QUANTITATIVE DIFFUSE REFLECTANCE SPECTROSCOPYliu.diva-portal.org/smash/get/diva2:246012/FULLTEXT01.pdf · "Intramyocardial oxygen transport by quantitative diffuse reflectance spectroscopy

QUANTITATIVE DIFFUSE REFLECTANCE SPECTROSCOPY

– myocardial oxygen transport from vessel to mitochondria

Department of Biomedical Engineering

Division of Biomedical Instrumentation

Linköping University

SE-581 85 Linköping, Sweden

© Tobias Lindbergh 2009, unless otherwise noted.

All rights reserved.

ISBN 978-91-7393-522-7

ISSN 0345-7524

Printed by LiU-Tryck, Linköping, Sweden, 2009

Till Åsa

ABSTRACT

In the field of biomedical optics, diffuse reflectance spectroscopy (DRS) is a frequently used

technique for obtaining information about the optical properties of the medium under

investigation. The method utilizes spectral difference between incident and backscattered light

intensity for quantifying the underlying absorption and scattering processes that affects the

light-medium interaction.

In this thesis, diffuse reflectance spectroscopy (DRS) measurements have been combined

with an empirical photon migration model in order to quantify myocardial tissue chromophore

content and status. The term qDRS (quantitative DRS) is introduced in the thesis to emphasize

the ability of absolute quantification of tissue chromophore content. To enable this, the photon

migration models have been calibrated using liquid optical phantoms. Methods for phantom

characterization in terms of scattering coefficient, absorption coefficient, and phase function

determination are also presented and evaluated. In-vivo qDRS measurements were performed

on both human subjects undergoing routine coronary artery bypass grafting (CABG), and on

bovine heart during open-chest surgery involving hemodynamic and respiratory provocations.

The application of a hand-held fiber-optic surface probe (human subjects) proved the clinical

applicability of the technique as the results were in agreement with other studies. However,

problems with non-physiological variations in detected intensity due to intermittent probe-

tissue discontact were observed. Also, systematic deviations between modeled and measured

spectra were found. By model inclusion of additional chromophores revealing the

mitochondrial oxygen uptake ability, an improved model fit to measured data was achieved.

Measurements performed with an intramuscular probe (animal subjects) diminished the

influence of probe-tissue discontact on the detected intensity. It was demonstrated that qDRS

could quantify variations in myocardial oxygenation induced by physiological provocations,

and that absolute quantification of tissue chromophore content could be obtained.

The suggested qDRS method has the potential of becoming a valuable tool in clinical

practice, as it has the unique ability of monitoring both the coronary vessel oxygen delivery

and the myocardial mitochondrial oxygen uptake ability. This makes qDRS suitable for

directly measuring the result of different therapies, which can lead to a paradigm shift in the

monitoring during cardiac anesthesia.

LIST OF PAPERS

This thesis is based on the following five papers, referenced in the text with their roman

numerals.

I. T. Lindbergh, M. Larsson, I. Fredriksson, and T. Strömberg, "Reduced scattering

coefficient determination by non-contact oblique angle illumination: Methodological

considerations", in Progress in Biomedical Optics and Imaging - Proceedings of SPIE,

(San Jose, CA, 2007), p. 64350I 1-12.

II. E. Häggblad, T. Lindbergh, M.G.D. Karlsson, M. Larsson, H. Casimir-Ahn, E.G.

Salerud, and T. Strömberg, "Myocardial tissue oxygenation estimated with calibrated

diffuse reflectance spectroscopy during coronary artery bypass grafting", Journal of

Biomedical Optics 13, 054030 (2008).

III. T. Lindbergh, E. Häggblad, H. Casimir-Ahn, M. Larsson, E.G. Salerud, and T.

Strömberg, "Improved model for myocardial diffuse reflectance spectra including by

including mitochondrial cytochrome aa3 and methemoglobin", submitted.

IV. T. Lindbergh, M. Larsson, Z. Szabó, H. Casimir-Ahn, and T. Strömberg,

"Intramyocardial oxygen transport by quantitative diffuse reflectance spectroscopy in

calves", submitted.

V. T. Lindbergh, I. Fredriksson, M. Larsson, and T. Strömberg, " Spectral determination of

a two-parametric phase function for polydispersive scattering media", Optics Express

17, 1610-1621 (2009).

The following paper is related to the thesis, but not included:

M. Sundberg, T. Lindbergh, and T. Strömberg, "Monte Carlo simulations of

backscattered light intensity from convex and concave surfaces with an optical fiber

array sensor", Progress in Biomedical Optics and Imaging - Proceedings of SPIE, (San

Jose, CA, 2005).

ABBREVIATIONS

ATP Adenosinetriphosphate

BaSO4 Bariumsulfate

CABG Coronary artery bypass grafting

CCD Charge-coupled device

cyt aa3 cytochrome aa3, also called cytochrome c oxidase

cyt aa3,ox oxidized cytochrome aa3

cyt aa3,red reduced cytochrome aa3

DRS Diffuse reflectance spectroscopy

ECC Extra-corporeal circulation

EM Electro-magnetic

ETC Electron transport chain

Gk Gegenbauer kernel

Hb Hemoglobin

HbO2 Oxygenated hemoglobin

He-Ne Helium-neon

HG Henyey-Greenstein

IR Infrared

LAD Left anterior descending artery

LDF Laser Doppler flowmetry

LVAD Left ventricle assisting device

metHb methemoglobin

metMb metmyoglobin

Mb Myoglobin

MbO2 Oxygenated myoglobin

MC Monte Carlo

mfp Mean free path

mfp� Reduced mean free path

OP Optical phantom

qDRS quantitative Diffuse Reflectance Spectroscopy

QN Quantum number

RBC Red blood cell

rnd random number, uniformly distributed in the interval � �0 1

SCT Spectral collimated transmission

SRDR Spatially resolved diffuse reflectance

UHT Ultra-high temperature

UV Ultra-violet

TABLE OF CONTENTS Chapter 1 INTRODUCTION................................................................................................. 1

Chapter 2 AIMS OF THE THESIS ....................................................................................... 5

Chapter 3 OXYGEN TRANSPORT IN THE MYOCARDIUM .......................................... 7 3.1 OXYGEN CARRIERS .................................................................................................... 9

3.1.1 HEMOGLOBIN........................................................................................................ 9 3.1.2 MYOGLOBIN ........................................................................................................ 10

3.2 OTHER HEMEPROTEIN DERIVATIVES.................................................................. 10 3.3 MITOCHONDRIAL OXYGEN CONSUMPTION ...................................................... 11

3.3.1 CYTOCHROMES AND THE ELECTRON TRANSPORT CHAIN .................... 11 Chapter 4 PRINCIPLES OF LIGHT-TISSUE INTERACTIONS ...................................... 13

4.1 SCATTERING ............................................................................................................... 15 4.1.1 THE SCATTERING COEFFICIENT..................................................................... 15 4.1.2 PHASE FUNCTIONS............................................................................................. 16 4.1.3 THE REDUCED SCATTERING COEFFICIENT................................................. 19

4.2 ABSORPTION............................................................................................................... 20 4.2.1 PHYSICAL PRINCIPLES...................................................................................... 21 4.2.2 THE ABSORPTION COEFFICIENT AND THE BEER-LAMBERT LAW ........ 24 4.2.3 MYOCARDIAL CHROMOPHORES.................................................................... 25

4.3 TOTAL ATTENUATION COEFFICIENT AND THE ALBEDO ............................... 28 Chapter 5 PHOTON MIGRATION MODELS ................................................................... 29

5.1 MODIFICATIONS OF THE BEER-LAMBERT LAW................................................ 30 5.2 MONTE CARLO SIMULATIONS ............................................................................... 31

5.2.1 PHOTON LAUNCH ............................................................................................... 32 5.2.2 PHOTON ABSORPTION....................................................................................... 33 5.2.3 PHOTON SCATTERING AND PROPAGATION................................................ 33 5.2.4 PHOTON DETECTION OR CONTINUED PROPAGATION ............................. 34 5.2.5 SIMULATION POSTPROCESSING..................................................................... 35

Chapter 6 OPTICAL PHANTOMS..................................................................................... 37 6.1 PHANTOM CONSTRUCTION .................................................................................... 38

6.1.1 SCATTERING COMPONENTS............................................................................ 38 6.1.2 ABSORPTION COMPONENTS............................................................................ 40

6.2 PHANTOM CHARACTERIZATION........................................................................... 41 6.2.1 MONOCHROMATIC COLLIMATED TRANSMISSION ................................... 41 6.2.2 SPECTRAL COLLIMATED TRANSMISSION ................................................... 43

Chapter 7 QUANTITATIVE DIFFUSE REFLECTANCE SPECTROSCOPY ................. 45 7.1 SPECTRUM RECONSTRUCTION.............................................................................. 46

7.1.1 THE LIGHT SOURCE ........................................................................................... 46 7.1.2 INTENSITY REFERENCE MEASUREMENTS .................................................. 47 7.1.3 COLOR CORRECTION......................................................................................... 47 7.1.4 COMPLETE NORMALIZATION PROCEDURE ................................................ 48

7.2 CALIBRATION OF PHOTON MIGRATION MODELS ............................................ 49 7.2.1 THE EMPIRICAL MODEL ................................................................................... 49 7.2.2 THE MONTE CARLO MODEL ............................................................................ 51

7.3 CHROMOPHORE QUANTIFICATION ...................................................................... 53

7.3.1 THE EMPIRICAL MODEL ................................................................................... 53 7.3.2 THE MONTE CARLO MODEL ............................................................................ 55

Chapter 8 REVIEW OF THE PAPERS............................................................................... 57 8.1 PAPER I - Reduced scattering coefficient determination by non-contact oblique angle illumination - methodological considerations ...................................................................... 57 8.2 PAPER II -Myocardial tissue oxygenation estimated with calibrated diffuse reflectance spectroscopy during coronary artery bypass grafting .......................................................... 59 8.3 PAPER III - Improved residual when modeling myocardial diffuse reflectance spectra including mitochondrial cytochromes .................................................................................. 60 8.4 PAPER IV - Intramyocardial oxygen transport by quantitative diffuse reflectance spectroscopy in calves .......................................................................................................... 61 8.5 PAPER V - Spectral determination of a two-parametric phase function for polydispersive scattering liquids .......................................................................................... 63

Chapter 9 DISCUSSION ..................................................................................................... 65 9.1 CALIBRATION OF PHOTON MIGRATION MODELS ............................................ 65 9.2 OPTICAL PHANTOM COMPONENTS AND CHARACTERIZATION ................... 69 9.3 QDRS APPLICATIONS ON MYOCARDIAL TISSUE .............................................. 72

Chapter 10 CONCLUSIONS................................................................................................. 79

ACKNOWLEDGEMENTS ..................................................................................................... 81

REFERENCES......................................................................................................................... 85

Chapter 1 - Introduction

1

Chapter 1 INTRODUCTION

The work of the human heart is based on aerobic biochemical processes where the presence

of oxygen is vital. Oxygen is a prerequisite of the normal energy production in the myocytes

and consequently of a normal blood flow in both the systemic and the pulmonary circulation.

Atherosclerotic coronary heart disease causes a narrowing of the heart’s own vessels, leading

to a reduction or occlusion of the coronary arterial blood supply and hence oxygen supply to

the myocardium. This patophysiological process is causing chest pain or a myocardial

infarction depending on the severity and duration of warm myocardial tissue hypoxia. These

are serious emergencies requiring immediate medical attention. Despite treatment, nearly 450

000 patients died during 2005 in the USA alone, due to this condition1. Besides medication,

treatment often involves active interventional cardiology procedures such as percutaneous

coronary stent implants. In suitable cases, surgery is considered (coronary artery bypass

grafting (CABG)).

During CABG procedures, vessels from other parts of the body (usually from the lower leg or

the arms) are harvested and used to "by-passing" the strictures in the coronary artery system

that causes the impaired blood flow. During the operation, the blood flow in the grafts is

measured with ultra-sound techniques2-4. Other methods have also been proposed (for example;

thermodilution5 and magnetic resonance measurements6), but are at the moment not suitable

for routine clinical use. Laser Doppler Flowmetry have been proposed for measuring local

microcirculatory blood flow in the myocardium during CABG7. However, microcirculatory

blood flow measurements on a beating heart are difficult to perform due to motion artifacts.

Moreover, information about the blood flow alone is not sufficient when determining to

which extent the oxygen carried by the blood is transferred to the surrounding myocardial

tissue.

Although the global myocardial oxygen extraction during surgery can be assessed by

measuring the difference between the global arterial oxygen saturation and coronary sinus

oxygen saturation, it provides no or little information about regional variations in myocardial

oxygen supply.


2

Besides adequate coronary arterial oxygen saturation, a sufficient mitochondrial oxygen

uptake has to be ensured in order for the contractility in myocardial cells to function properly.

In the mitochondria, which can be considered as the cell’s "power plant", the oxygen is

utilized during production of ATP molecules (i.e. energy). In the mitochondrial membrane,

there exist several molecules called cytochromes. They are electron carriers in a process

called the electron transport chain (ETC), see section 3.3.1. Of special importance is the

cytochrome c oxidase, also called cytochrome aa3 � �cyt aa3 . Although the cytochromes do

not bind to the oxygen molecule itself, their ability to transport electrons is of vital importance

when oxygen molecules are utilized in the mitochondrial energy production process. A high

oxidation level of the cyt aa3 molecules reflects a sufficient ability for mitochondrial oxygen

utilization.

Since myocardial ischemia can exist in small confined areas there is a need to assess the local

myocardial oxygenation and mitochondrial oxygen consumption. Microdialysis is a technique

capable of measuring markers of cell injury and metabolite concentrations in the interstitial

fluid. However, despite that in-vivo sampling can be performed, laboratory analysis of the

interstitial fluid is required in order to achieve results8, 9, leaving no immediate feedback of

myocardial tissue status during surgery. Moreover, the microdialysis technique provides no

information on hemoglobin or myoglobin oxygenation.

Several studies have shown that the coronary hemoglobin oxygenation can be estimated with

optical spectroscopy techniques10-12. The key feature in making spectroscopy suitable for

monitoring hemoglobin oxygenation is that the characteristic light absorption spectra of the

hemoglobin molecule changes when oxygen binds to the molecule. In specific, human

oxygenated hemoglobin � �2HbO has two characteristic absorption peaks in the visible

wavelength region, occurring at wavelengths 542 and 576 nm, while human deoxygenated

hemoglobin � �Hb display only one absorption peak at 556 nm. These differences can be

assessed with a diffuse reflectance spectroscopy (DRS), where backscattered light from an

illuminated tissue is analyzed. With DRS, information about the hemoglobin oxygenation can

be obtained from the ratio � �HbO2 HbO2 Hbf f f� , where if denotes the fractional content of

component i.

In a way similar to hemoglobin, the cytochromes display changes in their absorption

properties depending on the oxidation status. This makes DRS suitable for quantifying the


3

ability for mitochondrial oxygen uptake. The first step towards the use of spectroscopy as a

tool for in-vivo monitoring of mitochondrial oxygen consumption (changes in the oxidation

status of cyt aa3) was taken in 1977 by Franz Jöbsis13. Since then, in-vivo studies where cyt

aa3 oxidation status is evaluated with spectroscopic techniques have relied on physiological

situations as reference points. Such situations (complete oxidation and reduction of cyt aa3)

can be achieved by exposure of chemical agents and by hemodynamic or respiratory

provocations14-16. Obviously, in clinical patient monitoring, physiological provocations that

completely reduce the cyt aa3 are not feasible.

In DRS, the backscattered light intensity does not only depend on the amount of

chromophores (light absorbing molecules; e.g. Hb , 2HbO , oxidized cyt aa3 and reduced cyt

aa3) in tissue, but also strongly on tissue scattering caused by, for example, cells,

mitochondria, and muscle fibers. Hence, to accurately quantify the Hb oxygenation, cyt aa3

oxidation level and the amount of tissue chromophores, the effect of light scattering needs to

be taken into account. Solutions to overcome this have been suggested. This includes second-

derivative spectroscopy where the light scattering effect is reduced17 and other spectroscopic

techniques where the light scattering is assumed to be constant during the measurements18.

However, none of those methods are able to measure the tissue chromophore content in

absolute units. The use of photon migration models taking into account both absorption and

scattering have been proposed to predict the diffuse reflectance spectra19, 20. By solving the

inverse problem (i.e. deducing absorption and scattering from a measured spectrum), both the

concentration and oxygenation of hemoglobin, as well as tissue scattering can be quantified.

Of central importance in these methods is the model calibration using optical phantoms with

known optical absorption and scattering properties.

Thus, a method that compensates for tissue scattering when simultaneously measuring

hemoglobin oxygenation and cyt aa3 oxidation status without the need for physiological

provocations, would have a great potential of becoming a tool for assessing myocardial

oxygenation and utilization - from the coronary vessels to mitochondria.

4

Chapter 2 – Aims of the thesis

5

Chapter 2 AIMS OF THE THESIS

The overall aim was to develop and evaluate methods and algorithms for tissue

characterization by quantitative diffuse reflectance spectroscopy (qDRS).

More specifically, this includes:

determination of the scattering coefficient, absorption coefficient, and phase function of

liquid optical phantoms,

calibration of light transport models using liquid optical phantoms,

in-vivo quantification of tissue chromophore volume fractions,

in-vivo studies of myocardial oxygen transport using qDRS during open-chest heart

surgery.

6

Chapter 3 – Oxygen transport in the myocardium

7

Chapter 3 OXYGEN TRANSPORT

IN THE MYOCARDIUM

Oxygen enters the body via the respiratory system, which can be divided into three different

parts; 1) the airways, 2) the lungs, and 3) the respiratory muscles21. The oxygen transition

from air to blood takes place via diffusion in the alveoli of the lungs. In human adults, the

total area active in the air-to-blood oxygen exchange is about 70 m2. During resting conditions,

an adult human performs about 12-20 respiration cycles every minute, giving a net air volume

exchange of about 6-10 liters/min, depending on the lung capacity21. However, during extreme

conditions such as high altitude climbing or competitive long-distance running, up to a 20-

fold increase in the alveolar ventilation can occur22.

