quantitative diffuse reflectance...
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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.
Chapter 1 - Introduction
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
Chapter 1 - Introduction
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.
Chapter 3 – Oxygen transport in the myocardium
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.
Chapter 3 – Oxygen transport in the myocardium
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
Chapter 3 – Oxygen transport in the myocardium
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 .
Chapter 3 – Oxygen transport in the myocardium
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.
Chapter 3 – Oxygen transport in the myocardium
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.
Chapter 4 – Principles of light-tissue interactions
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
Chapter 4 – Principles of light-tissue interactions
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
Chapter 4 – Principles of light-tissue interactions
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:
Chapter 4 – Principles of light-tissue interactions
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
+ �
- �
Chapter 4 – Principles of light-tissue interactions
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)
Chapter 4 – Principles of light-tissue interactions
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:
Chapter 4 – Principles of light-tissue interactions
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
Chapter 4 – Principles of light-tissue interactions
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
Chapter 4 – Principles of light-tissue interactions
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
Chapter 4 – Principles of light-tissue interactions
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
Chapter 4 – Principles of light-tissue interactions
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
Chapter 4 – Principles of light-tissue interactions
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:
Chapter 4 – Principles of light-tissue interactions
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.
Chapter 4 – Principles of light-tissue interactions
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.
Chapter 4 – Principles of light-tissue interactions
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.
Chapter 5 – Photon migration models
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:
Chapter 5 – Photon migration models
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
Chapter 5 – Photon migration models
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)
Chapter 5 – Photon migration models
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)
Chapter 5 – Photon migration models
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.
Chapter 5 – Photon migration models
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.
Chapter 6 – Optical phantoms
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.
Chapter 6 – Optical phantoms
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
Chapter 6 – Optical phantoms
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.
Chapter 6 – Optical phantoms
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
Chapter 6 – Optical phantoms
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
Chapter 6 – Optical phantoms
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
Chapter 6 – Optical phantoms
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.
Chapter 7 – Quantitative diffuse reflectance spectroscopy
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
Chapter 7 – Quantitative diffuse reflectance spectroscopy
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.
Chapter 7 – Quantitative diffuse reflectance spectroscopy
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.
Chapter 7 – Quantitative diffuse reflectance spectroscopy
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.
Chapter 7 – Quantitative diffuse reflectance spectroscopy
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
Chapter 7 – Quantitative diffuse reflectance spectroscopy
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).
Chapter 7 – Quantitative diffuse reflectance spectroscopy
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
Chapter 7 – Quantitative diffuse reflectance spectroscopy
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)
Chapter 7 – Quantitative diffuse reflectance spectroscopy
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.
Chapter 7 – Quantitative diffuse reflectance spectroscopy
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$
Chapter 8 - Review of the papers
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.
Chapter 8 - Review of the papers
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.
Chapter 8 - Review of the papers
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.
Chapter 8 - Review of the papers
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.
Chapter 8 - Review of the papers
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]
Chapter 8 - Review of the papers
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
Chapter 8 - Review of the papers
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
Chapter 9 - Discussion
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).
Chapter 9 - Discussion
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.
Chapter 9 - Discussion
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
Chapter 9 - Discussion
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.
Chapter 9 - Discussion
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.
Chapter 9 - Discussion
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.
Chapter 9 - Discussion
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
Chapter 9 - Discussion
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
Chapter 9 - Discussion
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
Chapter 9 - Discussion
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
Chapter 9 - Discussion
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.
Chapter 9 - Discussion
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
Chapter 9 - Discussion
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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