DIFFUSE OPTICAL TOMOGRAPHY AND

SPECTROSCOPY OF BREAST CANCER AND FETAL

BRAIN

Regine Choe

A Dissertation

in

Physics and Astronomy

Presented to the Faculties of the University of Pennsylvania in Partial

Fulfillment of the Requirements for the Degree of Doctor of Philosophy

2005

Arjun G. Yodh

Supervisor of Dissertation

Randall D. Kamien

Graduate Group Chairperson

c© Copyright 2005

by

Regine Choe

Dedication

This work is dedicated to

Mom & Dad,

Yookyung (Luke), Yujun (Camilo), Yejune (Agnes)

iv

Acknowledgements

When I was at a crossroads in deciding the graduate school, I ran across the Physics Today article

written by Arjun Yodh and Britton Chance (BC). The multidisciplinary aspect and clinical applica-

bility of diffuse optical imaging immediately seized my attention and became the deciding factor

in the end. I have been truly fortunate to be able to work in a superb environment created by Arjun

and BC with a wonderful ensemble of people. It is my great pleasure to acknowledge all of them

for enriching both academic and personal aspects of my life.

Arjun has always been a constant force which provided me with a big picture and guided me

to be a confident and independent researcher. He has taught me how to identify and approach the

problem with firm grasp of fundamental physical understanding. His critical scientific insights have

challenged and directed me to strive for intellectual advances. He has taught me how to deliever

the presentation with clarity and how to write scientific papers and grants. BC is a legendary figure

in diffuse optical community with full of brilliant innovative ideas and keen sense of research flow.

As my second advisor, he introduced me to the clinical fetal brain oxygen monitoring project in

the beginning years of my research. This exposure was invaluable in understanding the clinical

and physiological motivation, experimental instrument and protocol design. His trust, support and

hands-on approach have always fascinated me.

Besides my advisors, I was lucky to have two mentors who provided the specific research di-

rection and inspired me greatly along the way. I could not have survived my first year of research

without Nirmala Ramanujam, with whom I worked on the fetal project. Nimmi is a great teacher

with uncanny ability to explain the key concept with such clarity even the newcomers can under-

stand. She was always willing to spend time to brainstorm the direction of research in a systematic

manner and to discuss the results with great patience. She has become a role model for me. Joseph

v

Culver is a great experimental physicist who has taught me the ins and outs of the diffuse optical to-

mography of breast cancer. Joe has designed and established the very backbone of current research

instrumentation. Not only he was well-versed in the experiment, but also great in the theoretical

aspects of image reconstruction.

I often admire at the great ensemble of good-natured and brilliant members working in Arjun’s

laboratory. Turgut Durduran is such an invaluable friend and colleague that one may only hope

to meet once in a lifetime. Starting from the very first year of preparing for qualifying exams,

throughout ups and downs of graduate school (both academic and personal), and finally the pro-

cess of writing the thesis, he has given constant encouragement and strength to go on. His keen

insights and brilliat ideas shining through and his non-hesitant active approaches to research al-

ways inspire me. It has been an invigorating experience to collaborate with him on some projects

in the past, which I am looking forward to continuing. I enjoy working with the members of breast

cancer project: Alper Corlu, Kijoon Lee and Soren Konecky. Alpercigim has a flair for theoretical

development, providing fundamental basis for breast cancer imaging. He has given me a steady

academic and emotional support with a protectiveness of a younger brother. Kijoon and Soren are

like a breeze of fresh air with new ideas, helping in every possible way with great eagerness. I am

grateful to Chao Zhou who sometimes goes out of his way to help me even though we do not share

a project. Jonathan Fisher is a virtuoso in science and piano who has continuously amazes people

around him. He is my favorite late night snack buddy who gives me great advices on self-esteem

and confidence. I would like to also thank Hsing-wen for being there for me always. Also, I would

like to thank Guoqiang Yu, Ulas Sunar and David Busch for helpful exchange of information and

numerous discussions. Monika Grosicka-Koptyra is an indispensable member of our laboratory

who has helped me greatly on recruitment and measurements of patients. Her dedication to our

vi

project and eagerness to help are greatly appreciated.

During her short time in our laboratory, Anisa Nayeem established the starting point of clinical

connections when we did not have any clue. Leonid Zubkov, Cecil Cheung, Monica Holboke and

Joseph Giammarco were very helpful in experimental and theoretical side of Arjun’s laboratory.

In BC’s laboratory, I had great interactions with Yu Chen, Vasilis Ntziachristos, Xavier Intes and

Shoko Nioka. Gargi Vishnoi was a post-doc when we were doing fetal project together, who was

a supportive friend. Mary Leonard provided with her beautiful illustration for our presentations.

Dorothea Coleman (Dot) and Glen Fechner were always helpful in administrative aspects of re-

search and grants. Also, I would like to thank the business office in the Department of Physics

and Astronomy for their timely manner in handling the purchase orders and other financial re-

lated tasks, making research go smoothly. The environment of Physics Department was always

favorable. I enjoyed taking physics courses from various wonderful faculty members. Especially

I would like to thank my thesis committee members, Dr. Randall Kamien, Dr. Nigel Lockyer, Dr.

Gino Segre and Dr. Paul Heiney for their time and effort.

Our research could not have been possible without many clinical collaborators. Especially I

would like to thank Dr. Douglas Fraker for helping us launch the breast cancer imaging research in

the Hospital of the University of Pennsylvania and introduce us to numerous enthusiastic collabo-

rators. Dr. Brian Czerniecki and Dr. Julia Tchou have been very supportive and actively referred

the interested breast cancer patients to our study. Dr. Mark Rosen has introduced us to new ap-

plication of neoadjuvant chemotherapy monitoring and connected us with Dr. Angela DeMichele.

He is an enthusiastic and helpful collaborator who understands the strength and weakness of the

new technology. Dr. Mitch Schnall and Dr. Gautham Mallampati have helped us in comparing the

localization of breast tumor between MRI and optical method. I would like to also thank Lauren

vii

Sherman for neoadjuvant chemotherapy patient interface, Nancy O’Connor from Penn Tower, and

Kathleen McCarthy for referring patients from PPG study patient population along with Stephanie

Davis and Tamara April. For the fetal project, the animal model study was not possible without the

help of Dr. Mark Nijland and Dr. Peter Nathanielsz of Cornell University. Most of all, I would like

to thank volunteers and patients who participated in our clinical measurements for their generosity

and courage towards developing research for the good of future generation.

Lastly, I’d like to thank all my family and friends who have shaped who I am now. Among my

friends, I single out devoted friends who were there for me throughout my graduate years. Marky,

Saurav, Turgut and I formed a society µστρ exploring authentic ethnic cuisines from all around

the world. Their adventurous spirits towards trying new things made a lot of fond memories. Also,

I would like to thank compassionate Eylem for inviting me to dinners when I was too busy to cook

while writing this thesis. I would like to thank Jamie for giving me a patient and caring instructions

for the flight lessons. Through becoming a pilot, I have learned whole new level of self-control,

patience as well as actual piloting skill and came to terms with my own abilities. My parents have

always believed in me and supported me. My mother encouraged me to enjoy the moment while

trying my best. My father has been the center and driving force for scientific mindset of our family.

My brother Yookyung has shared his experties in medical illustrations by creating exceptionally

fine illustrations used in my paper and thesis. Also, he has been there for me in my time of hardship

along with Yujun and Agnes. I love them all.

I would like to end the acknowledgement with a quote from one of my favorite animations,

“Life is about the voyage, not the destination.”

viii

Abstract

Diffuse Optical Tomography and Spectroscopy of Breast Cancer and Fetal

Brain

Regine Choe

Arjun G. Yodh

Diffuse optical techniques utilize light in the near infrared spectral range to measure tissue phys-

iology non-invasively. Based on these measurements, either on average or a three-dimensional

spatial map of tissue properties such as total hemoglobin concentration, blood oxygen saturation

and scattering can be obtained using model-based reconstruction algorithms. In this thesis, diffuse

optical techniques were applied for in vivo breast cancer imaging and trans-abdominal fetal brain

oxygenation monitoring.

For in vivo breast cancer imaging, clinical diffuse optical tomography and related instrumen-

tation was developed and used in several contexts. Bulk physiological properties were quantified

for fifty-two healthy subjects in the parallel-plate transmission geometry. Three-dimensional im-

ages of breast were reconstructed for subjects with breast tumors and, tumor contrast with respect

to normal tissue was found in total hemoglobin concentration and scattering and was quantified

for twenty-two breast carcinomas. Tumor contrast and tumor volume changes during neoadju-

vant chemotherapy were tracked for one subject and compared to the dynamic contrast-enhanced

MRI. Finally, the feasibility for measuring blood flow of breast tumors using optical methods was

demonstrated for seven subjects.

In a qualitatively different set of experiments, the feasibility for trans-abdominal fetal brain

ix

oxygenation monitoring was demonstrated on pregnant ewes with induced fetal hypoxia. Prelimi-

nary clinical experiences were discussed to identify future directions.

In total, this research has translated diffuse optical tomography techniques into clinical research

environment.

x

Contents

Dedication iv

Acknowledgements v

Abstract ix

List of Tables xvii

List of Figures xxii

1 Introduction 1

1.1 Diffuse Optical Spectroscopy and Tomography . . . . . . . . . . . . . . . . . . . 1

1.2 Breast cancer imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Brief history of breast optical imaging: Before the Diffusion Approximation 6

1.2.2 Brief history of breast optical imaging: After the Diffusion Approximation 7

1.2.3 Breast optical imaging in our laboratory . . . . . . . . . . . . . . . . . . . 11

1.3 Fetal Brain Oxygenation Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.4 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2 Theory 17

xi

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2 General Analysis Flow Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.2.1 Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.2.2 Forward Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.2.3 Calculation of χ2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.2.4 Inverse problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.3 Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.3.1 Differential approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.3.2 Absolute approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.4 Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.4.1 Nonlinear Rytov Iterative Method . . . . . . . . . . . . . . . . . . . . . . 31

2.4.2 TOAST : single-spectral TOAST . . . . . . . . . . . . . . . . . . . . . . . 37

2.4.3 MTOAST : multi-spectral TOAST . . . . . . . . . . . . . . . . . . . . . . 41

3 Experimental Techniques 43

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.2 Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.2.1 Light sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.2.2 Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.2.2.1 Photodiode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.2.2.2 Avalanche Photodiode (APD) . . . . . . . . . . . . . . . . . . . 46

3.2.2.3 Photomultiplier Tube (PMT) . . . . . . . . . . . . . . . . . . . 46

3.2.2.4 Charge Coupled Device (CCD) . . . . . . . . . . . . . . . . . . 47

3.2.2.5 Image intensifier . . . . . . . . . . . . . . . . . . . . . . . . . . 48

xii

3.2.2.6 SNR comparison of detectors . . . . . . . . . . . . . . . . . . . 49

3.3 Frequency-domain Homodyne System . . . . . . . . . . . . . . . . . . . . . . . . 56

3.3.1 Frequency-domain System Schematic . . . . . . . . . . . . . . . . . . . . 56

3.3.2 Laser diode modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.3.3 I&Q demodulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.4 Continuous-wave CCD System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.5 System Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.5.1 Dynamic range of electronic components . . . . . . . . . . . . . . . . . . 63

3.5.2 Dynamic range of the whole system . . . . . . . . . . . . . . . . . . . . . 65

3.6 Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

3.6.1 1st generation parallel plate DOT instrument . . . . . . . . . . . . . . . . 67

3.6.2 2nd generation parallel plate DOT instrument . . . . . . . . . . . . . . . . 70

3.6.3 Frequency-encoded DOS instrument for fetal oximetry . . . . . . . . . . . 73

3.7 Validation with Tissue Phantoms . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

3.7.1 1st generation parallel plate DOT system phantom test . . . . . . . . . . . 75

3.7.2 2nd generation paralell plate DOT system phantom test . . . . . . . . . . . 76

3.8 APPENDIX: Tissue Phantom Recipes . . . . . . . . . . . . . . . . . . . . . . . . 81

3.8.1 Liquid Phantoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

3.8.2 Solid Phantoms : silicone . . . . . . . . . . . . . . . . . . . . . . . . . . 92

4 In vivo Diffuse Optical Tomography of Breast 97

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

4.2 Breast cancer: clinical side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

4.2.1 Classification of breast disease . . . . . . . . . . . . . . . . . . . . . . . . 98

xiii

4.2.2 Diagnostic procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

4.2.3 Histology grades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

4.2.4 Imaging methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

4.2.5 Treatment of breast cancer . . . . . . . . . . . . . . . . . . . . . . . . . . 101

4.3 Quantification of Normal breast properties . . . . . . . . . . . . . . . . . . . . . . 101

4.3.1 Optical Properties of Healthy Breast Tissue . . . . . . . . . . . . . . . . . 102

4.3.2 Physiological Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

4.3.3 Demographics and Optical Properties . . . . . . . . . . . . . . . . . . . . 106

4.4 Breast Cancer Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

4.4.1 CCD Raw data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

4.4.2 3D DOT reconstruction method . . . . . . . . . . . . . . . . . . . . . . . 111

4.4.3 Image orientation of 3D DOT reconstruction . . . . . . . . . . . . . . . . 112

4.4.4 3D reconstruction images . . . . . . . . . . . . . . . . . . . . . . . . . . 113

4.4.5 Comparison between single and multi-spectral approach . . . . . . . . . . 117

4.4.6 Tumor contrast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

4.5 Neoadjuvant Chemotherapy Monitoring . . . . . . . . . . . . . . . . . . . . . . . 122

4.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

4.5.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

4.5.2.1 Neoadjuvant chemotherapy & MRI protocol . . . . . . . . . . . 124

4.5.2.2 DOT protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

4.5.2.3 MRI Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . 128

4.5.2.4 DOT Transillumination . . . . . . . . . . . . . . . . . . . . . . 128

4.5.2.5 DOT Data Analysis: 3D Reconstruction . . . . . . . . . . . . . 129

xiv

4.5.2.6 Image correlation analysis between MRI and DOT . . . . . . . . 129

4.5.2.7 DOT tumor volume estimation . . . . . . . . . . . . . . . . . . 131

4.5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

4.5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

4.5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

4.6 Optical measurement of Blood flow in breast cancer . . . . . . . . . . . . . . . . . 143

4.7 Summary and Future Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

5 Dynamic Diffuse Optical Spectroscopy on Fetal Brain in utero 152

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

5.2 Trans-abdominal Near Infrared Oximetry of Hypoxic Stress in Fetal Sheep Brain

in utero . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

5.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

5.2.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

5.2.2.1 Animal Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . 153

5.2.2.2 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

5.2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

5.2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

5.3 Outlook towards translation to human . . . . . . . . . . . . . . . . . . . . . . . . 164

5.3.1 Preliminary Clinical Data . . . . . . . . . . . . . . . . . . . . . . . . . . 164

5.3.2 Clinical translation outlook . . . . . . . . . . . . . . . . . . . . . . . . . . 169

5.4 APPENDIX: Instrument optimization for Human Case . . . . . . . . . . . . . . . 173

5.4.1 Two-layer forward model . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

5.4.2 Incorporation of noise to two-layer model . . . . . . . . . . . . . . . . . . 174

xv

5.4.3 Sensitivity to fetal signal . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

5.4.4 Optimal Source Detector Separation . . . . . . . . . . . . . . . . . . . . . 176

5.4.5 Detectability of fetal signal in two-layer model: Inverse Problem . . . . . . 176

5.4.6 Instrument Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

6 Summary 181

Glossary 183

Bibliography 186

xvi

List of Tables

1.1 Information content comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.1 Detector specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.2 Example of SNR calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3.3 Parameters for laser diode RF modulation . . . . . . . . . . . . . . . . . . . . . . 58

3.4 Specification for VersArray:1300F . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.1 Frequency of breast disease . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

4.2 Average normal breast properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

4.3 Tumor contrast of individual subjects . . . . . . . . . . . . . . . . . . . . . . . . . 120

4.4 Tumor size measured with DCE-MRI . . . . . . . . . . . . . . . . . . . . . . . . 132

4.5 Tabulation of relative blood flow (rBF) . . . . . . . . . . . . . . . . . . . . . . . . 148

5.1 Fixed parameters for two-layer estimation . . . . . . . . . . . . . . . . . . . . . . 157

5.2 Summary of µa from clinical in utero data . . . . . . . . . . . . . . . . . . . . . . 167

xvii

List of Figures

1.1 Spectrum of absorption and scattering in the NIR . . . . . . . . . . . . . . . . . . 2

2.1 Measurement approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2 General analysis flow chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.3 Extrapolated Boundary Condition . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.4 Measurement Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.5 Effect of coupling coefficients on measured amplitude and phase . . . . . . . . . . 29

2.6 NRIM analysis flow chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.7 Reconstruction geometry for breast imaging . . . . . . . . . . . . . . . . . . . . . 35

2.8 TOAST analysis flow chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.1 Photodiode structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.2 Schematic of Photomultiplier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.3 Single CCD electrode and transfer mechanism . . . . . . . . . . . . . . . . . . . . 48

3.4 CCD chip layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.5 Characteristic response of detector . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.6 SNR of detectors with variation of incident light power . . . . . . . . . . . . . . . 54

3.7 Homodyne frequency-domain system . . . . . . . . . . . . . . . . . . . . . . . . 57

xviii

3.8 Laser diode style . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.9 RF modulation of laser diode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.10 I&Q demodulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.11 Electronic dynamic range measurement set-up . . . . . . . . . . . . . . . . . . . . 63

3.12 Effect of amplifier addition on dynamic range . . . . . . . . . . . . . . . . . . . . 64

3.13 Effect of offset subtraction on dynamic range . . . . . . . . . . . . . . . . . . . . 65

3.14 Amplitude linearity test set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

3.15 Amplitude linearity Test Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

3.16 Phase linearity test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

3.17 Parallel plate scanning transmission diffuse optical instrument . . . . . . . . . . . 69

3.18 Parallel plate scanning instrument electronics . . . . . . . . . . . . . . . . . . . . 69

3.19 Schematic of parallel plate diffuse optical tomography instrument . . . . . . . . . 71

3.20 Schematic of Fetal oximeter instrument . . . . . . . . . . . . . . . . . . . . . . . 73

3.21 Typical breast raw data from Scanning DOT set-up . . . . . . . . . . . . . . . . . 76

3.22 Measurement geometry for Scanning DOT . . . . . . . . . . . . . . . . . . . . . . 77

3.23 Linear response of Scanning DOT to optical properties variation . . . . . . . . . . 78

3.24 Fitted amplitude and phase vs separations . . . . . . . . . . . . . . . . . . . . . . 79

3.25 Ink titration of matching fluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

3.26 Silicone phantoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

3.27 Point spread function images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

3.28 Field of view images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

3.29 ICG titrated phantom images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

3.30 Reconstruction of a silicone breast shape phantom with embedded absorber . . . . 85

xix

3.31 µa of water and lipid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

3.32 Extinction coefficient of hemoglobins . . . . . . . . . . . . . . . . . . . . . . . . 87

3.33 Extinction coefficient of ICG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

3.34 Absorbance of India ink and liquid phantom measurement configuration . . . . . . 89

3.35 Intralipid µ′s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

3.36 Blood phantom measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

3.37 StO2 response with oxygen supply to blood phantom . . . . . . . . . . . . . . . . 92

3.38 Silicone (RTV-12) recipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

4.1 Histogram of normal breast properties . . . . . . . . . . . . . . . . . . . . . . . . 103

4.2 Blood saturation vs blood volume of healthy breasts . . . . . . . . . . . . . . . . . 104

4.3 Physiological noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

4.4 Correlation of blood and BMI . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

4.5 Correlation of scattering and BMI . . . . . . . . . . . . . . . . . . . . . . . . . . 107

4.6 Correlation of blood and age . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

4.7 Raw CW data for selected source position . . . . . . . . . . . . . . . . . . . . . . 109

4.8 Transillumination pictures of breasts . . . . . . . . . . . . . . . . . . . . . . . . . 111

4.9 Orientation of three-dimensional reconstructed DOT images . . . . . . . . . . . . 113

4.10 Tumor location of subject #103 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

4.11 3D reconstruction of breast (subject #103) with ductal carcinoma . . . . . . . . . . 115

4.12 Tumor location of subject #68 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

4.13 3D reconstruction of breast (subject #68) with adenocarcinoma . . . . . . . . . . . 117

4.14 Tumor location of subject #111 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

4.15 3D reconstruction of breast (subject #111) with multiple ductal carcinomas . . . . 119

xx

4.16 Tumor location of subject #95 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

4.17 3D reconstruction of breast (subject #95) with fibroadenoma . . . . . . . . . . . . 121

4.18 Tumor location of subject #69 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

4.19 Breast cancer image reconstruction using single-spectral method . . . . . . . . . . 123

4.20 Breast cancer image reconstruction using multi-spectral method . . . . . . . . . . 124

4.21 Tumor contrast (N=22 carcinomas) . . . . . . . . . . . . . . . . . . . . . . . . . . 125

4.22 Neoadjuvant chemotherapy timing diagram . . . . . . . . . . . . . . . . . . . . . 126

4.23 LABC tumor location . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

4.24 Transillumination of breast at 830 nm . . . . . . . . . . . . . . . . . . . . . . . . 128

4.25 MRI orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

4.26 Chemotherapy 3D THC images . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

4.27 Chemotherapy 3D µ′s images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

4.28 Chemotherapy 3D StO2 images . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

4.29 Chemotherapy DCE-MRI images . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

4.30 Correlation of tumor position between MRI and DOT . . . . . . . . . . . . . . . . 138

4.31 Tumor volume and THC contrast decrease with chemotherapy . . . . . . . . . . . 139

4.32 Hand-held blood flow probe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

4.33 Temporal auto-correlation curves of tumor and healthy breast tissue . . . . . . . . 146

4.34 Relative blood flow scans of a healthy breast and a diseased breast . . . . . . . . . 147

5.1 Fetal hypoxia ewe model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

5.2 NIRS Fetal hypoxia data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

5.3 NIRS fetal blood saturation during fetal hypoxia . . . . . . . . . . . . . . . . . . . 160

5.4 Correlation between NIRS and hemoximeter . . . . . . . . . . . . . . . . . . . . . 161

xxi

5.5 Two groups of fetal hypoxia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

5.6 Prototype Clinical Fetal Oximeter Instrument . . . . . . . . . . . . . . . . . . . . 165

5.7 Illustration of clinical in utero measurements . . . . . . . . . . . . . . . . . . . . 166

5.8 Summary of physiological parameters at prior, during and after birth . . . . . . . . 170

5.9 µa vs fetal brain depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

5.10 Approximation of in utero system to two-layer system . . . . . . . . . . . . . . . . 171

5.11 Effect of homogeneous fit on two-layer system . . . . . . . . . . . . . . . . . . . 172

5.12 Noise model incorporated Two-layer SNR . . . . . . . . . . . . . . . . . . . . . . 174

5.13 Fractional amplitude and phase difference between two-layer vs homogeneous . . . 175

5.14 Optimal source detector separtion . . . . . . . . . . . . . . . . . . . . . . . . . . 176

5.15 Comparison between homogeneous and two-layer model fit . . . . . . . . . . . . . 177

xxii

Chapter 1

Introduction

1.1 Diffuse Optical Spectroscopy and Tomography

Diffuse optical tomography (DOT) and spectroscopy (DOS) are non-invasive techniques used to

measure the optical properties of physiological tissue. In the near-infrared (NIR) spectral window

of 600 - 1000 nm, photon propagation in tissues is dominated by scattering rather than absorp-

tion. Photons experience multiple scattering events as they propagate deeply into tissue (up to

10 cm). The primary chromophores in this spectral window are oxygenated hemoglobin (HbO2),

deoxygenated hemoglobin (Hb), water (H2O) and lipid. Each chromophore possesses a distinct

spectrum as shown in Fig. 1.1(a). A weighted sum of the contributions from each chromophore

which correponds approximately to the tissue absorption coefficient (µa) is also shown. Here,

the concentration of each chromophore is adjusted to a value typically found in breast tissue: the

concentration of oxygenated hemoglobin (CHbO2) is ∼24 µM, the concentration of deoxygenated

hemoglobin (CHb) as ∼6 µM, and the tissue is assumed to contain a 31 % water and a 57 % lipid

contribution. This combination leads to total hemoglobin concentration, THC = CHb + CHbO2,

1

of 30 µM, and a blood oxygen saturation, StO2 = CHbO2/THC, of ∼80% (see Chapter 2 for

more details). Notice that absorption measurements at multiple wavelengths are required to extract

the concentration of each chromophore. Fig. 1.1(b) shows a typical scattering spectra found in the

breast tissue. The tissue scattering depends on the photon random walk step in the medium. The

reduced scatttering coefficient (µ′s) which is the reciprocal of the photon random walk step length,

is often modeled within a simplified Mie-scattering approximation [185, 188], i.e. µ′s(λ) = Aλ−b

where λ is the light wavelength. Notice that scattering is 100× larger than the absorption, and the

NIR scattering spectra is relatively flat in the near infrared.

650 700 750 800 850 900 950 10000

0.05

0.1

0.15

0.2

wavelength

µ a

HbO2HbH2Olipidtotal

(nm)

(cm

−1)

(a)

650 700 750 800 850 900 950 10000

2

4

6

8

10

12

wavelength

µ s′

(nm)

(cm

−1)

(b)

Figure 1.1: Spectrum of absorption and scattering in the NIR. (a) Spectra of major chromophoreswith adjusted concentrations found in typical breast tissue: oxygenated hemoglobin (HbO2) anddeoxygenated hemoglobin (Hb), water and lipid. (b) Scattering spectra. See text for details.

Accurate retrieval of tissue properties based on the DOS and DOT measurements requires that

absorption and the scattering be decoupled. A light transport model based on the diffusion approx-

imation [121] is widely used to describe photon propagation in the NIR. Using optical measure-

ments at multiple source-detector positions on the tissue surfaces, one can reconstruct the internal

2

distribution of the absorption coefficient (µa) and the reduced scattering coefficient (µ′s) in three-

dimensions based on the transport model. Physiological images of total hemoglobin concentration,

blood oxygenation, water and lipids are then derived from this information. Thus far DOT and DOS

have generated a lot of scientific interest and have been applied in various deep-tissue applications

including breast cancer imaging [62, 69, 102, 116, 119, 144, 165, 191, 194, 213, 222, 300], brain

functional imaging [80], stroke detection [23, 63, 133], muscle functional studies [148, 226, 285],

photodynamic therapy [273, 282], and radiation therapy monitoring [250].

I worked primarily on two major applications of DOT and DOS: breast cancer imaging and

fetal brain oxygenation monitoring. In the following sections, the clinical motivation and the brief

history of each application in photon migration field will be described.

1.2 Breast cancer imaging

Approximately one in nine women will develop breast cancer in their lifetime, and of these cancers,

approximately 30% will be fatal [2, 157]. Currently, several clinical methods are used in breast

cancer screening and diagnosis [95, 152]. The most common of these are palpation and X-ray

mammography. Other methods include ultrasound, magnetic resonance imaging (MRI), positron

emission tomography (PET), and surgical and needle biopsy. Some of these techniques rely on

intrinsic characteristics of breast tissue to image the breast or to identify lesions within it, while

others employ exogenous tracers or contrast agents. Similarly, some are useful in screening while

others are useful only in diagnosis.

The most effective screening technique at this time is X-ray mammography. X-Ray mammog-

raphy, however, has a ∼ 22% false negative rate in women under 50 [151]. The method cannot

accurately distinguish between benign and malignant tumors [131]; it has been shown in recent

3

studies to have lower sensitivity in pre-menopausal women [152] and to be of limited clinical

value for women under 35 years of age [126]. Furthermore, increased mammographic density can

arise in some post-menopausal women, for example due to hormone replacement therapy [14], or

cyclically during the menstrual cycle of younger women [280]; these effects reduce the effective-

ness of mammographic screening. Techniques such as MRI and ultrasound are sometimes used

in addition to X-Ray mammography, but have limitations such as high cost, low throughput, lim-

ited specificity (MRI) and low sensitivity (ultrasound). Thus, there is still a need to detect cancers

earlier for treatment [1, 32], to detect cancers missed by mammography [21, 110, 274], and to add

specificity to the mix, since the majority of invasive follow-up procedures (e.g. surgical biopsies)

are performed on normal or benign tissue [101].

Near-infrared (NIR) diffuse optical tomography (DOT) is based on the study of functional pro-

cesses and provides several unique measurable parameters with potential to enhance breast tumor

sensitivity and specificity. The techniques utilize non-ionizing radiation, are non-invasive, and

are often technologically simple and fast. Tissue optical absorption coefficients provide access to

blood dynamics, total hemoglobin concentration (THC), blood oxygen saturation (StO2), water

concentration (CH2O) and lipid content. These tissue properties are often substantially different in

rapidly growing tumors; for example, high concentrations of hemoglobin with low oxygen satura-

tion are suggestive of rapidly growing tumors [267, 268, 276] due to their high metabolic demand

and (sometimes) poor perfusion. In a different vein, an overall increase in organelle population due

to proliferation of cancer cells leads to an increase of optical scattering coefficients for the tumor.

Nuclei and mitochondria are major contibutors to reduced optical scattering coefficients [184] as

well as collagen in the extracellular matrix [255]. Finally, optical absorption, fluorescence, and

scattering of exogenous contrast agents that occupy vascular and extravascular space also provide

4

useful forms of sensitization.

The utility of DOT for tumor monitoring has been recently demonstrated with success for

neoadjuvant chemothrapy [49, 140]. Neoadjuvant chemotherapy (i.e. pre-operative chemother-

apy) is an important therapeutic approach for women with locally advanced breast cancer (LABC).

LABC generally refers to lesions larger than 5 cm that may or may not have spread beyond the

breast and axillary lymph nodes. If the patient responds to neoadjuvant chemotherapy, the size

of the primary tumor decreases, facilitating better control through surgery while potentially erad-

icating micro-metastatic disease [36]. Neoadjuvant chemotherapy enables a higher percentage of

patients to undergo breast conservation therapy without negatively impacting local recurrence rates

or long-term outcome when compared with adjuvant chemotherapy [98]. Additionally, the neoad-

juvant setting provides a means to monitor the effectiveness of chemotherapy by observing its

effects on the primary tumor in vivo.

Information about tumor response during chemotherapy may be useful for treatment optimiza-

tion. Physical examination, as well as mammographic and ultrasonographic evaluations sometimes

has limited utility for assessing tumor response due to chemotherapy-induced fibrosis [52, 243,

269]. While MRI has proved useful for defining the extent of residual disease when compared with

pathology [74,92], and while dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI)

has demonstrated ability to monitor tumor size and vascularity during neoadjuvant chemotherapy

using gadolinium contrast agents [74, 156, 261], the high cost and invasiveness of these methods

render them impractical for frequent (e.g. daily) monitoring. Frequent monitoring of vascularity is

important. Indeed a reduction of tumor angiogenesis from neoadjuvant chemotherapy in combina-

tion with hormone therapy has been confirmed by pathologic analysis [171].

5

The most effective clinical role for diffuse optical tomography (DOT) in the screening, di-

agnosis, and treatment monitoring of breast cancer has yet to be determined. However, it is

clear DOT provides exquisite functional information directly related to tumor patho-physiology

(e.g. metabolic activity, angiogenesis, and blood flow/concentration), and complementary to struc-

tural and functional information provided by conventional imaging. Furthermore, advances in

diffuse optical tomography of breast are critical for exploitation of the advances of molecular

imaging [190, 191, 277], an emerging field of medicine with promise of new generation optical

contrast agents.

1.2.1 Brief history of breast optical imaging: Before the Diffusion Approximation

Optical characterization of the breast has been attempted since 1929 [66] when the term diaphanog-

raphy was applied to shadowgraphs of breast tissue. The use of light to detect tumors in the breast

was first proposed by Cutler in 1929. Cutler hoped to distinguish between solid tumors and cysts in

the breast, but found it difficult to produce the necessary light intensity for diaphanography without

exposing the patient’s skin to extreme heat. Researchers in the 1930s and 1940s had little more

success, and the technique was temporarily abandoned. In the early 1980’s, however, essentially

the same class of transillumination measurement was renewed [16,35,108,131,178,183,209,225,

247, 272, 275] using light in regions of low tissue absorption (i.e. 600 nm to 1300 nm). Unfortu-

nately the high degree of breast tissue scattering distorted spectroscopic information and blurred

optical images as a result of the large distribution of photon pathways through the tissue, and a

study in 1990 [4] suggested the method was still inferior to traditional methods of breast imaging.

Thus widebeam transillumination proved largely inadequate for clinical use, because it was too

6

difficult to separate the effects of absorption and scattering within the tissue, and because the two-

dimensional “photographic” data was poorly suited for image reconstruction. The mathematical

modeling of light transport in tissues had not been developed sufficiently for optical tomography

to be readily employed.

1.2.2 Brief history of breast optical imaging: After the Diffusion Approximation

As a result of numerous scientific and technological advances in tissue optics since 1990, optical

mammography now appears feasible with levels of specificity and resolution superior to early

work. The most critical advance in the field of photon migration has been the recognition and

widespread acceptance that light transport over long distances in tissues is well approximated as a

diffusive process [42, 290, 291]. Using this physical model it is possible to quantitatively separate

tissue scattering from tissue absorption, and to accurately incorporate the influence of boundaries,

such as the air-tissue interface, into the transport theory [203, 204]. Waves of diffuse light energy

density [113], or their time-domain analogs [18, 72, 137, 203] propagate deeply in tissues (e.g.

∼10 cm) and obey rules such as refraction [197], diffraction [27, 100], interference [238], and

dispersion [245,260] as they encounter variations in tissue properties. The separation of scattering

and absorption afforded by the diffusion approximation has led to new, quantitative investigations

about the average concentrations of molecular species in a variety of highly scattering media [43,

78, 96, 97, 125, 203, 244, 252, 260, 281].

For the purposes of breast imaging, the most important contribution of the diffusion approxi-

mation has been to provide a tractable mathematical basis for tomographic image reconstruction.

Tomographic methods were not employed in the early transillumination patient studies, and are

7

crucial for recovery of information about breast tumor shapes and optical properties. Several ap-

proaches have been developed for diffuse optical tomography (DOT) [7, 8, 10, 12]. These include:

transport equation based schemes [230,232,242],backprojection methods [53,271], diffraction to-

mography in k-space and variants [46,167,180,240], perturbation approaches [6,11,198,241], the

Taylor series expansion approach [141–143,205,206,216], gradient based iterative techniques [13],

elliptic systems methods (ESM) [118, 155], truncated Newton schemes [233–236] and Bayesian

conditioning [89–91]. Other important and related theoretical advances include the development

of analytic inversion formalisms [174–177], development and clarification of differencing [207]

and differential [192] methodologies, and advances in the use of a priori information [154, 165].

