to speckle decorrelation times, �c. One of the factors that limitsthe accuracy of the blood flow changes measured with LSCI is the pres-ence of light scattered from static tissue elements. Traditional modelsthat relate speckle contrast to �c do not take into account the presenceof a static scattering layer such as the thinned or intact skull. Recently,we have taken advantage of the dependence of the speckle contraston camera exposure time to improve the accuracy of the �c values[10]. This approach is called multiexposure speckle contrast imaging


(MESI) and it enables accurate determination of flow changes even inthe presence of a static scattering layer. The MESI approach involvesboth a modified model and a modification to the experimental setupfor single-exposure LSCI.

MESI TheoryThe MESI approach is a straightforward extension to the traditionaltheory relating �c to K (T), which accounts for the presence of staticscattering. As discussed above, the field and intensity autocorrelationfunctions are related through the Siegert relation [Eq. (10.2)]. How-ever, in a sample with significant static scattering, the fluctuations inthe scattered field acquire an extra static contribution that causes therecorded intensity to deviate from Gaussian statistics such that theSiegert relation cannot be applied [38, 39]. In this case, a modifiedSiegert relation can be used of the form:

gh2 (� ) = 1 + A

∣∣g1(� )∣∣2 + B

∣∣g1(� )∣∣ (10.5)

where A = I 2f /(If + Is)2 and B = 2If Is/(If + Is)2, in which Is = Es E∗

srepresents the contribution from the static scattered light and If =〈EE∗〉 represents the contribution from dynamically scattered light.

This updated Siegert relation can be used to derive the relationbetween speckle contrast and speckle decorrelation time, �c, usingthe same approaches that have been used previously [9]. In addition,noise can be a significant contributor to the measured speckle con-trast. Sources of noise include shot noise, statistical sampling noise,and camera noise, and each of these sources can vary with exposuretime. Therefore, the spatial variance of any given speckle image willcontain contributions from dynamically scattered light, which is whatwe would like to quantify, as well as variance that arises from staticallyscattered light and noise sources. Recently, Parthasarathy et al. havederived a model that accounts for all of these components. Deriva-tion of this model can be found in Ref. [10], and the result is a robustspeckle contrast model that relates the measured speckle contrast tothe speckle decorrelation time:

K (T, �c) =(

�2 e−2x − 1 + 2x2x2 + 4 � (1 − � )

e−x − 1 + xx2 + vnoise

)1/2

(10.6)

where x = T/�c, � = If/(If + Is) is the fraction of light that is dynam-ically scattered, and vnoise is the spatial variance that arises from allthe noise sources in the image. Equation (10.6), therefore, representsan extension to the model of Eq. (10.4) that accounts for both dynamicand static light scattering. In general, the parameters, � and vnoise, will


be unknown for a given sample. Therefore, in order to use Eq. (10.6),speckle contrast measurements must be acquired at multiple expo-sure times. The instrument that was developed to accomplish this isdescribed next.

MESI InstrumentThe objective for developing a new speckle imaging instrument isbased on the need to acquire images that will obtain correlation timeinformation. The requirements include varying the exposure dura-tion, maintaining a constant intensity over a wide range of exposures,and ensuring that the noise variance is constant. In order to test themodel experimentally, we performed flow measurements on microflu-idic flow phantoms. To do this, the exposure duration of speckle mea-surements had to be changed, while ensuring that our conditions weresatisfied. To obtain speckle images at multiple exposure durations, wefixed the actual camera exposure duration and gated a laser diode dur-ing each exposure to effectively vary the speckle exposure duration Tas in Yuan et al. [6]. This approach ensures that the camera noise vari-ance and the average image intensity are constant. Directly pulsingthe laser limited the range of exposure durations that can be achieved.The lasing threshold of the laser diode dictated the minimum inten-sity and hence the maximum exposure duration that can be recorded.Consequently, the minimum exposure duration would be limited bythe dynamic range of the instruments. To overcome this limitation,the laser was pulsed through an acousto-optic modulator (AOM). Bymodulating the amplitude of the RF wave fed to the AOM, the inten-sity of the first diffraction order can be varied, enabling control overboth the integrated intensity and the effective exposure duration.

Figure 10.5 provides a schematic of the experimental setup. Adiode laser beam was directed to an AOM, and the first diffractionorder was directed toward the sample. The sample was imaged us-ing a 10× microscope objective, and images were acquired using an8-bit camera (Basler 602f). A microfluidic device was used as a flowphantom to investigate the effects of a static scattering layer on themeasured flow changes. A microfluidic device as a flow phantom hasthe advantage of being realistic and cost-effective, providing flexibil-ity in design, large shelf life, and robust operation. Our channels wererectangular in cross section (300 �m wide × 150 �m deep). The de-vice was fabricated in poly dimethyl siloxane (PDMS), and titaniumdioxide (TiO2) was added to the PDMS to give the sample a scat-tering background to mimic tissue optical properties. The preparedsamples were bonded on a glass slide to seal the channels as shownin Fig. 10.5. The sample was connected to a mechanical syringe pumpthrough silicone tubes, and a suspension (�s = 250 cm−1) of 1-�m-diameter polystyrene beads was pumped through the channels. For


300µm

150µm

GlassSlide

PDMSwithTiO2

Channel withmicrospheres

150µm

300µm

GlassSlide

PDMSwithTiO2


200µm staticscattering layer

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7Laser

AOM

RF Generator and Amplifier

Data AcquisitionComputers

Syringe PumpFluid in

Fluid out

Sample

10XObjective

Camera

ModulationI/P

Iris

(a)

(c)

(b)

FIGURE 10.5 (a) Experimental setup for multiexposure speckle imaging(MESI). The acousto-optic modulator (AOM) is used as a variable amplitudegate to the laser light, which enables the effective camera exposure time tobe varied over several orders of magnitude. (b) Speckle contrast images offlow through a microfluidics channel under different exposure times (0.1, 5,and 40 ms; scalebar = 50 �m). (c) Illustration of layered microfluidics flowphantoms used to quantify the effects of a static scattering layer on themeasured speckle correlation times. See also color insert.

the static scattering experiments, a 200-�m layer of PDMS with dif-ferent concentrations of TiO2 (0.9 and 1.8 mg of TiO2 per gram ofPDMS corresponding to �s

′ = 4 cm−1and �s′ = 8 cm−1, respectively)

was sandwiched between the channels and the glass slide to sim-ulate a superficial layer of static scattering such as a thinned skull(Fig. 10.5c).

MESI Measurements in Microfluidics Flow PhantomsThe setup in Fig. 10.5 was used to measure the exposure time-dependent speckle contrast in the microfluidics phantoms as the flowin the channels was varied from 0 to 10 mm/s in 1 mm/s incre-ments. The average spatial contrast, K (T), was quantified over an area


10−5 10−4 10−3 10−2 10−10

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

Exposure duration (s)

Sp

eckl

e V

aria

nce

(a.

u.)

µ’s: 0cm−1, 2mm/sec




ρ = 0.438±0.003

τc = 290.68±7.86 µs

ρ = 0.25±0.002

τc = 295.79±8.40 µs

ρ = 0.493±0.008

τc = 62.75±2.34 µs

ρ = 0.311±0.005

τc = 74.67±2.67 µs

0 1 2 3 4 5 6 7 8 9 100

50

100

150

200

250

Speed mm/sec

Dev

iati

on

in τ

c *10

0 /

(τc in

ab

sen

ce o

f st

atic

sca

tter

er)

Single Exposure (5ms)New Speckle Model

(a) (b)

FIGURE 10.6 (a) Multiexposure speckle measurements from two samples at twodifferent flow speeds. Solid lines represent measurements from samples without thestatic scattering layer. (b) Percent deviation in �c under different levels of staticscattering for different flow speeds. The plots illustrate the advantage of MESImeasurements in the presence of static scattering. See also color insert.

centered on the flow channel in each sample. For each measurementset, the K (T) values were fit to Eq. (10.6) with �c, � , and vnoise as fittingparameters. Figure 10.6a illustrates the ability of this model to con-sistently determine �c values even in the presence of static scatteringlayer. The symbols in Fig. 10.6a are the measured speckle variance andthe lines are fits of Eq. (10.6) to the measurements. Figure 10.6a demon-strates that for a given flow rate, the static scattering layer drasticallyalters the shape of the variance (or speckle contrast) with respect toexposure time. If speckle contrast measurements were taken at only asingle exposure time, significantly different values would be obtainedfor a given speed when the static scattering layer is present. However,the model of Eq. (10.6) is able to correctly predict the speckle decor-relation times. For example, at a flow speed of 2 mm/s, the �c valuesare ∼290 and 295 �s for the two different samples. In addition, thevalue of � , which represent the fraction of dynamically scattered light,changes from 0.44 to 0.25 when the static scattering layer is added tothe sample.

To further quantify the effects of a static scattering layer on theconsistency of �c estimates, the deviations in �c for each speed werequantified as the amount of static scatterer in the top layer was varied(Fig. 10.6b). For each speed, the variation in the estimated correla-tion times over the three different scattering cases was determined bycalculating the standard deviation of the correlation time estimates.Single exposure time estimates of �c were made using Eq. (10.3) foran exposure time of 5 ms. The single exposure estimates of �c vary bymore than 200% in the presence of the static scattering layer, whilethe estimates of �c obtained with the MESI technique [Eq. (10.6)] varyby less than 10%. Therefore, by taking into consideration the shape of


the speckle contrast versus exposure time, the MESI approach consis-tently estimates flow changes even in the presence of a static scatteringlayer.

10.5 Future DirectionsAlthough LSCI has been used for more than 25 yr, the basic ap-proach has remained almost unchanged. Over the past decade LSCIhas emerged as a very powerful technique for visualizing flow withexcellent spatial and temporal resolution. This property combinedwith relatively simple instrumentation has resulted in rapid adoptionin areas such as neurological research in animal models. Despite thesimplicity of single-exposure LSCI, one of the biggest challenges inthe future will be to improve the quantitative accuracy of LSCI. Ap-proaches such as the multiexposure speckle imaging (MESI) are thefirst step in future improvements that will enable quantitative com-parisons of baseline flow values across subjects. However, significantwork is still required to improve our understanding of the complexphysics underlying speckle imaging.

References1. A. Fercher and J. Briers, “Flow visualization by means of single-exposure

speckle photography,” Opt Commun, vol. 37, 1981, pp. 326–329.2. J. D. Briers and S. Webster, “Laser speckle contrast analysis (LASCA): A non-

scanning, full-field technique for monitoring capillary blood flow,” J BiomedOpt, vol. 1, 1996, pp. 174–179.

3. H. Bolay, et al., “Intrinsic brain activity triggers trigeminal meningeal afferentsin a migraine model,” Nat Med, vol. 8, 2002, pp. 136–142.

4. A. K. Dunn, et al., “Dynamic imaging of cerebral blood flow using laserspeckle,” J Cereb Blood Flow Metab, vol. 21, 2001, pp. 195–201.

5. A. J. Strong, et al., “Evaluation of laser speckle flowmetry for imaging corticalperfusion in experimental stroke studies: quantitation of perfusion and de-tection of peri-infarct depolarisations,” J Cereb Blood Flow Metab, vol. 26, 2006,pp. 645–653.

6. S. Yuan, et al., “Determination of optimal exposure time for imaging ofblood flow changes with laser speckle contrast imaging,” Appl Opt, vol. 44,2005, pp. 1823–1830.

7. D. D. Duncan and S. J. Kirkpatrick, “Can laser speckle flowmetry be madea quantitative tool?,” J Opt Soc Am A Opt Image Sci Vis, vol. 25, Aug. 2008,pp. 2088–2094.

8. J. D. Briers, “Laser Doppler, speckle and related techniques for blood perfusionmapping and imaging,” Physiol Meas, vol. 22, 2001, pp. R35–R66.

9. R. Banyopadhay, et al., “Speckle-visibility spectroscopy: a tool to study time-varying dynamics,” Rev Sci Instrum, vol. 76, 2005, p. 093110.

10. A. B. Parthasarathy, et al., “Robust flow measurement with multi-exposurespeckle imaging,” Opt Express, vol. 16, Feb. 2008, pp. 1975–1989.

11. R. Bonner and R. Nossal, “Model for laser Doppler measurements of bloodflow in tissue,” Appl Opt, vol. 20, 1981, pp. 2097–2107.

12. C. Ayata, et al., “Laser speckle flowmetry for the study of cerebrovascularphysiology in normal and ischemic mouse cortex,” J Cereb Blood Flow Metab,vol. 24, 2004, pp. 744–755.


13. K. R. Forrester, et al., “A laser speckle imaging technique for measuring tissueperfusion,” IEEE Trans Biomed Eng, vol. 51, 2004, pp. 2074–2084.

14. Y. Tamaki, et al., “Non-contact, two-dimensional measurement of tissue circu-lation in choroid and optic nerve head using laser speckle phenomenon,” ExpEye Res, vol. 60, Apr. 1995, pp. 373–383.

15. J. D. Briers, “Laser Doppler and time-varying speckle: a reconciliation,” J OptSoc AmA, vol. 13, 1996, pp. 345–350.

16. H. K. Shin, et al., “Vasoconstrictive neurovascular coupling during focal is-chemic depolarizations,” J Cereb Blood Flow Metab, vol. 26, 2005, pp. 1018–1030.

17. P. B. Jones, et al., “Simultaneous multispectral reflectance imaging and laserspeckle flowmetry of cerebral blood flow and oxygen metabolism in focal cere-bral ischemia,” J Biomed Opt, vol. 13, Jul. 2008, pp. 044007–044011.

18. P. Li, et al., “Imaging cerebral blood flow through the intact rat skull withtemporal laser speckle imaging,” Opt Lett, vol. 31, Jun. 2006, pp. 1824–1826.

19. A. Grinvald, et al., “Functional architecture of cortex revealed by optical imag-ing of intrinsic signals,” Nature, vol. 324, 1986, pp. 361–364.

20. S. Masino and R. Frostig, “Quantitative long-term imaging of the functionalrepresentation of a whisker in rat barrel cortex,” Proc Natl Acad Sci U S A,vol. 93, 1996, pp. 4942–4947.

21. S. Masino, et al., “Characterization of functional organization within rat barrelcortex using intrinsic signal optical imaging through a thinned skull,” Proc NatlAcad Sci U S A, vol. 90, 1993, pp. 9998–10002.

22. D. Y. Ts’o, et al., “Functional organization of primate visual cortex revealed byhigh resolution optical imaging,” Science, vol. 249, 1990, pp. 417–420.

23. A. K. Dunn, et al., “Simultaneous imaging of total cerebral hemoglobin concen-tration, oxygenation, and blood flow during functional activation,” Opt Lett,vol. 28, 2003, pp. 28–30.

24. T. Durduran, et al., “Spatiotemporal quantification of cerebral blood flowduring functional activation in rat somatosensory cortex using laser-speckleflowmetry,” J Cereb Blood Flow Metab, vol. 24, 2004, pp. 518–525.

25. B. Weber, et al., “Optical imaging of the spatiotemporal dynamics of cerebralblood flow and oxidative metabolism in the rat barrel cortex,” Eur J Neurosci,vol. 20, 2004, pp. 2664–2670.

26. A. K. Dunn, et al., “Spatial extent of oxygen metabolism and hemodynamicchanges during functional activation of the rat somatosensory cortex,” Neu-roimage, vol. 27, 2005, pp. 279–290.

27. B. M. Ances, et al., “Dynamic changes in cerebral blood flow, O2 tension, andcalculated cerebral metabolic rate of O2 during functional activation usingoxygen phosphorescence quenching,” J Cereb Blood Flow Metab, vol. 21, 2001,pp. 511–516.

28. H. K. Shin, et al., “Normobaric hyperoxia improves cerebral blood flow andoxygenation, and inhibits peri-infarct depolarizations in experimental focalischaemia,” Brain, vol. 130, 2007, p. 1631.

29. S. Zhang and T. H. Murphy, “Imaging the impact of cortical microcirculationon synaptic structure and sensory-evoked hemodynamic responses in vivo,”PLoS Biol, vol. 5, 2007, p. e119.

30. U. Dirnagl, C. Iadecola, and M. A. Moskowitz, “Pathobiology of ischaemicstroke: an integrated view,” Trends Neurosci, vol. 22, 1999, pp. 391–397.

31. G. Mies, T. Iijima, and K. A. Hossmann, “Correlation between peri-infarctDC shifts and ischaemic neuronal damage in rat,” Neuroreport, vol. 4, 1993,pp. 709–711.

32. D. N. Atochin, et al., “Mouse model of microembolic stroke and reperfusion,”Stroke, vol. 35, 2004, pp. 2177–2182.

33. A. J. Strong, et al., “Peri-infarct depolarizations lead to loss of perfusion inischaemic gyrencephalic cerebral cortex,” Brain, vol. 130, 2007, p. 995.

34. A. Leao, “Spreading depression of activity in the cerebral cortex,” J Neurophys-iol, vol. 7, 1944, pp. 359–390.


35. T. Back, et al., “Induction of spreading depression in the ischemic hemispherefollowing experimental middle cerebral artery occlusion: effect on infarct mor-phology,” J Cereb Blood Flow Metab, vol. 16, 1996, pp. 202–213.

36. A. J. Strong, et al., “Spreading and synchronous depressions of cortical activityin acutely injured human brain,” Stroke, vol. 33, 2002, pp. 2738–2743.

37. J. P. Dreier, et al., “Delayed ischaemic neurological deficits after subarachnoidhaemorrhage are associated with clusters of spreading depolarizations,” Brain,vol. 129, 2006, pp. 3224–3237.

38. P. A. Lemieux and D. J. Durian, “Investigating non-Gaussian scattering pro-cesses by using nth-order intensity correlation functions,” J Opt Soc Am A,vol. 16, 1999, pp. 1651–1664.

39. D. A. Boas and A. Yodh, “Spatially varying dynamical properties of turbidmedia probed with diffusing temporal light correlation,” J Opt Soc Am A,vol. 14, 1997, pp. 192–215.

P A R T 5Clinical Applications

CHAPTER 11Elastic-Scattering Spectroscopyfor Optical Biopsy: ProbeDesigns and AnalyticalMethods for ClinicalApplications

CHAPTER 12Differential PathlengthSpectroscopy

CHAPTER 13Angle-Resolved Low-Coherence Interferometry:Depth-Resolved LightScattering for DetectingNeoplasia

CHAPTER 14Enhanced Backscattering andLow-Coherence EnhancedBackscattering Spectroscopy


C H A P T E R 11Elastic-ScatteringSpectroscopy for

Optical Biopsy:Probe Designs andAnalytical Methods

for ClinicalApplications

Roberto Reif and Irving J. Bigio

11.1 IntroductionThe term elastic-scattering spectroscopy (ESS) refers to optical mea-surement of the spectral and/or directional properties of backscat-tered light, using geometries and distances such that the measuredlight has scattered only once or a few times. Although this meansthat methods relevant to the diffusion regime are not applicable,with ESS there is more information content available regarding mi-cromorphology. Thus, ESS enables assessment of superficial cellu-lar and subcellular structures in tissue, opening opportunities for awealth of minimally invasive diagnostic applications with clinicalrelevance.

263

264 C l i n i c a l A p p l i c a t i o n s

Turbid media can be characterized by their optical properties (e.g.,scattering and absorption); the scattering depends on the microscopicmorphological composition of the tissue (i.e., size, shapes, and size dis-tribution of the scattering centers), and the absorption depends on thebiochemical composition of the tissue (i.e., blood volume fraction andhemoglobin oxygen saturation). Tissues are generally heterogeneous,and all organ surfaces have layered structures. The surface layer ofany organ, called the epithelium, typically has a thickness between100 and 500 �m, is often glandular and generally plays a key role inthe function of the parenchyma. The epithelial layer is of special in-terest in optical diagnostics, as this is where all carcinomas originate,and is often where other diseases, such as inflammatory bowel dis-ease (IBD), are also initially diagnosed. Therefore, by monitoring thechanges in the micromorphology and biochemical composition of theepithelial tissue layer, through its optical properties, it is possible todiagnose noninvasively various pathologies at an early stage. More-over, the epithelium is readily with optical instruments accessible inhollow organs.

Models of spectral light reflectance enable extraction of the tissueoptical properties from optical measurements in vivo. As a simplifi-cation, most spectral light reflectance systems consist of a light source(often broadband white light), a wavelength-sensitive detector (e.g.,spectrometer), and a fiberoptic probe (FOP) that transmits light toand from the tissue of interest. The light source and the detector areusually controlled by a computer, and the FOP is often in, or near,contact with the tissue of interest and contains one or more opticalfibers. The spectral light reflectance measurement depends on boththe optical properties of the medium and the physical properties ofthe FOP; these include the fiber diameter, numerical aperture, probeangle, source–detector fiber separation, and index of refraction.

This chapter reviews a number of designs of FOPs that have beenused to obtain spectral reflectance measurements from small volumesof superficial tissues, with emphasis on sensitivity to the epitheliallayer. Different methods for analyzing spectral reflectance measure-ments are described briefly; however, an in-depth focus is providedfor an analytical model that has been derived by using empirical tech-niques and Monte Carlo simulations. In vivo results obtained fromstudies on patients with IBD are discussed, and an analysis of theinfluence of probe pressure on the tissue is examined.

11.2 Fiberoptic Probe DesignsSeveral FOP designs have been developed for fluorescence and re-flectance measurements [1–4]. These have addressed applicationswith attention to the epithelial layer, aiming for sensitivity to a

265E l a s t i c - S c a t t e r i n g S p e c t r o s c o p y f o r O p t i c a l B i o p s y

superficial thickness smaller than 500 �m. The depth of penetrationof the collected photons is dependent on the FOP geometry and theoptical properties of the sample [4–7]. In general, for these studies,measurements obtained at wavelengths for which there is a low ab-sorption coefficient will be more sensitive to deeper tissue structuresthan measurements obtained at wavelengths with high absorptioncoefficients. For example, wavelengths that overlap the hemoglobinSoret band or Q bands will, for most geometries, interrogate a moresuperficial volume of tissue compared with wavelengths in the red-NIR optical window range (∼650–1000 nm), assuming the scatteringproperties are similar. Moreover, in tissue, longer wavelengths typi-cally correspond to lower scattering coefficients.

The volume of tissue probed can be controlled by using differentFOP designs. Variables that can be controlled include the numericalaperture (NA) of the optical fibers, the fiber diameters and their angleto the tissue surface, and the source–detector separation. This sectiondiscusses several FOP design approaches that allow for collection ofphotons with sensitivity to small volumes of superficial tissues; thevarious geometries are illustrated schematically.

Single Optical Fiber ProbesAn FOP with a single optical fiber uses the fiber to both transmitlight to and collect light from the tissue of interest; therefore, it isboth the source and the detector, and the source–detector separationis effectively zero. Single optical fibers generally collect light fromtwo sources: (1) light that has interacted with the tissue beneath thesurface and (2) light that has been specularly reflected at the boundarybetween the fiber and the tissue. As a result, a correction for the surfaceFresnel reflection needs to be applied [8–10]. The specular reflectioncan be reduced by using a beveled tip [11]. Figure 11.1 shows the two

(a) (b)

FIGURE 11.1 Fiberoptic probe with a single optical fiber in (a) square and(b) beveled tip configurations.


cases for a single optical fiber with a square or beveled tip, where II isthe incident light and ISP is the specularly reflected light.

Differential Pathlength SpectroscopyDifferential pathlength spectroscopy (DPS) is the designation for atechnique that uses two optical fibers: one fiber that is both sourceand detector, and a second fiber that is only a detector [12–14]. Bysubtracting the light collected from the detector fiber (ID) from thelight collected by the source–detector fiber (ISD), a modification of thespectrum is effected that eliminates most of the diffuse backgroundlight coming from deeper tissue structures. This probe configuration isshown in Fig. 11.2. It is important to note that the source–detector fiberalso collects specularly reflected light as discussed earlier; therefore,its collected spectrum requires a correction. For this geometry, theaverage depth of light penetration (for the collected light) depends onthe diameters of the optical fibers. Chapter 13 describes this techniquein greater detail.

Angled ProbesThe most common FOP geometry used, in reported clinical studies,invokes parallel fibers at normal incidence to the tissue surface (e.g.,[2, 15, 16]). Nonetheless, it is possible to achieve more superficial sen-sitivity with simple geometry adjustments. With contact probes, theangle spread with which light enters a turbid medium from an opticalfiber depends on (in addition to the fiber NA) the angle of the fiber axisto the tissue surface and on the indices of refraction of the fiber and

FIGURE 11.2Fiberoptic probeconfiguration usedfor differentialpathlengthspectroscopy.


(a)

(b)

FIGURE 11.3 Angled fiberoptic probe configuration in a (a) nonparallel and(b) parallel geometry.

the medium. The angle of incidence can be controlled by polishinga beveled tip for coupling to the surface and commensurately tiltingthe fiber(s) with respect to the surface. This enables adjustment of thesensitivity of the collected light to different depths inside the turbidmedium. To achieve shallower penetration, the optical fibers can betilted toward each other [5, 7, 17–19] in a nonparallel geometry, or theycan be tilted in a parallel geometry [20], as depicted in Fig. 11.3.

The parallel FOP geometry is more sensitive to backscattering,while the nonparallel FOP geometry is more sensitive to forward scat-tering. According to Mie theory and Monte Carlo simulations, thebackscattering range is more sensitive to micromorphology changesthan the forward scattering regime [21]. Moreover, the nonparallelFOP would require a larger overall probe diameter size than the par-allel FOP; therefore, it would be more challenging to implement itsdesign within the working channel of an endoscope, which typicallyhas a diameter smaller than 3 mm.

Probes Incorporating Full and Half-Ball LensesClose proximity or overlap of the source and detector sites at the tissuesurface, using separate source and detector fibers, can be achieved


(a) (b)

FIGURE 11.4 (a) Half- and (b) full-ball lens fiberoptic probe.

with a design for bending the incident and collected light from thetissue by using a full [22, 23] or half-ball lens [17], as depicted inFig. 11.4. A limitation of this approach is that there is an unwantedspecular reflection from the ball–tissue interface, which constitutes asizable “background” signal.

Side-Sensing ProbesFor some applications (such as incorporation of the FOP inside abiopsy needle for measurements in a solid organ), the transmitted andcollected light should be transmitted through the side of the needle,approximately normal to the fiber axes [24, 25]. This side emission/collection can be accomplished by polishing the fiber tips at 45◦ tothe fiber axes, resulting in total internal reflection if the tip is in air.Generally, the tip can be reflectively coated to guarantee sidewaysemission/collection. Alternatively, a separate mirror or microprismcan be used at the tip of the fiber. One such configuration for side-directed FOP design is shown in Fig. 11.5.

Diffusing-Tip ProbesIf light exhibits a diffuse behavior before being collected, variationsof diffusion theory can be used to model the light reflectance at rela-tively small source–detector separations. This can be accomplished byincorporating a diffuser at the tip of the source fiber [26, 27] and using


FIGURE 11.5 Sideview transverse-emission fiberopticprobe.

a two-layered model based on diffusion theory. This method is validfor media with a reduced scattering coefficient much higher than theabsorption coefficient and is typically limited, in biological tissues, tothe wavelength range between 650 and 1000 nm. The configuration ofa diffuse-tip FOP is shown in Fig. 11.6.

FIGURE 11.6 Diffuse tip fiberoptic probe.


FIGURE 11.7 Polarized normally incident fiberoptic probe.

Polarized ProbesPolarized light maintains its polarization state under single-scatteringevents, as referenced to the scattering plane [28, 29]. Two or morescattering events are required to rotate linear polarization (or induceellipticity to circular polarization). Therefore, by illuminating with po-larized light, collecting parallel and crossed polarizations separately,and then subtracting the crossed polarization signal from the paral-lel signal, it is possible to reject much of the diffuse background light,which comes from deeper structures. The difference signal will mostlyresult from scattering events that occur superficially. Sokolov et al. [30]explored this idea using a noncontact setup, and derived an analysis,based on Mie theory, to characterize the size distribution of the scatter-ing centers. This concept has been expanded to specific FOP designs,which can have a normal [1] or oblique incidence [6, 31] at the tis-sue surface to enhance the sensitivity to superficial volumes. Figure11.7 represents the simplest geometry of a polarized normal-incidenceFOP. (The fiber tips must be configured in a line.)

11.3 Models for the Reflectance Spectra

Methods for Analyzing Reflectance SpectraSeveral methods have been developed for analyzing the reflectancespectra from biological tissues. Statistical methods for analyzing thewhole spectrum have been previously used. Although statisticalmethods do not extract the optical properties of the turbid media,they have been successful in classifying spectra representing differ-ent tissue pathologies. Some examples of statistical methods include


analyzing the area under the curve from spectra obtained frommelanoma [32]; linear discriminant analysis of principal componentsof spectra obtained from Barrett’s esophagus [33] and cervical cancer[34]; and neural network classification of breast cancer [35].

