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Breast Cancer Detection with Diffuse Optical Tomography

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PAGE 1

1 BREAST CANCER DETECTION WITH DIFFUSE OPTICAL TOMOGRAPHY By CHANGQING LI A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2006

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2 Copyright 2006 by Changqing Li

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3 ACKNOWLEDGMENTS First, I would like to thank Pr ofessor Huabei Jiang, for his co ntinuous support, trusts and precious advice during my study for the Ph.D. Prof essor Jiang is well-known in the field of optical tomography. His views and understandings on the research subjects ar e exceptional. As a professor, although his schedule is very tight, he is always availa ble to help me on my research whenever I have frustrations. What I have learne d and experienced in Professor Jiangs lab will definitely benefit my fu ture career and life. Secondly, my thanks go to my academic committee members: Dr. William Ditto, Dr. Mingzhou Ding, Dr. Sihong Song. Their comments a nd suggestions were very helpful to my study and research. Their valuable time spent on r eading my dissertation is highly appreciated. Thirdly, I would like to thank Dr. Steven Grobm yer, an assistant prof essor in the surgery department of University of Florida. As our clin ical research partner, Dr Grobmyer helps us to recruit many breast cancer patients. And I would lik e to thank the research scientist in our lab, Dr. Qizhi Zhang, for his help on both my study and my research. I also thank Dr. Zhen Yuan for his help on the algorithm development. Dr. Qian g Wangs suggestions on the experiments were always impressive. Miss Lin Chen, a graduate st udent in our lab, gave me lots of help in performing the clinical trial experiments. So did Dr. Xiaoping Liang. Their help is highly appreciated. Fourthly, thanks got to my wife, Pan Sh eng, for her support. Without her support and encouragement, I could not have gotten through my graduate study. And thanks go to my lovely son, Jonathan Li, for giving me so ma ny excellent memories and happiness. At last, thanks to NIH for the financial s upport on the breast can cer imaging project.

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4 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................3 LIST OF TABLES................................................................................................................. ..........7 LIST OF FIGURES................................................................................................................ .........8 ABSTRACT....................................................................................................................... ............14 CHAPTER 1 INTRODUCTION..................................................................................................................16 1.1 Breast Cancer Facts........................................................................................................ ..16 1.2 History of Optical Imaging...............................................................................................16 1.3 Optical Imaging of the Breast...........................................................................................17 1.4 Optical Diffusion Theory..................................................................................................23 1.5 DOT Reconstruction Algorithm.......................................................................................26 1.5.1 Forward Solution Procedure...................................................................................26 1.5.2 Inverse Solution Procedure.....................................................................................27 2 DOT IMAGING SYSTEM AND ITS CALIBRATION........................................................30 2.1 DOT Imaging System.......................................................................................................30 2.1.3 Source/detector Fiber Optic Probe.........................................................................31 2.1.4 Detection Unit........................................................................................................32 2.1.5 Gain Control...........................................................................................................33 2.1.6 Detector Sensitivity and Dynamic Range...............................................................34 2.1.7 Stability................................................................................................................ ...34 2.1.8 DC Offset/Noise Reduction....................................................................................35 2.1.9 Data Acquisition Unit.............................................................................................35 2.1.10 System Timing......................................................................................................36 2.2 DOT Imaging System Operation......................................................................................36 3 SYSTEM CALIBRATION AND DOT ALGORITHM REFINEMENTS............................45 3.1 System Calibration......................................................................................................... ...45 3.1.1 Image Reconstruction Algorithm...........................................................................45 3.1.2 Calibration Method.................................................................................................46 3.1.3 Experimental Methods and Materials.....................................................................48 3.1.4 Results and Discussion...........................................................................................48 3.2 Dual Mesh Method...........................................................................................................51 3.2.1 Dual Mesh Method.................................................................................................51 3.2.2 Experiments............................................................................................................53 3.2.3 Results and Discussion...........................................................................................53

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5 3.3 Source Intensity Optimization Method.............................................................................55 3.3.1 Source Intensity Optimization Methods............................................................56 3.3.2 Experiments............................................................................................................58 3.3.3 Results and Discussion...........................................................................................59 4 PARTICLE SIZE IMAGING: PHANT OM EXPERIMENTAL STUDIES..........................86 4.1 Measurement of Particle Size Distribu tion and Concentration in Heterogeneous Turbid Media................................................................................................................... ....86 4.1.1Materials and Methods............................................................................................86 4.1.2 Simulations and experiments..................................................................................89 4.1.3 Results.................................................................................................................. ..90 4.1.4 Discussion and Conclusions...................................................................................92 4.2 Imaging of Particle Size Distribution a nd Concentration in Heterogeneous Turbid Media.......................................................................................................................... ........93 4.2.1 Methods and materials............................................................................................93 4.2.2 Results and discussion............................................................................................94 4.3 Experimental Results from Concentrated Suspensions with Bi-modal Particle Size Distribution................................................................................................................... ......97 4.3.1 Experimental system and materials........................................................................97 4.3.2 Experimental results and discussion.......................................................................98 4.3.3 Conclusions..........................................................................................................103 5 EX VIVO AND IN VIVO STU DY OF TUMOR CELL SIZING.......................................119 5.1 Ex Vivo Study of Tumor Cells.......................................................................................119 5.2 Morphological Characteristics of Breast Tumors: In-Vivo Study with Multispectral Diffuse Optical Tomography............................................................................................120 5.2.1 Methods................................................................................................................120 5.2.2 Results..................................................................................................................121 5.2.2.1 Case studies: #1, 2 and 3: In filtrating ductal carcinomas...........................121 5.2.2.2 Case studies: #4, 5 and 6: Benign nodule or mass.....................................125 5.2.2.3 Statistical analysis and pa thological co-registration..................................129 6 SPECTRALLY CONSTRAINED IMAGING OF ABSORPTION CHROMORPHORES AND SCATTERING CONCENTRATION....................................147 6.1 Introduction............................................................................................................... ......147 6.2 Algorithms................................................................................................................. .....148 6.2.1 Spectrally Constrained Reconstruction with the Method from Literature...........148 6.2.2 Spectrally Constrained Reconstructi on with Scatterers Volume Fraction Method.......................................................................................................................150 6.3 Numerical Simulations...................................................................................................152 6.3.1 Reconstruction with the Method from Literature.................................................152 6.3.2 Reconstruction with the Scat tering Volume Fraction Method.............................153 6.4 In-Vivo Imaging with the Molar Absorption from References......................................155 6.5 Measurements of Molar Extinction Coefficients............................................................156

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6 6.6 Phantom Experiments.....................................................................................................159 6.7 In-Vivo Imaging with the Measur ed Molar Extinction Coefficients..............................160 7 CONCLUSIONS AND FU TURE STUDIES.......................................................................179 7.1 Conclusions................................................................................................................ .....179 7.2 Future Studies............................................................................................................. ....181 7.2.1 Imaging System and Calibrations.........................................................................181 7.2.2 Multi-modality Imaging.......................................................................................182 7.2.3 Scattering Theory.................................................................................................182 7.2.4 Clinical Studies.....................................................................................................183 LIST OF REFERENCES.............................................................................................................184 BIOGRAPHICAL SKETCH.......................................................................................................192

