NON-INVASIVE IMAGING OF BREAST CANCER WITH DIFFUSING NEAR-INFRARED LIGHT ...

152 Pages·2012·4.91 MB·English

NON-INVASIVE IMAGING OF BREAST CANCER WITH
DIFFUSING NEAR-INFRARED LIGHT
Soren D. Konecky
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
2008
Arjun G. Yodh
Supervisor of Dissertation
Ravi K. Sheth
Graduate Group Chairperson
�c Copyright 2008
by
Soren D. Konecky
Dedication
To everyone who reads this thesis.
iii
Acknowledgements
I could not have finished my graduate work without the help and support of many people. I have
learned a great deal about science and writing from my adviser Arjun Yodh. I am always amazed
by the breadth of his scientific knowledge and the variety of projects he supervises which span
both applied biomedical optics and fundamental physics. Despite his extremely busy schedule, he
keeps his door open and almost always makes time for us when we drop by to discuss something.
Perhaps the best part of working in Arjun’s lab is the friendly and supportive atmosphere he
fosters among the students, post-docs, and staff. During my first years in the group, Kijoon Lee,
Alper Corlu, Regine Choe, Turgut Durduran, Ulas Sunar, Jonathan Fisher, Chao Zhou, Guoqiang
Yu, and Hsing-Wen Wang taught me a great deal about diffuse optics. I am especially indebted to
Kijoon Lee, who made helping others a priority. Without his constant encouragement and help,
I might never have finished. David Busch joined the lab the same year I did. He is one of the
friendliest people I have ever met, and I am thankful for his camaraderie. Talking with David
is always fun, and I usually learn something as well. Han Ban, whose attention to detail and
shrewd questions have kept me on my toes, has been a good friend. I also thank Xiaoman Xing,
Erin Buckley, Meeri Kim, Elizabeth Wayne, Shih-Ki Liu, Dalton Hance, Glenn Fechner, Monika
Grosick-Koptyra, and Sophia Lee for their friendship and support.
I found a second home outside of the physics department in John Schotland’s group in the
department of Biomedical Engineering. There I learned to see DOT from a whole new perspective.
I cannot thank John enough for his constant support and encouragement, as well as for his insight
and clever ideas. I am also grateful to Vadim Markel, who has always been friendly and eager to
answer my questions. I also thank George Panasyuk. After hours of comparing the details of our
reconstruction codes, George and I now share a unique experience that I will always remember.
iv
I am also indebted to Joel Karp and members of his PET instrumentation group in the depart-
ment of Radiology. These members include Rony Wiener, Richard Friefelder, and Janet Saffer. I
especially wish to thank Rony for his optimism, and the hard work he put in for our project.
Finally and most importantly, I thank Marci, Maggie, Mom, Dad, and Josh for their love and
support.
v
Abstract
Non-Invasive Imaging of Breast Cancer with Diffusing Near-infrared
Light
Soren D. Konecky
Arjun G. Yodh
Diffuse optical tomography (DOT) is a new medical imaging technique that combines biomedical
optics with the principles of computed tomography. We use DOT to quantitatively reconstruct im-
ages of complex phantoms with millimeter sized features located centimeters deep within a highly-
scattering medium. A non-contact instrument is employed to collect large data sets consisting of
greater than 107 source-detector pairs. Images are reconstructed using a fast image reconstruction
algorithm based on an analytic solution to the inverse scattering problem for diffuse light. We also
describe a next generation DOT breast imaging device for frequency domain transmission data ac-
quisition in the parallel plate geometry. Frequency domain heterodyne measurements are made by
intensity modulating a continuous wave laser source with an electro-optic modulator (EOM) and
detecting the transmitted light with a gain-modulated image intensifier coupled to a CCD. Finally,
we acquire and compare three-dimensional tomographic breast images of three females with sus-
picious masses using DOT and Positron Emission Tomography (PET). Co-registration of DOT and
PET images is facilitated by a mutual information maximization algorithm. We also compare DOT
and whole-body PET images of 14 patients with breast abnormalities. Positive correlations are
found between both total hemoglobin concentration and tissue scattering, and fluorodeoxyglucose
(18F-FDG) uptake.
vi
Contents
Dedication iii
Acknowledgements iv
Abstract vi
List of Tables xi
List of Figures xiii
1 Introduction 1
2 Theory 8
2.1 Light Propagation in Tissue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.1 Diffusion Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.2 Analytical Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.3 Extrapolated Boundary Solutions . . . . . . . . . . . . . . . . . . . . . . 15
2.1.4 Finite Element Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Image Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.1 Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
vii
2.2.2 Scattering Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.3 Numerical Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.4 Block Diagonal Integral Equations . . . . . . . . . . . . . . . . . . . . . . 24
2.2.5 Singular Value Decomposition . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2.6 Inversion Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.2.7 Model Based Reconstructions . . . . . . . . . . . . . . . . . . . . . . . . 32
2.2.8 Multi-spectral Multi-frequency Reconstructions . . . . . . . . . . . . . . . 37
2.3 APPENDIX A: Derivation of boundary conditions . . . . . . . . . . . . . . . . . . 40
2.4 APPENDIX B: Calculation of Fourier coefficients . . . . . . . . . . . . . . . . . . 42
2.5 APPENDIX C: Finite element method . . . . . . . . . . . . . . . . . . . . . . . . 43
2.6 APPENDIX D: Rytov approximation . . . . . . . . . . . . . . . . . . . . . . . . 45
2.7 APPENDIX E: One dimensional integral equations . . . . . . . . . . . . . . . . . 48
2.8 APPENDIX F: Gradient and Hessian . . . . . . . . . . . . . . . . . . . . . . . . . 50
3 Experimental Validation 53
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.2 Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.3 Experimental Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.4 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.4.1 Reconstructed Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.4.2 Titration Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.5 Transverse resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.5.1 Theoretical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.5.2 Simulations and Experiments . . . . . . . . . . . . . . . . . . . . . . . . 65
viii
3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4 Next Generation Breast Scanner 69
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.2 Previous Generation Breast Scanner . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.3 Next Generation Breast Scanner . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.3.1 Frequency Domain CCD Detection . . . . . . . . . . . . . . . . . . . . . 72
4.3.2 Electro-optic Modulator . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.3.3 Source Position Switch . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.3.4 Patient Bed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.4 Initial Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.4.1 Measurement Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.4.2 Spectroscopy Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.4.3 Phantom Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.4.4 Human Subject . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5 Comparison with Positron Emission Tomography 96
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.2 Positron Emission Tomography (PET) . . . . . . . . . . . . . . . . . . . . . . . . 100
5.2.1 PET Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.2.2 PET Image Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.2.3 PET Intrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.3 DOT Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.3.1 Subject Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
ix
5.4 Image Co-registration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.5 Clinical Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.5.1 Whole-body PET and DOT . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.5.2 Breast-only PET & DOT . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6 Summary 119
Bibliography 122
x