The diffusion approximation to the Boltzman transport equationis a method that has successfully been used to determine the ab-sorption and reduced scattering coefficients of turbid media, underconditions appropriate to the diffusion approximation [36–38]. Thediffusion approximation is limited to media with a reduced scatteringcoefficient much larger than the absorption coefficient (�′

s >> �a),which occurs in biological tissues for the wavelengths between 650and 1000 nm, and for large separations, � , between the source andthe detector (� >> 1/�′

s). The volume of tissue probed with this tech-nique extends beyond the epithelial layer, and the optical propertiesextracted represent an average value for the larger tissue volume thatis sampled. Although there are limitations imposed by diffusion the-ory, extrapolations of this model have been used to extract opticalproperties from superficial tissue volumes, at small source–detectorseparations [39, 40], including the use of the diffusing-tip probe de-scribed earlier, with a two-layered diffusion model [26, 27].

Another method for analyzing a spectrum consists of buildinga static or dynamic database (or look-up table) of spectra obtainedfrom combinations of different optical properties, and then findingthe best fit of the measured spectrum to the database spectra. Thisenables extraction of the optical properties, although the solution is notalways unique—different combinations of absorption and reducedscattering coefficients can yield the same measured spectrum. Thedatabase can also be expanded with interpolations of the modeledresults. The database can be built by using Monte Carlo simulations[5, 41–45] or experiments with tissue phantoms [24].

Analytical models have been developed to describe the reflectancespectrum as a function of the optical properties of the turbid medium.A model can be derived from reflectance measurements obtained byusing Monte Carlo simulations or by experiments in tissue phantoms[13, 20, 46] or through theoretical analysis such as a modified spatiallyresolved diffusion method [44, 47, 48].

It is important to note that the reflectance at small source–detectorseparations is dependent on the phase function and anisotropy val-ues of the scattering centers [20, 49, 50]. The phase function has beentypically modeled by using Mie theory [28], the Henyey–Greensteinapproximation [51] or a modified Henyey–Greenstein approximation[45, 47]. Mie theory assumes that the scattering centers have a spher-ical shape. When a monodisperse suspension of spherical particlesis used, the Mie scatterers produce distinguishable oscillations as afunction of wavelength and angle. However, as the size distributionbroadens, the oscillations disappear [11], and the oscillatory signal can


be hidden by the background of diffusely scattered light from deepertissue structures [52]. Mourant et al. [53] obtained the phase functionof cells by using goniometric measurements. Because it is difficult toknow beforehand the true expressions of the phase function for a givensample of tissue, the models developed are simply an approximationbased on the phase functions used in the Monte Carlo simulationsor the actual phase functions of the scattering centers utilized in thetissue phantoms.

A Quantitative Analytical Model Well-Suitedto Superficial TissuesReif et al. [20] developed an analytical model of light reflectance based,empirically, on both Monte Carlo simulations and experiments withtissue phantoms. The model is valid at small source–detector separa-tions and is not restricted to media with reduced scattering coefficientmuch higher than the absorption coefficient; therefore, this model doesnot have the limitations imposed by diffusion-theory models. The par-allel FOP design was used to obtain and test this model. The derivationof the analytical model is briefly described here.

An FOP that consisted of two multimode optical fibers, with corediameters of 200 �m, an NA of 0.22 in air, and a center-to-center sep-aration of 250 �m, was fabricated for the experiments, and was mod-eled using Monte Carlo simulations. The Monte Carlo simulation codewas based on previous codes [54, 55] using a variance reduction tech-nique [56]. The experiments were run using a pulsed Xenon-arc lamp(LS-1130–3, Perkin Elmer, Waltham, MA) as a broadband light source,a spectrometer (S2000, Ocean Optics, Inc, Duendin, FL), and an FOPfor the delivery and collection of the light.

Liquid tissue test phantoms were prepared by using water,Intralipid-10% (Fresenius Kabim, Bad Homburg, Germany) as asource of scattering, and Indigo Blue dye (Daler-Rowney, Bracknell,England, UK) as an absorber. The reduced scattering coefficients forthe various preparations were determined by using a method of spa-tially dependent diffuse reflectance spectroscopy [57], and knownamounts of dye were added to the phantoms to obtain the known val-ues of the absorption coefficients. A calibration phantom with knownoptical properties was also prepared.

Reflectance values were obtained by dividing each phantom spec-trum by the spectrum obtained with the known calibration phantom.The integration time of the spectrometer was the same for the mea-surements taken by both the tissue phantoms and calibration phan-tom. Figure 11.8 displays plots of the reflectance obtained from MonteCarlo simulations and from the experiments on phantoms for mediathat scatter light but have no absorption added. The experimental re-sults shown are at a wavelength of 610 nm. It is observed that there


(a) (b)

FIGURE 11.8 Reflectance as a function of the reduced scattering coefficientin a nonabsorbing medium obtained with (a) Monte Carlo simulations and (b)experiments in tissue phantoms at 610 nm.

is a linear relationship between the reduced scattering coefficient andthe reflectance. Similar results have been obtained by other authors[13, 46, 58].

Reflectance measurements invoking both scattering and absorp-tion were then obtained from Monte Carlo simulations and from ex-periments with the test phantom preparations. Figure 11.9 presentsthe reflectance as a function of the absorption coefficient on a log–logscale for three different values of reduced scattering coefficient. Thevalues used for the absorption and reduced scattering coefficients arerepresentative of typical values found in biological tissues [59].

In Fig. 11.8, it was shown that the reflectance is linearly propor-tional to the reduced scattering coefficient when there is no absorption;however, Beer’s law states that the intensity decays exponentially asa function of the absorption coefficient. Therefore, we can model thecombined results with Eq. (11.1):

R = a�′s exp (−�a 〈L〉) (11.1)

(a) (b)

FIGURE 11.9 Reflectance as a function of the absorption coefficient obtainedwith (a) Monte Carlo simulations and (b) experiments in tissue phantoms at610 nm, for three values of scattering coefficient.


where 〈L〉 is the effective pathlength of the collected photons and a isthe constant that depends on geometrical factors that affect collectionefficiency. The effective pathlength in a reflectance FOP geometry canbe approximated as being inversely proportional to both the scatteringand absorption properties of the medium, as given by Eq. (11.2):

〈L〉 = b(�a�′

s

)c (11.2)

where b and c are constants to be determined empirically. The resultsin Fig. 11.9 were fit to the expression in Eq. (11.1), where �a and �′

swere known values, and a , b, and c were fitting parameters. It wasdetermined that the values of a , b, and c that gave the best fit to theexperimental data were 0.11, 0.22, and 0.2, respectively. These valuesare specific to the FOP design and geometry that was used for thesemeasurements.

Influence of Blood Vessel RadiusMost models assume a homogeneous distribution of scatterers andabsorbers in the turbid medium. However, for tissue, the strongest ab-sorbers in the UV–VIS–NIR region of the spectrum are oxyhemoglobinand deoxyhemoglobin. Hemoglobin is confined in red blood cells,which are compartmentalized in blood vessels. Therefore, hemoglobinis not homogeneously distributed throughout the tissue; rather, it canbe approximated as being contained in cylinders that represent bloodvessels. The influence of the inhomogeneous distribution of the ab-sorbers on the reflectance spectrum has been analyzed previouslyby several authors [60–63]. It was concluded that a correction fac-tor (Ccorr) should be applied to the absorption coefficient of biologicaltissues. The correction factor is a function of the product of the meanblood vessel radius and the absorption coefficient of blood. Althougheach publication arrived at a different analytical expression for thecorrection factor, they all produced similar results [64]. Svaasand etal. [61] proposed a simplified analytical expression for Ccorr, givenby Eq. (11.3), which has been incorporated into several reflectancemodels [14, 65].

Ccorr () ={

1 − exp [−2�a ,bl () r ]2�a ,bl () r

}(11.3)

where r is the mean value of the blood vessel radius, and �a,bl() isthe absorption coefficient of whole blood. Equation (11.4) is obtained


by combining Eqs. (11.1) to (11.3).

R () = IT () /IR ()IC (0) /IR (0)

= a�′s () exp

(−Ccorr () �a () b(

Ccorr () �a () �′s ()

)c

) (11.4)

The relative reflectance spectrum, R(), is obtained from the ratioof the tissue spectrum, IT(), divided by a reference spectrum obtainedfrom a spectrally flat diffuse reflector (Spectralon, Labsphere, NorthSutton, NH), denoted as IR(). It must be noted that the amplitude ofIR() is dependent on the distance between the probe and the diffusereflector, which is difficult to control with high consistency betweendifferent experiments. Consequently, the spectrum is normalized ata reference wavelength so that its amplitude is independent of thedistance between the probe and the diffuse reflector, and then thespectrum is further referenced to the spectrum obtained from an im-mersion calibration phantom with known optical properties, IC(0),where 0 is 610 nm.

The expressions for the wavelength dependence of the reducedscattering coefficient and absorption coefficient are given by Eqs. (11.5)and (11.6), respectively:

�′s () = d · −e (11.5)

�a () = f1 ( f2εHbO () + (1 − f2) εHb ()) (11.6)

where εHbO() and εHb() are the extinction coefficients of oxyhe-moglobin and deoxyhemoglobin, respectively, and d, e, f1, and f2

are constants.Figure 11.10 shows the absorption coefficient of hemoglobin in

whole blood as a function of wavelength for different oxygen satura-tion values. The blood concentration of hemoglobin is assumed to be150 g/l, which is a typical value for adult humans.

The strongest absorption of hemoglobin is at the shorter wave-lengths, especially at the Soret band at ∼420 nm, and the absorptionstrength at shorter wavelengths is approximately constant, indepen-dent of the oxygen saturation. Figure 11.11a depicts the correctioncoefficient as a function of the product of the absorption coefficientand the mean blood vessel radius, which has been calculated withEq. (11.3).

The correction factor has a value between 0 and 1; however, thetrue value of the product �a · r is difficult to determine when the cor-rection factor has a value close to 0 or 1. For demonstration purposes,two threshold values have been defined at 0.025 and 0.975 (dashedlines in Fig. 11.11a ), the assumption being that if the value of Ccorr


FIGURE 11.10 Absorption coefficient of hemoglobin in whole blood fordifferent oxygen saturation values. The concentration of hemoglobin in bloodis set to 150 g/l.

is between the threshold values, it will be possible to determine avalue for �a · r . Figure 11.11b plots the region for which the prod-uct of �a · r produces values of Ccorr between 0.025 and 0.975. Thedashed line represents the peak of the Soret absorption coefficientvalue of hemoglobin. The absorption coefficient values equal to thoseof the hemoglobin Soret band fall within the region of the correctioncoefficient for vessel radii smaller than 100 �m. As the FOP that wasused has a source–detector separation of approximately 250 �m, themeasurements obtained are sensitive to superficial volumes of tissue.Capillaries are found close to the tissue surface, near the base of the

(a) (b)

FIGURE 11.11 (a) The correction coefficient as a function of the product ofthe absorption coefficient and the blood vessel radius. (b) Region for whichthe product of the radius times the absorption coefficient produces correctioncoefficient values between 0.025 and 0.975.


FIGURE 11.12 Relative reflectance spectra for different blood vessel radii.

epithelium; the smallest capillaries have a radius of a few microns,while nearby arterioles it can be up to 20 �m. Therefore, the correc-tion factor is well suited for the typical values of vessel sizes in thesuperficial tissue volumes that are targeted.

To demonstrate how the relative reflectance spectrum depends onthe blood vessel radii, Eq. (11.4) was used to calculate three relativereflectance spectra. The oxygen saturation was set to 80%, the tissueblood volume fraction was set to 1%, and the reduced scattering co-efficient was modeled using Eq. (11.5), where e was set to a valueof 1.1 and d was set to a value such that �′

s (600 nm) = 10 cm−1. Theblood vessel radii used were 5, 10, and 20 �m. The relative reflectancespectra are shown in Fig. 11.12.

In conclusion, the mean blood vessel radius affects the relative re-flectance spectrum. The changes in the reflectance spectrum are morepronounced in wavelength regions with strong hemoglobin absorp-tion. Information about the mean vessel radius can be inferred fromthe presented analytical model.

11.4 In Vivo Application in a Human StudyAs the first test of the diagnostic potential of the analytical model, aclinical study was carried out using an optical biopsy tool that consistsof a normally-incident parallel FOP design and the analytical modelrepresented by Eq. (11.4). An ESS system was used in a study to testfor diagnosis of inflammatory bowel disease (IBD), which denotes agroup of inflammatory disorders of the large intestine. IBD diagnosisis generally performed in a colonoscopy procedure, which allows the


physician to observe inflammation, bleeding, or ulceration on the wallof the colon. During the examination, physicians typically take about30 biopsy samples, small samples of the colonic mucosa, generallyusing a biopsy forceps. The biopsies are then analyzed by a pathol-ogist with standard histology procedures. It would be advantageousto minimize or eliminate the need for biopsies by using an opticallyguided biopsy technique, which can rapidly sample a larger numberof sites, while collecting a smaller number of surgical tissue samplesfrom only the most suspicious sites.

For this study, a biopsy forceps was assembled, into which a FOPwas integrated. Two optical fibers with core diameters of 200 �m andNAs of 0.22 were incorporated in the center of a standard biopsy for-ceps. We refer to this tool as an “optical forceps.” The center-to-centerseparation of the fibers was approximately 250 �m, and the tips ofthe fibers were polished normal to the fiber axis such that contact isnormal to the tissue surface. Figure 11.13 is a photo of the tip of thebiopsy forceps with the two optical fibers located in the central cylin-drical structure. The optical forceps fits within the standard workingchannel of an endoscope and allows the clinician to obtain both areflectance measurement and a biopsy sample from the same tissuevolume. Therefore, the reflectance measurements and tissue samplesare accurately coregistered, providing a direct correlation with thehistology results obtained by the pathologist.

Reflectance measurements followed by a biopsy were performedin different locations of the colon walls of several patients. Five spec-tra were obtained from each site (within about 3 s) and averaged.

FIGURE 11.13 Biopsy forceps with two optical fibers incorporated in thecenter.


FIGURE 11.14Mean spectra forthe normal andinflamed IBDmeasurements.

Two pathologists classified every biopsy sample. If there was dis-agreement among the pathologists, a third pathologist was consultedto break the “tie.” Each biopsy was classified in one of several cat-egories, but the results were collected into two groups: normal andinflamed. The normal group included all the biopsy samples from nor-mal colonic mucosa (n = 35). The inflamed group (n = 24) includedall the biopsy samples of colitis from subclassifications of inactive(n = 12), mild (n = 7), moderate (n = 4), and inactive with surfacereparative change (n = 1). The means of the normal and inflamed IBDreflectance spectra are plotted in Fig. 11.14.

Each spectrum was fit to the model represented by Eq. (11.4) us-ing a Levenberg–Marquardt algorithm and a least-squares approach.The fitting algorithm was implemented with Matlab. Five parametersare obtained from the model: blood volume fraction ( f1), hemoglobinoxygen saturation ( f2), blood vessel radius (r ), and the two parame-ters (coefficients d and e) to define the reduced scattering coefficient,�′

s. The exponent of the power law (or Mie-theory “slope”), e, is di-rectly extracted. As the parameter d has no physical meaning, andits units depend directly on e such that the units of �′

s are in inverselength (i.e., cm−1), we describe the value of �′

s at 700 nm [�′s (700 nm) =

d· 700−e ). The Mie slope is a constant, which relates to the mean size ofthe scattering particles and can have a value ranging from about 0.37(particles much larger than the wavelength of the light) to 4 (particlesmuch smaller than the wavelength of the light—the regime knownas Rayleigh scattering) [21, 66, 67]. The blood volume fraction is cal-culated by assuming a blood hemoglobin concentration of 150 g/l,which is typical for human blood.

The parameters had the following constraints:

d, r ≥ 00.37 ≤ e ≤ 4and 0 ≤ f1, f2 ≤ 1.


FIGURE 11.15 Mean and standard deviation of the (a) blood volume fraction,(b) oxygen saturation, (c) mean blood vessel radius, (d) Mie slope, and (e)reduced scattering coefficient at 700 nm for normal and inflamed tissuesamples.

The starting points for all the parameters were the lowest valuesof the constraint ranges. Other starting points were tested, and thevalues for the parameters obtained converged; therefore, we can as-sume that the solution is unique. Model fits with R2 values less than0.9 were discarded. The discarded spectra had either features withnonphysiological meaning or part of the signal was saturated due tothe presence of blood on the probe. Figure 11.15 shows the mean andstandard deviation of the five parameters extracted by the model.

The parameters were analyzed with a fourth-order polynomialsupport vector machine (SVM) using least-squares fit and a leave-one-out test algorithm. The sensitivity, specificity, positive and negative


FIGURE 11.16Receiver operatingcharacteristiccurve for themodel.

predictive values obtained were 77.1%, 70.8%, 79.4%, and 68.0%, re-spectively. Figure 11.16 shows the receiver operating characteristic(ROC) curve of the model analysis.

11.5 Influence of Probe PressureSpectral reflectance measurements of biological tissues are often per-formed with a FOP held in contact with the tissue surface; therefore,the probe might apply pressure to the tissue. If the probe is not in con-tact, the reflectance and fluorescence can be affected by the probe-to-target distance [2, 68]. An ex vivo study has previously demonstratedthat the amount of pressure applied to a sample of tissue affects itsabsorption and reduced scattering coefficients [69]. It has also been re-ported that probe pressures with forces of less than 1 N, with a probediameter of 5 mm and an application time of 2 min, do not affect thefluorescence signal obtained on cervical tissues in vivo [70]. However,in general, the reflectance spectrum from biological tissues is affectedby the amount of pressure exerted by the FOP [65, 71].

Influence of Probe Pressure on Normal Colon Mucosa:A Preliminary Clinical StudyAn FOP with a two-fiber configuration, designed for normal inci-dence, was integrated with a calibrated spring device to measureprobe pressures (Fig. 11.17).

The probe can apply known pressure values up to 0.17 N/mm2,and it was used to take spectral reflectance measurements from normalcolon mucosa, on one patient. Fifteen measurements were obtainedfrom the normal colon mucosa under three conditions: (1) a probepressure of 0 N/mm2; (2) a probe pressure of 0.17 N/mm2, with mea-surements taken within the first 3 s; and (3) a probe pressure of 0.17N/mm2, with measurements taken after 3 s.


FIGURE 11.17 Pressure-sensitive fiberoptic probe.

Each spectrum was analyzed with the model described by Eq.(11.4), and the results were processed with the Support Vector Machinederived in the IBD study. It should be noted that the diagnostic train-ing set had been established with measurements obtained with uncon-trolled pressures. Moreover, only the specificity can be obtained be-cause data were only collected from normal colon mucosa. Figure 11.18shows the specificity obtained under the three conditions described.

When no pressure was applied, the specificity was above 90%.However, when a constant pressure was applied, and the measure-ments were obtained within the first 3 s, the specificity dropped to

100

80

60

40

20

0No

pressure

Spe

cific

ity (

%)

Pressure =0.17 N/mm2

0–3 s

3–6 s

Pressure =0.17 N/mm2

FIGURE 11.18 Specificity of measurements obtained from normal colonmucosa (see text for details).


approximately 70%. This value is comparable to the result obtainedin the IBD study, which may be indicative of the variability of mea-surements when no pressure control is implemented. Finally, whenmeasurements were obtained after applying a constant pressure andwaiting more than 3 s, the specificity dropped to approximately 60%.The variance in the results obtained with no pressure was smaller thanthe variance obtained under probe pressure, which would explain theincrease in specificity.

In conclusion, the specificity is affected by the amount of probepressure applied to the tissue and by the duration of the pressure. Wespeculate that the sensitivity, positive and negative predictive valueswould also be affected by the probe pressure. The next sections de-scribe a more rigorous quantitative study of the influence of the probepressure using an animal model.

Influence of Probe Pressure on Reflectance Measurements:A Quantitative Animal StudyThis section reports a study of the influence of probe pressure on spec-tral reflectance measurements of biological tissue in an animal modelin vivo. The thigh muscle of a mouse was used as a tissue modelbecause the volume of the tissue is large enough to be consideredsemi-infinite for the optical geometry of the probe (source–detectorseparation of approximately 250 �m), and because the muscle tissueis relatively homogeneous. A parallel, normal-incidence FOP was fab-ricated. The probe had a handle to which different weights could beattached, as shown in Fig. 11.19. The weights, added to the weight ofthe probe itself, resulted in applied pressures of 0.04, 0.09, 0.13, 0.17,and 0.2 N/mm2.

Ten mice were anesthetized and the skin over both thigh muscleswas removed, such that the muscles were exposed. The probe wasplaced perpendicular to the tissue surface of the muscle. Each exper-iment comprised five sets, and a set consisted of two measurements.The first measurement was obtained when the FOP was placed ingentle contact with the surface of the tissue such that there was nosignificant pressure applied to the muscle. The probe was held by afixture, as illustrated in Fig. 11.19. The second measurement was ob-tained by attaching one of the weights to the probe and loosening theprobe fixture, allowing the probe to slide vertically while maintain-ing a vertical orientation such that the pressure was applied normalto the tissue surface. Each spectrum was acquired within 5 s of theapplication of pressure. Subsequently, the probe was removed fromthe muscle, and at least a 30-s time delay was allowed for the tissue toreturn to its normal state prior to the next measurement. The set wasthen repeated at a different location on the muscle, with a differentpressure until all five weights were used. The order of the pressure


Probefixture

2.7 mm

250 µm

Tissue

Weight

FIGURE 11.19Schematic diagramof the experimentalsetup.

applied was randomized on each muscle; therefore, it is assumed thatthe influence of the previously applied pressure on each measurementis negligible. Results are summarized in Fig. 11.20.

Figure 11.20a shows an example of the relative reflectance andof the model fit at two different probe pressures. It can be readilynoted that a degree of desaturation is exhibited in the trace taken at0.2 N/mm2, compared with the trace at zero pressure.

The means and standard deviations of the five parameters ex-tracted from the model are presented in Fig. 11.20b– f . By inspection,the trends of the data appear to follow either a linear or exponentialrelationship with pressure; therefore, the mean value of each param-eter has been modeled as a function of the probe pressure with anexponential expression given by Eq. (11.7):

y = a0 + a1 exp (a2 · P) (11.7)

where a0, a1, and a2 are fitting coefficients, and P is the probe pressure.The results from the exponential fits are plotted as the solid lines in Fig.11.20b– f . The blood vessel radius, oxygen saturation, and Mie-theoryslope decrease with pressure, while the reduced scattering coefficientat 700 nm increases as a function of pressure. We hypothesize that thepressure applied by the probe compresses the blood vessels, conse-quently reducing the blood flow. This would explain the decrease inthe blood vessel radius and the desaturation of the blood due to the


(a) (b)

(c) (d)

(e) (f)

FIGURE 11.20 (a) Example of the relative reflectance and the respective fitsfor a measurement obtained with a pressure of 0 and 0.2 N/mm2. Mean andstandard deviations of (b) blood volume fraction, (c) oxygen saturation, (d)mean blood vessel radius, (e) Mie slope, and (f ) reduced scatteringcoefficient at 700 nm as a function of the probe pressure. The solid line isthe least-squared fit of Eq. (11.7) to the mean values of each parameter.

tissue oxygen consumption and disruption of the flow of oxygenatedblood arriving to the tissue. The probe pressure might also increasethe density of scatterers per unit volume, as a result of expelling fluid,which would be consistent with the increase in the reduced scatteringcoefficient.

The decrease in Mie slope is an indication that the scattering ismostly due to larger particles, which could be a consequence of in-creasing the relative density of large organelles per unit volume, but


a good understanding of this parameter will require further study.The mean blood volume fraction varies less than 20% for the range ofpressures applied and does not seem to follow a trend; therefore, itmight be assumed that the blood volume fraction is not dependent onthe probe pressure, which is counterintuitive. It is important to notethat the dominant contributors to the optical absorption in muscle arehemoglobin and myoglobin. The absorption spectrum of myoglobinis very similar to that of hemoglobin, and its concentration in mus-cle tissue is typically lower than that of hemoglobin [72, 73]; there-fore, its contribution to the optical absorption is less. Nonetheless,the blood volume is reduced when the blood vessels are compressed,whereas the concentration of myoglobin might increase, counteractingthe decrease in hemoglobin absorption. If so, the model would fit theabsorption spectra of a combination of hemoglobin and myoglobin,which could explain the apparent lack of change in the blood volumefraction.

Temporal Influence of Probe Pressure on ReflectanceMeasurements: An Animal StudyA constant probe pressure can also affect the optical properties asa function of time. Using the same experimental setup as describedin Fig. 11.19, a constant pressure of 0.17 N/mm2 was applied for aperiod of 60 s on the skin of six nude mice. While the probe was ap-plying pressure to the tissue, spectral reflectance measurements wereobtained every 0.5 s for 60 s. Each spectrum included the wavelengthsbetween 340 and 700 nm, and was fit to Eq. (11.4). Figure 11.21 showsthe results of the means and standard deviations of the five extractedparameters from the model as a function of time. It is noted that theparameters exhibit dynamic changes.

It is hypothesized that the probe pressure compresses the bloodvessels, consequently reducing the blood flow, which explains theinitial reduction in the average blood vessel radius. However, that pa-rameter recovers to its baseline value within 60 s, possibly indicatinglocal vascular or blood pressure response. The blood volume fractiondecreases quickly, indicating that blood is initially removed from theblood vessels, followed by a slow recovery trend. The oxygen satu-ration decreases monotonically as the tissue consumes the oxygen inthe local blood, since there is reduction of blood flow. The reducedscattering coefficient is unaffected by the pressure; however the Mieslope decreases, indicating that the scattering is due to a relative in-crease in the number of large particles, which could be a consequenceof increasing the density of large organelles per unit volume.

These results are consistent with changes observed with diffuseoptical tomography (DOT) measurements of breast tissues under dif-ferent compressions [74, 75].


(a) (b)

(c)

(e)

(d)

FIGURE 11.21 Mean and standard deviation of (a) blood volume fraction, (b)oxygen saturation, (c) mean blood vessel radius, (d) Mie slope, and (e)reduced scattering coefficient at 700 nm as a function of time for a probepressure of 0.17 N/mm2.

11.6 ConclusionsVarious FOP designs have been developed to enhance the sensitiv-ity to superficial volumes of tissue during spectral reflectance mea-surements. Several methods have been reported for analyzing the re-flectance spectra obtained from using these FOPs. An analytical modelfor the reflectance spectra, optimized for measurements of small su-perficial volumes, was presented. This model enables the quantitativeextraction of five physical parameters, which provide a basic descrip-tion of the underlying physiological properties of the tissue.


In most applications of reflectance spectroscopy, it is assumed thatthe turbid medium (or biological tissue) has a homogeneous distribu-tion of scatterers and absorbers throughout the medium. Most meth-ods that extract the optical properties use this approximation, whichis valid for most tissue phantoms, but not for biological tissues, whichhave an inhomogeneous distribution of the strongest absorbers. Theanalytical model presented here accommodates the compartmental-ized distribution of blood in real tissue.

The FOP designs discussed in this chapter are applied in contactwith the tissue of interest. The amount of probe pressure applied to thetissue and the duration of the pressure can have an impact on deter-mination of the local optical properties of the tissue and on diagnosticconsistency. Therefore, we submit that by limiting or controlling theamount of probe pressure, it will be possible to reduce the variabilityof spectral reflectance measurements. Consequently, we would expectimproved values of the sensitivity, specificity, positive and negativepredictive values with spectral reflectance measurements for early di-agnosis of different pathologies.

References1. Myakov A., L. Nieman, L. Wicky, U. Utzinger, R. Richards-Kortum, and K.

Sokolov, “Fiber optic probe for polarized reflectance spectroscopy in vivo: de-sign and performance,” J Biomed Opt 7, 388–397 (2002).

2. Pfefer T. J., K. T. Schomacker, M. N. Ediger, and N. S. Nishioka, “Multiple-fiberprobe design for fluorescence spectroscopy in tissue,” Appl Opt 41, 4712–4721(2002).

3. Utzinger U. and R. Richards-Kortum, “Fiber optic probes for biomedical opticalspectroscopy,” J Biomed Opt 8, 121–147 (2003).