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7 LIST OF TABLES Table page 3-1 Optical and geometric paramete rs used for Group 1 experiments.....................................84 3-2 Optical and geometric parameters used for Group 2 experiments.....................................84 3-3 Optical and geometric parameters used for Group 3 experiments.....................................84 3-4 Optical properties of the phantom ba ckground and the target for all 5 cases....................85 3-5 Optical properties of the target a nd background used in the six experiments performed...................................................................................................................... .....85 4-1 Reconstructed parameters from simulated da ta at different noise levels for simulation 1.............................................................................................................................. ..........116 4-2 Reconstructed parameters from simulated da ta at different noise levels for simulation 2.............................................................................................................................. ..........116 4-3 Reconstructed parameters from experi mental data using the peak and average scattering spectra of the target area..................................................................................116 4-4 Target materials of experiment set 1. The unit of volume is mL.....................................117 4-5 Target materials of experiment set 2. The unit of volume is mL.....................................117 4-6 Target materials of experiment set 3. The unit of volume is mL.....................................117 4-7 Reconstructed results of set1...........................................................................................117 4-8 Reconstructed results of set2...........................................................................................118 4-9 Reconstructed results of set3...........................................................................................118 5-1 Mean diameters and volume fraction of the nucleus and nucleolus found from the microscopic pictures and those of sca ttering particles calculated from the reconstructed images........................................................................................................146 6-1 Volume fraction of different particles in the background and the three targets for numerical simulation case 3.............................................................................................178 6-2 Concentrations of the absorption chromo rphores and Volume fractions particles for numerical simulation case4..............................................................................................178

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8 LIST OF FIGURES Figure page 2-1 Schematic of the experimental system...............................................................................37 2-2 Photographs of the experimental system...........................................................................38 2-3 Optical switch (a) Sc hematic and (b) photograph..............................................................39 2-4 Photographs of the ring structure.......................................................................................40 2-5 Internal and external connec tions of a silicon photodiode S8754.....................................40 2-6 Diagram of mounting conf iguration for one sensor...........................................................41 2-7 The detection board: (a ) Schematic;(b) layout...................................................................42 2-8 Flow chart of a det ector gain controller.............................................................................43 2-9 The control panel of the DOT imaging system..................................................................43 2-10 The LABVIEW control panel of the DOT imaging system..............................................44 3-1 Geometry of the phantom configuration............................................................................64 3-2 Reconstructed absorption and scattering images for the 3 cases in Group 1.....................65 3-3 Reconstructed absorption and scattering images for the 3 cases in Group 2.....................66 3-4 Reconstructed absorption and scattering images for the 3 cases in Group 3.....................67 3-5 1D profile of the absorption coefficient along the transect AB (see Figure. 3-1) for the image shown in Figure. 3-2a (a) and for image shown in Figure. 3-2d (b).................68 3-6 Four fine mesh elements generated from one coarse mesh element..................................68 3-7 Geometry of the ti ssue mimicking phantom......................................................................69 3-8 The a images (a-d) and s images (e-h) reconstructed for case 1 (4:1 a 2.8:1 s contrast, 15 mm off-center) phantom experiment........................................................70 3-9 The a images (a-d) and s images (e-h) reconstructed for case 2 (4:1 a 2.8:1 s contrast, 10 mm off-center) phantom experiment........................................................71 3-10 The a images (a-d) and s images (e-h) reconstructed for case 3 (4:1 a 2.8:1 s contrast, 5 mm off-cente r) phantom experiment..........................................................72

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9 3-11 The three-dimensional views of the recons tructed absorption coefficient images (a, c, e) in mm-1 and the reconstructed reduced scatte ring coefficient images (b, d, f)................73 3-12 Geometry of the phantom under study...............................................................................74 3-13 The absorption images reconstructed for case 1 (2:1 a contrast)....................................75 3-14 The absorption images reconstructed for case 2 (4:1 a contrast)....................................76 3-15 Reconstructed absorption images (rows 1 and 2) and scattering images (rows 3-5) for case 3 (2:1 a and s contrast).........................................................................................77 3-16 The absorption images reconstructed for case 4 (4:1 a and s contrast)........................79 3-17 The scattering images r econstructed for case 4 (4:1 a and s contrast).........................80 3-18 Recovered a values along a transect through th e centers of the target and background for the images at y=0 mm, z=2 mm...............................................................81 3-19 The absorption images (a and b) and scat tering images (c and d) reconstructed with the source optimization method for case 5 (4:1 a and s contrast)................................82 3-20 The absorption images (a and b) and scat tering images (c and d) reconstructed with the source optimization method for case 6........................................................................83 3-21 The source intensity obtained with th e uniform source intensity method and the source intensity distribution obtained with the source intensity optimization method......83 4-1 Simulated scattering spectra obtained fr om Mie calculation and the fittings based on the recovered particle size distribution and concentration at different noise levels........104 4-2 Reconstructed scattering images fo r Case 2 at 10 di fferent wavelengths........................105 4-3 Normalized exact (solid lines) and re constructed (dashed li nes) particle size distribution from phantom measur ements for Cases 1, 2 and 3.......................................106 4-4 Experimental scattering spectra obtained w ith different methods for Case 1 (left) and Case 3 (right)................................................................................................................. ...106 4-5 Scattering spectra: (a) The spectra genera ted by Eq. (5) and the Mie fittings using recovered particle parameters from simulated data.........................................................107 4-6 The DOT reconstructed absorption images (a1 to a10) and reduced scattering images (b1 to b10) at 10 different wavelengths...........................................................................108

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10 4-7 Reconstructed images of mean particle size (a, c) and concentr ation (b, d) for the 2.06 m (a, b) and 5.66 m (c, d) polystyrene cases, respectively...................................109 4-8 The reduced scattering coefficient images at 9 different wavelengths for experiment set1_1......................................................................................................................... ......110 4-9 The reduced scattering coefficient images at 9 different wavelengths for experiment set1_1. The global minimum error initial value is selected.............................................111 4-10 Reduced scattering coefficient at 10 wave lengths for 5 cases of experiment set1. Fixed value was applied for each case.........................................................................112 4-11 Reduced scattering coefficient at 10 wavele ngths for 5 cases of experiment set1. The value of corresponding to the global minimum error was applied for each case.......112 4-12 Reduced scattering coefficient at 10 wave lengths for 4 cases of experiment set2. Fixed value was applied for each case.........................................................................113 4-13 Reduced scattering coefficient at 10 wave lengths for 3 cases of experiment set 3. Fixed value was applied for each case.........................................................................113 4-14 The reconstructed diameter versus (a) the calculated scattering coefficient ratio of 1 m particles and 6 m particles and (b) the volume fraction of 1 m particles for experiment set 1...............................................................................................................114 4-15 The reconstructed diameter versus (a) the calculated scattering coefficient ratio of 1 m particles and 6 m particles and (b) the volume fraction of 1 m particles for experiment set 2...............................................................................................................115 5-1 The microscopic picture of (a) the tu mor tissue (400 time magnificent) and (b) the normal tissue (100 time magnificent)..............................................................................132 5-2 Experiment preparation: (a) the rem oved tissue was put inside the background phantom; (b) The tissue was covered with background phantom and examined by the system......................................................................................................................... .....132 5-3 Ex-vivo results: (a) The extracted nucleus concentration distribution in the tissue region and the intralipid concentratio n distribution in the background region................133 5-4 Mammogram films: (a) Right CC mammogram, (b) Right MLO mammogram for the right breast of a 52 years old patient (patient ID #G1)....................................................133 5-5 The constructed scattering images at 9 wa velengths from 638nm to 922nm (figs. a to i) of the examined breast for patient G1..........................................................................134 5-6 The extracted images of particle diameter s (a) and particle volume fraction (b) of the examined breast for patient G1........................................................................................134