The myocardium is among the most oxygen-consuming muscle tissues in the human body23,

and is sensitive to even short periods of insufficient supply of oxygen and nutrients24. In order

to satisfy this demand, the myocardium is equipped with a separate circulation system called

the coronary circulation. Although the exact anatomy of the myocardial blood supply system

varies between individuals, the absolute majority of the population has two main coronary

arteries; the right and left coronary artery, which branch into successively smaller vessels as

they cover the right and left ventricles of the heart, respectively. The major coronary arteries

are shown in Figure 1. After oxygen delivery in the myocardial capillary network,

deoxygenated blood is drained from the coronary circulation by the coronary venous system,

which can be divided into two subsystems; the left cardiac venous system and the right

cardiac venous system. Similar to the coronary arteries, the coronary vein system can be

further divided into smaller vessels.


8

Figure 1: Anterior view of the heart and the major coronary arteries. Reprinted and

modified with permission from Mayo Foundation for Medical Education and Research.

The greatest amount of work performed in the heart is performed by the left ventricle. Hence,

most of the oxygen delivered to the myocardium by the coronary circulation is consumed in

the left ventricular wall. In adult humans, its thickness during the diastolic phase is about 8

mm25. Several studies26, 27 have shown that the myocardial contractility and the energy

consumption increases transmurally, being smallest in the subepicardium, and largest in the

subendocardium. Therefore, to ensure adequate blood supply throughout the myocardium, a

portion of the coronary vessels lies deep into the myocardium, and is referred to as

subendocardial coronary arteries.

Figure 2: A segment of the ventricular wall, illustrating the different myocardial layers and

a subendocardial coronary artery. Reprinted with permission from Mayo Foundation for

Medical Education and Research.


9

In Figure 2, a schematic view of a portion of the left ventricular wall is shown, illustrating the

different layers of the left ventricular wall, the pericardium, and a coronary artery with a

branch into the myocardium. The local coronary blood flow is regulated by several

mechanisms; some originate from within blood vessels (e.g., myogenic and endothelial

factors), and some originate from the oxygen demand in the surrounding tissue23. Local

regulatory mechanisms act independently of extrinsic (nervous and hormonal) control

mechanisms. The balance between the local and extrinsic regulatory mechanisms co-operate

in order to maintain an optimal vascular tone for adequate blood flow, and hence also a

sufficient myocardial oxygenation.

3.1 OXYGEN CARRIERS

Almost all oxygen transported from the lungs into the artery system is bound to hemoglobin

molecules. They act as an oxygen carrier within the blood, although a small amount (about

1.5%) of O2 is dissolved in the plasma. In the coronary circulation system, the oxygen is

released from the hemoglobin and transported into the myocardial tissue, where it is

consumed within the mitochondria. Interestingly, the myoglobin present in myocardial tissue

binds the oxygen at lower partial oxygen pressure compared to that of hemoglobin. The

partial oxygen pressure at which the oxygen is released from myoglobin is very low ( 2.5�

mm Hg)28. Therefore, a portion of the oxygen delivered by the hemoglobin is bound to and

stored in myoglobin and thus not directly consumed in the mitochondria. The role of

myoglobin in the oxygen transport chain towards the mitochondria has been debated. It is now

believed to be as an oxygen reservoir only to be utilized in critical situations when sufficient

oxygen supply is endangered29, 30.

3.1.1 HEMOGLOBIN

Hemoglobin is a hemeprotein found in red blood cells of all higher vertebrates31.

Approximately 35% of the red blood cell (RBC) mass consists of hemoglobin. Normally,

human hemoglobin consists of four identical protein subunits, each associated with a heme

group. Each heme group is made up by an iron ion � �2+ 3+Fe Fe , surrounded by a molecular


10

"ring" containing nitrogen atoms and carbohydrates. The molecular weight of hemoglobin

(containing four protein subunits as described above), is 64 500 Daa32.

By binding to the iron ion, each heme group can bind one O2 molecule. Upon binding, the

Fe2+ ion oxidizes to form Fe3+, which is incapable of binding further oxygen molecules.

Because of the four identical protein subunits, each hemoglobin molecule can bind four O2

molecules. Once one oxygen molecule become bound to one of the iron ions, the molecular

shape of the hemoglobin changes in a way favorable for further binding between O2 and the

remaining iron ions. The phenomenon is called cooperative binding, and is the reason of the

well-known sigmoid shape of the hemoglobin dissociation curve.

3.1.2 MYOGLOBIN

Analogous to hemoglobin, myoglobin is a hemeprotein with very similar molecular structure,

differing in that is has only one protein subunit. Hence, one myoglobin molecule is able to

bind only one O2 molecule. Therefore, cooperative binding does not exist in myoglobin

oxygen binding. Hence, myoglobin display a dissociation curve that is different compared to

that of hemoglobin.

The molecular weight of myoglobin is around 17 000 Da33, and the molecules are bound

within the cytoplasmic regions in skeletal and heart muscles. Wittenberg reported the

myocardial myoglobin of most species to be around 200 μmole/kg wet weight33, which

correspond to 3.4 mg/g wet weight, using the molecular weight mentioned above. Lin et al.34

have reported concentrations between ~8 mg/g dry weight and ~11 mg/g dry weight, being

smallest in the right atrium, and highest in the left anterior papillary muscle.

3.2 OTHER HEMEPROTEIN DERIVATIVES

In addition to hemoglobin and myoglobin, there exist various forms of hemeprotein

derivatives in blood. Derivatives that have lost their oxygen binding capabilities, is referred to

as dyshemoglobins; carboxyhemoglobin, methemoglobin, cyanmethemoglobin,

sulfhemoglobin, and cyansulfmethemoglobin35. In methemoglobin (metHb), one of the heme

groups in human blood contains iron ions in the state Fe3+, which is the cause of the oxygen a Da = Dalton is a unit frequently used for molecular weight, and is defined as gram per mole; 1g mole .


11

binding disability. Typical concentration values of methemoglobin in human muscle tissue

during normal conditions are in the region of 0-1% of the total blood volume, but much larger

values can be seen during pathological conditions and following exposure to anesthetic agents

such, for example lidocaine36. Methemoglobin levels above 70% may cause death37.

3.3 MITOCHONDRIAL OXYGEN CONSUMPTION

All cellular functions in the human body can be performed only if they are provided with a

sufficient amount of energy. In a ventricular heart cell of an adult human, about 25% of the

volume is occupied by mitochondria24. In the mitochondrion, organic substances are

combusted through oxidation (oxidative metabolism), a process in constant need of a

continuous and adequate oxygen supply. The resulting molecule is the well-known ATP

(adenosinetriphosphate), which serves as the main store of cellular energy. The third

phosphate group is attached with a bond that carries a lot of potential energy. By splitting this

bond, energy can be utilized for biological work, such as muscle contractions.

3.3.1 CYTOCHROMES AND THE ELECTRON TRANSPORT CHAIN

Once the oxygen has been released from the oxygen carrier(s) hemoglobin (and during some

conditions, myoglobin), the 2O molecules act as electron acceptors in a process called the

electron transport chain (ETC). The main purpose of the ETC is to produce a proton � �+H

gradient over the inner mitochondrial membrane. The resulting electrochemical gradient is

necessary for the formation of ATP.

A detailed description of the electron transport chain will be complex and is not intended here.

A basic understanding of the electron transfer pathways and particularly the

oxidation/reduction state of complex IV is however needed to understand several of the

physiological conclusions presented in the discussion section of the thesis. An illustration of

the electron flow is shown in Figure 3 which display a segment of the inner mitochondrial

membrane, including the protein complexes I-V and the electron transport chain.


12

Figure 3: Schematic view of a segment of the inner mitochondrial membrane, the ETC and ATP

synthesis. Reprinted and modified with permission from PhD Camilla Ribacka, University of

Helsinki.

Complex I is the starting point of the ETC, as NADH (originating from the citric-acid cycle)

is oxidized. The electrons are transferred from complex I through the complexes II and III,

and finally arrive at complex IV where they reduce the 2O molecules into water according to + -

2 2O +4H +4e 2H O� . In complexes I-IV, the electrons are transferred by electron carrying

proteins called cytochromes. Similar to hemo- and myoglobin, they have a characteristic

absorption spectrum which makes spectroscopy suitable for studying the cytochrome

oxidation status. The cytochrome aa3 (cyt aa3) which exists in complex IV, is the key electron

carrier in the mitochondrial respiratory chain. A reduction of its oxidation level reflects a

decrease in cellular ATP production, which may in turn affect the mechanical function of the

heart. Compared to the hemeproteins, the cyt aa3 is a large molecule, with a molecular weight

of 200 000 Da38.

H+

NADH+H+ NAD +

succinate fumarateH+

QQH2

H+ H+

O2+4H+ 2H2OADP+Pi ATP

H+

e- e-

e- e-

Complex I: NADH dehydrogenase

Complex II: Succinate dehydrogenase

Complex III: bc1 complex

Complex IV: Cytochrome c

oxidase

Complex V: ATP synthase

cyt c

Inner mitochondrial space

Mitochondrial matrix

Chapter 4 – Principles of light-tissue interactions

13

Chapter 4 PRINCIPLES OF

LIGHT-TISSUE INTERACTIONS

One of the most classical debates ever in physics would probably be the one regarding the

origin and the true nature of light. A number of great scientists, such as Christiaan Huygens

(1629 – 1695), Sir Isaac Newton (1642 – 1727), James Clerk Maxwell (1831 – 1879),

Heinrich Hertz (1857 – 1894), Albert Einstein (1879 – 1955), and Louis de Broglie (1892 –

1987), have all been involved in, and contributed to, the development of different

representations of light. In the beginning of the debate, the major question was whether light

was a particle or a wave phenomenon. In the early 1900s, the birth of quantum mechanics

eventually provided the framework necessary to formulate the wave-particle duality. Its key

message was that all matter exhibits both wave and particle behavior at the same time.

In classical physics, the most intrinsic description of light would be to consider it as

electromagnetic (EM) radiation, with oscillating electric and magnetic fields39. The

mathematical description of EM radiation is formalized by employing Maxwell's equations40,

and does not fit into the major scope of this thesis, but can be found elsewhere41. Being the

most complete, but also the most cumbersome description, the EM representation is able to

quantitatively describe phenomena like polarization, interference, diffraction and Doppler

effects42. The wave propagation can be described by three vectors, E , B , and k , representing

the electric field, the magnetic field, and the wave propagation direction, respectively. An

illustration can be found in Figure 4.


14

Figure 4: An electromagnetic wave propagating in the positive x-direction. The oscillating electric

and magnetic fields are illustrated with the vectors E (solid vectors) and B (dashed vectors),

respectively. The wave propagation direction is given by the vector k .

When EM radiation propagates through biological tissue, multiple interactions occur, making

the direct application of Maxwell’s equations difficult. Depending on the application at hand,

more accessible representations than waves exist; rays and photons43. The ray representation is

often used when designing the geometrical properties of optical lens systems. Rays are

straight lines, and only govern information on the direction of propagation. The often used

term beam represents merely a collection of multiple rays. Together with the ray

representation, photons (eg. particles), may be the most intuitive representation of light. The

photon representation offers a relatively simple but powerful way of describing light

propagation (scattering and absorption) in various media, and is frequently used in biomedical

optics.

Photons are elementary particles with a certain amount of energy, E , given by the relation

E h � , where h is Planck’s constant � �� 346.626... 10 Js , and 1s� � �� is the frequency of

the electromagnetic radiation. Often � is expressed as c� � , where c is the speed of light,

and � is the wavelength. When using the photon representation of light, the interaction with

matter is described as transitions of discrete energy packages (quanta).

Photons within the wavelength interval ~400 nm to ~700 nm, (corresponding to an energy

interval of ~3.10 eV to ~1.77 eV), is often referred to as light42, 43. It is the human visual

perception of the energy in the visible wavelength interval, rather than the true physical nature

z

y

x

E

B

k


15

of the phenomenon itself, that has given rise to the term light. EM radiation in the adjacent

wavelength intervals to that of the visible region, are referred to as ultraviolet (UV) and

infrared (IR) light, respectively44. However, it should be noted that a strict definition of the

wavelength interval of the EM radiation considered as light does not exist, and other

wavelength intervals than the one mentioned here can be found in the literature39.

In this thesis, the primary focus is not to cover a complete framework regarding light

scattering and absorption theory, and an adequate understanding of the work presented in the

included papers can be achieved with the material presented in the subsequent sections of this

chapter.

4.1 SCATTERING

Consider EM radiation that propagates through any kind of medium. The energy of the

radiation will then interact with the surrounding medium, causing the electrons in the medium

to oscillate. The resulting dipole moments interfere both constructively and destructively,

giving rise to the final scattering pattern. In theory, equations that accurately describe the

light-medium interaction (and hence the resulting light propagation through the medium) for

each wave at each interaction could be established, but in biomedical optics, this is often not

applicable in practice due to the complex inhomogeneity of tissue45. Fortunately, the effect on

light propagation in tissue by biological structures (cells, nuclei, mitochondria)46 can be

understood without using the complete electromagnetic theory description.

4.1.1 THE SCATTERING COEFFICIENT

Figure 5: A collimated light beam incident to a spherical scattering particle.

Consider a collimated beam incident to a spherical scattering particle (Figure 5). 0I is the

intensity of the incident beam, I is the intensity of the unscattered light, and sn and

I0

I

ns

nm

z y x


16

mn � �s mn n� are the refractive index of the spherical scattering particle and the surrounding

medium, respectively. Due to the refractive index difference, the incident light rays are

refracted, thus deviating from the incident direction. A portion of the incident light will,

however, remain unscattered, and constitute the forward directed beam with intensity I . The

fraction of unscattered light can be estimated by considering the power � �P of the incident

light, 0P I A , where A is the cross-sectional area of the incident light beam. Schematically,

the power of the scattered light � �sP , can be represented by the expression s 0 e,sP I � , where

e, s� 2mm� �� is the effective �not the geometrical, which is denoted g, s� �2mm� �� cross-

sectional area of the scattering particle (subscript s). Since a portion of the incident light is not

scattered by the particle, e, s� should be interpreted as the fraction of the scattering particle

geometrical cross-sectional area that actually scatters light. The two (geometrical and

effective) cross-sectional areas of the scattering particle are related to each other according to

equation 1:

e, s e, s g, sQ� � , (1)

where e, sQ is a dimensionless scattering efficiency proportionality constant. A volume

containing multiple scattering particles governs a volume density of scatterers, which can be

denoted s� 3mm� �� . The product of the effective cross-sectional area and the volume density

of scatterers constitute the scattering coefficient, sμ 1mm� �� , which is of a central importance

within biomedical optics (see equation 2).

s s e, s� � � (2)

It is straight-forward to realize that a scatterer of high efficiency, will give a larger sμ

compared to a less efficient scatterer, due to a larger e, sQ . Also, a denser scattering medium

(large s� ) will result in a larger sμ compared to a less dense scattering medium. As the unit

of sμ suggests, the reciprocal of the scattering coefficient, s1 μ , can be interpreted as the

average path in a volume that light can travel without being scattered. s1 μ is also known as

the mean free path � �mfp .

4.1.2 PHASE FUNCTIONS

If we consider a single scattering event, the angle of deflection can be defined as in Figure 6,

assuming rotational symmetry around the original incident direction:


17

Figure 6: Photon deflection angle from a single scattering event.

The specific distribution of all possible scattering angles can be described by a probability

function, denoted � �p � , also known as the phase function. It can be obtained by considering

the intensity distribution in the horizontal plane from an illuminated cuvette containing a pure

scattering solution; see Figure 7, which shows the principle of a goniometric setup.

Figure 7: Goniometric setup for measurement of the probability function of scattering

angles.

The intensity distribution detected by the photo detector as a function of � , is a direct

mapping of the probability function. The mean of the cosine of all scattering angles, � �cos � ,

is defined as the anisotropy factor, denoted g . The anisotropy factor can be calculated by the

expression:

� � � � � � � �0

cos 2 sin cosg p d�

� � � � � � � , (3)

given that the following relation holds true:

�

z y x

Incident light

Photo detector

Cuvette containing scattering solution

+ �

- �


18

� � � �0

2 sin 1p d�

� � � � � . (4)

Generally, the biological tissue structures that scatter light vary greatly in size. The largest

structures are cells and nuclei, and when approximated to a spherical shape, they are in the

order of ~10 μm in diameter. The smallest structures are lipid membranes of different kinds,

having a diameter of ~0.01 μm46. If the wavelength of the interacting light � �� is comparable

to the diameter of the scattering particles � �d , the scattering processes are usually referred to

as Mie scattering. On the other hand, if d �� the scattering is referred to as Rayleigh

scattering. Since goniometric measurements �or other types of direct determination of � ��p � ,

of in-vivo tissue generally are impossible, the true distribution of scattering angles has to be

described using mathematical models and/or simplifications of � �p � .

Mie theory When the scattering particles are in the same size region as the wavelength of the interacting

light, the scattering can successfully be described by Mie theory, which was first introduced

by Gustav Mie 190847. Mie theory assumes homogeneous spherical scattering particles, and

utilizes two properties; the relational refractive index between the scattering particle and the

surrounding medium ( r s mn n n , where subscripts s and m are associated with the scattering

particle and the surrounding medium, respectively) and a size parameter � �m2x r n� � ,

where r is the radius of the scattering particle. However, the complete mathematical

description of the Mie solution is rather complex, and the details can be found elsewhere48. In

addition, when dealing with in-vivo measurements, the inhomogeneous distribution and the

variety of different scatterers make the Mie theory inappropriate.

Henyey-Greenstein phase function A widely used and often applicable phase function for description of light propagation in

biological tissue, is the Henyey-Greenstein (HG) phase function, often denoted � �HGp � 49. It

was first published in 1941, and described scattering of radiation in galaxies. However, it has

been found useful, yet simple, when describing light scattering in biological tissues50. The

expression for � �HGp � is given by equation 5:

� ��

2

HG 32 2

1 14 1 2 cos

gpg g

��

� . (5)


19

An accurate description of light propagation with source-detector distances shorter than ~1

mfp , requires not only knowledge abut the anisotropy factor, g , but also of the higher order

moments of the phase function. For this purpose, various modifications of the HG phase

function have been proposed51, where additional additive terms in equation 5 are included.