During the last few years, scientists in the field have begun to experimentally revisit the prob-

lem of optical mammography armed with these new ideas and approaches. Highlights of the first

wave of this experimental work, which did not carry out a rigorous 3D tomographical analysis, in-

clude: (1) Pilot human breast studies [102, 123, 210] employing point-to-point (tandem-geometry)

transillumination with diffuse photon density waves. This work used the phase of the diffusive

wave as a means to correct for edge effects in the optical mammography apparatus. The phase cor-

rection enhanced image contrast and demonstrated potential for improved optical mammography.

(2) Pilot transillumination (tandem-geometry) measurements of human breasts in the time domain

by European groups [47, 115–117, 214, 253, 258]; again, however, the analyses were approximate.

For example, in some cases optical properties were assigned by fitting to bulk Greens function

response curves [117], and in other cases non-linear perturbation theory [258] and random-walk

based theory [47] were used to improve upon the bulk approximation. (3) Pilot studies by Philips

Corp. using a 256×256 continuous wave (CW) instrument in the “pendant” geometry. Preliminary

results using modified back-projection and algebraic reconstruction technique (ART) algorithms

8

have been presented [54,132]. (4) Pilot studies using plane-wave illumination in the frequency do-

main to probe canine breast cancer differentiation following contrast agent injection. In this case,

back-reflected diffuse light was measured using an intensified CCD camera [229], thus attesting to

its feasibility with the fluorescent contrast agent approach.

In the second wave of clinical research, experimenters have finally begun to exploit the full

possibilities of the tomographic approach with emphasis on clinical measurements. We focus here

primarily on the work of other researchers. Pogue and coworkers and Jiang and coworkers have em-

ployed a cylindrical geometry with rings of source-detector pairs wrapped around the breast. Pogue

et al. [70, 221, 222] have reported quantitative hemoglobin images of the female breast acquired

through model-based reconstruction of near-infrared data. Their approach only uses in-plane data

for reconstruction (using 3 planes × 16 sources × 15 detectors at multiple wavelengths). Never-

theless, their reconstructions reveal tumor/normal tissue contrast in total hemoglobin concentration

and StO2 [70]. Jiang et al [144] carried out a 3D study on one patient with CW light at 785 nm,

observing two invasive ductal carcinomas at different locations. Their studies with more patients

were essentially 2D reconstructions of absorption (µa) and scattering (µ′s) at 785 nm. Again, they

observed absorption contrast in the invasive carcinomas (N=5) and a fibroadenoma (N=1) [145];

they also found evidence for cysts (low µa and µ′s) [119]. Barbour and coworkers carried out a

study in an essentially cylindrical (or conical) geometry [15]. They utilized three different pertur-

bations, one for each patient (i.e. deep breathing maneuver, breath holding and Valsalva maneuver),

to explore tumor response, and they found tumor contrast in oxygen supply/demand imbalance and

vasomotor response. Several groups have now begun incorporating optical techniques with other

imaging modalities. For example, Boas and coworkers [165] have co-registered DOT with x-ray

mammography in a ‘hard’ compression instrument. Thus far they have shown a priori spatial

9

information from a co-registered x-ray mammogram can constrain DOT regularization in recon-

struction of µa at 780 nm. This approach will be interesting in the future. There has also been

research, combining ultrasound with optical methods, e.g. Zhu/Yodh et al [299], Yodh/Tromberg

et al [130] and Zhu et al [297, 298, 300]. The DOT problem in this case is made more difficult by

the reflection geometry, and by poor definition of breast boundaries compared to other instruments

described above. Nevertheless, Zhu and coworkers have constructed 3D DOT total hemoglobin

concentration maps (assuming only absorption perturbation), identifying an in situ ductal carci-

noma (N=1) [297], and in other studies they have distinguished early-stage invasive carcinomas

(N=2) from benign lesions (N=17) [300]. Yodh, Chance, Schnall and coworkers [194, 195] have

combined time-domain DOT with MRI in a ‘soft’ parallel-plate compressed breast geometry that

appears to be more sensitive to hemodynamic tumor signatures compared to ‘hard’ compression.

Their most important contributions thus far are the direct verification of tumors by both techniques,

and the study of differential uptake of contrast agents in malignant tumors. More groups have be-

gun to incorporate DOT into MRI environment to utilize high spatial resolution information from

MRI to constrain DOT for better quantification [33]. Finally, 3D DOT fluorescence imaging in

phantoms has been accomplished [109]; this may be important for future studies with contrast

agents and optical techniques.

In addition to tomographic imaging, there has been significant spectroscopic research recently

on tumors and normal tissues providing more insight about their optically-derived properties [41,

140, 146, 202, 249, 251, 259] by correlating to physiological parameters such as body-mass-index,

age, breast thickness, radiographic density, paranchemal type, etc. Especially, intrasubject and in-

tersubject variability of those properties are reported, which emphasizes the importance of relative

measure of tumor to normal contrast of the same subject [212, 215, 246, 248].

10

The photon migration community, especially in breast cancer imaging, is at the critical point

in identifying tumor contrast. Photon migration breast cancer research is constantly evolving to-

wards (1) better quantification (3D imaging with multiple source detector positions), (2) extensive

exploration of physiological parameters (multiple wavelength, correlation with histo-pathology

[222, 278]), (3) co-registration with other imaging modalities and (4) therapy monitoring.

1.2.3 Breast optical imaging in our laboratory

During the last decade our laboratory has made substantive contributions to problems in dif-

fuse optical tomography. We published the first experiments demonstrating tomographic recon-

struction of absorption and scattering heterogeneities [198], we were among the first groups to

show how to reconstruct the lifetime and concentration of fluorophores in tissues [199], and we

introduced a methodology whereby diffused temporal light field correlation functions are used

to reconstruct heterogeneous dynamical flow properties [24, 29]. In a different vein, we have

investigated the fundamental resolution and characterization limitations of diffuse optical tech-

niques [28, 166, 168], and we have combined the optical methods with other imaging modalities

such as ultrasound [130,299] and MRI [192–195] so structural information from the second imag-

ing modality may be optimally coupled with the optical technique to improve the accuracy of as-

signed tissue optical properties [200]. We also continue to develop theoretical tools for DOT which

have, for example, elucidated the resolution and sensitivity trade-offs associated with specific ge-

ometries and instrumentation [65], enabled experimenters to choose optimal source wavelengths

for clinical experiments [58], and clarified the conditions for which differential measurements are

well suited for quantitative tomography [192]. Finally we have consistently pushed DOT towards

11

in vivo applications, for example, in brain hemodynamics and metabolism [63, 88], in tumor biol-

ogy [182], and in breast tumor detection and characterization.

Most recently (and relevant for this thesis), we have successfully assembled a parallel-plate

soft-compression apparatus for diffuse optical tomography of breast, and we have begun clinical

studies with the instrument at the Hospital of the University of Pennsylvania (HUP) [49, 62, 81].

Our second generation parallel-plate instrumentation is unique in the community: our sources and

detectors are based predominantly on continuous-wave (CW) light, our CCD-based detection is

simple and massively parallel compared to all other instrumentation, we collect multiple views

of the breast in the device and so execute and produce full three-dimensional reconstructions,

and our soft compression parallel-plate geometry is attractive for comparison to MRI and x-ray

mammography as well as for maximizing hemodynamic contrast. Two sensible figures of merit

for DOT imaging systems are total data, and data rate (defined as a product of source-number times

detector-number times number-of-wavelengths divided by total-acquisition-time). Our current data

rates exceed those of all existing instruments, in most cases by 100× (See Table 1.1).

With this instrumentation, we demonstrated theoretically and experimentally that it is possible

to carry out 3D diffuse optical tomography with CW light. We showed that DOT reconstructions

based on measurements at multiple optical wavelengths (simultaneously) enable experimenters to

efficiently and uniquely separate scattering from absorption, as well as the contributions of one

chromophore from another chromophore [57, 58]. Our clinical pilot studies show that tumors

are detectable and characterizable with the diffuse optical method (Chapter 4, Section 4.4); they

can even be tracked during neoadjuvant chemotherapy [49] (Chapter 4, Section 4.5). In light of

searching for additional optical contrast, we show that blood flow measurement by optical method

is feasible and show distinction among different breast tumors (Chapter 4, Section 4.6).

12

Group type Ns Nd Nλ Ntotal τ data rate(Hz)this thesis (2nd gen.) CW 48 2.28×105 6 6.5×107 8.4 min 6.6×107

Schmitz et al [239] CW 25 32 4 3.2×103 0.32 s 8640Colak et al [54] CW 225 225 3 1.5×105 6 min 540

Iftimia et al [134] CW 64 64 3 1.2×104 12 min 17McBride et al [181] FD 16 15 × 3 6 4.3×103 30 s 42

Li et al [165] FD 40 9 1 3.6×102 1.5 min 4Chen et al [44] FD 12 8 2 1.9×102 NA NA

Godavarty et al [109] FD 27 128 1 3.5×103 NA NAFranceschini et al [102] FD 1 2340 2 4.6×103 3 min 2.6Ntziachristoset al [194] TD 24 8 1 1.9×102 80 s 2.4

Cubeddu et al [258] TD 1 3000 4 1.2×104 5 min 40Rinneberg et al [115] TD 1 2000 2 4.0×103 5 min 13Schmidt et al [237] TD 32 32 1 1.0×103 ∼10 min 1

Table 1.1: Comparison of instruments used in the photon migration field in terms of informationcontent. Ns: number of sources, Nd: number of detectors, Nλ: number of wavelength, Ntotal:total number of data (= NsNdNλ), τ : acquisition time. Data rate is defined as Ntotal/τ . (CW:continuous-wave, FD: Frequency-domain, TD: Time-domain method)

1.3 Fetal Brain Oxygenation Monitoring

Hypoxic-ischemic damage to the fetal brain can result in permanent neurodevelopmental impair-

ment or death [257, 263, 264]. Early detection of fetal cerebral hypoxic-ischemia is thus important

for timely intervention. Current non-invasive antepartum screening and diagnostic tools for fetal

well-being in utero include the non-stress test (fetal heart rate monitoring) and the biophysical pro-

file (fetal heart rate monitoring and ultrasound). Fetal heart rate monitoring, however, probes fetal

cerebral hemodynamics and oxygenation indirectly, and has a high false-positive rate [161, 173].

This has led to an increased number of unnecessary Cesarean sections and premature deliver-

ies [223]. Clearly, the development of devices to directly monitor fetal cerebral oxygenation and

hemodynamics could improve the specificity of antepartum tests. Near-infrared (NIR) diffuse

optical spectroscopy has the potential to non-invasively monitor fetal cerebral oxygenation and

hemodynamics in utero. NIR light is non-ionizing and the power levels used are harmless to the

13

body, making this technology safe under continuous exposure. Additionally, NIR technology can

be designed to be fast and portable and is therefore suitable in a clinical setting.

A few researchers have developed and employed NIR oximeters to monitor neonatal cerebral

oxygenation [45,77,122,127,158]. More recently, a trans-vaginal NIR fetal oximeter [73,103] has

been developed, but can only be used during labor after the amniotic membrane has ruptured.

Development of a non-invasive transabdominal NIR fetal oximeter is challenging, but if suc-

cessful could provide a direct assessment of fetal cerebral oxygenation and hemodynamics be fore

labor and delivery. The feasibility of transabdominal NIR continuous wave (CW) spectroscopy was

first explored by Ramanujam et al [227, 228] during a non-stress test. Subsequently, Zourabian et

al developed a transabdominal NIR CW oximeter with the capability to detect fetal arterial pulses

in utero [301]. In addition, theoretical and experimental tissue phantom investigations have been

performed to understand NIR photon diffusion through the fetal brain in utero [138, 270]. Col-

lectively, these studies suggest transabdominal NIR photon diffusion measurements through the

fetal brain in utero are possible. However, due to limitations of the instrumentation and analytical

models employed in these studies, it has not as yet been possible to quantify fetal cerebral blood

saturation or blood volume in utero.

To demonstrate the feasibility of transabdominal NIR spectroscopy for detecting and quantify-

ing fetal hypoxia in utero, we designed a fetal hypoxia model using pregnant ewe. We have built

a multi-wavelength NIR frequency-domain instrument with the capability to perform NIR pho-

ton diffusion measurements through tissue over a wide range of source-detector separations and a

two-layer numerical diffusion model to accurately quantify the fetal cerebral blood saturation. We

have shown good agreement between fetal blood saturation determined by the transabdominal NIR

method, and arterial and venous fetal blood saturation quantified from fetal blood samples using a

14

hemoximeter (gold standard) [50] (Chapter 5, Section 5.2).

1.4 Thesis Outline

In this thesis, I describe the theory and the experimental DOS/DOT techniques used for breast

cancer imaging and fetal brain oxygenation monitoring. I will also present physiological results

for each application. Chapter 2 describes the theory behind DOS/DOT. Chapter 2, Section 2.2

outlines the general analysis structure common to DOS and DOT, and the remaining sections of

Chapter 2 go into details about DOS and DOT respectively. Section 2.4 describes and compares

two different DOT algorithm developed in our laboratory.

Chapter 3 describes experimental techniques starting from design issues to validation with tis-

sue phantoms. Chapter 3, Section 3.2 briefly discusses specification parameters and signal-to-noise

characteristics of light source and detector components for the application. Detailed schematics of

the frequency-domain homodyne system and CCD-based continuous wave system are introduced

in the following sections respectively. In Section 3.5, the electronic and optical characterization

method of the instrument is outlined. The details of specific instruments used for the breast imag-

ing and fetal oximeter are summarized in Section 3.6. These instruments are further characterized

extensively using various tissue phantoms reflecting the specific requirement of the application, in

Section 3.7.

Chapter 4 explores various optical contrast of breast cancer using three-dimensional DOT im-

age reconstruction. The medical terminology regarding breast cancer diagnosis is briefly intro-

duced in the Section 4.2. Healthy breast optical properties are quantified in Section 4.3 to identify

variations due to intrinsic breast heterogeneity and dependence on demographic features. In Sec-

tion 4.4, three-dimensional reconstructed images of THC, StO2, and µ′s are presented. Particularly,

15

THC and µ′s show higher values in the tumor than in the surrounding tissue which correlate well

with other imaging modalities such as X-ray mammography, ultrasound or MRI. In Section 4.5,

the utility of DOT to monitor neoadjuvant chemotherapy is demonstrated by comparing with the

MRI. The potential enhancement of the breast cancer contrast based on blood flow measurement

is introduced in Section 4.6.

Chapter 5 explores the feasibility of quantitative fetal oximetry in utero. In Section 5.2, the

accurate quantification of NIR fetal oximetry using two-layer model is demonstrated in an induced

fetal hypoxia model using pregnant sheep. In Section 5.3, a preliminary study on human in a

Cesarean section scenario is discussed for issues regarding translating the technology to clinical

situations. In the following section, based on these issues, a method to optimize the instrument for

clinical setting is described.

Chapter 6 summarizes the thesis and future work.

16

Chapter 2

Theory

2.1 Introduction

The propagation of photons through turbid media such as tissue is often first described by the

Boltzman transport equation [37, 67]. Generally, solutions of the Boltzman equation are computa-

tionally intensive and time consuming. Fortunately, for the most DOT applications the Boltzman

transport equation is well approximated by the photon diffusion equation. The derivation of pho-

ton diffusion equation from the transport equation is given clearly in reference [22]. We adopt

the photon diffuse equation as our starting point. The photon diffusion equation has the following

form:

∇ · (D(r)∇Φ(r, t))− µa(r)Φ(r, t)−1

v

∂Φ(r, t)

∂t= −S(r, t). (2.1)

Here r is the position vector, t is time and v is the speed of light in the medium [cm/s]. D(r) ∼=

13µ′s(r)

[87] is the photon diffusion coefficient, µ′s(r) [cm−1] is the reduced scattering coefficient,

and µa(r) [cm−1] is the absorption coefficient. Φ(r, t) is the photon fluence rate [Watt/cm2] and

S(r, t) is the isotropic light source term [Watt/cm3].

17

The behavior of Φ(r, t) near the boundary of the turbid medium is described by partial current

boundary conditions (i.e. mixed Dirichlet-Neuman boundary condition) [121, 150, 159, 296],

∂Φ(r)

∂n= −αΦ(r), (2.2)

where n is the vector normal to measurement boundary, α is related to the refractive index mis-

match at boundary via the following: α =(

1−Reff1+Reff

)

3µ′s2 , Reff ∼ −1.44

n2 + 0.71n + 0.668 + 0.63n

and n = ninnout

[114,150]. Typically, the source is modeled as a single isotropic point source placed

1/µ′s into the medium.

Time

Inte

nsity Input

Output

CW

(a)

Time

Inte

nsity

FD

(b)

Time

Inte

nsity

TD

(c)

Figure 2.1: Measurement approaches: (a) Continuous-wave, (b) Frequency-domain, (c) Time-domain measurement types (solid line: input light source, dashed line: output detected signal)

Three types of measurements are used widely in the community: continuous-wave (CW),

frequency-domain (FD), and time-domain (TD) measurements. Figure 2.1 illustrates the input light

source (solid line) and the output signal (dotted line) for each measurement type. Continuous-wave

measurements employ a light source whose intensity does not vary with time; the detector mea-

sures the transmitted intensity which is affected by the medium. Frequency-domain measurements

18

employ a light source which is amplitude modulated in the radio-frequency (RF) range. The de-

tector measures the amplitude of the transmitted diffuse photon density wave and its phase shift

relative to the input. Time-domain measurements employ a short input light pulse (i.e. typically

less than 1 nanosecond) and detect a delayed and temporally broadened output pulse.

Equation 2.1 further reduces to the following equation for the FD case.

FD : ∇ · (D(r)∇Φ(r))−(

µa(r)−iω

v

)

Φ(r) = −S(r). (2.3)

In the FD case, we have assumed Φ(r, t) = Φ(r)e−iωt, and the e−iωt terms have factored

out, since the detected signals are modulated at the same frequency as the light source (ω: light

source modulation frequency). For the CW case, Equation 2.3 simplifies since ω = 0. Equations

2.1 through 2.3 are used to compute Φ(r), given µa(r) and µ′s(r). This is often referred to as the

forward problem.

The relative placement of light sources and detectors define measurement geometry. In a par-

allel plate design similar to X-ray mammography or MRI, in vivo tissue lies between two planes

where light sources residing in one plane and detectors residing in the other plane. This geometry

is called as the trasmission geometry. However, most organs are not accessible to transmission

geometry due to signal-to-noise issue. In this case, remission geometry is utilized where the light

sources and detectors reside in the same plane (i.e. at the surface of the tissue). Multiple scattering

enables photons to deviate from the straight path and reach the detectors placed in the same plane.

Cylindrial geometry is also used for mostly breast and sometimes neonate brain. This geometry

can be thought as the mixture of remission and transmission depending on the relative position of

source and detectors.

19

Using Equation 2.1, it is usually desirable to compute optical properties from measurements

of Φ(r) on the tissue surface. This is called the inverse problem. The inverse problem can be

formulated in various ways depending on the application and measurement design. Diffuse optical

spectrscopy (DOS) treats the reconstruction space as either homogeneous or composed of a limited

number of piecewise homogeneous regions. Therefore, the number of unknowns (i.e. the bulk op-

tical properties of each region) is usually much less than the number of measurements. For Diffuse

optical tomography (DOT), the reconstruction space is discretized into large number of volume

elements or voxels. The optical properties of each voxel are the unknowns to be reconstructed.

To deal with the heterogeneous response of light sources and detectors (which we will refer

to as source-detector coupling coefficients), two different approaches are often employed. Differ-

ential reconstruction utilizes a reference measurement to normalize out the variations of source

detector coupling. In time-series measurements, a reference measurement comes from baseline

data before some physiological perturbation. In other cases, a reference measurement is made on

a tissue phantom with well-known optical properties. In an absolute reconstruction, the coupling

coefficients are treated as additional unknowns to be estimated.

When defining the unknowns to reconstruct, it is also desirable to impose additional spectral

constraints based on known properties of physiological tissues. Spectral constraints on the sample

absorption arise from the well-known spectrum of each chromophore. The absorption coefficient

at each light wavelength is related to these chromophore contributions as follows:

µa(λ, r) =L∑

l=1

εl(λ)Cl(r). (2.4)

Here εl(λ) is the extinction coefficient, Cl(r) the concentration of the lth chromophore and L

20

is the total number of chromophores. In physiological case, major chromophores are oxygenated

hemoglobin (HbO2), deoxygenated hemoglobin (Hb), water (H2O) and lipid. The extinction coeffi-

cients, εHb, εHbO2, εH2O, εlipid only depend on wavelength λ and has the dimension of [cm−1/µM].

The extinction coefficients are well documented in literature and can be found in the Appendix Sec-

tion 3.8.1 at the end of Chapter 3. The concentrations of these chromophores CHb, CHbO2, CH2O,

Clipid are given in [µM]. The scattering constraint comes from the observation that scattering in

tissue follows a simplified Mie-scattering approximation [185, 188] reasonably well, i.e.

µ′s(λ, r) = A(r)λ−b(r), (2.5)

where A(r) is called the scattering prefactor and b(r) is called the scattering power (and is related

to the particle size and density, index of refraction of scatterers and the medium). In conventional

schemes (which we will denote as the single-spectral method), absorption (µa(r)) and scattering

coefficients (µ′s(r)) at each wavelength are first determined, and then the resulting absorption co-

efficients are used to extract chromophore concentrations using Equation 2.4. In the multi-spectral

method (or the a priori spectral approach), the chromophore concentrations and scattering proper-

ties are reconstructed directly in a single step using data at all wavelengths with spectral constraints

(Equation 2.4 and 2.5). Since the chromophore concentrations and the scattering amplitudes and

prefactors are treated as unknowns instead of the optical coefficients at each wavelength, the num-

ber of unknowns is reduced significantly. The amount of computer memory increases with multi-

spectral method. However, it depends on the reconstruction scheme; the Jacobian based approach

requires a significant memory, whereas the nonlinear conjugate gradient based approach does not

21

require significant memory. Moreover, Durduran [80] has shown that multi-spectral approach re-

duces the detrimental effects of interparameter crosstalk and misestimation of sample geometry.

After the reconstruction of chromophore concentrations, useful physiological parameters may

be derived, i.e. the total hemoglobin concentration THC = CHb + CHbO2and the tissue blood

oxygen saturation StO2 = CHbO2/THC.

In the following section, DOS and DOT are further developed for each of the clinical applica-

tions to be presented. First, a general analysis scheme common to the DOS and DOT is presented

in a flow chart style in Section 2.2. Following the general format, individual DOS algorithms for

various measurement configurations are presented. Then two different reconstruction schemes de-

veloped for DOT breast cancer imaging in the framework of single-spectral and in multi-spectral

approaches are also illustrated.

2.2 General Analysis Flow Chart

The goal of diffuse optical tomography (DOT) is to accurately estimate the distribution of opti-

cal properties in a tissue volume from non-invasive optical measurements on the surface of the

medium. Various algorithms can be utilized to estimate optical properties. These algorithms dif-

fer depending on the choice of photon propagation model, measurement type and geometry, and

optimization scheme. A generalized outline of model-based optical property reconstruction is de-

scribed in the flow chart (Figure 2.2).

Here x is a vector of unknown properties. Depending on whether the algorithm is based on

the single-spectral method or the multi-spectral method, x can be the optical properties (µa and

µ′s) or the chromophore concentrations and scattering factors (Cl, A, and b), respectively. The ini-

tialization process consists of reading in the measurement data, defining the reconstruction space,

22

Begin

Initialization

Solve forward problem

Calculate χ2

Criteria? End

Solve inverse problem

Update x +∆x→ x

No

Yes

Figure 2.2: General analysis flow chart for model-based optical properties reconstruction.

and assigning initial guess for x(r). r denotes position within the sample volume. The forward

problem computes the fluence rate, Φ(r), on the sample surface given light source information

and optical property distribution x(r). χ2 quantifies the discrepancy between the calculated and

measured fluence rate; its value determines whether to update x(r) and iterate again or stop the

calculation. If the stopping criteria is not met, the inverse problem estimates ∆x for the next it-

eration. After updating x, the process is iterated until the stopping criteria for χ2 is met. In the

following sections, each step is described in detail.

2.2.1 Initialization

At this first stage, measurement data are read in. Each piece of measurement data is associated with

source position vectors, rs (s = 1, . . . Ns) and a detector position vector rd (d = 1, . . . Nd(s)).

23

Nd(s) is the number of detectors associated with the sth source which may be different per source,

since the measurement data is selected to be above the noise level. Usually these vectors are located

on the surface of the medium. The measured fluence rate of the sample, Φm(rs, rd), and that of

reference measurement, ΦRm(rs, rd), are recorded.

The three-dimensional medium is discretized with nodes or volume elements centered on, rk

(k = 1, . . . Nv). For the initialization purpose, an initial µ-map (in particular, µa(rk) and µ′s(rk))

of the sample and reference needs to be assigned. Then calculation of sample fluence rate Φc(rk)

and reference fluence rate ΦRc (rk) is possible.

2.2.2 Forward Problem

The solutions (Φc(rk) and ΦRc (rk)) for the forward problem in the diffusion regime are generally

subdivided into analytic solutions and numerical solutions. The analytic solutions are available

for simple geometries such as infinite, semi-infinite, slab, cylinder, and embedded spheres in those

geometries [6, 203, 217]. The numerical solutions are available via the finite difference method

(FDM) or the finite element method (FEM). Numerical approaches are critical for complicated

geometries and heterogeneous distributions of optical properties.

2.2.3 Calculation of χ2

χ2 describes the discrepancy between measured and calculated fluence rates. The specific form of

χ2 may differ depending on whether the reconstruction scheme is based on differential or absolute

reconstruction, and on whether the reconstruction uses Born or Rytov type [196] approaches. (For

brief account of Born and Rytov approximations, refer to Section 2.4.1).

24

2.2.4 Inverse problem

The inverse problem can be thought as the minimization of χ2 problem with respect to unknown

x. The solution for the DOT inverse problem can vary depending on the methods employed:

backprojection method [53, 271], analytic method [46, 167, 180, 240], linear method [196, 198]

and nonlinear method [13] (See Reference [7, 8, 107] for reviews). In the following sections, two

different types of nonlinear DOT methods which have been developed in our laboratory, will be

outlined.

2.3 Spectroscopy

In our laboratory, frequency-domain, multi-spectral diffuse optical spectroscopy is widely used for

the quantification of bulk optical properties of the medium. At the initialization step, the mea-

sured fluence rate Φm(λ, r) is recorded and the initial guess for the unknowns assigned. For the

frequency-domain measurement, the measurable quantities at each wavelength and detector posi-

tion are the amplitude (Am) and the phase shift (θm) with respect to the input source. The measured

fluence rate is written as

Φm(rs, rd) = ξseiθs · ξdeiθd ·Am(rs, rd)eiθm(rs,rd), (2.6)

where ξs and θs are the amplitude and phase of the source coupling and ξd and θd are the amplitude

and phase of the detector coupling. In the multi-spectral method, the unknowns are chromophore

concentrations and the scattering factors. For instance, when the optical properties of the homo-

geneous liquid phantom made with India ink and Intralipid (as described in Chapter 3, Section

3.8.1) are to be recovered, the unknowns are Cink, A and b. When the bulk optical properties of

25

physiological tissue (with the assumption of homogeneous medium) is under investigation, the un-

knowns are CHb, CHbO2, CH2O, Clipid, A and b. Since the calculated fluence rate Φc(λ, r) is often

described in terms of µa and µ′s, one needs to decompose the initial guess using Equation 2.4 to

solve the forward problem. (See Appendix Section 3.8.1 for extinction coefficients.)

positive source

extrapolatedboundary

negative image

source fiberdetector fiber

z=0z0

zb

zbz0+

z

n in

outn

z=-zp

z=-zb

Figure 2.3: Source and image configurations for extrapolated boundary condition.

The analytic solutions of the forward problem for semi-infinite and slab geometry with extrap-

olated boundary conditions are widely used in most DOS analyses. For the extrapolated boundary

condition [5, 76, 94, 121], the fluence rate is set to zero at an extrpolated boundary located at a

distance zb outside the medium i.e. Φ(ρ, z = −zb) = 0. The method of images depicted in Figure

2.3 can be used to construct the solution by placing a negative image source at the opposite side

of the extrapolated boundary. In this extrapolated boundary case, the position of negative image

source is at −zp = −(z0 + zb) since the source is placed at z0 (1/µ′s inside the medium). The

configuration of source and image for the semi-infinite and slab geometry is depicted in Figure 2.4.

The analytic frequency-domain solution for the semi-infinite geometry (Figure 2.4(a)) with

26

z=0

z=dz=2dz=3d

z=4d

z=-2dz=-d

z=-3d

z=-zz=0z=z 0

p

z

(a) (b)positive imagenegative image

sourcesource

Figure 2.4: Source and image configurations for measurement Geometry of (a) Semi-infinitemedium and (b) Slab.

extrapolated boundary conditions is [217, 218]

Φ(ρ, z) =vS

4πD

(

exp(ik√

ρ2 + (z − z0)2√

ρ2 + (z − z0)2− exp(ik

√

ρ2 + (z + zp)2√

ρ2 + (z + zp)2

)

, (2.7)

where k2 = −vµa+iωD , z0 = 1

µ′s, zp = z0 + 2zb, zb = 2

3µ′s

1+Reff1−Reff

, Reff = −1.44/n2 + 0.71/n +

0.668 + 0.064n. z is the axis perpendicular to the medium, and ρ is the radial distance parallel

to the medium, as can be seen in Figure 2.3 and Figure 2.4(a). The filled circle represents the

light source displaced 1µ′s

inside the medium [203] and the open circle is the imaginary negative

source displaced an equal distance (zb) away from the extrapolated boundary where the fluence

rate becomes zero. This solution is used in Chapter 3, Section 3.7 for bulk optical properties

assessment of tissue phantom, in Chapter 4, Section 4.3 in calculating bulk optical properties of

healthy breasts, and in Chapter 5, Section 5.3 for preliminary assessment of clinical data.

The analytic frequency-domain solution for the slab geometry (Figure 2.4(b)) with extrapolated

27

boundary conditions is [55, 217]

Φ(ρ, z) =vS

4πD

(

m=∞∑

m=−∞

exp(ik√

ρ2 + (z − z+,m)2√

ρ2 + (z − z+,m)2−

m=∞∑

m=−∞

exp(ik√

ρ2 + (z − z−,m)2√

ρ2 + (z − z−,m)2

)

,

(2.8)

where z+,m = 2m(d+2zb)+ z0, z−,m = 2m(d+2zb)− 2zb− z0 for m = 0,±1,±2, ..., and d is

the slab thickness. The slab solution is constructed with a series of imaginary sources arising from

two air-tissue boundaries (Figure 2.4(b)). In practice, we use up to 5th term for m. The remaining

terms are usually quite small. This solution is used for analysis in Chapter 4, Section 4.3.

The presence of source detector coupling coefficients in the multiple source detector configu-

ration requires attention: differential and absolute approaches will be described in the following

sections. These approaches have distinct forms of χ2. Once χ2 is defined, various optimiza-

tion functions can be used to find the combination of unknowns which minimize χ2. Usually the

Nelder-Mead simplex method [189, 224] is utilized for our spectroscopy approaches.

2.3.1 Differential approach

When perturbative physiological measurements (Chapter 5, Section 5.2) are possible, the source

coupling coefficient problem becomes considerably simpler. Since the probe is fixed in the same

position under the same condition throughout the perturbation, the source detector coupling coef-

ficients are normalized out.

Typically we use χ2 of the form

χ2 =

Nλ∑

w=1

Ns∑

s=1

Nd∑

d=1

∣

∣

∣

∣

Φm(λw, rs, rd)

ΦRm(λw, rs, rd))− Φc(λw, rs, rd))

ΦRc (λw, rs, rd))

∣

∣

∣

∣

2

, (2.9)

where Nλ, Ns, and Nd are the number of wavelengths, sources and detectors respectively.

28

2.3.2 Absolute approach

Where there is no reference measurement, one needs to explicitly consider the effect of source

and detector coupling coefficients. In particular, the retrieval of optical properties of the matching

fluid of the 2nd generation parallel-plate DOT instrument (described in Chapter 3, Section 3.6.2)

relies on the absolute approach. Raw data of amplitude and phase shift is shown with respect to

the source and detector separations in Figure 2.5. The presence of source and detector coupling

coefficients leads to significant deviation of data points from the expected amplitude and phase

(normalized respctively to the measured values) for a homogeneous medium. This deviation does

not arise for the one source and one scanning detector configuration (Chapter 3, Section 3.6.1).

1 2 3 4 5 6−6

−5

−4

−3

−2

−1

0

ρ (cm)

log

(r2 *A

mp

litu

de)

(a)

1 2 3 4 5 6−0.5

0

0.5

1

1.5

2

ρ (cm)

Ph

ase

(rad

)

(b)

Figure 2.5: Effect of coupling coefficients on measured amplitude and phase of homogeneousmedium. (a) Amplitude and (b) Phase plotted versus source detector separations. Amplitude andphase are measured on a homogeneous matching medium using frequeny-domain, multiple sourcedetector instrument (Chapter 3, Section 3.6.2). Significant deviation from semi-infinite solution(solid line) shows the effect of the coupling coefficients on data.

An implicit way to estimate the source and detector coupling coefficients while fitting for the

chromophore concentration and scattering factors was developed. In this method, we defined χ2

29

to be normalized with the measured fluence rate,

χ2 =

Nλ∑

w=1

Ns∑

s=1

Nd∑

d=1

∣

∣

∣

∣

Φm − ΦcΦm

∣

∣

∣

∣

2

. (2.10)

We use Nelder-Mead simplex method to update the unknowns. At each iteration, when Cl, A

and b are updated, they are decomposed into µa(λ) and µ′s(λ) by Equation 2.4. For these µa(λ)

and µ′s(λ), coupling coefficients are estimated in the following two-step process. First, detector

coupling coefficients are estimated by summing over all the sources.

ξd(µa, µ′s) =

1

Ns

Ns∑

s=1

Ac(µa, µ′s)

Am(2.11)

θd(µa, µ′s) =

1

Ns

Ns∑

s=1

θc(µa, µ′s)− θm, (2.12)

where the calculated amplitude is Ac = |Φc| and the calculated phase is θc = arg(Φc). Then,

source coupling coefficients are estimated by summing the ratio of adjusted fluence rate over all

the detectors.

ξs(µa, µ′s) =

1

Nd

Nd∑

d=1

Ac(µa, µ′s)

ξd ·Am(2.13)

θs(µa, µ′s) =

1

Nd

Nd∑

d=1

θc(µa, µ′s)− θm − θd. (2.14)

These source detector coupling coefficients depend on µa(λ) and µ′s(λ) through Φc, which depends

on the updated unknowns at each iteration. The iteration continues until χ2 reaches the stopping

criterion.