4. Zhu C., Q. Liu, and N. Ramanujam, “Effect of fiber optic probe geometry ondepth-resolved fluorescence measurements from epithelial tissues: a MonteCarlo simulation,” J Biomed Opt 8, 237–247 (2003).

5. Liu Q. and N. Ramanujam, “Sequential estimation of optical properties ofa two-layered epithelial tissue model from depth-resolved ultraviolet-visiblediffuse reflectance spectra,” Appl Opt 45, 4776–4790 (2006).

6. Nieman L., A. Myakov, J. Aaron, and K. Sokolov, “Optical section-ing using a fiber probe with an angled illumination-collection geome-try: evaluation in engineered tissue phantoms,” Appl Opt 43, 1308–1319(2004).

7. Wang A. M. J., J. E. Bender, J. Pfefer, U. Utzinger, and R. A. Drezek, “Depth-sensitive reflectance mesurements using obliquely oriented fiber probes,”J Biomed Opt 10, 044017 (2005).

8. Moffitt T. P. and S. A. Prahl, “In vivo sized-fiber spectroscopy,” Proc SPIE 3914,225–231 (2000).

9. Moffitt T. P. and S. A. Prahl, “Sized-fiber reflectometry for measuring localoptical properties,” IEEE J Sel Top Quant. Elec 7, 952–958 (2001).

10. Prahl S. A. and S. L. Jacques, “Sized-fiber array spectroscopy,” Proc SPIE 3254,348–352 (1998).

11. Canpolat M. and J. R. Mourant, “Particle size analysis of turbid media witha single optical fiber in contact with the medium to deliver and detect whitelight,” Appl Opt 40, 3792–3799 (2001).


12. Amelink A., M. P. L. Bard, S. A. Burgers, and H. J. C. M. Sterenborg, “Single-scattering spectroscopy for the endoscopic analysis of particle size in superficiallayers of turbid media,” Appl Opt 42, 4095–4101 (2003).

13. Amelink A. and H. J. C. M. Sterenborg, “Measurement of the local opticalproperties of turbid media by differential path-length spectroscopy,” Appl Opt43, 3048–3054 (2004a).

14. Amelink A., H. J. C. M. Sterenborg, M. P. L. Bard, and S. A. Burgers, “In vivomeasurement of the local optical properties of tissue by use of differentialpath-length spectroscopy,” Opt Lett 29, 1087–1089 (2004b).

15. Bigio I. J. and S. G. Bown, “Spectroscopic sensing of cancer and cancer therapy,”Cancer Biol Ther 3, 259–267 (2004).

16. Bigio I. J. and J. R. Mourant, “Ultraviolet and visible spectroscopies for tissue di-agnostics: fluorescence spectroscopy and elastic-scattering spectroscopy,” PhysMed Biol 42, 803–814 (1997).

17. Arifler D., R. A. Schwarz, S. K. Chang, and R. Richards-Kortum, “Reflectancespectroscopy for diagnosis of epithelial precancer: model-based analysis offiber-optic probe designs to resolve spectral information from epithelium andstroma,” Appl Opt 44, 4291–4305 (2005).

18. Wang A., V. Nammalavar, and R. Drezek, “Experimental evaluation of an-gularly variable fiber geometry for targeting depth-resolved reflectance fromlayered epithelial tissue phantoms,” J Biomed Opt 12, 044011 (2007a).

19. Wang A., V. Nammalavar, and R. Drezek, “Targeting spectral signatures ofprogressively dysplastic stratified epithelia using angularly variable fiber ge-ometry in reflectance Monte Carlo simulations,” J Biomed Opt 12, 044012(2007b).

20. Reif R., O. A’Amar, and I. J. Bigio, “Analytical model of light reflectance forextraction of the optical properties in small volumes of turbid media,” ApplOpt 46, 7317–7328 (2007).

21. Mourant J., T. Fuselier, J. Boyer, T. M. Johnson, and I. J. Bigio, “Predictions andmeasurements of scattering and absorption over broad wavelength ranges intissue phantoms,” Appl Opt 36, 949–957 (1997a).

22. Schwarz R. A., D. Arifler, S. K. Chang, I. Pavlova, I. A. Hussain, V. Mack,B. Knight, R. Richards-Kortum, and A. M. Gillenwater, “Ball lens coupled fiber-optic probe for depth-resolved spectroscopy of epithelial tissue,” Opt Lett 30,1159–1161 (2005).

23. Schwarz R. A., W. Gao, D. Daye, M. D. Williams, R. Richards-Kortum, andA. M. Gillenwater, “Autofluorescence and diffuse reflectance spectroscopy oforal epithelial tissue using a depth-sensitive fiber-optic probe,” Appl Opt 47,825–834 (2008).

24. Bargo P. R., S. A. Prahl, T. T. Goodell, R. A. Sleven, G. Koval, G. Blair andS. L. Jacques, “In vivo determination of optical properties of normal and tu-mor tissue with white light reflectance and an empirical light transport modelduring endoscopy,” J Biomed Opt 10, 034018 (2005).

25. Lubawy C. and N. Ramanujam, “Endoscopically compatible near-infraredphoton migration probe,” Opt Lett 29, 2022–2024 (2004).

26. Tseng S., A. Grant, and A. Durkin, “In vivo determination of skin near-infraredoptical properties using diffuse optical spectroscopy,” J Biomed Opt 13, 014016(2008b).

27. Tseng S., C. K. Hayakawa, J. Spanier, and A. J. Durkin, “Determination ofoptical properties of superficial volumes of layered tissue phantoms,” IEEETrans Biomed Eng 55, 335–339 (2008a).

28. Bohren C. F. and D. R. Huffman, Absorption and Scattering of Light by SmallParticles, Wiley-Interscience, New York (1983).

29. Jacques S. L., http://omlc.ogi.edu/classroom/ece532/class3/mie math.html,1998.

30. Sokolov K., R. Drezek, K. Gossage, and R. Richards-Kortum, “Reflectance spec-troscopy with polarized light: is it sensitive to cellular and nuclear morpho-logy,” Opt Exp 5, 302–317 (1999).

http://omlc.ogi.edu/classroom/ece532/class3/mie_math.html


31. Nieman L. T., C. Kan, A. Gillenwater, M. K. Markey, and K. Sokolov, “Probinglocal tissue changes in the oral cavity for early detection of cancer using obliquepolarized reflectance spectroscopy: a pilot clinical trial,” J Biomed Opt 13, 024011(2008).

32. A’Amar O. M., R. D. Ley, and I. J. Bigio, “Comparison between ultraviolet-visible and near-infrared elastic scattering spectroscopy of chemically inducedmelanomas in an animal model,” J Biomed Opt 9(6), 1320–1326 (2004).

33. Lovat L. B., K. Johnson, G. D. Mackenzie, B. R. Clark, M. R. Novelli, S. Davies,M. O’Donovan, C. Selvasekar, S. M. Thorpe, D. Pickard, R. Fitzgerald, T. Fearn,I. Bigio, and S. G. Bown, “Elastic scattering spectroscopy accurately detectshigh grade dysplasia and cancer in Barrett’s oesophagus,” Gut 55, 1078–1083(2006).

34. Mirabal Y. N., S. K. Chang, E. N. Atkinson, A. Malpica, M. Follen, andR. Richards-Kortum, “Reflectance spectroscopy for the in vivo detection of cer-vical precancer,” J Biomed Opt 7, 587–594 (2002).

35. Bigio I. J., S. G. Bown, G. Briggs, S. Lakhani, D. Pickard, P.M. Ripley, I.G. Rose,and C. Saunders, “Diagnosis of breast cancer using elastic-scattering spec-troscopy: preliminary clinical results,” J Biomed Opt 5, 221–228 (2000).

36. Doornbos R. M. P., R. Lang, M. C. Aalders, F. W. Cross, and H. J. C. M. Steren-borg, “The determination of in vivo human tissue optical properties and abso-lute chromophore concentrations using spatially resolved steady-state diffusereflectance spectroscopy,” Phys Med Biol 44, 967–981 (1999).

37. Farrell T. J. and M. S. Patterson, “A diffusion theory model of spatially resolved,steady-state diffuse reflectance for the noninvasive determination of tissueoptical properties in vivo,” Med Phys 19, 879–888 (1992).

38. Kienle A. and M. S. Patterson, “Improved solutions of the steady-state and thetime-resolved diffusion equations for reflectance from a semi-infinite turbidmedium,” J Opt Soc Am A 14, 246–254 (1997).

39. Sun J., K. Fu, A. Wang, A. W. H. Lin, U. Utzinger, and R. Drezek, “Influenceof fiber optic probe geometry on the applicability of inverse models of tissuereflectance spectroscopy: computational models and experimental measure-ments,” Appl Opt 45, 8152–8162 (2006).

40. Zonios G., L. T. Perelman, V. Backman, R. Manoharan, M. Fitmaurice, J. VanDam, and M. S. Feld, “Diffuse reflectance spectroscopy of human adenomatouscolon polyps in vivo”, Appl Opt 38, 6628–6637 (1999).

41. Bevilacqua F., D. Piguet, P. Marquet, J. D. Gross, B. J. Tromberg, and C. De-peursinge, “In vivo local determination of tissue optical properties: applicationsto human brain,” Appl Opt 38, 4939–4950 (1999b).

42. Palmer G. M. and N. Ramanujam, “Monte Carlo-based inverse model for cal-culating tissue optical properties. Part I: theory and validation on syntheticphantoms,” Appl Opt 45, 1062–1071 (2006a).

43. Palmer G. M., C. Zhu, T. M. Breslin, F. Xu, K. W. Gilchrist, and N. Ramanu-jam, “Monte Carlo-based inverse model for calculating tissue optical proper-ties. Part II: application to breast cancer diagnosis,” Appl Opt 45, 1072–1078(2006b).

44. Pfefer T. J., L. S. Matchette, C. L. Bennett, J. A. Gall, J. N. Wilke, A. J. Durkin,and M. N. Ediger, “Reflectance-based determination of optical properties inhighly attenuating tissue,” J Biomed Opt 8, 206–215 (2003).

45. Thueler P., I. Charvet, F. Bevilacqua, M. St. Ghislain, G. Ory, P. Marquet, P.Meda, B. Vermeulen, and C. Depeursinge, “In vivo endoscopic tissue diagnos-tics based on spectral absorption, scattering and phase function properties,”J Biomed Opt 8, 495–503 (2003).

46. Zonios G. and A. Dimou, “Modelling diffuse reflectance from semi-infiniteturbid media: applications to the study of skin optical properties,” Opt Exp 14,8661–8674 (2006).

47. Bevilacqua F. and C. Depeursinge, “Monte Carlo study of diffuse reflectanceat source-detector separations close to one transport mean free path,” J Opt SocAm A 16, 2935–2945 (1999a).


48. Hayakawa C. K., B. Y. Hill, J. S. You, F. Bevilacqua, J. Spanier, and V. Venu-gopalan, “Use of the -P1 approximation for recovery of optical absorption,scattering and asymmetry coefficients in turbid media,” Appl Opt 43, 4677–4684 (2004).

49. Canpolat, M. and J. R. Mourant, “High-angle scattering events strongly affectlight collection in clinically relevant measurement geometries for light trans-port through tissue,” Phys Med Biol 45, 1127–1140 (2000).

50. Mourant J. R., J. Boyer, A. H. Hielscher, and I. J. Bigio, “Influence of the scatter-ing phase function on light transport measurements in turbid media performedwith small source-detector separations,” Opt Lett 21, 546–548 (1996).

51. Henyey L. G. and J. L. Greenstein, “Diffuse radiation in the galaxy,” AstrophysJ 93, 70–83 (1941).

52. Perelman L. T., V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat,S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford,and M. S. Feld, “Observation of periodic fine structure in reflectance frombiological tissue: a new technique for measuring nuclear size distribution,”Phys Rev Lett 80, 627–630 (1998).

53. Mourant J., J. P. Freyer, A. H. Hielscher, A. A. Eick, D. Shen, and T. M. Johnson,“Mechanisms of light scattering from biological cells relevant to noninvasiveoptical-tissue diagnostics,” Appl Opt 37, 3586–3593 (1998).

54. Prahl S. A., M. Keijzer, S. L. Jacques, and A. J. Welch, “A Monte Carlo modelof light propagation in tissue,” Proc SPIE 5, 102–111 (1989).

55. Wang L., S. L. Jacques, and L. Zheng, “MCML – Monte Carlo modeling oflight transport in multi-layered tissues,” Comput Met Prog Biomed 47, 131–146(1995).

56. Hiraoka M., M. Firbank, M. Essenpreist, M. Cope, S. R. Arridge, P. Van DerZee, and D. T. Delpy, “A Monte Carlo investigation of optical pathlength ininhomogeneous tissue and its application to near-infrared spectroscopy,” PhysMed Biol 38, 1859–1876 (1993).

57. Nichols M. G., E. L. Hull, and T. H. Foster, “Design and testing of a white-light, steady-state diffuse reflectance spectrometer for determination of opticalproperties of highly scattering systems,” Appl Opt 36, 93–104 (1997).

58. Johns M., C. A. Giller, D. C. German, and H. Liu, “Determination of the reducedscattering coefficient of biological tissue from a needle-like probe,” Opt Exp 13,4828–4842 (2005).

59. Cheong W. F., S. A. Prahl, and A. J. Welch, “A review of the optical propertiesof biological tissues,” IEEE J Sel Top Quant Elec 26, 2166–2185 (1990).

60. Liu H., B. Chance, A. H. Hielscher, S. L. Jacques, and F. K. Tittel, “Influence ofblood vessels on the measurements of hemoglobin oxygenation as determinedby time-resolved reflectance spectroscopy,” Med Phys 22, 1209–1217 (1995).

61. Svaasand, L. O., E. J. Fiskerstrand, G. Kopstad, L. T. Norvang, E. K. Svaasand,J. S. Nelson, and M. W. Berns, “Therapeutic response during pulsed laser treat-ment of port-wine stains: dependence on vessel diameter and depth in dermis,”Las Med Sci 10, 235–243 (1995).

62. Talsma A., B. Chance, and R. Graaf, “Correction for the inhomogeneities inbiological tissue caused by blood vessels,” J Opt Soc Am A 18, 932–939 (2001).

63. Verkruysse W., G. W. Lucassen, J. F. de Boer, D. J. Smithies, J. S. Nelson, andM. J. C. van Gemert, “Modelling light distributions of homogeneous versusdescrete absorbers in light irradiated turbid media,” Phys Med Biol 42, 51–65(1997).

64. van Veen R. L. P., W. Verkruysse, and H. J. C. M. Sterenborg, “Diffuse-reflectancespectroscopy from 500 to 1060 nm by correction for inhomogeneous distributedabsorbers,” Opt Lett 27, 246–248 (2002).

65. Reif R., M. S. Amorosino, K. W. Calabro, O. A’Amar, S. K. Singh, and I. J.Bigio, “Analysis of changes in reflectance measurements on biological tissuessubjected to different probe pressures,” J Biomed Opt 13, 010502 (2008).

66. Graaf R., J. G. Aarnoudse, J. R. Zijp, P. M. A. Sloot, F. F. M. de Mul, J. Greve, andM. H. Koelink, “Reduced light-scattering properties for mixtures of spherical


particles: a simple approximation derived from Mie calculations,” Appl Opt 31,1370–1376 (1992).

67. Nilsson A. M. K., C. Sturesson, D. K. Liu, and S. Andersson-Engels, “Changesin spectral shape of tissue optical properties in conjunction with laser-inducedthermotherapy,” Appl Opt 37, 1256–1267 (1998).

68. Papaioannou T., N. W. Preyer, Q. Fang, A. Brightwell, M. Carnohan, G. Cottone,R. Ross, L. R. Jones, and L. Marcu, “Effects of fiber-optic probe design andprobe-to-target distance on diffuse reflectance measurements in turbid media:an experimental and computational study at 337 nm,” Appl Opt 43, 2846–2860(2004).

69. Shangguan H. Q., S. A. Prahl, S. L. Jacques, L. W. Casperson, and K. W. Gre-gory, “Pressure effects on soft tissue monitored by changes in tissue opticalproperties,” Proc SPIE 3254, 366–371 (1998).

70. Nath A., K. Rivoire, S. Chang, D. Cox, E. N. Atkinson, M. Follen, andR. Richards-Kortum, “Effect of probe pressure on cervical fluorescence spec-troscopy measurements,” J Biomed Opt 9, 523–533 (2004).

71. Ti Y. and W. Lin, “Effects of probe contact pressure on in vivo optical spec-troscopy,” Opt Exp 16, 4250–4262 (2008).

72. Casavola C., L. A. Paunescu, S. Fantini, and E. Gratton, “Blood flow and oxygenconsumption with near-infrared spectroscopy and venous occlusion: spatialmaps and the effect of time and pressure of inflation,” J Biomed Opt 5, 269–276(2000).

73. O’Brien P. J., H. Shen, L. J. McCutcheon, M. O’Grady, P. J. Byrne, H. W. Fer-guson, M. S. Mirsalimi, R. J. Julian, J. M. Sargeant, R. R. M. Tremblay, andT. E. Blackwell, “Rapid, simple and sensitive microassay for skeletal and car-diac muscle myoglobin and hemoglobin: use in various animals indicates func-tional role of myohemoproteins,” Mol Cell Biochem 112, 45–52 (1992).

74. Boverman G., Q. Fang, S. A. Carp, E. L. Miller, D. H. Brooks, J. Selb, R. H. Moore,D. B. Kopans, and D. A. Boas, “Spatio-temporal imaging of the hemoglobinin the compressed breast with diffuse optical tomography,” Phys Med Biol 52,3619–3641 (2007).

75. Carp S. A., T. Kauffman, Q. Fang, E. Rafferty, R. Moore, D. Kopans, andD. Boas, “Compression-induced changes in the physiological state of the breastas observed through frequency domain photon migration measurements,”J Biomed Opt 11, 064016 (2006).

C H A P T E R 12DifferentialPathlength

Spectroscopy

H. J. C. M. Sterenborg, C. van der Leest, S. C. Canick, J. G. J. V. Aerts,and A. Amelink

12.1 Basic Concepts

IntroductionWhite light reflection spectroscopy has been under investigation forin vivo characterization of biological tissues for several decades (1).Three basic steps can be distinguished in this type of spectroscopicmeasurements: (i) the measurement of the diffuse reflectance over abroad range of wavelengths, (ii) calculation of scattering and absorp-tion spectra from the measured reflection spectra, and (iii) interpre-tation of the scattering and absorption spectra in terms of scatteringmechanisms (Mie, Raleigh) and absorbing components (hemoglobin,oxyhemoglobin, water, fat, etc.). Step (ii) requires mathematical mod-eling of light transport in tissue. There are many possibilities for calcu-lating light distributions in diffuse media once the optical propertiesand the geometry of the medium are given. What we need for step (ii)is a solution to the inverse problem: from light distribution to opticalproperties. A very popular approach to this is diffusion theory. Solu-tions to the inverse problem are available for various geometries andin the time domain, frequency domain, and CW mode.

Previous work in our group was based on excellent work by TomFarrell who developed an inverse solution for spatially resolved dif-fuse reflectance (2). For this approach we developed an experimental

293


setup that was based on a single source fiber delivering broadbandwhite light to the surface of tissue and used nine collection fibers tomeasure the diffuse reflectance at 2–20 mm distance from the source.This approach worked excellently in homogenous optical phantoms,but in vivo, such as in human breast tissue (3), the results were not sat-isfactory. Observations made in this study were that Farrell’s inversesolution fitted perfectly to the measurements on the optical phantoms,but in vivo a lot less so. In addition, in the phantoms, the absorptionspectrum calculated from the measurement matched with the absorp-tion spectrum and the amount of the absorber we put into the phantomin a range of nearly 3 orders of magnitude and failed where diffusiontheory predicted it should fail. On the other hand, the in vivo mea-surements did not fit well with the known absorbers present in tissue,and the total amount of the components based on these measure-ments were often higher than physically possible (i.e., more than 1 g ofwater plus fat per cubic centimeter of tissue). We hypothesized thatthis was related to the inhomogeneous nature of tissue. In the spa-tially resolved approach, sampling volumes are in the order of a fewcubic centimeters. At this scale, inhomogeneities like blood vesselsmay disturb the validity of the diffusion approach. This motivated usto look for methods with smaller sampling volumes.

White light reflectance measurements using a much smaller sam-pling volume were developed by the group of Irving Bigio (see Chap.11). This technique called elastic scattering spectroscopy (ESS) usesonly a single collection fiber at a predetermined distance from thesource fiber (4). With this method, sampling volumes in the orderof a few cubic millimeters are reached (5). This dramatically im-proves the fit of the absorption spectrum to the spectra of knownabsorbers (6).

We were challenged to use white light reflection spectroscopy toinvestigate early cancer in the bronchial mucosa. As the thickness ofbronchial mucosa and superficial submucosa is in the order of 100–200 �m, we decided that we needed a method sampling even smallervolumes than used in ESS. Investigating early mucosal lesions witha larger sampling volume would dilute any potential contrast withinformation from deeper layers, which might compromise the diag-nostic power of the technique. We developed a new technique calleddifferential pathlength spectroscopy or DPS that resembles ESS butused a subtraction method to obtain a very shallow sampling depth.

Main Properties and FeaturesDPS uses two optical fibers that are in contact with the diffuse mediumthat is measured. One of the two fibers (dc) is used to deliver whitelight to the medium; both fibers (dc and c) collect light from the

295D i f f e r e n t i a l P a t h l e n g t h S p e c t r o s c o p y

CoreCladding

c-fiber

dc-fiber

Tissue

FIGURE 12.1 BasicDPS measurementgeometry: twooptical fibers tightlytogether in contactwith the tissue.One delivering light(d) and bothcollecting light (c).

medium (Fig. 12.1). The DPS spectrum is formed by subtracting thec-spectrum from the dc-spectrum. Photons traveling deep into thetissue have an equal chance of getting detected by either fiber, andtheir contribution to the DPS spectrum will be subtracted away. Pho-tons that stay close to the dc-fiber have a larger chance of gettingdetected by the dc-fiber than by the c-fiber. Hence, the DPS spectrumconsists mainly of photons that never left the vicinity of the dc-fiberand thus have traveled only superficially through the medium.

To test if our method was indeed mainly sensitive to signals fromsuperficial layers, we performed an experiment in a two-layer opticalphantom with two clearly distinguishable scattering properties. Theseexperiments showed that when using 400 �m core optical fibers, oursubtraction technique sampled to a depth of 150–200 �m. To investi-gate this further, we performed Monte Carlo simulations over a broadrange of scattering coefficients. In these calculations we found, a bit toour surprise, that the pathlength of the photons making up the differ-ential signal appeared to be constant over a broad range of scatteringcoefficients. This was confirmed with a set of phantom experimentsusing mixtures of polystyrene spheres and Evans Blue. Photon path-lengths estimated were around 300 �m. Thus, with a sampling depthof less than half the pathlength, we come to sampling volumes in theorder of 0.01 mm3. It is clear that DPS appears to be perfectly suitableto probe the bronchial mucosa and superficial submucosa (7). A firstset of clinical measurements in the lungs showed a very characteristicbehavior with clear differences between normal mucosa and cancer(8).

PathlengthClassically, photon pathlengths in diffuse media depend strongly onoptical properties and probe geometry. Geometrical parameters herewould be the (relative) NA of the fibers and the fiber diameter. In aphantom experiment, we estimate the pathlengths of the photons in


0.1

1

10

0.001 0.01 0.1 1 10

200400600800Model

µadfiber

τ/d f

iber

FIGURE 12.2 Optical pathlength as a function of the absorption coefficient,relative to the fiber diameter.

the DPS spectrum by comparing phantoms with identical scatteringcoefficients but with known differences in absorption coefficients. Weuse

〈�〉 = 1�a (max)

ln(

DPS (max)no absorber

DPS (max)absorber

)(12.1)

where 〈�〉 is the estimated pathlength, max stands for the wavelengthof maximum absorption of the added absorber, DPSno absorber standsfor the DPS spectrum of scattering component only (Intralipid), andDPSabsorber stands for the DPS spectrum with the known amount ofabsorber added. In systematically performed phantom experiments(Fig. 12.2), we have shown that for �adfiber � 1, the pathlength is con-stant and nearly equal to the fiber diameter dfiber, while for largervalues of �adfiber, the pathlength becomes inversely proportional to�a (9). The scattering dependence of the pathlength is given in Fig.12.3. For �sdfiber � 1, the pathlength is far from constant. This is thesingle scatter region. For larger scattering coefficients, a small scat-tering dependence of the pathlength remains. Recently Kanick et al.(10) developed an empirical description of the DPS pathlength that isvalid over a wide range of absorption and scattering coefficients (0.1≤ �a ≤ 12 mm−1; 1.5 ≤ �s ≤ 42 mm−1) and fiber diameters (100 �m≤ dfiber ≤ 1 mm):

〈�〉 = dfiber1 + (�sdfiber)−n

1 + (�adfiber)n (12.2)


0.1

1

10

0.01 0.1 1 10 100

τ/d f

iber

µsdfiber

FIGURE 12.3 Optical pathlength as a function of the scattering coefficient,relative to the fiber diameter.

where n is an empirically determined constant with value 0.53 ±0.09. By using Eq. (12.2) pathlengths between 80 and 940 �m weremeasured in optical phantoms and were predicted with an accuracyof 8.4%.

For biologically realistic values of the scattering coefficients, thepathlength decreases only slowly with scattering, and in this situationDPS can be used as a technique to measure absolute concentrations ofchromophores. The accuracy of the method is then only determinedby the uncertainty in the scattering coefficient. From Eq. (12.2) wecan derive that in the range of relevant scattering coefficients and afiber diameter of 400 �m, a variation of a factor of 10 in the scatteringcoefficient (10 ≤ �s ≤ 100) results in a pathlength of 510 �m with anuncertainty of ±15%.

Basic Mathematical Analysis of SpectraDPS spectra such as those in Figs. 12.4 to 12.6 look very similar tothe general picture we see in reflection- and elastic-scattering spec-troscopy: a slight overall decrease in signal when going from the blueto the near-infrared wavelengths indicating Mie scattering and sev-eral characteristic absorption bands from blood (11). To translate ourspectra accurately in terms of biologically relevant parameters, wemust model the shape of these DPS spectra and fit these models tothe measured spectra. To do so we could try to analyze what exactlyis going on right in front of the dc-fiber. However, the part that canbe modeled analytically—the diffuse part of the light—has been sub-tracted away. What remains to form the DPS-spectrum is that partof the photon distribution for which no analytical models exist. Be-cause Monte Carlo methods do not allow inverse calculations, the only


0

1

2

3

4

5

6

7D

PS

-sig

nal

-6-4-20246

300 400 500 600 700 800 900 1000

Wavelength (nm)

wei

ghed

res

idue

FIGURE 12.4 Typical DPS spectrum measured endoscopically on normalbronchial mucosa with fit of the model of Eq. (12.4) and noise weighedresidues.

remaining option here is empirical modeling. The development of ourmathematical model to describe the DPS spectra was based on care-ful analysis of Monte Carlo simulations, phantom experiments, and alittle trial and error. The basic equation with which we analyze DPSspectra is

DPS () = �s () e(−��a()) (12.3)

where �s() stands for the scattering coefficient, �a() for the absorp-tion coefficient, and � for the pathlength. Absorption and scatteringare wavelength-dependent functions and in principle also the path-length � . However, as indicated above within reasonable limits, thepathlength can be considered constant.


0

1

2

3

4

5

6

7D

PS

-sig

nal

-6-4-20246

wei

ghed

res

idue

300 400 500 600 700 800 900 1000

Wavelength (nm)


12.2 DPS Measurements In Vivo

Main FeaturesA typical DPS spectrum measured in vivo is shown in Fig. 12.4. Clearlyvisible are the blood absorption dips on a background of Mie scatter-ing, as described earlier. A fit was made applying Eq. (12.3) on thesecurves, using Mie scattering and blood absorption:

�s () = a(

0

)b

�a () = �(StO2�

oxyHemoa () + (1 − StO2) �Hemo

a ()) (12.4)


0

1

2

3

4

5

6

7D

PS

-sig

nal

-6-4-20246

300 400 500 600 700 800 900 1000

Wavelength (nm)

wei

ghed

res

idue


where a and b are Mie scattering parameters, 0 = 800 nm, � the bloodvolume fraction, and StO2 the oxygen saturation of the blood. Theresulting curve shown in Fig. 12.5 shows that the model roughly fitsthe data above 450 nm. In this fit we intentionally ignored the lowerwavelengths because the violet absorption band would have seriouslyworsened the fit. The resulting parameters are listed in Table 12.1.