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11 5-7 Mammogram films: (a) CC mammogram, (b) MLO mammogr am for the right breast of a 50 years old patient...................................................................................................135 5-8 The reconstructed scattering images at 9 wavelengths from 638nm to 922nm (Figs. a to i) of the examined breast for patient #G2....................................................................136 5-9 The extracted images of particle diameter s (a) and particle volume fraction (b) of the examined breast for patient #G2......................................................................................136 5-10 The reconstructed scattering images at 4 wavelengths from 733nm to 840nm (Figs. a to d) of the examined breast for patient G8.....................................................................137 5-11 The extracted images of particle diameter s (a) and particle volume fraction (b) of the examined breast for patient G8........................................................................................137 5-12 Mammogram films: (a) MLO and (b) CC mammography of the right breast for patient #S5.................................................................................................................... ...138 5-13 The reconstructed absorpti on coefficient images for the right breast of the patient #S5 at 9 wavelengths from 638nm to 922nm (a to i).......................................................138 5-14 The reconstructed scattering images at the right breast of the patient #S5 at 9 wavelengths from 638nm to 965nm (a to i).....................................................................139 5-16 Mammogram films: (a) CC and (b) MLO ma mmography of the left breast for patient #S7............................................................................................................................ .......140 5-17 The reconstructed scattering images of the examined breast at 9 wavelengths from 638nm to 965nm (a to i) for patient #S7..........................................................................140 5-18 The reconstructed particle diameter imag e (a) and the particle volume fraction image (b) of the examined breast for patient #S7.......................................................................141 5-19 Mammogram films: (a)RMLO, (b)RML images of the patient #S9...............................141 5-20 The reconstructed scattering images of the right breast for patient #S9 at 9 wavelengths from 638nm to 965nm (a to i).....................................................................142 5-21 The reconstructed particle diameter imag e (a) and the particle volume fraction image (b) of the right breast for patient #S9...............................................................................143 5-22 Average values of recovered mean di ameter and volume fraction of scattering particles for 8 benign cases and 4 malignant cases, respectively....................................143 5-23 The peak value of the recovered volume fr action in the target region versus the peak value of mean diameter in the target region.....................................................................144 5-24 The pathological microscopic pictures of tumor cells for patient #G1 ( shown in a), #G2 (shown in b) and #G3 (shown in c)..........................................................................145

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12 6-1 Reconstructed concentration images of H bo2 (a), Hb (b) and water (c) and images of equivalent diameters (d) and volume fraction (e)............................................................166 6-2 The exact images of volume fraction (a ) and diameters (b) and the reconstructed images of volume fraction (c) and diam eters (d) with the method described in subsection 6.2.1 when only th e volume fraction and diam eters are reconstructed..........166 6-3 The geometry of the numerical simulati ons for case 3 (a) and case 4 (b), where D=70 mm, d=20 mm and Doffset=40 mm....................................................................................167 6-4 The reconstructed volume fractions imag es for 150 nm particles (a, d), 1000 nm particles (b, e) and 6000 nm particles (c, f).....................................................................167 6-5 The reconstructed images of concentrati ons of Hbo2, Hb, water and volume fractions of 1000 nm particles and 6000 nm particles from leftmost column to rightmost column......................................................................................................................... .....168 6-6 The reconstructed concentration images of Hbo2 (a, f), Hb (b, g)j, water (c, h) and volume fraction images of 1000 nm particles (d, i) and 6000 nm particles (e, j) for patient 1 and for patient 2................................................................................................168 6-7 The container for molar absorption meas urements. The upper pa rt is the drinking water bottle and the bottom part is composed of Cling Wrap.........................................169 6-8 The liquid solution inside the container is ready for the measurements. The Cling Wrap contacts with fiber probes......................................................................................169 6-9 The absorption coefficients of water from the reference (triangle) and measurements of Intralipid solution (diamonds).....................................................................................170 6-10 The molar absorption of oxy-hemoglobin from the reference (solid line) and measurements of blood solution wi th different concentrations.......................................170 6-11 The molar absorption of deoxy-hemoglobi n from the reference (solid line) and measurements of blood solution wi th different concentrations.......................................171 6-12 Reconstructed images of to tal hemoglobin concentrations (1st row) in unit of M, oxygen saturation (2nd row), water concentration (3rd row) in percentage and scatterers volume fraction (4th row) in percentage of phantom experiments...................172 6-13 Chromophores concentration images a nd scatterers volume fraction image in percentage (j) reconstructe d with the measured molar spectra, using method 1 (1st row), method 2 (2nd row) and method 3 (3rd row) for clinical case S5............................173 6-14 For clinical case S5, chromophores con centration images rec onstructed with the molar spectra from reference, using method 1 (1st row) and method 2 (2nd row) for clinical case S5............................................................................................................... ..173

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13 6-15 For clinical case S7, chromophores con centration images a nd scatterers volume fraction image in percentage (j) reconstructed with the measured molar spectra, using method 1 (1st row), method 2 (2nd row) and method 3 (3rd row).....................................174 6-16 For clinical case S7, chromophores con centration images rec onstructed with the molar spectra from reference, using method 1 (1st row) and method 2 (2nd row)............174 6-17 For clinical case S28, chromophores con centration images a nd scatterers volume fraction image in percentage (j) reconstructed with the measured molar spectra, using method 1 (1st row), method 2 (2nd row) and method 3 (3rd row).....................................175 6-18 For clinical case G1, chromophores con centration images a nd scatterers volume fraction image in percentage (j) reconstructed with the measured molar spectra, using method 1 (1st row), method 2 (2nd row) and method 3 (3rd row).....................................176 6-19 For clinical case G14, Chromophores con centration images and scatterers volume fraction image in percentage (j) reconstructed with the measured molar spectra, using method 1 (1st row), method 2 (2nd row) and method 3 (3rd row).....................................177

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14 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy BREAST CANCER DETECTION WITH DIFFUSE OPTICAL TOMOGRAPHY By Changqing Li December 2006 Chair: Huabei Jiang Major Department: Biomedical Engineering Diffuse optical tomography (DOT) is emerging as a potential imaging technique for breast cancer detection. Compared with the rou tine x-ray mammography which gives only the structural images of breast tissue, DOT provides not only the structural in formation, but also the functional images including oxyhemoglobin, deoxyhem oglobin, lipid and water content as well as the morphological images including nucleus size and volume fraction. The goal of this thesis study is to obtain these structur al, functional and morphological cont ents of breast tissue using a multi-spectral DOT reconstruction approach. This study involves imaging hardware implementation and software development necessary for achieving the goal. The imaging system and reconstruction software implemented are test ed and evaluated using extensive simulations, tissue-like phantom experiments and in vivo clinical studies. A compact diffuse optical tomography system, specifically designed for breast imaging, is constructed. The system consists of 64 silicon photodiode detectors, 64 excitation points, and 10 diode lasers in the near-infra red region, allowing multi-spectral, three-dimensional optical imaging of breast tissue. The system performance and optimization through a calibration procedure are detailed. The system is evalua ted using tissue-like phantom and clinical experiments. Quantitative 2D and 3D images of absorption and reduced scattering coefficients

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15 are obtained from these experimental data. Two methods, dual mesh met hod and source intensity optimization method, are implemented for improv ed 3D DOT reconstructions and validated by tissue-like phantom experiments. Reconstruction algorithms fo r obtaining tissue morphological images are described. Quantitative images are successfully reconstructe d in terms of the size, location and tissue morphology of target from both tissue phantom and in vivo data. Initial clinic al results show that the scattering particle size and volume fraction at cellular level are potential new parameters that could be used for differentiating malignant from benign lesions. A new method, namely spectrally constraine d DOT, is also developed to directly reconstruct tissue chromophore c oncentrations and volume fract ion of scatte ring particles simultaneously. The absorption extinction co efficient spectra of oxy-hemoglobin, deoxyhemoglobin as well as the absorption spectrum of water are measured using a mixture of human blood and Intralipid solution with the imaging system developed. The quality of the reconstructed images is improved substantially wh en the measured spectra are utilized, compared with that of the images recovered with the spectra obtained from the literature.