30

2.4 Imaging

Two different imaging software packages were developed and employed in our laboratory for

breast cancer imaging. The first software, which will be referred to as “Nonlinear Rytov Itera-

tive Method (NRIM)”, was developed by Dr. Monica Holboke [128, 129]. NRIM has mainly been

used for analyzing the tissue phantom measurements to characterize DOT instrumentations [62].

For clinical data analysis, use of NRIM turned out to be challenging mainly because of its exces-

sive computational memory requirements; NRIM computes the Jacobian (weight matrix) explic-

itly. Another approach, TOAST (Time-resolved Optical Absorption and Scattering Tomography)

developed originally by Arridge et al [13] is based on the nonlinear conjugate gradient method;

it has significant memory overhead reduction compared to NRIM. Therefore a collaboration with

Dr. Simon Arridge’s group was initiated. The CW version of TOAST was adapted to our imag-

ing geometry and further developed at UPENN to include the multi-spectral approach [57, 58].

Furthermore, envelope-guided spatially variant regularization [56] and source-detector coupling

coefficient [162] fitting were incorporated.

In the following section, the details of NRIM, the single-spectral TOAST (original version),

and the multi-spectral TOAST (MTOAST) are described. Explicit forms of equations are presented

to bring out clear distinction among the algorithms.

2.4.1 Nonlinear Rytov Iterative Method

NRIM [128, 129] was first developed using a single-spectral approach. The unknown variables to

fit are the absorption coefficient µa and the reduced scattering coefficient µ′s. Furthermore, this

code was customized for breast imaging wherein we take reference measurement of matching fluid

(Intralipid/India ink). It is also suitable for differential measurement before and after contrast agent

31

injection. The following flow chart (Figure 2.6) shows more of the details for the inverse problem

(which can be compared with that of TOAST in the following section).

Begin

Initialization

Calculate Φ(x)

Calculate χ2

criteria? End

Calculate G(rd, rk)

Set up Jacobian J

Solve J∆x = y

Update x +∆x→ x

No

Yes

Figure 2.6: Nonlinear Rytov Iterative Method (NRIM) analysis flow chart

In the initialization step, the 3D space is discretized into an nx × ny × nz Cartesian grid (with

position vector given as rk). There is an option to read in an initial guess for µa(rk) and D(rk) as

well as reference properties.

Using a finite difference method [160], Equation 2.3 in combination with the partial current

boundary condition (Equation 2.2) becomes a matrix equation. For given µa(rk) and D(rk),

Φ(rk) is calculated using the preconditioned conjugate gradient method (linear conjugate gradient

method, to be described later in this section). This forward problem is solved for each source.

32

Using the reference µ-map, the reference calculated fluence rate ΦRc is determined. For the

0th iteration, Φ is calculated using the initial guess µ-map. For the following tth iterations, Φc is

calculated using the updated µ-map.

The perturbation due to the heterogeneous variation of optical properties from the background

is approximated by a Born or Rytov expansion [147,196]. In the Born approximation, Φ(r, rs) is a

linear superposition of the incident (background, Φ0) and scattered (heterogeneous, Φsc) diffusive

waves : Φ(r, rs) = Φ0(r, rs) + Φsc(r, rs). In the Rytov approximation, the contributions from

the incident and scattered parts are expressed in exponential fashion : Φ(r, rs) = exp[φ0(r, rs) +

φsc(r, rs)]. This leads to the derivation of Equation 2.16, which provides the update scheme for

optical properties deviation.

χ2 is defined in the Rytov fashion.

χ2 =1

2

Ns∑

s=1

Nd∑

d=1

[

ln

(

Φm(rs, rd)

ΦRm(rs, rd)

ΦRc (rs, rd)

Φc(rs, rd)

)]2

(2.15)

Here, Φm is the measured fluence rate and Φc is the calculated fluence rate based on the forward

problem. ΦRm and ΦRc are the measured and calculated fluence for reference measurements.

The stopping criteria is defined as|χ2t−χ

2

t−1|

χ2

t−1

< STOP CRITERION, where χ2t denotes χ2 at

tth iteration and STOP CRITERION a user-defined value (e.g. 1.0× 10−3).

Using the diffusion equation, Green’s theorem and Rytov expansion [6, 11, 198, 241, 289], one

can show

∫

∇G(rd, r) · ∇Φc(r, rs)∆D(r)d3r +∫

G(rd, r)Φc(r, rs)∆µa(r)d3r

Φc(rs, rd)

= −ln(

Φm(rs, rd)

ΦRm(rs, rd)

ΦRc (rs, rd)

Φc(rs, rd)

)

(2.16)

33

where the Green’s function is the solution to

∇ · (D(r)∇G(r))−(

µa(r)−iω

v

)

G(r) = −δ(rd, r), (2.17)

for the sample medium, where ∆µa(r) = µa(r) − µ0a(r) and ∆D(r) = D(r) − D0(r) with

background µ0a and D0.

The discretization of the integrals for dth detector and sth source leads to the following;

G(rd, r1)Φ(r1, rs)∆µa(r1)

Φ(rs, rd)+G(rd, r2)Φ(r2, rs)∆µa(r2)

Φ(rs, rd)+ · · ·+

∇G(rd, r)|r=r1· ∇Φ(r, rs)|r=r1

∆D(r1)

Φ(rs, rd)+∇G(rd, r)|r=r2

· ∇Φ(r, rs)|r=r2∆D(r2)

Φ(rs, rd)

+ · · · = −ln(

Φm(rs, rd)

ΦRm(rs, rd)

ΦRc (rs, rd)

Φc(rs, rd)

)

. (2.18)

Since there is one such equation for each source and detector pair, a matrix equation for allNsd

(total number of source and detector pairs, i.e. Nsd =∑Ns

s=1Nd(s)) is

GΦ|r1Φ

GΦ|r2Φ · · · ∇G·∇Φ|r1

Φ∇G·∇Φ|r2

Φ · · ·...

......

...

∆µa(r1)

∆µa(r2)

...

∆D(r1)

...

∆D(rN )

=

−ln(

ΦmΦRm

ΦRcΦc

)

s=1,d=1

−ln(

ΦmΦRm

ΦRcΦc

)

s=1,d=2

...

−ln(

ΦmΦRm

ΦRcΦc

)

s=Ns,d=Nd

(2.19)

If one simplifies the notation,

Jx = y (2.20)

34

As can be seen from Equation 2.19, explicitly built-up of Jacobian J is of size 2×Nsd×Nv. This

requires significant computer memory [57].

One needs to “invert J” and solve for x =

[

∆µa ∆D

]T

. One can also add regularization

such as

(JTJ + γCTC)x = JTy. (2.21)

γ is the regularization parameter and C is the regularization operator.

XY

Zz

xy

Light source plane at y=0

Detection plane at y = Y

cx cy zc( )

Figure 2.7: Reconstruction geometry for breast imaging (Chapter 3, Section 3.6.2).

For our breast cancer imaging case (Chapter 4), we used a spatially variant regularization

[62, 216] of the form

γ(rk) = lc + le

[

exp

(

(

2(yk − yc)Y

)2)

+ exp

(

(

xk − xcX

)2

+

(

zk − zcZ

)2)

− 2

]

(2.22)

where xc, yc, zc are center coordinate of reconstruction dimension of X,Y, Z (as shown in Figure

2.7) and setting C = I. lc and le are the regularization parameters corresponding to the center and

edge of the image respectively. Note that y is the axis perpendicular to the source and detection

35

planes.

We solve the matrix equation 2.21 using the linear conjugate gradient method. The linear

conjugate gradient method (CGM) is an iterative method to solve linear systems with positive

definite coefficient matrices [189]. Let W = JTJ+ γCTC and v = JTy to simplfy the Equation

2.21 to Wx = v. The linear CGM algorithm is given as follows [189].

Given x0;

Set r0 ←Wx0 − v, p0 ← −r0, t← 0;

while rt 6= 0

αt ←rTt rt

pTt Wpt

xt+1 ← xt + αtpt

rt+1 ← rt + αtWpt

βt+1 ←rTt+1rt+1

rTt rt

pt+1 ← −rt+1 + βt+1pt

t← t+ 1

end

where r is a residual defined as r(x) ≡Wx− v, and p is a conjugate search direction.

This problem of minimizing the residual is equivalent to minimizing Ψ(x) = 12x

TWx−vTx,

where ∇Ψ = r(x). αt is one-dimensional minimizer of the quadratic function Ψ along xt + αtpt

for updating xt. βt is the scalar for determining next conjugate direction given by conjugacy

36

property, based on residuals.

2.4.2 TOAST : single-spectral TOAST

TOAST (Time-resolved Optical Absorption and Scattering Tomography) is a DOT software pack-

age developed by Arridge et al [13]. The CW version of TOAST is employed for our breast cancer

DOT application. The flow chart below (Figure 2.8) depicts the outline of the algorithm with

emphasis on the details of inversion.

Begin

Initialization

Calculate Φ(x)

Calculate χ2

criteria? End

Calculate η(rs, rk)

Calculate ∂χ2

∂x

Solve for ∆x using CGM

Update x +∆x→ x

No

Yes

Figure 2.8: TOAST analysis flow chart

The initialization step is similar to the previously described Nonlinear Rytov Iterative Method.

An extra feature in the initialization of TOAST is the ability to assign a heterogeneous distribution

37

for the refractive index for rk. The forward problem is solved using the finite element method [11].

The χ2 is defined as in Equation 2.15. The stopping criteria is defined as|χ2t−χ

2

t−1|

(χ2t+χ

2

t−1)/2+ε

≤

STOP CRITERION, where ε is 1 × 10−10 and STOP CRITERION is a user-defined value (typ-

ically 1 × 10−5). Instead of forming an explicit Jacobian, TOAST solves for

[

∆µa ∆D

]T

by

using the gradient of χ2 as the search direction in nonlinear conjugate gradient method.

Nonlinear conjugate gradient method is used for large-scale nonlinear optimization problem

[189]. The Polak-Ribiere nonlinear CGM to solve a general nonlinear function f(x) is as follows.

Given x0

Evaluate f0 = f(x0), ∇f0 = ∇f(x0)

Set p0 = −∇f0, t← 0

while ∇ft 6= 0

Find αt that minimizesf(xt + αtpt)

Set xt+1 ← xt + αtpt

Evaluate ∇ft+1

βPRt+1 ←∇fTt+1(∇ft+1 −∇fk)

||∇fk| |2

pt+1 ← −∇ft+1 + βPRt+1pt

t← t+ 1

end

Particularly in our case, f(x) = χ2(x). The gradients of χ2 (∇f(x)) with respect to the

38

unknowns µa and D needed in nonlinear CGM are given by

∂χ2

∂µa

∣

∣

∣

∣

rk

=

Ns∑

s=1

Nd∑

d=1

ln

(

Φm(rs, rd)

ΦRm(rs, rd)

ΦRc (rs, rd)

Φc(rs, rd)

)

1

Φc(rs, rd)G(rd, rk)Φc(rk, rs) (2.23)

∂χ2

∂D

∣

∣

∣

∣

rk

=

Ns∑

s=1

Nd∑

d=1

ln

(

Φm(rs, rd)

ΦRm(rs, rd)

ΦRc (rs, rd)

Φc(rs, rd)

)

1

Φc(rs, rd)∇G(rd, rk) · ∇Φc(rk, rs) (2.24)

The gradients depend on Φm, ΦRm, Φc, ΦRc at source rs and detector positions rd. They also

depend on the Green’s function G evaluated at each voxel rk for dth detector and Φc evaluated at

each voxel for sth source. In order to calculate the gradients, one needs to solve the Equation 2.3

for Ns times and Equation 2.17 for Nd times. Note that the use of gradients instead of explicit

Jacobian results in significant reduction of computer memory compared to the Jacobian case.

However, a change of variables can reduce the number of calculation and speed up the recon-

struction. One can modify the Equation 2.17 by multiplying∑Nd

d=1 ln(

Φm(rs,rd)ΦRm(rs,rd)

ΦRc (rs,rd)Φc(rs,rd)

)

1Φc(rs,rd)

on each side of equation.

Nd∑

d=1

ln

(

Φm(rs, rd)

ΦRm(rs, rd)

ΦRc (rs, rd)

Φc(rs, rd)

)

1

Φc(rs, rd)

[

∇ · (D(rk)∇G(rk, rd))−(

µa(rk)−iω

v

)

G(rk, rd)

]

= −Nd∑

d=1

ln

(

Φm(rs, rd)

ΦRm(rs, rd)

ΦRc (rs, rd)

Φc(rs, rd)

)

1

Φc(rs, rd)δ(rk, rd) (2.25)

39

If one define the following variables which sums over all detectors per source,

η(rs, rk) =

Nd∑

d=1

ln

(

Φm(rs, rd)

ΦRm(rs, rd)

ΦRc (rs, rd)

Φc(rs, rd)

)

1

Φc(rs, rd)G(rk, rd) (2.26)

ν(rs, rk) =

Nd∑

d=1

ln

(

Φm(rs, rd)

ΦRm(rs, rd)

ΦRc (rs, rd)

Φc(rs, rd)

)

1

Φc(rs, rd)δ(rk, rd) (2.27)

then the Equation 2.25 transforms into the following equation,

∇ · (D(rk)∇η(rs, rk))−(

µa(rk)−iω

v

)

η(rs, rk) = −ν(rs, rk) (2.28)

The gradients are then expressed in terms of new variable η(rs, rk) which depends on rs.

∂χ2

∂µa

∣

∣

∣

∣

rk

=

Ns∑

s=1

η(rs, rk)Φ(rs, rk) (2.29)

∂χ2

∂D

∣

∣

∣

∣

rk

=

Ns∑

s=1

∇η(rs, rk) · ∇Φ(rs, rk) (2.30)

One only needs to solve Equation 2.28 Ns times in order to calculate gradients as opposed to

solving Green’s equation for all detectors per source.

In summary, nonlinear CGM updates ∆x (x = µa, µ′s) for our application as follows. For

given initial values for x, χ2 (Equation 2.15) and the gradients of χ2 are evaluated (Equation 2.30).

The initial search direction is given by the ∇χ2(x0). Once the initial steps were taken (including

the calculation of gradients), the factor α which minimizes χ2 along the direction x+ αp is found

by inexact line search one-dimensionally. Then unknowns x are updated by the search direction p

scaled by α. For the calculation of the next search direction, ∇χ2 is evaluated to compute scaling

factor β for the current search direction.

40

2.4.3 MTOAST : multi-spectral TOAST

Several new techniques have been implemented into TOAST by us: (1) multi-spectral method, (2)

envelope-guided spatially variant regularization, (3) source detector coupling fit, and (4) geometric

constraint for image segmentation.

In diffuse optical community, quantitative imaging using continuous-wave (CW) method has

been controversial because of nonuniqueness of CW solution to the photon diffuse equation [9].

Since there is no unique solution, crosstalk between absorption and scattering is quite significant,

which in turn affects the accuracy of derived physiological parameters. Yet the CW approach offers

several advantages over frequency-domain or time-domain approaches: good signal to noise, sim-

plicity of technology, low cost per detection channel, and (most importantly for us) being readily

adaptable for lens-coupled CCD data acquisition to yield high spatial information for reliable 3D

reconstruction. Some research groups have devised a scaling approach [208, 287] to circumvent

this problem, which depends on their instrument and reconstruction geometry.

Corlu et al has shown that a multi-spectral approach helps to overcome the nonuniqueness

problem in CW imaging [58]. His implementation of this multi-spectral approach to nonlinear

Conjugate Gradient inverse algorithm (TOAST) is well-documented in the reference [57] with the

methodology to find optimal CW wavelengths.

The distinct differences between single-spectral and multi-spectral TOAST are (1) Definition

of unknown, (2) χ2 form, and (3) gradients of χ2 with respect to unknowns. The unknowns are

typically chromophore concentration Cl, A, and b (l = 1, . . . L).

The multi-spectral χ2 is different from single-spectral χ2 in that there is an additional summa-

tion over the wavelength, and the spectral constraint governs the optical properties µa(λ, r) and

µ′s(λ, r) which changes Φ(λw, rs, rd). The multi-spectral χ2 is further modified to include the

41

envelope-guided spatial variant regularization term [56],

χ2 =1

2

Nλ∑

w=1

Ns∑

s=1

Nd∑

d=1

(

ln

(

Φm(λw, rs, rd)

ΦRm(λw, rs, rd)

ΦRc (λw, rs, rd)

Φc(λw, rs, rd)

))2

+Q (2.31)

where Q =∑N

k=1 γ(rk)||µ(rk) − µ0(rk)||2, γ(rk) is given by Equation 2.22 and µ stands for

solution vector (either µa, D or both).

The gradient of χ2 is then calculated with respect to multi-spectral unknowns Cl, A and b.

∂χ2

∂Cl

∣

∣

∣

∣

rk

=∂χ2

∂µa

∂µa∂Cl

= εl(λ)∂χ2

∂µa

∣

∣

∣

∣

rk

(2.32)

∂χ2

∂A

∣

∣

∣

∣

rk

=∂χ2

∂µ′s

∂µ′s∂A

= λ−b(rk)∂χ2

∂µ′s

∣

∣

∣

∣

rk

(2.33)

∂χ2

∂b

∣

∣

∣

∣

rk

=∂χ2

∂µ′s

∂µ′s∂b

= −A(rk)λ−b(rk)ln(λ)∂χ2

∂µ′s

∣

∣

∣

∣

rk

(2.34)

where ∂χ2

∂µais given by Equation 2.23 and ∂χ2

∂µ′sby

∂χ2

∂µ′s

∣

∣

∣

∣

rk

= 3D2Ns∑

s=1

Nd∑

d=1

ln

(

Φm(rs, rd)

ΦRm(rs, rd)

ΦRc (rs, rd)

Φc(rs, rd)

)

1

Φc(rs, rd)∇G(rd, rk) · ∇Φc(rk, rs).

(2.35)

For breast imaging, a geometric constraint is utilized to give a good initial guess for the re-

construction. This additional technique only involves the changes in the input field to MTOAST,

and not the internal algorithmic changes. The gist of the geometric constraint is to fix the optical

properties of matching fluid based on the frequency-domain measurements and not to allow the

matching fluid region to update its optical properties. Only the breast region is allowed to update

its multi-spectral unknowns such as CHb, CHbO2, CH2O, and A. The specific methodology used

for our breast imaging application is described in Chapter 4, Section 4.4.2 in detail.

42

Chapter 3

Experimental Techniques

3.1 Introduction

In this chapter, experimental techniques are outlined. The choice of light sources, detectors and

electronic components depends on the physiological application. First the light sources and detec-

tors used in the DOS/DOT field are introduced. Then, the frequency-domain homodyne system

which is used in all experimental applications in this thesis is described. Specification of the

CCD-based instrument is described in the separate section. In the next section, the methods to

test electronical components and to characterize the whole system for dynamic range are outlined.

Then the specific instrumentation used for each application is described in detail. For breast cancer

imaging, there were two parallel plate instruments: Frequency-domain scanning system and CCD-

based hybrid system. For fetal oximetry, a multi-wavelength, multi-optode frequency-encoded

DOS instrument was developed. Validation and characterization of the system as a whole was

carried out using tissue phantoms.

43

3.2 Components

3.2.1 Light sources

Three types of light sources are used for DOS and DOT applications : white light, light emitting

diodes (LED), and laser diodes.

White light sources have gained more attention recently, because the importance of multiple

wavelength schemes has been recognized [19, 273]. The spectrum of most white light sources

extends over the visible range and into the near-infrared. Tungsten incandescent lamps radiate light

by heating tungsten filaments. Halogen lamps are essentially efficient high performance tungsten

lamps, with iodine or bromine in the fill gas to return evaporated tungsten to the filament. Arc

discharge lamps operate by ionizing xenon or mercury gas with a short high-voltage pulse and then

allowing the capacitor to discharge through the now-conductive gas. Typically white light sources

are utilized with a monochromator or a series of spectral filters.

In light emitting diodes, free electrons moving across a diode junction combine with holes

from the P layer. In this process, photons are generated. The photon energy is set by the energy

drop between the conduction band and the valence band.

In laser diodes (or diode lasers), a population inversion is induced in the P-N junction region.

Stimulated emission results from this population inversion and a net light amplification and lasing

is achieved by an optical cavity formed with the reflective coatings at opposite ends of the crystal.

Laser diodes are used widely for DOT applications. They are highly monochromatic and respond

rapidly to variations in the driving current.

44

3.2.2 Detectors

In the following sections, various detectors commonly used in our field are described with the focus

on the characteristics of signal and noise.

3.2.2.1 Photodiode

P

I

N

DepletionRegion

-+

+ -

+ -

(a)

P

N

DepletionRegion

+ -

+

+

-

-

(b)

Figure 3.1: Photodiode structure of (a) PIN diode and (b) Avalanche Photodiode. Reproduced fromreference [111]

The photodiode is a robust and inexpensive detector for relatively high light levels. Light with

energy greater than band-gap energy hits the photodiode, excites electrons into the conduction

band, and creates a hole in the valence band. An electric field in the depletion layer drives electrons

to the N layer and holes to the P layer. The external circuit collects this photocurrent. This process

is illustrated in Figure 3.1(a) for PIN photodiode. PIN photodiode includes an intrinsic region

between the P and N layers, which results in the expansion of depletion region and thus broader

spectral response. PIN photodiode does not have internal gain mechanism. The need of external

45

amplifier introduces substantial noise. The current is propotional to incident power in normal

operating range.

3.2.2.2 Avalanche Photodiode (APD)

The avalanche photodiode is a high-speed, high-sensitive photodiode with an internal gain mecha-

nism through a reverse-bias voltage. The electron-hole pairs are generated from exposure to light

with higher photon energy than band gap energy. A reverse voltage applied to the PN junction of

the APD causes the electrons to drift towards N layer and holes towards P layer. An avalanche

effect occurs when the electron-hole pairs acquire sufficient energy to create additional pairs by

colliding with the crystal lattice as shown in Figure 3.1(b). The gain of APD could reach up to

100 [111].

3.2.2.3 Photomultiplier Tube (PMT)

Photomultiplier tube (PMT) is a sensitive detector which amplifies the input light signal 105− 106

times with almost no additional noise. It is usually selected for high speed or low light level

detection. It is suitable for single photon counting applications when the rate photons strike the

photocathode is below 100 MHz.

Figure 3.2 illustrates how the PMT converts light into a detectable electric signal. The PMT

first converts the photon which strikes a photocathode into a photoelectron by the photoelectric ef-

fect. Amplification is performed through a dynode chain, which consists of 8 to 12 metal plates. A

potential of around 100 volts applied between the photocathode and the first dynode accelerates the

photoelectron into the dynode. Upon striking the dynode, 5 - 6 secondary electrons are produced.

These electrons are accelerated into the next dynode by a potential difference and get multiplied

46

faceplate

PhotocathodeDynodes

Anode last dynode

vacuum

stem

stem pin

focusing electrode

LIGHT

secondary electron

Figure 3.2: Schematic of typical photomultiplier with some electron trajectories (in red). Repro-duced from Hamamatsu manual [120].

by 5 - 6 times each. These cascading effect produces 105 − 106 electrons at the anode.

3.2.2.4 Charge Coupled Device (CCD)

The charged coupled device (CCD) is a solid state sensor with a wafer of silicon crystal. When

the silicon is exposed to light, the photoelectric effect generates electrons from the silicon bonds.

These free electrons are collected by CCD electrodes (as shown in Figure 3.3(a)) at the interface

created by positive surface potential to form an extremely thin but very dense inversion layer. The

amount of charge deposited in the inversion layer is often described by the hypothetical concept

of the potential well. In Figure 3.3(b), the charge transfer mechanism is illustrated using a three-

phase CCD structure as an example [20]. In a three-phase CCD, three sets of electrode strips make

one pixel where the charge accumulates on the electrode biased more positively than the other

two. The charge is transferred by making the adjacent electrode potential raised while the first

lowered. Figure 3.4 shows the CCD chip structure [169] consisted of parallel and serial electrodes

and amplifier on a silicon chip. The channel stops restrain electrons from moving along the length

of electrode, thus defining the extent of the pixel. The charges in potential wells columns are

47

shifted in parallel onto a serial register. Then the charges in the serial register gets shifted out

onto the output node. At this stage, on-chip hardware binning can be incorporated to increase the

signal-to-noise ratio. The charges are then amplified by an on-chip amplifier and digitized.

inversion layer

depletion layer

p-type semiconductor

oxide

electrode

(a)

0 V +V 0 V0 V

+V 0 V0 V

+V 0 V0 V

+V

0 V

potential wellcontaining charge

(b)

Figure 3.3: (a) Single CCD electrode, (b) Charge transfer mechanism of CCD electrodes (three-phase CCD system). Reproduced from reference [20].

3.2.2.5 Image intensifier

An image intensifier is a vacuum tube device consisting of a photocathode input, microchannel

plate, and the phosphor screen. The electrons due to photoelectric effect are accelerated and multi-

pled through microchannel plate (MCP) via mechanism analogous to photomultiplier, to the phos-

phore screen where the light is released upon striking the coating. The image intensifier can be

combined with CCD to detect in ultra-low-light conditions and resolve extremely short temporal

phenomena by biasing the photocathode with respect to the MCP.

48

1 2 3 1 2 3 1 2 3 1 2 3

one pixel

silicon chip

output amplifier

parallel transfer electrodes

serial output register electrodes

channel stop diffusion

123123123123

Figure 3.4: CCD chip layout for three-phase CCD system. First, charges collected at each electrodeare shifted along parallel electrodes onto serial register electrodes. Then the charges are shifted tothe output amplifier. Reproduced from reference [169].

3.2.2.6 SNR comparison of detectors

The dynamic range of the detector is characterized by a low limit set by the noise equivalent power

(NEP) from dark current, a middle linear region composed of various noise sources, and a high

limit set by saturation (Figure 3.5). It is important to identify and characterize the linear region

of system to optimize measurements for given application. The characterization of this region in

the overall electronic-optical system will be described in the following section 3.5. In this section,

intrinsic limitation arising from the choice of detector is closely examined.

When the incident light photons arrive at the detector, not every photon produces electrons.

This factor is commonly characterized by the quantum efficiency η (number of electrons produced

/ incident number of photons), which is given in percentage. Also, for APD and PMT, it is given

49

Noise Equivalent Power

Linear response region

Saturation

Input Power (W)

DetectorResponse (V)

Figure 3.5: Characteristic response of detector to the input light power

as the detector sensitivity in [A/Watt]

Sk =IkPin

, (3.1)

where Ik is the photocurrent [A] and Pin is the incident light power in [Watt]. The quantum

efficiency η and the detector sensitivity Sk are related by

η =hc

λqSk, (3.2)

where h is Plank’s constant (6.63×10−34 J×s), c is the speed of light (2.99×108 m/s), q is electron

charge (1.60× 10−19 coulomb), and λ is the light wavelength (in [m]).

There are three major noise factors in photodiode and photomultiplier: shot noise due to in-

cident photon statistics, dark current induced noise, and thermal noise. The shot noise associated

with current flow across a potential barrier is given by ishot =√2qBI [A] where I is the average

50

dc current [A] and B is the bandwidth [Hz] [201]. The shot noise due to the photocurrent Ik is

iphoton =√2qBIk, where the shot noise is in fact proportaional to

√nphoton, where nphoton is the

equivalent number of photons after degradation caused by imperfect conversion caused by quantum

efficiency η. Since Ik is proportional to the incident light power, the photon shot noise increases

with respect to the increase of Pin (in square root fashion). The lower end of this relation is limited

by the noise from the dark current Idark, which is present even there is no input light. The param-

eter is usually given in terms of Noise equivalent power (NEP), where PNEPSk =√2qBIdark.

These noise factors are given at the point where no amplification has yet taken place, such as at the

cathode of PMT or before the avalanche effect in APD. Thermal noise is due to thermal agitation of

electrons within a resistance and given by ithermal =√

4kTB/R, where k is Boltzman’s constant

(1.38× 10−23 J/K), T is absolute temperature [K], and R is the load resistance [Ω]. Thermal noise

usually sets the lower limit on the noise present in an electronic circuit.

To calculate the signal-to-noise ratio (SNR) of a PMT, we consider the signal and noise after

the amplification process of the detector. The amplified current is then Isignal = GIk = GSkPin

where G is gain and the noise is given as

inoise =√

2qBG2Ik + 2qBG2Idark. (3.3)

Here, the thermal noise component is ignored since PMT is a current source. SNR is then calcu-

lated via Isignal/inoise. This simplified relationship applies to PMT with the assumption that gain

is quite large and there is minimal additional noise coming from the amplification process (i.e.

dynode chains). In photon counting mode, one could approximate dark noise contribution to be

zero since the discriminator threshold could be set up to reject dark count (i.e. shot-noise limited).

51

However, in the case of the APD, it is more complicated due to its different amplification

mechanism. Dark current in the APD is categorized into surface leakage current Ids which does

not go through the multiplication process and an internal current Idg generated inside the silicon

substrate. The non-uniformity of ionization induces “excess noise” during the multiplification

process. The Equation 3.3 becomes

iAPDnoise =

√

2qBG2F (Ik + Idg) + 2qBIds +4kTB

R(3.4)

where F is excess noise factor related to gain G. In PIN photodiode, usually the thermal noise

plays a major role in the noise contribution since there is no gain mechanism.

The calculation of signal and noise of the CCD takes a different form as follows. There are

four major noise sources associated with the CCD; dark current noise, read noise, shot noise and

fixed-pattern noise. Due to the thermal energy within the silicon lattice of the CCD, dark current

is generated. The statistical fluctuation of dark current (dark current noise) can be reduced by

cooling the CCD with thermoelectric coolers (TEC) or liquid nitrogen. Read noise is the random

noise associated with the process of quantifying the electronic signal on the CCD, especially from

on-chip pre-amplifier. Shot noise arises from the inherent variation of the incident photon flux.

Fixed-pattern noise is a dominant noise at relatively high light level, resulting from differences in

sensitivity among pixels or photo-response nonuniformity.

Within the light level below where the saturation begins, the signal-to-noise ratio can be calcu-

lated by

SNRCCD =ηNpt

√

ηNpt+ (Ndt)2 +N2r

(3.5)

where η is the quantum efficiency, Np is the photon flux (photons/pixel/second), t is the integration

52

time (seconds), Nd is the dark current (electrons/pixel/second, in short form e−/p/s), and Nr is

the read noise (electrons RMS/pixel, e−/p) due to the on-chip amplifier. Given Pin at one pixel,

Np = λPin/h/c.

For detectors commonly used in our laboratory, SNR for incident power level can be calculated

using the specification information summarized in Table 3.1. SNR of APD, PMT and CCD is

plotted with respect to the incident light power in the horizontal axis in Figure 3.6. The bandwidth

B was assumed to be 1 Hz. The load registance of APD is order of 1 GΩ. The APD inside

the module C5331-04 is S2384. The excess noise index is 0.3, therefore the excess noise factor

F = G0.3. Also, as a quick comparison, PMT with improved quantum efficiency in NIR region

was considered with photon-counting mode (PMT: III-V. η = 15 % in NIR, G = 106, maximum

cathodecurrent = 1 pA.).

type model NEP (W/√Hz) sensitivity η gain Idark

APD S2384 4 × 10−13 0.5 A/W 32 % 30 1 nA (after gain)PMT R928 1.3 × 10−16 0.02 A/W 3 % 107 30 nA (anode)type model Nr(e

−1/p) full well η exposure time Nd(e−1/p/s)

CCD Versarray 8 200,000 e−1 37 % 500 ms 0.5

Table 3.1: Parameters needed for estimating signal-to-noise ratio for detectors commonly used inour instrument. Noise equivalent power (NEP), sensitivity and quantum efficiency are given forλ = 800 nm.

It should be noted that incident light power in Figure 3.6 is per unit detector, i.e. area of

detection was not considered into the calculation yet. For each detector, the incident power range

up to the onset of saturation is shown. The lower limit of APD (S2384) is governed mainly by

the dark current noise component. The cross-over to photon shot noise limited region happens

around 10−10 W. In reality, APD does come with built-in amplifier as a module (C5331-04), whose

significant noise factor was not considered in this calculation. Therefore its SNR in the high light

53

10−18

10−16

10−14

10−12

10−10

10−8

10−1

100

101

102

103

104

Incident light power (W)

Sig

nal

/No

ise

PMT: R928APD: C5331−04CCD: VersarrayPMT: III−V

Figure 3.6: Signal-to-noise ratio (SNR) vs incident light power. SNR of PMT, APD and CCDcommonly used in our instrument are estimated based on the specification given in Table 3.1.PMT with improved photocathode material is shown as PMT: III-V. When SNR = 1, the detectorperformance is limited by the noise. Since the high end of linear range is limited by the saturationpoint, only the incident light power range up to the saturation is shown for each detector (i.e.maximum CCD SNR is 500.).

power range appears to be quite high. PMT R928 in our laboratory is used in analog mode (i.e.

not photon counting mode) and not cooled. Thus, the lower light is limited due to the presence

of dark current noise, but it quickly goes into photon shot noise limited linear region from 10−15

W to its saturation ∼ 2 × 10−10 W (saturation due to anode linearity limit). This large dynamic

range enables us to employ various combination of multiple source detector separations needed for

imaging geometry. The specific CCD that we are using for breast cancer imaging has high quantum

efficiency. However, the maximum SNR is limited by its linear full well, which is the number of

electrons that the individual CCD pixels can hold before spilling over into adjacent wells.

Figure 3.6 gives an impression that CCD will be definitely the detector of choice. However, one

54

should not use this figure assuming the same amount of incident light falls onto each detector unit

in the real scenario. In the experimental setting, one usually would like to use the same source light

power onto the turbid medium of interest and see how the different detectors respond. The incident

light power Pin for unit detector depends on detector-specific parameters such as the collection

area. That is,

Pin = |Φ(rs, rd, µa, µ′s)| ·Adet · floss (3.6)

where Adet is the detector area, floss is the loss factor associated with inefficiency from fiber

coupling and factor relating to N.A. of detector [93], and |Φ| is the fluence rate intensity in medium

(with optical properties µa, µ′s) with source positioned at rs, detector positioned at rd.

If we assume a homogeneous medium with typical optical properties measured at source de-

tector separations of 6 cm, |Φ| ∼ S × 10−6 [Watt/cm−2] (Equation 2.7). Also, if we assume S= 1

mW and general loss factor floss to be 0.05 for simplicity, then one can see the area of the detector

plays a big role in determining Pin. We usually use 6 mm diameter fiber for PMT R928 and 3

mm diameter fiber for APD C5331-04. For CCD, 0.3 cm pixel size is assumed which is similar to

what we use in our measurement. The bandwidth B was taken as 2 Hz (to match the usual CCD

exposure time of 500 ms). From this detection area differences, incident power and SNR for the

signal level are summarized in Table 3.2. SNR of PMT is larger than that of CCD and much larger

than that of APD.