Technical improvements to the setup, expanding the wavelengthrange to 350 nm, not only yielded an excellent view on the Soret ab-sorption band of hemoglobin but also indicated an issue requiringimprovement: The Soret absorption band of blood around 415 nm ap-peared to be systematically overestimated by the model. This has todo with a phenomenon called pigment packaging. In this wavelengthrange, the absorption of hemoglobin in blood vessels is so high thatit partly shields itself from the incoming light. The intensity of this


Parameter Function Value

a Mie amplitude (-) 3.08 ± 0.01

b Mie slope (-) −0.99 ± 0.01

� Blood volume (%) 1.37 ± 0.03

StO2 Saturation (%) 75 ± 4.0

Reduced-� 2 All points 83.7

Reduced-� 2 For points above 450 nm 2.59

TABLE 12.1 Parameter Values Resulting from Fitting the Simple Model to theMeasurements from Fig. 12.4, Using Only the Datapoints Above 450 nm

effect, and hence the correction factor, depends on the “packing di-ameter”; that is, the diameter of the areas of high concentration. Inour case this refers to the diameter of the blood vessels. We have de-rived a correction for this phenomenon previously and introduced theeffective absorption coefficient �′

a (12):

�′a () =

(1 − e(−2R�a())

)2R

(12.5)

where R stands for the radius of the blood vessel. This correction as-sumes packing of the absorber in cylinder-shaped vessels. A slightlydifferent correction can be derived for different packing shapes (13).Our approach to cylindrical-shape packing may become problem-atic if we go from cylindrical microvessels to the smallest capillarywhere single red blood cells pass from time to time. Not only do thered blood cells have complicated noncylindrical shapes, but they alsochange shape continuously while passing through the smallest capil-laries. Hence, for simplicity, and because it seems to fit well, we usethe cylindrical correction factor even for diameter values that sug-gest single red blood cells rather than a well-filled cylindrical vessel.This is important to keep in mind when interpreting the values of thisparameter.

The packing effect is not limited to hemoglobin, but affects all ab-sorbers present in the blood vessel. Any other vascular absorber can beadded to the absorption of hemoglobin and oxyhemoglobin before thepacking correction is performed. Any absorber that is homogenouslydistributed over the tissue can be added after the packing correction:

�′a ()

= �

(

1 − exp(−2R

(St O2�

oxyHemoa () + (1 − St O2) �Hemo

a ())

+ �othera ()

))2R

+�homa () (12.6)




b Mie slope (-) −1.01 ± 0.01

� Blood volume (%) 1.56 ± 0.06.

StO2 Saturation (%) 80 ± 4.0.

R Vessel radius (�m) 6.0 ± 0.3.


Reduced-� 2 For points above 450 nm 2.68

TABLE 12.2 Parameter Values Resulting from Fitting the Simple Model to theMeasurements from Fig. 12.5

where �othera stands for the other vascular absorbers and �hom

a foran additional homogenously distributed absorber. The resulting fitand the residue spectrum for a typical measurement are shown inFig. 12.5, and the parameter values from this fit in Table 12.2. Judg-ing from the values of � 2, we have a much better fit here (signifi-cantly better at p < 0.05 F-test) when looking at the entire wavelengthrange. As expected the improvements are limited to the <450 nmband.

Additional Spectral FeaturesJudging from the details of the remaining residual spectra there aretwo additional spectral features that can be added. First, there appearsto be a small absorption band around 450 nm. The exact nature of thisabsorber is presently unknown. It resembles serum-bound bilirubin.In addition, small discrepancies in the short wavelength range suggestan additional feature in this region. In bloodless samples, we also seethis discrepancy as a steep rise in the DPS signal toward the shorterwavelengths, suggesting that Mie scatter alone is not the completestory. Hence, we add Raleigh scatter:

�s () = a(

0

)b

+ c(

0

)−4

(12.7)

Fitting this to the measured spectrum gives a much better result(Fig. 12.6). The resulting � 2 shown in Table 12.3 again indicates a betterfit than the previous one in Table 12.2 (significantly better at p < 0.05F-test). The residue spectrum is now close to the measurement noiseover the entire spectral region.

The nature of the blue absorber has yet not been unveiled. A po-tential candidate is bilirubin. However, the bilirubin spectra availablein various databases do not fit well. These spectra are all dissolved in




b Mie slope (-) −0.67 ± 0.03

c Raleigh amplitude (-) 0.17 ± 0.01

� Blood volume (%) 1.81 ± 0.04


R Vessel radius (�m) 5.4 ± 0.2

q Blue absorber (�M) 6.2 ± 0.6



aggressive organic solvents such as acetone, because bilirubin is quitelipophilic. In vivo bilirubin binds to serum proteins, which is knownto alter its absorption spectrum. This binding, however, is stronglyinfluenced by other proteins present and hence may cause a variablespectrum (14).

In breast tissue (Fig. 12.7), the additional blue absorption dip ismuch more prominent and appears to be different in shape. In thiscase, most likely, we are dealing with betacarotene. Here too, majorspectral differences are observed with the betacarotene absorptionspectrum measured in organic solvents (15). Figure 12.7 shows a fitof Eq. (12.2) using betacarotene dissolved in fat as the blue absorber.The resulting fit parameters are shown in Table 12.4.

Confidence IntervalsAn important question that remains when parameter values are ex-tracted from a measurement is how well the values can be trusted.The � 2 fit we use to find the best fit can help us here, as the � 2 valueexpresses the difference between measurement and model in a statis-tically relevant way. It does so by comparing the difference betweenmeasurement and fit to the measurement noise for each pixel. By vary-ing the parameters and calculating the change in � 2, we can find outhow sensitive the goodness of fit is to changes in the parameters. Thisgives us information on how well defined the best parameters for thisparticular fit are. We calculate the confidence intervals mathematicallyby calculating the inverse of the second derivative function of the � 2

function at the minimum value for � 2, that is, the covariance matrix.Note that confidence intervals calculated in this way do not accountfor errors due to models that do not fit well (16).


0

0.5

1

1.5

2

2.5

3

3.5DPS-signal

-6-4-20246

300 400 500 600 700 800 900 1000

Wavelength (nm)

wei

ghed

res

idue

FIGURE 12.7 Typical DPS spectrum measured in normal fatty breast tissueusing a fiberoptic needle with a fit of Eq. (12.7), and betacarotene as blueabsorber.



b Mie slope (-) −1.18 ± 0.04

c Raleigh amplitude (-) 0.09 ± 0.02

� Blood volume (%) 2.2 ± 0.1


R Vessel radius (�m) 4.0 ± 0.5

q Betacarothene (�M) 48 ± 1




12.3 Clinical MeasurementsBy analyzing the spectra in the way described above, we translate theDPS spectra into parameters that have a direct relation to the biology ofthe tissue. This makes it possible to strategically pick clinical applica-tions with a logical chance of success. Blood volume, vessel diameter,and microvascular saturation describe the local vasculature of the tis-sue and might be used to detect or maybe even quantify angiogenesis,an early step in the development of cancer. In addition, Mie scatteringis thought to be related to intracellular morphology. According to Mietheory, the observed wavelength dependence of light scattering [i.e.,the value of the b parameter in Eqs. (12.4) and (12.7)] suggests thatlight scattering is dominated by structures of sizes around 100 nm(17). Sensitivity to both absorption and scattering indicates that DPShas potential for early diagnosis of cancer.

Diagnosis of cancer in the upper airways is usually performed onthe basis of a biopsy taken during bronchoscopy. A major problemin this procedure is that it is not easy to find the right spot to takethe biopsy. To investigate if DPS measurements can be of any valuehere, we performed DPS measurements by inserting a fiberoptic probethrough the working channel of an endoscope and collected data onmore than 250 patients who came to the hospital for a routine diagnos-tic bronchoscopy. Figure 12.8 shows the distribution of the values forthe microvascular saturation measured with DPS in 341 separate sus-pect lesions in the upper airways grouped by their histopathologicaldiagnosis. It clearly illustrates that the saturation decreases with in-creasing malignancy. However, we see very large variations betweenindividual measurements. For instance, the StO2 has an average of69.3 and a standard deviation of 22.5. These variations in saturationseem to increase with increasing malignancy. Moreover, the variationsare much larger than the experimental uncertainty derived from theconfidence interval of the fits, which for the StO2 are on average 3.1%.We see similar effects for most other parameters. Hence, we believethat the parameters we measure, such as the microvascular saturation,are subject to a strong biologic variation. As a consequence, replacinghistological classification, by classification based on a single DPS pa-rameter does not appear to be feasible.

Obviously a multivariate approach is indicated here. As the vari-ation in parameters is most likely caused by biological phenomena,the standard deviation of multiple measurements within one lesionmay have additional descriptive value and together with the averagevalue of the parameters can be used as inputs for a multivariate anal-ysis. We constructed a multiple regression model based on the sevenparameters from Table 12.3, and we used the average values per lesionas well as their standard deviations. We added the sex and age of eachpatient as additional inputs. All calculations were performed using


100806040200

100806040200

Normal

Inflammation

Metaplasia

Mild dysplasia

Severe dysplasia

Carcinoma in situ

Adenocarcinoma

Squamouscell carcinoma

Small cell lungcancer

Non smallcell lung cancer

FIGURE 12.8 Box and whisker plot of the saturation values measured on lungcancers with different histological classifications.

MedCalc (version 9.6.3.0) from MedCalc Software (Mariakerke, Bel-gium). In this approach, we rejected parameters from the model whosecontribution has a significance level with a p value larger than 0.1. Theanalysis finds a significant contribution for a number of parameters,summarized in Table 12.5. Striking is the fact that both average val-ues and standard deviations are presented in the list of significantlycontributing parameters. In addition, the parameters related to thevasculature as well as the blue absorber appear to be the strongest.The bad news, however, is that we find a value for R2 of 0.26. Thismeans that despite the strong correlations we find, our regressionmodel only describes 26% of all variations in the data. Consequently,a large fraction of the lesions is classified wrong by this model. Weobtained similar results with a k-Nearest Neighbor algorithm (18).

Apparently, we asked a little too much of our data. A question re-quiring a less detailed answer is whether a lesion is cancer or not. Thisis a very relevant clinical question, especially in bronchoscopy whereadding technology to improve the sensitivity of diagnostic imaginghas so far always resulted in unacceptable decrease in specificity (19).A fiberoptic measurement aiding in the decision whether to take abiopsy on a suspicious lesion could improve the overall specificity


Parameter Function P Value

Parameters contributing significantly

StO2 Saturation (%) <0.0001

sd q Standard deviation blue absorber (�M) <0.0001

sd � Standard deviation blood volume (%) 0.0004

sd R Standard deviation vessel radius (�m) 0.0010

R Vessel radius (�m) 0.0012

sd a Standard deviation Mie amplitude (-) 0.0722

sd c Standard deviation Raleigh amplitude (-) 0.0742

Age 0.0490

A parameter was removed when the p value of the significance of its contributionwas more than 0.1.

TABLE 12.5 Descriptive Value of the Various Parameters Used in the MultipleRegression Model to Predict the Histological Classification of a Lesion

of the combined diagnostic procedure. To test this concept we per-formed a logistic regression analysis on our data, using the same 16input parameters, discussed above. Again the analysis finds a numberof parameters with a significant correlation with the data and is sum-marized in Table 12.6. Again the microvascular saturation appears tobe the strongest contributor (column: without ID); both vascular andmorphological parameters are present. Also, apart from the saturationwhose mean value is involved, the intralesion variability in parame-ters as expressed in the standard deviations appears to be importantfor other parameters. The performance of the model to predict theneed for a biopsy is displayed in Fig. 12.9. The study was performedover a period of 4 years. Within that time, different bronchoscopistsat different hospitals with different patient populations participatedin the study. Interestingly, adding an ID number for each broncho-scopist without any assumptions on potential differences in their in-dividual patient populations significantly improved the performance(p = 0.001). With this approach we can now reduce the number ofbiopsies by 50%, while missing only 7% of all cancers. The latter is notbad for a diagnostic procedure whose overall sensitivity is estimatedto be between 30% and 70%.

A benefit of measuring optical parameters that have a direct rela-tion to tissue physiology is demonstrated in Fig. 12.10, which showsan unplanned success. Here we plotted the survival of patients witha lung tumor that has reached stage IV. The main difference betweenstage IV and lower stages is the presence of metastases. There is a clear


Parameter Function P Value

Parameters contributing significantly Without ID With ID

StO2 Saturation (%) <0.0001 <0.0001

sd R Standard deviationvessel radius (�m)

0.0054 -

sd q Standard deviation Blueabsorber (�M)

0.00018 <0.0001

a Mie-amplitude (-) - 0.0092

sd a Standard deviationMie-amplitude (-)

0.0038 0.0159

sd b Standard deviationMie-slope (-)

- <0.0001

sd c Standard deviationRaleigh amplitude (-)

0.0044 0.0176

ID Bronchoscopists ID - <0.0001

A parameter was removed, as the p value of the significance of its contributionwas more than 0.1.

TABLE 12.6 Descriptive Value of the Various Parameters Used in the LogisticRegression Model Predicting the Need for a Biopsy

0 20 40 60 80 100Percentage of lesions biopsied

20

0

40

60

80

100

Per

cent

age

of c

ance

rs m

isse

d

Without IDWith ID

FIGURE 12.9 ROC curves for predicting the necessity to take biopsy. Theupper curve is for a Logistic regression model differentiating betweendifferent bronchoscopists. The lower for a model that does not.


0 100 200 300 400 500 600

100

80

60

40

20

0

Sur

viva

l pro

babi

lity

(%)

Saturation> 60%

Saturation< 60%

Time after bronchoscopy (day)

FIGURE 12.10 Kaplan–Mayer survival curves for stage IV lung tumors.Patients with an average saturation larger than 60% have a significantlylonger survival.

and statistically significant difference in survival between patientswith an average high saturation and a low saturation (p = 0.0017).The difference in saturation between the two groups is rather large:the same statistics are obtained with saturation cut off values from55% to 65%. For stages I to III the difference is totally absent. This phe-nomenon can be used in the decision as to which treatment option toselect for a patient. The usual combination of fractionated radiother-apy with chemotherapy is a lengthy procedure. For some patients, theexpected benefits of this approach will come too late. These patientscan either be saved from unnecessary suffering from the side effectsof the treatment or may be selected from a more aggressive therapeu-tic approach. In addition, the staging process is not always very easy.Especially the presence of metastasis is not always clear and severalstage IV patients may in fact be erroneously classified as stage III.

12.4 ConclusionDifferential pathlength spectroscopy selects photons of a known path-length based on detection geometry. This is a unique feature that dis-tinguishes it from other approaches to fiberoptic spectroscopy. It hasmany advantages. As the pathlength determines the sampling vol-ume and the fiber diameter determines the pathlength, it is possibleto tailor the sampling volume to the geometry of the problem underinvestigation. In addition, a pathlength independent of optical prop-erties ensures that the same tissue volume is sampled by all wave-lengths in a spectrum. As a result the spectral analysis fits the measure-ment up to the measurement noise. The latter enables us to translate


measurements into biologically relevant parameters that play a directrole in the biology of the problems investigated.

References1. Anderson, R. R. and J. A. Parrish (1981). The optics of human skin. J Invest

Dermatol 77, 13–19.2. Farrell, T. J., M. S. Patterson, and B. Wilson (1992). A diffusion theory model

of spatially resolved, steady-state diffuse reflectance for the noninvasive de-termination of tissue optical properties in vivo. Med Phys 19, 879–888.

3. van Veen, R. L. P., H. J. C. M. Sterenborg, A. W. K. S. Marinelli, and M. Menke-Pluymers (2004). Intraoperatively assessed optical properties of malignant andhealthy breast tissue used to determine the optimum wavelength of contrastfor optical mammography. J Biomed Opt 9, 1129–1136.

4. Bigio, I. J. and J. R. Mourant (1997). Ultraviolet and visible spectroscopiesfor tissue diagnostics: fluorescence spectroscopy and elastic-scattering spec-troscopy. Phys Med Biol 42, 803–814.

5. Mourant, J. R., I. J. Bigio, D. A. Jack, T. M. Johnson, and H. D. Miller (1997).Measuring absorption coefficients in small volumes of highly scattering me-dia: source–detector separations for which path lengths do not depend onscattering properties. Appl Opt 36, 5655–5661.

6. Reif, R., O. A’amar, and I. J. Bigio (2007). Analytical model of light reflectancefor extraction of the optical properties in small volumes of turbid media. ApplOpt 46, 7317–7328.

7. Amelink, A., M. P. Bard, S. A. Burgers, and H. J. Sterenborg (2003). Single-scattering spectroscopy for the endoscopic analysis of particle size in superfi-cial layers of turbid media. Appl Opt 42, 4095–4101.

8. Amelink, A., H. J. Sterenborg, M. P. Bard, and S. A. Burgers (2004). In vivomeasurement of the local optical properties of tissue by use of differentialpath-length spectroscopy. Opt Lett 29, 1087–1089.

9. Kaspers, O. P., H. J. Sterenborg, and A. Amelink (2008). Controlling the opticalpath length in turbid media using differential path-length spectroscopy: fiberdiameter dependence. Appl Opt 47, 365–371.

10. Kanick S. C., Sterenborg H. J. C. M., and A. Amelink (2009). Empirical modelof the photon path length for a single fiber reflectance spectroscopy device.Opt. Express 17, 860–871.

11. Mourant, J. R., I. J. Bigio, J. Boyer, R. L. Conn, T. Johnson, and T. Shimada(1995). Spectroscopic diagnosis of bladder cancer with elastic light scattering.Lasers Surg Med 17, 350–357.

12. van Veen, R. L. P., W. Verkruysse, and H. J. C. M. Sterenborg (2002). Diffuse-reflectance spectroscopy from 500 to 1060 nm by correction for inhomoge-neously distributed absorbers. Opt Lett 27, 246–248.

13. Finlay, J. C. and T. H. Foster (2004). Hemoglobin oxygen saturations in phan-toms and in vivo from measurements of steady-state diffuse reflectance at asingle, short source–detector separation. Med Phys 31, 1949–1959.

14. Ash, O. K., M. Holmer, and C. S. Johnson (1978). Bilirubin–protein interactionsmonitored by difference spectroscopy. Clin Chem 24, 1491–1495.

15. van Veen, R. L. P., A. Amelink, M. Menke-Pluymers, C. van der Pol, and H.J. C. M. Sterenborg (2005). Optical biopsy of breast tissue using differentialpath-length spectroscopy. Phys Med Biol 50, 2573–2581.

16. Amelink, A., D. J. Robinson, and H. J. C. M. Sterenborg (2008). Confidenceintervals on fit parameters derived from optical reflectance spectroscopy mea-surements. J Biomed Opt 13, 05040144.

17. Ramachandran, J., T. M. Powers, Carpenter S., A. Garcia-lopez, J. P. Freyer,and J. R. Mourant (2007). Light scattering and microarchitectural differencesbetween tumorigenic and non-tumorigenic cell models of tissue. Opt Express15, 4039–4053.


18. de Veld, D. C. G., M. J. Witjes, M. Scuricina, H. J. C. M. Sterenborg, and J.L. N. Roodenburg (2002). Autofluorescence spectroscopy for the detection of(pre) malignamncies of the oral mucosa-dependence on anatomical location.In: 2002 Gordon Conference on Lasers in Medicine and Biology [Abstract].

19. Hirsch, F. R., S. A. Prindiville, Y. E. Miller, W. A. Franklin, E. C. Dempsey,J. R. Murphy, P. A. Bunn, Jr., and T. C. Kennedy (2001). Fluorescence versuswhite-light bronchoscopy for detection of preneoplastic lesions: a randomizedstudy. J Natl Cancer Inst 93, 1385–1391.


C H A P T E R 13Angle-ResolvedLow-CoherenceInterferometry:Depth-Resolved

Light Scattering forDetecting Neoplasia

Adam Wax, Yizheng Zhu, and Neil Terry

13.1 IntroductionElastically scattered light has been used for biomedical applicationssuch as the study of cellular morphology [1–4] as well as the diagno-sis of dysplasia, a precancerous tissue state [5–10]. Variations in scat-tering distributions as a function of angle or wavelength have beenused to deduce information regarding the size and relative index ofrefraction of scatters including cells and subcellular objects such asnuclei and organelles. Information generated by light scattering sys-tems has been used diagnostically to detect tissue changes includingneoplastic changes (those leading to cancer). As examples, Backmanand colleagues have used light scattering spectroscopy to detect dys-plasia in the colon, bladder, cervix, and esophagus of human patients[5], and other researchers [7, 9] have used light scattering to detectBarrett’s esophagus, a metaplastic condition with a higher probability

313


of leading to dysplasia. All these techniques rely on intensity-basedmeasurements, which lack the ability to provide results as a functionof depth in the tissue.

Angle-resolved low-coherence interferometry (a/LCI) combineslow-coherence interferometry with angle-resolved scattering. Similarto optical coherence domain reflectometry (OCDR) [11] and optical co-herence tomography (OCT) [12], a/LCI uses a broadband light sourcein an interferometry scheme in order to achieve optical sectioningwith a depth resolution set by the coherence length of the source.Angle-resolved scattering measurements capture light as a functionof the scattering angle and use this information to deduce the aver-age size or other optical properties of the scatterers. Combining thesetechniques allows construction of a system that can measure averagescatter size as a function of depth in the sample. There are numer-ous interesting applications of this technology, the most significantto date is determining the state of tissue health based on the averagemeasurements of cell nuclei size. Significantly, it has been found thatas tissue changes from normal to dysplastic, the average cell nucleisize increases [8, 10, 13].

The a/LCI technique was first validated in studies of polystyrenemicrospheres [14], where it was shown that subwavelength sensitiv-ity and accuracy could be obtained by comparing measured angularscattering distributions to the predictions of Mie theory. Cell nuclearmorphology was then studied using monolayers of cultured HT29 ep-ithelial cells [3], a line of human tumor cells. This study expanded thesignal processing method to compensate for the nonspherical and in-homogeneous nature of cell nuclei. Significantly, subwavelength pre-cision and accuracy were also obtained.

More recently, a/LCI has been used to study quantitative changesin tissue as a function of tissue health. The first study was in a ratesophageal carcinogenesis model [8]. Changes in the size and tex-ture of cell nuclei due to neoplastic transformation were observed insitu via quantitative measurements of basal epithelial cell nuclei ap-proximately 50–100 �m below the tissue surface. These measurementswere made without the use of exogenous contrast agents or tissue fix-ation and were compared to histopathological images to establish thata/LCI can diagnose low-grade and high-grade dysplasia with greataccuracy. The grading criteria established in this study were used ina prospective follow-on study [10] to demonstrate that a/LCI coulddetect dysplasia with 91% sensitivity and 97% specificity.

Following the study of rat tissue, a fiber optic implementation ofa/LCI was developed [15] and applied to study intact ex vivo humantissue from esophagogastrectomies [13]. Tissue was opened longitu-dinally and sampled with the a/LCI system within 2 h of resection.Scanned areas were marked, and the a/LCI results were then com-pared to pathological classification for those locations. The system

315A n g l e - R e s o l v e d L o w - C o h e r e n c e I n t e r f e r o m e t r y

was clearly able to differentiate between normal and dysplastic tis-sues, but there were not a sufficient number of data points in thisstudy to generate meaningful statistics. More recently, a portable ver-sion of the a/LCI system with a flexible endoscopic probe was usedto scan intact human esophagi in the pathology laboratory within 1 hof esophagogastrectomies [16]. Results of this study showed that thea/LCI system has the potential to differentiate between normal squa-mous, inflamed gastric, and low-grade dysplastic tissue by analyzingthe depth-resolved nuclear morphology data.

This chapter will review the development of the a/LCI instrumen-tation including the significant advances in speed that have enabledthe subsecond data acquisition necessary for potential clinical use.Details of the data processing will be provided. Several studies willbe described starting with the first test with polystyrene microspheresthat proved the basic a/LCI concepts and ending with the most recentstudy in ex vivo intact human esophagi executed in a clinical setting.

13.2 Instrumentation

Early ImplementationsThe a/LCI technique is a synthesis between optical coherence tomog-raphy (OCT), an optical sectioning imaging technique [11, 12], andLSS, the method described above for determining subcellular struc-ture. The former technique produces tomographic images of the mi-croscopic structure of biological tissues. However, conventional OCTimplementations lack the resolution to quantitatively assess changesin cellular features. In contrast, as described in the previous section,LSS can accurately determine the size of cell nuclei but relies on po-larization gating or modeling to remove multiply scattered photons.a/LCI is an alternative method for isolating single scattering and, un-like LSS, it provides the ability to selectively probe subsurface layers inorder to construct depth-resolved tomographic images. Early efforts tocombine these two methods sought to include multiple wavelengthsof broadband light in a Michelson interferometer [17]. Instead, a/LCItakes a different approach and recovers structural information by ex-amining the angular distribution of backscattered light using a singlebroadband light source. a/LCI measures the transverse component ofthe momentum transfer associated with the light scattering processby mixing the light backscattered by a cell sample with a referencefield with a variable transverse momentum, that is, the angle of prop-agation. This technique is closely related to a previous interferometricmethod for measuring the optical phase-space distribution of a lightfield [18]. This section presents the optical design of the a/LCI scheme,which permits measurement of angular scattering distributions,


Sample

L3

L4L2

L1

P

SLD SLD

M

∆y = 0

∆l

D

Detector

to ADC

BS

Sample(b)(a)

L3

L4L2

L1

P

M

∆l

∆y

D

Detector

to ADC

BS

FIGURE 13.1 (a) Schematic of the a/LCI Michelson-based interferometersystem, illustrating the detection of backscattered light. The photocurrent isdigitized by an analog-to-digital converter (ADC). The distances betweenelements are as follows: Plane P to L1 = 10 cm = f1, L1 to BS = 10 cm,BS to L2 = 4.5 cm = f2, L2 to M = 4.5 cm, BS to L3 = 4.5 cm = f3, L3 toSample = 4.5 cm, BS to L4 = 10 cm = f4, L4 to Plane D = 10 cm.(b) Schematic of the interferometer system illustrating the displacement oflens L2 in order to vary the angle that the reference beam crosses thedetector plane. (Source: Taken from Ref. [3].)

the theoretical basis that permits structural information to be extractedfrom the scattering distributions, and details studies that demonstrateits ability to measure the structure and organization of biological cells.

The first implementation of a/LCI [14] used a Michelson interfer-ometer with a movable mirror and lens in the reference arm to map outthe distribution of backscattered light as a function of angle and depthin the sample (Fig. 13.1). This approach measured angular backscatterover a range of ∼27.5◦, but the system required up to 40 min to ac-quire the data for a 1-mm2 point in a sample. This implementation didprove the feasibility of the idea and show that comparison of angularscattering intensity to Mie theory calculations generated an accuratemeasurement of average scatterer size [14].

With a/LCI, as in conventional low-coherence interferometry, thelight from a broadband source, such as a superluminescent diode(SLD), is split by a beamsplitter (BS) into a reference beam and an inputbeam to the sample. The reference beam is reflected by a mirror (M)and recombined at BS with light reflected by the sample. The mixedfields generate an interference pattern provided that the two opticalpathlengths are matched to within the coherence length of the source.In order to separate the interference signal from the DC backgroundand low-frequency noise, a heterodyne signal is generated by trans-lating the reference mirror (M) at a constant velocity. This causes theheterodyne beat intensity to oscillate at the corresponding Dopplershift frequency. The beat intensity is determined by calculating


the power spectrum of the digitized photocurrent and applying abandpass filter to the signal at the heterodyne frequency. This yieldsa signal that is linearly proportional to the squared amplitude of thedetected signal field.∗

Measured a/LCI spectra depict the mean square heterodyne sig-nal as a function of scattering angle, referenced to the exact backscat-tering direction. The a/LCI system employs four achromatic imaginglenses (L1–L4; focal lengths f1– f4) to permit the measurement of angu-lar scattering distributions. These lenses are arranged to form multiple4 f imaging systems, which image both the phase and amplitude ofthe light field [19].

The reference field is made to cross the detector plane at a variableangle by scanning lens L2 ( f2 = 4.5 cm) a distance �y perpendicularto the beam path. It can be shown using Fourier optics that this trans-lation causes the reference field to be reproduced in the plane of thedetector (D) with its angle of propagation changed by �T = 2�y/f2,but its position unchanged [19]. The pathlength of the light throughthe system remains unchanged as the lens is translated transverselyto the beam path. In order to preserve this property of the imagingsystem, L2 is moved longitudinally in conjunction with the referencemirror M along the direction of the beam path, while the length ofthe reference arm is varied. Figure 13.1b illustrates the effects of trans-versely scanning lens L2 in the imaging system using ray traces. It canbe seen that light is now collected at a specific angle relative to thebackscattering direction.