The two-parametric Gegenbauer-kernel phase function In 1980, Reynolds and McCormick introduced an approximate two-parameter phase function

for a broad range of scatterer types found in the atmosphere, in the ocean as well as in

biological structures52. The proposed phase function can be developed both in a closed form as

well as generated by a series of Gegenbauer polynomials53. As the name implies, the

probability function behavior is determined by two parameters, denoted Gk� and Gkg . The

subscript "Gk" stands for Gegenbauer-kernel, because of the Gegenbauer polynomial

connection, and this notation will be used throughout this thesis. It should be stressed that

Gkg are not to be associated with the anisotropy factor previously described. The

Gegenbauer-kernel phase function, � �Gkp � is given by equation 6:

� ��

Gk

GkGk Gk

22Gk Gk Gk

Gk 12 2 2Gk Gk Gk Gk

(1 )

(1 ) (1 ) 1 2 cos

g gpg g g g

�

��

��

�

� � . (6)

By setting Gk 0.5� in equation 6, the HG phase function is obtained. For Gk 0.5� � , the

anisotropy factor can be calculated according to equations 7:a,b

� ��

� � � ��

Gk Gk

Gk Gk

2 2 2Gk Gk Gk Gk Gk

2 2Gk Gk Gk Gk

2 1 1 1,

2 1 1 1

g L g g gg L

g g g

� �

� �

�

�

� � �

� . (7:a,b)

Reynolds and McCormick concluded in their original work, that when assuming the ideal case

of spherical scatterers with known size, diameter in the range 3 240d� � μm, and relative

refractive index in the range r1.015 1.25n� � , the proposed � �Gkp � more closely represent

the scattering pattern than the HG phase function52. In paper V in this thesis, the Gk phase

function for milk has been estimated54.

4.1.3 THE REDUCED SCATTERING COEFFICIENT

When scattered a sufficient number of times, the light propagation in a medium can be

described utilizing the reduced scattering coefficient, sμ � , which is defined as:


20

� �s s 1μ μ g� . (8)

An illustration of how sμ � (within a homogeneous medium) describes light propagation in

relation to sμ and g is given in Figure 8.

Figure 8: Schematic drawing illustrating the physical meaning of sμ � in relation to μs and g.

The thickest line (vertical, downward direction in Figure 8) illustrates the incident light. The

intermediate thickness arrows represent two single, isotropic, scattering events with the

optical pathlength equal to s1 μ � . The thinnest arrows represents light scattering along two

different paths, each including ten scattering events. As seen in the figure, the light

propagation described by the ten single scattering events can, on a macroscopic scale, be

represented by the reduced scattering coefficient.

Analogous to the case s1mfp μ , the reduced mean free path is defined as s1mfp μ �� . The

sμ � and mfp� are terms frequently used in biomedical optics when light propagation at

distances greater than a couple of mfp are studied.

4.2 ABSORPTION

As described in the beginning of this chapter, the interaction between light and matter can be

described as transfer of energy. In absorption processes, energy from the incident light is

transferred to the tissue. For an understanding of how the absorption takes place, we first

consider the "simplest" case; light absorption of a free atom, and the electron transitions as a

response to incident light. Then, additional ways in which a molecule containing two or more

s1 μ �

s1 μ �

s1 μ


21

atoms can change its total energy, are described. Finally, energy changes in more complex

molecules are considered.

4.2.1 PHYSICAL PRINCIPLES Electronic transitions In an atom, the potential energy associated with an electron, is usually defined to be equal to

zero at an infinite distance between the center of the atom and the electron itself. An electron

at a finite distance from the atom center is defined to govern a negative potential energy.

According to quantum mechanics, each electron in an atom is described by four quantum

numbers (QN), see Table 1.

Quantum numbers (QN) Notation Allowed values Principal QN k positive integers 1, 2, 3, ...

Angular momentum QN l integers 0, 1, 2, ..., k-1 Magnetic QN ml integers –l, -l+1, ..., l-1, l

Spin QN ms +½, -½ Table 1: Quantum numbers and its allowed values for an electron in an atom.

In contrast to the view of classical physics, the quantum mechanic description of an electron

is a wave function, distributed in a certain geometrical region called orbital, or "electron

cloud". In principal, the energy of an electron (and thus the distance to the center of the atom)

in an atom depends on the principal quantum number k. Orbitals with the same k, is said to

belong the same electron shell. Within each shell (same k), there are k different shapes of

orbitals, each described by the l quantum number. Electrons with the same k, but different l, is

said to belong to different subshells of the main shell k. Furthermore, electrons with the same

k and l, can be distinguished from each other by its magnetic quantum number ml. As seen in

Table 1, there are 2 1l � possible orbitals having the same k and l. The geometrical

interpretation of the magnetic quantum number would be the spatial orientation of the orbital.

Finally, each orbital (each possible combination of k, l, and ml) can have either +½ or -½ as its

spin quantum number ms, which can be interpreted as the rotational direction around its own

axis, given that the electron is regarded as a classical particle, eg. a charged ball.

Now, Pauli’s exclusion principle, which is a central principle within quantum mechanics,

states that two electrons can not have the same quantum number configuration55. This,

together with the fact that the energy level of each electron correspond to a certain quantum

number configuration (k, l, ml, ms), gives that light absorption by an atom can be described by

a change in the quantum number configurations of the electrons (electronic transition). It


22

follows from the above that only discrete steps of energy due to electron transitions, can occur.

The absorption lines of hydrogen when exposed to a continuous EM spectrum (in the visible

region) can be seen in Figure 9.

Figure 9: Hydrogen absorption lines in the visible wavelength region. Reprinted and

modified with permission from Astronomy & Astrophysics Department, The Pennsylvania

State University, US. Note: Specific wavelengths are only given as illustrative examples.

Vibrational and rotational energy Molecules contain more than one atom, and the energy depends not only on the quantum

number configuration of each electron within each atom, but also on vibrational and rotational

movements of the complete molecule. Consider the diatomic molecule O2, in Figure 10.

Figure 10: Schematic illustration of vibrational (left panel) and rotational (right panel)

energy of a diatomic (O2) molecule.

The vibrational energy between the two atoms can be represented by a connective spring (left

panel of Figure 10). The rotation of the molecule will be centered around the center of mass,

if one considers the two atoms as classical particles (right panel of Figure 10). Expressions for

the vibrational and rotational energies are given in equations 9 and 10, respectively55:

410 486 434 656

� �nm�

Vibrational energy, Evib Rotational energy, Erot

O O O O


23

vib 012 2

hE n ��

� � � � � !

n = 0, 1, 2, 3, ... (9)

� � � �2

rotI

1 22

J J hE

M� �

. J = 0, 1, 2, 3, ... (10)

Equation 9 can be recognized as the expression for the energy governed by a harmonic

oscillator, where 0� is the frequency of the masses. In equation 10, IM is the moment of

inertia, and J is a quantum number defined as a function of the previously described ml and ms,

see chapter 7 in Ohanian55 for details. The complete description of the quantum number J

requires an extensive review of several quantum mechanical relations, which would exceed

the scope of this thesis. Here, it is sufficient to realize that because of the quantized nature of

ml and ms, J is quantized, and hence also Erot. As in the mono-atomic case with hydrogen, a

schematic view of oxygen absorption lines in the visible region is shown in Figure 11.

Figure 11: A schematic view of oxygen absorption lines in the visible wavelength region.

Reprinted and modified with permission from Astronomy & Astrophysics Department, The

Pennsylvania State University, US. Note: Specific wavelengths are only given as

illustrative examples.

Absorption by complex molecules In biological tissues, free atoms does not (generally) exist, and the structures involved in light

absorption are usually very complex compared to free atoms. When not subjected to dynamic

external stimulation, the molecular arrangement in all matter is always ordered in such a way

that the electron distribution correspond to the lowest energy state permitted by the static

circumstances (for example, temperature). In the case with the O2 molecule, the vibrational

and rotational movements have only one and two degree(s) of freedom(s), respectively, giving

a limited number of ways to respond to external stimuli. Molecules in biological tissues,

� �nm� 449 532 628 452 546 658 500 557 669


24

however, often contain a great number of atoms and sub-molecular structures. As a

comparison to the diatomic O2 molecule, the molecular model of heme, a component

responsible for oxygen binding in hemoglobin, is shown in Figure 12.

Figure 12: Molecular model of heme. Unmarked big spheres are carbon (C) atoms,

unmarked small spheres are hydrogen (H) atoms. Fe = iron, N = Nitrogen, S = Sulfur.

It is straight-forward to realize that the number of ways in which the heme molecule can

change its total energy when absorbing light, are extremely large. While electronic transitions

have energies corresponding to the UV to IR range, vibrational transitions typically

correspond to the IR range. Rotational transitions display even lower energies, from the far IR

to sub-millimeter wavelength range39. However, in large molecules, electronic transitions as

well as changes in the rotational and vibrational energies often occur simultaneously, and

complex interactions of electron orbitals gives rise to even more possible energy levels. Due

to the large number of possible energy levels, the absorption as a function of wavelength for

such molecules are usually smooth functions instead of displaying the sharp peaks for mono-

and diatomic configurations seen in Figure 9 and Figure 11. Absorption spectra for some

biological light absorbers will be discussed in section 4.2.3 in this chapter.

4.2.2 THE ABSORPTION COEFFICIENT AND THE BEER-LAMBERT LAW

An absorber exposed to a collimated incident light beam, absorb a portion of the light through

the processes described earlier. Analogous to the case with the scattering coefficient, the

geometrical and effective cross-sectional area of the absorber can be defined by simply

replacing the subscript "s" with "a" in equations 1 and 2 (subscript "a" representing

absorption), see equations 11 and 12:

Fe

N N

N N S

S

S

S


25

e, a e, a g, aQ� � , (11)

a a e, a� � � . (12)

The incident light not absorbed by the absorber, continues to propagate with the initial

direction, 0� " (� as in Figure 6). This allows us to define the following relation:

adI μ I dx , (13)

for a collimated light beam travelling along the x-direction through a non-scattering,

absorbing, homogeneous medium. Integration with respect to x, gives:

a

0μ xI I e . (14)

Equation 14 is recognized as the well-known Beer-Lambert law, which describes the relation

between the incident light intensity and the intensity of the light that remain unabsorbed after

travelling through a medium with absorption coefficient μa and of thickness x.

4.2.3 MYOCARDIAL CHROMOPHORES

In the field of biomedical optics, molecules that absorb light in the visible wavelength region

and are present in biological tissue, are usually called chromophores. Depending on a number

of different properties (chemical structure, size, geometrical shape, etc.), each molecular

species governs a specific relation between magnitude of absorption and the energy of the

incident light, referred to as an absorption spectrum, eg. the absorption coefficient as a

function of wavelength; � �aμ � 1mm� �� . The ability to absorb light can also be described by

using the absorptivity � �a � 1 1L g mm � � � � , or the molar absorptivity � �# � 1 1L mole mm � � � � . The latter is frequently used in reference literature, and also referred to as

the specific extinction coefficient, � �eμ � 1 1M mm � �� . Here, M is the symbol for molar,

which is a concentration unit defined as 1mole L .

When including absorption in analytic photon migration models or Monte Carlo models, a

conversion of the absorption measure into the absorption coefficient � �aμ � is desired, as will

be demonstrated in the next main chapter of the thesis. Conversion from the specific

extinction coefficients μe into the absorption coefficient μa, has been described by Prahl56, and

is shown in equation 15:


26

� � e

aw

ln 10m

� ��

, (15)

where � �ln is the natural logarithm, � is the density -1g L� �� and wm is the molecular

weight 1g mole� �� of the substance of interest.

It is important no note that the nomenclature as well as the units, when it comes to expressing

absorption, varies a lot. Concentrations are often expressed as millimolar, � �mM , and cm-1 is

often used when expressing � �aμ � , � �a � , and � �# � . For example, if one wants to express

the absorption coefficient in units of 1mm , and the specific extinction coefficient is given in

units of 1 1mM cm , equation 15 has to be modified according to:

��

� �1 1

1 1

ea

wmM to Mcm to mm

ln 101 100010

μμ

m�

(16)

In heart tissue, chromophores have been reported to be oxygenized and deoxygenized

hemoglobin and myoglobin (HbO2, Hb, MbO2 and Mb, respectively), water (W), fat (lipid)14,

57, 58, and oxidized and reduced cytochrome aa3 (cyt aa3,ox and cyt aa3,red, respectively)13, 59, 60.

Water and fat obviously do not participate in the oxygen transport, but have to be accounted

for when describing the light transport in myocardial tissue. The absorption spectra for hemo-

and myoglobin, both in their oxygenized and deoxygenized form, are very similar to each

other. Myoglobin displays a positive �-translation of about 2-4 nm compared to hemoglobin,

and attempts have been made in order to distinguish between hemoglobin and myoglobin

absorption58, 61, 62.

In Figure 13, the absorption spectra of hemoglobin, methemoglobin, water and lipid can be

seen. The absorption data of hemoglobin and water were compiled from Zijlstra35 and

Buiteveld et al.63, respectively. The water absorption data is, in Buiteveld et al., given in m-1.

Hemoglobin absorption data is, in Zijlstra et al., given in 1 1mM cm � �� , and has been

translated into 1mm� �� by using equation 16. Lipid absorption data was compiled from van

Veen et al.64.


27

500 550 600 650 700 750 80010−6

10−4

10−2

100

102

104

HbO2

Hb

metHb

Lipid

Water

Wavelength [nm]

μ a [mm

−1]

Figure 13: Absorption coefficients, � �aμ � 1mm� �� , of oxygenated and deoxygenated

human hemoglobin, methemoglobin, water and lipid.

Determination of the absorption spectra for both the oxidized and reduced form of the

mitochondrial chromophore cyt aa3, have been subjected to extensive attempts during the

years. The difference extinction spectrum (reduced – oxidized) has been published by Liao

and Palmer 199665, while the extinction spectrum for both the oxidized and reduced form has

been measured by Ph.D. John Moody, University of Plymouth, and is published at the BORL

tissue spectra web site66. In Figure 14, the oxidized and reduced forms of cyt aa3 as measured

by Moody, can be seen. Translation from eμ to aμ has been performed according to equation

16.


28

500 550 600 650 700 750 800100

101

102

cyt aa3, red

cyt aa3, ox

Wavelength [nm]

μ a [mm

−1]

Figure 14: Absorption coefficients, � �aμ � 1mm� �� , of oxidized and reduced form of

cytochrome aa3.

4.3 TOTAL ATTENUATION COEFFICIENT AND THE ALBEDO

Two additional terms frequently used in biomedical optics, is the total attenuation coefficient, defined as: t a sμ μ μ � , (17)

and the albedo, defined as the ratio between the scattering coefficient and the total attenuation

coefficient:

s

a s

μalbedoμ μ

�

. (18)

Chapter 5 – Photon migration models

29

Chapter 5 PHOTON MIGRATION MODELS

Light propagation in tissue can be described using different frameworks. Radiation theory is

based on Maxwell’s equations, which is briefly mentioned in the beginning of chapter 4. This

representation is frequently used when theoretical descriptions of light propagation are made.

Radiation theory is regarded as the most complete description of the true properties of EM

radiation propagation and interaction with surrounding media. When studying biological

tissues, the heterogeneous distribution of several different particles disable the direct

application of radiation theory for description of light propagation67. However, if polarization

and diffraction effects are disregarded, the photon propagation through inhomogeneous media

(for example, biological tissue) can be described as transport of neutral particles, and the

Boltzmann transport equation can be applied.

Monte Carlo (MC) simulation is another approach to model light propagation that is

conceptually different from the analytical expressions mentioned above. The technique is

extensively used within different fields, for example; medical dosimetry68, meteorology69, and

probability theory70. The core idea when applying MC as a tool for photon migration

modeling in biological tissue is to consider the photon as a particle, and assign each photon a

random pathlength and propagation direction based on probability distributions defined by the

optical properties; aμ , sμ , � �p � , and the refractive index of the tissue. By repeating this for a

large number of photons, reliable results can be attained.

Both MC simulations, as well as utilization of Beer-Lambert law modifications, when

describing light transport in tissue and for determination of sμ and/or aμ , are two approaches

of central importance in the work presented in this thesis. Therefore they are described

separately in the two following sub-chapters.


30

5.1 MODIFICATIONS OF THE BEER-LAMBERT LAW

As described earlier (section 4.2.2), the Beer-Lambert law relates the product between the

optical thickness and the absorption coefficient of a medium, to the transmitted intensity I

when illuminated with an intensity 0I . In 1988, Delpy et al.71 suggested a modification of the

Beer-Lambert law, in order to encompass the effect of simultaneous light absorption and

scattering when light propagates through a medium. This suggested modification have been

revisited by Kocsis et al.72, and the expression for the attenuation Att is presented in equation

19:

0ln a

IAtt PL μ GI

� � �� !

. (19)

PL is the total mean optical pathlength of the detected photons, and G is a geometry-

dependent factor representing intensity loss by scattering72.

Given that the changes in chromophore concentration are sufficiently small and G can be

assumed to be constant (scattering properties does not change), and that the absorption in the

medium of interest changes homogeneously, the difference in Att � �Att$ between two

occasions, t1 and t2, can be written as:

t1a

t2

ln IAtt PL μI

� �$ $� �

! . (20)

Unfortunately, the approximations required for equation 20 to hold true, may not be

applicable to all biological tissues. Even if this conditions are fulfilled, evaluation

measurements on human skin have shown that the method can display large deviations from

expected values73.