Even though this calculation is more of back-of-the-envelope type, it qualitatively matches

with our experimental observations. In the real experimental set-up, the use of APD for 6 cm

source detector separation is not so practical. This can be seen from the incident power being

very close to its NEP. With more inefficient coupling, Pin can easily become similar to NEP.

On the other hand, PMT has been used extensively for large source detector separations without

55

type model coupling detection area (cm−2) Pin SNRAPD S2384 3 mm fiber 0.07 3.5× 10−12 W 8PMT R928 6 mm fiber 0.28 1.4× 10−11 W 660CCD Versarray 0.3 mm pixel 4.5× 10−4 9.0× 10−14 W 180

Table 3.2: Example of SNR calculation of our commonly used detectors in the standard breastmeasurement for λ = 800 nm. Depending on the detection area, the incident input power (Pin tothe detector varys and thus affect SNR.

difficulties. Note that Pin on a CCD pixel is much lower than that of APD or PMT due to its area

even though the capability of CCD to detect low incident power seems to be better than PMT due

to its excellent quantum efficiency. (Area was not from the physical CCD-chip dimension, but the

magnified imaging area by the lens typically found in the experiment.) However, SNR retrieved is

still reasonable for the geometry that we are currently using. One could argue that by averaging

over many number of pixels to cover larger collection area may vastly improve the SNR. However,

each pixel is limited by its read noise (which is higher than several photons) and averaging over

pixels with no response may not necessarily improve SNR by many-fold as expected. Whereas in

PMT, larger collection area can be utilized to enhance the light detectability since it is not limited

by read noise.

3.3 Frequency-domain Homodyne System

3.3.1 Frequency-domain System Schematic

The schematic of the homodyne frequency-domain system is illustrated in Figure 3.7. The local

RF oscillator provides a modulated waveform for the laser diode and the reference signal for the

in-phase and quadrature (I&Q) demodulator. The RF modulated light from the laser diode is

coupled to the turbid medium through optical fibers. Depending on the multiplexing method,

56

RF local oscillator

LPFLPF

Turbidmedium

Detector

I&QDemodulator

Computer

Splitter

AmplifiersAttenuators

Filters

AD board

Laser Diode

Optical switch

Figure 3.7: General Homodyne frequency-domain system (LPF: low pass filter). RF local oscilla-tor provides the reference signal to I&Q demodulator while modulating the laser diode. The source,detector positions and wavelengths are multiplexed using a combination of optical switches. Thenthe attenuated signal through the turbid medium is detected by the detector, goes through properamplification and filtering. I&Q demodulator with low pass filter extracts amplitude and phaseinformation which are recorded in computer through analog-to-digital (AD) board.

optical switches or optical combiners are used for wavelength and optode position changes. The

attenuated signal after propagating through the turbid medium is detected by either a PMT or an

APD. The signal goes through bandpass filter and amplifirs before reaching the I&Q demodulator.

The I&Q demodulator computes the amplitude and phase of the detected signal with respect to the

reference signal. The details of I&Q demodulator are described in the Section 3.3.3.

3.3.2 Laser diode modulation

In RF modulation of laser diode, one needs to first choose the driving circuit which can drive

the laser diode in continuous wave mode with good stability. The driving circuit depends on the

57

polarity of the laser diode and the monitor photodiode. There are four common types of laser diode

configurations depending on the polarities of the laser diode and photodiode connection as shown

in Figure 3.8. The photodiode embedded within the laser diode circuitry is used for regularizing

the laser diode output by feedback circuit. In naming the style, we are following the conventions

used by Thorlab, Inc. in their catalog [256].

cathode

anode

(a)

LD

PD

Style A

(b)

LD

PD

Style B

(c)

LD

PD

Style C

(d)

LD

PD

Style D

(e)

Figure 3.8: (a) Diode polarity, (b) Laser diode style A, (c) Laser diode style B, (d) Laser diodestyle C, (e) Laser diode style D. LD stands for laser diode and PD stands for photodiode.

Most of our laser diodes were modulated using laser diode driver chips from Sharp: IR3C01

for the laser diode style B and IR3C07 for the laser diode style C.

laser style Rr Cr Lr Rc Cc Rv

IR3C01 B 47Ω 45pF (f=70MHz) 330µH 20Ω 22µF 20kΩ22pF (f=140MHz)

IR3C07 C 47Ω 45pF (f=70MHz) 100µH 10Ω 22µF 100kΩ22pF (f=140MHz)

Table 3.3: Parameters for laser diode RF modulation

Rr, Cr and Lr are the parts essential to RF modulation. If one omits Rr, Cr and Lr from the

circuit in Figure 3.9, the laser diode will operate in CW mode. Rr = 47Ω was chosen to give 50

Ω impedance when combined with internal resistance of 3 ∼ 5 Ω of powered laser diode. Cr is

58

1

2

3

4

7

6

5

8

IR3C01

RF in

Rr Cr Lr

Laser diode(style B)

Rc

Cc

-12 V

Rv

+5 V

TTL High = ONTTL Low = OFF

LDPD

(a)

1

2

3

4

7

6

5

8

IR3C07

RF in

Rr Cr Lr

Laser diode(style C)

Rc

Cc

Rv

+5 V

TTL High = ONTTL Low = OFF

LDPD

(b)

Figure 3.9: RF modulation diagram for laser diodes (a) IR3C01 for laser diode style B, (b) IR3C07for laser diode style C. Without Rr, Cr and Lr, the laser diodes operate in CW-mode.

chosen to match the RF input frequency, i.e. f ∼ 12πRC where R = 50Ω (Cr = 45pF for f = 70

MHz, Cr = 22pF for f = 140 MHz). Lr is added to prevent the RF signal from passing into

the laser diode chip. Rc, Cc and Rv values vary depending on the laser diodes. Rv is a variable

resistor with maximum resistance value given by the Table 3.3. Therefore, the tabulated values are

not absolute and are included only as a reference.

3.3.3 I&Q demodulator

The heart of the homodyne frequency-domain detection is the I&Q demodulator (Figure 3.10).

Suppose the reference signal isREF = Ar sin(ωt) and the detected signal isDET = Ad sin(ωt+

θ), where θ is the phase shift with respect to the reference. In the I&Q demodulator, the reference

signal is split into two, one of which goes through a 90o phase shifter. The detected signal is

also split into two, but they do not go through the phase-shifter. The multiplication of unshifted

59

90 shifto

0 shifto

Reference signal

Detected signal

I(t) Q(t)

Figure 3.10: Schematic of In-phase and Quadrature (I&Q) demodulator.

reference and detected signals occur at in-phase section.

I(t) =Ar2

sin(ωt) · Ad2

sin(ωt+ θ) + I0

= A cos(θ)−A cos(2ωt+ θ) + I0 (3.7)

where A = ArAd8 and I0 is the DC offset when the RF is absent. In the quadrature section, 90 o

shifted reference and unshifted detected signals get multiplied.

Q(t) =Ar2

cos(ωt) · Ad2

sin(ωt+ θ) +Q0

= A sin(θ) +A sin(2ωt+ θ) +Q0 (3.8)

where Q0 is the DC offset when the RF is absent. The low pass filter following at I and Q

output selects out the high frequency signal components. Therefore, IDC = A cos θ + I0 and

60

QDC = A sin θ + Q0 are the final output signal arriving at data acquisition point. The amplitude

and phase of the detected RF signal is then

A =√

(IDC − I0)2 + (QDC −Q0)2 (3.9)

θ = tan−1(

QDC −Q0IDC − I0

)

(3.10)

It is a standard practice to measure the DC offset I0 and Q0 by blocking the light input to the

detection system.

3.4 Continuous-wave CCD System

In this section, specification of CCD camera used in the second generation CCD-based parallel

plate instrument (Section 3.6.2) is discussed. A 16-bit thermoelectically cooled CCD array (Ver-

sArray:1300B, Roper Scientific) is operated at 500 ms exposure time, 2×2 on-chip binning at

high-sensitivity amplifier setting for the region of interest covering an imaging area of 16 cm ×

11 cm onto 570 × 400 binned pixels. The specification is summarized in Table 3.4. Binning of

the image increases SNR at the cost of resolution. On-chip binning which happens at the hardware

level yields higher SNR given exposure time. This feature can also be used to decrease exposure

time for the same level of SNR. The use of ROI in conjunction of binning makes the CCD trans-

fer time shorter than that of the full frame (450 ms for our ROI, 1.8 second for full frame). The

spectral response of this CCD is good for near-infrared range. The quantum efficiency is above

60 % from 380 - 850 nm with its peak around 550 nm (92 %), decreasing towards longer wave-

length (30 % for 950 nm). (Back-illuminated device has better quantum efficiency compared to the

front-illuminated device.)

61

CCD sensor E2V CCD36-40; back-illuminated device (with AR coating)CCD format 1340 × 1300 imaging pixels; 20 × 20-µm pixels

100% fill factor; 26.8 × 26.0-mm imaging areasingle pixel full well 200,000 e− - 300,000 e−

User-selectable gains 0.5×, 1×, 2× (low-noise mode)Read noise 8 e− rms at 1 MHz (high-sensitivity amplifier)

Dark current 0.1 e−/p/s at -40oC operationNonlinearity < 2%

Nonuniformity ≤ 4% over entire CCD areaDynamic range 16 bitsFrame readout < 1.8 seconds for full frame at 1 MHzDark current < 0.5 e−/p/s at -50 oC

Operating temperature -40 oC with TEC (backfilled)Thermostating precision 0.05oC over entire temperature range

Table 3.4: Specification of CCD array, VersArray:1300F

For our CCD, dark current noise is 0.1 e−/p/s (electron/pixel/second) and read noise is 8 e−/p

for the high-sensitivity amplifier. For 500 ms exposure time, the dark current noise is 0.05 e−/p

which is considerably smaller than the read noise. The saturation point is when the potential well

is full (∼200,000 electrons), which corresponds to 1.5× 10−13 W. Since the read noise defines the

limitation of the signal, the dynamic range of CCD is obtained by usually dividing linear full well

by read noise. In order to take full advantage of the dynamic range, an appropriate A/D converter

is selected for each camera. The gain is defined in terms of electrons/ADU (analog-to-digital unit).

Suppose the gain is set to 1×, then 1 ADU corresponds to ∼3 electrons (linear full well / 216).

However, for this particular CCD, the conversion factor was set as 4 e−/ADU, 2 e−/ADU, and

1e−/ADU (which is referred as gain setting). Depending on the gain setting, the saturation due to

the full potential well may not happen before it is limited by digitization limit (216 ADU). For the

example presented in Table 3.2 (i.e. Pin = 4.5× 10−14 Watt), assuming 70% quantum efficiency,

the number of electrons deposited in a pixel is 63,000 e− which corresponds to 31,500 ADU for

medium gain. The order of magnitude of this matches with the experimentally measured value.

62

3.5 System Characterization

Once the instrument is designed and assembled, the characteristic dynamic range needs to be quan-

tified. It is important to first identify the dynamic range of major electronic components, since the

instrument design goal is to build the system limited by the optical components (i.e. detectors),

not by the electronic components. Then the dynamic range of the whole system including the

electronic and optical components is measured to characterize the system. This methodology is

demonstrated in the following sections using a one detector channel frequency-domain homodyne

system.

3.5.1 Dynamic range of electronic components

Attenuator

Power Splitter

70 MHz Oscillator

I&Q Demodulator

LPF LPF

Referencesignal

Amplifiers,etc.

AD board

Computer

Inputsignal

Figure 3.11: Schematic of electronic dynamic range measurement set-up using electronic attenua-tor.

63

In determining the dynamic range of electronic components, we started by testing the response

of I&Q demodulator with input signal variation. Then we added amplifiers one by one to see if

there is any degradation due to addition of amplifiers.

The schematic of the test set-up is described in Figure 3.11. A 70 MHz local oscillator signal is

split into two. One provides the reference signal for the I&Q demodulator. The other is attenuated

and serves as the detected signal to the I&Q demodulator. Amplitude response measured for each

RF input signal is plotted for three cases in Figure 3.12: (1) only I&Q demodulator was present, (2)

I&Q demodulator and two amplifiers were present and (3) I&Q demodulator and three amplifiers

were present. The dynamic range defined by I&Q demodulator is RF input of -60 dBm to -5 dBm.

The addition of amplifiers do not limit this range, but merely shifts the range to lower RF input by

its gain factor (i.e. With two amplifier, the dynamic range is -120 dBm to -65 dBm).

-140 -120 -100 -80 -60 -40 -20 0 20

-60

0

-20

-40

-80

-100

20

RF input signal (dBm)

Measured amplitude (dBm)

2 amplifiers3 amplifiers

IQ only

Figure 3.12: Effect of amplifier addition on the electronic dynamic range. 2 amplifiers: test of twoamplifiers and I&Q demodulator, 3 amplifiers: test of three amplifiers and I&Q demodulator

64

The I and Q output contains the DC offset (I0, Q0) as in Equation 3.10. As shown in Fig-

ure 3.13, offset subtraction improves the amplitude dynamic range especially at the low end and

significantly improves the phase stability.

−40 −30 −20 −10 0 10−40

−30

−20

−10

0

10

RF input (dBm)

Am

plit

ud

e (d

Bm

)

before offset subtractionafter offset subtraction

(a)

−40 −30 −20 −10 0 100

50

100

150

200

250

RF input (dBm)P

has

e (d

egre

e)

before offset subtractionafter offset subtraction

(b)

Figure 3.13: Effect of offset subtraction on dynamic range. (a) Amplitude vs RF input, (b) Phasevs RF input. Offset subtraction improves the dynamic range at low RF input and the phase stability.

3.5.2 Dynamic range of the whole system

The dynamic range of the whole system combining the electronic and optical components is as-

sessed using the set-up illustrated in Figure 3.14. The light emitted from light source is reduced by

a mechanical attenuator and then split into two beams by 1×2 fiber splitter. One beam goes to an

optical power meter and the other one goes to the detection part of the optical system. The signal

response of the detection system to the attenuated light signal is plotted against the light signal

measured by the optical power meter in Figure 3.15(a). Figure 3.15(b) shows the deviation of the

measured value from the fitted linear line over the dynamic range. Typically, we choose the range

by the deviation of ± 1%. In this example, the dynamic range is -50 ∼ -10 dBm. Note this range

65

is smaller than the electronic dynamic range of previous section. However, this dynamic range can

be extended further with use of attenuators.

OpticalPowermeter

1x2 fiber splitter

Detectionelectronics

Light Source

Mechanical attenuator

Figure 3.14: Amplitude linearity test set-up

The phase accuracy is tested using the set-up shown in Figure 3.16(a). The optical fiber end

mount and lens are separated by the focal length of the lens so that the light is parallel after exiting

the lens. Then another lens focuses the beam into fiber coupled to the detector. The mount and first

lens are moved as a unit while the distance between the two lenses is varied. The change in the

distance between the two lenses produces a change in phase. Since the modulation frequency is 70

MHz, the expected phase change is 0.84o/cm. Typical linear response in phase at fixed amplitude

within the instrument dynamic range is shown in Figure 3.16(b).

66

−70 −60 −50 −40 −30 −20 −10 0

−60

−40

−20

0

20

40

60

Power (dBm)

Am

plit

ud

e (d

Bm

)

measuredfit

Dynamic Range

−50 −40 −30 −20 −10−3

−2

−1

0

1

2

3

Power (dBm)

Err

or

(%)

Dynamic Range

Figure 3.15: Amplitude linearity Test data. (a) Amplitude vs power in linear scale, (b) Amplitudeerror (%)

3.6 Instrumentation

3.6.1 1st generation parallel plate DOT instrument

The 1st generation parallel plate transmission DOT instrument is utilized for quantification of

bulk properties of healthy female breasts [81] (Chapter 4, Section 4.3). The instrument uses three

wavelengths - 750nm, 786nm and 830nm, and employs a scanning, fiber-coupled PMT detector

(R928, Hamamatsu) for detection. The system is characterized by a noise equivalent power of

≈ 0.1pW/√Hz, a linearity in amplitude of less than 1%, and a phase drift of 0.25o over 80 dB

(with use of attenuators). We calibrated the instrument over a broad range of input powers in order

to extend this range. For transmission measurements the signal variation is typically only ≈30

dB. In clinical measurements we utilize a single source position due at the center of the scanning

region. The lasers are amplitude modulated at 140 MHz to produce diffuse photon density waves

(DPDWs) in the medium. The amplitude and phase of the DPDW is recovered using a homodyne

IQ-demodulation scheme [288] (Section 3.3.3).

67

Detectionelectronics

Light Source

Mechanical attenuator movable

lens unit lens

0 2 4 6 8 10 120

2

4

6

8

10

12

expected phase shift (degree)

exp

erim

enta

l sh

ift

(deg

ree)

Figure 3.16: (a) Phase linearity test set-up, (b) Phase linearity test data. Measured phase shift (indegree) vs expected phase shift (in degree) at fixed amplitude within the linear dynamic range.

For the in vivo measurements the volunteer lies in the prone position and her breast is inserted

into a small tank filled with a matching-fluid solution of Intralipid and india-ink mixture (see Figure

3.17). The detector is scanned along the output plate glass surface. The source is attached to the

movable compression plate which applies a gentle compression to the breast. Usually the range of

compression is 4.5 cm to 7 cm. It takes ≈ 15 minutes to acquire data from a 9.6 cm (x) by 4.8 cm

(y) scan region with 153 (17×9) points. We note that the feedback from volunteers was generally

positive; in comparison to the X-ray mammography, they felt that the soft-compression of the DOT

instrument did not cause discomfort. Figure 3.18 shows the detailed electronics of the set-up. We

took two sets of data for each volunteer: 1) From the tank filled with the matching fluid, without

the breast; this data enables us to normalize for instrument response for imaging purposes, 2) From

the tank filled with the matching fluid and the volunteer’s breast. The Intralipid/ink solution helps

to reduce the detrimental effects of breast boundaries by acting as a matching medium.

68

Electronics

X−Y scanningstage

Detector Fiber

Source Fiber

Intralipidbox

Compressionplate

Source on opposite plane

Image View

Detector grid

Figure 3.17: A sketch of the prototype clinical table. The volunteer lies in the prone position withher breast inserted into the tank through an openning on the bed. Soft compression is applied onthe source plane and detector scans a 2D grid on the opposite plane. Image view shows the sourcedetector positions as seen in the data.

PMT

AmplifiersDigital Attenuator

FiltersIQ Demodulator

Diode Lasers:750nm, 786nm, 830 nm3 2x1 Optical Switches

140 MHz OscillatorPower Splitter

X-Y steppermotors

Intralipid box

Detector Fiber

Source Fiber

RF shielded NIM Bins Reference

OutputI-output

Q-output

Figure 3.18: Parallel plate scanning instrument electronics consists of three wavelength laserdiodes and 140 MHz homodyne system with PMT.

69

3.6.2 2nd generation parallel plate DOT instrument

Based on the experience gained by the first generation parallel plate instrument, the second gener-

ation instrument was developed with the focus on imaging [62]. A schematic of the DOT instru-

ment is shown in Figure 3.19. The hybrid system combines frequency-domain (FD) remission and

continuous-wave (CW) transmission detection. This parallel-plane DOT system has been exten-

sively characterized for breast cancer imaging using various tissue phantoms and a healthy female

volunteer [62] (Chapter 3, Section 3.7.2) and used extensively for breast cancer imaging (Chapter

4, Section 4.4 and 4.5).

The table was designed so that when the female subject lies on it in the prone position, both

her breasts are inside a breast box (60 × 22 × 23 cm) extending underneath the table. A breast

is typically centered and softly compressed between a movable compression plate and a parallel

viewing window with cranio-caudal compression. The compression distance varied from 5.5 - 7.5

cm, depending on breast size. The breast box was coated black and designed to hold the matching

fluid which has optical properties similar to human tissue. The matching fluid was made with

Liposyn III (30 %, Abbott Laboratories, Chicago, IL) as a scattering agent and India ink (Black

India 4415, Sanford, Bellwood, IL) as an absorption agent. The optical properties of the matching

fluid were fixed so that µa(786nm) = 0.05 cm−1 and µ′s(786nm) = 8 cm−1. The absorbance of

the ink solution was checked after each measurements with a spectrophotometer (Ocean Optics,

USB2000).

Four laser diodes at 690, 750, 786 and 830 nm were sinusoidally intensity modulated at 70

MHz. The modulation depth for each wavelength was 86 %, 99 %, 72 % and 67 % respectively.

Later on, 650 and 905 nm CW laser diodes were added to the instrument (along with optimization

of acquisition time from 12 minutes to 8.4 minites). Combination of optical switches (DiCon Fiber

70

(a)

Source Plane Detector Plane

12.8 cm

6.4 cm

15.6 cm

9.0 cm3mmSource

FD detectors

detectors984

(b)

Figure 3.19: Schematic of parallel plate diffuse optical tomography instrument. (a) Frequency-domain (FD) remission and continuous-wave transmission measurements are performed simulta-neously on a female subject lying in the prone position. (b) The source plate contains 45 sourcepositions and 9 FD detectors. 984 detection points with 3 mm spacing are selected from CCD datafor image reconstruction.

Optics) making 6× 2 connection was used for wavelength switching. The light output was relayed

to a 2× 48 switch (DiCon Fiber Optics, GP700) in order to access the various light source positions

on the compression plate. The compression plate had 45 fibers in 9 × 5 grid with a spacing of

1.6 cm (12.8 cm × 6.4 cm). The optical fibers embedded in the compression plate was of 200

µm diameter (FIS). Time-multiplexing was used for both wavelength and position switching. In

particular, wavelengths are multiplexed for given source position.

71

Nine 3 mm diameter fiber bundles were connected to the frequency-domain detection module,

interlaced in a 3 × 3 grid on the compression plate as shown in Figure 3.19(b). A homodyne

technique [288] was utilized to extract the amplitude and phase of the detected remission signal.

The electrical signal from the avalanche photodiode (APD, Hamamatsu C5331-04) is amplified

(Mini-Circuits ZFL-500LN, 24 dB), filtered by a band pass filter (Mini-Circuits BLP-70), and

then amplified again (Mini-Circuits ZFL-500HLN, 19 dB). An I&Q demodulator (Mini-Circuits

ZFMIQ-70D) with a series of low pass filters (Mini-Circuits SLP-1.9 and 100 Hz RC circuit)

extracts the amplitude and phase by comparing the signal with the reference signal driving laser

diodes [288]. The frequency-domain measurements are used for accurate quantification of bulk

properties of human tissue and matching fluid, thus improving our initial guess for the image

reconstruction.

A lens-coupled 16-bit CCD camera system was used for collecting CW transmission data with

an anti-reflection coated glass viewing window. A lens (Nikkor AF 50 mm F/1.4D) relayed the

detection plane (inner glass window in contact with breast) onto the CCD chip (2.68× 2.6 cm). To

reduce ambient light, a long-pass color-glass filter (630 nm, CVI Laser Inc.) was placed in front of

the lens and a light shielding box was placed surrounding the space between the viewing window

and the camera. A thermoelectrically cooled CCD pixel array (Roper Scientific, VersArray:1300F,

1340 × 1300 pixel) was used for light detection, with 1140 × 800 pixel region of interest (ROI)

and 2 × 2 on-chip binning, resulting frame size of 570 × 400 pixels covering a detection area of

16 × 11 cm (as described in Section 3.4).

72

Figure 3.20: Schematic of (a) the trans-abdominal probe and (b) the NIR frequency domain instru-ment to which the probe is coupled.

3.6.3 Frequency-encoded DOS instrument for fetal oximetry

We designed a multi-wavelength, multi-separation NIR frequency-domain instrument and probe

for trans-abdominal NIR spectroscopy [50] (Chapter 5, Section 5.2). Figure 3.20 shows a schematic

of the trans-abdominal probe and the NIR frequency-domain instrument to which the probe is cou-

pled. The probe was designed as a linear array consisting of 2 detector fibers and 6 source fibers.

This probe is capable of performing NIR photon diffusion measurements at a total of 12 source-

detector separations ranging from 1.8 to 9.5 cm. However, in this study, NIR photon diffusion

measurements at 8 source-detector separations ranging from 1.8 to 4 cm (Figure 3.20(a)) were

73

sufficient for retrieval of fetal cerebral blood saturation. The instrument consists of a light source

module and two detection modules. It is described in detail by Yu et al. [293]. Laser diodes at 675

nm, 786 nm and 830 nm are intensity modulated with three different local radio frequency (RF)

oscillators operating at around 70 MHz. The light output from each laser diode are combined using

a fiber combiner into a single optical fiber. In this manner, the single optical fiber can simultane-

ously deliver light output from the three frequency encoded laser diodes [288,293]. The total light

output from the single optical fiber was 15 mW (3 mW at 675 nm, 9 mW at 786 nm and 3 mW at

830 nm respectively). An optical prism switch was used to direct the light output from the single

optical fiber to the six source fiber positions on the trans-abdominal probe.

The detection module consists of an avalanche photodiode (APD), and two amplifiers, with a

band pass filter between them. The output from the detection module is connected to a demodu-

lation unit, which consists of three In-phase and Quadrature-phase (I&Q) demodulators. The in-

phase and quadrature-phase signals are low-pass filtered, digitized, and then converted into diffuse

wave signal amplitude and phase. Total acquisition time for the NIR photon diffusion measure-

ments at the three wavelengths and 12 source-detector separations was 1 second.

This instrument has been extensively tested in tissue phantom and rat brain studies [293]. The

noise equivalent power is less than 10 pW/√Hz and the dynamic range is greater than 70 dB

(amplitude errors < ± 1% and phase error < 1o.). The instrument has very low inter-channel

crosstalk (< -80 dB) and good long-term stability (amplitude errors < ± 1% and phase error < 1o

in 30 minutes).

74

3.7 Validation with Tissue Phantoms

Liquid phantoms serve as the gold standard to test the instrument and the algorithm using a com-

bination of absorbers and scatterers with known spectra. The titration of absorbers is useful for

testing the µa response of the overall system. Similarly, the titration of scatterers tests the µ′s re-

sponse. Indocyanine Green (ICG) is helpful for checking the spectral response since its spectra

has a well-defined peak in the NIR spectrum. Ultimately, titration of hemoglobin simulates the

global response from human tissue. The recipe for constructing liquid phantoms is described in

Section 3.8.1. However, solid phantoms are useful in simulating more tissue-like geometry and do

not deteriorate as fast as the liquid phantom. For imaging purposes, a compressible solid phantom

was developed as described in Section 3.8.2.

3.7.1 1st generation parallel plate DOT system phantom test

Typical raw data of breast is shown in Figure 3.21, overlayed with the forward data generated

from a fit based on the semi-infinite homogeneous medium analytic solution and a fit based on the

finite difference method (FDM). FDM fit was based on two regions of different optical properties

(breast and matching fluid regions) as shown in Figure 3.22(b). Particularly, NRIM described

in Chapter 2, Section 2.4.1 was modified to calculate bulk optical properties by summing up the

weight matrices only within the breast region and not allowing the matching fluid region to update

optical properties. The dispersion of amplitude and phase from the semi-infinite fit is mainly due

to the boundary effect, as can be seen from the FDM fit.

The scanning-based 1st generation instrument has been characterized by extensive phantom

studies [64, 82–85]. In particular, the phantom experiment was devised to best model the actual

breast measurement geometry as described. Balloons filled with different concentrations of ink

75

5 5.5 6 6.5 7 7.50

0.005

0.01

0.015

0.02

r (cm)

Am

p (n

orm

)FD Meas Semi−inf

(a)

5 5.5 6 6.5 7 7.5−0.5

0

0.5

1

r(cm)

Pha

se (

rad)

Semi−infFD Meas

(b)

Figure 3.21: (a) Amplitude and (b) phase vs source detector separation from a healthy female breasttissue showing the measured data (Meas) and fits with semi-infinite (Semi-inf) and finite differencemethod (FD). FD simulates the spread of measurement from semi-infinite due to boundary effect.

and Intralipid (Figure 3.22(c)) were used as a simulated breast. The balloons were inserted into

the breast box filled with the matching fluid to fill a volume occupied by the average breast tissue

volume found in the clinical measurements. A large fraction of balloon was kept above the match-

ing fluid level to simulate the chestwall. The background properties of the matching fluid were µa

= 0.05 cm−1 and µ′s = 8 cm−1 at 786 nm. The retrieved bulk optical properties of fifteen balloon

phantoms using FDM fit are fairly linear in comparison with the expected value as shown in Figure

3.23. Even though there are some deviation, it shows a fairly linear relation.

3.7.2 2nd generation paralell plate DOT system phantom test

First, the frequency-domain part of the instrument was tested on accuracy of retrieving optical

properties of homogeneous medium. Typical matching fluid optical properties fitted from RF semi-

infinite solution with coupling coefficient as described in Section 2.3.2 is presented in Figure 3.24.

The response of the DOT instrument to overall µa change of the medium was tested by ink titration

76

x

y

x

y

20cm

10cm

2.7cm

Background Measurement Geometry

Volunteer Measurement Geometry

11cm

6cm

air(y=-3.6)

air

z

y

source white detector

glass

z

y

source white

detector glass

2.7cmair(y=-3.6)

6cm 6cm

x

y

2.7cm

Baloon Measurement Geometry

11cm

6cm

air

z

y

source white

detector glass

2.7cm

6cm

balloon filled with intralipid and ink held in the tank.

Figure 3.22: Measurement geometry for three cases: (a) background, (b) breast, and (c) tissuephantom are shown with the corresponding boundaries. The shaded regions show the estimatedbreast volume in the segmentation process. The source boundary is diffuse white reflecting and thedetection plane is clear glass.

to the matching fluid (i.e. the tank was filled with matching fluid of varying µa with the method

described in Appendix Section 3.8.1). Figure 3.25 shows good linear response of DOT instrument

up to µa = 0.08 cm−1, which is well within the breast optical properties range.

Then, to test the imaging capability of our instrument, various imaging phantoms were devel-

oped for breast cancer imaging application as shown in Figure 3.26. The first two are mostly for

differential type of measurements, each object simulating tumor with higher absorption or scatter-

ing than the rest of the tissue. Figure 3.26(b) was aimed to provide the flexibility to change optical

77

0.02 0.04 0.06 0.080.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

µa real

µ a rec

on

5 10 15 20

5

10

15

20

µs’ real

µ s’ rec

on

Figure 3.23: Linear response of Scanning DOT to optical properties variation. µa variation (left)and µ′s variation (right)

properties of the object easily by changing liquid solutions and pumping into it. Figure 3.26(c)

shows a silicone-based phantom mimicking a compressed breast with chestwall extension.

We evaluated the resolution performance of our system using point spread function (PSF)

measurements. We used small strongly absorbing point-like objects, specifically 0.4 cm diame-

ter sphers with µa = 2.0 cm−1 and µ′s = 8 cm−1. Two such objects were arranged at r1 = (-2.5,

3.0, 0.0) and at r1 = (2.3, 3.0, 0.0). Reconstructions were performed for a range of regularization

constants lc from 0.001 to 1000. Typically, NRIM (Chapter 2, Section 2.4.1) was used. The re-

constructed µa(786 nm) images from lc = 0.1 are depicted in Figure 3.27. The cross-sections are

evaluated at the FWHM and they are dependent on the regularization constants. There is gener-

ally a trade off between resolution and image noise. By considering the ratio between the object

contrast and the image noise (CNR), the optimal regularization constant can be chosen. For this

experiment, a 3D point spread function with FWHM of 1.1 × 1.13 × 1.1 cm is obtained.

We also evaluated the ability of the system to image an extended tissue volume and to re-

construct a heterogeneous medium with multiple objects. We dispersed 15 cubic silicone tissue

phantom objects of µa = 0.2 cm−1 and µ′s = 8 cm−1 (0.8 cm edge) throughout the measurement

78

1 2 3 4 5 610

−6

10−4

10−2

1 2 3 4 5 60

1

2λ=690 nm µ

a=0.038, µ

s’=8.4 cm−1

1 2 3 4 5 610

−6

10−4

10−2

1 2 3 4 5 60

1

2

1 2 3 4 5 610

−6

10−4

10−2

1 2 3 4 5 60

1

2

1 2 3 4 5 610

−6

10−4

10−2

ρ (cm)

No

rmal

ized

Am

plit

ud

e

1 2 3 4 5 60

1

2

ρ (cm)

Ph

ase

(rad

)λ=750 nm

λ=786 nm

λ=830 nm

µa=0.056, µ

s’=7.6 cm−1

µa=0.057, µ

s’=6.7 cm−1

µa=0.049, µ

s’=7.1 cm−1

Figure 3.24: From top to bottom, 690, 750, 786, and 830 nm. Left to right, amplitude vs separationsand phase vs separations.

volume filled with the matching fluid of µa = 0.05 cm−1 and µ′s = 8 cm−1. The reconstructed

µa(786 nm) images with lc = 0.1 is shown in Figure 3.28 with isosurfaces at µa = 0.092 cm−1. The

reconstructed objects are well separated in all three dimensions. The spatially variant regulariza-

tion has provided fairly consistent sensitivity and resolution throughout the volume.

To evaluate the ability to characterize the concentrations of different chromophores in a tissue

phantom, two 3.2 cm3 flow cells (Figure 3.26(b)) were used. One was filled with an ink contrast

(higher µa than the background matching fluid) and the other was filled with an ICG contrast. Mul-

tiple measurements were performed with the titration of ICG while fixing the ink concentration.

The reconstructed µa at all 4 wavelengths were combined to calculate concentration map of ink and

ICG respectively. The concentration images sucessfully distinguish between the ink and the ICG

79

0.04 0.06 0.08 0.1 0.12 0.140.04

0.06

0.08

0.1

0.12

0.14

Expected µa (cm−1)

Ret

riev

ed µ

a (cm

−1)

Figure 3.25: µa at 786 nm measured and quantified using DOS is plotted with respect to theexpected µa calculated from spectrophotometric measurement.

as shown in Figure 3.29. Moreover, the integrated signals (volume× concentration [cm3µM ]) are

accurately retrieved for ICG concentration variations within the physiological region.