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16 CHAPTER 1 INTRODUCTION 1.1 Breast Cancer Facts The American Cancer Society estimates that 211,240 women will be diagnosed with invasive breast cancer, as well as approximate ly an additional 58,490 women will be diagnosed with in situ breast cancer, a nd 40,410 women will die of cancer of the breast in 2005. Only lung cancer accounts for more cancer deaths in women. Based on rates from 2000-2002, 13.22% of women born today will be diagnosed with cancer of the breast at some time during their lifetime. This number can also be expressed as 1 in 8 wo men will be diagnosed with cancer of the breast during their lifetime.1 1.2 History of Optical Imaging Breast cancer is caused by the cancer cells which are characteri zed by the uncontrolled division and the ability to invade into the normal tissues and spread to the whole body. The stage before the spreading is called in situ, meaning that the tumor is happened locally and is not invasive. When a tumor or a lump is palpable in the breast, it is usually one centimetre in size and contains one million cells approximately. It is estimated that a lump of this size may take one to five years to be developed. The cancer ma y metastasize, or spr ead to other tissues by lymphatics or blood during the development period. The earlier the cancer is detected, the lower risk for patients to have it spread and the higher probability to have it cured. Optical imaging allows the possibility of earlier breast cancer de tection due to its uniqu e feature of functional imaging. Furthermore, the physical examinati on has only 20% to 30% specificity for lesion detections. And annual mammography screening pr ovides higher specificity and sensitivity of breast lesion detection. However, the patients are under risk with exposure to x-ray radiations

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17 frequently. The non-ionized optical imaging can be used to screen the breasts frequently without any side effects. Earlier time, optical imaging was called tran sillumination or diaphanography, in which the white light cast on a breast directly a nd the shadow of the breast was reviewed.2 This technology was further improved by using the red light and near infrared (wavelength from 600 nm to 800 nm) since the photons at these wavelengths could penetrate deeper into the breast.3 However, the clinical trail results of the improved transillumination showed that the method failed to detect tumors less than 2cm inside the breast due to the dominated scattering.4-5 This is unacceptable for the breast screening since the screening resolution is required to be a few millimeters at least. The optical imaging for breast cancer detec tion has made substantial progress recently due to the improved mathematical models of optical transportation, much more powerful computation tools, and advanced measuremen t technologies. The mathematical models are introduced in subsection 1.4. The models are solv ed by the finite element method, differential method or other methods. All these methods n eed heavy computation. The powerful and cheap computer makes the heavy computation possibl e and feasible for many scholars. With the progress in electronics, there are many advanced optical measurement tools available, such as photomultiplier tube (PMT), photodiodes, CCD. Th ese tools measure the photon flying time, the amplitude and phase of high frequency modulated light or the light intensity of continue-wave light. These accurate measurements allow a good quality of optical imaging. 1.3 Optical Imaging of the Breast Optical imaging attracts more and more scholar s because of its unique features. At first, it is non-ionized. There are no side effects for the optical breast imaging. So the patient can do breast screening frequently. Second ly, compared with other methods the cost of optical imaging is lower. Thirdly, optical imaging is efficient to differentiate between the soft tissues because the

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18 optical absorption is proportional to the concen trations of hemoglobin, water and lipid in the tissues. Finally, optical imaging is both a func tional and morphological imaging method. It is able to image the concentrati ons of oxy-hemoglobin, deoxy-hem oglobin, water and lipid of the examined tissues using the optical absorption spectr a. And it is also able to obtain the particle (such as nucleus) size distribution and density in the tissues using the scattering spectra. This special feature makes the optical imaging a po ssible method to detect the breast cancer earlier than other methods such as mammography, ultrasound, MRI and PET. Mammography is the most widely accepted method for breast cancer screening. Despite its advantages, mammography has a high false positive rate because it can not differentiate the beni gn and malignant tumors efficiently. And mammography makes the patient expos e to the x-ray radiati on. As an adjunct to the mammography, the breast ultrasound is used to de termine whether a lump is filled with fluid or solid mass. Ultrasound works well for dense breasts. Ultrasound breast imaging is still under investigation for further improvements. Current breast MRI clinical appl ications include the evaluation of the extent of cancer in breast be fore surgery, imaging the breast with silicone augmentation and evaluating the exte nt of chest wall to assist the surgery. Breast MRI is more expensive than mammography, ultrasound and op tical imaging. Positron emission tomography (PET) of breast can determine whether a tumor is malignant or benign. Bu t its spatial resolution is very low. And PET is also very expensive. Optical breast imaging method is based on the fa ct that the optical properties of diseased and normal breast tissues are different.6-10 At NIR wavelength, the absorption in carcinoma is significantly higher than in ad jacent uninvolved tissues. The difference between diseased and normal tissues is as high as 100% in the near infrared region due to the increased hemoglobin

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19 concentration in tumor.8 It was also reported that there wa s a four-fold increase in blood volume in diseased breast compared to the normal tissu e due to the increased blood vessels and size.11 Although the mechanisms of photon propaga tion in breast tissues have not been understood completely, pilot in vivo measur ements of endogenous opt ical properties and endogenous tumor contrast have been reported.12-23 The reported results were promising. For example, Gu et al.12 reported that cysts rangin g from 1-4 cm in diamet er can be quantitatively imaged. Cysts can be differentiated from solid br east tumors because cysts generally demonstrate lower absorption and scattering coefficients compared with the surrounding normal tissue, whereas solid tumors show conc urrent higher absorption and sca ttering related to the normal tissue. The use of exogenous cont rast agents has also studies.23 For example, Indocyanine green (ICG) was demonstrated to enhanc e breast tumor contrast in vivo.23 All the reported results suggest that the optical imaging is a potential diagnostic method. So far, several groups including our own ha ve developed reconstruction algorithms for optical image reconstructions in frequency domain24-26, time domain27 and CW domain28-31, or in a hybrid (frequency/continuous-wave) domain.32 We are interested in the CW domain DOT due to its simple hardware implementation comp ared with the frequency and time domain DOT. While we and other groups have shown that the CW method could extract the absorption coefficient and the reduced scattering coefficient images quantitatively twoand threedimensionally using tissue mimicking phantoms and in vivo tissues at the specific wavelengths,28,30,32 it is still a very challe nging problem to obtain the quantitative images at the wavelengths in the region from 600 nm to 1000 nm due to the worse signal noise ratio at both the short and long wavelengths such as 600 nm and 1000 nm. Because the spectroscopy in the whole region is needed in order to ex tract the optical scatte rers size and volume fr action, it is necessary

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20 to further improve our current algorithm by using methods su ch as the dual mesh method,32-34 and source intensity optimization.35 We built our first generation DOT system using single photomultiplier tube (PMT) detection.28 Even though it was extremely slow, it allowe d us to obtain the first successful 2D and 3D optical imaging of in vivo breast tissue based on CW approaches.36-37 Recently we developed the second generation optical imagi ng system using 16 PMTs and 3 wavelengths.38 Significant in vivo breast imaging results have been generated from this second generation machine12 while active clinical studies are still on-goi ng using this system. In order to acquire the functional and morphology images, 3 wavelengths are not enough and more laser modules at different wavelengths are needed.39-40 A new system with 10 wavelengths which are capable of fast data collection is needed. When light propagates through mammalian tissues the scatterers are cell organelles of various sizes, such as nucleus and mitochondria which have higher refr active index than the surrounding cytoplasm.41 Perelman et al. have shown that light singly backscattered from an epithelial layer of tissue such as the skin has a wavelength-depe ndent periodic pattern.42 They found that the periodicity of the pattern increa sed with nuclear size a nd the amplitude of the periodic signal was related with the density of nucleus. After an alyzing the periodic pattern, the nucleus size and density could be extracted. However, the peri odic pattern was overwhelmed by the diffuse background or by the multiple scattered lights since the backsca ttered light is only a small portion of the scattered light. One way to overcome the problem is to use a model to mathematically describe the single backscattere d light. But this method has to be remodeled for different tissues under investig ation which is inconvenient.42 Another robust approach, also proposed by Backman et al., is to use polarized light to differentiate th e single scattered light