Another model, also based on modifications to the original Beer-Lambert law, that include the

effect of simultaneous changes in both absorption and scattering, has been presented by

Jacques in 200319. The light transport in tissue is here described by T (i.e. the intensity as a

function of sμ � and aμ ), which is an expression involving second order polynomials �K and

�L in sμ � , and an exponential dependence on aμ , according to:


31

� � as a

2s s

2s s

, μ LT μ μ K e

K a b μ c μ

L d e μ f μ

�

� � � �

� � � �

. (21)

In equation 21, a f are numerical constants, which can be determined by performing

calibration measurements on multiple optical phantoms (see section 7.2). It should be noted

that equation 21 can be used to describe the intensity both in transmission and reflectance

model19. However, as described earlier, only applications of reflectance mode is considered in

this thesis.

Taking the natural logarithm of equation 21, we have:

� �� s a aln , lnT μ μ K μ L� . (22)

In equation 22, we see that � �ln K is a term representing the intensity loss due to scattering

which is similar to the term G in equation 19. The term aμ L represents intensity loss due to

absorption (however L is influenced by sμ � ). The method presented by Jacques provides a

simple way of calibrating the light transport model T , which, in turn, enables absolute

quantification of chromophore content.

5.2 MONTE CARLO SIMULATIONS

As described in the beginning of this chapter, analytical solutions to the transport equation

require approximations, of which several are not allowed for biological tissues. The MC

technique is a numerical technique for photon migration in media not restricted to the

approximations described above. Instead, the issue of computational time is the limiting factor.

When MC is used as a tool to determine sμ and/or aμ via inverse problem solving procedures

(which is a common application), a large number of simulations often are required in order to

cover the expected range of parameters of interest. In such cases, straight-forward (brute-

force) application of the MC technique can result in unrealistic calculation times, and

different refinements in order to reduce the calculation time and number of simulations are

often needed. Examples of such refinements are rescaling of an original simulation to obtain


32

simulation results for other sμ and g 74, and a post-simulation process to include absorption

effects on the detected photons75.

Although MC setups are able to model light propagation through arbitrary complex media, the

central steps in the photon migration can be divided into; 1) launching, 2), absorption 3)

scattering/moving, 4) termination or continued propagation (iterate from step 2). Those steps

are described in the following example. Restrictions such as refraction/reflection in

geometrical objects within the medium of interest, or in glass cuvette walls when simulating

light propagation in optical phantoms, can be handled with ray-optics and is in this description

not considered as a part of the core idea in MC simulations.

Below is an example, where the principles of the main steps in MC simulation of light

propagation are described.

5.2.1 PHOTON LAUNCH

Consider a homogeneous, geometrically infinite medium with absorption and scattering

coefficient aμ and sμ , respectively, and phase function � �p � . The light source is a pencil

beam with direction � � � �, , 0,0, 1ux uy uz . Generally, the most convenient choice is to let

origo coincide with the position of the light source. However, any choice of launch position is

of course possible. The step length, SL , of the first step (and all other steps) is described by:

� �

t

ln rndSL

μ

, (23)

where rnd is a random number, uniformly distributed in the interval � �0,1 , and sampled at

every step for each individual photon. Before moving, each photon is assigned an individual

weight number � �0 1w , representing the relative intensity of the photon. The first photon

position � �1 1 1, ,x y z after photon launching can be expressed as:

1 0

1 0

1 0

x x ux SLy y uy SLz z uz SL

� � �

. (24)


33

5.2.2 PHOTON ABSORPTION

From a physical point of view, a photon either exists or does not exist. However, in MC

setups, the weight number introduced in the description of photon launching, is a convenient

way of expressing the absorption effects, which is done by reducing the weight number

according to:

ai i-1

t

1 , i=1,2,3, ...μw wu

� � � �

! (25)

where "i" represents the index of interaction for each photon. If each photon would be tracked

until it crosses any geometrical limits set by the user, or until they are detected, the calculation

time would in most cases be unrealistic. This problem can be solved by using the so-called

Russian roulette. First, a pre-defined weight threshold value is set (typically between 0 10w

and 0 1000w ). If the photon weight falls below this value, rnd is generated, and compared to

a pre-defined value p �also chosen within the interval � ��0,1 , representing the probability of

termination. If rnd p� , the photon is terminated. On the other hand, if rnd p% , the photon

weight is increased (due to energy conservation) by a factor 1 p , and then continue its

propagation.

5.2.3 PHOTON SCATTERING AND PROPAGATION

After reducing its weight, and if it is still alive, the photon will be scattered into a new

propagation direction, determined by the phase function. The MC technique allows

incorporation of different phase functions, as well as the case of isotropic scattering. The

deflection angle from its current propagation direction, � , are calculated based on the phase

function, while the azimuthal angle, & , are assumed to be randomly chosen from a uniform

distribution in the interval � �0,2� . Then the direction of the new trajectory is transformed into

Cartesian coordinates, and the photon position is updated.

HG phase function When utilizing the HG phase function, the deflection angle � can be expressed analytically:

� �22

2 HGHG HG

HG HG

1arccos 1 21 2

gg gg g rnd

�� ! ! !

. (26)


34

Gk phase function As in the HG phase function case, the resulting deflection angle when using the two-

parametric Gk phase function (see section 4.1.2), can be expressed analytically as:

� �1

GkGk22

Gk GkGk

1arccos 1 12

rndg gg H

��

� �� ! ! !

, (27)

where H equals:

� �

� � � �

Gk

Gk Gk

22Gk

2 2Gk Gk

1

1 1

gH

g g

�

� �

� . (28)

Photon position update With known � and & , it is possible to calculate the new photon position, � �i+1

, ,x y z ,

according to:

� � � � � ��

� � � � � ��

� � � � � ��

i+1 i 2

i+1 i 2

2i+1 i

sincos sin cos

1

sincos sin cos

1

sin cos 1 cos

x z y x

z

y z x y

z

z z

x x SL u u u uu

y y SL u u u uu

z z SL u u

�& & �

�& & �

� & �

� �� !� �� !

� �

, (29)

where � �, ,x y zu u u is the components of the current (index "i") direction of propagation.

5.2.4 PHOTON DETECTION OR CONTINUED PROPAGATION Detection In order to obtain usable results from MC simulations, a detector has to be implemented into

the code. Technically, the detector is implemented in the code as a geometrical object, with

known position, size, and refractive index. If a photon propagates into this geometrical region,

the photon is regarded as detected, and parameters of interest (typically; number of emitted

photons and accumulated number of detected photons, position, total path length, weight,

propagation direction etc.) are stored.


35

Continued propagation As long as the photon remains within the geometrically pre-defined space of interest, is not

detected, and not eliminated due to a sufficient number of weight reductions, the steps

described in the previous section 5.2.3 is repeated.

5.2.5 SIMULATION POSTPROCESSING

Consider a case where the photon distribution in a medium, illuminated by an infinitely

narrow light beam or containing a point source, are to be simulated for a large number of aμ

and sμ combinations. Provided that the absorption and scattering components are

homogeneously distributed and that the medium can be considered as semi-infinite, the result

from an original simulation setup with s s,origμ μ and a 0μ can be recalculated to represent

results of a new simulation setup with s s, newμ μ and a a, newμ μ . This is done in two steps: 1)

rescaling of the detected positions of each individual photon, and 2) compensation of the

absorption effects due to a, new 0μ � .

Rescaling of photon positions Given that a 0μ , tμ equals sμ in equation 23. Then, the step length SL is inversely

proportional to sμ . If, for example, s, orig s,new2μ μ , the new step length � �newSL will be twice

as long as the original one � �origSL . If the position of the detected photon "i" in the original

simulation are denoted � �i i i det, orig, ,x y z , the rescaling of each detected photon can be written as:

� � � �i i i i i idet,new det,orig

, , , ,x y z k x y z (30)

and

new origSL k SL , (31)

where s, orig s, newk μ μ .

Compensation for absorption effects

Since the original simulation is performed with a 0μ , each detected photon will have a

weight number orig 1w . The total relative intensity drop of each detected photon due to

absorption effects, neww , can be calculated by straight-forward application of the Beer-

Lambert law (equation 14), given the total pathlength of each individual photon.

36

Chapter 6 – Optical phantoms

37

Chapter 6 OPTICAL PHANTOMS

Theoretically, an optical phantom can be made of virtually any type of material, as long as

the optical properties of interest - may it be refractive index, scattering/absorption coefficient,

polarization properties, etc. - are known or at least consistent over time. In the field of

biomedical optics, optical phantoms are usually referred to as media (solids, gels, liquids) that

are capable of mimicking light distribution relevant to tissue76. During the years, efforts have

been made for constructing both solid as well as liquid optical phantoms, both having their

suitable application areas.

Of course, a desired property of an optical phantom is that the optical properties should be

consistent over time, because of the frequent utilization as reference objects in measurement

system calibration procedures. Despite great efforts in producing long-term reliable optical

phantoms, this has shown not to be an easy task76, 77. Liquid optical phantoms, especially those

involving biological substances, are likely to change the optical properties over time due to

biological processes. Solid optical phantoms are sensitive to factors like UV radiation and

mechanical stress.

An alternative to long-term stable optical phantoms, may be to use phantoms displaying

unchanged optical properties for only a short period (typically 6-12 hours) of time54, 78, but that

instead can be made up by readily available components, such as ink as absorber, and milk,

different fat nutrition solutions, or polystyrene spheres as scatterers78. The main drawback is

of course the limited life-time. Characterization of this kind of optical phantoms can be made

by several different techniques. The perhaps most used characterization method, collimated

transmission79, is fairly easy to handle. Other characterization methods that are frequently

used are spatially resolved diffuse reflectance (SRDR)80, and integrating sphere

measurements81. Methods of importance regarding the work in this thesis, are oblique angle

illumination82, 83, and goniometry84, although they are not that well-known as the previously

mentioned methods.


38

In this thesis, only liquid optical phantoms consisting of milk or polystyrene spheres as

scattering media and ink as absorber have been used. The phantoms have been used both as

evaluation objects when developing measurement techniques for sμ � and phase function

determination (papers I and V, respectively) as well as calibration phantoms when using

photon migration models and inverse problem solving for determination of tissue

chromophore concentration and oxygenation/oxidation status (papers II, III, and IV).

Collimated transmission has been used as reference method when characterizing the phantoms

(i.e. measuring the absorption and scattering coefficients).

6.1 PHANTOM CONSTRUCTION

A major issue when constructing liquid optical phantoms is to ensure proper mixing of the

scattering and absorbing components, and also to maintain the homogeneity of the liquid

throughout the phantom life-time. The precision needed when mixing the different

components of an optical phantom is, of course, to some extent determined by the application

at hand. In this thesis, both volumetric (pipetting) and weighing (precision scale) methods

have been used. When using the latter method, knowledge about the different component

volume densities are required in order to calculate proper volumes.

Typical values of a suitable volume of an optical phantom are in the range of 100 to 500 mL.

The smaller the volume, the greater the risk for introducing effects such as boundary effects,

stray light influences etc. When mixing the different components, it should also be ensured

that large enough volumes are used in order to reduce errors due to precision limitations

inherent from either the pipette or precision scale instrumentation.

6.1.1 SCATTERING COMPONENTS

A great variety of scattering components when constructing optical phantoms can be seen,

ranging from biological materials such as lipid based emulsions to polymer microspheres.

Oxide powders (titanium or aluminum) are also widely used76. For liquid optical phantoms,

the oxide powders seem to be less frequently used compared to lipid emulsions and polymer

microspheres. Only the two latter are covered in this sub-chapter.


39

Polystyrene microspheres In the absolute majority of cases where microspheres are used as optical phantoms, it is

assumed that the microspheres appear as single objects and are homogeneously distributed

throughout the suspension. Then, the scattering properties of the microspheres can

successfully be described by Mie theory, given that the sphere diameter, wavelength of the

incident light, relative refractive index, and number density (particle concentration) are known.

In paper I, efforts were made to construct liquid optical phantoms by using mono-dispersive

polystyrene microsphere suspensions as scattering component. However, inconsistencies were

detected when performing multiple series of sμ � measurements using the oblique angle

technique. Therefore, electron microscopy photos were taken on randomized samples of the

suspensions, and a few representative photos with different field-of-views are shown in Figure

15. Methods for detecting and reversing aggregation have been suggested85, but requires

additional investigations by electron microscopy in order to ensure that the reversion process

has succeeded.

Figure 15: Electron microscopy images of an aggregated mono-dispersive microsphere

suspension (particle radius 155 μm). Note: The color space has been inverted for clarity.

Indications of microsphere aggregation can be seen when performing the collimated

transmission measurements, by logging the transmitted intensity for a fixed d (see Figure 16),

over a period of time (>~1 min). It is then likely that complexes consisting of a large number

of aggregated microspheres, such as those in Figure 15, right panel), passes through the

collimated light beam, producing sharp "dips" in the recorded intensity, I (see Figure 16). Fat emulsions Because of the problems encountered when using the microspheres, eventually the

experiments in paper I were performed using milk as scattering component instead. The

scattering properties of milk depend on the size distribution and the refractive index

differences of fat globules and casein micelles86. The milk used in the work described in this

thesis, have been ultra-high temperature (UHT) treated, which is a process performed to


40

prolong the expiration date. During the treatment, homogenized milk is rapidly heated to

above 135°C for 2-5 seconds. As described earlier in this chapter, this type of liquid optical

phantoms can be expected to deteriorate after typically 6-12 hours. Visual inspection showed

that substantial clotting of fat globules occurs after 12 hours if stored in room temperature, in

scattering phantoms containing milk and water.

There exist several other fat emulsions, such as Intralipid, Vasolipid, ClinOleic, and

Lipovenoes, which are all primarily designed to serve as nutrient solutions. The light

scattering component in those fat emulsions is soy-bean oil particles. It should be noted that

for the above mentioned solutions, there exist different fat concentrations, ranging from

approximately 10% to 30%. For Intralipid 10%, Staveren et al. have described that there are a

heterogeneous distribution of particle diameters ranging from 25 to 675 nm87. Although milk

does not contain soybean oil particles, the chemical structure are similar to the fat emulsions,

in that it contains a heterogeneous distribution of scattering particle sizes. Therefore, to

predict the scattering properties utilizing Mie theory is in these cases not as straight-forward

as in the polystyrene microsphere case. Attempts have been made to use Mie theory and

assume scatterer size distributions restricted to a linear decay in the logarithmic size scale78.

Nevertheless, the HG phase function is widely accepted and used for describing light

propagation in biological tissues and optical phantoms involving biological substances. For

measurements encompassing small source-detector separations (close to one mfp� ), the two-

parametric Gk phase function has been proven useful54.

6.1.2 ABSORPTION COMPONENTS

As in the case with scattering components, various materials are used as absorbers in optical

phantoms. The absorption component in liquid optical phantoms is usually ink or dye77, 88. The

great number of different inks available on the commercial market can (roughly) be divided

into two groups; water-based and oil-based. When constructing water-based (liquid) optical

phantoms, it is important to use water-based ink in order to ensure a homogeneous

distribution of the absorbers. The lipid-based ink shows a lipid affinity greater than the water

affinity, and is more prone to form large, unwanted lipid-ink structures. In this thesis, ink with

different colors (red, blue, green, and black) from Coloris Ink, Stefan Kupietz KG, Germany,

have been used.


41

6.2 PHANTOM CHARACTERIZATION

Before using optical phantoms as reference objects or in calibration procedures, knowledge of

the optical properties is essential. Consequently, the choice of method for characterization of

these properties is crucial, and should be paid great attention. One of the most widely used

method is collimated transmission. Although the method has been described frequently in the

literature79, 89, it is essential in this thesis, and is described separately in the following sub-

chapter. The method has been used as a reference method for measurements of the scattering

and/or absorption coefficient in all included papers in the thesis. One important note is that

when optical phantoms displaying dependent scattering behavior are used, characterization of

sμ through the use of the collimated transmission should not be performed on dilutions of

those phantoms, because of reasons further discussed in chapter 9.2.

6.2.1 MONOCHROMATIC COLLIMATED TRANSMISSION

A schematic view of the collimated transmission setup used in paper I is shown in Figure 16.

Figure 16: A schematic drawing of a setup used for monochromatic collimated transmission

measurements.

By measuring I as a function of d (typically 5-15 data points), and straight-forward

application of the Beer-Lambert law (equation 14), we can calculate the absorption (scattering)

coefficient of the sample of interest according to equation 32:

0

a (s) ln I dI

� � � � � !

. (32)

When measuring the scattering coefficient, the concentration of the sample of interest should

be chosen in order to avoid contribution from multiple scattered photons. Consider Figure 17:

I

I0

He-Ne laser

Variable sample thickness, d

Vertically adjustable transparent cylinder

Light detector

Cuvette

Mirrors

Adjustable pinholes


42

Figure 17: A collimated light beam propagating through a cuvette containing an aqueous

scattering solution. Left panel: Correct relationship between medium thickness and

concentration of scatterers in order to avoid multiple scattered photons. Right panel: Too

dense scattering medium in relation to medium thickness giving rise to multiple scattered

photons.

It can be understood from the left panel of Figure 17, that virtually all contributions to the

transmitted intensity I, are inherent from unscattered photons, thus giving a "correct" situation

for measuring the scattering coefficient. On the other hand, when the concentration of

scattering particles increases (right panel), photons that have been scattered multiple times can

still emerge from the cuvette in a direction coinciding with the optical axis of the system, and

thus falsely contribute to the detected intensity I. These photons are crossed out in Figure 17.

These false contributions become more prominent with increasing concentration of scatterers

and also with increasing distance d, the latter because of a reduced contribution from

unscattered photons when d increases.

Other parameters, such as the phase function of the scattering solution, also have to be

considered when discussing multiple scattered photons re-entering the original light

propagation direction. Light propagating through a medium (according to Figure 17) with

very forward-scattering properties (g close to unity), are more likely to contain multiple

scattered photons when exiting the cuvette in the forward direction, compared to when

travelling through a more isotropic scattering medium.

Optical axis


43

Considering all factors together, an exact value for the maximum distance d that could be

used during a measurement series, is hard to establish, but generally it should not exceed 1-3

mfp.