Previous tissue phantoms are all small objects (less than 3.2 cm3) suspended inside the match-

ing fluid. However, in vivo breast measurement involves tissue which has different constituents

from the liquid suspended in the matching fluid. This is simulated by using a breast shaped sili-

cone phantom with an embedded object with tubings as shown in Figure 3.26(c). One can change

the optical properties of the embedded object (which simulates a cancer) by flowing different con-

centration of Intralipid/ink solution. Figure 3.30(a) is the reconstructed images with the reference

measurement being the same silicone phantom at different titration stage (smaller ICG concentra-

tion) in the embedded object. The location of the reconstructed absorber matches well with the

expected location. (Confirmed by slicing the silicone phantom in half.) This simulates the case for

extrinsic contrast injection where the breast without the injection serves as the reference. In this

80

(a) (b) (c)

Figure 3.26: Photos of (a) two 1 cm3 silicone cube, (b) hollow cylindrical container with tubingsenabling changes of liquid inside (flow cell), and (c) breast shaped silicone with extension for thechestwall

case, source coupling coefficients problem diminishes since the signal difference is only coming

from the injection. Figure 3.30(b) is the reconstruction result with the matching fluid as the ref-

erence measurement, with geometric constraint approach. This reconstruction is most similar to

our in vivo breast measurement, where it relies on the intrinsic contrast (Chapter 2, Section 2.4.3

and Chapter 4, Section 4.4.2). The quality of reconstructed image is not as good as the extrinsic

contrast simulation case (Figure 3.30(a)), but the location is fairly accurate. We are in the process

of refining the reconstruction technique to improve image accuracy.

3.8 APPENDIX: Tissue Phantom Recipes

3.8.1 Liquid Phantoms

The absorbers typically utilized in constructing liquid tissue phantoms are ink, ICG, Hb, HbO2,

H2O and lipid. Except the ink spectrum, well established spectra of the absorbers are available in

OMLC homepage (http://omlc.ogi.edu/spectra/, accessed January 2001). In Figure 3.31, the water

and lipid spectras are presented in µa [cm−1]. The spectra of Hb and HbO2 are shown in extinction

81

y (cm)

y (cm)x (cm)

x (cm)

x (cm)

y (cm)

z (cm)

z

0.090.080.070.060.05(cm )-1

8 6 4 2 0-2-4-6-8

5

-10

10

-50

105

0

-5

0

5

-5 0 5

50-5

-8-6-4-2 0 2 4 6 8

z (cm)246

2 4 6

Figure 3.27: Reconstructed µa map of two point spread function like objects with high absorption

coeffiencient ε [cm−1 M] (Figure 3.32). ICG spectra changes depending on the suspension medium

(water or plasma) as shown in Figure 3.33. The absorption spectrum of India ink (Figure 3.34(a))

is measured with the spectraphotometer. It is presented in absorbance Ab(λ) = − log I(λ)I0(λ)

where

I is the transmitted intensity through the absorbing sample of 1 cm thickness and I0 is the initial

light intensity. India ink is typically utilized for its monotonical spectra makes it easy to produce

expected absorption when testing µa response of the instrument at one wavelength. General con-

figuration for liquid tissue phantom measurement in semi-infinite geometry is shown in Figure

3.34(b).

According to van Staveren’s Mie theory approximation [262], µ′s of 10 % Intralipid is given by

82

x (cm) y (cm)

z (cm)

Figure 3.28: Reconstructed µa map of fifteen 1 cm3 objects suspended in the matching fluid

the following

µs = 2.54× 109 × λ−2.4 (3.11)

g = 1.1− 0.58× 10−3λ (3.12)

µ′s = µs(1− g) (3.13)

where λ is in [nm] and µs and µ′s are in [cm−1]. µ′s of 0.8 % Intralipid usually used for our

experiments are presented in Figure 3.35. (There is a consistent discrepancy between this expected

value and the measured scattering value. This may be attributed from the difference in scattering

83

Ink & ICG flowable phantom

Figure 3.29: Respective concentration maps of ICG and ink based on reconstructed µa.

medium we are using (Liposyn III) and van Staveren used (Intralipid).)

Recipe : Standard Ink/Intralipid solution

(a) Calculation of Ink concentration for desired absorption

First, one needs to dilute the ink concentration to either 1 % or 10 %. If the total liquid volume

is less than 10 l, 1 % dilution is adequate. For the optical mammography, we need 26 l of the

matching fluid, so we need the ink of 10 % dilution.

The absorbance of the ink solution to be used should be measured with the spectrophotometer,

ideally on the day of the measurement. Typical dynamic range of spectrophotometer is up to

84

4

13x 10

−3

4

13x 10

−3

Figure 3.30: Reconstructed µa (cm−1) image of a silicone breast shape phantom with an embeddedabsorber. (a) Using a measurement on the same silicone phantom with smaller absorption in theabsorber as the reference, (b) Using a measurement on the matching fluid as the reference.

absorbance of 4. Diluting the ink solution to 0.1 % of the original concentration decreases its

absorbance to measurable level. Measure the ink absorbance spectra with spectrophotometer with

water as a reference sample.

If the measured absorbance is Ab(λ), µa(λ) = ln(10)×Ab(λ). The conversion factor ln(10)

stems from the fact that bases of log are different (i.e. Ab = log10I0I and µa = ln I0I ). This µa is

that of 0.1 % diluted version of the original concentration. Therefore, one needs to multiply 10 for

1 % ink and 100 for 10 % ink.

From the titration relation Cbefore×Vbefore = Cafter×Vafter (C: concentration, V : volume)

can be modified as the following, since µa is proportional to the concentration, µbeforea ×V before+

µinka ×V ink = µaftera ×V after. Especially when calculating the amount of absorber concentration

to be used for desired total µa, one needs to take water absorption into the consideration.

(b) Calculation of Intralipid concentration for desired scattering

µ′10% Intralipids can be obtained from the Equation 3.11. Usually, 20 or 30 % Intralipid solutions

are readily available. Therefore, one needs to scale µ′s values accordingly. The volume of Intralipid

to be used can be calculated by µ′befores × V before + µ′intralipids × V intralipid = µ′afters × V after.

85

600 700 800 900 10000

0.1

0.2

0.3

0.4

0.5

wavelength

Water

abso

rpti

on

co

effi

cien

t(cm

−1)

(nm)

(a)

600 700 800 900 10000

0.01

0.02

0.03

0.04

0.05

wavelength

abso

rpti

on

co

effi

cien

t

Lipid

(nm)

(cm

−1)

(b)

Figure 3.31: µa spectra of (a) water and (b) lipid

(c) Example

Suppose that we want to make a solution of µa = 0.05 cm−1 and µ′s = 8 cm−1 at 786 nm for

total volume of 26 l. We will use 10 % diluted ink and 30 % Intralipid. How much volume of

ink and intralipid solution are needed? Suppose the measured absorbance of 0.1 % ink solution is

Ab(786nm) = 1.50. Then in order to get the absorbance of 10 % ink, a factor of 100 should be mul-

tiplied. Also, there is already absorption due to water to be taken into account, i.e. µH2Oa (786nm)

= 0.021 cm−1.

For absorption,

µinka = ln(10)×Ab× 100 = ln(10)× 1.50× 100 = 345

0.021× (26000− V ink) + 345× V ink = 0.05× 26000

V ink = 2.19ml.

86

200 400 600 800 10000

100

200

300

400

500

600

wavelength (nm)

exti

nct

ion

co

effi

cien

t (c

m−1

/µM

) HemoglobinsHbO2Hb

(a)

600 700 800 900 10000

1

2

3

4

5

wavelength (nm)

exti

nct

ion

co

effi

cien

t (c

m−1

/µM

) HemoglobinsHbO2Hb

(b)

Figure 3.32: Extinction coefficient of hemoglobins (a) 200 - 1000 nm, (b) 600 - 1000 nm

For scattering,

µ′30% intralipids = 3× µ′10% intralipid

s = 3× 102 cm−1

0× (26000− V 30% intralipid) + 305× V 30% intralipid = 8× 26000

V 30% intralipid = 682ml.

If one wants to increase the absorption of above solution to µa = 0.07 cm−1, then the extra

amount of ink to be added can be calculated by

0.05× 26000 + µinka × V new ink = 0.07× (26000 + V new ink)

V new ink = 1.5ml.

87

600 700 800 900 10000

0.5

1

1.5

2x 10

5

wavelength(nm)

exti

nct

ion

co

effi

cien

t (c

m−1

/M) ICG

ICG in waterICG in plasma

(a)

600 650 700 750 800 850 9000

0.2

0.4

0.6

0.8

1

wavelength (nm)

No

rmal

ized

ab

sorb

ance

ICG in waterICG in plasma

(b)

Figure 3.33: (a) Extinction coefficient of ICG (10 µM concentration). (b) Normalized spectra ofICG in water and plasma.

Recipe : ICG solution

The ICG preparation used for clinical study is prduced by Akorn, Inc, under the tradename of IC-

Green. It is usually available in 25mg IC-Green accompanied by 10ml ampules of sterile aqueous

solvent. Since the molecular weight of ICG is 775, this combination makes 3.2 mM solution. For

ICG injection study, we use 0.25 mg/kg dose. However, depending on the preparation variation,

the actual concentration may be different. For spectrophotometric measurement, diluting 45 µl of

this ICG solution into 10 ml water (∼14 µM ) gives the measurable absorbance.

For example, suppose that we want to make a solution of ∆µICGa = 0.1 cm−1 at 786 nm for

800 ml total volume. There is a significant shift in ICG spectra with increase of concentration.

Figure 3.33(a) is the extinction coefficient for ∼ 10 µM concentration range. For our purpose,

this spectra can be utilized: the extinction coefficient ε at 786 nm is 110210 cm−1/M . How much

88

650 700 750 800 850 900 9500

0.5

1

1.5

2

2.5

3

wavelength (nm)

abso

rban

ce

(a) (b)

Figure 3.34: (a) Absorbance spectra of India ink and (b) General configuration for liquid phantommeasurement in semi-infinite geometry

volume of 3.2 mM ICG solution is needed to make ∆µICGa = 0.1 cm−1 of 800 ml total volume?

3.2× V ICG =∆µICGa

ln(10)× ε × total volume

V ICG = 100 µl.

Recipe : Blood phantom

First, determine the concentration of human blood by spectrophotometer measurement. Usually

1% dilution of blood results in good SNR range of spectrophotometer. Use the measurements at

541 nm, 550 nm and 576 nm to determine the total hemoglobin concentrations Ct. Assuming

the blood sample is a mixture of oxygenated and deoxygenated hemoglobins, decompose the con-

centrations based on three wavelengths using known extinction coefficient of Hb and HbO2 from

Figure 3.32(a).

89

600 700 800 900 10000

2

4

6

8

10

12

wavelength (nm)µ s′ (

cm−1

)

µs′ of 0.8% Intralipid

Figure 3.35: Intralipid µ′s base on van Staveren [262]

Then determine the total volume of blood model (Vt). When diluting the blood, Phosphate

Buffered Saline (PBS) should be used to maintain blood cells at pH=7.4. (The oxygen saturation

of blood diagram shifts with ∆pH = 0.2 difference.) The volume of Intralipid is determined by the

same way as described before. The volume of the blood samples is then determined by Vafter =

Cafter × Vt/Ct.

For deoxygenation, either yeast or N2 can be used. Yeast induces complete deoxygenation

since it consumes the oxygen. 3-5 grams per liter is adequate. Full oxygenation is obtained by

bubbling O2 into the blood model. NIR probe should be placed sufficiently far away from the

bubbling O2, as shown in Figure 3.36. Typical StO2 response measured by DOS is presented in

Figure 3.37. StO2 increased fairly fast when the oxygen was turned on and decreased slowly due

to yeast when the oxygen was off. Large downward arrows indicate the time when the blood was

added to the solution. A cycle of oxygen on and off was repeated at each blood titration. Around 0

% and 90% StO2 were achieved at each oxygen off and on period respectively. The last cycle StO2

90

was noisy since the addition of blood increased absorption significantly as to affect the signal-to-

noise of measurements.

Figure 3.36: Configuration for blood phantom measurement in semi-infinite geometry.

The type of blood (such as whole blood, red blood cells and so on), type of anti-coagulation

agent and expiration date can be found on the cover of the blood bag (from American Red Cross).

For research purposes, we get the blood cells which are not suitable for transfusion. The expiration

date is based on the transfusability. If possible, one needs to get the most recently expired blood.

The blood should be stored in the refrigerator at 1-6 oC. It is usually good up to one month. (Blood

cells can live up to 4 months. However, by the time we get the blood from American Red Cross,

it already consists with portion of dead cells. Live cells make up 10 % of total after 4 months.)

Sampling different sites of the blood bag is possible using sampling site coupler or 3-way stop

cock.

When handling blood, one should wear lab coat, safety glasses and gloves for possible spill or

splash. Also, one handling blood needs to get the Hepatitis shots in advance as well as to take the

training course.

When the experiment is over, dispose needles and pipet tips in the bio-hazard sharps container.

91

Figure 3.37: StO2 response with oxygen supply to blood phantom. StO2 increased fairly fast whenthe oxygen was turned on and decreased slowly due to yeast when the oxygen was off at eachblood titration stage. Large downward arrows indicate the time when the blood was added to thesolution.

Dispose other materials in a bio-hazard bag. The bio-hazard bags need to be autoclaved before

pick-up. Add bleach to the containers exposed to blood and blood model itself. Then drain through

the sink. At UPENN, the Principal Investigator should contact the building administrator to have

SMI (infectious waste hauler) come pick up bio-hazard materials. Also, he has to have an exposure

control plan.

3.8.2 Solid Phantoms : silicone

RTV 12 silicone product (GE Silicones) consists of two parts : RTV 12A (base compund) and

RTV 12C (Curing agent). RTV 12A is 80 % Polydimethylsiloxane, 10 % MQ Resin, Benzene

and Toluene. RTV 12C is 5 % Dibutyl Tin Oxide solution, 20 % Ethyl Silicate 40, 20 % Amino-

propyltriethoxysilane, 5 % 1,2,4-Trimethylbenzene and Naphtha (mineral spirits 60 %). It is quite

92

harmful. Especially one should avoid inhalation and contact with skin and eyes. It is also flamm-

bale with flash point at 32 oC.

The weight ratio of 20:1 of RTV 12A : RTV 12C is recommended by the manufacturer. How-

ever, increased 10:1 volume ratio is used for making silicone model to accelerate the curing rate.

The density of silicone is similar to water, so weight ratio approximates volume ratio. RTV 12

product makes a bit cloudy silicone when mixed. Other products like RTV 615 makes clear sili-

cone. RTV 12 was chosen because of the price being the lowest. Recommended curing time is 72

hours, but 24 hours are enough to pull it out of the mold.

As an absorbing agent, carbon black (Raven 5000 Ultra II, Columbian Chemistry Company) is

used. The mean particle size of the carbon black is around 8 nm. Titanium Dioxide (TiO2) is used

as a scattering agent. We used TiO2 from Sigma (T-8141) for most of the solid phantoms.

Silicone adheres to most of the plastic materials. Even if it does not adhere, sides in contact

with the container do not cure as fast as the exposed side to the air. Therefore we built several kinds

of mold that can be taken apart easily after the silicone is cured. Teflon tape (PTFE Teflon tape :

McMaster Carr) is applied on the surface of the mold to easily separate the silicone when cured.

The amount of absorbing and scattering agent to induce the desirable absorption and scattering

was determined empirically. 9 silicone phantoms of the same breast shape (Figure 3.26(c)) with

varying concentration of carbon black and TiO2 were constructed and measured with 1st generation

parallel-plate DOT instruments (frequency-domain). The absorption formula was extracted from

the linear relationship between phantoms under µa = 0.1 cm−1 as shown in Figure 3.38. However,

we did not get the linear relationship with variation of TiO2 amount and µ′s, so one should not

blindly believe the optical properties expected from the recipe. Unlike the liquid phantom, there

are many places the nonlinearity could arise and thus a lot more work is needed. It is provided as a

93

reference point to start and I recommend anyone using this recipe to measure the optical properties

of these tissue phantoms using independent means.

0 2 4 6 8 100

0.05

0.1

0.15

0.2

carbon black (mg)

abso

rptio

n co

effic

ient

(cm

−1)

Figure 3.38: Silicone (RTV-12) recipe : Carbon black amount vs µa

Recipe: Silicone

Initially, we have tried making the silicone phantom by mixing absorption and scattering agents

into RTV12A. Since RTV12A is too viscous, the agents settle down to the bottom of the cured

silicone. Then we tried mixing agents into RTV12C. This has resulted in homogeneous mixing.

One can calculate the amount of carbon black by

total carbon =µa + 0.0068

0.0203× total volume (ml)

1650 (ml).

The recipe is in a complicated form since it was derived from the fixed breast shape of 1650 ml.

Assuming we use 8 mg carbon in 10 ml solution, volume of carbon solution = total carbon×108 .

94

The amount of TiO2 for scattering is

total TiO2 = 3.6 (g)× µ′s7.5× total volume (ml)

1650 (ml).

Mix total TiO2 into 100 ml of RTV12C (using breast mold).

Example

Breast shape phantom with µa = 0.045 cm−1, µ′s = 7.5 cm−1, Volume = 1650 ml.

1. In 10 ml vial, put 10 ml of RTV12C (←(a)). In 100 ml container, put 100 ml of RTV12C

(←(b)).

2. Put 8 mg of carbon black into (a). In this case, ‘zeroing’ with (a) on a scale and add carbon

black directly into (a). Put 3.6 g of TiO2 into (b).

3. Vortex (a) and (b) for 30 seconds at full speed.

4. Ice bath sonicate (a) and (b) for 1 hour. Ice bath : put ice cube in the sonicator. (because

RTV 12C has very low flash point) Sonication helps breaking the aggregated particles down.

5. Meanwhile, measure 50 ml of RTV12C into a beaker and measure 1500 ml of RTV12A into

a mixing pale.

6. After the sonication, pour 3.2 ml of (a) and all of (b) into the beaker with RTV12C. Mix

well.

7. Pour the mixture of RTV12C into RTV12A. Mix really well. Using high speed mixer is not

recommendable since it traps a lot of air bubbles.

8. Pour into a mold. (pour almost up to the brim.)

95

9. Place the mold inside the descicator or bigger container connected to vacuum pump to pump

the air bubbles out.

10. Take the phantom out after one or two days.

* underlined quantities are to be calculated for different optical property using the formula.

* One needs to use glass bottles for RTV12C. It reacts with plastics.

96

Chapter 4

In vivo Diffuse Optical Tomography of

Breast

4.1 Introduction

The clinical DOT experiments and results on in vivo female breasts are presented in this chapter.

(The clinical motivation for spectroscopical imaging of breast cancer is described in Chapter 1.)

To familiarize the reader with clinical terminology of breast cancer cases, one section outlines

the breast tumor classification, diagnostic and treatment procedure. In the following section, we

quantified the optical properties of healthy in vivo breasts and their dependence on demographic

parameters to assess the inter-patient variation. A tumor contrast index was derived based on

three-dimensional DOT of breast with tumor and was compared with MRI and pathology. Then,

the treatment monitoring capability of DOT was explored for a patient going through neoadjuvant

chemotherapy with comparison to MRI. Lastly, the feasibility of optical blood flow measurements

97

for breast cancer diagnosis and detection was explored and its impact on oxygen metabolism esti-

mation of breast cancer is discussed.

4.2 Breast cancer: clinical side

4.2.1 Classification of breast disease

The classification and the description of breast disease in terms of pathology is summarized from

[164].

There are four categories in benign breast disease which may mimic carcinoma: inflammations,

fibrocystic changes, proliferative breast disease, and benign tumors. Inflammations of the breast

include acute mastitis, periductal mastitis, mammary duct ectasia, fat necrosis and granulomatous

mastitis. Inflammations are rather uncommon. Among these, acute mastitis happens mostly in the

lactating period. Fat necrosis is the liquification of fat and formation of mass related to trauma,

previous surgical intervention, or radiation therapy. Fibrocystic changes include cysts (abnormal

membrane sac containing semitranslucent, turbid fluid), fibrosis (scarring due to rupture of cysts

into the adjacent stroma) and adenosis (abnormal formation or enlargement of glandular tissue).

These changes mimic carcinoma by producing palpable lumps, mammographic densities of calci-

fications, or nipple discharge. Proliferative breast disease such as epithelial hyperplasia, sclerosing

adenosis, and small duct papillomas increase the risk of cancer. Fibroadenoma is a new growth

composed of both fibrous and glandular tissue, which is the most common benign breast tumor.

Fibroadenoma usually occurs in young women.

The malignant breast adenocarcinoma is divided into two groups: In situ (noninvasive) car-

cinoma and invasive (infiltrating) carcinoma. In situ carcinoma includes ductal carcinoma in situ

98

which is the most common type of noninvasive carcinoma and lobular carcinoma in situ. Inva-

sive carcinoma includes invasive ductal carcinoma which is the most common type in all breast

cancers, invasive lobular carcinoma, medulary carcinoma, mucinous (colloid) carcinoma, tubular

carcinoma and invasive papillary carcinoma. Other rare variants of malignant breast cancer are

sarcomas, lymphomas and inflammatory breast cancer.

The frequency of breast disease is represented in the following table composed of the patient

population seen in a surgical outpatient department.

No disease Fibrocystic changes Fibroadenoma miscellaneous benign Cancer30 % 40 % 7 % 13 % 10 %

Table 4.1: Frequency of breast disease from patient population seen in a surgical outpatient depart-ment [164]

4.2.2 Diagnostic procedures

Screening mammograms are conducted to separate normal from abnormal findings and identify pa-

tients who need further evaluation. When the abnormalities are detected, a diagnostic mammogram

is performed.

The tissue samples from the lesion are obtained for more definite diagnosis by histopathology.

Fine needle aspiration (FNA) is a sampling of cells for microscopic examination by cytopathologist

for indication for malignancy. Core biopsy takes out a small punched-out tissue using larger needle

than the one used in FNA. Sometimes core biopsy is guided by X-ray mammography, ultrasound,

or MRI. Excisional biopsy is aimed at removal of the abnormal tissue. Samples from biopsy are

frozen and examined by the pathologist for preliminary diagnosis. If a malignancy is found, further

immunoperoxidase analysis is performed to find out hormone receptor status.

99

4.2.3 Histology grades

A modified Scarff-Bloom-Richardson grading system gives scores ranging from 1 to 3 in three cat-

egories: tubule formation (% of carcinoma composed of tubular structures), nuclear pleomorphism,

and mitotic count. The “grade” is calculated by adding the scores. The survival rate decreases at

higher grades.

4.2.4 Imaging methods

Mammography is the most common diagnostic imaging modality using X-ray radiation. It is most

effective in detecting abnormalities in fatty tissue. It is not useful for women under the age of 40

due to the high glandularity of their breasts. Imaging views often used for screening mamography

are cranio-caudal (head-to-foot), sagittal and oblique (cranio-caudal view shifted to include axillary

tail) views.

Ultrasound is currently used as an adjuvant for X-ray mammography, particularly for mammo-

graphic findings inconsistent in different views, for lesions not seen on the X-ray mammography

or to differentiate cysts. It is a primary diagnostic tool for women under the age of 30. Clinical

ultrasound gives a two-dimensional image which is perpendicular to the plane where the transducer

is placed.

MRI is still considered a research modality due to expense and low throughput. It has high

sensitivity (true-positive rate), but low specificity (false-negative rate). It may be the most effective

modality for invasive lobular carcinoma which is difficult to detect in mammography, and for

women with breast implants. False-negative interpretations have been reported particularly for

DCIS, due to occasional lack of tumor angiogenesis and poor enhancement. Three-dimensional

MRI images can be seen in either sagittal, axial, or coronal views, depending on the application.

100

(The tomographic views are illustrated in Figure 4.25(a)).

4.2.5 Treatment of breast cancer

The treatment strategy varies depending on the grade and stage of the cancer. A localized car-

cinoma can be removed with local excision (lumpectomy), which is termed “breast conserving

surgery”. Depending on the extent of breast removal, there are different types of mastectomy. A

simple (total) mastectomy removes only the breast tissue. A modified radical mastectomy removes

the entire breast and axillary lymph nodes. A radical mastectomy refers to the removal of breast

tissue, axillary nodes, and chestwall muscle under breast.

Surgical procedures may be combined with adjuvant therapy such as hormonal therapy, chemother-

apy, and/or radiation therapy. In cases of locally advanced breast cancer, “neoadjuvant chemother-

apy” is performed prior to the surgery to reduce the tumor size and eradicate the cancer cells.

Radiation therapy uses ionizing radiation (X-rays and gamma rays) to affect cells by activation of

radiation-response genes, cell-cycle arrest and radiation-induced cell death. Chemotherapy uses

anti-cancer drugs to stop the growth or multiplication of cancer cells. Since these drugs work

most effectively on cells that divide rapidly, it kills cancer cells more effectively than normal cells.

However, cells in blood, mouth, intestinal tract, nose, nails, vagina and hair are also affected.

4.3 Quantification of Normal breast properties

The optical and physiological properties of 52 healthy breast tissue [81] are quantified using the

first generation parallel plate FD scanning instrument (Chapter 3, Section 3.6.1).

We modeled our parallel plate geometry as an infinite slab, bounded on one side by a glass win-

dow (the detector plane) and on the other side by a white plate (the source plane). Previously [83]

101

we have shown that the chest wall affects the acquired data by effectively extending the diffusive

medium above the tank; in practice this makes our infinite slab approximation even better. Special

care was taken during the data acquisition to center the source and the detector grid on the breast

tissue; however, occasionally some regions from outside the breast tissue were also in the field of

view. In such cases we ignored grid points near the boundaries in our analyses. The solution for an

infinite slab is obtained using image sources and is well known (Equation 2.8). For chromophore

analysis, we employ a multi-spectral approach that utilizes a priori spectral information to reduce

inter-parameter crosstalk [86].

We formulate the inversion problem in terms ofCHbO2,CHb,A and b using a multi-spectral ap-

proach. Thus we globally analyze the whole set of data, instead of analyzing each wavelength inde-

pendently and then combining the results. This approach substantially reduces the inter-parameter

cross-talk [86].

In the calculation we define and minimize χ2 =∑ |Φm − Φc|2 where Φm is the measured

fluence and Φc is the calculated fluence. The sum is over the source detector pairs and all wave-

lengths. We use the Nelder-Mead simplex (direct search) method implemented in MATLAB func-

tion “fminsearch” to fit for the unknowns by minimizing χ2. We then calculate blood saturation (=

StO2) and blood volume (=THC) from the relevant hemoglobin concentrations.

4.3.1 Optical Properties of Healthy Breast Tissue

In order to establish a range of optical and physiological properties for the healthy breast tissue,

we now look at histograms of the fitted properties. The results are summarized in Figure 4.1. The

values define the expected physiological range. Mean and standard deviation are shown in Table

4.2.

102

0.02 0.04 0.06 0.08 0.10

10

20

30

µa (cm−1)#

of

Vo

lun

teer

s

830786750

2 4 6 8 10 12 14 160

10

20

30

µs′ (cm−1)#

of

Vo

lun

teer

s

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

20

40

x100%# o

f V

olu

nte

ers

10 20 30 40 50 60 700

10

20

30

µ M# o

f V

olu

nte

ers

Blood Saturation

Blood Volume

Figure 4.1: Starting from top left shows µa, µ′s, blood saturation and blood volume histograms.

λ(nm) 750 786 830

µa(cm−1) 0.046 ± 0.024 0.041 ± 0.025 0.046 ± 0.027

µ′s(cm−1) 8.7 ± 2.2 8.5 ± 2.1 8.3 ± 2.0

B. Vol (µM ) 34 ± 9B. Sat. (%) 68 ± 8

Table 4.2: Average optical properties and physiological parameters from the histograms.

103

10 20 30 40 50 60 700

10

20

30

40

50

60

70

80

90

100

B. Volume (µ M)

B. S

atu

rati

on

(%

)

Figure 4.2: Blood saturation vs blood volume with the dashed lines indicating the ranges for normaltissue from the mean and standard deviation of the healthy breast tissue.

It might be expected that tumors and other diseased tissue are distinguished by the relative

value of their total hemoglobin concentration and blood oxygen saturation. For example, malignant

tumors might be expected to have high blood volume with a low oxygen saturation since both a

higher blood content and higher metabolism are necessary to achieve tumor growth in proliferating

tumor cells [255]. Figure 4.2 shows blood saturation plotted vs blood volume for each breast.

The dashed lines indicate the range of blood volume and blood saturation for normal breasts from

Table 4.2. The error bars for each individual are obtained by the standard deviation of repeated

measurements of the same breast. In order to use endogeneous contrast effectively in DOT, tumor

tissue properties should lie in one of the “other” regions defined on this plot.

The normal state of the tissue covers a wide range of optical properties and it could be expected

that the heterogeneity of the tissues would induce a similar variation within an individual. This

could reduce tumor contrast. The ability to recover all the available physiological information is

crucial in order to relate parameters such as the blood volume and blood saturation to increase

specificity. Ideally an imaging instrument should combine a large number of wavelengths with

104

0 10 20 30 0.9

1

1.1

Minutes

amp

/<am

p>

Breast

0 10 20 30 0.9

1

1.1

Minutesam

p/<

amp

> Intralipid

Figure 4.3: Normalized amplitude measured on breast and Intralipid sample by visiting same 17points ten times every two minutes.

abundant spatial information.

4.3.2 Physiological Noise

Apart from the well characterizable noise due to electronics, optics and positioning of the sources

and detectors, there is as additional noise in the measurements due to the changes in the physio-

logical state of the tissue during the measurements. Respiration, movement, heart beat, blood flow

downstream from the hanging breast are some factors that contribute to this “noise”.

In order to estimate the effect of physiological noise on our measurements, the scanning de-

tector was modified to visit the same point ten times every two minutes. This was repeated for

seventeen different points. The results are shown in Figure 4.3 where we plot time series of nor-

malized amplitude (phase not shown) obtained from measurements on an Intralipid sample and on

a breast tissue in vivo. We find that signals from the Intralipid sample are stable within 1 − 2%

whereas on the breast tissue the dispersion is up to 5− 10%. This provides us with an estimate of

the physiological noise in our experiments.

We also performed repeated measurements of the same breast with minimal movement of the

105

15 20 25 30 35 4010

20

30

40

50

B. V

olu

me

(µ M

)

BMI (kg/m2)15 20 25 30 35 400

20

40

60

80

100

B. S

atu

rati

on

(%

)

BMI (kg/m2)

Figure 4.4: Left: Blood Volume vs BMI with a decaying exponential fit (correlation coefficient0.42), Right: Blood Saturation (correlation coefficient 0.03) vs BMI

breast. By comparing repeated measurements, we find that the average standard deviation is 11%

for µa, 4% for µ′s, 4% for blood saturation and 5% for blood volume (see for example error bars in

Figure 4.2). These values are consistent with the variations in the amplitude and phase observed in

Figure 4.3.

4.3.3 Demographics and Optical Properties

As mentioned above, it might be expected that optical properties would show a variation with

demographics. Pogue et al [219, 220] used a similar system geared towards imaging and reported

that blood volume had a correlation with body mass index (BMI) which is related to the weight and

height of an individual. They did not report any strong correlation between any other quantities

and BMI or age. Cerussi et al [38,39] reported weak correlation between blood volume and b with

age (as well as some other quantities that are not available to us).

Our findings are shown in Figure 4.4 for correlations with BMI. We see a similar correlation

of blood volume to BMI as reported by Pogue et al [219, 220]. A higher BMI indicates more

tissue fat content. In compositional studies a higher fat content correlates with a lower blood

106

15 20 25 30 35 404

6

8

10

12

14

µ s ′ (cm

−1)

BMI (kg/m2)

Figure 4.5: µ′s at 830nm vs BMI with a decaying exponential fit. Other wavelengths show similartrends. The correlation coefficient is 0.46.

10 20 30 40 50 60 7010

20

30

40

50

age

B. v

olu

me

(µ M

)

10 20 30 40 50 60 700

20

40

60

80

100

age

B. S

atu

rati

on

(%

)

Figure 4.6: Left: Blood Volume vs age, Right: Blood Saturation vs age

content [75, 105, 163, 255, 279, 286]. The correlation coefficient is significanly higher for blood

volume than blood oxygen saturation (0.42 vs 0.03).

We also observed a similar correlation of BMI and µ′s as shown in Figure 4.5. Cerussi et

al [38, 39] showed that the scattering power and µ′s change with the fat content. BMI is also a

measure of the tissue fat content hence this result is in agreement with the their reasoning.

Figure 4.6 shows the correlation with age. Our results again indicate an agreement with Pogue

et al [249]; we do not see any clear correlations.

Our study had a different sensitivity than Cerussi et al who showed that there is considerable

107

change in breast properties with age. Their main result is that older breast tissue has a different

water and lipid content which effects the scattering and absorption properties of the tissue. Their

instrument was particularly sensitive to this aspect because it measured mainly the outer ∼1 cm of

the breast tissue and had many wavelengths which allowed accurate derivation of the wavelength

dependence of the scattering. Our results, by contrast, sample a larger tissue volume in transmis-

sion geometry and has a vast spatial information rather than spectral information. Therefore, we

sample the fatty tissue as well as the nodules and vasculature extensively. This is a weakness for

our measured properties in terms of correlating them with demographics, age and hormonal sta-

tus, however, it is imperative to establish these properties in our geometries since most imaging

systems rely on sampling a large volume of breast tissue. It has previously been reported that the

differences in the acquisition geometry changes the computed bulk properties in extensive studies

by Cubeddu et al [60, 61].

4.4 Breast Cancer Imaging

4.4.1 CCD Raw data

For three-dimensional reconstruction of optical and physiological parameters for breast cancer

patients, the second generation parallel-plate CCD-based hybrid instrument was utilized (Chapter

3, Section 3.6.2). The sequential nature of data acquisition produces a set of 2D continuous wave

CCD intensity maps. An example of a set of reference and in vivo breast raw data with a 786 nm

light source is shown in Figure 4.7. The two-dimensional CW intensity images taken with CCD

for three central sources of source plate (Figure 3.19(b)) is shown. There is a significant difference

in the source power between source positions and wavelengths due to non-uniform response of our

108

switch and fiber coupling. Each intensity image shown in Figure 4.7 is scaled by its own minimum

and maximum range. The absolute values between images are therefore not comparable.

The intensity images of the matching fluid in lower row of Figure 4.7 are characterized by its

concentric distribution of intensity with the maximum intensity occuring at the source position.

The intensity images of typical in vivo breast in upper row of Figure 4.7 show significant deviation

from concentric distribution observed from homogeneous matching fluid medium. This deviation

arises from the boundary effect between the breast and the matching fluid as well as the breast

heterogeneity (especially at the boundary where the breast is touching the detection glass).

source 23source 22 source 24

breast measurements

matching fluid measurements

16 cm

11 cm

Figure 4.7: Measured CW intensity images of breast (upper row) and matching fluid (lower row)at source position 22, 23, and 24 (three central sources in the middle row of source plane shown inFigure 3.19(b)).