An important feature of the a/LCI system is the lateral displace-ment of lens L3 relative to lens L1. This translation results in the inputbeam entering the sample at an angle of 240 mrad (13.8◦) and permitsthe use of the full angular aperture of the lens to be used to collect an-gular backscattering data, rather than only the half-angle that wouldbe possible with normal incidence. In the current scheme, the max-imum clear aperture limits the angular scans to a total range of 480mrad (27.5◦). The angular resolution, �res = 1.4 mrad (0.08◦), is givenby the diffraction angle of the 0.45-mm diameter collimated beam in-cident on the sample. Because the a/LCI spectra are symmetric aboutthe exact backscattering direction, the system is implemented so thatthe scan begins in the exact backscattering direction and extends 480mrad away from that direction. As discussed above, the light entersthe sample at an angle of 240 mrad relative to the sample surface.

∗It has been previously noted in Ref. [18] that by measuring the mean squareheterodyne beat, the detected signal is related to the Wigner distribution of thesignal field convoluted with that of the reference field. In the current experiments,the angular resolution is sufficiently small that the signal may be regarded as theWigner distribution of the backscattered field.


Note, however, that the exact backscattering direction is antiparallelto the input beam, regardless of the orientation of the sample surface.

The construction of a second-generation a/LCI led to a signif-icant improvement in signal fidelity. The key advance behind thisnew system was enabled by using a Mach–Zehnder interferometerwith acousto-optical modulators (AOMs) [15]. The AOMs create afrequency shift between the signal and reference beams, resulting ina heterodyne beat signal of 10 MHz when the two are combined.This modulation frequency was 1000 times the Doppler shift usedin the previous system and permitted much faster signal acquisitionwith lower noise levels. Detection of signal as a function of angle anddepth was controlled using a movable lens and mirror, respectively.This system is still in active use [20] and can acquire one full scan inapproximately 5 min.

The second-generation a/LCI system (Fig. 13.2) was able to greatlyimprove the quality of the signals through advances in several keycomponents. The system benefits from the use of a mode-lockedTi:Sapphire laser (o = 830 nm; FWHM bandwidth 10 nm) as a lightsource. Although the lower bandwidth reduces the obtained depthresolution, the availability of up to 1 W of power, with 100 mW usedtypically, enables a higher dynamic range of measurements. The sig-nal fidelity is also improved by the use of AOMs to create the offset infrequency that will generate a heterodyne beat signal when the twofields are mixed. The light from the source is split into signal and ref-erence fields by a beamsplitter and each is given a frequency shift of110 or 120 MHz. This results in a heterodyne beat at 10 MHz when thefields are mixed at beamsplitter BS2. By exploiting the short coherencelength (30 �m) of the source, the detected signal field is resolved by

Spectrumanalyzer L1

RR

∆z

∆y

ω

D1L2 L3

Reference beamω + 10 MHz

BS L4

L5BS2

D2

M

Input beam

Sample

FIGURE 13.2 Second-generation a/LCI system based on a Mach–Zehnderinterferometer geometry. Here, translation of lens L2 enables the angle of thedetected scattering signal to be varied. (Source: Taken from Ref. [10].)


its optical pathlength. Information about the signal field is obtainedat various depths within the sample by translating retroreflector (RR)to vary the pathlength of the reference field by 2�z. However, unlikethe previous system, the translation of the retroreflector does not ap-preciably influence the frequency of the heterodyne signal. Becausethe signal is now independent of variations in the scan speed of theretroreflector, the frequency of the heterodyne beat is more stable, re-sulting in a higher fidelity measurement. In addition, the system usesa balanced detector (D1 and D2, New Focus Model 1807) and de-modulates the photocurrent using a spectrum analyzer (HP 8594E),resulting in better signal-to-noise ratio and faster acquisition timesthan the previous a/LCI prototype while offering the same precisionand accuracy for obtaining structural information [20].

The second-generation system measures the angular distributionof the scattered field by scanning lens L2 a distance �y perpendicularto the beam path. This system permits selective detection of the lightthat arrives at the plane of L2 traveling at an angle � = �y/ f2 relativeto the optical axis, where f2 = 10 cm is the focal length of L2. Lens L1( f1 = 10 cm) is included to alter the wavefront of the reference field tocompensate for the effects of L2. Lenses L3 and L4 form a 4 f system,imaging both the phase and amplitude of the scattered field onto theplane of lens L2. Lens L5 ( f5 = 10 cm) is included so that L4 does notfocus the input beam on the sample but instead recollimates it into apencil beam.

Frequency-Domain ImplementationThe early implementations of a/LCI, described above, relied on phys-ically changing the optical pathlength to control the depth in the sam-ple from which data are acquired. This parallels the time-domain im-plementation of optical coherence tomography (TD-OCT). In the OCTfield, it was shown [21] that there is a significant advantage in opti-cal signal-to-noise ratio (OSNR) to be gained by using a frequency-domain implementation. Here, intensity is measured as a functionof wavelength, typically by using a spectrometer, and then Fouriertransformed to yield a depth-resolved reflection profile from a singledata acquisition. Frequency-domain optical coherence tomography(FD-OCT) has quickly become the standard in the OCT community,referred to as spectral domain or Fourier-domain OCT. In a similarfashion, a/LCI can be implemented with a broadband light sourceand a spectrometer to capture depth information in a single integra-tion of the spectrometer instead of physically moving a mirror [22].

In addition to the increase in speed needed to make a/LCI clini-cally feasible, it was also necessary to develop a fiber optic probe thatwould allow interrogation of tissue sites. This advance was achievedby the use of a coherent fiber bundle in the return path from the sample


to capture multiple scattering angles simultaneously [15]. The fiberbundle is used to obtain interferometric data by combining scatteredlight with a reference field and then imaging the distal end of the fiberbundle onto the entrance slit of an imaging spectrometer. A singleframe from the imaging spectrometer now contains scattering inten-sity as a function of wavelength and angle. Fourier transforming on aline-by-line basis generates scattering intensity as a function of opti-cal pathlength and angle. The acquisition speed is now limited by theintegration time of the spectrometer and can be as short as 20 ms. Thesame data that initially required tens of minutes to acquire can nowbe acquired ∼105 times faster.

A schematic of the Fourier-domain version of the a/LCI systemis given in Fig. 13.3. In this scheme, the source is a superluminescentdiode (SLD) with a fiber-coupled output. A fiber splitter separatesthe signal path (90%) and the reference path (10%). The output of thedelivery fiber is collimated using lens L1, but because it is offset fromthe optical axis, the collimated beam is delivered to the sample at anoblique angle. Backscattered light is collimated by L1 and collected bythe fiber bundle, which is located in a conjugate Fourier plane to thesample. At the distal end of the fiber bundle, light from each fiber isimaged onto the spectrometer using a 4 f imaging system comprisedby lenses L2 and L3. The light from the reference arm fiber is attenuated

FIGURE 13.3 Schematic of a/LCI system: (a) light is provided bysuperluminescent diode (SLD); sample and reference light are generated byfiber splitter (FS); sample arm consists of illumination fiber and fiber bundle(FB); lenses L2, L3, and L4 provide collimation. Beamsplitter (BS) combinessample and reference arm light, which is then incident on the imagingspectrometer. (b) Optical geometry of probe tip with illumination fiber (DF),lens L1, and collection fiber (FB). (Source: Taken from Ref. [15].)


by a neutral density filter (NDF) and collimated by lens L4. Light fromthe sample and reference arm are mixed by a cube beamsplitter (BS)and incident on the entrance slit of an imaging spectrometer. Datafrom the imaging spectrometer are transferred to a computer for signalprocessing via the USB interface. The computer also provides controlof the imaging spectrometer.

Control of the light polarization is an important issue for maximiz-ing optical signal and comparing angular scattering with the modifiedMie scattering model [23]. The light from the SLD passes through anoptical isolator (OI), and the polarization of the illumination light iscontrolled by a polarization controller (PC1). Polarization maintainingfiber is used to carry the illumination light from PC1 to the sample. Asecond polarization controller (PC2) is used to optimize the polariza-tion of the light passing through the reference arm with the scatteredlight from the sample arm.

The optical geometry at the sample is shown in Fig. 13.3b, wherethe illuminating fiber comes in on the right side, passes through lensL1, and illuminates the tissue. Scattered light is then collimated bylens L1 and collected by the fiber bundle. The fibers in the bundle arelocated at one focal length from the lens, and the sample is one focallength on the other side of the lens. This configuration maximizes theangular range of the detected signal and minimizes stray light due tospecular reflections.

Portable SystemMost recently, the a/LCI system has been enhanced to allow oper-ation in a clinical setting. Specifically, the system has been modifiedfrom that described in Ref. [15] to include a manipulatable fiber probe.In the previous system, when the fiber probe was manipulated, bire-fringence in the fibers caused changes in the polarization of both thesignal and reference fields, resulting in sharp changes in the detectedsignal. This limitation meant that in the tissue studies with this sys-tem [13], the fiber probe was required to remain fixed during scans. Bycarefully controlling the polarization in the delivery fiber, using polar-ization maintaining fibers and inline polarizers, the new system allowsmanipulation of the handheld wand without introducing birefringenteffects. In addition, the new system employed an antireflection-coatedball lens in the probe tip, which reduced reflections that had limitedthe depth range of the previous system.

Figure 13.4 shows a picture of the portable system. A 2 ft × 2 ftoptical breadboard is used as the base for the system, with the source,fiber optic components, lens, beamsplitter, and imaging spectrome-ter mounted to the optical breadboard. An aluminum cover was builtto protect the optics. A fiber probe with a handheld probe was con-structed enabling easy access to tissue samples for testing. The left side


FIGURE 13.4 Picture of portable a/LCI system with handheld fiber probe onthe left and the optical engine on the right. The computer is not shown.(Source: Taken from Ref. [16].)

of Fig. 13.4 shows the white sample platform where tissue is placedfor testing. The handheld probe is then used by the operator to se-lect specific sites on the tissue from which to acquire a/LCI readings.The entire system rests on a lab cart with pneumatic tires for ease oftransport and minimization of vibration and shock.

13.3 Processing of a/LCI SignalsIn order to determine structures based on measured angular distri-butions, a/LCI signals must be processed and then analyzed. In thefrequency-domain a/LCI system, light levels on the CCD array aredigitized and sent to the computer via universal serial bus (USB) forsignal processing using algorithm software written in LabVIEW.

Each pixel in the CCD array corresponds to a specific combinationof wavelength and scattering angle. The detected signal can be relatedto the signal and reference fields (Es, Er) by

I (m, �n) = ⟨|Er(m, �n)|2⟩+ ⟨|Es(m, �n)|2⟩+ 2Re

⟨Es(m, �n)E∗

r (m, �n) cos(�)⟩ (13.1)

where � is the phase difference between the two fields, (m, n) corre-sponds to a particular pixel, and 〈·〉 denotes a temporal average.


Data Processing for PhantomsThe steps for converting raw pixel data to size measurements, as de-scribed in Ref. [15], are as follows:

1. The average intensities of the sample and reference beams aresubtracted from I .

2. At each scattering angle, the spectrum in wavelength () isinterpolated to wavenumber (using k = 2�/).

3. Any chromatic dispersion in the system is corrected numeri-cally using empirical parameters.

4. At each scattering angle, the spectrum as a function of wave-number is 1D Fourier transformed to generate signal as a func-tion of optical pathlength (or depth in the sample).

5. The angular distribution is divided by the normalized refer-ence field, which varies smoothly from 0.5 to 1.

6. The scaled data are squared to yield scattered intensity versusangle and pathlength.

7. High-frequency noise is reduced by binning the angular data.

8. The angular data for a particular depth (optical pathlength)are compared to previously generated Mie theory predictions.Chi-squared values are calculated for each theoretical predic-tion for scatterer diameters ranging from 3 to 20 �m in 0.1 �mincrements.

9. The minimum chi-squared value is determined by searchingthrough all values generated, and the corresponding size isreported.

The uncertainty in the measurements is given as the Mie theorydiameters where the minimum chi-squared value is doubled.

Data Processing for Cell NucleiAlthough the above data analysis procedure is suitable for determin-ing the size of polystyrene microspheres, it must be modified in orderto extract useful structural information regarding cell nuclei. As dis-cussed in detail in Ref. [20], several features of cell nuclei will preventaccurate size determination when the angular data are compared di-rectly to the predictions of Mie theory. First, one must consider that Mietheory predicts scattering by a homogenous dielectric sphere, while,for most cells, the nucleus is not a sphere but rather a spheroid. In ad-dition, the presence of inhomogeneities in and around the nucleus canalso complicate interpretation of the angular scattering distribution.


The a/LCI analysis algorithm for extracting nuclear size informa-tion from cells and tissues consists of four steps:

1. A region of interest is selected from the raw data for analysis. Usu-ally, a depth is chosen corresponding to a specific tissue layer.For analysis of the human tissues presented below, the analy-sis was conducted in an automated fashion at 30 �m intervals,corresponding to the coherence length of the SLD light source,which dictates the achieved depth resolution.

2. The data are low-pass filtered to remove high-frequency oscilla-tions in the angular distribution. Because the angular distribu-tion is Fourier transform related to the two-point correlationfunction, removing oscillations over fine angular scales corre-sponds to suppressing scattering arising from long correlationdistances. Physically, this step removes the contribution toangular scattering arising from coherent scattering by neigh-boring cell nuclei, which are necessarily spaced at distancesgreater than the cell size. This effect was explored and char-acterized in a previous study [24] that systematically variedcell spacing to show that the a/LCI analysis method was ableto make accurate size determinations in the presence of co-herent scattering by adjacent cell nuclei. In the human tissuestudies, described below, the filtering step is accomplishedautomatically by the analysis software.

3. The data are further processed using a second-order polynomial toremove the background trend from the processed data. The primaryorigin of the background trend is due to scattering by smallsubcellular organelles and inhomogeneities in the nucleus.Because the size of these scatterers is comparable to the wave-length of light used in a/LCI, they cause low-frequency oscil-lations compared to the range of the angular measurements.The fit is subtracted from the data to isolate the oscillatorycomponent due to diffraction, as described in Ref. [20].

4. The final step is to compare the processed angular distribution withMie theory distributions, which have also had the backgroundtrend removed. Each theoretical distribution is fitted using asecond-order polynomial, and then this trend is subtractedfrom the distribution to yield the oscillatory component. Fordetermining the size of cell nuclei, the calculated distribu-tions are based on a Gaussian distribution of scatterer sizes,characterized by a mean diameter (d), a standard deviation(d) in the size parameter, a range of refractive indices of thenuclei (nnucleus), and a range of refractive indices of the cyto-plasm (ncytoplasm). In the human tissue data presented below,the relative refractive index of the nucleus (nnucleus/ncytoplasm)is described as a nuclear density.


As a final note, when fitting data from cells and tissues, it is impor-tant to establish criteria that a unique fit has indeed been found. Thereare two such checks that are incorporated into our automated anal-ysis software. First, the chi-squared value of the best fit is comparedto that obtained when the data is compared to a “null-solution,” con-sisting of scattering that is constant versus angle. Passing this checkindicates that the achieved fit is meaningful. The second check is de-termined by comparing the chi-squared value of the best fit with thenext best-fitted size. If the best-fit chi-squared value is not 10% lowerthan the next best value, the fit is discarded as nonunique. Statistically,this criterion corresponds to a reduction of the nonconfidence interval(compliment of the confidence interval) by a factor of 2.

13.4 Validation Studies

Polystyrene MicrospheresValidation of a/LCI measurements has been accomplished by mea-suring the scattering distribution of polystyrene microspheres [15].Typically, samples consisting of a solution of microspheres (n = 1.59,1% by mass) suspended in a mixture of 80% water and 20% glycerol(n = 1.36) to provide neutral buoyancy.

As an example of such validation, typical microsphere data ob-tained with the clinical frequency-domain a/LCI system are shownin Fig. 13.5. In this figure, data are shown for light scattered by a sam-ple of 12.01 �m polystyrene microspheres (NIST traceable from DukeScientific) in solution with a mean free path (MFP) of 381 �m. The429-�m OPL between the reflection from the front of the coverslip

0.15

0.25

0.35

0.450 0.5

OPL/2n =142 µm

Optical pathlength (mm)

Ang

le (

rad)

1.0 1.5

FIGURE 13.5 Contour plot of angular scattering by a suspension of 12.0 �mbeads atop a coverslip as a function of optical pathlength (OPL). Light areasindicate increased scattered intensity. (Source: Taken from Ref. [15], withpermission.)


(a) (b)1.0

1.0

0.8

0.6

0.4

0.2

0.80.6

0.4

0.2

0.15

|E(θ

)|2

χ2 val

ue (

a.u.

)

0.25Angle (rad) Diameter (µm)

DataMie theory

0.35 0.45 11 12 13

FIGURE 13.6 (a) Angular distribution cross section of Fig. 13.3 data and bestfit Mie theory distribution. (b) Minimization of � 2 value to determine best fitand uncertainty. (Source: Taken from Ref. [15], with permission.)

and the beginning of the scattering from the microspheres behind thecoverslip provides an accurate measurement of the thickness of theNo. 1 coverslip, t = OPL/(2n) = 142 �m.

A cross section of 50 �m within one MFP of the sample surfaceis averaged to yield the angular scattering distribution (Fig. 13.6).This distribution (dots), when compared to Mie theory, yields a sizemeasurement of 12.0 ± 0.2 �m, which is in excellent agreement withthe actual size. The determination of the best fit is shown in Fig. 13.6b,which shows the minimization of the chi-squared parameter.

To demonstrate the capability of the system across a range of clini-cally relevant size, polystyrene microspheres of sizes 6.0, 8.0, 9.7, 12.0,and 15.0 �m were probed (Duke Scientific and Polysciences; MFPs 190,254, 309, 381, and 476 �m, respectively) using the frequency-domainsystem [15]. Figure 13.7 shows a plot of the a/LCI-determined meandiameter versus the NIST-traceable mean diameter. The r2 value for

16

14

12

10

8

6

6

a/LC

I mea

n si

ze (

µm)

8

r2 = 0.9997

NIST mean size (µm)

10 12 14 16

FIGURE 13.7 Measured sizes of polystyrene microspheres using a/LCIsystem with error bars versus NIST sizes. (Source: Taken from Ref. [15], withpermission.)


these data is 0.9997, thus demonstrating the ability of the a/LCI systemto accurately determine the sizes of scatters over a range encompass-ing nuclear sizes seen in healthy and precancerous tissues [5, 9, 13].

In Vitro Cell StudiesThe a/LCI approach for measuring nuclear morphology was first de-scribed in experiments with monolayers of epithelial cells (HT29) [3].Figure 13.8 shows the a/LCI data for light scattered by a sample ofHT29 cells. The square of the magnitude of the scattered field is plottedas a function of the scattering angle relative to the exact backscatteringdirection. The size distribution of the cell nuclei is obtained by com-paring the angular scattering distribution to the predictions of Mietheory using the process described above.

Figure 13.9 shows the oscillatory part of the light scattering dataextracted from the raw data. In order to determine the structural prop-erties of the cell nuclei, the oscillatory part of the distribution is com-pared to similarly extracted components of theoretical distributionscalculated using Mie theory. The best fit is found by minimizing thechi-squared value between the processed data and theory. For the data(solid line) of Fig. 13.9, the best fit (dashed line) is obtained for a the-oretical distribution of light scattered by a Gaussian distribution ofspherical particles with a refractive index mismatch of 1.46/1.37 =1.066, a 9.7-�m mean diameter and a 1/e width of 5% (0.49 �m).

In this first series of a/LCI experiments with epithelial cells [3],a/LCI data were analyzed for four cell monolayer samples. Randomlysampled spatial points, 0.45 �m in diameter, were examined on eachsample. Twelve measurements were analyzed and the nuclei were

1.4

1.0

0.6

0.2

0.0 0.1 0.2

Angle (rad)

0.3 0.4

|E(θ

)|2

FIGURE 13.8 Typical a/LCI spectra from HT29 epithelial cells. The spectra areshown as the mean square heterodyne signal as a function of scatteringangle, relative to the exact backscattering direction. The data are normalizedto the scattered intensity in the exact backward direction. (Source: Taken fromRef. [3] with permission.)


0.2

0.1

0.0

−0.1

−0.2

0.0 0.1 0.2

Angle (rad)

0.3 0.4

|E(θ

)|2 −

O(θ

4 )

FIGURE 13.9 Oscillatory part of the light scattering data (solid line) comparedto the best-fit theoretical distribution (dashed line) obtained using Mie theory.This part of the light scattering data is used to extract the size and sizedistribution of the epithelial cell nuclei. (Source: Taken from Ref. [3] withpermission.)

found to have a mean refractive index difference of 1.066 ± 0.007,a Gaussian distribution of sizes with a mean diameter of 9.9 �m ±0.6 �m, and a 1/e width of the distribution of 0.69 ± 0.16 �m. Forcomparison, quantitative image analysis (QIA) was executed usinga photomicrograph (Fig. 13.10) of a typical monolayer of HT29 cells,which had been fixed in formalin and stained with hemotoxalin andeosin. The QIA yielded a mean diameter of 10.6 ± 0.4 �m, and thedistribution of sizes was found to have a width of 0.6 �m, both ingood agreement with the a/LCI results.

FIGURE 13.10 Photomicrograph of a typical HT29 cell monolayer after fixationand staining. Length scale indicated by the 10 �m bar. (Source: Taken fromRef. [3] with permission.) See also color insert.


Once the contribution of the cell nuclei to the light scattering signalhas been found, the remaining portion can be analyzed to determinethe organization of smaller structures within the cell and nucleus.This component of the scattered light is analyzed by identifying thespatial correlation of the smaller structures obtained through Fouriertransform of the a/LCI angular scattering data [25]:

�[|E(��)|2] ∝ ⟨∂�(�r ′

⊥)∂�(�r ′

⊥ + r ��)⟩ ≡ �� (r ) (13.2)

In this expression, the mean squared field, E , as a function of scatteringangle, �, is related to the two-point correlation function, �� (r ), of thesample as a function of separation, r , along the direction given by �,the scattering angle relative to the backscattering direction. When thenuclear contribution to the scattering is properly modeled, the small-structure component of the a/LCI data takes the form of a power lawdistribution in �, leading to an inverse power law in the two-pointcorrelation function. The density variations scale as

�� (r ) ∝ r−� (13.3)

where � is the power law exponent found by fitting the Fourier-transformed data. The fact that the spatial dependence of the cor-relation function takes the form of an inverse power law indicatesthe fractal or self-similar nature of the sample. Fractal organization ofstructure is usually defined in terms of a fractal dimension, D, whichcan be related to the power law exponent by D = 3 − �.

Figure 13.11 shows the two-point correlation function, �(r ), ob-tained by taking the Fourier transform of the residual distributionof the light scattering data shown in Fig. 13.8. The straight line on

1.0

0.1

2 5

Correlation distance (µm)

10 20

Γ(r)

FIGURE 13.11 Correlation function obtained by Fourier transform of residuallight scattering data. The data (solid line) are best fit by a power law (dashedline), indicating the self-similar nature of smaller structures within the modelepithelial cells. (Source: Taken from Ref. [3] with permission.)


this log–log plot clearly shows the inverse power law dependence ofthe correlations, indicating the fractal nature of the light scatteringfrom subcellular structures. In this case �(r ) ∼ r−�, where � = 1.15.The exponent of the power law of the correlation function gives in-sight into the fractal nature of the smaller structures. It is related tothe fractal dimension D = 1.85 of these structures. For the data in thea/LCI experiments [3], the average correlation exponent was foundto be � = 1.21± 0.10, corresponding to a fractal dimension, D = 1.79±0.10.

Since these first a/LCI experiments with in vitro cells, there havebeen a number of further experiments that have measured nuclearmorphology [3, 23, 26–28]. Chapter 4 covers the results of these exper-iments in detail. Table 13.1 summarizes the nuclear morphology dataobtained from these various experiments.

13.5 Tissue Studies

Animal StudiesAnimal models of carcinogenesis are important tools for understand-ing cancer development as well as for evaluating prospective chemo-preventive and therapeutic agents. The a/LCI technique was initiallyvalidated in the rat esophageal carcinogenesis model [8] and later ap-plied in additional studies [10]. The processing of tissue samples andthe results of these studies are now discussed.

Measured a/LCI data from the systems described above consistof the angular distribution of scattered light, which contains informa-tion about the tissue structure, as a function of depth within the tissue.The light scattered from a particular depth is selectively detected us-ing coherence gating. The effects of scattering by layers superficial tothose of interest have been discussed previously [14] and are negligi-ble for typical depths of 50–100 �m selected for analysis of epithelialtissues.

The diameter of the a/LCI probe beam, approximately 400–500 �m for all systems to date, enables a single layer of a few hundredcells to be sampled at once, providing an average nuclear morphol-ogy measurement within the probe volume. The use of an averageminimizes the effect of cell-to-cell variations in nuclear morphologysuch as irregular nuclear shape and variations in density arising fromdiffering phases of the cell cycle.

Because a/LCI obtains the scattering distribution as a functionof depth, the selection of a region of interest (ROI) for analysis is animportant consideration. In squamous epithelial tissues, the basal celllayer of the esophageal epithelium has been found to be a diagnos-tically useful ROI. The basal layer is identified by the topmost sharp

a/LCI Nuclear QIA Nuclear AdditionalCell Line Diameter (�m) Diameter (�m) Descriptors Ref.

HT29 9.9 ± 0.6 10.6 ± 0.4 FD = 1.79 ± 0.10 [3]

T-84 9.9 ± 0.5 9.9 ± 0.5 n/a [23]

3T3 13.2 ± 1.0 12.9 ± 0.4 n/a

Caco-2 14.6 ± 0.7 14.4 ± 0.65 n/a

Murine macrophage

Major axis 10.53 ± 0.47 10.30 ± 0.47 Aspect ratio = 0.62 [26]

Minor axis 6.50 ± 0.23 6.39 ± 0.34 Aspect ratio = 0.62

Porcine chondrocyte

Salinity 330 mOsm 6.96 ± 0.07 6.96 ± 0.06 n/a [26]

400 mOsm 6.60 ± 0.05 6.78 ± 0.07 n/a

500 mOsm 6.45 ± 0.08 6.57 ± 0.07 n/a

MCF-7

T -matrix analysis 9.51 ± 0.34 9.52 ± 0.44 Aspect ratio = 0.69 [27]

Mie theory 9.47 ± 0.34 9.52 ± 0.44 n/a

FD = 1.63 ± 0.44,FD = 1.95–2.13 (treated)

[28]

TABLE 13.1 Summary of a/LCI Measured Nuclear Morphology Data for Several Cell Types

331


peak in the density profile of the tissue, obtained by integrating thea/LCI data over angle. We note that a thickened keratin layer may beobserved for some tissue samples that can cause the basal layer to beas deep as 200 �m. In addition, a spurious peak may be observed atthe tissue surface if precautions are not taken to avoid this specularreflection, such as introducing the beam to the tissue at an obliqueangle or using a coupling fluid. Although multiple scattering is moresignificant at these depths, previous studies have shown that the os-cillations in the angular distribution used to determine size are stillevident [14]. In our studies of tissues from the respiratory tract, theepithelium presents as a single cell layer atop the stroma. In this case,the topmost layer is chosen for analysis. In more complex tissue archi-tectures, such as columnar epithelium, selection of an ROI may be amore difficult task. In our studies with human epithelial tissues fromBarrett’s esophagus (BE) patients [13], a summary measure of the av-erage nuclear morphology in the superficial 150 �m was used. Furtherstudies with an updated system [16] have shown that measurementsfrom the basal layer of human esophageal epithelium, approximately275 �m beneath the tissue surface, also provide diagnostically im-portant information. For the experimental studies described below,the a/LCI data from the selected ROI of each sample was processedand analyzed to determine the mean diameter of the cell nuclei, asdescribed above in Sec. 13.3.

The a/LCI data are processed and analyzed to determine the nu-clear morphology of the associated sample. In previous studies [8, 10,13, 29], the chief morphological descriptor used for classifying tissueswas the mean size of the cell nuclei. However, additional descrip-tors such as the relative refractive index [30] and the nuclear texture,quantified using fractal dimension [26, 28], have also been examinedto assess their diagnostic capacity as a biomarker.