6.2.2 SPECTRAL COLLIMATED TRANSMISSION

In the monochromatic setup described above, the absorption or scattering coefficient can only

be determined for the specific wavelength of the light source. Often a continuous absorption

or scattering spectrum is desired for the sample of interest. By using a broadband light source,

optical fibers for light guiding, and two fiber collimators, a setup similar to that described in

Figure 16 can be constructed and is shown in Figure 18.

Figure 18: A schematic drawing of a setup used for spectral collimated transmission

measurements.

Most of the experimental considerations described in the monochromatic case, also apply for

spectral collimated transmission (SCT). However, even more attention should perhaps be paid

to situations involving highly forward-scattering media. Collimation of a broadband light

beam offers in practice more difficulties than collimation of a laser beam. This may result in

detection of photons that emerge from the sample with a direction close to, but not perfectly

parallel to the optical axis. The effect could, to some extent, be avoided by allowing enough

distance between the cuvette and the collecting fiber collimator.

Below are two examples of the spectral scattering and absorption coefficients measured by the

setup described in Figure 18.

Vertically adjustable transparent cylinder

Light source

Cuvette

Fiber collimators Spectroscope

Variable sample thickness, d


44

500 600 700 8000

5

10

15

ab

cd

Wavelength [nm]

μ s [mm

−1]

500 600 700 8000

0.5

1

1.5

2

Red

Blue

Black

Wavelength [nm]

μ a [mm

−1]

Figure 19: Left panel: Spectral scattering coefficient of four different UHT milk (1.5% fat content) dilutions.

Fractional milk content: a) 1/8, b) 1/4, c) 1/2, d) 1. Right panel. Spectral absorption coefficients of red, blue,

and black Coloris Ink. Each of the components have been diluted according to 1 ink : 500 water.

Chapter 7 – Quantitative diffuse reflectance spectroscopy

45

Chapter 7 QUANTITATIVE DIFFUSE

REFLECTANCE SPECTROSCOPY

Attempts to define the single term spectroscopy beyond its trivial translation "to view a

spectrum", based on the greek term skopein = to view90, would be very hard because of the

great variety in the areas of application. Dividing spectroscopy into two categories; classical

and modern, can serve as a first categorization91. The very first step towards formalization of

classical spectroscopy was taken by Sir Isaac Newton in 1666, by introducing the term

"spectrum", describing the dispersion of sunlight into a continuous series of colors. The birth

of modern spectroscopy coincides with the early development of the laser technology around

1960. Through its highly collimated, monochromatic EM radiation and high intensity, laser

light enabled new possibilities within atomic and molecular spectroscopy.

DRS is a branch within spectroscopy that is based on analysis of backscattered light that has

propagated through a scattering and absorbing medium. Among the first applications of the

technique was the analysis of chemical compounds such as oxide powders, performed in the

early 1960’s92-95. Early DRS studies involving analysis of biological chromophores such as

hemoglobin were presented in the late 1970’s96, 97.

The term "quantitative"a is first described in relation to spectroscopy (although not DRS), in

the discovery of the "Fraunhofer lines" (1814), when Joseph Fraunhofer (1787-1826)

quantified the intensity drops of certain wavelengths in the solar spectrum due to EM

radiation absorption of chemical elements. In theory, as soon as two values of the same

parameter (for example, intensity) are compared and related to each other, it can be

considered as quantification. More accurately, this type of quantification should be denoted

relative quantification. There are numerous examples of applications of this relative qDRS

procedure involving biological chromophores13, 59, 98, 99. In this thesis, quantitative diffuse

reflectance spectroscopy (qDRS) is referred to measurements where absolute concentration

measures are determined.

a The Latin word ”quantus” means: 1) how great; 2) how much; 3) many. Latin derivations include; quantificare, quanta, quantitas, quantum, quantitatio.


46

7.1 SPECTRUM RECONSTRUCTION

The fundamental idea of spectroscopy is to observe changes in light intensity as a function of

wavelength. An ideal case of detecting the diffusively backscattered light would mean that the

instrumentation does not alter the light intensity and color emerging from the medium under

investigation. Clearly, this is not possible. In all optical systems designed for light detection,

the instrumentation (lens packages, optical fibers, prisms, gratings, CCD’s etc.), introduce

changes in the original light distribution as it propagates from the light source, being guided

to and from the medium under investigation through optical components, and finally being

detected by the detector device. In order to compensate for these effects, controlled calibration

measurements have to be performed, and are individually described in relation to the example

illustrated in Figure 20.

Figure 20: A light source, a spectroscope, and a fiber-optic probe showing fiber

arrangement and light propagation directions.

7.1.1 THE LIGHT SOURCE

Most light sources can display temporal intensity and color variations. By simultaneous

registration of spectra detected by fibers A � �lampM and C � �tissueM , measured spectra from

the medium under investigation can be normalized with its corresponding light source

spectrum. Effects in the measured tissue spectrum due to variations in lamp source intensity

and color, is then eliminated in the lamp-normalized spectrum tissue lamp,tissueM M . The

subscript "lamp, tissue" denotes the lamp spectrum at the tissueM occasion.

Light source

Spectroscope

Fiber-optic probe head

Heart tissue

A

C B

lampM tissueM


47

7.1.2 INTENSITY REFERENCE MEASUREMENTS

It is easy to realize that the coupling efficiency at both the lamp and spectroscope connector

can vary due to dis- and reconnection of the fiber-optic probe. In cases where comparisons

between spectral intensities from different occasions are of interest, the influences on tissueM

from the above mentioned effects have to be compensated.

One way of solving this problem is to perform an intensity reference measurement � �intrefM

on an object with optical properties consistent over time, in addition to the measurements on

the medium of investigation. Lamp normalization of intrefM should be performed analogous to

the case described in section 7.1.1, forming intref lamp, intrefM M . The expression:

� ��

tissue lamp, tissueintrefnormtissue

intref lamp,intref

M MM

M M , (33)

enables comparison of spectral intensities recorded at arbitrarily chosen occasions.

Each time a reference measurement is performed, it is crucial that all parameters having an

impact on intensity and/or color of the measured spectra; ambient light, probe position

relative to the reference object, mechanical vibrations etc., can be reproduced with high

accuracy. Although the key feature of using a reference is the non-changing optical properties

of the reference material, materials with very large intensity variations or sharp spectral

peaks/dips in the reflectance spectrum, should be avoided.

7.1.3 COLOR CORRECTION

Ideally, tissueM would represent the spectrum as seen at the boundary between the heart tissue

and fiber B. However, the optical components of the spectroscope and color dispersion in

fiber C will introduce changes not associated with the optical properties of the medium under

investigation. This can be compensated for by performing a white-normalization, or

equivalently, a white-correction measurement. In practice, the diffuse reflectance spectrum of

an object with 100%a reflectivity in the wavelength region of interest, is measured � �whiteM .

a In practice, 100% reflectivity cannot be achieved. Tightly packed BaSO4 powder typically display 98% reflectivity in the visible wavelength region.


48

Lamp normalization of whiteM should be performed as described in section 7.1.1, forming

white lamp, whiteM M .

The expression:

� ��

tissue lamp, tissuewhitenormtissue

white lamp,white

M MM

M M , (34)

normalizes tissue lamp,tissueM M so that any color and intensity influences due to fiber C and

optical components of the spectroscope are eliminated.

7.1.4 COMPLETE NORMALIZATION PROCEDURE

It can be realized from sections 7.1.2 and 7.1.3 that if the intensity reference object is

constructed of a material displaying close-to 100% reflectivity in the wavelength region of

interest, white correction and the intensity reference measurement are performed in a single

measurement. Unfortunately, manufacturing of a mechanical robust intensity reference

containing a perfectly white surface may not always be feasible. In addition, performing

white-calibration measurement in a clinical setting can be unsuitable, as it may involve

handling of 4BaSO -powder which is toxic.

As long as the optical properties of the intensity reference are consistent over time, the

complete normalization (white correction and intensity reference measurement) of tissueM can

be performed in two separate steps, performing only the intensity reference measurement at

every occasion. Then, white correction can be performed at a separate occasion. The complete

normalization procedure would then be:

� ��

� ��

1 2

tissue lamp, tissue intref lamp,intrefnormtissue

intref lamp,intref white lamp,white

t t

M M M MM

M M M M

�� , (35)

where 1t and 2t represents two different occasions, independent in time.


49

7.2 CALIBRATION OF PHOTON MIGRATION MODELS

In section 4.2.3, the absorption spectra of several myocardial chromophores were presented.

As seen in Figure 13 and Figure 14, the chromophores display spectral characteristics,

occurring as peaks or dips in � �aμ � . Those characteristics can be utilized in relative fitting

procedures of the photon migration models described in chapter 5 to measured data. However,

this only enables relative quantification of the chromophore tissue content. In order to obtain

absolute concentration measures, the photon migration model has to be calibrated using

optical phantoms with known optical properties.

7.2.1 THE EMPIRICAL MODEL

Equation 21 describes an empirical model for light transport in tissue. The two expressions K

and L contains in total six coefficients to be determined by fitting against measured

calibration data from optical phantoms with known sμ � and aμ . To obtain optimal fitting

between � �s a,T μ μ� and measured data in practical qDRS applications, the ranges in sμ � and

aμ have to be chosen such that they will cover the expected optical properties of the medium

under investigation. The empirical light transport model calibration procedure is described

below through an example involving 56 optical phantoms with optical properties in the ranges

� � 1s 0.6 3 mmμ � ' and � � 1

a 0.01 2.88 mmμ ' .

Calibration example The calibration measurement data are normalized according to equation 35, and are denoted

normcalM . Characterization of the optical phantoms (measuring sμ and aμ by monochromatic

collimated transmission using a He-Ne laser) is done at 633� nm. Fitting of T (equation

21) against normcalM with respect to a f are performed at the same wavelength, by

minimizing the residual expression defined as:

� � � ��

s a

s a norm633nm cal 633nm

,, 1

T μ μE μ μ

M��

�� , (36)

in a least-square sense, using the Levenberg-Marquardt algorithm. The optimally fitted model

and the corresponding residual expression are denoted � �*s a,T μ μ� and � �*

s a633nm

,E μ μ�

� ,

respectively. For 633� nm, normcalM and � �*

s a,T μ μ� are shown in Figure 21.


50

0 0.5 1 1.5 2 2.5 3 3.5

10−1

100

μs´ [mm−1]

Inte

nsity

[−]

T *(μs´,μa)+ Mcal

norm

Figure 21: norm

calM and optimally fitted model intensity, � �*s a,T μ μ� at 633� nm.

Figure 22 shows the residual expression � �*s a

633nm,E μ μ

�

� .

0 0.5 1 1.5 2 2.5 3 3.5−0.5

0

0.5

1

μs´ [mm−1]

[−]

Figure 22: Residual expression � �*

s a633nm

,E μ μ�

� .

The maximum deviation between measured and the optimally fitted model data for all

absorption levels but the highest involved in the calibration procedure

� �� 1a 0.01 2.88 mmμ ' , is 8.8%. However, for the highest absorption level � �1

a 2.88mmμ ,

the mean deviation over sμ � is 41.4%, with an apparent trend of decreasing deviation with

increasing sμ � .

μa


51

It should be noted that when the range(s) in sμ � and/or aμ are expected to be large, the use of

second-order polynomials �K and �L when calibrating the light transport model may display

substantial deviations from measured calibration data. In 2005, Bargo et al.20 proposed a fiber-

based endoscopy system together with an extension of equation 21, involving polynomials of

order 15 to be used for in-vivo determination of optical properties in normal and tumor tissue.

7.2.2 THE MONTE CARLO MODEL

While knowledge about sμ � and aμ of the calibration phantoms is sufficient to calibrate the

empirical photon migration model, the wavelength dependent refractive index, and more

importantly the phase function of the calibration phantom, are required when calibrating the

MC photon migration model. In the work presented in this thesis, two ways of calibrating the

MC photon migration model describing the backscattered light detected by a fiber-optic probe,

have been used (paper V). The first calibration procedure involved a polystyrene microsphere

suspension (referred to as absolute calibration) as a reference object, while the other

procedure only involved calibration between different source-detector separation distances

(referred to as relative calibration).

In this chapter, the principle of both methods is described using the calibration procedure in

paper V as an example.

Absolute calibration

To calibrate the MC photon migration model using an optical phantom, the phase function has

to be known to accurately describe the light scattering. A non-absorbing, monodispersive

polystyrene suspension with known particle radius, r , is suitable as a calibration phantom,

since Mie theory can be directly applied to describe the light scattering without the need for

experimental phase function measurements.

The first step is to determine the wavelength dependent scattering coefficient, � �sμ � , of the

polystyrene suspension, which is done by SCT measurements. (The wavelength dependent

refractive index, � �n � of the polystyrene suspensions is often given by the manufacturer, and

methods for refractive index determination do exist100, 101).


52

The second step is to employ MC to simulate the diffuse reflectance spectra for the

wavelength region of interest from the polystyrene suspension. The � �sμ � determined by

SCT, � �n � and r are used as input parameters to the MC calculations. The specific probe

geometry, such as source-detector separations and refractive index mismatch between probe

and the suspension, have to be accounted for when simulating the detected spectra.

The third step is to measure the diffuse reflectance spectrum from the polystyrene suspension,

and compare it to the simulated spectra. The ratios between the mean intensity (over the

selected wavelength region) of the measured and simulated spectra, define the calibration

factors, here denoted absA . The MC simulated spectra and the measurement spectra normalized

according to equation 35 for a fiber-optic surface probe containing four different source-

detector separations, denoted 1 4toD D (230, 690, 1150, and 1610 μm ) are shown in the left

panel of Figure 23.

Relative calibration

The main difference between this calibration procedure compared to the absolute calibration

case, is that no optical phantom is required. However, for the relative calibrated photon

migration model to be useful, multiple source-detector separations are needed, since the

relative calibration involves intensity comparisons between fibers.

The relative calibration factors between detection fibers are obtained by uniformly illuminate

the detector fibers of the probe. To ensure uniform illumination, the probe can be submerged

in a highly scattering suspension acting as a diffusive medium which is illuminated by, for

instance, a broadband light source. As the absolute magnitude of the relative calibration

factors is arbitrarily and does not contain any information, the calculated calibration factors

can be normalized by their mean. This results in calibration factors centered around unity,

which may be a more convenient set of factors. The relative calibration factors in the example

are denoted relA


53

500 550 600 650 700 750 80010−6

10−5

10−4

Wavelength [nm]

Inte

nsity

[−] D1

D2D3D4

1 2 3 40.75

0.8

0.85

0.9

0.95

1

1.05

1.1

D [#]

[−]

Figure 23: Calibration measurements using a polystyrene microsphere suspension. Measured

(black) and simulated (gray) spectra for 1 4D . Measured spectra are normalized by absA . Right

Panel: absA for 1 4D from the microsphere suspension measurement (*) and relA from the uniform

illumination measurement (�). Both series are normalized by their mean value.

7.3 CHROMOPHORE QUANTIFICATION

Once the photon migration models described in section 7.2 are calibrated, they can be used for

quantification of chromophore concentrations in a medium under investigation. The common

strategy for both models is to solve the inverse problem by fitting the model to measured data,

using two scattering parameters (see section 7.3.1 and 7.3.2), the volume fractions of

chromophores and in some cases, chromophore status parameters, as fitting variables. For the

empirical, the procedure for solving the inverse problem is described in sub-section 7.3.1,

using examples similar to the work presented in papers II-IV. For the MC photon migration

model, a possible procedure for chromophore volume fraction determination is presented,

although it has not been applied in the work in this thesis.

7.3.1 THE EMPIRICAL MODEL

Determination of the coefficients a f in equation 21, provide an expression for predicting

the light intensity as a function of sμ � and aμ , recorded by the fiber-optic probe at hand. For

the investigated tissue in papers II-IV, the reduced scattering coefficient sμ � was assumed to

conform to the expression:

sμ (� �� , (37)


54

where � and ( are fitting parameters. In the inverse problem solving procedures, the

following expression was instead used:

s 700μ

(��

� �� !

. (38)

The normalization of � in equation 38, make � govern the level and ( the wavelength

dependence of sμ � .

The total absorption in the medium under investigation ( aμ in equation 21) is written as a

linear combination of the chromophore absorption spectra. For instance, if Hb , 2HbO , lipid

and water are assumed as chromophores in an investigated tissue with unknown Hb oxygen

saturation, the aμ can be written as:

� �� 2a Hb Hb a,HbO Hb a,Hb lipid a,lipid water a,water1μ f S μ S μ f μ f μ � � � , (39)

where if is the tissue volume fraction of chromophore i, HbS is the fractional oxygen

saturation of Hb, and a, iμ is the absorption spectrum of chromophore i. By combining

equations 21, 38, and 39, the light transport model � �s a,T μ μ� can now be translated into a

function of the parameters i Hb, , , andf S� ( .

Before the parameter fitting is performed, the measurement spectrum of the tissue under

investigation should be normalized according to equation 35. Determination of the fitting

parameters is then done by minimizing the expression:

� �i Hbnormtissue

, , ,1

T f SE

M� (

. (40)

The minimization of equation 40 was in papers II-IV performed by employing the Levenberg-

Marquardt algorithm, which is suitable for optimization of non-linear problems102.

The total absorption expression, exemplified in equation 39, can be extended to include the

chromophores of interest for each application at hand. It is straightforward to realize that the

model curve fitting to measured spectra can only be performed in wavelength regions where

the absorption spectra of all chromophores are accessible.


55

7.3.2 THE MONTE CARLO MODEL

The idea of chromophore quantification through the use of inverse problem involving MC, is

to compare pre-simulated MC spectra for different combinations of sμ � and aμ , with

measured spectra. In contrast to the empirical model case, the technique presented in this

section does not require a-priori knowledge of the optical properties of the medium under

investigation. The original simulation used in the calibration of the MC photon migration

model (see section 7.2.2) can be utilized, rescaled, and post-processed to predict the detected

intensity as seen by the probe, for arbitrarily sμ � and aμ combinations.

As in the empirical model case, an expression describing the reduced scattering coefficient

(see equation 38) is required. Also a total tissue absorption expression (see equation 39)

containing the tissue chromophore concentration and status parameters as fitting variables,

has to be provided by the user.