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21 from multiple scattered light background.43 It was reported that the in itially polarized light lost its polarization after scattered propagation in turbid media such as biological tissues.44-46 In contrast, the single backscattere d light kept its polarization.47 After subtracti ng the unpolarized light, the polarized component of the backscattered light from the epithelial layer of the tissue was obtained. An alternative approach to differe ntiate the backscattering from background is to utilize a probe geometry that optimizes the detection of si ngle scattered light.48 It was demonstrated that the single opti cal fiber approach was highly sens itive to the light backscattered from layered superficial tissues. Cells have complicated structures and the organelles inside a cell vary in size from a tenth of micron to 10 microns. A ll the organelles contribute to the scattering which complicates the cell scattering phenomena. With fiber-optic, polarized elastic-scatte ring spectroscopy techniques, Mourant et al. estimated that the average scatterer radius in tissue was from 0.5 to 1.0 m, which is much smaller than the nucleus.49 Using the polarized light spectroscopy, the particle size distribution in ma mmal cells was measured and the results suggested that small particles (possibly the mitochondria) contribute mo st to the scatteri ng. However, other subcellular structures, such as the nucleoli and the nucleus, may also contribute significantly.50 Backman et al. demonstrated that the spectrum of the single backscattering component was capable of providing the cell nucl ei size distribution, which means the single backscattering was dominated by the nucleus.51 Scattering spectra in multi-spectral disuse optical tomography (MSDOT) have been relatively less explored. This is hampered larg ely by the strong crosstal k between absorption and scattering contrasts that occurred in earlier DOT reconstructions, which was reduced/eliminated only recently by various image enhancement schemes.31,52 In pure optical spectroscopy studies as

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22 described above, it has been show n that scattering spectra are correlated with tissue morphology. These experimental studies have suggested that bo th nuclei and mitochondria contribute to tissue scattering significantly. On the ot her hand, it is well known in path ology that tumor cells/nuclei are considerably enlarged relative to normal ones.53 Thus significant clin ical value would be resulted from the exploration of scattering sp ectra in MSDOT. Thus far scattering spectra in MSDOT have been studied with a simple power law,54-55 which was originated from spectroscopy studies with homogeneous media.56-59 The advantages of the power law are its simplicity and reasonable accuracy under certai n conditions. The disadvantage is that the constants in the power law have no clear physical meanings and that particle size distribution and concentration cannot be dire ctly obtained from this empirical relationship. Currently, two noninvasive optical imaging methods are used to measure particle size distribution. One is the light scattering spectroscopy (LSS),60 in which polarized light was delivered to the epithelial tissue and the single ba ckscattering light that ke pt the polarization was analyzed to extract the morphologi cal features and the refractive index of the scatterers. This method is limited primarily to s uperficial surface imaging. The othe r one, which we are trying to further develop, is a tomographic imaging method based on multi-spectral diffuse optical tomography,61-62 in which the tomographic scattering images of tissue at multiple wavelengths were obtained with diffuse opti cal tomography and the scattering spectra were then used to extract the scatterers size information with a Mie theory based reconstruction method. To utilize the Mie theory for particle/nucleus sizing, severa l assumptions are generally made: particles are spherical; no particle-particle interactions exist; and the photon diffusion equation is valid which means that light scattering is much larger than the absorption. While the reasonable results have been obtained based on above assumptions,61-62 we plan to investigat e them further to see

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23 whether better results co uld be extracted if more complicated models such as Wentzel-KramersBrillouin (WKB) model was applied.63 Conventionally, two separate sequential step s are deployed to calculate the functional images. At first, the absorption images at diffe rent wavelengths are reconstructed by DOT. Then the contributions to the abso rption images from each ti ssue chromophore are calculated.15 Recently, a new approach for extracting the ti ssue chromophores is that tissue chromophore concentrations and Mie scattering factors are r econstructed directly by exploiting the spectral priori information.55 Corlu et al. show that the new met hod works very well in the CW domain with the linear inverse method to update the parameters iteratively. While the chromophore concentration image quality is improved substantially due to the reduction of the reconstructed parameters by exploiting a priori spectral cons trained technique, the cross talk between the scattering parameters a and b limited its applic ations. The new method applications to our nonlinear iterative DOT algorithm will also be inve stigated in this dissertation to determine whether image quality could be further improved. 1.4 Optical Diffusion Theory Boltzmann transport equation describes in coherent photon propa gation through highly scattering media such as tissue. The e quation in time domain is written as t s r q s d t s r s s r t s r r s t c 14 s tr (3.1) where t s r is the radiance [W/(cm2 sr)] at position r at time t, propagating along the unit vector s r r r s a tr is the transport cross section at position r r a and r s the absorption and scattering coefficients, are the in verse of the absorption and scattering mean free path respectively. c is the speed of light in the medium. The function s s is the probability

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24 density function over all solid angels of the change in phot on propagation direction from s to s due to an elastic scattering ev ent which satisfies the condition: 1 s d s s 4 t s r q is the photon power generated at position r along direction s This equation reflects the energy conservation in the medium. However, the equation often must be simplified to be mathematically manageable. One way to simplify it is to expand the equation with spherical harmonics and truncate the series at the Nth term, namely PN approximation. Thus the quantities in equation 3.1 can be expressed as L L L m m L m L 2 1s Y t r 4 1 L 2 t s r (3.2) L L L m m L m L 2 1s Y t r q 4 1 L 2 t s r q (3.3) cos P 4 1 L 2 s s L L L 2 1 (3.4) where 2 14 1 L 2 is the normalization factor, m LY the spherical harmonic of order L at degree m, LP Legendre polynomial of order L. P1 approximation is obtained when N=1 from the PN approximation. After simplification, the following equations are obtained: t r q ) t r ( r ) t r ( J ) t r ( r t c 10 0 0 s tr (3.5) ) t r ( q ) t r ( J r ) t r ( 3 1 ) t r ( J r t c 11 s 1 tr (3.6)

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25 where ) t r ( ) t r (0 0 is the photon fluence, T 0 1 1 1 1 1 1 1 1 1) t r ( ) t r ( ) t r ( 2 i 1 ) t r ( ) t r ( 2 1 ) t r ( J the photon flux. The P1 approximation can be further simplif ied by making the following assumptions: 0 t J 0 q 1. (3.7) The approximation, namely diffuse approximation, is usually justified only if the scattering coefficient is much lager than the absorption coe fficient in order to satisfy the first assumption, 0 t J The second assumption, 0 q 1 means that the photon source is isotropic. The diffuse approximation leads to the following equation, namely diffusion equation, in the time domain t r q t t r c 1 t r t r r D0 a (3.8) or in the frequency domain r q r c i r r r D0 a, (3.9) or in the continue wave domain r q r r r D0 a (3.10) where s a3 1 r D is the diffusion coefficient, s 1 s1 the reduced scattering coefficient and r q r q0 0 0 the isotropic source. In infinite homogeneous media, the solu tion to the diffusion e quation can be obtained through the Green function method. However, for realistic finite homoor hetero-geneous media such as tissue, the boundary effects/conditions must be accounted for.