The first a/LCI study of rat esophagus [8] reported the a/LCI-measured nuclear morphology and its correlation with histology. Inthis study, the data (Fig. 13.12) showed an increase in mean nuclearsize with neoplastic progression. The average nuclear size in normaltissues was found to be 9.55 ± 0.23 �m, increases to 10.5 ± 0.56 �m forlow-grade dysplasia (LGD) and to 14.4 ± 0.21 �m for high-grade dys-plasia (HGD). A statistically significant difference was found betweenthe normal and LGD mean sizes (p < 0.001), and between normal andabnormal (LGD + HGD) mean sizes (p < 0.005). A decision thresholdwas established using logistic regression, which yielded 80% sensi-tivity and 100% specificity in distinguishing normal and dysplastictissues. The original study did not report the refractive index of thenucleus relative to the cytoplasm obtained from the a/LCI data, butwas later included in a review article [30]. The relative refractive indexof the nuclei in normal tissues was found to be 1.052 ± 0.0051 and thatof the dysplastic tissues was found to be 1.051 ± 0.0082. This is not a


Rat esophagus study I

1.04

1.045

1.05

1.055

1.06

1.065

1.07

1.075

8 9 10 11 12 13 14 15

Mean nuclear size (µm)

Rel

ativ

e re

frac

tive

ind

ex

Normal

LGD

HGD

FIGURE 13.12 Nuclear morphology of epithelial tissues from the ratesophagus. (Source: Taken from Ref. [30].)

statistically significant difference (p = 0.74). However, visual inspec-tion of the data in Fig. 13.12 reveals an obvious outlier. Upon removalof this point from analysis, the average for the dysplastic tissues dropsto 1.049 ± 0.0031. Although this result is still not statistically signifi-cant, the p-value drops dramatically to p = 0.07.

The second a/LCI study of rat esophagus [10] was a prospec-tive study that used the decision line from the first study to classifytissues. This study consisted of two cohorts of animals examined atseveral time points. The data were originally presented for the meannuclear size as a function of neoplastic progression and at multipletime points. Here, the data across time points are reviewed using asingle diagnostic metric. For the first cohort of animals in the secondstudy, the mean nuclear diameter was found to be 9.09 ± 1.06 �mfor the normal tissues and 11.86 ± 1.16 �m for the dysplastic tissues,a highly statistically significant difference (p < 0.0001). The relativerefractive index of the nuclei in these tissues was found to be 1.047 ±0.0051 for the normal tissues and 1.041 ± 0.0038 for the dysplas-tic tissues. This was also a highly statistically significant difference(p < 0.001). In the second cohort of animals in this study, the meannuclear diameter was found to be 8.80 ± 0.51 �m for normal tissuesand 12.07 ± 1.73 �m for dysplastic tissues, a highly statistically sig-nificant difference (p < 0.0001). The relative refractive index of thenuclei in these tissues was found to be 1.057 ± 0.0068 for the normaltissues and 1.051 ± 0.0094 for the dysplastic tissues. This difference


Hamster trachea study

1.025

1.03

1.035

1.04

1.045

1.05

1.055

1.06

1.065

1.07

5 7 9 11 13 15 17

Mean nuclear size (µm)

Rel

ativ

e re

frac

tive

ind

ex

Dysplastic

Normal

FIGURE 13.13 Nuclear morphology of epithelial tissues from the hamstertrachea. (Source: Taken from Ref. [30].)

was not found to be statistically significant but is comparable to thesignificance in the first study (p = 0.077).

More recently a pilot a/LCI study was executed to assess the sensi-tivity of the approach to detecting neoplastic progression in the ham-ster trachea [29]. As this was designed to be a pilot study, it onlycontained a limited number of samples. This study reported both themean nuclear diameter and relative refractive index for normal anddysplastic tissues, shown graphically in Fig. 13.13. The mean nucleardiameter was found to be 7.00 ± 1.09 �m for the normal tissues andincreased to 11.19 ± 3.2 �m for the dysplastic tissues, a statisticallysignificant difference (p = 0.03). The relative refractive index of thecell nuclei was found to be 1.057 ± 0.0064 for the normal tissues and1.048 ± 0.012 for the dysplastic tissues. This difference was not foundto be statistically significant but was consistent with the significanceof the studies above (p = 0.06).

The use of a/LCI nuclear morphology measurements is a poten-tially powerful method for detecting dysplasia in epithelial tissues.The a/LCI method offers the advantage that no tissue sectioning, fix-ation, or staining agents are required. For animal studies, the a/LCImethod offers several benefits over traditional analysis as well. First,the ability to obtain nuclear morphology data without tissue process-ing enables additional immunohistochemistry studies, which maynot be possible after tissue fixation. Further, the a/LCI method hasbeen shown capable of detecting neoplastic changes earlier than other


bioassay methods, such as tumor metrology measurements [10]. Fi-nally, because a/LCI can detect unusual cell states such as apoptosis[8, 10], the method can be applied to assess the efficacy of candidatechemopreventive agents in animal models.

Human Esophageal EpitheliumAfter validating the a/LCI system using animal tissues, tests wereconducted on ex vivo human tissue samples. The first results werereported in Ref. [13] and consisted of tissue samples from three pa-tients with dysplastic Barrett’s esophagus (BE) who underwent esoph-agogastrectomies, where the lower portion of the esophagus and partof the stomach are surgically removed. The tissue was opened longi-tudinally and data were taken within 2 h of resection. These studiesshowed a high sensitivity and specificity for distinguishing dysplas-tic BE tissue from healthy columnar tissue (Fig. 13.14), as would befound in the gastric epithelium. No nondysplastic BE tissue was en-countered.

More recently an additional study [16] was conducted using thenew portable system described above in the section “Portable Sys-tem.” Significantly, the a/LCI system was transported to the pathol-ogy clinic and data were taken within 1 h of resection. Similar to

FIGURE 13.14 Scatter plot of pathological tissue classification vs. meannuclear diameter and mean relative refractive index over superficial 150 �mof tissue. Dashed line indicates potential decision line for identifyingdysplastic tissue in Barrett’s esophagus. (Source: Taken from Ref. [13], withpermission.)


Base of tissue layer

6.0

7.0

8.0

9.0

10.0

11.0

12.0

13.0

14.0

1.020 1.030 1.040 1.050 1.060 1.070 1.080

Nuclear densityN

ucle

ar d

iam

eter

(µm

)

LGD

Gastric

Squamous

Average over 150 µm

8.0

9.0

10.0

11.0

12.0

13.0

14.0

1.035 1.040 1.045 1.050 1.055 1.060 1.065

Nuclear density

Nu

clea

r d

iam

eter

(µm

)

LGD

GastricSquamous

FIGURE 13.15 Scatter plot of average nuclear density and average nuclear diameterfor each pathological tissue classification based on a/LCI data from (a) superficial150 �m and (b) bottom of epithelial layer for each tissue sample. (Source: Takenfrom Ref. [16], with permission.)

the previous study, the tissue was opened longitudinally and datawere acquired from multiple sites. The handheld optical probe wasused, allowing precise selection of the location for each data point.The scanned points were then bracketed with India ink to allow foraccurate comparison of the a/LCI results to pathological classification.

In this second study of ex vivo tissue, three types of tissue from asingle specimen were tested, including normal squamous tissue fromthe esophagus, normal-appearing gastric tissue from the stomach, andBarrett’s tissue in the esophagus. As with the previous ex vivo study,no nondysplastic BE tissue was observed. Detailed descriptions of thetrends in the nuclear morphology data as a function of depth werereported in the original study [16].

The results from this study were consolidated into a set of graphsto provide an overview of the diagnostic capacity of the a/LCI method(Fig. 13.15). Upon comparing the nuclear morphology data as an aver-age over the top 150 �m of the tissue sample, the a/LCI results showedexcellent sensitivity (ability to detect diseased tissue) in this data setwith all of the low-grade dysplasia points below 1.05 in nuclear den-sity and above 11.0 �m in average cell nuclei size. When using thedecision line created in Ref. [13] and shown in Fig. 13.14, 100% sensi-tivity (6/6) was obtained. The specificity (ability to determine normaltissue) was 54% (5/9), with three gastric points and one squamouspoint mixed in with the low-grade dysplasia.

This low specificity might be viewed as a potential limitation ofthe technique. However, when one considers that the gastric tissuewas inflamed due to gastritis, it is not surprising that the nuclearmorphology for the superficial layer could not be used to distinguishit from low-grade dysplasia. To distinguish inflamed from dysplastictissues, analysis of the a/LCI data for the base of the epithelial layer


instead of the surface layer was used. This was enabled by the greaterdepth range achieved by the newer system, over 1 mm compared with∼150 �m with the first version.

The data from the basal layer showed excellent sensitivity (100%)with all low-grade dysplasia data points exhibiting a nuclear densitybelow 1.06 and a nuclear diameter above 8 �m. The specificity here(78%) is better than in the case of the surface tissue, with just two squa-mous points mixed in with the low-grade dysplasia. The improvementin specificity obtained by analyzing deeper tissue layers suggests thata/LCI depth-resolved nuclear morphology measurements may be apowerful way to distinguish inflammation from dysplasia.

13.6 ConclusionSignificant development of a/LCI technology has been realized sinceits first uses. The first system took as long as 40 min to acquire the datafor a single sample point compared to the current systems, which arecapable of acquiring data in less than a second. Progress has also beenmade in reducing the physical size of the system. Systems that wereoriginally laid out across an entire optics table now occupy a smallfootprint atop a portable cart. Further, by developing a fiber opticmethod for acquiring angular distributions, the technology develop-ment has been translated to in vivo endoscopic application.

The next significant step in development of a/LCI for clinical use isa trial using in vivo human tissue. Indeed, a clinical study is underwayat the time of this writing. The study is designed to compare a/LCImeasurements acquired during standard endoscopic surveillance ofBarrett’s esophagus tissues with pathology analysis of biopsy samplestaken from the same locations.

Another area of focus will be the determination of the biomark-ers with the highest sensitivity and specificity. Current analysis hasfocused on using average nuclear diameter and nuclear density at par-ticular depths in the tissue sample. Given the range of data availablefrom each reading, additional biomarkers such as scattering intensityor detailed analysis of the tissue profile as a function of depth mayimprove tissue classification.

With these and other advances, the trajectory of translating thea/LCI technology from laboratory feasibility experiments to clini-cal development and ultimately deployment as a widely used cancerscreening tool will continue.

13.7 AcknowledgmentsGrant support was provided by the National Institutes of Health (Na-tional Cancer Institute R33-CA109907) and the National Science Foun-dation (Bioengineering and Environmental Systems 03–48204).


References1. Backman, V., V. Gopal, M. Kalashnikov, K. Badizadegan, R. Gurjar, A. Wax, I.

Georgakoudi, M. Mueller, C. W. Boone, R. R. Dasari, and M. S. Feld, Measuringcellular structure at submicrometer scale with light scattering spectroscopy.

IEEE J Select Top Quant Electron 2001. 7(6): pp. PII S1077–260X(01)11252–11259.

2. Mourant, J. R., T. M. Johnson, S. Carpenter, A. Guerra, T. Aida, and J. P. Freyer,Polarized angular dependent spectroscopy of epithelial cells and epithelial cellnuclei to determine the size scale of scattering structures. J Biomed Opt 2002.7(3): pp. 378–387.

3. Wax, A., C. H. Yang, V. Backman, K. Badizadegan, C. W. Boone, R. R.Dasari, and M. S. Feld, Cellular organization and substructure measured usingangle-resolved low-coherence interferometry. Biophys J 2002. 82(4): pp. 2256–2264.

4. Wilson, J. D., C. E. Bigelow, D. J. Calkins, and T. H. Foster, Light scattering fromintact cells reports oxidative-stress-induced mitochondrial swelling. Biophys J2005. 88(4): pp. 2929–2938.

5. Backman, V., M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G.Muller, Q. Zhang, G. Zonios, E. Kline, T. McGillican, S. Shapshay, T. Valdez,K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M.Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, Detection of preinva-sive cancer cells. Nature 2000. 406(6791): pp. 35–36.

6. Drezek, R., M. Guillaud, T. Collier, I. Boiko, A. Malpica, C. Macaulay, M. Follen,and R. Richards-Kortum, Light scattering from cervical cells throughout neo-plastic progression: influence of nuclear morphology, DNA content, and chro-matin texture. J Biomed Opt 2003. 8(1): pp. 7–16.

7. Lovat, L. B., D. Pickard, M. Novelli, P. M. Ripley, H. Francis, I. J. Bigio, and S. G.Bown, A novel optical biopsy technique using elastic scattering spectroscopyfor dysplasia and cancer in Barrett’s esophagus. Gastrointest Endosc 2000. 51(4):pp. 4919.

8. Wax, A., C. Yang, M. G. Muller, R. Nines, C. W. Boone, V. E. Steele, G. D. Stoner,R. R. Dasari, and M. S. Feld, In situ detection of neoplastic transformationand chemopreventive effects in rat esophagus epithelium using angle-resolvedlow-coherence interferometry. Cancer Res 2003. 63: pp. 3556–3559.

9. Wallace, M. B., L. T. Perelman, V. Backman, J. M. Crawford, M. Fitzmaurice,M. Seiler, K. Badizadegan, S. J. Shields, I. Itzkan, R. R. Dasari, J. Van Dam,and M. S. Feld, Endoscopic detection of dysplasia in patients with Barrett’sesophagus using light-scattering spectroscopy. Gastroenterology 2000. 119(3):pp. 677–682.

10. Wax, A., J. W. Pyhtila, R. N. Graf, R. Nines, C. W. Boone, R. R. Dasari, M. S.Feld, V. E. Steele, and G. D. Stoner, Prospective grading of neoplastic change inrat esophagus epithelium using angle-resolved low-coherence interferometry.J Biomed Opt, 2005. 10(5): 051604.

11. Youngquist, R. C., S. Carr, and D. E. N. Davies, Optical coherence-domainreflectometry—a new optical evaluation technique. Opt Lett, 1987. 12(3):pp. 158–160.

12. Huang, D., E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang,M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, Opticalcoherence tomography. Science 1991. 254(5035): pp. 1178–1181.

13. Pyhtila, J. W., K. J. Chalut, J. D. Boyer, J. Keener, T. D’Amico, M. Gottfried,F. Gress, and A. Wax, In situ detection of nuclear atypia in Barrett’s esopha-gus by using angle-resolved low-coherence interferometry. Gastrointest Endosc2007. 65(3): pp. 487–491.

14. Wax, A., C. Yang, V. Backman, M. Kalashnikov, R. R. Dasari, and M. S. Feld,Determination of particle size by using the angular distribution of backscat-tered light as measured with low-coherence interferometry. J Opt Soc Am A,2002. 19(4): pp. 737–744.


15. Pyhtila, J. W., J. D. Boyer, K. J. Chalut, and A. Wax, Fourier-domain angle-resolved low coherence interferometry through an endoscopic fiber bundle forlight-scattering spectroscopy. Opt Lett 2006. 31(6): pp. 772–774.

16. Brown, W. J., J. W. Pyhtila, N. G. Terry, K. J. Chalut, T. D’Amico, T. A. Sporn,J. V. Obando, and A. Wax, Review and recent development of angle-resolvedlow-coherence interferometry for detection of precancerous cells in humanesophageal epithelium. IEEE J Select Topics Quant Electron 2008. 14(1): pp. 88–97.

17. Yang, C., L. T. Perelman, A. Wax, R. R. Dasari, and M. S. Feld, Feasibility offield-based light scattering spectroscopy. J Biomed Opt 2000. 5(2): pp. 138–143.

18. Wax, A. and J. E. Thomas, Optical heterodyne imaging and Wigner phase spacedistributions. Opt Lett 1996. 21(18): pp. 1427–1429.

19. Wax, A., C. Yang, R. R. Dasari, and M. S. Feld. Angular light scattering studiesusing low-coherence interferometry. In: V. V. V. Tuchin, J. A. Izatt, and J. G. Fu-jimoto, eds. Coherence Domain Optical Methods in Biomedical Science and ClinicalApplications. San Jose, CA: SPIE. 2001.

20. Pyhtila, J. W., R. N. Graf, and A. Wax, Determining nuclear morphology usingan improved angle-resolved low coherence interferometry system. Opt Express2003. 11(25): pp. 3473–3484.

21. Choma, M. A., M. V. Sarunic, C. H. Yang, and J. A. Izatt, Sensitivity advantage ofswept source and Fourier domain optical coherence tomography. Opt Express2003. 11(18): pp. 2183–2189.

22. Pyhtila, J. W. and A. Wax, Rapid, depth-resolved light scattering measurementsusing Fourier domain, angle resolved low coherence interferometry. Opt Ex-press 2004. 12(25): pp. 6178–6183.

23. Pyhtila, J. W. and A. Wax, Polarization effects on scatterer sizing accuracy an-alyzed with frequency-domain angle-resolved low-coherence interferometry.Appl Opt 2007. 46(10): pp. 1735–1741.

24. Pyhtila, J. W., H. W. Ma, A. J. Simnick, A. Chilkoti, and A. Wax, Analysis oflong range correlations due to coherent light scattering from in-vitro cell arraysusing angle-resolved low coherence interferometry. J Biomed Opt 2006. 11(3):34022.

25. Mandel, L. and E. Wolf, Optical Coherence and Quantum Optics. New York: Cam-bridge University Press, 1995.

26. Chalut, K. J., S. Chen, J. D. Finan, M. G. Giacomelli, F. Guilak, K. W. Leong,and A. Wax, Label-free, high-throughput measurements of dynamic changes incell nuclei using angle-resolved low coherence interferometry. Biophys J 2008.94(12): pp. 4948–4956.

27. Giacomelli, M. G., K. J. Chalut, J. H. Ostrander, and A. Wax, Application ofthe T-matrix method to determine the structure of spheroidal cell nuclei withangle-resolved light scattering. Opt Lett 2008. 33(21): pp. 2452–2454.

28. Chalut, K. J., J. H. Ostrander, M. G. Giacomelli, and A. Wax, Light scatteringmeasurements of subcellular structure provide noninvasive early detection ofchemotherapy-induced apoptosis. Cancer Res 2009. 69(3): pp. 1199–1204.

29. Chalut, K. J., L. A. Kresty, J. W. Pyhtila, R. Nines, M. Baird, V. E. Steele, andA. Wax, In situ assessment of intraepithelial neoplasia in hamster trachea ep-ithelium using angle-resolved low-coherence interferometry. Cancer EpidemiolBiomarkers Prev 2007. 16(2): pp. 223–227.

30. Wax, A. and J. W. Pyhtila, In situ nuclear morphology measurements usinglight scattering as biomarkers of neoplastic change in animal models of car-cinogenesis. Dis Markers 2008. 25(6): pp. 291–301.


C H A P T E R 14Enhanced

Backscattering andLow-Coherence

EnhancedBackscattering

Spectroscopy

Jeremy D. Rogers, Vladimir Turzhitsky, Young Kim, and Vadim Backman

14.1 Principles of Enhanced Backscattering

Overview and Further ReadingAs light is scattered from a random medium, much of it is scatterednearly uniformly in all directions and is referred to as diffuse reflec-tion. This can be observed by looking at a piece of white paper. As youmove your head around at different angles to the paper, the appar-ent brightness does not change much. If there is a flat surface to themedium, there may be a specular or mirror-like reflection in additionto the diffuse reflection. The specular reflection can be observed forpaper by holding the paper up between your eye and a light and look-ing at the reflection of the light at grazing incidence. An increase inbrightness of the reflection can be seen around the specular reflectionangle. Glossy paper has a proportionally greater specular reflection.

341


More rigorously, the function that describes the reflected light as afunction of angle is the bidirectional reflectance distribution function(BRDF). In the ideal limit of a diffuse reflector, the BRDF is uniformand the reflection does not depend on angle at all. This ideal diffusereflector is called a Lambertian reflector. Diffuse white objects withonly minuscule specular reflection such as paper, white reflectancestandards, or clouds are said to be almost Lambertian.

The way in which light scatters from a medium can contain awealth of information about the properties of that medium. Whenstudying the backscattered light from random media, it is usually im-portant to separate the specular reflection from the diffuse reflection.This is accomplished by tilting the surface relative to the angle ofincident illumination to send the specular reflection off to one side.

For random media, the BRDF is typically close to uniform in thebackscattered direction. Surprisingly, however, there can be a peak inintensity in the retroreflection direction. This phenomenon is calledenhanced backscattering (EBS) or coherent backscattering (CBS).

This peak in intensity can be explained in several ways. Histori-cally, the phenomenon has been framed in the context of condensedmatter physics. From this perspective, the phenomenon is closely re-lated to Anderson localization, which predicts that the quantum me-chanical wave nature of particles can prevent diffusion of electrons incertain random lattices. Anderson predicted this phenomenon in 1958[1], and later a more relaxed version called “weak localization” wasintroduced. In 1971, de Wolf discussed a similar phenomenon for elec-tromagnetic waves reflecting from atmospheric turbulence [2]. Thenin 1983–1984 Kuga, Tsang, and Ishimaru reported a retroreflectionfrom a dense suspension of spherical beads [3, 4], and in 1985 vanAlbada and Lagendijk reported the observation of weak localizationof light in a random medium [5]. Akkermans et al. described a theo-retical study of EBS in 1986 and from there an explosion of papers canbe found in the literature describing various aspects of EBS [6]. Figure14.1 shows a schematic of light scattering from a random mediumwith larger arrows corresponding to relatively stronger reflections inthe specular and retroreflection directions.

Theory of EBSRigorous theoretical treatments of EBS can be found in many papersand books [7–11]. One particularly good reference is chapter 14 of“Multiple Scattering of Light by Particles” by Mishchenko et al. [12].These descriptions make use of many ideas from condensed matterphysics. Another way to explain the phenomenon is based on inter-ference of scattered rays (or waves) and may be easier to interpretfor those with less background in condensed matter physics. In this

343E n h a n c e d B a c k s c a t t e r i n g a n d L E B S S p e c t r o s c o p y

Randommedium

FIGURE 14.1 Light scattered from a random medium is scatterednonuniformly as a function of angle. The scattering function is called thebidirectional reflectance distribution function (BRDF) and includes specularand diffuse reflections. Around the retroreflection angle, there is often anarrow peak in intensity due to enhanced backscattering (EBS).

section, this simplified conceptual description and theory based onthe interference of light waves is outlined.

Conceptually, the principle of EBS is that when a beam of lightenters a scattering medium, bits of it are diffusely scattered in alldirections, but in the reverse direction there is an increase in intensitydue to constructive interference. Imagine that a diffusely scatteringbody (turbid medium) is illuminated by a plane wave and we followa scattered fragment of the beam as it bounces around in the medium.By connecting the scattering points with a line segment, we can definea scattered ray. This ray follows a random path and eventually exits. Insome cases, the ray may happen to exit in the backward direction 180◦

from the angle of incidence as shown in Fig. 14.2. The illuminationis a collimated set of parallel rays, so when a ray exits in the reversedirection, there must be an inbound ray traveling in the exact oppositedirection that enters the medium at the point of the exiting ray. As lightpropagation is reversible, the inbound ray must follow the same pathas the first ray, but in the opposite direction, exiting where the first rayentered. Because these two rays travel the same path, they must travelthe same distance and therefore have the same optical pathlength orphase. If these rays are brought together with a lens, they will interfereconstructively in the reverse direction.

In reality, these rays are just conceptual quantities describing aportion of a scattered wave. Each time a part of the wave scatters,a new wavelet is formed that diverges from the scatterer. The ray is


Random media (tissue)

FIGURE 14.2 A ray entering a scattering medium and exiting in the reversedirection antiparallel to the illumination will be coincident with a second raytraveling in the opposite direction. Because light propagation is reversible,this ray will follow the same path through the medium and exit where the firstray entered. This ray pair will have the same optical path and hence the samephase allowing for constructive interference in the reverse direction.

simply a line following the propagation of some part of the scatteredand rescattered wave. When the ray exits, it does not exit only at asingle exit angle, but also exits as a wave with portions traveling anddiffracting in all directions. Because of this, the exiting ray does notneed to exit exactly at 180◦ to form a ray pair.

The pair of counter-propagating rays forms a pair of exit rays withthe same phase separated by some transverse distance. This pair ofrays can be called a time-reversed path pair because the propagationof one ray looks just like the propagation of the other ray if time werereversed. This ray pair acts much like a double pinhole, and the re-sulting interference pattern is a cosine diffraction pattern with fringespacing determined by the wavelength and the distance between thepinholes. The random medium produces many path pairs with dif-ferent separations, and so there are many diffraction patterns withdifferent orientations and fringe spacings.

The cosine fringe patterns from all the path pairs add up to formthe backscattered light distribution as shown in Fig. 14.3. Althoughthe phase of each path in a path pair is the same, different path pairsgenerally have different lengths and hence different phase from oneanother. As each pair of pinholes has a different phase, the diffractionpattern from each is statistically independent and on average can besummed incoherently. At the retroreflection angle (180◦ from the angleof incidence), the fringe patterns are always maximum (bright fringe)and the sum of all these fringe patterns will also be a maximum.


−300 −200 −100 0 100 200 3000

1

2Path pairs

Radius (µm)

−0.015 −0.01 −0.005 0 0.005 0.01 0.0150

0.5

1Fringes from each path pair

−0.015 −0.01 −0.005 0 0.005 0.01 0.0150

1

2Incoherent sum of fringes (normalized)

Angle (rad)

FIGURE 14.3 Each coherent path pair can be thought of as a double pinhole.Each pair contributes a characteristic cosine fringe pattern. When these fringepatterns are added incoherently, the result is a peak at the retroreflectionangle with twice the intensity of the background at larger angles.

However, at other observation angles, some fringe patterns cast abright fringe while others cast a dark fringe. The sum of all fringepatterns at these larger observation angles will be half that at theretroreflection angle. This is the fundamental reason for the intensitypeak in the retroreflection direction.

The shape of the EBS peak is determined by the probability distri-bution, P(r, �), of the exit position relative to the entry points. Neglect-ing the incoherent background, the Fourier transform of P(r, �) givesthe EBS peak, which for rotationally symmetric distribution, reducesto the one-dimensional Fourier–Bessel transform:

IEBS(�) = FT{P(r, �)} =∫ ∞

02�r P(r )J0(rk sin(�))dr (14.1)

The notation used here is that the one-dimensional function P(r )is a slice along some direction of the two-dimensional function P(r, �).In the limit of long traveling rays, the distribution P(r ) is given by the


so-called photon diffusion solution to the radiative transfer equation.In this limit, the shape of the EBS peak was worked out theoreticallyby Akkermans et al. for isotropic scattering and is described by

IEBS(�) = 38�

(1 + 2z0

l+ 1

(1 + lk�)2

(1 + 1 − exp(−2z0k�)

lk�

))(14.2)

where z0 is a constant, k is the wave number, and l is the mean freepath [6]. Figure 14.4 shows a plot of Eq. (14.2).

Although the double pinhole explanation does a good job of em-bodying the major features of EBS, there are a few things to note.First, the description has not included the effect of single scattering.The fraction of light that is scattered only once is called the singlescatter fraction. This value depends on the properties of the scatteringmedium. Single scattered light cannot contribute to low-coherence en-hanced backscattering (LEBS), because there is no separation of thepath pairs. The effect of the single scatter fraction is to reduce the en-hancement factor from the theoretical limit of twice the backgroundto some smaller value between one and two. Similarly, this does notinclude the effect of polarization (or depolarization) of the scatteredlight.

The other deviation from the ideal case is the effect of speckle. EBSis a coherent phenomenon, and typically, the illumination is a lasersource with very long temporal coherence. As with any randomly

−1 −0.5 0 0.5 11

1.2

1.4

1.6

1.8

2

Angle (deg)

Inte

nsity

(no

rmal

ized

to b

ackg

roun

d)

FIGURE 14.4 An example of a theoretical EBS peak calculated from Eq.(14.2) with parameters l = 20, k = 10, and z0 = 7. The values werenormalized to the value at large angles.


scattered temporally coherent light, a major feature is highly pro-nounced speckle. This speckle often dominates the EBS effect, ob-scuring the observation of the EBS peak. In the path-pair descriptionabove, the fringe pattern from each coherent path pair was added inco-herently, but when the temporal coherence is very large and the pathsare stationary, the sum is actually coherent. To suppress the effect oflaser speckle, many ensemble configurations of the scattering pathsmust be averaged. This can be accomplished by taking many inde-pendent measurements and averaging or by spinning or moving thesample during the integration time of the detector. For liquid samplessuch as bead suspensions, this averaging is accomplished for mostpractical exposure times by the Brownian motion of the scatteringparticles.