The pre-simulated MC intensities can be represented by a multi-dimensional intensity array,

with the dimensions � , sμ � and aμ . For each wavelength � �� where measured data exist, the

array contains intensity values as a function of sμ � and aμ . The minimal number of

wavelengths required to solve the inverse problem, is determined by the total number of

fitting variables in equations 38 and 39. The difference between the measured and MC

simulated probe intensities (i.e. spectra), is minimized by optimizing the fitting variables in

equations 38 and 39.

56

Chapter 8 - Review of the papers

57

Chapter 8 REVIEW OF THE PAPERS

8.1 PAPER I - Reduced scattering coefficient determination by non-contact

oblique angle illumination - methodological considerations

Paper I was focused on construction of optical phantoms and determination of the reduced

scattering coefficient. The technique has previously been presented by Jacques and Wang82,

and was modified in order to increase the robustness, the dynamic range of detectable back-

scattered light intensities, and precision in determining sμ � .The optical phantoms were

characterized by monochromatic collimated transmission � �633nm� , and were used as

reference objects when the proposed method was evaluated.

The key idea in the oblique angle setup is that a sample � �a sμ μ �� is illuminated with a

known, non-normal angle, using a collimated light beam. The diffuse reflectance profile from

the sample, can then be modeled as the reflectance from a virtual isotropic point source at a

distance of 1 mfp� , measured along the geometrical light path from the point of incidence to

the center of the isotropic point source; see Figure 24,

Figure 24: Principles of the oblique angle illumination technique.

where � is the angle of incidence, measured from the surface normal, �r is the horizontal

distance of the isotropic point source relative to the point of incidence, ns and nm is the

refractive index of the surrounding medium and the medium itself, respectively. From Figure

24, sμ � can be identified as:

sn

mn

s1 μ �

� r$


58

� �

sm

sinμ

n r�� $

. (41)

As proposed by Wang and Jacques, sμ � is dependent on aμ when the absorption and the

reduced scattering coefficients of the medium is comparable. A modification of the original

sμ � expression (equation 41) was proposed, including an additive aμ -dependent term in the

original expression. The modified expression is shown in equation 42.

� �

s as

sin0.35μ μ

n r��

$ . (42)

The factor 0.35 in the additive aμ -term was tested theoretically (by MC simulations) and

experimentally in the original publication. However, in paper I, it was found that the minimal

absorption influence on the calculated sμ � was obtained by subtracting a0.78 μ instead of the

proposed a0.35 μ . The 0.78 factor was determined by, for each fixed aμ of the optical

phantoms used in the study, minimizing the differences between calculated sμ � (see figure 8

in paper I). This way of calculating the 0.78 factor, assumed that the product of � �1 g and

sμ � �si.e. μ � was independent of aμ .

The anisotropy factor (denoted ,2r Dg$ in paper I) was determined according to

� �s s 1μ μ g� , since sμ for the milk was readily accessible via the collimated transmission

measurements, and sμ � was calculated based on equation 41 (or 42). The anisotropy factor

(denoted MC fitg in paper I) was also determined by solving the inverse problem of fitting MC-

simulated SRDR profiles calculated for sμ and aμ as determined by collimated transmission,

and a number of anisotropy factor values ranging from 0.7 to 0.82, to measured SRDR data.

In the simulations, the HG phase function was used. In addition, the anisotropy factor

(denoted LDFg in paper I) was for comparison determined by a laser Doppler flowmetry (LDF)

technique. In short, the LDF technique utilizes the shape of the Doppler power spectrum for a

known system geometry, concentration and velocity distribution of the scatterers in the

medium under investigation, to estimate the scattering phase function (and hence the

anisotropy factor). The mean anisotropy factor values at 633 nm� for the three different

methods, ,2r Dg$ , MC fitg , and LDFg were 0.73, 0.74, and 0.77, respectively, which all were in

agreement with other studies103, 104.


59

8.2 PAPER II -Myocardial tissue oxygenation estimated with calibrated diffuse

reflectance spectroscopy during coronary artery bypass grafting

Paper II was designated to development of a qDRS method for measurement of in-vivo

myocardial oxygenation. A photon migration model previously presented19, was used and

modified to model myocardial tissue scattering and absorption. The model was calibrated

using a set of optical phantoms covering the expected range of optical properties � �s aandμ μ� .

By model fitting against measured myocardial tissue diffuse reflectance spectra, tissue

chromophore fractions and the sum of hemoglobin and myoglobin oxygenation were

calculated by solving the inverse problem. The method was clinically applied and evaluated

during routine CABG surgery of 10 human subjects.

The ranges in the optical properties of the calibration phantoms were set to � � 1s 2 10 mmμ '

and � � 1a 0.01 2.88 mmμ ' . Vasolipid was used as phantom scattering component, and g was

set to 0.7 according to Flock105 and Driver106. Coloris Ink was used as absorber.

Tissue oxygenation was assessed at five different surgical phases; before aortic cross-

clamping (baseline), after aortic cross-clamping and cardioplegic infusion (postcardioplegic

infusion), before the release of the aortic cross-clamp (prereperfusion), after the release of the

aortic cross-clamp (postreperfusion), and after surgery when the extra-corporeal circulation

(ECC) is completely phased out (postCABG). Both at the proximal and the distal site,

measurements were performed in three different points (1-3 corresponding to the proximal

site, and points 4-6 corresponding to the distal site, see Figure 25) and spectra from 1-3 and 4-

6, respectively, were averaged in order to reduce the effect of tissue heterogeneity.


60

Figure 25: The measurement sites on the heart. Sites 1- 3 are proximal to the stenosis, and sites 4-6

are distal to the stenosis. Actual sites for each patient were determined by the surgeon using

anatomical markers for identification. Reprinted with permission from Ph.D. Erik Häggblad,

Linköping University.

The average 2R value for the fitted model spectra at the distal site, was 0.96, ranging from

0.86 to 0.99. For recordings with low 2R values within this range, the model spectra

overestimated the measured spectra at wavelengths near 510 nm� and near 620 nm� .

Mean tissue oxygenation values proximal to the stenosis were 47.7%, 76.2%, 57.7%, and

62.1%, for the baseline, postcardioplegic infusion, postreperfusion, and postCABG phases,

respectively. Corresponding values distal to the stenosis were 54.5%, 68.1%, 70.1%, and

67.5%, respectively. For both the proximal and distal measurements, the mean tissue

oxygenation increased when comparing postcardioplegic infusion to baseline, which indicates

a good metabolic conservation of the myocardium when entering the cardiac arrest phase.

During cardiac arrest, tissue oxygenation decreased slightly, indicating a low metabolic need.

Comparison of postreperfusion to baseline, tissue oxygenation increased both at the proximal

and distal sites.

8.3 PAPER III - Improved residual when modeling myocardial diffuse

reflectance spectra including mitochondrial cytochromes

Paper III was based on the same measurements performed in paper II, but the absorption

expression in the photon migration model included additional chromophores compared to the

absorption expression used in paper II. Methemoglobin, and the reduced and oxidized forms

of cyt aa3 was included in the light transport model. This reduced the characteristic spectral

deviations in the fitted model spectra found in paper II.

The spectral fitting of this new model was evaluated by comparing the 2R values to the ones

from paper II, and additionally by visual inspection of the residual spectra

� �* *s a tissue,norm, 1E T M� �� , where *T was the optimally fitted model, and tissue,normM was

the measured spectrum normalized according to equation 35 in the thesis. The average 2R

value for the fitted model spectra for all recordings was 0.99, ranging from 0.92 to 1.00.


61

The trends in Hb+MbS were comparable to those in paper II, although the values were on

average 4% units higher in this study. However, fewer statistically significant differences

were found in this paper, compared to paper II. The cyt aa3O was higher than 95% for all

surgical phases, and with opposite trends as in Hb+MbS . In addition, the mean Hb+Mbf were

calculated and reported to be 1.6%, ranging from 1.5% to 1.7%. Corresponding values for

cyt aa3f were 0.58%, ranging from 0.50% to 0.73%.

8.4 PAPER IV - Intramyocardial oxygen transport by quantitative diffuse

reflectance spectroscopy in calves

Paper IV involved development of an intramuscular fiber-optic probe to be used for in-vivo

qDRS measurements on myocardial tissue. The measurement setup was evaluated in the

animal laboratory during open-chest surgery involving hemodynamic and respiratory

provocations of seven calves.

In five calves, denoted group A, the fraction of inspired oxygen level, I, O2F was varied in

three steps; 21%, 50%, and 100%, with a duration of three minutes each. Measurements were

performed continuously throughout the variations. In two cases, measurements were also

performed during initiation of cardiac arrest in the end of the experiments.

In one of the two calves denoted group B, I, O2F was held at 100% while the speed of an

implanted LVAD pump was varied in three different steps; 6000 rpm, 7500 rpm, and 10000

rpm during one minute per phase. Following that, the LVAD speed was maintained at 10000

rpm while I, O2F was varied according to 50%, 21%, 50%, and 100%. The duration of each

I, O2F was one minute. The second individual in group B was subjected to a constant LVAD

pump speed at 7500 rpm, while the I, O2F was varied according to 21%, 50%, and 100%, with

a duration of one minute per phase.

The probe placement for the two groups together with a schematic drawing is shown in Figure

26.


62

Figure 26: Left panel: Schematic view of the fiber-optic probe tip. Middle panel: Fiber-optic probe

placement in animals from Group A. Right panel: Fiber-optic probe placement in animals from

Group B, including the LVAD. The probe placement is highlighted with a white arrow.

The light transport model was based on equation 21, but was calibrated on optical phantoms

using milk as scatterer with another set of optical properties;

μs´=[0.16 0.32 0.64 1.28]�=632.8 nm mm-1 and μa=[0 0.01 0.05 0.1 0.2 0.4 0.8 1.6]�=632.8 nm

mm-1. The anisotropy was set to 0.84. The absorption expression for bovine heart tissue

involved Hb , 2HbO , cyt aa3,ox , cyt aa3,red , metHb and water.

In group A, the mean Hb+MbS ranged from 19% to 28% when I, O2F was increased. The cyt aa3O

was above 97% for all individuals and all phases. Hb+MbS during cardiac arrest were lower

than 5%.

In group B, Hb+MbS displayed similar trends as in group A when I, O2F was manipulated. The

absolute Hb+MbS levels, however, were higher in this group compared to group A, indicating

that the LVAD pump lower the myocardial metabolic need. The maximum Hb+MbS value (44%)

was found in the second individual during I, O2F =100%, LVAD speed of 7500 rpm.

The use of an intramuscular probe greatly reduced the influence of movement artifacts and

probe-tissue discontact - problems that were obvious in papers II-III where a surface fiber-

optic probe was used. However, during insertion of the probe, bleeding was sometimes

visually noted. Potentially, this could influence the estimated tissue volume fraction of

0.8 4.5

10.0

[mm]


63

hemoglobin. Also, pulsatile variations in the estimated amount of hemoglobin were found,

which may indicate the presence of larger vessels close to the measurement site.

8.5 PAPER V - Spectral determination of a two-parametric phase function for

polydispersive scattering liquids

Paper V presented a method for determination of a two-parametric � �Gk Gkand g� phase

function of polydispersive liquids, for example milk or fat emulsions, by combining MC

simulations of photon migration and DRS measurements performed at different source-

detector distances. Two ways of intensity calibration of a fiber-optic probe system were

presented, one involving a single optical phantom containing polystyrene microspheres

(absolute calibration), the other involving only relative intensity calibration between different

source-detector distances (relative calibration).

In the absolute calibration case, the mean radius of the microspheres was 155 μm107, and the

refractive index was based on water108 and polystyrene109. The MC setup consisted of a semi-

infinite slab representing the microsphere suspension, with sμ determined from a SCT

measurement. The suspension was assumed to be non-absorbing. The calibration factors

� �absdenoted , where subscript "abs" represents absolute calibrationA were calculated as the

ratio between the mean intensity in the wavelength range 500-800 nm of the measured and the

simulated spectra.

In the relative calibration case, the detector fibers were uniformly illuminated by lowering the

fiber-optic probe tip into a high-scattering polystyrene suspension illuminated from below by

a white halogen lamp. The relative calibration factors � �relA were then calculated as in the

absolute calibration case.

The ranges for Gk� and Gkg in the MC simulations used for solving the inverse problem,

were 0.025-0.5 and 0.7-0.9, respectively, with 7 steps in the Gk� space and 11 steps in the

Gkg space. One original sμ was used in the simulations, and a rescaling procedure (see the

article and section 5.2.5 in this thesis) was applied in the MC simulation post-processing to

obtain results for different sμ (in total 31 values, as determined by the resolution in � ). The

diffuse reflectance spectra were calculated for 4 different source-detector distances ranging


64

from 230 μm to 1610 μm. In total, the complete MC generated intensity array had the lengths

(dimensions) � � � � � � � � � �Gk 1 4 1 47 11 31 4 4Gkg OP D� � ) ) ) ) , where OP and D are

abbreviations for "optical phantom" and "detector index", respectively. Denoting the

simulated and measured intensities MCI and measI , respectively, the Gk� and Gkg were

determined by minimizing the expressions:

� � � ��

MC

me

Gkabs Gk

bas a s

, , , ,, 1

, , /g OP D

E gOP

ID DI A

� ��

� (43)

and

� � � ��

� ��

1

MC Gk MC Gkrel Gk

meas rel meas rel , ,

, , , , , , , ,, 1

, , / , , /OP D

I g OP D I g OP DE g

I OP D A D I OP D A D�

� � � ��

� �

� �� !

, (44)

where x

denotes averaging over variable x. The two-parametric phase function was

determined utilizing different combinations of OP and D . 4OP was excluded from phase

function analysis due to dependent scattering behavior (hence likely to affect the phase

function) and 4D was excluded due to intensities below two standard deviations of the

detector dark noise.

When utilizing all available data; 1 3OP and 1 3D , the spectral shape of the optimally fitted

Gk� and Gkg was similar to each other in the absolute and relative case, respectively. As

intuitively expected, the deviations between simulated and measured spectra were larger when

only subsets of OP and D were utilized in the phase function fitting procedure.

As an evaluation of the calculated phase function, DRS measurements were performed on

three optical phantoms containing the above described milk as scattering component and three

different concentrations of blue Coloris ink as absorber. The measurements were compared to

MC simulated spectra, both for the absolute and relative calibrated cases. To include the

effect of absorption in the simulated spectra, the technique described in section 5.2.5 were

applied. For all absorption concentrations and source-detector distances, the rms-errors were

below 13.4% in the absolute calibrated case, and below 7.3% in the relative calibrated case.

Chapter 9 - Discussion

65

Chapter 9 DISCUSSION

The work performed in this thesis has come to emerge into two different areas; 1)

construction and characterization �determination of sμ � , aμ , and � ��p � of liquid optical

phantoms (papers I and V); 2) development and application of photon migration models to be

used for qDRS measurements, with emphasis on in-vivo measurements on myocardial tissue

(papers II-IV), but also on optical phantoms (paper V).

The development of the photon migration models and the applications on myocardial tissue

(papers II-IV), as well as the development of optical phantom construction and

characterization methods (papers I and V), have all progressed side-by-side and have

benefited from each other. In this chapter, optical phantom construction and characterization,

calibration of the photon migration models, and the qDRS applications on myocardial tissue

are discussed separately, despite that diffuse reflectance spectroscopy has been used both for

assessment of myocardial tissue status (paper II-IV) as well as for characterization of optical

phantoms (paper V). Section 9.3 covers both methodological issues of qDRS applications on

myocardial tissue, and relevant physiological findings.

9.1 CALIBRATION OF PHOTON MIGRATION MODELS

In DRS studies involving photon migration models, absolute quantification of chromophore

concentrations cannot be performed without the use of optical phantoms as reliable calibration

objects. Several techniques, both analytical and MC based, involving calibration of photon

migration models have been proposed. Zonios et al.110 used a single source-detector separation

and a light transport model, based on Farrell et al.´s111 diffusion theory model, calibrated

against measurements on a large number of optical phantoms. For small source-detector

separations, Mourant et al.112 showed that the diffusion model fails to accurately model the

diffuse reflectance. In Zonios´ study, this was considered, but two main arguments were

presented in favor of the suggested method. Firstly, within the ranges of optical properties of

interest, more rigorous (numerical) solutions to the diffusion approximation did not


66

significantly improved the performance of the proposed model. Secondly, the presented

analytical expression was considered more intuitive and applicable. However, the largest

deviations between the suggested model and measured diffuse reflectance were observed

when s aμ μ� * . In paper II, the ranges in sμ � and aμ were � � -10.42 1.30 mm and

� � -10.20 2.17 mm , respectively, in the wavelength range � �530 585 nm�' . This makes the

method suggested by Zonios et al. unsuitable for myocardial applications. Finlay and Foster113

presented an application of a hybrid 3P -diffusion descriptiona of light propagation on murine

tumor tissue in mice. This approach enabled measurements at smaller source-detector

distances than allowed by the diffusion approximation approach presented by Zonios et al.

Also, the requirement that a sμ μ �� was eliminated. Still, deviations between model and

measurement spectra were prominent at small � �0.7 mm+ source-detector separations.

Compared to determination of hemoglobin oxygen saturation, the determination of absolute

tissue concentrations were more sensitive to errors in model spectra. This is in agreement to

the findings in paper III (see sub-section "The empirical model" below).

The empirical model In contrast to the case with microspheres where Mie theory is applicable, � �p � of fat-based

emulsions or milk cannot be easily determined. However, in paper II-IV, an empirical photon

migration model � �s a,T μ μ� was used, and the calibration procedure only required knowledge

of sμ � and aμ of the optical phantoms. Collimated transmission was used for sμ and aμ

determination, while the anisotropy factor g was taken from the literature.