109

A quick composite look at the attenuation level of the raw breast data with respect to the homo-

geneous reference data can be offered by constructing a transillumination picture. This approach

is inspired by the earlier transillumination works [16,35,108,131,178,183,209,225,247,272,275]

where widebeam or plane-wave illumination were used. We define the detected intensity at detec-

tion position, rd, due to source number, s, to be I(s, rd). We construct a two-dimensional tran-

sillumination picture by summing the contribution of all sources, and normalizing with reference

data I0(s, rd) summed over all the sources, i.e.

T (rd) = −log(

∑Nss I(s, rd)

∑Nss I0(s, rd)

)

. (4.1)

Transillumination may reveal the signal contrast due to the presence of the tumor (Figure 4.8(a),

compare with subject # 68 results in Figure 4.13), but most of time it shows sensitivity to the

presence of surface blood vessels near detector plane (Figure 4.8(b)). In the latter case, the transil-

lumination picture can aid in identifying image artifacts due to surface structures. Black ellipsoidal

lines show the ellipsoid-approximated breast boundaries; outer line is the largest extent of breast

and inner line is the breast touching the detection plane. The attenuation level is higher in breast

than in the matching fluid for T > 0 and vice versa. In Figure 4.8(a), the tumor is located in

middle inner quadrant of the right breast, which correponds to the high attenuating enhancement

in this view. Note the attenuation level is relatively low inside the breast and T ∼ 0 far outside

of the breast, since the region is occupied by the matching fluid. The effect of perturbation due to

presence of breast is seen outside of the breast boundary due to its diffusive nature (i.e. T 6= 0 at

the boundary). In Figure 4.8(b), the tumor is located in middle outer quadrant of the left breast,

which correponds to the left outer side of the breast outline. The nipple is shown at the middle

110

lower and the blood vessel nearby the detection plane is clearly seen, which was also observed in

an outline photograph.

−8 −4 0 4 8

−2

0

2

4

6

8−0.3

−0.2

−0.1

0

0.1

0.2

0.3

(a)

−8 −4 0 4 8

−2

0

2

4

60.2

0.4

0.6

0.8

1

1.2

(b)

Figure 4.8: Transillumination pictures of two breasts. Black ellipsoidal lines show the ellipsoid-approximated breast boundaries; outer line is the largest extent of breast and inner line is the breasttouching the detection plane. All dimensions are in centimeter.

4.4.2 3D DOT reconstruction method

Three-dimensional (3D) images are reconstructed from the data using the multi-spectral recon-

struction method with Envelope-guided spatially variant reconstruction described in Chapter 2,

Section 2.4.3.

Specifically, the geometric constraint is applied as following. We define the unknowns to be

CHb, CHbO2, CH2O, Clipid and A. We fix the b value according to bulk values obtained from the

frequency-domain measurements. Since our particular imaging geometry involves space occupied

by breast and matching fluid, image segmentation of breast and matching fluid was used through-

out the calculation. The breast region was approximated as a 3-dimensional half-ellipsoid based on

its outline in the photo taken prior to measurement scan. To assign background and initial values to

the two regions, the bulk optical properties of matching fluid were derived from frequency-domain

111

reference measurements made on the box when it was completely filled with matching fluid. The

breast optical properties were derived from frequency-domain measurements in contact with breast

surface. A homogeneous semi-infinite analytic solution of the frequency-domain diffusion equa-

tion with multi-spectral approach [81] was utilized to fit directly for the bulk CHb, CHbO2, CH2O,

A and b in each region. The scattering power, b, was allowed to take on different values in the breast

and matching fluid, respectively. Usually, µbackgrounda inside the breast was then fixed as combi-

nation of 31% water or bulk CH2O estimated from frequency-domain measurement and 57% lipid

absorption (from literature [163, 279, 286]). µbackgrounda for the matching fluid region was fixed

at the fitted bulk µa of the matching fluid. µbackgrounda inside the breast was then fixed as combi-

nation of 15 % water (estimated from frequency-domain measurement of bulk CH2O) and 57 %

lipid absorption (from literature [163, 279, 286]).For the initial guess, CHb, CHbO2and A were as-

signed to the breast and the matching fluid based on the bulk measurements, e.g. zero hemoglobin

concentration in the matching fluid region. After the reconstruction of CHb(r), CHbO2(r) and

A(r), 3D images of total hemoglobin concentration (THC(r) = CHb(r) + CHbO2(r)), blood oxy-

genation saturation (StO2(r) = CHbO2(r)/THC(r)) and scattering µ′s(r, λ) = = A(r)λ−b(r) were

constructed.

4.4.3 Image orientation of 3D DOT reconstruction

Figure 4.9 shows the orientation of the three-dimensional reconstructed DOT image. A series

of slices along the y axis are arranged from left to right, from the source plane to the detector

plane, respectively. Each slice represents a 16 × 11 cm image in x-z plane, with the caudal-

cranial view (i.e. from feet to head, same as the CCD camera view). The orientation of each

image is such that the left side of the image slice is lateral (towards outer side of breast) and

112

right side is medial (towards middle of the breasts) for the left breast, and vice versa for the right

breast. For convenience of presentation, slices at selected spatial intervals are presented. Since the

reconstructed data on FEM nodes is interpolated to regular grid of 0.2 cm spacing, each slice has

0.2 cm of pixel size in the x and z directions.

Figure 4.9: Orientation of three-dimensional reconstructed DOT images. Caudal-cranial slice s(foot to head) were arranged left to right, from source to detector plane. The left side of eachimage is lateral and right side is medial.

4.4.4 3D reconstruction images

Representative three-dimensional reconstructed images are shown for three malignant cancer cases

and one benign tumor case. For these cases, 31 % water and 57 % lipid concentration were assumed

and b distribution was fixed according to fitted value from FD measurement. We then reconstructed

CHbO2, CHb andA. The first malignant cancer case shows a cancer near nipple area and the second

malignant case shows a cancer far away from the nipple. The third malignant cancer case shows

two cancers, of which one was subject to core biopsy. In the benign fibroadenoma case, DOT did

not detect the mass in the quandrant where mass was present. For each case, summary of radiology

113

and histopathology report is presented to give information about the tumor. Radiologists who have

experiences in breast cancer MRI compared DOT and MRI and confirmed the position of lesion.

Subject #103: invasive ductal carcinoma (malignant)

Subject #103 was a 53 year old postmenopausal female with a 2 × 2 × 2 cm subareolar mass.

The cancer was located near nipple of the right breast as shown in Figure 4.10. The mammogram

measured a 1.5 cm mass, ultrasound measured the mass to be 1.1 × 1.3 × 1.8 cm, and MRI

measured it to be 2.2 × 2.1 cm. A representative sagittal MRI containing the nipple is shown

in right subfigure of Figure 4.10. (The enhancement near the chestwall was deemed to be DCIS,

but histology did not find DCIS.) The histopathology analysis after mastectomy revealed invasive

ductal carcinoma behind the nipple of 2 × 2 × 2 cm size and benign proliferative breast within the

axillary tail of 5 × 3.4 × 2 cm size.

Invasive Ductal Carcinoma

Benign Proliferative Breast Disease

5cm

Photo (caudal-cranial view)

medial lateral

Figure 4.10: Tumor location of subject #103 (near nipple). Left: location of tumor in frontal view,Center: location of tumor in caudal-cranial breast outline photograph by CCD, Right : sagittalMRI showing the enhancement of tumor due to high uptake of gadolinium.

Figure 4.11 shows the reconstructed DOT images of total hemoglobin concentration (THC),

blood oxygen saturation (StO2) and reduced scattering coefficient (µ′s) at 786 nm. There is an

enhancement of THC and µ′s near nipple area which correponds to radiologist-confirmed cancer

position. StO2 does not show any enhancement corresponding to the mass, but the StO2 value near

the nipple area is lower than near the chestwall.

114

Total hemoglobin concentration (µM)

28

56

invasive ductal carcinoma proliferative disease?

Blood oxygen saturation (%)

50

100

µs′ at 786nm (cm−1)

5

35

16 cm

11 cm

∆ y = 1 cm sourceplane

detectorplane

Figure 4.11: 3D reconstructed images of THC, StO2 and µ′s at 786nm of subject #103, right breastwith ductal carcinoma

Subject #68: Adenocarcinoma (malignant)

Subject #68 was a 41 year old premenopausal female with an adenocarcinoma in her right breast.

According to X-ray mammography, ultrasound and MRI, the cancer was 4 cm in size and located

in the middle inner quadrant (3 o’clock). In our CCD camera view, the cancer is located at the left

side of nipple near the chestwall as shown in Figure 4.12(b).

High THC and µ′s enhancement of∼2 cm size spans from y = 1 cm to 5 cm, corresponding to 3

o’clock position in Figure 4.13. There are slight shift between radiologist-confirmed mass position

and DOT-enhanced position. However, this could rise from the difference in the compression

scheme between the MRI and DOT as well as the variation in breast positioning.

Subject #111: Multiple invasive ductal carcinoma (malignant)

Subject #111 was a 59 year old female with invasive ductal carcinoma in her right breast. She had

115

(a) (b)

Figure 4.12: Tumor location of subject #68. (a) In frontal view, the tumor is located in middleinner quadrant about 3-4 o’clock of the right breast. (b) In caudal-cranial CCD view, it correpondsto the left side of the breast. All dimensions are in centimeter.

two masses at 2 o’clock (2.0 cm) and at 10 o’clock detected by X-ray mammography, ultrasound

and MRI. Ultrasound-guided core biopsy with 15 gauge needle on 10 o’clock mass was performed

8 days before optical measurement, which found invasive ductal carcinoma with high grade nuclei.

In the optical measurement, bruise due to recent core biopsy was observed in lower outer quadrant

of the right breast (Figure 4.14).

In THC and µ′s images (Figure 4.15), two distinct enhancements corresponding to 2 and 10

o’clock are observed. The extension of 10 o’clock enhancement through the middle sections in y

direction could be attributed to the bruise effect induced by core biopsy. An interesting distribution

of StO2 is noticeable where the biopsied area near the detection plane has much lower oxygen

saturation.

Subject #95: fibroadenoma (benign)

Subject #95 was a 34 year old premenopausal female with a fibroadenoma in her right breast. X-

ray mammography detected a mass at 9 o’clock, 4 cm from the nipple of size (0.6 × 1.2 × 2.0

cm) as shown in Figure 4.16. The histopathology analysis done after the lumpectomy found 1.5

116

Total hemoglobin concentration (µM)

6

13

Adenocarcinoma

Blood oxygen saturation (%)

50

100

µs′ at 786nm (cm−1)

5

25

Figure 4.13: 3D reconstructed images of THC, StO2 and µ′s at 786nm of subject #68, right breastwith adenocarcinoma

cm fibroadenoma.

The reconstructed images in Figure 4.17 do not show noticeable contrast near the mass. This

may be due to lack of vasculature around the fibroadenoma. However, some fibroadenoma may

develop a vasculature. We need to measure more benign cases to assess the feasibility of using

optical contrast to distinguish between benign and malignant cases. There is an image artifact

appearing near source plane, which warrants the improvement of reconstruction scheme in the

future.

4.4.5 Comparison between single and multi-spectral approach

Subject #69: invasive ductal carcinoma (malignant)

Subject #69 was a 56 year old postmenopausal female with invasive and in situ ductal carcinoma

in her left breast (Figure 4.18). X-ray mammography detected a mass behind the nipple of 1.5 cm

117

Figure 4.14: Tumor location of subject #111. (a) In frontal view, the tumors are located at 2 and 10o’clock of the right breast. (b) In caudal-cranial CCD view, 2 o’clock mass correponds to the leftside and 10 o’clock mass corresponds to the right side of the breast. The biopsied 10 o’clock massis associated with core-biopsy induced bruise extending through lower outer quadrant, as shown indark color in this outline photograph. All dimensions are in centimeter.

spiculated mass associated with pleomorphic calcifications (category 5). MRI also found spicu-

lated mass of 2 cm in size in the subareolar position. The histopathology analysis done after the

mastectomy reported firm 2.1 cm area with adjacent but separate area of 0.4 cm, which are invasive

and in situ ductal carcinoma with local lobular features.

For comparison between single-spectral and multi-spectral reconstruction approaches we re-

constructed CH2O as well as CHbO2, CHb and A for subject #69. (Descriptions of single-spectral

and multi-spectral approaches are in Chapter 2.) The contrast arising from the water concen-

tration has been observed by other groups and its physiological implication has been empha-

sized [140, 259]. Our previous analysis was concentrated in reconstructing CHbO2, CHb and A

due to limited number of wavelengths. However, it is important to consider the water concentra-

tion in the reconstruction and it is our future direction to increase light sources sensitive to water

region. For the existing data, the reconstruction of additional parameter CH2O was explored in the

context of comparing single-spectral and multi-spectral approaches. Lipid concentration was fixed

as 57%. The reconstructed images of THC, StO2, µ′s at 786nm and CHbO2using single-spectral

approach are presented in Figure 4.19 and those using multi-spectral approach are presented in

118

Total hemoglobin concentration (µM)

15

30

invasive ductal carcinoma biopsied carcinoma

Blood oxygen saturation (%)

50

100

µs′ at 786nm (cm−1)

5

30

sourceplane

detectorplane ∆ y = 1 cm

11 cm

16 cm

Figure 4.15: 3D reconstructed images of THC, StO2 and µ′s at 786nm of subject #111, right breastwith multiple ductal carcinomas.

Figure 4.20. In both cases, invasive ductal carcinoma is detected by the enhancement of THC and

µ′s. However, the reconstructed water concentration using the single-spectral approach show nega-

tive concentration, which was probably to compensate a false increase in THC. The multi-spectral

method provides a more robust water concentration within the physiological range.

4.4.6 Tumor contrast

In order to quantify tumor contrast, an average (p) and a standard deviation (σp) was calculated

THC, StO2, µ′s in each image. The tumor region was defined by p > p + 2 × σp, since values

greater than 2 × σp have a 95% chance to be different from the average with the assumption of a

gaussian distribution. For StO2, threshold of p < p−2×σp was considered based on tumor hypoxia

hypothesis; this did not yield any tumor region. Tumor regions estimated from THC and µ′s were

119

Figure 4.16: Tumor location of subject #95. (a) In frontal view, the tumor is located at 9 o’clockof the right breast. (b) In caudal-cranial CCD view, 9 o’clock mass correponds to the right side ofthe breast. All dimensions are in centimeter.

averaged to define the average tumor region. Relative THC (rTHC = THCtumor/THCnormal)

was calculated by averaging THC in the tumor region and outside the tumor region as defined

above. Relative µ′s (rµ′s) and relative StO2 (rStO2) were defined in the same way. rTHC error

bars were estimated based on standard deviation of THCtumor and THCnormal. Relative µ′s (rµ′s)

and relative StO2 (rStO2) error bars were defined in the same way. We define an optical index

(OI) which is a combination of the tumor contrast by OI = rTHC·rµ′srStO2

to explore the possibility

of maximizing optical contrast. The concept of the optical index was first introduced in our com-

munity by Tromberg group [40]. In other imaging modality, it is a common practice to devise an

index to maximize the contrast. Individual values of rTHC, rStO2, rµ′s and OI for breast cancer

images shown in previous section as examples are summarized in Table 4.3.

subject comment rTHC rStO2 rµ′s OI

68 tumor 1.26±0.11 1.03±0.04 2.01±0.44 2.45103 tumor 1.29±0.13 0.86±0.14 1.74±0.20 2.62111 tumor 1.44±0.14 1.06±0.05 1.83±0.30 2.48111 biopsied 1.44±0.17 1.03±0.07 2.81±0.54 4.11

Table 4.3: Tumor contrast rTHC, rStO2, rµ′s and Optical index OI for individual subjects arepresented.

120

Total hemoglobin concentration (µM)

18

36

Fibroadenoma O

Blood oxygen saturation (%)

50

100

µs′ at 786nm (cm−1)

5

15

Figure 4.17: 3D reconstructed images of THC, StO2 and µ′s at 786nm of subject #95, right breastwith fibroadenoma.

The tumor contrasts (rTHC, rµ′s, rStO2) from twenty-one subjects with carcinomas are plot-

ted in a bar graph in Figure 4.21. The standard errors for total of 22 carcinomas are shown as error

bars in Figure 4.21. Note that rStO2 is around 1 and does not vary much. Combined contrast

index OI is 2.63±0.29.

Using three-dimensional DOT, we observed high tumor contrast compared to adjacent normal

tissue for 21 subjects with breast carcinomas. High THC contrast of tumor has also been reported

by other groups [70, 140, 144, 145, 221, 222, 297, 300], and has been supported by histopathologic

analysis of microvessel density counts [222]. The scattering contrast is still illusive since no careful

comparable histopathologic analysis has not been done for scattering contrast and also due to the

absorption and scattering crosstalk issues. Nevertheless, the hypothesis that the increased number

of scattering organells due to proliferation of cells and the increased fibrosis would increase the

scattering support our finding. Some groups also see some scattering contrast [70], but not to

121

Figure 4.18: Tumor location of subject #69. (a) In frontal view, the tumor is located behind thenipple of the left breast. (b) In caudal-cranial CCD view, it correponds to slightly above the nipple.

the extent we found. Since our CW wavelengths were not optimal, we do expect the presence

of absorption-scattering crosstalk in our reconstructed data. The modification of instrument to

incorporate optimal wavelengths are currently underway.

In the next section, the dynamic changes in the DOT-derived physiological tumor contrast with

a treatment (neoadjuvant chemotherapy) will be presented.

4.5 Neoadjuvant Chemotherapy Monitoring

4.5.1 Introduction

Jakubowski et al [140] have recently demonstrated the capability of diffuse optical spectroscopy

(i.e. as opposed to diffuse optical imaging) for monitoring neoadjuvant chemotherapy in a breast

cancer patient. (The clinical motivation for neoadjuvant chemotherapy monitoring is described in

Chapter 1, Section 1.2.) This important paper introduced a new clinical application to the field.

However, quantification of breast cancer properties from spectroscopic data alone requires assump-

tions about tissues (e.g. homogeneous media, etc.) which reduce the fidelity of their results [26].

In addition, the remission measurement geometry used in their experiments is primarily useful for

palpable, near-surface tumors.

122

Total hemoglobin concentration (µM)

15

50

invasive ductal carcinoma

Blood oxygen saturation (%)

50

100

µs′ at 786nm (cm−1)

5

20

Water concentration (%)

−50

100

Negative water concentration

Figure 4.19: 3D reconstructed images of THC, StO2, µ′s at 786nm and CHbO2of subject #69, left

breast with invasive carcinoma using single-spectral method. Lipid concentration was fixed as 57%. Note the negative water concentration at the cancer site.

The potential of diffuse optical imaging as a chemotherapy monitoring tool has not yet been

explored. We present a case study which demonstrates the feasibility of this approach. We have

utilized a 4-wavelength near-infrared hybrid DOT instrument with continuous wave transmission

and frequency-domain remission detection for breast imaging [62]. Our subject had a locally

advanced invasive ductal carcinoma, and underwent 4 cycles of Adriamycin plus Cytoxan and 4

cycles of Taxotere prior to surgery. DCE-MRI were performed at 3 time points throughout the

therapy. After completion of Adriamycin cycles, we tracked the subject with DOT at 3 time points.

Three-dimensional DOT images of total hemoglobin concentration, oxygenation and scattering

123

Total hemoglobin concentration (µM)

17

26

invasive ductal carcinoma

Blood oxygen saturation (%)

50

100

µs′ at 786nm (cm−1)

5

20

Water concentration (%)

25

50

Figure 4.20: 3D reconstructed images of THC, StO2, µ′s at 786nm and CHbO2of subject #69, left

breast with invasive carcinoma using multi-spectral method. Lipid concentration was fixed as 57%.

were reconstructed. We found that tumor volume and total hemoglobin tumor-to-normal contrast

decreased over the course of neoadjuvant chemotherapy. Furthermore, tumor volume changes

measured by DOT showed good correlation with DCE-MRI measurements of the same subject.

4.5.2 Methods

4.5.2.1 Neoadjuvant chemotherapy & MRI protocol

A 35-year-old premenopausal Caucasian female underwent neoadjuvant chemotherapy for invasive

ductal carcinoma in her left breast at the Hospital of the University of Pennsylvania. The therapy

124

0

0.5

1

1.5

2

2.5

3

Tu

mo

r/N

orm

alrTHC rStO

2 rµ

s’ OI

Figure 4.21: Tumor contrast of 22 carcinomas. rTHC, rStO2 and rµ′s are the relative ratiobetween tumor and normal. OI is an optical index defined as rTHC·rµ′s

rStO2.

consisted of 4 cycles of doxorubicin (Adriamycin, 60 mg/m2) plus cyclophosphamide (Cytoxan,

600 mg/m2, regimen denoted as AC) followed by docetaxel (Taxotere, 100 mg/m2, regimen de-

noted as T ). Herein we will refer to the treatment as “AC” followed by “T ”. Each cycle was

taken at 3 week intervals. She participated in the MRI research study CALGB150007/150012 :

“Contrast Enhanced Breast MRI and Correlative Science Studies to Characterize Tumor Response

in Patients Undergoing Neoadjuvant Chemotherapy for Locally Advanced Breast Cancer (I-SPY)”

(PI: L. Esserman, MD, MBA). The timing diagram for chemotherapy and imaging measurements

(MRI and DOT) is provided in Figure 4.22.

DCE-MRI measurements were performed at the following time points: one week before chemother-

apy (pre-chemotherapy), week 12 following completion of AC, but prior to initiation of Taxotere

(T ) therapy, and week 23 following the completion of Taxotere therapy, but prior to surgical tu-

mor removal (mastectomy). MRI of the breast was performed at 1.5T (General Electric, Signa,

Milwaukee, WI) using in-house sagittal compression receiver coils [135]. At each time point,

the DCE-MRI measurement consisted of sagittal high-resolution thin section three-dimensional

125

-0 3 6 9 12 15 18 21 24

Chemotherapy

Adriamycin+Cytoxan TaxotereSurgery

weeksImaging

MRI DOT

Figure 4.22: Neoadjuvant chemotherapy timing diagram. Four cycles of AC (Adriamycine +Cytoxan) therapy were followed by four cycles of Taxotere therapy, and then by a mastectomy.Arrows indicate timing of MRI and DOT measurements.

T1-weighted spoiled gradient echo imaging of the affected breast performed before, and twice

following, bolus intravenous administration of 0.1 mmol/kg gadolinium diamide (Omniscan c©,

Nycomed, Princeton , NJ).

The patient underwent simple mastectomy following the 8th chemotherapy cycle. The surgical

sample was inspected grossly and margins were inked in a standard fashion. The sample was then

oriented anatomically, and sagittally sectioned to correspond to the MRI imaging plane. Gross

inspection revealed an indurated area of abnormal, firm tissue in the superior breast measuring 1.5

cm in anterior-posterior dimension. This area was evaluated histologically with Hematoxylin and

Eosin staining.

4.5.2.2 DOT protocol

DOT instrumentation used for measurements is described in Chapter 3, Section 3.6.2. Before each

DOT measurement, informed consent was obtained from the patient in accordance with University

of Pennsylvania Institutional Review Board. Based on the tumor location identified by palpation

(Figure 4.23(a)), the breast position with respect to the viewing window was optimized (Figure

126

4.23(b)). Then a soft compression was applied to hold the breast in a stable position. The com-

pression distance was fixed at 7.5 cm. A snapshot of the breast outline was taken by the CCD

camera before filling the box with the matching fluid (Figure 4.23(b)). After filling, the diffuse

optical image scan was conducted for 12 minutes. After human subject measurements, reference

optical measurements were performed on the box filled completely with matching fluid. For the

reference measurements, a silicone (RTV12 with carbon black and TiO2) block was placed on top

of the box to extend the diffuse medium in a manner analogous to the subject’s chestwall, and

thus avoid signal saturation due to the air boundary. DOT measurements were performed at 10,

14, and 19 weeks after the first AC cycle (see Figure 4.22). These time points correspond to after

the fourth AC (4th chemotherapy), the first Taxotere (5th chemotherapy), and the third Taxotere

chemotherapy cycles (7th chemotherapy), respectively.

(a)

5 cm

2 cm

11 cm

16 cm

(b)

Figure 4.23: Tumor location. (a) According to X-ray mammogram, ultrasound and MRI, theprimary tumor was located at the 12 o’clock position in the left breast. (b) Photo of breast outline incaudal-cranial view (feet to head view). The location of the tumor was approximated by palpationprior to DOT measurement and is indicated by a circle.

127

4.5.2.3 MRI Data Analysis

Tumor measurements by MRI were performed through analysis of enhancing tumor pixels. Sub-

traction imaging (post-gadolinium minus pre-gadolinium) was employed as required. Maximum

intensity projections in the sagittal and axial planes were obtained to facilitate accurate tumor mea-

surement in three orthogonal dimensions. A radiologist with breast MRI experience measured the

tumor in three orthogonal planes. Tumor volume was then computed assuming an ellipsoid shape.

4.5.2.4 DOT Transillumination

The transillumination pictures of breast at different chemotherapy time points are presented in

Figure 4.24. The transillumination picture offers a quick composite look at the attenuation level of

the raw breast data with respect to the reference data as described in Section 4.4.1. It also enabled

us to identify surface features which may correlate with image artifacts.

After 4th Chemotherapy

After 5th Chemotherapy

After 7th Chemotherapy

Transillumination at 830 nm

16 cm

11 cm

Figure 4.24: Transillumination of breast at 830 nm normalized with respect to reference measure-ment, offering a composite view of attenuation level.

128

4.5.2.5 DOT Data Analysis: 3D Reconstruction

The details of the data analysis scheme is described in previous Section 4.4.2. The reconstruction

volume was a 16 cm× 7.5 cm× 16 cm region, extending into the chestwall area. In this volume, a

finite element mesh with 58087 nodes was used by the finite element method based forward solver

to calculate Φc. Φm was constructed by sampling and smoothing the CCD data on a 41 × 24

grid (total 984 detection points, Figure 3.19(b)) with 3 mm spacing for each source. Hemoglobin

concentrations CHb(r), CHbO2(r), and the scattering prefactor A(r) were chosen as unknowns to

be reconstructed while other variables such as water concentration, CH2O(r) and lipid concentra-

tion, Clipid(r) and scattering power, b(r) were fixed as described below. For image segmentaion

using a geometric constraint, the breast region was approximated as 3D ellipsoid based on Figure

4.23(b). µbackgrounda inside the breast was then fixed as a combination of 15% water (estimated

from frequency-domain measurement of bulk CH2O) and 57% lipid absorption. µbackgrounda for

the matching fluid region was fixed at the fitted bulk µa of the matching fluid. The unknowns to be

reconstructed were CHb, CHbO2and A. After the reconstruction of unknowns at each voxel r, 3D

images of THC(r), StO2(r) and µ′s(r) at 786 nm were constructed.

4.5.2.6 Image correlation analysis between MRI and DOT

As shown in Figure 4.25(a), there are three standard orientation of views in tomography. Since

the compression schemes of MRI (sagittal) and DOT (axial) are different, a true one-to-one image

comparison without distortion is not possible.

In order to compare the tumor positions obtained by MRI with those obtained by DOT, one

must derive a transformation relating coordinates in the MRI axial image to coordinates in the DOT

axial image. We developed a simple scaling transformation for this purpose, which by its nature

129

Coronal

Sagittal

Axial

x

yz

(a)

YMRI

ZMRI

rMRItumor

YDOT

ZDOT

rDOTtumor

Sagittal view

max

max

max

max

(b)

Figure 4.25: (a) Orientation of MRI view. (b) A sagittal view of MRI (top) and DOT (bottom)showing differences in compression. A linear scaling transformation scheme was utilized to findthe tumor center with respect to the nipple in DOT image (rtumorDOT ) from MRI rtumorMRI .

cannot account for all of the deformations arising from breast compression in orthogonal directions.

The schematic of the transformation is illustrated in Figure 4.25(b). First, the breast dimensions

of corresponding ‘central’ image slices (i.e. slices containing the nipple) were compared. We

derived linear scale factors from the ratio of breast length and breast width in these corresponding

central slices. In particular we defined scale factors α = XmaxDOT /X

maxMRI , β = Y max

DOT /YmaxMRI , and

γ = ZmaxDOT /ZmaxMRI , where Xmax

i , Y maxi , Zmaxi is the longest linear dimension of the breast in the

X , Y , Z direction of the ith (MRI or DOT) image.

130

We located the tumor center and tumor boundaries in the MRI image by finding the region with

high intensity due to large gadolinium uptake. We then rescaled the tumor center coordinate rtumorMRI

to rtumorDOT by multiplying by scaling factors (i.e. α, β and γ). The tumor boundaries are defined

in this rescaled fashion as well. Importantly, the tumor in the DOT image lies approximately

within the volume defined by the rescaling based on pre-chemotherapy MRI. We note this scaling

approach assumes linear deformation and does not account for elastic differences between tumor

and surrounding tissue. Future models will be developed to account for elastic variations and

deformation due to the different compression schemes.

4.5.2.7 DOT tumor volume estimation

To define a tumor volume in the DOT images, a threshold based on the standard deviations of the

reconstructed parameters was introduced. First, DOT parameters were decomposed into µa and µ′s

at 690, 750, 786 and 830 nm. Then for each image (THC, StO2, CHb, CHbO2, and µa, µ′s at the

4 wavelengths) an average (p) and a standard deviation (σp) was calculated. The tumor region was

defined by p > p+2×σp, since values greater than 2×σp have a 95% chance to be different from

the average with the assumption of a gaussian distribution. The average tumor volume (and stan-

dard deviation) was calculated by averaging all tumor regions defined by all images except StO2

(where the variation did not exceed 2 × σp). Relative THC (rTHC = THCtumor/THCnormal)

was calculated by averaging THC in the average tumor region and outside the tumor region as

defined above. rTHC error bars were estimated based on standard deviation of THCtumor and

THCnormal.

131

4.5.3 Results

According to the X-ray mammography, ultrasound, and MRI, the primary cancer was located at the

12 o’clock position in the left breast as shown in Figure 4.23. The mammography and ultrasound

reported adjacent multiple masses, the largest being 2.1× 2.2× 2.1 cm in size at pre-chemotherapy

time points. Pre-chemotherapy DCE-MRI measured the tumor size to be 5.3 × 2.2 × 2.7 cm.

MRI has been shown to be more accurate in depicting the size and overall extent of tumor than

mammography or ultrasound [30, 92, 186]. Tumor size estimation by DCE-MRI at different time

points is summarized in Table 4.4. The approximate tumor location in prone position assessed by

palpation was ∼ 8.5 cm from the nipple along the breast contour. In our camera view (caudal-

cranial view), this tumor location corresponds to a distant upper central position from the nipple as

shown in Figure 4.23(b).

Time Tumor size Tumor volumepre-chemotherapy 5.3 × 2.2 × 2.7 cm 16.5 cm3

after completion of AC cycles 3.8 × 1.4 × 1.8 cm 5.0 cm3

after completion of T cycles 3.0 × 1.6 × 1.3 cm 3.3 cm3

Table 4.4: Tumor size measured with DCE-MRI at different time points during neoadjuvantchemotherapy (AC : Adriamycin + Cytoxan, T : Taxotere). Tumor volume was estimated byassuming ellipsoidal tumor shape.

The transillumination images in Figure 4.24 show high signal attenuation at the surface blood

vessel and around the upper central region particularly for data taken after the 4th chemotherapy

cycle. This surface blood vessel was first identified through observation while positioning and was

confirmed with DCE-MRI images. The transillumination picture is quite sensitive to such surface

features.

Three-dimensional DOT images of total hemoglobin concentration (THC), reduced scattering

132

coefficient (µ′s) at 786 nm and blood oxygen saturation (StO2) are presented in Figures 4.26, 4.27,

4.28 respectively. In each figure, images from left to right correspond to 3D DOT image slices

taken from source to detector planes. The DOT images corresponding to different time points

within the chemotherapy cycle, are arranged from top to bottom. Colorbar scales are fixed from 5

to 15 cm−1 for µ′s at 786 nm, and from 50 to 100% for StO2. However, colorbar scales for THC are

not fixed and are adjusted at each time point to maximize the THC color contrast between tumor

and normal region. The THC scale was adjusted so its maximum value was twice its minimum

value; this preserves the percentile changes in the colorbar.

In the THC images (Figure 4.26) after the 4th chemotherapy cycle, a high THC region is

found in slices near the source plane (1 - 3 cm deep from surface) and near the upper central

part of the breast. The lesion position corresponds to the tumor location estimated initially by

palpation at 12 o’clock and 8.5 cm away from nipple (as shown in Figure 4.23). After the 5th

chemotherapy cycle, the tumor region is still identified by THC contrast near the source plane and

in the upper central region. However, the contrasted region appears smaller than the corresponding

region after the 4th chemotherapy cycle. Also, the average THC decreased significantly (i.e. from

21.4 ± 1.4 µM to 9.1 ± 0.5 µM). The THC distribution after the 7th chemotherapy cycle is more

homogeneous throughout the slices compared to previous chemotherapy cycles. Within the original

tumor margins, the high THC region shifts towards outside of the tumor, leaving a relatively low

THC region occupying most of the tumor extent. The average THC increased slightly between 5th

and 7th chemotherapy from 9.1 ± 0.5 µM to 12.5 ± 0.6 µM.

Figure 4.27 exhibits a similar trend. It shows higher µ′s values in the tumor region, and this

region with high µ′s shrinks over the course of treatment. The µ′s range does not vary as dramati-

cally as the THC, and gives a higher contrast ratio between tumor and normal tissue. Slices near

133

15

30After 4th Chemotherapy Total Hemoglobin Concentration ( µM )

Invasive Ductal Carcinoma

6

12After 5th Chemotherapy Total Hemoglobin Concentration ( µM ) x

z

8

16After 7th Chemotherapy Total Hemoglobin Concentration ( µM )

16 cm

11 cm

∆ y = 1 cm

source plane(head)

detector plane(feet)

Figure 4.26: Three-dimensional reconstructed total hemoglobin concentration images. Imageslices from source to detection plane are presented at 1 cm intervals in caudal-cranial view, fromleft to right. DOT images corresponding to after 4th, 5th and 7th chemotherapy were arrangedfrom top to bottom.

the detection plane are affected by artifacts related to large vessels. These artifacts bear close re-

semblance to the transillumination picture in Figure 4.24, which is sensitive to large blood vessels

on the surface near the detection plane. This effect is also apparent in the THC images, but to a

much lesser degree. Therefore, slices near the detection plane (i.e. within 1 cm) were excluded in

calculations of average values of THC, StO2 and µ′s.

StO2 images in Figure 4.28 were relatively homogeneous and do not show contrast in the tumor

region (i.e. not exceeding 2 × σp). Note, however, the overall StO2 value decreased significantly

after the 5th chemotherapy cycle and remained constant thereafter (i.e. from 81.2 ± 1.4% to 59.9

± 0.6% to 61.1 ± 1.0%).