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26 1.5 DOT Reconstruction Algorithm There are two procedures involved in the DOT image reconstruction. The first one is the forward solution procedure, in which the distribu tion of light in the medium of interest is predicted. The second one, the inverse solution procedure, is used to iteratively update the initially guessed optical propert y distribution of the medium through an optimization method such as Newton method by minimizing the square d difference between the data computed from the diffusion equation and measured around the surface of the medium. 1.5.1 Forward Solution Procedure Since an analytical solution to the Boltzma nn transport or the di ffusion equation is not available in a realistic situation, numerical meth ods must be used for most cases. Finite element method (FEM) is a natural choice because it can be used to solve the diffusion equation in inhomogeneous media with an arbitrary geomet ry, although other numerical methods such as finite difference method64, finite volume method65 and boundary element method66 have been used in DOT. The FEM applications in DOT have been discussed in details elsewhere68-69. Here we follow Paulsen and Jiang69 and briefly describe the FEM method in the CW DOT. Using the finite element discretization, th e stead-state photon diffuse equation coupled with the type III boundary conditions, n D can be transformed into the following matrix form b A (3.11) where is the BC coefficient related to the intern al reflection at the boundary; the elements of matrix A are D ai j a i j ij where indicates integration over the problem domain; b is M 1ds Sj j i j i; ) r r ( S S0 0 where 0S is the source strength and

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27 ) r r (0 is the Dirac delta function for a source at 0r; ; M is the number of boundary nodes; i and j are locally spatially varying Lagrangian basis functions at nodes i and j, respectively. The vector N 2 1, , is the photon density. Four critical parameters (the BC coefficient the source strength S0, and the initial guess of D and a ) should be accurately determined by a pr eprocessing data optimization scheme for the forward computation. We assume all the s ource intensities are the same and equal to S0. The pre-processing data optimization scheme for determining the four initial parameters is discussed in detail elsewhere [Nic and Jiang, 2000]. Briefly, -square errors,2 1 M 1 ) c ( m 2~ X i i i, are minimized as the function of the above four pa rameters, where M1 is the number of boundary measurements (for example M1=64), m i is the measured photon density from a given experimental heterogeneous medium, and ) c ( ~ i is the computed photon density from a numerical simulation of a homogeneous medium with the same geometry as the experimental medium. Given reasonable ranges for the four parameters, the minimum 2X corresponds to the best initial guess of the four parameters. 1.5.2 Inverse Solution Procedure An example of inverse solution procedure is given here based on Taylor expansion or Newton method. We assume that th e computed and/or the measured are analytic functions of D and a, and that D and aare independent parameters. then can be Taylor expanded about an assumed (D,a) distribution, which is a perturbation away from some ot her distribution, (D ~ ,a ~ ), and the expansion is expressed as,

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28 a a a aD D D ~ D ~ (3.12) where D D ~ D and a a a ~ If the assumed optical prope rty distribution is close to the true one, the high order items in the expansion can be neglected and we obtain c oJ (3.13) where aL M 2 a M 1 a M K M 2 M 1 M aL 2 2 a 2 1 a 2 K 2 2 2 1 2 aL 1 2 a 1 1 a 1 K 1 2 1 1 1D D D D D D D D D J (3.14) T aL 2 a 1 a K 2 1D D D (3.15) T o M o 2 o 1 o (3.16) T c M c 2 c 1 c (3.17) and o i and c i are observed and calculated data for i=1,2,M measurements, Dk for k=1,2,,K and al for l=1,2,,L are the reconstruction optical parameters. In order for equation 3.13 invertible, regularizatio n method is used and expressed as c o T J I J T J (3.18)

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29 where I is the identity matrix w ith the size of 2NN, N is the node number of the finite element mesh, is the regularization parameter, JT is the transposed Jocabian matrix, is the updating vector defined by equation 3.15.

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30 CHAPTER 2 DOT IMAGING SYSTEM AND ITS CALIBRATION 2.1 DOT Imaging System The imaging system is schematically shown in Figure 2-1. Light beams from ten laser modules are transmitted to the optical switch, whic h sequentially passes one of the beams to 64 pre-selected points at the surface of the phant om or breast via source fiber bundles. The ring structure or fiber optic/tissue interface holds th e 64 source and 64 detection fiber bundles. Light from the 64 detection fiber bundles are sensed by the detection units, which convert the light intensity into voltage signals. The computer co llects the signals through a data acquisition board. The DC motor near the ring is used to adjust the diameter of the ring. Two CCD cameras are mounted underneath the ring to monitor the cont act between the tissue an d fiber optics. Figures 2-2a and 2-2b show photograph of the entire imaging system where we can see that all the optical and electronic components are housed under the exam tabl e. The individual components are detailed below. 2.1.1 10-wavelength Laser System 10 fiber-coupled laser modules at different wavelengths are used as CW laser sources. Each laser module is a compact integrated package of laser driv er, thermoelectric cooler and temperature controller. The output power can be set from zero to maximum by adjusting the output control voltage from 0 to 5 volts. The pi gtail fibers are 100um in diameter and have a numerical aperture (NA) of 0.22. Table 2-1 gives more detailed information about these laser modules. 2.1.2 Optical Switch A programmable 10x64 optical switch (GP700-4-1, Dicon Fiberoptics, Richmond, CA), controlled by a LABVIEW program through RS-232 remote interface, is used to deliver light

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31 from lasers to the source fiber bundles. The co nfiguration diagram and photograph of the optical switch are shown in Figures 2-3a and 2-3b, respectively. Inside the optical switch, there is a dual switch that works in tandem to deliver light to the target. The function of the left switch is to choose the wavelength and the other to select the source fibers. 100 m fibers with FC connectors inside the optical switc h, connected to the pig-tail fi bers from the 10 laser modules, are used for light receiving/coupl ing. The insertion loss and back reflection are in the range from 0.56 to 1.15 dB and from -30.20 to -23.80 dB, respectively. The maximum crosstalk between any two channels is -80 dB. The la ser output passes through the op tical switch via 100um-diameter fibers, and is then coupled to 1mm-diameter source fiber bundles. 2.1.3 Source/detector Fiber Optic Probe Figures 2-4a and 2-4b show photographs of the source/detector fi ber optic array. It consists of a diameter-adjustable cone-shaped frus tum containing four planes/rings of fiber optic bundles (RoMack, Williamsburg, VA). In each plan e/ring, 16 detector fiber bundles (2.0 mm in diameter) are arranged equally spaced around the annulus with another 16 source fiber bundles (1.0mm in diameter) interspersed between the det ector bundles. This fiber-optic/tissue interface was custom designed and constr ucted with high precision. The synchronized radial motion of fibers is realized through mechan ical fingers that are driven by a DC motor. The diameter of the fiber array can be adjusted between 4.0 and 15.0 cm to fit different breast sizes. The height of the four-layer fiber array covers 2.0 cm. The fiber optic probe is mounted right below an aperture on the exam table. During a clinical imaging measurement, the patient places her breast through the aperture so that the breast comes in contact with th e fiber optic array. While the four-layer fiber optics is good enough to image the tissue volume for most cases in which we are currently interested, different

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32 vertical positioning can be realized through the vertical tran slation of the ring The position of the four planes/rings of fiber optic bundles is extended up intentionally. This allows the fiber optic probe to be positioned close to th e patients chest wall if necessary. 2.1.4 Detection Unit Low noise light sensors, silicon photodiodes (S8745, Hamamatsu, Bridgewater, NJ) are chosen for low level light measurement. Each sensor integrated into a sma ll package, consists of a large area silicon photodiode (D 1), an operation amplifier, a feed back resistance (Rf = 1G ) and a capacitance (Cf = 5pF), as shown in Figure 25. The external feed back resistors, Rf1, Rf2 and Rf3, are used to adjust the feedback ga in. By controlling the relay (8L02-05-01, COTO Technology) switches (switch 1, switch 2 and switch 3), the sensor gain can be set to one of four gains (gain0, gain1, gain2 and gain3). The gain sw itching is discussed in detail in section 4.B below. Four detection boards are made with 16 sensors mounted on each board. There are 64 sensors totally in the detection unit, which r eceive light intensities delivered from the 64 detection fiber bundles simultaneously. Figure 26 shows the diagram of mounting configuration for one sensor as well as the coupling between the detection fi ber bundle and th e silicon window of the sensor. The ten pins of each sensor are eas y to be bent/broken. To protect the pins, one piece of plastic is used to hold the sensor and the pl astic is attached to the circuit board to insure that there is no relative moveme nt between the plastic and the circuit board once the pins are soldered on the circuit board. The plastic also isolates the circuit board from the grounded aluminum box, which shields any external electric/magnetic noises. Figure 2-7a shows the schematic of a circuit board we design ed. The 4-16 decoder is used to select the sensors. A four-bit digital signal from the computer is sent to the decoder directly.