When using an empirical photon migration model, the optical properties of the calibration

phantoms have to be chosen such that they will cover the expected optical properties of the

medium under investigation. In practice, this can offer substantial difficulties, especially in

situations were no, or little a-priori information is available. Fortunately, for both human

myocardium (papers II-III) and bovine myocardium (paper IV), there are several studies

where myocardial absorption and scattering properties are given114-116. In paper II, the range in

estimated tissue sμ � was -10.38 1.30mm , while the calibration range in sμ � was -10.6 3.0 mm . In total, 7% of the analyzed spectra displayed a minimum sμ � outside (lower

than) the calibration range. In paper IV, estimated tissue sμ � ranged from -10.17 mm to -12.28 mm , and the calibration range were -10.16 mm to -11.28 mm . In this study, only 2.2%

a Originally presented by E.L. Hull and T.H. Foster, "Steady-state reflectance spectroscopy in the P3 approximation", Journal of the Optical Society of America A: Optics and Image Science, and Vision 18(3), 584-599 (2001).


67

of the analyzed spectra displayed sμ � outside (greater than) the calibration range. For both

studies, estimated tissue aμ values were within the interval of the optical phantom grid. This

shows that even if a-priori knowledge about the optical properties of the medium under

investigation exist, it can be difficult to choose proper ranges when configuring the phantom

grid.

In the calibration procedure, inspection of � �*s a,E μ μ� showed that the intensity deviations

between model and measurement spectra, was within +/-8.8% (mean of <0.5%) in paper II

and III, except for the calibration phantoms with -1a 2.88 mmμ . If the intensity of a typical

baseline measurement spectrum in paper II was altered correspondingly (multiplied by

1+0.088 and 1-0.088, respectively), the resulting deviations in the free fitting parameters

Hb+Mbf and Hb+MbS , were within 21% and 6.5%, respectively. The fitting parameters and� (

remained unaffected. Hence, the estimated tissue chromophore fractions are more sensitive

than the saturation parameter to intensity deviations in the calibration procedure.

Theoretically, the number of optical phantoms required in the calibration procedure, is

determined by the number of unknown coefficients in the light transport expression (equal to

6 in equation 21) if the calibration procedure is performed at a single wavelength.

Alternatively, the sμ � and aμ of a single calibration phantom can be determined by SCT, and

the calibration can be performed at 6 different wavelengths. Still, the requirement that the

calibration procedure should cover the expected optical properties of the medium under

investigation has to be fulfilled. Typically for milk, a maximum sμ � of more than two times

the minimum sμ � , cannot be achieved in the visible wavelength range. Therefore, in

applications were the range in sμ � or aμ of the medium under investigation can be expected to

be large, multiple phantom calibration should be chosen in favor of using a single phantom.

In 2005, Bargo et al.20 presented a modified version of the method originally presented by

Jacques19. Calibration measurements were performed on 64 optical phantoms made of

Intralipid, India Ink, and water. In Bargo´s study, the light transport was modeled by the

expression � � � � � �a 1 s

1 s 2 s

μ L μC μ e C μ

� � � � , where 1C , 1L , and 2C are polynomial expression of

orders 4, 15, and 15, respectively. The use of this high-order polynomials was necessary to

achieve acceptable model fit to measured calibration data 20. The required degrees of the

polynomials 1C , 2C , and L had to be determined from case to case. This may suggest that

other models should be considered instead of introducing increasingly cumbersome

extensions to the original model.


68

The Monte Carlo (MC) model In the absolute calibration procedure in paper V, a monodispersive polystyrene microsphere

suspension was used as a calibration phantom. The main reason was that Mie theory can be

applied to accurately describe the phase function, provided that the size distribution and

refractive index of the spheres are known. However, if the microsphere suspension suffers

from undetected aggregation (or other phenomena that affects the scattering properties in

uncontrolled ways), the sμ obtained from the SCT characterization will be affected.

The calculated calibration factor for each source-detector distance was defined as the ratio

between the measured and simulated intensities, averaged over the wavelength range 500-800

nm. A "wrong" sμ (due to factors discussed above) used as input to the MC simulations of

fiber-optic probe intensities, will therefore affect the calculated calibration factor for each

source-detector distance. In turn, erroneous MC simulated intensities will affect the estimation

of Gk� and Gkg . This inseparable connection between the accuracy in the SCT sμ

determination of the polystyrene microsphere suspension and the accuracy in determination of

Gk� and Gkg by the proposed absolute calibrated method, is important to note. However, in

most cases aggregation of the microspheres will be detected when performing the SCT

measurements, since large complexes of clotted microspheres will produce sharp dips in the

detected intensity (see section 6.1.1).

It would be interesting to compare the phase function estimation in paper V with a direct

phase function measurement in a goniometry setup, as performed by Michels et al84. Ideally,

such measurements should be performed for similar concentrations as in paper V, since the

casein micelles in milk is known to "disintegrate and form small submicelles"117. However,

goniometry measurements on high-scattering liquids require very small cuvettes in order to

obtain emerging photons that have been single-scattered.

Regardless if absolute or relative calibration is utilized, the requirement of multiple optical

phantoms is eliminated. Furthermore, once the MC photon migration model is calibrated, the

MC grids used for solving the inverse problem when determining, for example, chromophore

concentrations or the phase function (paper V) of the medium under investigation, can be

extended to encompass arbitrarily chosen optical properties � �s aandμ μ 54. However, one

drawback with the MC method is that it requires precise knowledge about the probe geometry

(core/cladding dimensions of the fibers) and optical properties (refractive index of the fibers


69

and the surrounding probe material). Theoretically, this offers little problems, but small

imperfections in the optical fiber surface can introduce errors in the simulated diffuse

reflectance intensities, that are hard to accurately compensate. It is therefore advisable to

include some measurements on a few numbers of phantoms covering the expected range of

optical properties to confirm that the simulation input data are valid.

9.2 OPTICAL PHANTOM COMPONENTS AND CHARACTERIZATION

Regardless if optical phantoms are used for calibration or evaluation, it is crucial that the

optical properties of interest can be characterized by a "golden standard" technique. While the

precision governed by such a technique is rather simple to determine, it is usually very hard to

give an answer regarding the accuracy of the obtained results. If the purpose of making a

specific phantom is to only construct an object with unchanged optical properties over time,

but with less strict demands regarding accuracy, a reference method with high precision

prioritized over high accuracy should be chosen. In contrast, for clinical measurements aiming

at absolute tissue chromophore content quantification, it is of great importance that the

calibration phantoms are characterized with high accuracy.

The choice of components As stated in chapter 6, there are numerous types of substances capable of mimicking the

scattering and absorption properties of biological tissue. If one limits the choice to liquids, the

number of potential agents that could be used for phantom construction is still considerable.

In paper I, efforts were made to construct scattering liquid optical phantom containing

polystyrene microspheres. One advantage of using microspheres as a scattering component is

that Mie theory can be applied to accurately describe the scattering properties of the medium.

Unfortunately, aggregation of the microspheres into large complexes (which was the case in

paper I), made the suspension useless as reference objects. In this thesis, the scattering

component used in the studies was eventually changed to UHT milk with a fat content of

1.5%. Other scattering components, also based on fat particles as scatterer, have been

investigated and characterized by Michels et al78. In their work, it was concluded that optical

properties of fat emulsions can vary greatly, even if samples from the same brand are used.

Therefore, the chosen fat emulsion should be characterized whenever a phantom is

constructed.


70

In paper I, it was discovered that oil-based inks displayed limited solubility in water. Long-

time (~1-5 min) collimated transmission measurements of a solution containing UHT-milk,

oil-based ink, and water, displayed sharp and temporally random decreases in transmitted

intensity values. The most likely explanation is that the ink forms large droplets, and/or bind

to the scattering components (fat particles) due to the more similar molecular structure

compared to water, and that such structures occasionally enter the light beam, causing the

intensity to drop. Collimated transmission measurements on solutions containing the same

scattering component (UHT-milk), water-soluble ink, and water, displayed none of the above

described intensity variations over time. This further strengthens the conception that when

constructing liquid optical phantoms using fat-based scattering components, water-soluble ink

should be used. However, it cannot be ruled out that the use of such components completely

eliminate the chemical effects discussed above.

Visual inspection of stray light from a collimated light beam passing through a cuvette

containing an aqueous dilution of the ink of interest, is an easy and convenient way of

revealing the presence of scattering behavior in ink solutions. More qualitatively, spectral

collimated transmission measurements of such solutions �measurements of �tμ , will, in

addition to the characteristic peaks due to the component-specific � �aμ � , result in a baseline

level of the estimated � �tμ � , strictly greater than zero. In such cases, it can be realized from

the relationship t s aμ μ μ � that the true absorption coefficient of the ink solution, is

overestimated due to s 0μ � .

Methodological considerations In Michels’ extensive work, the optical properties of six different fat emulsions with a fat

concentration range of 10% to 30%, were measured78. The scattering coefficient of the fat

emulsions was characterized by collimated transmission, while SRDR measurements were

employed for sμ � and aμ determination by inverse calculation of the diffusion equation. The

phase function of the emulsions was determined by a goniometric setup. As pointed out in

that study, the goniometry technique was associated with substantial challenges, such as

experimental compensations for refraction index mismatches, and correction algorithms for

the rectangular cuvette geometry. The latter can be simplified by using cylindrical cuvettes

instead, as presented by Forster et al118. However, then problems with distortion of incident

marginal rays are introduced, due to the non-normal incidence relative to the cuvette surface.


71

Another technique for determination of sμ , aμ , and g , has been presented by Yaroslavsky et

al119. The study involved evaluation measurements on tissue-like phantoms (milk) and porcine

myocardium. The proposed method was based on measurements utilizing a double-integrating

sphere in combination with MC calculations of the total transmittance � �tT , the diffuse

reflectance � �dR and the collimated transmittance � �cT for a given detector geometry. The

work are very well performed and several experimental difficulties are adressed (such as

elimination of multiple-scattered photon contributions in the collimated transmission

measurements and light loss in the edge of the sample of interest). However, the inverse

problem (matching MC calculations of t d c, , and T R T to measured data) are solved iteratively,

and each iteration involves quasi-Newton algorithms for estimation of the Jacobi matrix. This

steps may seem cumbersome in comparison to more straight-forward methods for optical

properties determination.

Application of the oblique angle illumination method for determination of sμ � , originally

presented by Wang and Jacques82, are according to the authors, straightforward and quick.

This method was further developed and evaluated in paper I. The proposed procedure (5

consecutive images) for determination of the hot-spot eliminated, or at least reduced, the

influence of speckle pattern. In order not to introduce a false dislocation of the calculated hot-

spot position due to this effect, a sufficient number of images should be recorded. A

suggestion of such a number would be when the hot-spot positions calculated from each

individual image are homogeneously distributed around the position determined from the

averaged image.

In paper I, no algorithm for calculation of aμ was presented, but SRDR profiles based on sμ

and aμ determined by collimated transmission, and g determined in three different ways

� �,2 LDF, , and in the paperr D MC fitg g g$ was compared to measured SRDR data. Given that the

anisotropy is known, one way of including determination of aμ in the method, would be to 1)

guess an initial a, initμ of the medium under investigation, 2) calculate sμ � from equation 41, 3)

determine aμ by matching MC simulated (based on sμ � from step 2, and multiple aμ ) to

measured SRDR data, 4) iterate from step 2, with the modification that sμ � should be

calculated according to equation 42. In each iteration, the range of aμ in step 3 should be

chosen such that the range � � � �a amin maxμ μ� �� is sufficiently large to result in a (at least,

local) minimum when comparing the MC simulated SRDR data to measured data.


72

As was concluded in paper I, a number of calibration measurements compensating for

vignetting effects, detector linearity, extensive image processing in the hot-spot determination

algorithm, and optimal correction for aμ effects, have to be performed when using the oblique

angle illumination technique for determination of optical properties. In addition, if applied to

tissue such as a human forearm, the calculated spatially resolved diffuse reflectance profile

proved to be very sensitive to variations in tissue-lens distances (data not shown in the

publication). These questions the "straight-forward and quick" application of the method as

proposed in the original publication. However, the fact that the method offers a non-touch

approach for in-vivo determination of optical properties is promising in clinical applications

where non-touch conditions are of importance.

When the scattering particle density in optical phantoms used for calibration is high enough to

display dependent scattering, it is important that the characterization of sμ � �sor μ � is

performed for the scattering particle concentration at hand. In papers II-IV, the range of both

sμ � and aμ of the calibration phantoms are large compared to paper I. Zaccanti et al.120 have

shown that for optical phantoms containing Intralipid 20% with a volume fraction of

scatterers exceeding 0.01, dependent scattering behavior occurs. In short, this phenomenon

arises when the distance between particles are comparable with the incident wavelength(s). In

paper V, the optical phantom with the highest sμ (denoted 4OP in the article) clearly displays

dependent scattering behavior. To avoid influences from multiple scattered photons during

phantom characterization by collimated transmission, the maximum sample thickness should,

as stated in section 6.2, not exceed 3 mfp . For highly scattering media, this could offer

experimental challenges. The setup for SCT measurements that has been developed in this

work, is able to perform measurements with a sample thickness resolution of 5 μm . Assume

that 10 consecutive measurements have to be made in order to obtain a reliable SCT

determination of sμ . From the relationship s1mfp μ , it can be seen that measurements of

liquids with up to -1s 20 mmμ * can be performed.

9.3 QDRS APPLICATIONS ON MYOCARDIAL TISSUE

The method based on a fiber-optic surface probe used in papers II-III, offered problems with

probe-tissue discontact and with varying, non-controllable probe-tissue pressure. The primary

reason of choosing a surface probe in these studies was that it allowed measurements on

multiple sites without penetrating the tissue. In a proof-of-concept study displaying the


73

possibilities of myocardial oxygenation monitoring by near-infrared spectroscopic imaging,

Nighswander-Rempel et al.121 showed that spatial variations in Hb+Mb oxygenation levels are

substantial, although specific levels were not given in that study. Frank et al.122 have shown

that regional values of myocardial Hb oxygenation in patients suffering from angina can vary

between 0%to 60% during comparable clinical conditions as in papers II-III. The use of a

surface probe enabled compensation for the spatial heterogeneity effects by averaging spectra

from individual measurement sites (three points proximal to the left anterior descending artery

(LAD) stenosis and three points distal to the LAD stenosis), before applying the curve fitting

algorithm.

For the distal sites, the Hb+MbS displayed an increase from 54.5% to 68.1% when comparing

postcardioplegic infusion to baseline. This may indicate a decreased myocardial oxygen

uptake in case of unchanged oxygen supply. From a clinical point-of-view, this is expected

since the cardioplegic infusion is performed to ensure adequate myocardial preservation

during surgical phases involving cardiac arrest123. However, the proposed qDRS method does

not separate the Hb and Mb oxygenation. The cold crystalloid cardioplegic infusion causes a

dramatic blood (and consequently, Hb) decrease in the coronary circulation system and as a

consequence the relative Mb contribution to tissue absorption increases. Compared to Hb, Mb

releases oxygen at much lower 2pO 28. Therefore, the observed increase in Hb+MbS when

comparing cardioplegic infusion to baseline may partly be influenced by an increased

contribution of oxygen saturated myoglobin. Also, the temperature of the cardioplegic

solution used in papers II-III was kept at 4 8 C " until infusion. The infusion into the

coronary circulation system causes a rapid cooling effect. The dissociation curve of

hemoglobin is left-shifted by a temperature decrease, lowering the number of released oxygen

molecules at a given partial oxygen pressure. Thus, any hemoglobin left in the coronary artery

system during cardioplegic infusion, will decrease its ability to release oxygen.

During cardiac arrest, the mean Hb+MbS decreased from 68.1% to 58.3%, indicating a low, but

existent metabolic need. PostCABG mean Hb+MbS was higher compared to baseline; 67.5% vs.

54.5%. Clinically, this reveals that the coronary circulation, and hence the myocardial tissue

oxygenation, has benefited from the surgery since the oxygen supply of the portion of the

myocardium distal to the stenosis was enhanced.

In paper II, it was found that the optimally fitted model displayed characteristic deviations

from the measured spectra in a great majority of cases. The model spectra overestimated the


74

measured spectra in the wavelengths intervals 520-530 nm and 580-630 nm. Interestingly,

absorption spectra of cyt aa3,ox and cyt aa3,red display characteristic absorption peaks at

wavelengths coinciding with the two intervals mentioned above. Moreover, recent studies

have shown that the presence of metHb can be detected by DRS124, and that elevated

concentrations of methemoglobin can occur during lidocaine induced anesthesia36 (which was

the case in papers II-IV). Therefore, the focus in paper III, was to re-analyze data from paper

II with cyt aa3,ox, cyt aa3,red and metHb included in the aμ expression in � �s a,T μ μ� . This

yielded a substantial improvement in the model fit to measured data, as evaluated both by the

residual spectra *E (see section 8.3 for further details) and by comparison of 2R -values.

Especially the inclusion of cyt aa3 was of great importance, both regarding improved model

fitting, but also as an eventual marker of mitochondrial oxygen utilization in the myocardial

tissue.

Provided that the solution of the inverse problem is a global minimum, the rms-error in *E

can not decrease when chromophores are added in the aμ expression in the model. If a

chromophore, C , not present in the medium under investigation is added to the absorption

expression in the light transport model, the calculated fraction Cf will equal zero, and the

deviation in model spectra compared to measurement spectra will be equal to the curve fitting

case without chromophore C . In paper III, the inclusion of cyt aa3,ox, cyt aa3,red and metHb

resulted in an increase in the average 2R value (for all measurements) from 0.96 to 0.99. Also, *E was greatly reduced in terms of spectral characteristic deviations from zero. Other

chromophore configurations (i.e. absorption expressions) were tested and evaluated in terms

of 2R values and residual spectra inspection, but were found to produce only small

improvements in the spectral fit. Together, this strengthens the validity of the extended aμ

expression used in papers III.

