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

  • View
    212

  • Download
    0

Embed Size (px)

Transcript

  • 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 Arjuns 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 Schotlands 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