The EBS peak is usually characterized by two values, the enhance-ment factor E (ratio of the peak to the background) and the width W(full width at half maximum). The enhancement factor depends onthe single scatter fraction and on the depolarization ratio, which inturn depends on the type of scattering. The width is proportionalto the wavelength and inversely proportional to the transport meanfree path. Generally, the width is approximately 2/(3kl ′s), where l ′s =ls/(1 − g) is the transport mean free path and g is the anisotropy factorcalculated as the average cosine of the scattering angle for the medium.

Applications of EBSBecause the shape (width and enhancement factor) of EBS depends ona medium’s scattering properties, it can be used as a means to charac-terize scattering media. In practice, EBS has been used to characterizematerials ranging from industrial solids to astronomical objects. EBSfrom biological tissue was first observed by Yoo et al. [13], and theestimation of optical properties using EBS was performed by Yoonet al. [14]. However, application to tissue characterization has provendifficult due to speckle and the large value of l ′s, resulting in a verynarrow peak.

14.2 Low-Coherence Enhanced BackscatteringThere are several limitations to the EBS technique, which make its usechallenging for characterizing biological materials. First, the transportmean free path in tissue is typically quite large and can exceed mil-limeters. This results in an extremely narrow EBS peak on the orderof 0.001◦ and such a narrow peak is difficult to detect, much less re-solve. Second, the laser speckle from the background usually obscuresthe peak. Many independent measurements are needed or a movingsample is required to reduce the speckle and allow observation of theEBS peak. These challenges have been mitigated by the development


of a related technique called low-coherence enhanced backscattering(LEBS) [15, 16]. LEBS makes use of a source with partial spatial coher-ence to broaden the peak and reduce speckle. The technique employsa white light source that allows the study of the wavelength depen-dence of the effect and enables more information to be extracted aboutthe material properties. The finite spatial coherence also has the effectof limiting the interaction depth of the light. This effect is of great im-portance in characterizing stratified materials such as tissue becauseit provides a means to isolate the signal from a layer, that is, the ep-ithelium where many cancers originate.

Enhanced Backscattering of Partially Coherent LightThe fundamental difference between EBS and LEBS is the use of par-tially spatial coherent illumination. In the case of EBS, the illuminationbeam is a highly coherent plane wave. As such, there is no restrictionon the lateral separation of ray pairs that can interfere. With LEBS, onthe other hand, the illumination beam has a finite spatial coherencelength, and the degree of interference of ray pairs is reduced as theseparation increases.

One way to think of the effect of spatial coherence is to considerthat the P(r ) distribution is effectively reduced by the coherence func-tion C(r ). The LEBS peak is then the Fourier transform of P(r ) × C(r ).The resulting effective ray distribution is narrower, and so the LEBSpeak is wider than the EBS peak from the same scattering medium.Conceptually, the effect is to limit the contribution of larger ray sepa-rations.

ILEBS(�) = FT{P(r )C(r )} =∫ ∞

02�r P(r )C(r )J0(rk sin(�)) dr (14.3)

An alternative way to think of the effect of partial spatial coher-ence is to consider LEBS as the superposition of many EBS peaks fromeach point within the source. Superposition implies that the LEBSpeak can be found by convolving the EBS peak with the source dis-tribution. Each point of the source is incoherent and independent ofeach other point, so each point produces its own EBS peak and theseare all summed up in the end. Because the coherence function C(r ) isthe Fourier transform of the source function S(�) (van Cittert-Zerniketheorem), the convolution can be done inside the Fourier domain andbecomes a multiplication. Hence, the two ideas are mathematicallyidentical, but each perspective has advantages when considering var-ious aspects of LEBS.

ILEBS(�) = FT{P(r ) × C(r )} = FT{P(r )} ∗ FT{C(r )} = IEBS(�) ∗ S(�)

(14.4)


−1 −0.5 0 0.5 11

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

Inte

nsit

y (n

orm

aliz

ed to

bac

kgro

und)

EBS: lS’=20LEBS: LSC=32LEBS: LSC=24

LEBS: LSC=18

−0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.41

1.005

1.01

1.015

1.02

1.025

1.03

1.035

1.04

1.045

1.05

Angle (deg)Angle (deg)In

tens

ity

(nor

mal

ized

to b

ackg

roun

d) EBS: TheoreticalMC: g=0.10MC: g=0.92

FIGURE 14.5 (Left) Reduced EBS peaks computed by convolution of the theoreticalEBS peak from Ref. [6] with a circ() function corresponding to the source size. TheEBS peak was generated using the same parameters as the previous EBS curve. Fora 500-nm wavelength, the spatial coherence length corresponding to each angularsource size is shown in the legend. When the spatial coherence length is on theorder of the transport mean free path, the effect is primarily a reduction in intensityat small angles. (Right) In the low-coherence regime, the transport mean free path(500 �m here) is much larger than the spatial coherence length (50 �m). Thetheoretical EBS peak (dashed) is shown for reference along with the peaks computedfrom Monte Carlo simulation of P (r ) for two different values of anisotropy factor g.

A first step toward LEBS from EBS is to convolve the theoreticalcurve given by Eq. (14.2) with a finite extended source. This result (Fig.14.5, left) is a broader peak with some of the characteristics of LEBS.However, this is not sufficient to explain LEBS, because Eq. (14.2) wasderived for the “diffusion” regime and does not accurately representP(r ) for small values of r . Because LEBS peak shape is dominated bythe shape of P(r ) at small r , the resulting LEBS peak is sensitive tofactors such as anisotropy g (see Chap. 1 for discussion of g), whichdoes not appear in Eq. (14.2). In the diffusion regime, g only changesthe effective length scale, but does not change the shape of the peak.In LEBS, the shape is very dependent on changes in g. For example,on the right of Fig. 14.5, two peaks plotted from Monte Carlo simu-lations are shown with the same value of transport mean free path,l ′s = 500 �m, and spatial coherence, Lsc = 50 �m, but different valuesof g. The change in the peak shape is clear.

Observation of Low-Coherence Enhanced BackscatteringDeveloping an instrument for observing LEBS is in many ways muchsimpler than for EBS. A diagram showing the important componentsof an LEBS instrument is shown in Fig. 14.6. The instrument mustdeliver partially spatially coherent light to the sample and collect thescattered light with good angular resolution. The illumination beamhas a spatial coherence determined by the angular distribution of thesource. A small aperture is illuminated incoherently, for example, by a


Tis

sue

Incoherentsource

Beamsplitter

Imagingspectrometer

Lens

Aperture

FIGURE 14.6 Diagram of a system for observing LEBS. The incoherent sourcecan be an arc lamp focused onto the aperture. The aperture size and focallength determine the spatial coherence length. A relative tilt between thebeam and the sample surface ensures that the specular reflection does notobscure the LEBS peak.

Xenon arc lamp. The light diverging from this aperture is collimated,and the spatial coherence length is determined by the collimating lensfocal length, wave number, and the aperture radius,Lsc = f/(kr ). Theillumination beam is sent through a beamsplitter to the sample. Ide-ally, the sample is placed close the exit pupil of the illumination system.The scattered light is then collected by a lens and focused onto a detec-tor. For LEBS spectroscopy, the detector is an imaging spectrometer.The collection lens acts to map the angular distribution of scatteredlight onto the detector so that each pixel element corresponds to areflection angle from the sample.

Characteristics of LEBSThe LEBS peak differs from a typical EBS peak in several key ways. Themost obvious change relative to EBS is a significantly broader peakand a reduction in speckle. The broadening of the peak is a result ofthe convolution with the extended source as described previously.

The speckle that normally obscures the peak in the case of a sin-gle ensemble measurement with EBS is the result of coherent ratherthan incoherent summation of the fringe patterns produced by thepath pairs. The incoherent summation of the fringe patterns is validwhen backscattering is obtained for many ensembles or many config-urations of the scattering medium. In EBS, this can be accomplishedby moving the sample during the integration of the signal (spinningsample, Brownian motion, etc.) or by taking many measurements with


small changes in sample position and adding the resulting intensities.In the case of LEBS, this is accomplished automatically because withinan illumination spot, there are many independent coherence areas.Each coherence area contributes an ensemble to the total intensityand results in a reduced speckle. Thus, a single LEBS reading aver-ages such multiple independent coherence volumes and easily revealsan enhanced backscattering peak without any need for ensemble orconfiguration averaging.

Another key aspect of LEBS is related to the absence of signal fromlarge path separations. The effect of limiting large path separationshas the additional benefit of limiting the depth of penetration [17].Because the path separation is statistically related to the path depthfor a given medium, the effect of limiting the path separation is toadditionally limit the depth of penetration of the rays. The problem hasbeen studied using a combination of analytical methods and MonteCarlo simulations [18], and it was shown that the depth of penetrationhas a strong dependence on Lsc for values of Lsc � ls’. Monte Carlosimulations confirmed that the depth of penetration can be limited tomuch less than the transport mean free path by using a short spatialcoherence length.

zmp ∝ g1/3

(1 − g)2/3

(ls�L2

sc

)1/3(14.5)

This aspect of LEBS is quite advantageous for studying biologicaltissues that are inherently stratified. Given a tissue’s average scatteringproperties ls and g, the penetration depth can be tuned to the desiredvalue by adjusting the spatial coherence Lsc.

It is also important to note that the Fourier-transform relationshipbetween the LEBS peak and P(r ) implies a close relationship betweenangle in the peak and ray separation r . In other words, the signal thatcontributes to LEBS peak at a certain angle is due to ray pairs up toa corresponding separation r . The statistical relationship between rand the depth z that a ray reaches relates the angle to the depth ofpenetration. By analyzing the signal as a function of angle, there is adegree of depth profiling inherent in a given LEBS measurement [17].

Finally, a major advantage of LEBS is the fact that it can be ob-tained using a broad range of wavelengths simultaneously. The use ofa white light source enables spectroscopic studies of LEBS. Figure 14.7shows an example of LEBS spectral measurement including the an-gular dependence on one axis and spectral dependence on the other.Characterizing the scattering properties of a medium as a functionof wavelength can provide an abundance of information about thescattering medium (see Chap. 2, “Light Scattering from ContinuousRandom Media,” in this book). Typically, the LEBS spectra from bio-logical tissue exhibit a trend as a function of the wavelength, and the


450500

550600

650

−1

−0.5

0

0.5

10

0.005

0.01

0.015

0.02

Wavelength (nm)

LEBS peak from tissue

Angle (deg)

Inte

nsity

(a.

u.)

FIGURE 14.7 An example of a measured LEBS peak showing the dependenceon angle and wavelength. See also color insert.

slope depends on the overall size distribution of intraepithelial struc-tures contributing to the backscatters [19]. LEBS spectroscopic signalscan potentially be more sensitive to fluctuations of refractive indexon various scales ranging from subcellular compartments, large or-ganelles, to cells because it originates from the self-interference effectwithin the localized coherence volume [20, 21].

Theory of LEBS in TissueModeling LEBS from biological tissue can be broken down into threetasks. (1) Derive the scattering properties (ls , g) of a medium from thestatistical parameters that describe the refractive index distribution.(2) Relate the optical properties to a probability distribution P(r ) ofray paths exiting the medium. (3) Convert the path distribution to anangular distribution of scattered light.

Task (1) was discussed in Chap. 2, “Light Scattering from Contin-uous Random Media,” and has an analytical solution that dependson the model used to describe the medium. Task (3) is also well char-acterized and can be analytically solved using the Fourier-transformrelationships described previously. The difficulty lies in task (2) whereno analytical solution yet exists for light transport over short dis-tances. In the limit of large path separations, the solution converges tothe diffusion approximation, but given the significance of short path


separations in LEBS due to limiting effect of the spatial coherencelength, the diffusion approximation does not apply. Although someapproximations can be made [22], the most robust way to solve theproblem is to employ numerical methods such as Monte Carlo simu-lations [23].

14.3 Applications of Low-Coherence EnhancedBackscattering Spectroscopy

Colorectal CancerColorectal malignancies rank as one of the leading causes of can-cer deaths in the United States, underscoring the public health im-perative for developing effective cancer prevention strategies. Thenumber of new cases of colorectal cancer (CRC) was estimated to be108,070 in 2008, resulting in 49,960 deaths [24]. The lifetime risk ofan American developing colorectal cancer is as high as 6%. Fortu-nately, colon cancer is eminently curable when diagnosed early, al-though the disease is usually asymptomatic at these early stages. Thetypical symptoms such abdominal pain, change in bowel habits, andweight loss only present themselves at advanced stages. Indeed, morethan half the newly diagnosed colorectal cancer cases already havemetastasis. Thus, widespread asymptomatic population screening isof paramount importance in reducing colorectal cancer fatalities.

There are a number of endoscopic, radiological, or fecal analysis-based screening modalities available. Colonoscopy has been demon-strated to significantly decrease colon cancer occurrence by re-moving precursor adenomas. The total mucosal evaluation withcolonoscopy is the “gold standard” for colon cancer screening. Al-though colonoscopy is clearly the most effective modality of cancerprevention, there are several issues that preclude its widespread usefor population screening. Screening the entire at risk population (∼60million Americans older than 50 yr) with colonoscopy is impracticalfor a variety of reasons including expense, lack of sufficient numbersof trained endoscopists, patient reluctance, and complication rate. Inaddition, even in expert hands, sensitivity is not perfect with a missrate of more than 25% for adenomas [25]. A recent report demonstratedthat among experienced endoscopists there was a two-fold differencein an adenoma detection rate [26], underscoring the difficulties in pro-viding high-quality endoscopic evaluation for the entire population.Unfortunately, the most widely used initial screening techniques suchas fecal occult blood test (FOBT) suffer from low sensitivity [27]. As aresult, approximately only one-third of patients are diagnosed as hav-ing colon cancer at a localized stage [24]. Therefore, the developmentof novel risk-stratification techniques that help clinicians to identifypatients who will benefit from colonoscopy is imperative [28].


Since the concept of “the field effect” in oral cancers was first pro-posed by Slaughter in 1953 [29], results from numerous studies havevalidated the concept in almost all types of epithelial cancers. Thefield effect is in fact increasingly considered a general phenomenonof most types of epithelial cancers including CRC [30, 31]. Some risk-stratification approaches in colon cancer utilize the “field effect” con-cept, the proposition that the genetic/environmental milieu that re-sults in a neoplastic lesion in one area of the colon should be detectablethroughout the colon [30]. For example, analysis of the uninvolved(histologically normal) mucosa in the rectum for use as a marker ofthe field effect could have significant implications for CRC screening.Currently, the most widely used marker of the field effect is the dis-tal colon adenomatous polyps detected by examining the rectum andlower colon using flexible sigmoidoscopy. However, flexible sigmoi-doscopy suffers from both low sensitivity and low positive predictivevalue. Less than half of subjects harboring proximal adenomas have asentinel adenoma within reach of a flexible sigmoidoscope [32]. There-fore, the development of technologies for the detection of the fieldeffect, which are sensitive, cost-effective, and minimally invasive, isof great benefit.

There are currently two well-established animal models of coloncancer: (1) Azoxymethane (AOM)-treated rats as a model system forcolon cancer and (2) multiple intestinal neoplasia (MIN) mouse modelof intestinal tumorigenesis, replicating the human syndrome, famil-ial adenomatous polyposis. These animal models involve multistepprocesses in which cells accumulate multiple genetic, molecular, andmorphological alterations as they progress to a more malignant phe-notype. Among the multistep processes, emerging evidence indicatesthat the aberrant crypt foci (ACF) in the human colon may be theprecursor of the adenomatous polyp. Progression through the ACF,adenoma, and carcinoma sequence is governed by specific cellular andgenetic events. For instance, inhibition of apoptosis is a criticalearly step in colon carcinogenesis, enabling the otherwise short-livedcolonocyte to acquire the requisite mutations for neoplastic trans-formation, while cell proliferation in the uninvolved mucosa fostersclonal expansion of the initiated colonocytes. There are numerous mu-tations that accumulate leading to a progression through the multistepprocesses. Such events in human colon carcinogenesis are accuratelyreplicated in the AOM-treated rat model. Approximately 50% of an-imals treated with AOM will develop adenomas or carcinomas, andthus the AOM-treated rat is a robust model of human colon cancer.In the MIN mouse model, adenomatous polyposis coli (Apc) trun-cation leads to spontaneous intestinal tumorigenesis, thus replicatingthe human syndrome, familial adenomatous polyposis. However, thismodel is limited by the fact that adenomas are preferentially locatedin the small intestine with very few occurring in the colon. The AOM


rat and MIN mice models are complementary because they describeenvironmental and genetic risks of cancer development, both of whichplay an important role in human CRC development.

LEBS Detection of Early Cancerous Alterationsin Colon CarcinogenesisThere have been a series of experimental studies that have utilizedLEBS for detecting the field effect. The first experiments measuredchanges in LEBS from the epithelium of the AOM-treated rat modelof colon cancer [15–17]. These findings indicated that marked ar-chitectural aberrations can be optically detected with LEBS. The de-tected changes preceded development of conventional morphologicaland cellular markers of colon carcinogenesis. The progression of thechanges measured with LEBS mirrored the progression of the dis-ease, yet the measurements were collected from normal uninvolvedmucosa. In a later study of LEBS in the MIN mouse model, the spectralsignatures were also found to be dramatically altered in the putativelyuninvolved (i.e., histologically normal) mucosa at an early time pointof carcinogenesis [33]. These changes were highly correlated with thetemporal progression of the animal model and were spatially localizedto the proximal small intestine where the genetic mutation is knownto have the most significant effect at later time points. The findingsfrom animal models were thereafter corroborated with ex vivo hu-man studies, where changes in the LEBS signal from the uninvolvedmucosa were compared to the presence of adenomatous lesions else-where in the colon [19, 34]. In a report of the human study, the spec-tral LEBS signal was characterized by several parameters, includingwidth, enhancement, spectral slope, and correlation decay rate [34].Although the rectal LEBS signal could be affected by the proximityto an adenoma (i.e., adenoma location in proximal colon vs. distalcolon), the rectal LEBS marker was significantly altered in patientsharboring neoplasia, irrespective of location. LEBS signals correlatedmost highly with the presence of advanced adenomas. These lesionshave the largest chance of progressing into cancer and are clinicallythe most significant precancer for detection and removal. It was foundthat LEBS could detect advanced adenomas with 100% sensitivity, 80%specificity, and an 89.5% area under the receiver operator characteris-tic curve. Indeed, the technique shows great promise for applicationsof early CRC screening. It is important to recognize that changes inthe scattering properties of tissue can have an observable effect onLEBS parameters even when the change is not readily observable us-ing traditional optical microscopy or histology. LEBS quantifies theproperties of a large epithelial area of tissue, equivalent to the areaof the illumination spot, while typical microscopy techniques quali-tatively image a smaller field of view.


As an example of the information obtained in the LEBS signal, letus examine the spectral dependence of the LEBS enhancement, alsoreferred to as the LEBS spectral slope. Monte Carlo simulations haveshown that enhancement is inversely proportional to the transportmean free path for weakly scattering media [22]. According to scatter-ing theory discussed in Chap. 2, “Light Scattering from ContinuousRandom Media,” the spectral dependence of the reduced scatteringcoefficient (the inverse of the transport mean free path) and, therefore,LEBS enhancement factor E is related to the type of the refractive in-dex (and, therefore, mass density) correlation function. If the spectraldependence is of the form of a power law, then �′

s ∝ 1/

4−2m, wherem is a parameter defining the type of the correlation function. For thisequation to be valid, two conditions have to be satisfied. (i) The lengthscale of refractive index correlation lc is large compared to 1/k (k isthe wave number): klc � 1. This condition is equivalent to the strongforward-scattering regime and is typically satisfied in tissue. (ii) Pa-rameter m < 2. For m > 2, �′

s loses its dependence on wavelength forlarge klc.

The type of refractive index correlation given by m is describedin detail in Chap. 2. We remind the reader that m < 3/2 correspondsto the mass fractal density correlation with the mass fractal dimen-sion D = 2m: �′

s ∝ 1/4−D. Mass fractal dimension should not be con-fused with other definitions of the fractal dimension: values of D canonly vary between 0 (for a point-like objects) to 3 for a space-fillingmass density. Experimentally determined value of m can, in princi-ple, exceed 3/2. Values of m such that 3/2 < m < 2 correspond to amedium with a stretched exponential mass density correlation, m = 2corresponds to an exponential correlation, and, finally, a mediumwith m >> 1 is described by a Gaussian mass density correlation.For m > 2, the spectral dependence flattens out and the type of themass density correlation can no longer be accurately deduced fromthe power law–dependence of the spectrum alone. For a small spectralrange, the exponent can be measured by normalizing the derivative,2m − 3 = (dE/d)(/E) (this is because E ∝ LSC�′

s ∝ 1/3−2m). LEBSdata suggest that in colonic mucosa m < 3/2 and, thus, (dE/d) isa measure of the mass fractal dimension of tissue: (dE/d)(/E) =D − 3.

As a demonstration of the sensitivity of LEBS to these histologi-cally unapparent changes in D that occur during precancerous devel-opment, we adapt work from animal model and human studies thathave been carried out examining the spectral slope of LEBS [34, 35].Figure 14.8 is an adapted result from animal model studies showingthe change in mass fractal dimension due to precancerous alterations.The 6-wk-old MIN mice have a significantly larger fractal dimensionthan the age-matched Wild Type control mice (p < 0.005) as shown in


1.5

1.7

1.9

2.1

2.3

2.5

Control AOM

Mas

s fr

acta

l di

men

sion

1.5

1.7

1.9

2.1

2.3

2.5

Wild type MIN

Mas

s fr

acta

l di

men

sion

830.0 = p2400.0 = p

(b)(a)

FIGURE 14.8 Comparison of mass fractal dimension measured with LEBSfrom animal models of colorectal carcinogenesis. A significant increase in themass fractal dimension from LEBS measurements was seen for 6-wk-old MINmice (a) and AOM-treated rats (b). (Source: Figure adapted from Ref. [35].)

panel a . The increase in fractal dimension is also seen 2 wk after AOMtreatment in rats (panel b). In both models, the early time point of themeasurement is prior to the development of adenomas and indicatesthat architectural changes precede the onset of lesion formation. Thesechanges are observed in tissue spanning a large area of the colonic mu-cosa and are not likely to be localized to the site of a future adenoma.One can therefore infer that LEBS has recorded a quantitative measureof the field effect.

Optical detection of the field effect of colorectal carcinogene-sis would have significant clinical implications, especially if accom-plished at an easily accessible location such as the rectum. A recent

2.2

2.4

2.6

2.8

No dysplasia Advancedadenoma

Mas

s fr

acta

l di

men

sion p = 0.012

FIGURE 14.9 Comparison of mass fractal dimension measured from LEBSsignal in rectal human biopsies that were obtained during routinecolonoscopy. A significantly larger fractal dimension (p = 0.012) wasobserved in patients harboring advanced adenomatous lesions than controlpatients where no dysplastic changes were observed during colonoscopy.(Source: Figure adapted from Ref. [34].)


study of the field effect has quantified rectal LEBS changes associ-ated with the presence of adenomatous lesions elsewhere in the colon[34]. This 219-patient study reported significant associations betweenLEBS measurements and the presence of adenomas elsewhere in thecolon. Because adenomas are one of the best available markers of thefield effect surpassed only by full-fledged cancer, it is again reason-able to deduce that the LEBS measurement is quantifying the fieldeffect. In Fig. 14.9, the average value of the mass fractal dimension isshown to be significantly different between patients with no dysplas-tic findings as compared with patients with colonoscopic findings ofadenomatous lesions (p = 0.012). As was seen with the animal mod-els, measurements in the presence of the field effect again indicate alarger mass fractal dimension. Accurate optical detection of the fieldeffect could have significant implications for CRC screening. The de-velopment of a fiber-optic probe to collect an LEBS signal may lead toa simple risk-stratification method to identify patients who will ben-efit from colonoscopy. This may enable a primary care physician todetermine a need for colonoscopy during a patient’s annual physicalexamination.

References1. P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys Rev

Lett 109, 1492–1505 (1958).2. D. A. de Wolf, “Electromagnetic reflection from an extended turbulent medium:

cumulative forward-scatter single-backscatter approximation,” IEEE Trans AP-19(2) 254–262 (1971).

3. Y. Kuga and A. Ishimaru, “Retroreflectance from a dense distribution of spher-ical particles,” J Opt Soc Am A 1, 831–835 (1984).

4. L. Tsang and A. Ishimaru, “Backscattering enhancement of random discretescatterers,” J Opt Soc Am A 1, 836–839 (1984).

5. M. P. van Albada and A. Lagendijk, “Observation of weak localization of lightin a random medium,” Phys Rev Lett 55, 2692–2695 (1985).

6. E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent backscattering of light bydisordered media: analysis of the peak line shape,” Phys Rev Lett 56, 1471–1474(1986).

7. J. P. Fouque, Diffuse Waves in Complex Media. Kluwer Academic Publishers,Dordrecht, The Netherlands (1999).

8. W. Brown and K. Mortenson, Scattering in Polymeric and Colloidal Systems, CRCPress, London (2000).

9. P. Sebbah, Waves and Imaging Through Complex Media. Kluwer Academic Pub-lishers, Dordrecht, The Netherlands (2001).

10. B. van Tiggelen and S. Skipetrov, Wave Scattering in Complex Media: From The-ory to Applications. Kluwer Academic Publishers, Dordrecht, The Netherlands(2003).

11. P. Sheng, Introduction to Wave Scattering, Localization and Mesoscopic Phenomena,Springer-Verlag, Heidelberg (2006).

12. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light byParticles. Cambridge University Press, Cambridge, MA (2006).

13. K. M. Yoo, G. C. Tang, and R. R. Alfano, “Coherent backscattering of light frombiological tissues,” Appl Opt 29, 3237–3239 (1990).


14. G. Yoon, D. N. Ghosh Roy, and R. C. Straight, “Coherent backscattering inbiological media: measurement and estimation of optical properties,” ApplOpt 32, 580–585 (1993).

15. Y. L. Kim, Y. Liu, V. M. Turzhitsky, H. K. Roy, R. K. Wali, and V. Back-man, “Coherent backscattering spectroscopy,” Opt Lett 29(16), 1906–1908(2004).

16. Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, and V. Backman, “Low-coherentbackscattering spectroscopy for tissue characterization,” Appl Opt 44(3), 366–377 (2005).

17. Y. L. Kim, Y. Liu, V. M. Turzhitsky, R. K. Wali, H. K. Roy, and V. Backman,“Depth-resolved low-coherence enhanced backscattering,” Opt Lett 30(7), 741–743 (2005).

18. H. Subramanian, P. Pradhan, Y. L. Kim, and V. Backman, “Penetration depthof low-coherence enhanced backscattered light in subdiffusion regime,” PhysRev E 75(4 Pt 1), 041914 (2007).

19. H. K. Roy, Y. L. Kim, Y. Liu, R. K. Wali, M. J. Goldberg, V. Turzhitsky, J. Horwitz,and V. Backman, “Risk stratification of colon carcinogenesis through enhancedbackscattering spectroscopy analysis of the uninvolved colonic mucosa,” ClinCancer Res 12(3), 961–968 (2006).

20. Y. L. Kim, P. Pradhan, H. Subramanian, Y. Liu, M. H. Kim, and V. Backman,“Origin of low-coherence enhanced backscattering,” Opt Lett 31(10), 1459–1461(2006).

21. S. B. Haley, and P. Erdos, “Wave propagation in one-dimensional disorderedstructures,” Phys Rev B 45(15), 8572–8584 (1992).

22. M. Xu, “Low-coherence enhanced backscattering beyond diffusion,” Opt Lett33(11), 1246–1248 (2008).

23. H. Subramanian, P. Pradhan, Y. L. Kim, Y. Liu, X. Li, and V. Backman, “Photonrandom walk model of low-coherence enhanced backscattering (LEBS) fromanisotropic disordered media: a Monte Carlo simulation,” Appl Opt 45(24),6292–6300 (2006).

24. A. Jemal, R. Siegel, E. Ward, Y. P. Hao, J. Q. Xu, T. Murray, and M. J. Thun,“Cancer statistics, 2008,” CA Cancer J Clin 58(2), 71–96 (2008).

25. J. C. van Rijn, J. B. Reitsma, J. Stoker, P. M. Bossuyt, S. J. van Deventer, andE. Dekker, “Polyp miss rate determined by tandem colonoscopy: a systematicreview,” Am J Gastroenterol 101(2), 343–350 (2006).

26. W. Atkin, P. Rogers, C. Cardwell, C. Cook, J. Cuzick, J. Wardle, and R. Ed-wards, “Wide variation in adenoma detection rates at screening flexible sig-moidoscopy,” Gastroenterology 126(5), 1247–1256 (2004).