MRI images projected in sagittal and axial views are shown in Figure 4.29 for the pre-chemotherapy

point, after AC therapy (week 12) and after Taxotere therapy (week 23). The intensity ranges were

134

5

15After 4th Chemotherapy µs’ at 786 nm (cm−1)

5

15After 5th Chemotherapy µs’ at 786 nm (cm−1)

5

15After 7th Chemotherapy µs’ at 786 nm (cm−1)

sourceplane(head)

detectorplane(feet)

Figure 4.27: Three-dimensional reconstructed images of µ′s at 786 nm. Image slices from sourceto detection plane are presented at 1 cm intervals in caudal-cranial view, from left to right. DOTimages corresponding to after 4th, 5th and 7th chemotherapy were arranged from top to bottom.

fixed among images at different time points. The intensity of the DCE-MRI image is higher in the

tumor due to increased tumor vascularity and gadolinium contrast uptake. Before chemotherapy,

the tumor is clearly seen around 12 o’clock to 1 o’clock (upper quadrant in sagittal view, near center

in axial view). After completion of chemotherapy cycles, the size and intensity of the enhancing re-

gion decreased significantly. Upon completion of chemotherapy, MRI demonstrated an amorphous

5 - 6 cm non-enhancing soft tissue region with only a scattered punctate form of enhancement. The

majority of the visible mass at this time point was poorly enhancing and was deemed to represent

fibrosis. The tumor position and volume measured by DCE-MRI is summarized in Table 4.4.

Histology revealed extensive fibrosis with focal areas of inflammation, but with few vessels.

However, viable tumor cells, morphologically identical the original core biopsy specimen (obtained

prior to chemotherapy) were identified. They were diffusely scattered throughout the fibrotic region

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50

100After 4th Chemotherapy Blood Oxygen Saturation (%)

50

100After 5th Chemotherapy Blood Oxygen Saturation (%)

50

100After 7th Chemotherapy Blood Oxygen Saturation (%)

sourceplane(head)

detectorplane(feet)

Figure 4.28: Three-dimensional reconstructed blood oxygen saturation images. Image slices fromsource to detection plane are presented at 1 cm intervals in caudal-cranial view, from left to right.DOT images corresponding to after 4th, 5th and 7th chemotherapy were arranged from top tobottom.

as individual cells and small groups. No macroscopical viable tumor mass was identified.

In both MRI and DOT, the tumor was found in 12 o’clock, many centimeters away from the

nipple. In an attempt to assess the correlation between MRI and DOT images, the simple scaling

transformation scheme described earlier was performed with the assumption that nipple and tumor

center are good common reference points. The DOT axial image slice corresponding to rescaled

tumor center, rtumorDOT (with respect to nipple position), is shown along with the corresponding MRI

axial image slice in Figure 4.30(a). The tumor center found in MRI (X) and DOT (square) agrees

well with employment of this transformation. To show the extent of the tumor in detail, the axial

DOT images with smaller y intervals (0.4 cm) are shown in Figure 4.30(b). Higher THC contrast

in DOT are distributed in three-dimensions approximately within the tumor margins defined from

the scaled MRI data.

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Sagittal view Axial view

Pre-chemotherapy

After completion ofAC cycles

x

zz

y

7.5 cm

9 cm

7.5 cm

18 cm

After completion ofTaxotere cycles

Figure 4.29: Dynamic-contrast enhanced MRI images of left breast. From top to bottom, rep-resentative sagittal and axial slices along highest tumor contrast are shown for each time point :pre-chemotherapy, after completion of AC cycles, and after completion of Taxotere cycles.

The tumor volume was defined independently for MRI and DOT. MRI tumor volume was de-

termined by a radiologist, whereas DOT tumor volume was determined by thresholding from the

distribution of DOT parameters. Figure 4.31(a) shows the decrease of tumor volume with progres-

sion of chemotherapy. MRI results show the tumor size decreased significantly after completion

of AC cycles. There is a general trend of decreasing tumor volume in MRI and DOT respectively.

The degree of change is different between MRI and DOT, but direct comparison is not possible

because the measurement time-point mismatch. The coinciding time-point is just after the 4th

137

YMRI

ZMRI

rMRItumor

YDOT

ZDOT

rDOTtumor

x

Z MRI

MRIX

DOTX

ZDOT

max

max

max

max max

max

max

max

(a)

15

30After 4th Chemotherapy cycle Total Hemoglobin Concentration ( µM )

∆ y = 0.4 cm Sourceplane (y=0)

y=3.2 cm

(b)

Figure 4.30: Correlation of tumor position in three-dimensions. (a) Tumor center position fromMRI image (a X in the axial slice) is transformed by a linear scaling scheme to the DOT coordinates(a square in the corresponding DOT axial slice). The scaled tumor center (a square) lies within ahigh total hemoglobin concentration region. (b) The scaled tumor boundaries around the tumorcenter is superimposed in three-dimensional DOT images. Axial images shown with smaller yintervals (0.4 cm) show the extent of the tumor in detail.

chemotherapy cycle (completion of AC), where tumor volume measured by DOT is greater than

tumor volume measured by MRI. We note that DOT tumor volume can be overestimated due to

the ill-posed nature of DOT, which introduces blurring [62]. In DOT, there was a significant tumor

volume decrease in each chemotherapy cycle accompanied by rTHC decrease in Figure 4.31(b).

Significant decreases of rTHC were observed after the 5th chemotherapy cycle, which is the first

Taxotere chemotherapy. The rTHC after 5th and 7th chemotherapy cycles are equivalent, but

138

accompanied with significant tumor volume decrease, implying tumor neo-vasculature regression

with chemotherapy.

0 3 6 9 12 15 18 21 240

5

10

15

20

25

30

35V

olum

e (c

m3 )

Weeks after 1st Chemotherapy Cycle

Tumor Volume

MRIDOT

1st 2nd 3rd 4th 5th 6th 7th 8th chemotherapy

DOT 0.21 ± 0.10 cm3

AC cycles T cycles

(a)

0 3 6 9 12 15 18 21 241

1.1

1.2

1.3

1.4

Weeks after 1st Chemotherapy Cycle

THCtumor

/THCnormal

DOT

rTH

C

(b)

Figure 4.31: (a) Decrease of tumor volume quantified by DOT and MRI, (b) Change of rTHC inthe tumor volume. Significant decrease in rTHC is noted before and after the 5th chemotherapy.

139

4.5.4 Discussion

We have demonstrated three-dimensional DOT images of total hemoglobin concentration (THC),

tissue blood oxygenation (StO2), and scattering coefficient are useful for localizing, quantifying

and tracking breast cancer based on vascularity during neoadjuvant chemotherapy. THC and scat-

tering showed localized contrast between the cancer and the normal region. The THC increase in

tumor is expected due to angiogenesis accompanying tumor growth [255]. The enhancement of

scattering might be expected based on changes in nuclear size and on the increase in concentration

of organelles such as mitochondria due to the high metabolism in cancer cells [255]. Generally,

StO2 might have been expected to be lower in the tumor region due to high oxygen demand, how-

ever this effect was not apparent.

The localized changes of these physiological parameters over time clearly demonstrate the

dynamic imaging capability of the DOT method. The DOT measurements were carried out at time

points just after completion of AC (Adriamycin+Cytoxan) cycles and then just after the first and

third Taxotere cycles. The anti-vascular and apoptotic effects of taxane [104] are consistent with

the significant decrease in tumor vasculature as measured in the tumor THC contrast, the tumor

volume decrease, and the intensity decrease from DCE-MRI. Interestingly, the variations in average

THC appear to be qualitatively correlated with measurements of patient hematocrit over the same

time period, which varied from 38% to 33% to 36%. The trends observed by DOT and MRI are

consistent with pathologic findings about the effectiveness of chemotherapy. The carcinoma cells

in the post-chemotherapy stage were finely and diffusely dispersed in fibrous connective tissue

which represented the bulk of the residual mass. This remaining viable tumor was detected by MRI

as focal enhancements and by DOT as small but positive THC contrast. Even though there was

no significant spatial contrast in StO2 for this subject, a significant decrease of average StO2 was

140

observed over time; this type of information might also be useful for chemotherapy monitoring,

since tumor response can depend on the oxygenation of the tumor and surrounding tissues [265,

266].

Jakubowski et al [140] reported THC and H2O as major contrast factors, but did not report the

behavior of scattering. In our case, water concentration was estimated by the frequency-domain

measurements and was then fixed for continuous-wave image reconstruction. In addition to fix-

ing the water and lipid concentration, we have tried fitting for the water concentration, but the

reconstructed water concentration did not change much from its initial value. This may be because

our measurements used only 4 wavelengths (< 900nm), all of which were outside of the water-

sensitive range. As for the scattering contrast, it is possible that some portion of this signal may

arise from absorption-scatter image cross-talk, since the wavelengths used to discern chromophores

and scattering were not optimized [58]. The scattering artifact near the detection plane resembled

the blood vessel in transillumination, and thus raises concerns about scattering-absorption cross-

talk. However, our 3D simulations with noise in the same geometry find less than 20% cross-talk

between THC and scattering, whereas the observed scattering contrast (averaged over tumor vol-

ume) amounts for more than a 60% increase over the normal tissues. We therefore suspect that the

observed scattering contrast may indeed originate, at least partially, from tumor physiology.

To improve quantification of tumor optical contrast and validate the DOT method in clinical

settings, several improvements are underway. Laser sources at optimal wavelengths for separation

of chromophore contributions including water and scattering should further improve quantification

accuracy. Currently, the imperfect tumor region correlation between MRI and DOT data arises

because the linear approximations we have made for rescaling image do not account for the shift

141

of tumor due to compression and deformation of the breast. Better modeling of the elastic defor-

mation of breast in different compression geometries is under investigation. For better correlation

between DOT and MRI, it would be ideal to synchronize measurement time and employ the same

compression schemes. In this present study, it was not possible to synchronize DOT and MRI

due to logistics of two separate research protocols and the constraints of patient availability. The

improved coordination of DOT and MRI is now being performed for neoadjuvant chemotherapy

patients. The measurement of additional pathologic parameters such as microvessel density or nu-

clei size will be invaluable in correlating with tumor vasculature and scattering factors and thus

confirming DOT findings; these parameters are not routinely measured in the clinic. Finally, with

respect to monitoring, more frequent DOT measurements should improve the therapeutic value of

this technique.

4.5.5 Conclusion

We have demonstrated 3D diffuse optical tomography for monitoring physiological tumor re-

sponses during neoadjuvant chemotherapy in a single patient with a locally advanced breast cancer.

We have also compared our results to dynamic contrast enhanced magnetic resonance imaging and

pathologic analysis of the same patient. Three-dimensional reconstructed total hemoglobin con-

centration and scattering images successfully localized tumors and quantified the tumor volume

decrease and the THC contrast decrease over the course of chemotherapy. These physiological

parameters, measurable by DOT, may help to improve our understanding of chemotherapy mech-

anisms, and hold potential to play a role in assessment of treatment response.

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4.6 Optical measurement of Blood flow in breast cancer

Until now, blood flow has been a quantity that is inaccessible to deep tissue optical methods. Our

laboratory has pioneered the development of diffuse correlation spectroscopy (DCS) for measure-

ment of blood flow in deep tissues (for a recent review see Durduran [80]) carrying out extensive

validation and demonstrating its utility. In the following, we explore the blood flow contrast of

breast tumors following an approach to DOS advanced by Tromberg’s group [139,140] which uses

hand-held spectroscopic probes. They have demonstrated its utility in measuring both the static

tumor contrast as well as changes in contrast due to chemo-therapy, hormonal status and age. Such

hand-held probes are attractive since they allow development of portable instruments and therefore,

frequent measurements with little patient disconfort. Our approach in this work is similar and uses

a hand-held probe that is scanned over the normal tissue and the palpable tumor regions, except we

measure blood flow.

Blood flow in breast cancer is an important quantity to monitor which also provides a novel

contrast over methods that measure essentially tumor morphology. Some amount of differentiation

capability was demonstrated between malignant and benign tumors [170] as well as the ability to

monitor various therapies [71, 79, 172]. Therefore, we expect that diffuse correlation spectroscopy

to be of value since the instruments are inexpensive, portable and the signals are robust. It is further

known that the metabolic changes can preceed dimensionally measurable changes [31] which have

been accessible to traditional imaging or clinical palpation methods. DCS can also be readily

combined with DOS measuring oxygenation and therefore, calculating the oxygen metabolism of

the tumors making this parameter more accessible.

There have been previous attempts to measure blood flow in the breast using PET [17,283,284],

color and power doppler ultrasound [59,149,170] and MRI [71]. PET studies were limited in extent

143

but have shown that blood flow tends to increase in malignant tumors. Ultrasound techniques

on the other hand were used from late 80s to end of 90s and have been inconclusive as to the

clincial utility of the technique. PET was limited because of its cost and availability, whereas

ultrasound techniques had poor signal-to-noise and low contrast. Ultrasound techniques are also

biased towards large vessels and therefore to issues such as arterio-venous shunting. MRI studies

require research instrumentation and are limited by their signal-to-noise.

In this investigation, we have recruited three subjects with palpable tumors, two subjects with

mammographically identified calcification and two healthy subjects. The measurements were car-

ried at Hospital of University of Pennsylvania and were approved by the Internal Review Board.

Briefly, subjects were asked to lay back in the supine position, thus flattening the breast and in-

creasing tumor accesibility. An experienced researcher marked the position and the extent of the

tumor on a transparency paper with a grid for the record of tumor position. Then she used the

hand-held probe shown in Figure 4.32 to scan in horizontal and vertical directions in 2 cm incre-

ments across the tumor. Two scan directions were used to check the repeability of the signal and

ensure that variations were not due to changes in the probe pressure. In the case of healthy volun-

teers, an arbitrary region was drawn as the tumor site and a measurement was obtained by scanning

across that region. This measurement provided information about heterogeneity of blood flow in

breast tissue. Average optical properties necessary for analysis were obtained from separate DOS

measurements of same patients as explained elsewhere [49].

Details of the instrument are described elsewhere [80]. Briefly, a long coherence laser (Crysta

Laser, NV) operating in continous wave mode at 785nm is coupled to a 1×4 optical switch (Di-

con, CA) and used to serially switch between four source positions. Four fast, photon-counting

avalanche photodiodes (Perkin Elmer, Canada) coupled to four single mode fibers were used to

144

2.5 cm

Hand-heldProbe

DCS Dets.Sources

Tumor

Figure 4.32: Hand-held probe with four source-detector pairs is scanned horizontally and verticallyin 2 cm increments spanning the estimated tumor region as well as the surrounding healthy tissue.

detect the intensity fluctuations of the surface speckles. The TTL output is fed to a four-channel

custom build correlator board (Correlator.Com, NJ) and the resulting intensity auto-correlation

functions are recorded by a computer. A complete set of data is acquired every 6 seconds and five

such sets are acquired at each position. For this study, we disregard the crossed source-detector

pairs and record the position of each of the four source-detector positions directly across from each

other (separation of 2.5 cm) from each scanned position. The recorded correlation functions are

then fit to a solution of the diffuse photon correlation correlation equation [80] to obtain an index

proportional to the blood flow. The results are normalized to the mean value of the measurements

of the healthy tissue and the standard deviation is reported as the error bar. We, therefore, report

the averaged relative blood flow (% rBF) at each position.

Figure 4.33 shows four correlation curves from two patients. When blood flow increases, the

temporal auto-correlation function decays more rapidly. It is evident that the blood flow is larger

in the tumor region (compare dark and light curves) in both cases. Figure 4.34 shows horizontal

and vertical profiles from one malignant tumor and one healthy breast. There is very little variation

observable in the healthy breast, where as the blood flow increased in both directions over the

145

−6 −5 −4 −3 −21

1.1

1.2

1.3

1.4

log(τ) (sec)

g 2 (τ)

TumorNormal

(a)

−6 −5 −4 −3 −21

1.1

1.2

1.3

1.4

log(τ) (sec)

g 2 (τ)

TumorNormal

(b)

Figure 4.33: Temporal auto-correlation curves measured in tumor (dark) and healthy (light) tissuefrom two patients. Faster decay corresponds to increased blood flow.

tumor indicating that the observed contrast is due to the tumor and not because of the natural

heterogeneity of the breast.

In order to quantify the blood flow change in the tumors, we have used the estimated tumor

outline and tabulated the mean (± standard deviation) rBF in that region. Table 4.5 shows the dis-

tribution of the values for all subjects. Three groups are visible; (1) there is very little heterogeneity

in the healthy breast (2.7 % variation), (2) the blood flow of malignant tumors is increased to 230

% of healthy tissue, whereas, (3) there is only a moderate increase in benign tumors (to 153 %).

Although, the power of the statistics of this study is not enough to conclusively claim differentia-

tion, we note that these results are in qualitative agreement with previous Doppler ultrasound and

PET results [17, 59, 149, 170, 283, 284] where ∼ 470-550 % increases in blood flow were reported

in malignant tumors with smaller contrast in benign cases. In studies with larger populations, blood

flow indices were used to differentiate upto nine different types of breast diseases [170].

These findings clearly demonstrate that we are able to optically detect robust changes in blood

flow in palpable tumors. Futher studies with more source-detector pairs are now being undertaken

to analyze the potential partial volume effects that may influence our results. We note that these

146

−6 −4 −2 0 2 4 650

100

150

200

250

300

350

Position

rBF

HealthyPatient

(a)

−6 −4 −2 0 2 4 650

100

150

200

250

300

350

Position

rBF

HealthyPatient

(b)

Figure 4.34: Relative blood flow (rBF) scans from one patient with a malignant tumor and a healthyvolunteer are shown for both (a) horizontal and (b) vertical scans.

147

ID rBF (± std) (%) type1 100.5 ± 13.4 healthy2 105 ± 86 healthy (large std)3 144 ± 21 benign, calcification4 163 ± 26 benign, calcification5 184 ± NA malignant6 212 ± 98 malignant7 298 ± 51 malignant

Table 4.5: Tabulation of relative blood flow (rBF) measured at the estimated tumor regions fromall subjects grouped as healthy, benign and malignant diseases.

palpable tumors are relatively superficial and previous optical studies [139, 140] have shown that

source detector separations around 2.5 cm can probe them in a repeatable manner. Additionally,

if we assume that the palpable region corresponds to roughly the same depth from the skin, the

partial volume effects are further divided out by normalizing to the healthy tissue blood flow. In

the future, we will acquire data with a hybrid instrument [80] in order to measure the oxygenation

and total hemoglobin concentrations changes simultanously and estimate the changes in oxygen

metabolism of the tumors. The instruments are built on small clinical carts and the study time is

relatively short (∼ 10 minutes). Therefore, it is feasible to acquire data at each patient visit and in

the triage area. We anticipate these methods will be clinically useful for therapy monitoring, dose-

adjustment and potentially for assesing the efficacy of the therapy from the first week, therefore,

avoiding unnecessary discomfort to the patients.

4.7 Summary and Future Outlook

Using DOT/DOS technique, we have quantified in vivo healthy breast properties and demonstrated

the detection and quantification of breast tumor contrast against the surrounding nondiseased tis-

sue. Also, treatment monitoring capability of three-dimensional DOT was demonstrated for a case

148

of locally advanced breast cancer going through neoadjuvant chemotherapy. Blood flow measure-

ments of breast shed light as an additional optical parameter to aid in classification of breast cancer.

The theoretical and experimental techniques involving DOT/DOS are constantly evolving to

better quantify the breast tumor properties. For our current CCD-based instrument, our reconstruc-

tion is largely based on CW component of data, where we need to consider crosstalk between ab-

sorption and scattering. Our current wavelengths are not optimal for separating this crosstalk [57].

However, the simulation using current wavelength only yielded 20 - 30 % crosstalk between THC

and scattering, which implies our scattering contrast is not wholly due to the crosstalk. Care-

ful tissue phantom studies using in vitro hemoglobin will help identify this issue, but the origin

of scattering contrast in in vivo measurement still is obscure. It is shown that microvessel den-

sity correlates well with total hemoglobin concentration measured by DOT [222]. Retrospective

histopathology correlation study with emphasis on the microvessle density and other parameter

highlighting the source of scattering would be beneficial linking the microscopic histology and

macroscopic DOT measurement.

Another technical difficulty we have faced during clinical measurements is the current and

intrinsic limitation of parallel plate design to accommodate lesions near axillary tail and chestwall.

Also, near the chestwall, the side of the breast is exposed to the boundary of air and the matching

fluid, which needs careful modeling. We are currently in the process of adding optimal wavelengths

and optimizing the table design to enable more breast tissue to be inside our imaging volume

without being exposed to the air boundary. In the extreme case of breast cancer near axillary tail

and chestwall, we are utilizing the portable DOS/DCS instrument.

In some in vivo measurements, the reconstructed images could be contaminated with source

and detector artifacts. These may be coming from source detector coupling mismatch between

149

the breast and the matching fluid. In addition to the use of source detector coupling fit, various

approaches are devised to reduce these effects which may degrade the quantification of breast

cancer. The quantification of breast cancer could be substantially improved using a priori spatial

information from other imaging modalities [33, 34, 165, 294]. In our laboratory, initial phantom

measurements incorporating the scanning ultrasound has shown good quantification capability.

Incorporation of ultrasound to accommodate clinical measurement geometry is anticipated to give

additional capability to our current DOT scheme.

We are currently in the beginning stage of new breast cancer imaging technology where we

are validating our results against the gold standard or the existing imaging modalities such as X-

ray mammography, ultrasound and/or MRI. In section 4.5, the correlation study between MRI

and DOT on a locally advanced breast cancer showed reasonable agreement even with use of

simple scaling approach. More elaborate modeling considering the elastic deformation of breast

is needed, which may require the hardware modification and careful coregistration scheme using

markers. Of course, the measurements of MRI and DOT in the same table would be ideal for

coregistering purpose. With careful design, CCD-based DOT system could be also incorporated

into MRI environment.

We have briefly mentioned the construction of the optical index based on the relative tumor

contrast of optical properties for carcinoma cases. Additional measurement such as blood flow

could be added into the index. Or the metabolism derived from the blood flow and saturation can

be added as another parameter. This concept of optical index could lead to identification of optical

properties which discern the benign and malign tumors. More in vivo data on various kinds of

tumor is needed to explore the possibility.

150

Neoadjuvant chemotherapy setting has emerged as an ideal platform to demonstrate the moni-

toring capability of DOT. With recently established collaboration, more coordinated measurements

of DOT with MRI are being performed in our laboratory. However, more frequent DOT measure-

ments are desirable since the significant physiological changes relating to treatment efficacy may

happen within a week [140]. Then the treatment efficacy could be assessed in the similar ap-

proach taken by Yu et al [292], Wang et al [273] and Sunar et al [250]. We have recently acquired

DOT measurements with Indocyanine Green (ICG) injection for some neoadjuvant chemotherapy

patients. In addition of enhancement of optical contrast, the kinetics of ICG could reveal the infor-

mation on the blood flow characteristics in the breast tissue. With current instrument, we can only

follow the kinetics on fixed source position. More rapid instrument enabling switching between

multiple source position during 5 minutes interval would be ideal for ICG kinetics monitoring

purpose. Comparing the blood flow information extracted from ICG kinetics and the blood flow

information from the Diffuse correlation spectroscopy may be interesting.

151

Chapter 5

Dynamic Diffuse Optical Spectroscopy

on Fetal Brain in utero

5.1 Introduction

The ultimate goal of fetal brain project is to develop an accurate non-invasive trans-abdominal

monitoring device for the fetal brain oxygenation state, while the fetus is still in the uterus. The

clinical motivation and brief history regarding the fetal oximetry project is described in the Chapter

1, Section 1.3. In the following sections, the feasibility of in utero fetal brain oxygenation moni-

toring is demonstrated using a pregnant ewe model with induced fetal hypoxia. Then the prospect

of translating this technology to clinical setting is discussed in the following section based on the

preliminary clinical experience.

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5.2 Trans-abdominal Near Infrared Oximetry of Hypoxic Stress in

Fetal Sheep Brain in utero

5.2.1 Introduction

The goal of this study was to demonstrate the feasibility of trans-abdominal NIR spectroscopy

for detecting and quantifying fetal hypoxia in utero in a pregnant ewe model (n = 5). We have

built a multi-wavelength NIR frequency-domain instrument with the capability to perform NIR

photon diffusion measurements through tissue over a wide range of source-detector separations.

We also developed a two-layer numerical diffusion model (for the maternal and fetal layers) to

quantify fetal cerebral blood saturation in utero. Good agreement was found between fetal blood

saturation determined by the trans-abdominal NIR method, and arterial and venous fetal blood

saturation quantified from fetal blood samples using a hemoximeter (gold standard). We conclude

trans-abdominal NIR oximetry has the capability to quantify different degrees of hypoxia in the

fetal brain in utero.

5.2.2 Materials and Methods

5.2.2.1 Animal Protocol

Five pregnant ewes (132-144 days gestation) were evaluated in this study. The animals were han-

dled according to the National Institutes of Health guidelines of the Institutional Animal Care and

Use Committee. The protocol consisted of the following steps: (1) anesthesia and catheteriza-

tion of the pregnant ewe, (2) catheterization of the fetus, (3) catheterization of the ewe for aortic

occlusion, and (4) NIR photon diffusion measurements and fetal blood sampling during baseline,

hypoxia and recovery.

153

Transabdominal probe

amniotic sac

maternalskin

detector fiber

source fiber

d : distance between probe and brain

aortic occlusion through catheterwith balloon

probe

Figure 5.1: Fetal hypoxia ewe model

First, the pregnant ewe was anesthetized with halothane [187]. The carotid artery was catheter-

ized for maternal arterial blood sampling and blood pressure monitoring. Second, the uterus was

exposed by a mid-line abdominal incision, and a small hysterotomy was performed to expose the

fetus for catheterization. The left brachial artery was catheterized for fetal arterial blood sampling

and the right brachial artery was catheterized for fetal blood pressure monitoring. The jugular vein

was catheterized for fetal venous blood sampling. The fetal body was then placed back in the

uterus. The uterus was tied around the fetal neck (purse-string method) to expose the fetal head

for the trans-abdominal NIR measurements. The exposed head was placed directly underneath the

maternal skin and secured by suturing its ears to skin. The purse-string approach was employed

to minimize the effect of the uterus in this pilot investigation. Third, a catheter with an inflatable

balloon was inserted through the femoral artery of the pregnant ewe for aortic occlusion. Aortic

occlusion through the femoral artery of the pregnant ewe is expected to directly reduce uterine

154

blood flow to the fetus, but have a minimal effect on maternal oxygenation. Finally, the probe was

placed on the maternal abdomen directly above the fetal head as shown in Figure 5.1. The details

of the instrument are described in Chapter 3, Section 3.6.3. The NIR measurements commenced

and were performed continuously during the entire baseline-hypoxia-recovery cycle. Fetal arterial

and venous blood samples were drawn during the baseline NIR measurement. Then the balloon

was inflated to block uterine blood flow and induce fetal hypoxia. The balloon was inflated until

the fetal blood pressure dropped rapidly. The inflation was maintained for 209± 38 seconds. Then

the balloon was deflated and the fetus was allowed to recover. Blood samples were drawn from

fetus every 30 seconds during hypoxia and once after recovery. Maternal arterial blood samples

were sampled and checked periodically to ensure the maternal arterial saturation was not perturbed

by aortic occlusion.

The thickness of the maternal layer was measured with a caliper to be 4.0 ± 0.4 mm. The

thickness of the fetal skull was obtained postmortem and it was 5.0 ± 0.5 mm. Maternal arte-

rial oxygen saturation, fetal arterial oxygen saturation (SaO2) and fetal venous oxygen saturation

(SvO2) were quantified from the fetal blood samples with an OSM3 Hemoximeter (Radiometer

Medical, Coppenhagen).

5.2.2.2 Data Analysis

The general steps for analysis of the NIR photon diffusion measurements are as follows. The

reflected photon fluence Φ(µa(r, λ), µ′s(r, λ)) at the surface of the medium is measured. It depends

on absorption coefficient (µa) and reduced scattering coefficient (µ′s) and the separation between

the source and detector, r, at a given wavelength λ. µa and µ′s are determined by minimizing χ2 =

∑ |ΦmΦbm− ΦcΦbc|2, where Φm is the measured fluence and Φc is the fluence calculated using a photon

155

diffusion model. Φbm and Φbc are the measured and calculated baseline fluences, respectively in the

initial normoxic state (i.e. before the hypoxic perturbation). After µa is determined, concentrations

of oxy-hemoglobin (CHbO2) and deoxy-hemoglobin (CHb) are calculated [291]. Total hemoglobin

concentration (THC = CHb + CHbO2) and tissue blood oxygen saturation (StO2 = (CHbO2

/THC)

× 100) are then easily determined.

The data analysis procedure employed in this study consisted of three steps: (1) construction of

Φm from NIR measurements, (2) formulation of Φc from two-layer diffusion model using a priori

spectral and spatial information, and (3) retrieval of fetal blood saturation from χ2 minimization

(see below for details).

Sliding window (4 second) averaging was used to smooth the amplitude (Am) and phase (θm)

data measured over the time course of the normoxia-hypoxia-recovery cycle in each study. The

measured fluence Φm(r, λ) = Am exp(iθm). The baseline fluence measurement Φbm was deter-

mined by averaging the first 100 data points from the amplitude- and phase-time curves during the

initial normoxic state of the fetus.

A numerical solution to the diffusion equation for a two-layer model was used to generate Φc.

Two-layer diffusion models have been investigated by a number of researchers using analytical

[3, 29, 153, 211, 231] or numerical solutions [68, 295]. Here, the finite difference method was used

to numerically solve the diffusion equation for a three-dimensional, two-layer model of the in utero

system. In this model, the tissues unperturbed by aortic occlusion were approximated as the top

lay er whose thickness is d; this layer includes the maternal skin, fetal head skin and the f etal

skull. The fetal brain was incorporated as the bottom layer. Strictly speaking the fetal skin is also

influenced by hypoxic perturbations, but since thi s layer is quite thin (≈1 mm) it was considered

part of the top layer.

156

Incorporation of a priori spectral information about the absorbers and scatterers in the tis-

sue reduces the number of unknowns and the inter-parameter cross-talk between µa and µ′s [81].

The wavelength dependence of µa is determined by the concentration of tissue absorbers and

their wavelength dependent extinction coefficients. Specifically, µa(λ) = εHbO2(λ)CHbO2

+

εHb(λ)CHb+µbga (λ) where λ is the wavelength, ε is the extinction coefficient, C is the concentra-

tion and µbga is the background absorption contributed by water and lipid. µ′s is often modeled by a

Mie scattering formula in this wavelength range, i.e. µ′s(λ) = Aλ−b where A and b are determined

by scatterer size and density. Instead of treating µa and µ′s at each wavelength as unknowns, we use

the absorber concentrations and scattering parameters A and b as unknowns in the Φc calculation,

and analyze all wavelengths simultaneously.

parameters top bottomd 8 - 10 mm NA

µbga (λ) 0.76 µH2Oa +0.12 µlipida 0.76 µH2O

a +0.12 µlipida

b 0.5 0.5µ′786nms 9.5 cm−1 9.5 cm−1

baseline THC 80 µM 80 µMbaseline StO2 80% 0.43 SaO2+0.57 SvO2

Table 5.1: The values of fixed parameters in data analysis. A was determined by b and µ′786nms .

Since CHb and CHbO2of fetal brain are the major parameters of interest and make the largest

contribution to the signal variation, we fixed all other parameters. Table 5.1 shows the fixed pa-

rameters for each layer of the two-layer model. In the top layer, d was fixed based on thickness

measurements of the maternal skin, fetal skin and fetal skull postmortem. The background µbga (λ),

the scattering properties A and b, the baseline THC of both layers, and the baseline StO2 of the top

layer were assumed based on values reported in the literature [179, 254, 286]. The StO2 values of

the bottom layer were obtained from the hemoximeter measurements during the normoxic baseline

157

in each cycle. Specifically, the baseline StO2 value for the fetus (bottom layer) was determined

using a compartmental model [63] where StO2 is made up of 43% SaO2 and 57% SvO2. Since

the aortic occlusion protocol is expected to perturb fetal hemodynamics only, the top layer THC

and StO2 were assumed to be the same as the baseline throughout the cycle. Once all the fixed

parameters were defined for the calculation of Φc, the MATLAB function, fminsearch, utilizing

the Nelder-Mead Simplex method (iterative method) was used for χ2 minimization in order to ex-

tract fetal brain CHb and CHbO2. In order to test the effect of the fixed parameters on the error

propagation in the two-layer diffusion algorithm, each parameter was varied within a range (≈ ±

25%) reported in the literature. An error analysis indicated that the two-layer diffusion algorithm

was relatively insensitive to variations in the majority of fixed parameters. Variation in these fixed

parameters resulted in at most 2% variation in the fetal blood saturation values. The assumptions

relating the arterial and venous contribution to the fetal baseline StO2 were limiting parameters

in our calculations. Varying the arterial/venous contribution from 43/57% [63] to 30/70% [124]

resulted in 0.5-5% variation in calculated fetal StO2, depending on the level of hypoxia. This

variation was the basis for the fetal StO2 error bars.

5.2.3 Results

Normalized measurements of amplitude (Am/Abm) and phase-shift (θm − θbm) vs. time at a source-

detector separation of 4.0 cm during a normoxia-hypoxia-recovery cycle is shown in Figure 5.2

at wavelengths 690, 786 and 830 nm. The amplitude and phase were normalized to the baseline

amplitude and phase. The effects of hypoxia are particularly evident in the amplitude vs. time

trace. The decrease in amplitude at 675 nm and increase at 830 nm indicates a relative increase in

the deoxy-hemoglobin concentration and a relative decrease in the oxy-hemoglobin concentration,

158

0 200 400 600 800 1000 1200 14000.4

0.6

0.8

1

1.2

1.4

Time (sec)

Am

/ A

mb

(a)

600 800 1000 1200 1400 1600 1800 2000−0.04

−0.02

0

0.02

0.04

0.06(b)

Time (sec)

θ m −

θmb

(ra

d) 675 nm786 nm830 nm

Inflation Deflation

Figure 5.2: Normalized measurements of amplitude (Am/Abm) and the phase-shift (θm − θbm) vs.

time measured at a source-detector separation of 4.0 cm during a normoxia-hypoxia-recovery cycleat wavelengths of 675, 786, and 830nm. The amplitude and phase were normalized to the baselineamplitude and phase, which were averaged from the first 100 data points in the time trace.

which is the expected trend for hypoxia. The amplitude at 786 nm, which is close to the isos-

bestic point of hemoglobin, exhibits an intermediate response. Time traces at other source-detector

separations showed similar trends, but with different magnitudes. No obvious physiological inter-

pretation could be drawn from the phase data.