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33 Once a sensor is selected, the external feedback resistors are connected with pin4 and pin6 such that the gain is adjusted by the gain switch co ntroller, whose function is to reduce the gain whenever the output is saturated and to increase the gain whenever the output is below 0.2 V. The controller sends the gain stat us (digital signal) to the computer. The signal output from the inverting amplifier is subsequently sent to a low-pass filter with a cutoff frequency of 10 KHz. Finally, the output signal from the low-pass f ilter, is sent to the A/D board. The A/D board collects only one output at a time from each tim e. The whole detection unit has four detection boards, hence four channels of data can be ac quired at the same periods and 16 times of data collection are needed for all th e 64 detection channels. Figure 2.7b shows the layout of the detection board, which is designed by the ORCAD. 2.1.5 Gain Control When all the three gain switches are off, the detector gain is set to maximum (gain0). Whenever one of the switches is on, the other two must be off. The gain ratio, gain0: gain1: gain2: gain3, is 27000:900:30:1. Figure 2-8 is a schematic, showing ho w the three switches are controlled. Once the output voltage is larger than 9.9V, the controller sw itches the gain to next level and the voltage is reduced by a factor of 30 to the level of 0.33 V, shown by arrows 2, 4, and 6. Whenever the output voltage is less than 0.2V, the gain is swit ched to upper level and the voltage is amplified by a factor of 30, shown by arrows 1, 3, an d 5. The hysteresis loop makes the controller insensitive to small signal fluctuations. All the detector gains are set to gain1 initially. Most signal levels are between 0.2 and 9.9V, and the signal-to-noise ratio (SNR) is as high as 20 0:1 since the background noise measured in dark room is around 1 mV. But for a very large size phantom or breast tissue (e.g.,

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34 larger than 10 cm), the minimum output is as small as 20mV at gain0. The SNR is then deteriorated to 20:1 in this case. 2.1.6 Detector Sensitivity and Dynamic Range According to the data sheet of S8745 provi ded by Hamamatsu, photon sensitivity (S) of the detector is 0.3V/nW at 673 nm. Using a la ser module of 673 nm and neutral density (ND) filters, the photon sensitivity of a representative photodiode sensor is measured. With a power meter, optical signal directed to the sensor is measured at different levels of laser input. Photon sensitivity for one detector at gain 0 (maximum ga in), gain 1, gain 2 and gain 3 (minimum gain) is 0.23V/nW, 7.7V/uW, 0.257V/uW and 8.5V/m W, respectively. At gain 0, there are no externally connected resistors and the photon sens itivity is approximately equal to that provided by the manufacture data sheet. The slight differe nce is due to the loss occurred in the fiber coupling. The maximum output voltage of a detector un it is 9.9V while the minimum output voltage or the electronic noise level is 1mV. At gain 3, the maximum detectable optical intensity is mW m W V V164 1 / 5 8 9 9. At gain 0, the noise equivalent intensity is pW nW V mV 34 4 / 23 0 1 Thus the dynamic range can be calculated to be 2.682108. 2.1.7 Stability For testing the stability, one laser module and one detector are chosen randomly. Laser beam with a power of 40 mw is sent to the opt ical switch, then to a 5 cm diameter phantom through one source fiber bundle. The diffused light delivered by a detector fiber bundle is measured by a photodiode detector. The data po ints are acquired every 10 seconds and the output voltage is normalized. The measurement fluctuation is less than 0.5%.

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35 2.1.8 DC Offset/Noise Reduction The DC offset came from the preamplifier and the low pass filters deteriorates the system performance. Before each experiment, the DC offs et of each detection cha nnel is collected. The setup is the same as that for experiments except the laser sources were off. The maximum offset is below 1mV. Both optical and electronic noises exist in the system. Optical noises are from the laser modules and ambient environment. Electronic nois es come from the electrical power grounding, fluctuation of power supply, electromagnetic di sturbance, digital ground ing of the computer, preamplifier in the photodiodes, operational am plifier offset, and resi stance variation in the resistors. Since the experiments are performed in a dark room, influence from environmental light can be eliminated. To remove the rema ining noises, the following routine methods are applied: low pass filers at a cutoff frequency of 1 KHz, a sealed aluminum box for each detection unit, a Tantalum capacitor to remove th e power supply fluctuation and other standard techniques. 2.1.9 Data Acquisition Unit The data acquisition unit is comp osed of PCI-DAS6035 and PCI-DDA08/12 (Measurement Computing, Middleboro, Massach usetts). PCI-DAS6035 is a 16-bit resolution A/D board with a maximum ADC rate of 200 KS/s. It has 8 differential ch annels, four of them are used currently (one for each board). The di gital I/O ports of PCI-D DA08/12 are configured as two 8255 mode 0 emulations, each consisting of four ports: port A (8 bits), port B (8 bits), port C high (4 bits), and port C low (4 bits). Th ese digital I/O lines either send digital signal to the decoder or receive the gain status from the boards. A LABVIEW program controls the operation of the data acquisition unit.

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36 2.1.10 System Timing When the gain of a sensor is set to gain0, the cutoff frequency of operational amplifier equals 32 Hz. To increase signal quality, 150 ms settling time used before the signal is converted by the A/D board when the sensor gain is set to ga in0. Most sensors need to be set at gain0 for large size phantoms or tissues due to the associ ated small SNR. For each illumination position, the detection unit needs 2.4 second s to collect all the data. The optical switch operates at the speed of 330 ms per switching action. Thus fo r 64 illumination and 64 detection positions, the total data acquisition time is about 2.9 minutes per wavelength. For a ten-wavelength measurement, the data collection time adds up to 29 minutes. 2.2 DOT Imaging System Operation Before the imaging experiment, the system should be powered for half an hour for warm up. Figure 2-9 shows the power buttons of the sy stem. Usually, the optical switch is powered at first, then the computer, and at last the laser modules. Th e switching power supply for the computer will affect the boot of th e optical switch if the computer is powered before the optical switch. Since our imaging system can only cover 2 cm s lice of a breast at one imaging time, doctor has to tell us which breast of the patient has problems and the approximate location of the abnormality in the breast from the mammography films. When the patient comes, the consent form must be read and signed by the patient. Th e examined breast is positioned in correct location by the operator. Figure 2-10 shows the LABVIEW control pane l of the imaging system. Operator changes the output data file names, one for voltage sign als and the other for gain stages of corresponding voltage signals. Then the numbe r of detection layers and the number of laser modules are selected from the control panel. At last, the syst em runs automatically for the data acquisition.

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37 The collected data will be calibrated and then used for the DOT image reconstruction using our finite element based algorithms. 64 detection fiber bundles 10 fibers Computer Optical switch Detection units 64 source fiber bundles Data acquisition boards DC motor CCDs Laser current controllers 10 lasers Figure 2-1. Schematic of the experimental system.

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38 (a) (b) Figure 2-2. Photographs of the experimental system.

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39 3(a) 3(b) Figure 2-3. Optical switch (a) Schematic and (b) photograph. Motor1 Motor2 INPUT OUTPUT 10 . . . 2 1 0 1 2 . . . . . . . . 63 64 0 Laserbeam

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40 (a) (b) Figure 2-4. Photographs of the ring structure. Figure 2-5. Internal and external conn ections of a silicon photodiode S8754.

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41 Aluminum Box Screw Plastic Circuit Board Detection Fiber Bundle PinsSensor Aluminum Fiber Holder Figure 2-6. Diagram of mounting configuration for one sensor.