27. T. F. Imperiale, D. F. Ransohoff, S. H. Itzkowitz, B. A. Turnbull, M. E. Ross,and C. C. S. Grp, “Fecal DNA versus fecal occult blood for colorectal-cancerscreening in an average-risk population,” New Engl J Med 351(26), 2704–2714(2004).

28. H. K. Roy, V. Backman, and M. J. Goldberg, “Colon cancer screening—the good,the bad, and the ugly,” Arch Intern Med 166(20), 2177–2179 (2006).

29. D. P. Slaughter, H. W. Southwick, and W. Smejkal, “Field cancerization in oralstratified squamous epithelium: clinical implications of multicentric origin,”Cancer 6(5), 963–968 (1953).

30. B. J. M. Braakhuis, M. P. Tabor, J. A. Kummer, C. R. Leemans, and R. H. Brak-enhoff, “A genetic explanation of slaughter’s concept of field cancerization:evidence and clinical implications,” Cancer Res 63(8), 1727–1730 (2003).

31. G. D. Dakubo, J. P. Jakupciak, M. A. Birch-Machin, and R. L. Parr, “Clinicalimplications and utility of field cancerization,” Cancer Cell Int 7(2) (2007).

32. J. M. E. Walsh and J. P. Terdiman, “Colorectal cancer screening—scientific re-view,” JAMA 289(10), 1288–1296 (2003).

33. H. K. Roy, Y. L. Kim, R. K. Wali, Y. Liu, J. Koetsier, D. P. Kunte, M. J. Goldberg,and V. Backman, “Spectral markers in preneoplastic intestinal mucosa: an ac-curate predictor of tumor risk in the min mouse,” Cancer Epidemiol BiomarkersPrev 14(7), 1639–1645 (2005).


34. H. K. Roy, V. Turzhitsky, Y. L. Kim, M. J. Goldberg, P. Watson, J. D. Rogers, A.J. Gomes, A. Kromine, R. E. Brand, M. Jameel, A. Bogovejic, P. Pradhan, and V.Backman, “Association between rectal optical signatures and colonic neoplasia:potential applications for screening,” Cancer Res 69: 4476–4483 (2009).

35. Y. L. Kim, Y. Liu, V. M. Turzhitsky, H. K. Roy, R. K. Wali, H. Subramanian, P.Pradhan, and V. Backman, “Low-coherence enhanced backscattering: reviewof principles and applications for colon cancer screening,” J Biomed Opt 11(4),041125 (2006).

Index

Page numbers followed by f and t indicate figures and tables.

AAbsorbing boundary conditions

(ABCs), 53Absorption and Scattering by Small

Particles (Bohren/Huffman),23

Absorption coefficient, 14Acousto-optic modulator

(AOM), 255Albedo, 13a/LCI. See Angle-resolved

low-coherence interferometrya/LCI instrumentation

animal studies, 330–335,331t, 333f, 334f

frequency-domainimplementation,319–321, 320f

portable system, 321–322,322f

signal, processing ofcell nuclei, data

processing,323–325

phantoms, dataprocessing, 323

validation studieshuman esophageal

epithelium,335–337, 335f, 336f

a/LCI instrumentation,validation studies (Cont.)

in vitro cell studies,327–330, 327f,328f, 329f

polystyrenemicrospheres,325–327, 325f,326f

Alhasen of Basra, 3AMD. See Antimitotic drugsAngle-resolved low-coherence

interferometry (a/LCI),128–134, 314–319,330–333

Anisotropy coefficient, 14Antimitotic drugs (AMD),

230–235AOM. See Acousto-optic

modulatorAxis of symmetry, 44

BBackscattering, 19Barber, P. W., 25Beer-Lambert-Bouguer law,

145Bidirectional reflectance

distribution function (BRDF),342

361

362 I n d e x

Biological tissue, structure ofcell organization

overview, 8cytoskeleton, 7endoplasmic reticulum,

7epithelial cells, 8–9inner membrane, 7mitochondria, 6–7nuclear envelope, 5–6nucleolus, 6nucleus and, 5outer membrane, 7types of, 5

Blood flow, laser speckleimaging

functional activation,248–253

general comments, 241LSCI applications,

247–248MESI and, 253–258single-exposure, 242–247,

243f, 244fmeasurements, 245steps in, 245

Bohren, C. F., 23Booker-Gordon formula, 34Born, Max, 32Born approximation, 15–16, 31,

32BRDF. See Bidirectional

reflectance distributionfunction

CCerebral blood flow (CBF),

247CLASS, 156f, 157f. See Confocal

light absorption andscattering spectroscopic

Colorectal cancer (CRC),353–355

Computational lightscattering codes, summary of,23–27

Confocal light absorption andscattering spectroscopic(CLASS), 153–165, 154f, 159t,160f, 161f, 162f, 163f, 164f

Confocal reflectance microscopyangular dependence and,

172basic instrument, 180–182experimental data,

178–180, 179flight scattering in,

171–190literature for, 188–190Monte Carlo simulations,

182–188, 182f, 183f, 184f,185f, 187f

theory mapping, 177–178Connective tissue

collagen fibers and, 10identification of, 10structure of, 10

Continuous random media1D random media, 44–452D random media

mean differentialscattering codesection, 42–43

mean scatteringcoefficient,43–44

3D random media, 34fmean differential

scattering crosssection, 33–37, 36f,37f

mean scatteringcoefficient, 37–40,39f, 40f

simplifyingapproximations,40–42, 41f

introduction, 31–33media samples, generation

of, 45–47CRC. See Colorectal cancerCytoskeleton, 7

363I n d e x

Dda Vinci, Leonardo, 3DDA. See Discrete dipole

approximationDifferential cross section,

13Differential pathlength

spectroscopybasic concepts

general comments,293–294

main features,294–295, 295f

main properties,294–295, 295f

mathematicalanalysis, 297–299,298f

pathlength, 295–297,296f, 297f

clinical measurements,303–309, 306f, 307t, 308f,309f

DPS measurementsadditional features,

302–303, 304f,304t

confidence intervals,303

main features,299–302, 300f,301t, 302t

Dipole factor, 36Discrete dipole approximation

(DDA), 26Draine, B. T., 26

EEBS. See Enhanced

backscatteringElastic scattering spectroscopy

(ESS), 263Electron microscope (EM),

144Endoplasmic reticulum (ER),

7, 8

Enhanced backscattering (EBS)applications of, 347LEBS and

applications of,353–358

characteristics of,350–352, 352f

colon carcinogenesis,355–358, 357f

colorectal cancer,353–355

observation of,349–350, 350f

partially coherentlight, 348, 349

theory of, 352–353overview of, 341–42principles of, 341–358theory of, 342–347, 343f,

344f, 345f, 346fEpithelial cells

classification of, 8–9thickness of, 9types of, 8–9

Equiphase sphere (EPS), 20ER. See Endoplasmic reticulumESS. See Elastic scattering

spectroscopyEwald’s sphere, 17Extracellular matrix (ECM), 5,

195

FFarrell, Tom, 293Far-ultraviolet range (FUV), 145fCM. See Fluorescence confocal

microscopeFDTD. See Finite-difference

time-domainFecal occult blood test (FOBT),

353Fiberoptic probe (FOP), 264,

278Finite-difference time-domain

(FDTD), 21, 26–27, 45–47, 49,50, 51–53, 54–55, 118

364 I n d e x

Flatau, P. J., 26Fluorescence confocal

microscope (fCM), 180FOBT. See Fecal occult blood testFOP. See Fiberoptic probeForward scattering theorem, 13FUV. See Far-ultraviolet range

GGaussian model, 35, 42–43, 44,

45, 60–62, 61fGeneralized Multipole Techniques

for Electromagnetic and LightScattering, 26

General subcellular structure,135–137, 137f

Golgi apparatus, 7, 8Graphics processing unit (GPU),

27, 100

HHafner, Christian, 26Henyey-Greenstein phase

function, 35, 194, 270–272Hill, S. C., 25Hoekstra, A. G., 26Holographic optical coherence

imagingdigital holography,

223–225, 224fFourier-domain

holography, 221–222,222f

Huffman, D., 23Huygens-Fresnel principle,

189

IIBD. See Inflammatory bowel

diseaseILSA. See Inverse light scattering

analysisInflammatory bowel disease

(IBD), 264, 277Inner membrane, 7Interference structure, 19

Interferometric syntheticaperture microscopy (ISAM)

alternate acquisitiongeometric, 91

background of, 79–81, 79fbiological applications,

100–106clinical applications,

100–106compact forward model,

83–87, 86fcross-correlation

technique, 96cross-validation of ISAM,

97–98, 97fexperimental

implementation, 92–101general comments for,

77–78imaging tumor

development, 106inverse scattering

procedure, 89–90ISAM processing, 98–100,

99fnumerical simulations,

90–91, 91foptical biopsy, 102phase reference technique,

94–95, 95fphase registration

hardware solutions,93–94

postprocessing and,95–96

phase stability, 92–93physics of data

application, 81–83, 82fpractical limitations,

100–101rigorous forward model,

87–89surgical guidance,

102–106, 103f, 104f, 105ftheory of, 81–91three-dimensional ISAM,

96–97, 97f

365I n d e x

Inverse light scatteringanalysis (ILSA), 115, 120, 128,130

ISAM. See Interferometricsynthetic aperturemicroscopy

LLaser capture microdisection

(LCM), 196, 204Laser speckle contrast imaging

(LSCI), 241, 247–248, 249,250f

Laven, Philip, 23LCM. See Laser capture

microdisectionLEBS. See Low-coherence

enhanced backscatteringLevenberg-Marquardt

algorithm, 279Light Scattering by Particles:

Computational Methods(Barber/Hill), 25

Light scattering modelsapproximate solutions to,

15–22basics of, 10–15biological tissue, structure

of, 4–10cell biology and, 115–138computational light

scattering codes review,22–27

historical overview, 3–4introduction to, 3–4inverse light scattering

analysisill-conditioned

problem, 28nonuniqueness

problem, 27–28light scattering software

summary, 24tMaxwell’s equations and,

49–73Light scattering spectroscopy

(LSS), 143

Living tissue, motility-contrastimaging

dynamic light scatteringheterodyne, 217–219,

217fplanar, 215–216single-mode,

214–215, 215fspacial homodyne,

217–219, 217fvolumetric, 216

holographic opticalcoherence imaging,221–225, 227–229, 228f,229f

motility-contrast imaging,230–234, 231f, 232f

multicellular tumorspheroids, 226f

prospects of, 234–236,235f

Low-coherence enhancedbackscattering (LEBS), 346,348–353, 349f, 350f, 352f

LSCI. See Laser speckle contrastimaging

LSS. See Light scatteringspectroscopy

Lysosomal morphology,121–127, 123t, 125f, 126f

MMaxwell’s equations

FDTD modelingapplications

backscatteringsensitivity, 62–64,63f

Born approximationvalidation, 60–62,61f

Liu’s Fourier-basisPSTD technique,64

precancerouscervical cells,57–60, 58f, 59f

366 I n d e x

Maxwell’s equations, FDTDmodeling applications (Cont.)

vertebrate retinalrod, 55–57, 56f

FDTD techniques andadvantages of, 51–53Yee-algorithm FDTD

technique, 53–55PSTD modeling

applicationsenhanced

backscattering,65–67, 66f, 67f

multiple lightscattering, 69–72,70f, 71f, 72f

optical phaseconjugation,68–69, 68f, 69f

total scattering crosssection, 65, 65f

MCML. See Monte Carlo MultiLayered

MESI. See Multiexposure laserspeckle contrast imaging

Mie, Gustav, 153Mie theory, 20–21, 23–25, 54, 70,

123, 124, 128, 130, 153,270–272, 284, 314, 323–324

Mitochondria, 6–7, 8Mitochondrial morphology,

116–121, 117fMonte Carlo Multi Layered

(MCML), 182Monte Carlo simulations,

177–178, 179, 182–188, 182f,183f, 184f, 185f, 187f, 198,272–274

MSRI. See Multispectralreflectance-imaging

Multiexposure laser specklecontrast imaging (MESI),253–258

future directions, 258instrument, 255–256,

256f

Multiexposure laser specklecontrast imaging (Cont.)

measurements, 256–258,257f

theory, 254–255Multispectral

reflectance-imaging (MSRI),252

NNA. See Numerical apertureNewton, Isaac, 3Nuclear morphology, 127–135,

131f, 133fNucleolus, 6Nucleus, 5Numerical aperture (NA), 78, 174

OOCT. See Optical coherence

tomographyOPC. See Optical phase

conjugationOptical biopsy

angled probes, 266–267differential pathlength

spectroscopy, 266, 267fdiffusing-tip probes,

268–269, 269ffiberoptic probe designs,

264–265full and half-ball probes,

267–269, 268fgeneral comments,

258–259in vivo application,

277–281, 278f, 279f, 280fpolarized probes, 270, 270fprobe pressure influence

on normal colonmucosa, 281–282,282f

on reflectancemeasurements,283–286, 284f,285f, 286–287, 287f

367I n d e x

Optical biopsy (Cont.)reflectance spectra models

blood vessel radiusand, 274–277,276f, 277f

method for analysis,270–272

quantitative model,272–274, 273f

side-sensing probes, 268,268f

single optical fiber probes,265, 265f

Optical coherence tomography(OCT), 77, 79–81, 79f, 173, 181,188–190, 314, 319

Optical phase conjugation(OPC), 68–69, 68f, 69f

Optical scatter image ratio(OSIR), 117, 117f

Optical scatter imaging (OSI),117

OSIR. See Optical scatter imageratio

Outer membrane, 7

PPDT. See Photodynamic therapyPerfectly matched layer (PML),

54Peri-infarct depolarization (PID),

251Phase function, 13Photodynamic therapy (PDT),

121PID. See Peri-infarct

depolarizationPML. See Perfectly matched

layerPseudospectral time-domain

(PSTD), 49, 50

QQuantitative image analysis

(QIA), 328

RRaman scattering, 146f, 147Rayleigh-Gans-Debye (RGD)

approximation, 17, 153Rayleigh scattering, 16, 38Reflectance-mode confocal

microscope (rCM), 180, 181fRefractive index (RI), 31Region of interest (ROI), 330RER. See Rough endoplasmic

reticulumRI. See Refractive indexRipple structure, 19ROI. See Region of interestRough endoplasmic reticulum

(RER), 7, 8

SSAR. See Synthetic aperture

radarScattering amplitude, 12Scattering coefficient, 14Scattering cross section, 12Scattering efficiency, 13Scattering matrix, 12SER. See Smooth endoplasmic

reticulumSignal-to-noise ratio (SNR), 78,

100SLD. See Superluminescent

diodeSmooth endoplasmic reticulum

(SER), 7, 8SNR. See Signal-to-noise ratioSpatial-Fourier-spectrum

method, 45Spectroscopic microscopies

absorption and scattering,144–147, 146f

applications, 159–165, 160f,161f, 162f, 163f, 164f

cells and subcellularstructures, 150–153,151f, 152f

CLASS and, 153 –159, 154f,156f, 157f, 159t

368 I n d e x

Spectroscopic microscopies(Cont.)

elastic light scattering,147–150, 148f


Stroke, 250–253, 252fSuperluminescent diode (SLD),

320Support vector machine (SVM),

280Synthetic aperture radar (SAR),

86

TtCM. See Transmission-mode

confocal microscopeTE. See Transverse electricTEM. See Transmission electron

microscopeTissue types, optical properties

of, 9Tissue ultrastructure scattering,

199fdiagnostic imaging,

206–207, 207fex vivo measurements,

199felectron microscopy,

204–206, 205fmicrosampling

reflectancespectroscopy,200f, 202

phase-contrastmicroscopy,202–204, 203f, 204f

Tissue ultrastructure scattering(Cont.)


measurementunderstanding,195–197, 196f, 197f

therapeutic imaging,108

Total cross section, 13Total scattering cross section

(TSCS), 60–61, 65, 65f, 71Transmission electron

microscope (TEM), 163Transmission-mode confocal

microscope (tCM), 180,181f

Transverse electric (TE), 42TSCS. See Total scattering cross

section

VVolume equivalence principle,

32

WWentzel-Kramers-Brillouin

(WKB) approximation, 19Whispering-gallery-mode

(WGM), 20Whittle-Matern family of

correlation, 35Wreindt, Thomas, 25

YYurkin, M. A., 26

FIGURE 3.1 Visualizations of the FDTD-computed optical E -field standingwave within the retinal rod model for TMz illumination at free-spacewavelengths 0 = 714, 505, and 475 nm. (Source: Piket-May et al. [18].)

(a)

(a) Nucleus only

(c) Nucleus and cytoplasm (d) Cell with organelles

Scattering angleScattering angle

(b) Cytoplasm only1000

Wav

elen

gth

(nm

)

900

800

700

6000°

1000

900

800

700

6000°50° 100° 150°

1000

900

800

700

6000° 50° 100° 150°

50° 100° 150°

1000

900

800

700

6000° 50° 100° 150°

–6

–5

–4

–3

–2

–1

0

1

–6

–5

–4

–3

–2

–1

0

1

–6

–5

–4

–3

–2

–1

0

1

–6

–5

–4

–3

–2

–1

0

1

(b) (c) (d)

FIGURE 3.2 Visualizations of the FDTD-computed optical scattering of fourmodels of a cell: (a) nucleus only, (b) cytoplasm only, (c) nucleus andcytoplasm, and (d) nucleus and cytoplasm containing organelles. The scalecorresponds to the log of the scattered intensity. (Source: Drezek et al. [19].)

Normal cell

Scattering angle

Wavelength (nm)

Wav

elen

gth

(nm

)

1000 0

–0

–2

–3

–4

–5

–6

–7

900

800

700

600

102

100

10–2

10–4

600

Inte

grat

ed in

tens

ity

Inte

grat

ed in

tens

ity0 – 20°

160 – 180°

80 – 100°

0 – 20°

160 – 180°

80 – 100°

700 800 900 1000Wavelength (nm)

102

100

10–2

10–4

600 700 800 900 1000

0° 50° 100° 150°

Normal cell

Scattering angle

1000 0

–0

–2

–3

–4

–5

–6

–7

900

800

700

6000° 50° 100° 150°

FIGURE 3.3 (Top) Visualizations of the FDTD-computed optical scattering frommodels of normal (left) and dysplastic (right) cervical cells. The scalecorresponds to the log of the scattered intensity. (Bottom) Integratedscattered intensities over three angular ranges for normal (left) anddysplastic (right) cervical cells. (Source: Drezek et al. [19].)

FIGURE 3.6 Visualizations of the FDTD-computed optical scattering signaturesof a 4-�m-diameter particle with a volume-averaged refractive index navg =1.1. (a) Homogeneous particle; (b) inhomogeneous particle with refractiveindex fluctuations �n = ± 0.03 spanning distance scales of approximately50 nm; and (c) inhomogeneous particle with refractive index fluctuations�n = ± 0.03 spanning distance scales of approximately 100 nm. (Source: X.Li et al. [26].)

FIGURE 3.11 PSTD simulation of the OPC phenomenon. The physicaldimension of the simulation region is 320 �m × 600 �m. The electric fieldsat various time-steps throughout the evolution are shown: (a) 200 fs, (b)1000 fs, and (c) 2400 fs. As light scatters through the cluster of dielectriccylinders, the wavefront gradually spreads out due to diffraction. After theOPC effect of the PCM, light back-traces and refocuses back to the originallocation where it first emerged. (Source: S. H. Tseng and C. Yang [37].)

Section A Section Ba

b

c

d

e

f

A

B

Beam

Focus

Raster scan

FIGURE 4.11 Resected human breast tissue imaged with spectral-domaindetection interferometry. The beam is scanned in the geometry shown at thetop. En face images are shown for depths located at 591 �m (Section A) and643 �m (Section B) above the focal plane. (a,d) Histological sections showcomparable features with respect to the (b,e) OCT data and (c, f ) the ISAMreconstructions. The ISAM reconstructions resolve features in the tissue,which are not decipherable from the OCT data. (Source: This figure is adaptedfrom Ref. [3].)

FIGURE 6.1 Energy diagram showing excitation and various possible physicalrelaxation mechanisms for (a) Rayleigh scattering, (b) fluorescencescattering, (c) two photon scattering, (d) phosphorescence scattering, (e)Raman scattering, ( f ) CARS scattering.

FIGURE 6.5 Schematic of the prototype CLASS/fluorescence microscope.

FIGURE 6.8 Fluorescence image of the suspensions of carboxylate-modified1.9 �m diameter microspheres exhibiting red fluorescence (left side), theimage reconstructed from the CLASS data (middle), and the overlay of theimages (right side).

FIGURE 6.9 Fluorescence image of the mixture of three sizes of fluorescentbeads with sizes 0.5 , 1.1, and 1.9 �m mixed in a ratio of 4:2:1 (left side),the image reconstructed from the CLASS data (middle), and the overlay of theimages (right side).

FIGURE 6.10 Image of live 16HBE14o- human bronchial epithelial cells withlysosomes stained with lysosome-specific fluorescence dye (left side), theimage reconstructed from the CLASS data (middle), and the overlay of theimages (right side).

FIGURE 6.11 The time sequence of CLASS microscope reconstructed imagesof a single cell. The cells were treated with DHA and incubated for 21 h. Thetime indicated in each image is the time elapsed after the cell was removedfrom the incubator.

Tissue Tissue

(a) (b)

Wavelength

Irra

dian

ce

Detection cone

FIGURE 8.1 (a) A tomographic measurement scheme showing point sourceand point detectors used to measure diffusely scattered light in a tissueblock. (b) An illustration of microsampling imaging technique where highlylocalized illumination and detection scheme is used to measure the localscatter spectrum directly.

Micro sampling imaging White light image H &E

Phase contrast

(a) (b)Gene expression Electron microscopy

FIGURE 8.2 (a) A schematic of the microsampling imaging system, whereconfined illumination and confocal detection are used to sample the localscatter spectrum in bulk tissue. (b) An illustration showing data from othercomplementary modalities obtained along with the optical imaging data tohelp understand the origins of light scatter signatures in tissue.

Normal tissue from breast biopsy

Average irradiance Average irradianceNormal breast tissue

Invasive breast carcinoma

Combination of all three pa-rameters in RGB channel

log(rel. scatter ampl.) log(rel. scatter ampl.)

Rel. scatter power Rel. scatter power

200

20406080

20 1020406080

20 40 60 80100120100

5

-5

0

406080

20406080

10050 100 150

2 20406080

10020 40 60 80

2

10

5

0

-5

1

0

100120

1

0

10050 100 150

10050 100 150

20 20

100200300400

200 400 600

20

20605040302010

605040302010

10

040 60 80 120100

406080

100

10

0

400

600

800200400600800 12001000

Invasive carcinoma from breast biopsy

FIGURE 8.5 Spatial distribution of scatter parameters, with white light imagesat top and three types of derived scatter parametric data below, for a normalbreast tissue sample (left column) and an invasive carcinoma sample (middlecolumn). Compound images of the parameters are shown at the right.

Phase contrast + H&E Overlay and selectROI based on H&E

Isolate pixels andexport toMATLAB

Phase contrastanalysis

Analyze distributionof pixel values

20×

FIGURE 8.7 An illustration of data extraction procedures from thephase-contrast images obtained from an unstained section of a breastcarcinoma specimen.

Num. density

HbT Oxy Wat

Scatt. ampl. Mean sizeScatt.

FIGURE 8.9 Reconstructed NIR images of a 73-yr-old female subject with a3.5-cm IDC in her left breast. Images showing the plane of the tumor in thebreast, sliced in a coronal view. The panel of images shows total hemoglobinconcentration (HbT), oxygen saturation (Oxy), water fraction (Wat), scatterpower (Scatt. Power), and amplitude (Scatt. Ampl.), as well as effective <a>(Mean Size) and N (Num. Density) images.27

FIGURE 9.11 Constant-depth one-dimensional sections of a healthy tumor(left) and a tumor cross-linked with glutaraldehyde (right). The vertical axis isframe number at a rate of one frame per second. (Source: Reprinted fromRef. [31].)

FIGURE 9.12 Autocorrelation graphs of fixed-depth time-sequence data for ahealthy tumor at selected depths (left) and for tumors at a fixed depth butdifferent metabolic conditions (right).

FIGURE 9.13 Color-coded motility metric of a healthy tumor at selecteddepths. The healthy outer shell shows strong cellular or subcellular motion,while the necrotic core is quiet. (Source: Reprinted from Ref. [31].)

FIGURE 9.14 Motility maps of a tumor responding to 2 �g/ml of theantimitotic drug, Nocodazole, as a function of time from the initial state (firstframe) to 119 min after the dose. (Source: Reprinted from Ref. [31].)






0 0.05 0.1 0.15 0.2

0 2 4 6 8 10 12

1

1.05

1.1

Time (s)

Rel

ativ

e C

BF

(a)

(b)

FIGURE 10.3 LSCI can be used to quantify both the spatial and temporal dynamicsof stimulus-induced brain activation. The sequence of images in part (a) illustratesareas of the brain where blood flow is increased due to electrical forepawstimulation in a rat. The color bar indicates the fractional increase in blood flow. Theplot in part (b) demonstrates the temporal dynamics of the blood flow changes withinthe center of activation.

0

0.5

1

1.5

2

0

0.5

1

1.5

0 10 20 30 40 50 600

0.5

1

1.5

0

Time (m)

HbOHbRHbTCBFCMRO2

Scat

isch

emic

cor

epe

num

bra

non-

isch

emic

0 20 40 60 80 100

Laser

CCD

QTHlamp

filterwheel

filter wheelfront view

DCmotor

fibersensor

CCD

long passfilter

short passfilter

(a) (c)

(b)

FIGURE 10.4 Application of LSCI to cerebral ischemia. (a) The spatial bloodflow gradient following occlusion of an artery can be visualized using LSCI.The middle cerebral artery was occluded just outside the top region of theimage and the color map shows the relative blood flow, expressed as apercentage of preischemic flow. (b) LSCI and multispectral reflectanceimaging can be performed simultaneously to image multiple hemodynamicparameters. (c) Time courses of changes in oxyhemoglobin (HbO),deoxyhemoglobin (HbR), total hemoglobin (HbT), blood flow (CBF), oxygenconsumption (CMRO2), and scattering during a stroke. The three graphsdemonstrate the changes in each of these parameters in three spatialregions (ischemic core, penumbra, and nonischemic cortex).

300µm

150µm

GlassSlide

PDMSwithTiO2


150µm

300µm

GlassSlide

PDMSwithTiO2


200µm staticscattering layer

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7Laser

AOM

RF Generator and Amplifier

Data AcquisitionComputers

Syringe PumpFluid in

Fluid out

Sample

10XObjective

Camera

ModulationI/P

Iris

(a)

(c)

(b)

FIGURE 10.5 (a) Experimental setup for multiexposure speckle imaging(MESI). The acousto-optic modulator (AOM) is used as a variable amplitudegate to the laser light, which enables the effective camera exposure time tobe varied over several orders of magnitude. (b) Speckle contrast images offlow through a microfluidics channel under different exposure times (0.1, 5,and 40 ms; scalebar = 50 �m). (c) Illustration of layered microfluidics flowphantoms used to quantify the effects of a static scattering layer on themeasured speckle correlation times.

10−5 10−4 10−3 10−2 10−10

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

Exposure duration (s)

Sp

eckl

e V

aria

nce

(a.

u.)





ρ = 0.438±0.003

τc = 290.68±7.86 µs

ρ = 0.25±0.002

τc = 295.79±8.40 µs

ρ = 0.493±0.008

τc = 62.75±2.34 µs

ρ = 0.311±0.005

τc = 74.67±2.67 µs

0 1 2 3 4 5 6 7 8 9 100

50

100

150

200

250

Speed mm/sec

Dev

iati

on

in τ

c *10

0 /

(τc in

ab

sen

ce o

f st

atic

sca

tter

er)

Single Exposure (5ms)New Speckle Model

(a) (b)

FIGURE 10.6 (a) Multiexposure speckle measurements from two samples at twodifferent flow speeds. Solid lines represent measurements from samples without thestatic scattering layer. (b) Percent deviation in �c under different levels of staticscattering for different flow speeds. The plots illustrate the advantage of MESImeasurements in the presence of static scattering.

FIGURE 13.10 Photomicrograph of a typical HT29 cell monolayer after fixationand staining. Length scale indicated by the 10 �m bar. (Source: Taken fromRef. [3] with permission.)

450500

550600

650

−1

−0.5

0

0.5

10

0.005

0.01

0.015

0.02

Wavelength (nm)

LEBS peak from tissue

Angle (deg)

Inte

nsity

(a.

u.)

FIGURE 14.7 An example of a measured LEBS peak showing the dependenceon angle and wavelength.

Documents

Biomedical applications of light scattering