February 2004 Chuck DiMarzio, Northeastern University 10471-8a-1

ECEU692Subsurface Imaging

Course NotesPart 2: Imaging with Light (3):

Strong ScatteringProfs. Brooks and DiMarzio

Northeastern University

Spring 2004

February 2004 Chuck DiMarzio, Northeastern University 10471-8a-2

Topic Outline

• Our Old Scattering Model– What We Left Out

• Phase Functions• Multiple Scattering• Computational Approaches

– Reduced Albedo– Photon Migration– Monte-Carlo– A Simple 2-Layer Model

February 2004 Chuck DiMarzio, Northeastern University 10471-8a-3

Recall Weak Scattering: What is Wrong?

February 2004 Chuck DiMarzio, Northeastern University 10471-8a-4

Imaging and Multiple Scattering

Localized Probing;(e.g. Confocal microscopy,Optical Coherence Tomography,Two-photon microscopy)

Multi-View Tomography;(e.g. Diffusive Optical Tomography)

February 2004 Chuck DiMarzio, Northeastern University 10471-8a-5

Single Scattering Phase Function

10057p2-1 here

February 2004 Chuck DiMarzio, Northeastern University 10471-8a-6

Multiple Scattering (1)

• Scattering Angles Add

• Think in 2 Dimensions

• Total isi

• PDF is Convolution of Individual PDF’s

February 2004 Chuck DiMarzio, Northeastern University 10471-8a-7

Multiple Scattering (2)

• Computational Approaches– Reduced Albedo

– Photon Migration

– Monte-Carlo

• Issues– Multiple Scattering

– Internal Reflection• Integrated Fresnel

Put 10057p2-2 here

February 2004 Chuck DiMarzio, Northeastern University 10471-8a-8

Photon Migration

• Assumptions– Radiative Transport

Equation– Taylor Series for

Radiance– Boundary Conditions

• Result– Diffusion-Like

Equation for Photon Density

• Solution– Photon Density Wave

• DC or AC

– Complex k (Lossy Wave)

– Details Another Day

February 2004 Chuck DiMarzio, Northeastern University 10471-8a-9

Reflection vs. Albedo: Example

Patterson, Michael S., Ephraim Schwartz, and Brian C. Wilson, “Quantitative Reflectance Spectrophotometry for the Noninvasive Measurment of Photosensitizer Concentration in Tissue During Photodynamic Therapy,” Photodynamic Therapy Mechanisms, SPIE Volume 1065, 1989. Pp. 115--122.

W’,

Tra

nspo

rt A

lbed

o

February 2004 Chuck DiMarzio, Northeastern University 10471-8a-10

Monte-Carlo Models

• Loop on Photons– Launch

– Loop on Particle• Random Distance

• Scatter or Absorb

• Random Angle

– Exit - Save Data

• Compute Statistics

• Widely Applicable• Accurate Phase

Function not Needed?• Computationally

Intensive

February 2004 Chuck DiMarzio, Northeastern University 10471-8a-11

Monte-Carlo Operation

1a. Launch

1b. RandomDistance

1c. Scatter or Absorb

1d. Random Direction

1e. Continue or Exit:If Exit, count asReflection or Transmission

2-N. Next Photons

Refl

Radius

N+1. SummarizeStatistics

February 2004 Chuck DiMarzio, Northeastern University 10471-8a-12

Simple Skin Model

sc

Epidermis

Dermis

Re Rd()

Venous Hb

Arterial Hb

R

100m

2 mm

Stratum Corneum

• Rsc and Re

– No desired signal

• Rd < Rd (no blood),

– Rd contains wanted signal

• Neglecting

– index of refraction changes

– multiple scattering between

layers

– specular reflections. Thanks to Peter Dwyer atLucid Technologies and MGH

February 2004 Chuck DiMarzio, Northeastern University 10471-8a-13

Optical Properties of Human Tissue

HbO2

Hb

Water

Melanin

Epidermis Dermis

Absorption

Dermis

Epidermis

Epidermis

Dermis, Hb, HbO2

Scattering

AnisotropyHb, HbO2

February 2004 Chuck DiMarzio, Northeastern University 10471-8a-14

Sample Monte-Carlo-Model Spectra for Tissue

Inputs:•Epidermis = 0.065 mm•Dermal Hb = 0.12 mM

Outputs:•Reflectance (Shown)•Radially Resolved Reflectance•Angular Resolved Reflectance

No Hb

HbO2

Hb

February 2004 Chuck DiMarzio, Northeastern University 10471-8a-15

R = Rsc + Re + Rd

Simplified Skin Model Equations

as

seTRR

2

0

R = Rsc + Re + Rd

Hb SpectralSignatures

+

February 2004 Chuck DiMarzio, Northeastern University 10471-8a-16

Simplified Skin Model Equations (Cont.)• Want to find s = oxygen saturation of Hb

• a depends on sa = oxycs +deoxyc(1-s) + a0

oxy = Molar absorption coefficient of oxy-Hbdeoxy = Molar absorption coefficient of deoxy-Hbc = Concentration of Hbs = Oxygen saturation fractiona0 = Other chromophores besides blood

• Approximation: wavelengths close together only a depends on

February 2004 Chuck DiMarzio, Northeastern University 10471-8a-17

Simplified Skin Model Equations (Cont.)

• Grouping some variables together, to solve for s

)1)(()()(

1)( 0 ssBcA

RRdeoxyoxy

se

as

TA

2

0

seT

Bc2

1)(

• Four equations, four unknowns (BC)AR0

s