In Figure 5.3 two examples of the fetal blood saturation obtained from NIR trans-abdominal

spectroscopy and from fetal blood samples quantified with the hemoximeter are presented. There

is a decrease in blood saturation with inflation and an increase in blood saturation with deflation of

the balloon. The blood saturation determined from the two-layer model fit shows good agreement

with the hemoximeter results. Herein the two-layer diffusion model fits of blood saturation will be

denoted as fetal tissue blood saturation (StO2).

159

0 200 400 600 800 1000 1200 14000

20

40

60

80

100

time (sec)

Blo

od

sat

ura

tio

n (

%)

Two−layer fitArterialVenous

Inflation Deflation

(a)

100 200 300 400 5000

20

40

60

80

100

time (sec)

Blo

od

sat

ura

tio

n (

%)

(b)

Inflation Deflation

Figure 5.3: Two examples of the fetal blood saturation obtained from NIR trans-abdominal spec-troscopy and from fetal blood samples quantified with the hemoximeter. ‘Two-layer fit’ is theblood saturation quantified by NIRS using two-layer model fit, ‘Arterial’ is arterial fetal blood and‘Venous’ is venous fetal blood measured by the hemoximeter.

The correlation between fetal blood saturation measured by trans-abdominal NIR spectroscopy

(NIRS) and hemoximeter was also examined. NIR blood saturations StO2 were selected from

points in the time traces where fetal arterial and blood samples were withdrawn. Blood saturation

values were calculated using the previously described compartmental model [48, 63, 106] from

the fetal arterial and venous blood saturations (measured from the fetal blood samples using the

hemoximeter). These values served as the gold standard.

A linear relationship between the NIR and hemoximeter fetal blood saturation over a wide

range of blood saturation values is observed in Figure 5.4, with a correlation coefficient R equal to

0.76 (p < 0.01).

The blood saturation data were obtained from normoxic, hypoxic and intermediate data points

(n = 47), collected from seven hypoxic cycles (n = 7). Notice that the variance in blood saturation

increases as the fetus progresses from a normoxic to a hypoxic state. Furthermore, there is a

poorer correlation between the NIRS and hemoximeter measured blood saturation in the lower

160

0 20 40 60 80 1000

20

40

60

80

100

Blood saturation by Hemoximeter(%)

Blo

od

sat

ura

tio

n b

y N

IRS

(%)

Figure 5.4: Linear relationship between the fetal blood saturation measured by NIR instrument andhemoximeter over a wide range of blood saturation values with a correlation coefficient R equal to0.76 (p < 0.01).

range of blood saturations. This may be because the blood saturation of the fetus in this range was

transient, so it was difficult to perfectly synchronize the NIR measurements and the blood sample

withdrawals.

The baseline state (before inflation of the balloon) and stable hypoxic state (while the balloon is

in the fully inflated state) was considered for further assessment of comparison. The difference be-

tween the baseline state and stable hypoxic state for the NIRS (∆StO2) and hemoximeter (∆ShO2)

blood saturations are compared in Figure 5.5. The data is shown for two groups of hypoxia. Mod-

erate hypoxic cycles (n = 3) are grouped with ∆StO2 = 30 ± 7% and severe hypoxic cycles (n =

4) are grouped with ∆StO2 = 60 ± 5%. A paired t-test analysis shows ∆StO2 and ∆ShO2 are

statistically similar within the moderate and the severe group (p < 0.05 for null hypothesis). An

unpaired t-test shows that the difference between moderate and severe ∆ShO2 is significant (p <

161

0

10

20

30

40

50

60

70

SO

2(bas

elin

e) −

SO

2(hyp

oxi

a) (

%) ∆ShO2 (Hemoximeter)

∆StO2 (NIRS)

Moderate Hypoxic Group (N=3)

Severe Hypoxic Group (N=4)

Figure 5.5: Difference in blood saturation between the baseline state and stable hypoxic state forthe NIRS (∆StO2) and hemoximeter (∆ShO2) measured blood saturations. The data is shown fortwo groups of hypoxia.

0.05). This is true for ∆StO2 as well.

5.2.4 Discussion

This study demonstrates for the first time, the feasibility of using trans-abdominal NIR spec-

troscopy for detecting and quantifying fetal hypoxia in utero. The pregnant ewe model is a

widely used model for studying fetal physiology and was ideally suited for this proof-of-principle

study. Perturbations of fetal blood saturation were performed in a controlled manner and fetal

arterial and venous blood saturations determined from fetal blood samples served as a reliable

gold standard to which the NIR measured blood saturations could be compared. The multi-

wavelength, multi-separation NIR frequency domain instrument coupled with the numerical two-

layer diffusion model proved capable of retrieving fetal blood saturation in utero, accurately and

162

non-invasively. The frequency-domain technique is more effective than the previous CW tech-

niques [227, 228, 270]; the former is better able to decouple absorption from scattering, which

is important for quantifying oxy- and deoxy-hemoglobin concentrations in tissue. The two-layer

numerical diffusion model also represents a significant improvement over the widely used homo-

geneous model; the former model was clearly able to deconvolve fetal from maternal blood satu-

rations, rather than volume-averaging them. When the homogeneous model was used on this fetal

data under the same condition, it underestimated the change in blood saturation. Multi-wavelength

NIR photon diffusion measurements enabled the use of a priori spectral information to reduce

number of unknowns (absorbers) in the two-layer diffusion model. Finally, NIR reflectance mea-

surements at multiple source-detector separations probe different tissue depths, thus optimizing the

deconvolution of fetal from maternal signals using the two-layer diffusion model.

In this study, several modifications were made to the pregnant ewe model to simplify the fetal

hypoxia protocol. First, hypoxia in the fetus was indirectly induced through aortic occlusion of

the maternal femoral artery. Alternative approaches for inducing fetal hypoxia are to lower the

maternal blood saturation by lowering the fraction of inspired oxygen (FiO2) or through umbilical

cord occlusion. These alternative approaches were evaluated in preliminary studies. The problem

with lowering maternal FiO2 was that both maternal and fetal blood saturations were affected

and therefore the perturbation was not unique to the fetus. With the umbilical cord occlusion

approach, fetal morbidity and mortality were significant. Another modification made in this study

was the uterine layer was removed from the field during trans-abdominal NIR spectroscopy of the

fetus. The protocol was simplified in this manner to first establish the accuracy of quantifying fetal

cerebral blood saturation, for the case in which the overlying layers are not affected by the hypoxic

perturbation. The success of this pilot investigation sets the precedent for future animal model

163

studies. In future studies, the complexity of the additional uterine layer and different perturbation

approaches will be investigated. Additionally, a larger number of animals will be studied to obtain

more statistically significant results.

5.3 Outlook towards translation to human

We now discuss the future outlook of the fetal brain project with focus on the traslation to human

case based on the experience gained from the preliminary C-section clinical data.

5.3.1 Preliminary Clinical Data

Preliminary clinical data were collected using a simple dual wavelength, dual light source frequency-

domain spectroscopy with one detector channel (Figure 5.6). Two 750 nm laser diodes (Sharp,

LT031MD and LT030MD) and two 780 nm laser diodes (Sharp, LT024MD) were amplitude mod-

ulated by a 70 MHz local oscillator (Wilmanco, VSA-70+13dBm). LT031MD was used for larger

source detector separation because of its higher power. The laser diodes were time-shared at a

frequency of 1.25 Hz. Two pairs of a 750 nm and a 780 nm laser diodes were coupled to an optical

fiber (diameter = 1mm, N.A. = 0.37) by a laser diode power combiner (Oz optics) respectively.

The laser outputs were balanced to give similar level by adjusting the attenuator embedded in the

power combiner. The laser outputs after an optical fiber were about 1 mW. The optical fibers

were mounted on a probe at two different distance from a detector. A photomultiplier tube (PMT,

Hamamatsu, H5783-01) was used for the detection. The detected signal is amplified by a series

of amplifiers (Mini-circuits, ZFL-2000, MAN-1LN) and a filter (Mini-circuits, PLP-90). A homo-

dyne scheme based on a I&Q demodulator (Mini-circuits, MIQY-70D) with lowpass filters was

used to detect the amplitude and phase of the diffuse photon density wave (DPDW) [288].

164

Turbid Medium

I&QDemodulator

I

Q

LPF

LPF

A/D D/A

Bandpass filter

computer

RFsource

750 nm(10 mW)

780 nm(20 mW)

Time share (10 Hz)

amplifier

(70 MHz)

Optical Fiber( 1 mm dia., 0.37 N.A. )

( H.V. = 1000 V )

(60~90 MHz)

PMT

combiner

LD

LD

LD

LD

Figure 5.6: Schematic diagram of dual wavelength dual source homodyne frequency-domain spec-troscopy

The coupling coefficients from detectors and light sources were corrected by reference mea-

surements on a solid homogeneous tissue phantom (made of lesin) with known optical properties

accompanied for each clinical measurement.

A clinical protocol was designed to include post-partum measurements on a newborn neonate

to correlate with the pre-partum transabdominal measurements on a pregnant woman (Figure 5.7).

An elective Cesarean section was chosen particularly for this purpose since the time between the

transabdominal measurements and delivery is more controllable than in a labor. When available,

the cord gas was analyzed for oxygen saturation. The protocol was approved by the Internal Review

Board at the University of Pennsylvania.

When a patient consented to participate in the study, the location of fetal head was found by

hand-held ultrasound tranducer which was in regular use in the hospital. A pre-partum measure-

ment was done on the patient’s abdomen right after anesthesia was administered to her and before

the Cesarean section operation began. When the neonate was delievered, a post-partum measure-

ment on neonate’s forehead was performed. For rare occasions, we had access to the fetal forehead

165

right before the umbilical cord was cut by using sterilized field over the probe.

In the pre-partum measurement, a soft black rubber probe with two optical fibers for light

sources placed at 3 cm and 7 cm from a PMT respectively was used. TO-8 PMT was mounted

directly on the probe and was operated at high voltage of 1000 V to maximize the signal to noise

ratio at separation of 7 cm. The probe was placed directly over the fetal head after it was located

by ultrasound transducer. The ultrasound also provided information on the distance between the

maternal abdomen and fetal skull. In the post-partum measurement, a soft black rubber probe with

one optical fiber placed at 3 cm from an optical bundle coupled to a PMT was used on a neonate

forehead.

(a) (b)

(c) (d)

Figure 5.7: Illustration of clinical in utero measurements. (a) Transabdominal measurement on thematernal abdomen, (b) Inside view of transabdominal measurement, (c) Direct fetal brain measure-ments before detechment of the umbilical cord during Cesarean section, (d) Direct neonate brainmeasurements after birth

It was feasible to use the instrument to follow this protocol in the Cesarean section environment

166

without causing much extra delay for the operation. However, the improvement in the probe design

would be much anticipated for the future study. Especially PMT was difficult to use in the operation

environment due to its sensitivity to ambient stray light. Fast shutter mechanism to protect PMT

from being exposed to the ambient light directly should be implemented as well as the general

isolation of stray light.

The optical properties and blood oxygenation obtained from single-spectral semi-infinite ho-

mogeneous medium fit (as described in Section 2.3) and Beer-Lambert law are summarized in the

following. (A) is from the transabdominal measurements at source detector separation of 3 cm and

(B) is from that of 7 cm. (C) is from the neonatal forehead measurement after the umbilical cord

was detached. Typically, measurement (C) was carried out 17 ± 6 minutes after the birth.

N µ750nma µ780nma µ′750nms µ

′780nms THC (mM) StO2 (%)

(A) 8 0.059±0.018 0.060±0.023 9.7±1.7 8.5 ± 1.9 0.085 ± 0.050 69 ± 17(B) 20 0.060±0.018 0.059±0.019 7.0±1.3 6.8 ± 1.2 0.080±0.041 59±31(C) 13 0.174±0.074 0.142±0.046 7.7 ± 3.9 8.0±3.4 0.24±0.083 44±20

Table 5.2: Summary of µa from clinical in utero data

N , number of subjects measured is different in each measurements. Dual source configuration

measurements were not available from the beginning of the study ((A) and (B)). For some cases

where the neonate’s state needs care, we did not have access to the neonate measurements in (C).

Since the fetal head has higher absorption coefficient as shown in (C), µa at separation 7 cm (B) is

expected to be higher than that of at 3 cm (A).

The averaged µas agree with those found in the literature. Fishkin et al [99] reported the normal

abdomen µa = 0.0626 ± 0.003 cm−1 and µ′s = 9.11 ± 0.15 cm−1 for source-detector separation

of 2.7 cm at 811 nm which is congruent with values found in (a). Gratton et al [112] reports human

forehead µa = 0.16 cm−1 and µ′s = 7.3 cm−1 at 715 nm. Matcher et al [179] reports human

167

forehead µa = 0.16 ± 0.01 cm−1 and µ′s = 9.4 ± 0.7 cm−1 at 800 nm for 14 adult subjects. The

averaged absoprtion coefficients at separation 3 and 7 cm (Table 5.2 (A) and (B)) do not exhibit

the difference. For individual patients, when the fetal head depth was less than 2.3 cm, µa at 7 cm

was greater than µa at 3 cm as expected. However, µa contrast between the separations were quite

small. µ′s at 7 cm is consistantly lower than µ′s at 3 cm. Whether this is truly physiological result

or this is due to µa and µ′s crosstalk or coupling coefficient offset, it is rather ambiguous at this

point since there were only marginal number of measurements to satisfy the number of unknowns

and the coupling coefficients were assumed to be the same in the solid phantom and the tissue.

The effects of coupling coefficient have recently gained considerable interest. The magnitude of

coupling coefficient would be such that not to affect homogeneous fit too much but would be large

enough to skew the sensitivity to embedded objects or layers [25].

Neonate blood saturation is lower than expected. This has been observed in the animal stud-

ies on piglets and lambs [51] and also observed by Hueber et al [133]. They attributed this to

wavelength dependent effective background absorption coefficient whose origin could be model

mismatch.

For three cases, measurements on the fetal forehead right before the umbilical cord was de-

tached were available. In these cases, the blood saturation from the fetus correlated linearly in

positive direction with maternal blood saturation whereas the neonate saturation (C) was not. How-

ever, fetal blood saturation was much lower than maternal blood saturation in this case. Also, for

the case blood saturation was monitored within a few minutes after umbilical cord detachment,

blood saturation of neonate increased with time which was also monitored with pulse oximeter on

neonate’s finger. Same phenomena has been reported by Isobe et al [136]. From these observa-

tions, one can draw a hypothesis that the fetal blood saturation may be lower and increases after the

168

umbilical cord is detached. This suggests the difficulties in the original study design in correlating

the neonate blood saturation to transabdominal blood saturation unless the neonate is accessible

for measurements within minutes after birth.

Figure 5.8 summarizes above observation by showing a bar graph of µa and µ′s at 750 and

780 nm, THC and StO2 of transabdominal measurement (N=15) at separation 7 cm, fetal head

measurement (N=3), and neonatal head measurement (N=10). Transabdominal THC is much lower

than that of fetal head and neonate head. µ′s does not seem to be significantly different from each

group. However, StO2 of fetal head is extremely low.

Low neonate blood saturation indicates the need of incorporation of more wavelength to the

instrument. Lack of contrast in absorption coefficients at short and long separations indicates either

the measurements at source detector separation of 7 cm is not sensitive enough to the fetal signal or

the over-simplified homogeneous model of in-utero system is underestimating the effect of fetus.

Even though the comparison between averaged µa at source detector separation 3 cm and 7

cm did not yield much difference, this can be easily attributed to model mismatch (i.e. not using

two-layer model). The clinical data still reveal the encouraging trend in Figure 5.9, where the µa

at source detector separation of 7 cm decreases with increase of the fetal brain depth measured by

the ultrasound. Since the absorption of fetal brain is higher than that of maternal layer, as the fetal

brain depth is smaller, the expected absorption from homogeneous fit would be higher due to more

signal contribution from fetal brain.

5.3.2 Clinical translation outlook

In order to translate the technology developed in Section 5.2 to clinical settings, further improve-

ments must be considered. Implementation of the two-layer diffusion model required information

169

0

0.05

0.1

0.15

0.2

0.25

µ a (cm

−1 )

750nm786nm

Transabdominal Fetal head Neonate head 0

2

4

6

8

10

12

µ s′ (cm

−1 )

750nm786nm

Transabdominal Fetal head Neonate head

0

0.05

0.1

0.15

0.2

0.25

0.3

Tot

al h

emog

lobi

n co

ncen

trat

ion

(mM

)

Transabdominal Fetal head Neonate head 0

20

40

60

80

100

Blo

od o

xyge

n sa

tura

tion

(%)

Transabdominal Fetal head Neonate head

Figure 5.8: Summary of physiological parameters (µa, µ′s, THC, and StO2) at prior (transabdomi-nal, N=15), during (fetal head, N=3) and after birth (neonate head, N=10).

about several variables: top layer thickness which served as a priori spatial information, and fetal

baseline blood saturation from the hemoximeter measurements. Other parameters were assumed

according to the literature values, and their variation resulted in minimal influence on the fetal

blood saturation calculation. In clinical studies, the top layer thickness can be measured by ul-

trasound. Other available parameters such as maternal arterial blood saturation can be utilized to

further constrain the variables. However, the baseline fetal blood saturation is not available in the

clinical environment. If the baseline fetal blood saturation had been overestimated, the algorithm

would have underestimated the severity of hypoxia in the fetus and vice versa. Absolute quan-

tification of baseline fetal blood saturation is possible with measurements at more source-detector

170

1.5 2 2.5 3 3.5 40

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

fetal head depth (cm)µ a (

cm−1

) at

750

nm

Figure 5.9: µa measured at source detector separation of 7 cm using transabdominal DOS vs fetalbrain depth measured by ultrasound

separations and more wavelengths [58] (with extensive calibration [25]). The other major difficulty

arises because the distance from the maternal abdomen to the fetal brain is 2-4 cm [227] in humans.

For the clinical situation, the two-layer approximation is especially crucial since the optical

properties of maternal layer and fetal head are distinctively different as well as the sheer dimension.

To explore the degree of influence in human case, two-layer system consisting of maternal layer

(mostly fat) and fetal head as shown in Figure 5.10 is simulated with optical properties assigned

from clinical study.

Figure 5.10: Approximation of in utero system to two-layer system

171

Most of the signal gets diluted due to the presence of meternal fat layer, and it is a function

of the layer thickness. This is illustrated in Figure 5.11, where the two-layer data from the optical

properties similar to clinical in utero system are generated using finite difference method. Then

two-layer data at source detector separation of 3 and 7 cm were fitted to the semi-infinite homoge-

neous solution (Equation 2.7). Also, fit using two-layer solution is presented. The homogeneous

fit underestimates the optical properties, resulting in somewhat in-between values between the fe-

tal head and maternal layer properties. The degree of degradation is more pronounced for the

shorter source detector separation as expected. Given the underestimation of optical properties by

homogeneous solution, it is clear that one needs to fully utilize the two-layer approximation.

2 2.5 3 3.5 4 4.50.06

0.08

0.1

0.12

0.14

0.16

0.18

Thickness of the top layer (cm)

µ a (cm

−1 ) two−layer fit

semi−infinite fit at 7cmsemi−infinite fit at 3cmexpected value

(a)

2 2.5 3 3.5 4 4.56

7

8

9

10

11

12

Thickness of the top layer (cm)

µ s′ (cm

−1 )

(b)

Figure 5.11: Effect of homogeneous fit on two-layer system. (a) Fitted absorption coefficient usinghomogeneous solution and two-layer solution from the simulated data based on a two-layer model,(b) Fitted reduced scattering coefficient.

This requirement of two-layer in turn needs optimization of the instrumentation towards mea-

suring at larger source detector separations than used in the animal study. The method to determine

172

the optimal source detector separation and the choice of detectors is illustrated in Appendix (Sec-

tion 5.4).

Even with the optimized instrument, the validation of this technique in the clinical setting is

still problematic. Additional animal study may be necessary before taking to the clinic. Especially

the animal model should be designed to reflect the similar thickness of maternal layer as the hu-

man case. Also, the effect of uterine layer should be assessed as well as exploring different type

of oxygen perturbation to the fetus. In the clinical C-section setting, correlating neonatal blood

oxygen saturation with umbilical cord is not effective since the neonate’s oxygen level rises rather

rapidly after birth. The best correlation would be through measurement on fetal head right be-

fore the umbilical cord is detached. For this measurement, better probe design which can readily

accommodate sterile requirement of operation is needed. The access to the hypoxic fetus would

be necessary in the end. Ideal setting for validation of this technique may lie in the fetal surgery

environment where the fetus is taken out of womb for surgical intervention and put back.

5.4 APPENDIX: Instrument optimization for Human Case

This appendix section is included to illustrate the methodology of estimating the optimal source

detector separation by forward-model based SNR calculation.

5.4.1 Two-layer forward model

The two-layer model used is a three dimensional rectangular block (21 cm × 14 cm × 7 cm)

consisting of two different layers of different optical properties: a top layer simulating the maternal

layer and a bottom layer simulating the fetal head. Typically µa1 = 0.06 cm−1 and µ′s1 = 8.0 cm−1

for the top layer and µa2 = 0.15 cm−1 and µ′s2 = 6.0 cm −1 for the bottom layer was used. The

173

0 2 4 6 8 10 12 140

20

40

60

80

100

120

source detector separation (cm)O

vera

ll si

gnal

/ no

ise

2.0 cm2.5 cm3.0 cm

Figure 5.12: Noise model is incorporated into the two-layer signal to give overall signal to noise.This reflects the signal to noise decrease with increase of source detector separations. Layer thick-ness of 2 cm (solid line), 2.5 cm (dashed line), 3 cm (dotted line) are shown.

µa1 and µ′s1 were from the average clinical data from measurements at 3 cm separation (Table 5.2

(B),(C)). The boundaries were set as absorbing (n = 1.0) in all sides except one side (maternal

abdomen) with air to tissue index mismatched boundary (n = 1.4). After the optical properties of

each layer and the thickness of the top layer was assigned for each voxel, finite difference method

was used to solve the diffusion equation for this geometry [129].

5.4.2 Incorporation of noise to two-layer model

A noise model described in Chapter 3, Section 3.2.2.6 is utilized to generate the noise which

depends on the signal level. In the following the case where Psource = 20 mW, floss = 0.05, Adet

= 0.1 cm2 was considered to convert the fluence from forward model shown in Figure 5.12. The

overall signal to noise starts decreasing after source detector separation of 8 cm in both cases. By

increasing the factors Psource and ∆A, and decreasing floss shift the curve in Figure 5.12 to right

side of horizontal axis.

174

0 2 4 6 8 10 12 140

20

40

60

80

100

source detector separation (cm)

Rel

ativ

e am

plitu

de (

%)

2.0 cm2.5 cm3.0 cm

(a)

0 2 4 6 8 10 12 140

5

10

15

20

25

30

source detector separation (cm)

Pha

se d

iffer

ence

(de

gree

) 2.0 cm2.5 cm3.0 cm

(b)

Figure 5.13: Fractional (a) amplitude difference in percentage and (b) phase difference in degreeare obtained between the amplitude from two-layer system and amplitude from homogneous sys-tem with top layer optical properties at different source detector separations. It is a measure ofsensitivity to the bottom layer optical properites. Layer thickness of 2 cm (solid line), 2.5 cm(dashed line), 3 cm (dotted line) are shown.

5.4.3 Sensitivity to fetal signal

The sensitivity to the signal from the bottom layer is obtained by treating the contribution of fetal

signal on the overall signal is a perturbation caused due to its presence as contrasted to the case

where the whole region is homogeneous with optical properties of maternal layer. In the Figure

5.13, the fractional amplitude difference between two-layer case at top layer thickness of 2 - 4

cm and the homogeneous case of µa1 = 0.06 cm−1 and µ′s1 = 8.0 cm−1 are plotted against the

source detector separations. It shows that the fractional differences increases with increase of

separations. The fractional differences decrease with increase of thickness. As expected before,

the sensitivity to fetal signal increases with source detector separations and decrease with maternal

layer thickness.

175

0 2 4 6 8 10 12 140

100

200

300

400

500

source detector separation (cm)D

iffer

entia

l sig

nal /

noi

se

2.0 cm2.5 cm3.0 cm

Figure 5.14: Differential signal to noise corresponding to fetal signal is plotted. Optimal sourcedetector separation exist at the maximum differential signal to noise. Layer thickness of 2 cm (solidline), 2.5 cm (dashed line), 3 cm (dotted line) are shown.

5.4.4 Optimal Source Detector Separation

Decrease of overall signal (Figure 5.12) and increase of sensitivity (Figure 5.13) with increase of

source detector separation competes with each other in detection of fetal signal. Multiplying the

overall signal and sensitivity gives the differential signal over noise which is the SNR from fetus.

In Figure 5.14, this effective SNR from fetus peaks at certain optimal source detector separation

where the effects of overall signal and sensitivity are balanced. The optimal separations increase

with increase of layer thickness. The optimal separations range around 8 - 10 cm. However,

the overall differential signal to noise ratio decreases with increase of layer thickness. Therefore

for thickness of 4 cm, even if the optimal separation is selected the measurement will give poor

information on fetus since the effective SNR is so low.

5.4.5 Detectability of fetal signal in two-layer model: Inverse Problem

Ultimately, the detectability of fetal signal relies on the ability of the model based inversion algo-

rithm to extract fetal information accurately. Therefore, two-layer diffusion model based inversion

176

1 1.5 2 2.5 3 3.5 40.04

0.06

0.08

0.1

0.12

0.14

0.16

Thickness of the top layer (cm)

µ a (cm

−1 )

(a)

1 1.5 2 2.5 3 3.5 44

5

6

7

8

9

10

Thickness of the top layer (cm)

µ s′ (cm

−1 )

homogeneous fit at 3cmhomogeneous fit at 7cmtwo layer fit of top layertwo layer fit of bottom layer

(b)

Figure 5.15: Comparison between the homogeneous model fit and the two-layer model fit. In theforward data, amplitude noise based on (a) and random phase noise of 0.1o were added. Then it isfitted to semi-infinite homogeneous analytic solution at source detector separation of 3 cm (cross)and 7 cm (filled triangle). The optical properties of top layer (open circle) and bottom layer (filledcircle) are give by fitting to a two-layer numerical solution.

algorithm was developed using the finite difference method based diffusion equation solver as for-

ward model. In the clinical situation, we can take advantage of the fact that the thickness of the

maternal layer can be measured with the ultrasound technique. In order to retrieve the optical prop-

erties (i.e. µa1, µ′s1, µa2 and µ′s2), Nelder-Mead Simplex algorithm was used to update the optical

properties of each layers until χ2 = Σ(ΦmΦ0m− Φc

Φ0c) where Φm is measured sample fluence, Φ0m is

measured baseline fluence, Φc is calculated sample fluence, Φ0c is calculated baseline fluence, is

minimized.

The detectability of fetal signal, that is the ability of the inverse algorithm to retrieve accu-

rate fetal information in the presence of realistic noise factors is demonstrated for noise-model

incorporated simulated data and compared with fitting result from homogeneous model.

Random amplitude noise based on the realistic noise model was added on the forward data

177

generated for two-layer and homogeneous case using finite difference method for two-layer mea-

surement and baseline measurement. This simulates the experimental situation where the signal

deteriorates with increase of source detector separation. However, constant random noise of 0.1o

was added to the phase. Differential signal between two-layer and homogeneous baseline was then

used as inputs for the inverse procedures. Crosses and filled triangles in Figure 5.15 are given by

fitting to homogeneous analytic solution for semi-infinite geometry at 3 cm and 7 cm respectively.

Open circles and filled circles are top layer and bottom layer optical properties obtained by fitting

to two-layer model based numerical solution at two source detector separations. Typically, the

short separation is fixed at 3 cm and longer source separation is determined by optimal source de-

tector separations found in Figure 5.14. The semi-infinite fit is stable with respect to the amount of

noise added. However, the fitted values approaches to the values of top layer as thickness of layer

increases. Even at thickness of 1 cm, optical properties do not reach those of bottom layer. Also,

the contrast between 3 and 7 cm result is inherently small which is consistent with the findings

in the clinical data analysis. The two-layer model fit, on the other hand, is sensitive to the level

of noise in the data. In this case, if the layer thickness exceeds 3 cm, the fit becomes unreliable.

However, the overall value reflects much better on the values of bottom layer than homogeneous

fit. The effective signal to noise should be at least higher than 10 to give accuracy up to 10 % in

absorption coefficient estimation of bottom layer. Estimation of top layer optical properties were

always much better (less than 5 %) and it seems to be less affected by the layer thickness.

5.4.6 Instrument Requirements

The methodology to predict the performance of the instrumentation for given system specification

described above can be applied to any sets of specification. It is shown for the given example that it

178

is feasible to detect fetal signal for thickness of 2 - 3 cm for NEP of system around 10−13W/√Hz

and thickness of 2 - 4 cm for NEP of system around 10−16W/√Hz at source detector separations

ranging 8 - 11 cm for modulated light source 20 mW.

So far, only a special case of two-layer was considered. However, the same methodology can

be applied for various optical properties and thickness variation. The optical properties and layer

thickness variation gives a range of signal. From a series of simulation of varying parameters, top

layer optical properties are found to be the main factors. Variation of µa1 = 0.02 - 0.12 cm−1 at

µ′s1= 8 cm−1 causes variation of amplitude signal in order of 107 across the optode separation of

3 - 10 cm. However, if the optode separation is chosen, the variation range is about 103 which can

be easily achieved experimentally. Variation of µ′s1 = 5 - 12 cm−1 at µa1 = 0.04 cm−1 is similar in

magnitude for fixed optode separation. The variation induced by the bottom layer optical properties

is at most order of 102 when the optical properties of top layer and thickness is fixed.

Therefore, when selecting the detector, NEP of the detector should be as small as possible,

detector area should be large and the dynamic range should be as large as possible. PMT is more

desirable to APD in terms of low NEP. However, dynamic range of PMT is smaller compared with

APD. When choosing the detectors, a detector with high gain and high anode sensitivity is favored

in terms of signal amplification. The chains of amplifiers can be selected such that the signal is

amplified not to be limited by A/D board resolution. Efforts to reduce the overall NEP should be

carried out for the detection system. Phase noise was not discussed in detail in this investigation.

However, phase noise contributes in raising the overall NEP. Heterodyne scheme may work better

than homodyne scheme in terms of phase noise. The comparison of two schemes are for future

investigation. Increasing modulated light source power increases the sensitivity to the bottom layer

detection. If the optode separations were fixed, modest dynamic range 103 − 104 per detection

179

position to give effective signal to noise much better than 10 is required to give reliable fit to two-

layer model. Coupling coefficients were not considered in much detail. However, their magnitude

may be large enough to obscure the sensitivity to fetal signal. Source detector combination should

implement scheme to fit for coupling coefficients reliably. For this at least 2 sources and 2 detectors

are needed. Increasing wavelength of light is expected to improve the fidelity in blood volume and

oxygenation evaluation.

180

Chapter 6

Summary

In this thesis, the motivation, theoretical background, experimental techniques and clinical results

on in vivo non-invasive breast cancer imaging and fetal brain oxygen monitoring using diffuse op-

tical tomography and spectroscopy were presented. For the breast cancer imaging application, the

quantification of tumor contrast based on total hemoglobin concentration and scattering through

three-dimensional DOT reconstruction is demonstrated as well as the monitoring capability fol-

lowing neoadjuvant chemotherapy. Also, a pilot study of blood flow measurement on breast cancer

cases is presented. The breast cancer imaging project is at an exploratory stage of finding the opti-

cal cancer contrast, constantly improving techniques for better quantification. The future direction

lies in the (1) improvement of the instrument focusing on multiple source detector positions, multi-

ple wavelength and speed, (2) incorporation of various techniques into reconstruction algorithm to

use a priori information and to reduce imaging artifacts, (3) active exploration of additional optical

parameters such as blood flow as well as establishing links with histopathology, (4) coregistration

with other imaging modality to complement each imaging technique, (5) threrapy monitoring for

181

treatment efficacy, and (6) active exploration of optical contrast agent usage which may make tran-

sition to cancer-specific targetting contrast agent.

For the fetal brain oxygen monitoring application, accurate quantification of fetal hypoxia using

two-layer model based diffuse optical spectroscopy was demonstrated using a pregnant ewe model

for aortic occlusion induced fetal hypoxia. The translation of this technique to the clinical setting

involves (1) construction of an optimized instrument for deep tissue detection, (2) a validation study

on the animal model with thickness of maternal layer similar to the human case, and (3) a carefully

designed clinical validation study (either in Cesarean-section or fetal surgical environment).

182

Glossary

—— SYMBOLS ——

ε Extinction coefficient.

λ Wavelength of Light usually in nano-meters (nm).

µa Absorption Coefficient.

µ′s Reduced Scattering Coefficient, µ′s = µs(1− g).

Φm Measured Photon-Fluence Rate of the sample.

ΦRm Measured Photon-Fluence Rate of the reference.

Φc Calculated Photon-Fluence Rate of the sample.

ΦRc Calculated Photon-Fluence Rate of the reference.

ω Laser/Source Modulation Frequency.

—— A ——

ADU Analog-to-digital unit.

APD Avalanche Photodiode.

183

—— C ——

CCD Charge Coupled Device.

CH2O Water concentration.

CHb Deoxygenated Hemoglobin concentration.

CHbO2Oxygenated Hemoglobin concentration.

Clipid Lipid concentration.

CW Continuous Wave.

—— D ——

DCE-MRI Dynamic Contrast Enhanced Magnetic Resonance Imaging.

DCS Diffuse Correlation Spectroscopy.

DOS Diffuse Optical Spectroscopy.

DOT Diffuse Optical Tomography.

DPDW Diffuse Photon Density Wave.

—— F ——

FD Frequency Domain.

—— H ——

H2O Water.

184

HbO2 Oxygenated Hemoglobin.

Hb Deoxygenated Hemoglobin.

—— I ——

ICG Indocyanine Green.

—— L ——

LABC Locally Advanced Breast Cancer.

—— M ——

MRI Magnetic Resonance Imaging.

—— N ——

NIR Near-infrared.

NIRS Near Infrared Spectroscopy.

—— P ——

PET Positron Emission Tomography.

PMT Photomultiplier tube.

—— R ——

rµ′s Relative reduced scattering coefficient (ratio between tumor and normal).

rStO2 Relative Tissue Oxygen Saturation (ratio between tumor and normal).

185

rTHC Relative Total Hemoglobin Concentration (ratio between tumor and normal).

—— S ——

SNR Signal-to-noise ratio.

StO2 Tissue Blood Oxygen Saturation.

—— T ——

TD Time Domain.

THC Total Hemoglobin Concentration.

186

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