In addition to Hb+Mb oxygenation values, the curve fitting algorithm also gives the

chromophore concentrations. During surgical phases where dramatic changes in myocardial

blood volume were expected, for example at cardioplegic infusion and aortic cross-clamping,

none of these changes were observed. One explanation would be that the non-controllable,

varying probe-tissue pressure affects the Hb+Mb concentration in the sample volume. Ti and

Lin125 have performed measurements on rat hearts with varying tissue-probe pressure, ranging

from 0 to 4.80 -2N cm . In their study, the intensity increase in the recorded diffuse

reflectance spectra in the wavelength interval 500 to 600 nm (where blood absorption is

prominent), was approximately 50% when changing the probe pressure from 0 to 4.80


75

-2N cm . During the work that resulted in papers II-III, the surgeon reported that in order to

maintain a fix probe position relative to the tissue, a larger probe-tissue pressure was required

during surgical phases involving heart beating compared to phases involving cardiac arrest.

Due to the arguments above, it is possible that the Hb+Mbf values reported in paper III should

be higher. The relative increase of the estimated Hb+Mbf should be most prominent during

surgical phases where the probe-tissue pressure is large. However, due to the inherent

complex situation during in-vivo open-chest surgery, it is hard to perform controlled

measurements in order to investigate the quantitative relationship between probe-tissue

pressure and its influence on the calculated tissue parameters.

In paper IV, an intra-muscular probe was used to perform in-vivo qDRS measurements on

bovine myocardium. The intra-muscular probe greatly reduced problems with movement

artifacts frequently occurring during measurements with the surface probe. A fixed insertion

site throughout the performed experiments could be achieved, and problems with varying

probe-tissue pressure were reduced. However, Staxrud et al. have shown that optical fiber

(diameter 0.5 mm) insertion into the cutis layer of the skin can cause local trauma followed by

a hyperemic response, which locally increase the blood flow126. A similar measurement probe

to the one used in paper IV has been used in the thesis by Fors, to assess local blood flow by

LDF7. In that thesis, it was concluded that it was likely that a small bleeding followed the

insertion of the probe.

In the majority of measurements performed with the intramuscular probe, a close correlation

between the frequency of variations in estimated Hb+Mb concentration and heart rate was

observed. The variations in Hb+Mb concentration should be interpreted as variations mainly

in Hb alone, since myoglobin is bound to muscle tissue, in contrast to hemoglobin which is

present only in blood. Between the five individuals, large differences in the amplitude of the

pulsatile behavior of the Hb+Mb concentration were found. In Tortora and Grabowski, it can

be seen that pulsatile variations in the blood flow are largest in the aorta, and smallest (absent)

in the veins21. Thus, it is likely that the large amplitude of the pulsatile variations indicate that

the probe has been placed close to a large arterial vessel.

The surface fiber-optic probe measurements were performed on human myocardium, while

the intramuscular measurements were performed on bovine myocardium. With this in respect,

an interesting finding was that intramuscular Hb+MbS (paper IV) was lower compared to

epicardial Hb+MbS (paper II-III). This may correspond to a higher myocardial oxygen uptake in


76

the subendocardium compared to the subepicardium, something that has been reported in

several studies. Vinten-Johansen and Weiss26 performed a study where myocardial oxygen

consumption in dogs during experimentally induced valvular aortic stenosis was evaluated. In

the control group (n=12), the mean venous oxygen saturation was 28% in the subendocardium,

and 37% in the subepicardium. Levy et al.127 measured the partial oxygen � �2pO and carbon

dioxide � �2pCO pressure in both the subepicardial and subendocardial layer in dog

myocardium during open-chest surgery. 2pO was higher in the subepicardial layer than in the

subendocardial layer �20.7 mm Hg vs. �13.5mm Hg whereas no change was observed in

2pCO �51mm Hg vs. �43mm Hg . Therefore, a study designed to perform simultaneous

subepicardial (surface probe) and subendocardial (intramuscular probe) measurements during

coronary circulation provocations in animal models.

One clinically interesting finding in paper IV was that the myocardial oxygen uptake

decreased in individuals where a LVAD pump was implanted. This mirrors a decreased

myocardial work and hence a decreased oxygen consumption. Moreover, a correlation

between Hb+MbS and LVAD pump speed was found, where an increase in LVAD speed

resulted in an increased Hb+MbS . This strongly indicates that the myocardial work needed in

order to maintain adequate systemic circulation is reduced when the heart is supported by a

LVAD. Future applications of the intramyocardial fiber-optic probe could therefore be to

evaluate LVAD implantations or other procedures where the purpose is to assist myocardial

function.

Unfortunately, no physiological provocations where substantial reduction in cyt aa3O could be

expected, have been made in any of the studies. In papers II-III the reason for this is obvious

since measurements were performed during routine CABG surgery of human subjects.

However, future animal experiments similar to those performed in paper IV, would greatly

benefit from including such provocations in order to further evaluate the algorithm

performance regarding cyt aa3O determination. However, unpublished data for manipulations in

cyt aa3O (90%, 70%, 50%, and 30%) of an optimally fitted spectrum can be seen in Figure 27.


77

500 550 600 650 700 750 80010−1

100

Wavelength [nm]

Inte

nsity

[−]

500 550 600 650 700 750 800−0.4

−0.2

0

0.2

0.4

Wavelength [nm]

[−]

Figure 27 Upper panel: Measured (black) and model (gray) in-vivo bovine intramyocardial spectra

during inhalation of 100% O2. The cyt aa3O have been manipulated to 90%, 70%, 50%, and 30%

compared to the complete oxidation (100%) level corresponding to the optimally fitted spectra.

The next uppermost model spectrum corresponds to cyt aa3 90%O , and the lowermost model

spectrum to cyt aa3 30%O . Other fitting parameters are as in the optimally fitted spectra. Lower

panel: Residual spectra Model Measured 1E for the cyt aa3O manipulations. The residual for

the optimally fitted spectrum is shown in black.

The maximal deviation in the optimally fitted spectra was 4.0%. For model spectra calculated

for the manipulated cyt aa3O (90%, 70%, 50%, and 30%), the maximal deviations were 8.3%,

15.1%, 23.4%, 32.4%, and 42.0%, respectively. The lower panel of Figure 27 shows

characteristic deviations in the wavelength regions 520-530 nm and around 600 nm. By

inspection of Figure 14, it can be seen that the absorption spectra of oxidized and reduced cyt

aa3 differ in these wavelength regions. The maximal difference between the optimally fitted

spectrum and the measurement spectrum is more than doubled when comparing the case of

cyt aa3 100%O to cyt aa3 90%O . Moreover, the maximal difference occurs at wavelengths

very close to the reported absorption peaks of both the oxidized and reduced forms of cyt

aa314, 66. This makes it reasonable to assume that changes in cyt aa3O can be detected at the

observed levels of cyt aa3f by the suggested qDRS method in this thesis.

Throughout the work performed in papers II-IV, the empirical light transport model presented

in equation 21 was used. It is likely that that the optical properties of myocardial tissue are

spatially heterogeneous. Despite this, sμ � and aμ in the tissue are estimated as a mean value


78

for the total sample volume. Although the sample volume are expected to be in the order of a

few (1-3) 3mm in the wavelength region used in papers II-IV, variations in aμ due to, for

example, the presence of a large vessel, may affect the results. Another problem encountered

during the measurements performed with the surface probe, was that the surface of the heart

of some individuals were covered with a fat layer. Yang et al.128 investigated the effect of fat

thickness on the diffuse reflectance intensity from a muscle in the near-infrared wavelength

region. In the empirical light transport model, there is no way spatial heterogeneities in optical

properties can be accounted for when solving the inverse problem.

Fredriksson et al.129 proposed a method that involves a MC model with separate layers with

different optical properties and variable thicknesses. In-vivo recorded spectra (human skin),

performed with two different source-detector separations, were collected and compared to a

set of pre-simulated reference spectra. Model validation was performed by inspecting the

layer thickness and optical properties that generated the best fit. Utilization of MC models in

combination with DRS measurements may offer a way to more accurately describe light

propagation in myocardial tissue.

Chapter 10 - Conclusions

79

Chapter 10 CONCLUSIONS

Three different techniques for estimating the optical properties of liquid optical phantoms

have been presented. The improved oblique angle illumination technique allowed for 'sμ

determination with an accuracy of 2.9%. Improvements involved: multiple exposure times for

an increased dynamic range; linearized detector intensity; and compensation for vignetting

effects. The spectral collimated transmission method determined sμ of highly scattering

liquids ( sμ < 120 mm ). This was possible using a glass rod submerged in the liquid, moved by

a precision stage in steps of 5 μm. The SRDR-based method estimated a two-parametric

Gegenbauer kernel phase function in sufficient detail to accurately describe the diffuse

reflectance spectra at source-detector separations in the region 0.23 mm to 1.2 mm, using

inverse MC technique. These estimation techniques allowed for using UHT milk as a readily

available and cheap alternative scattering component when constructing calibration and

evaluation phantoms with known optical properties relevant to myocardial tissue. To avoid

mixing problems water soluble inks should be used as absorbers.

The calibration of the empirical photon migration model using liquid optical phantoms

enabled absolute quantification of chromophore content. For calibration phantoms with

optical properties in the ranges � � -1s 0.16 3 mmμ � ' and � � -1

a 0 1 mmμ ' , the proposed

empirical photon migration model for the surface probe predicted the intensity at a source-

detector separation of 0.23 mm within 10% compared to measured calibration data. Due to

this, estimated tissue chromophore content can vary up to 21% and estimated Hb+Mb

oxygenation up to 6.5%.

The proposed calibrated DRS technique using the empirical photon migration model was

applied to in-vivo measurements during open-chest surgery. The hand-held surface fiber-optic

probe (papers II-III) displayed difficulties with controlling the probe-tissue pressure, and with

maintaining a fixed measurement site. By employing an intramuscular probe (paper IV),

problems with varying probe-tissue pressure and non-fixated probe position were to a large

extent overcome. However, insertion of the intramuscular probe into the myocardium is, due

to the invasive procedure, likely to cause a local trauma followed by a local minor bleeding.

Chapter 10 - Conclusions

80

Despite the probe positioning difficulties, estimated myocardial Hb+Mb oxygenation, cyt aa3

oxidation, and tissue chromophore concentrations were in ranges conformant with other

studies. Myocardial oxygen uptake was found markedly lower in the subendocardium

(intramuscular probe) compared to the subepicardial layer (surface probe), although

comparing human and bovine data. Regardless if a surface probe or an intramuscular probe is

employed for qDRS measurements using visible light on myocardial tissue, source-detector

fiber separations exceeding ~1 mm should not be used due to the high myocardial tissue

absorption.

Fitted model spectra displayed substantial deviations from measured spectra in wavelength

regions where metHb and cyt aa3 absorption have characteristic absorption peaks, when

excluding these chromophores from the model. Inclusion of these chromophores eliminated

the characteristic intensity deviations between model and measured spectra. This strongly

indicates that measured spectra from the myocardium contain information on cyt aa3.

In the future, special interest should be paid to monitor the cyt aa3O , since it is the final marker

of mitochondrial oxygen consumption. Although none of the performed experiments in this

thesis involved provocations in order to obtain a reduction in cyt aa3O , manual manipulations in

the tissue model showed that physiological changes in cyt aa3O are detectable by the proposed

qDRS method. This and other results indicate that qDRS could be used as a valuable tool for

monitoring not only the oxygen delivery but also the oxygen uptake in tissue.

Acknowledgements

81

ACKNOWLEDGEMENTS

During the last five years, I have been offered the opportunity to make a research journey

into the exciting border-zones between medicine and biomedical engineering. It would have

been both impossible and boring to perform such a journey without being guided,

accompanied and encouraged by a number of great supervisors, colleagues, and friends.

Below are some words to each one of you who made it all possible. However, to everyone

that has been involved in this thesis, mentioned or not mentioned below: THANK YOU!

Professor Tomas Strömberg, main supervisor. I am most grateful for sharing your research

ideas and for your sharp-minded supervision. Your ability to always be true to ethical

guidelines and never choosing the "easy paths" when confronted to difficult research

challenges is worth striving for, and it is something I will remember and have greatly

appreciated. Without your scientific and personal support during my work, this thesis would

not have become a reality. Finally, I come to think of a citation from one very well-known

movie: "Always two there are: a Master, and an Apprentice". Thank you, Tomas!

Ph.D. Marcus Larsson, mentor and co-supervisor. Your very deep knowledge within the

field of biomedical engineering and optics has sometimes been a life-saver during the work.

At times when I seemed to be hopelessly stuck in my research, your intuition has in amazing

ways guided towards the right decisions. And, perhaps the most important thing; even in the

darkest of times, you made going to work a positive thing! The answer to the question

whether I´m going to miss our tight scientific collaboration and our friendship, is definitely:

JA!

Professor, M.D. Henrik Casimir-Ahn, co-supervisor. You introduced me to cardio-thoracic

surgery, a field where the question regarding what life is really all about, becomes very

transparent. It has been fruitful, both personally and scientifically, to get to know you Henrik,

and your field of work. I think that your dedication to making people’s life better deserves the

deepest respect. Without your always pioneering and positive attitude to integration of

medicine and biomedical engineering, none of the true evaluations of the applications

presented in this thesis - to actually apply the techniques in a clinical setting - would have

been possible to realize.

Acknowledgements

82

M.D, Ph.D. Zoltán Szabó, consultant anesthesiologist and co-worker. You seem to be the

never-ending source of knowledge within the fields of myocardial metabolism and bio-

energetics! In the very interesting studies where myocardial oxygen transport has been studied

close to the cellular level, you have invaluably contributed to the physiological interpretations

of otherwise very puzzling results. Moreover, people with your passion for science are hard to

come by. The research community needs people like you and your sheer optimism. Besides

aiding me in my research, you have taught me to always "look on the bright side of life".

While being around you, it is impossible to be in a down mood!

Present and former group members, co-authors and other colleagues, not mentioned

above. Ingemar Fredriksson, your kind, compassionate, and confident way of being has

always been greatly appreciated. Erik Häggblad, a straight-forward fighter like you is always

needed in a winning team! Michail Ilias, thank you for introducing me to the department, and

for being a great support as long as it lasted. Reijo Jämsä, your presence boosted both my own

research and the overall social well-being of the department. Daniel MG Karlsson, whether it

is about laser-Doppler, spectroscopy, or fighter jets, you seem to put your whole heart in it. It

was great learning to know you! Hanna Karlsson, good luck in the exciting world of

spectroscopy and chromophores. Marcus Ressner, you are a very non-egoistic and kind

person! Göran Salerud, your deep-going philosophical mind has helped me in ways that are

hard to explain. However, one simple way of putting it is simply: thank you! Mikael Sundberg,

I enjoyed our scientific and personal discussions very much. And: although my right ear one

time was at danger, I was never really afraid... Håkan Örman (formerly Petersson), thanks for

your jolly manner, and for renewing my interest in country music! Also, thanks to Joakim

Henricson, Johannes Johansson, Gert Nilsson, Karin Wårdell, and Mattias Åström, for giving

valuable input on various chapters in the thesis.

Staff at the Department of Biomedical Engineering, each and every one of you has made

the department a warm and welcoming place to be in. The administrative as well as the social

and human support during my time have been like "travelling in first class"! Some of you

have, however, contributed to the research in more practical ways. Håkan Rohman,

constructor of measurement probes and optical instrumentation. One day in the laboratory,

you briefly mentioned the words "seeing is believing". Those words have meant more to be

than you could imagine. Per Sveider, constructor of intensity references and measurement

probes. Staff at Department of Thoracic surgery, Linköping Heart Center, University

Acknowledgements

83

Hospital and Staff at the Laboratory for experimental animal studies, Faculty of Health

Sciences. Thank you for your always positive attitude and your help during the measurements.

Special thanks go to M.D. Stefan Träff, M.D., Ph.D. Ewa Ahlgren, and perfusionist Ulf

Wallgren who explained several cardio-thoracic surgery moments in sufficient detail, yet in

an understandable way for a physicist! Research Engineer Bengt-Arne Fredriksson, HU

Core Facility. It may have been easy for you, but your contribution to my research saved a lot

of time and effort! Ph.D. Anders Pettersson, Perimed AB. I thought I understood physics.

Then I met you... Thank you for sharing your knowledge in spectroscopy from a perspective

different from mine!

NiMed, VR, VINNOVA, NovaMedTech and Perimed AB. This thesis has partly been

funded by NiMed (National competence centre for non-invasive medical measurements), VR

(Swedish Research Council), VINNOVA (Research and innovation for sustainable growth),

NovaMedTech (The Swedish Agency for Economic and Regional Growth), and Perimed AB.

Department of Biomedical Engineering, University hospital, Östergötland County

Council (ÖCC). The various forms of flexibility shown by ÖCC during the final stretch of

my thesis have been greatly appreciated, and special thanks go to Per Dahl and Anders P.

Karlsson.

Mina föräldrar Inga & Magnus, så långt mitt minne sträcker sig bakåt i tiden, så har Ni

alltid funnits där för mig, alltid ställt upp, alltid givit mig de bästa förutsättningar för att ta

mig fram i livet, alltid uppmuntrat. Utan Ert outtröttliga stöd, är det ingen som vet vem jag

hade varit! TACK! Min bror, svägerska, och brorsdotter Niklas, Mia, och Alice, de

senaste sex åren har innehållit djupa dalar och höga berg. Oavsett var på färden jag befunnit

mig, så har Ni funnits där för mig! Övrig släkt och vänner, jag kan inte nämna Er alla. Jag

hoppas att vi nu tillsammans hittar all den tid jag inte givit Er under denna resa!

Åsa! Under arbetet med denna avhandling har jag ibland tvivlat på min förmåga att nå målet.

Ju längre in i mörkret jag varit - oavsett om det har handlat om min forskning eller de andra

hinder jag har att möta i mitt liv - desto starkare har Du visat Dig vara. För detta känner min

tacksamhet inga gränser. Jag älskar Dig väldigt mycket, och hoppas att jag kan återgälda Dig

alla de uppoffringar Du gjort för min skull under de senaste dryga fem åren!

84

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85

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QUANTITATIVE DIFFUSE REFLECTANCE SPECTROSCOPYliu.diva-portal.org/smash/get/diva2:246012/FULLTEXT01.pdf · "Intramyocardial oxygen transport by quantitative diffuse reflectance spectroscopy