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42 switch ch1 switch ch2 switch ch16 S8745 (no 1) S8745 (no 2) S8745 (no 16) Pin 6 Pin 4 Pin 6 Pin 6 Pin 4 Pin 4 gain switch 1 gain switch 2 gain switch 3 Rf1 Rf2 Rf3 Inverter LP filter A/D board gain switch controller 4 to 16 decoder computer Digital I/O (a) (b) Figure 2-7. The detection board: (a) Schematic;(b) layout.

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43 Voltage Power 10 V 9.9 V 0.3 V 0.2 V Gain 0 Gain 1 Gain 2 Gain 3 1 2 3 4 5 6 1.164 mW Figure 2-8. Flow chart of a detector gain controller. Figure 2-9. The control panel of the DOT imaging system.

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44 Figure 2-10. The LABVIEW control pa nel of the DOT imaging system.

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45 CHAPTER 3 SYSTEM CALIBRATION AND DO T ALGORITHM REFINEMENTS 3.1 System Calibration We describe a new calibration method that takes advantages of both the reference phantom based method and the data optimiza tion scheme we devel oped. Various phantom experiments are performed using our newly deve loped silicon photodiodes-based DOT system in order to evaluate the calibration method. Th e dependence of the calib ration method on phantom size and optical properties is al so studied systemically. The re sults show that our new method can significantly improve the quality of quantitative absorption and scattering imaging even under the condition of very low absorption contrast. 3.1.1 Image Reconstruction Algorithm An iterative finite element based algorithm, previously described in details elsewhere69, is used for our image reconstruction of absorption a nd reduced scattering coefficients. Briefly, the stead-state photon diffuse equation ) r ( S ) r ( ) r ( ) r ( ) r ( Da (3.1) coupled with Type III boundary conditions, n D is transformed into the following matrix form of b A (3.2) by the finite element discretization, where (r) is the photon density, a(r) is the absorption coefficient; D(r) is the diffusion coe fficient which can be written as )] r ( ) r ( [ 3 / 1 ) r ( Ds a where ) r (s is the reduced scattering coefficient; ) r r ( S S0 0 is used where 0S is the source strength and ) r r (0 is the Dirac delta function for a source at 0r; n is the unit normal vector for the boundary surface; is the BC coefficient related to the internal reflection at the

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46 boundary; the elements of matrix A are D ai j a i j ij where indicates integration over the problem domain; b is M 1ds Sj j i j i; M is the number of boundary nodes; i and j are locally spatially varying Lagr angian basis functions at nodes i and j, respectively. Four critical parameters (the BC coefficient the source strength S0, and the initial guess of D and a) can be accurately determined by a preprocessing data optimization scheme28. Then a regularized Newtons method is us ed to update the initially guessed optical property (D and a) distribution iteratively in order to minimize an object function composed of a weighted sum of the squared difference betwee n computed and measured optical data at the medium surface. The pre-processing data optimization scheme for determining the four initial parameters is discussed in detail elsewhere28. Briefly, -square errors, 2 1 M 1 ) c ( m 2~ X i i i, are minimized as the function of the above four parame ters, where M1 is the number of boundary measurements, m i is the measured photon density from a given experimental heterogeneous medium, and ) c ( ~ i is the computed photon density from a numerical simulation of a homogeneous medium with the same geometry as the experimental medium. Given reasonable ranges for the four parameters, the minimum 2X corresponds to the best initial guess of the four parameters. 3.1.2 Calibration Method We present the calibration method here and provide further discussion about the method in subsection below. For a 2D imaging experiment, the calib ration procedure is described by the following six steps:

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47 A. Make a homogeneous phantom that has the same diameter as the heterogeneous phantom of interest. B. Perform experiments with the homogeneous pha ntom. For 2D imaging experiments, there are 16 transmitters and 16 receivers. Obtain a set of measured data ijD, where i is the transmitter number from 1 to 16 and j is the receiver number from 1 to 16. For each source i, light intensities from the 16 detectors are normalized. C. Find the initial values of absorption coefficient a reduced scattering coefficient s and the boundary conditions coefficient using ijD. These initial parameters are required by our nonlinear iterative algorithm and can be found us ing the pre-processing me thod briefly described in Subsection 2.1 above. D. Generate a 2D finite element mesh with th e same diameter as the phantom. Using a unit source intensity for the 16 illuminated positions, the 2D photon propagation is simulated with the optical properties a, s and the boundary conditions coefficient identified in Step C. This creates a new set of data ij D from the simulation. E. Obtain a factor matrix ijf using the following equation 16 ... 1 / j i ij D ij D ij f (3.3) F. Multiply fij by the data set (ijE ) from the heterogeneous phantom to get the final data set for image reconstruction: 16 ... 1 j i ij E ij f ij E (3.4)

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48 3.1.3 Experimental Methods and Materials This system has been described in detail in subsection 2.1. The phantom materials used consisted of Intralipid as scat terer and India ink as absorber. Agar powder (1-2%) was used to solidify the Intralipid and Indian ink solutions A single off-center ta rget was embedded in a homogeneous background phantom in these im aging experiments. Figure 3-1 depicts the geometrical configuration for the test cases under study. One 14-mm-diameter cylindrical hole was drilled in the homogeneous background phantom for inclusions of the target with various optical contrasts. Three groups of experiment s were performed to evaluate the calibration method. The three groups each contained three e xperiments with different phantom diameters and different levels of contrast in the target. The optical properti es and geometry properties used in Groups 1 to 3 experiments are detailed in ta bles 3-1 to 3-3. The op tical properties of the background phantoms for groups 1 to 3 are the same: a =0.005 mm-1 and s =1.0 mm-1. 3.1.4 Results and Discussion Figs. 3-2 to 3-4 present the reconstructed ab sorption and reduced sca ttering images from Groups 1, 2 and 3 experiments, respectively, wher e each set of imaging data was calibrated with the homogeneous phantom measurements from re ference 1 (50mm diameter; left column), reference 2 (75mm diameter; middle column), a nd reference 3 (100mm diameter; right column), respectively. We can see that the best image quality is achieved when both the imaging and reference phantoms have the same dimension (see left column in Figure. 3-2, middle column in Figure. 3-3 and right column in Figure. 3-4). Under this situati on, the recovered absorption and scattering images are quantitatively accurate in te rms of the location, size and optical properties of the target. The reconstruction of the background is overall of high quality without any artifacts for smaller dimension cases and with minimal sl ight artifacts for larger dimension cases. In

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49 particular, the very low absorption target is quantitatively resolved for all three background dimensions (Figure. 3-2a, Figure. 3-3b and Fi gure. 3-4c), which was impossible previously. Figure. 3-5 shows the one-dimensional (1D) prof ile of the absorption coefficient along the transect AB (see Figure. 3-1) for the images show n in Figs. 3-2a and 3-2d. This demonstrates a close quantitative examination of the selected images. Other cases have similar quality. When the imaging data were calibrated using homogeneous phantom measurements having different dimension than the heterogene ous phantom of interest, the quality of the recovered images is clearly degraded (Figs. 3-2 to 3-4). These degradations are generally shown as a ring-pattern artifact (Fig s. 3-2b and 3-2e; Figs. 3-4b, 4-4d and 3-4e) or a few millimeters shifting of the target toward th e center of the background (Figs. 32c and 3-2f; Figs. 3-3a and 33d). It is interesting that ther e is no target shifti ng for all cases with the phantom of 100mm diameter. In general, the target is clearly detectable for most cases and the reconstruction is quantitative except for two cases with 100mm diam eter phantom (Figs. 3-4j and 3-4k) where the recovered value of the reduced scattering coefficient is incorrect. Quantitatively the improvement in image reconstruction with proper calibration is striking. For example, for the 1. 4:1 absorption contrast experiment s, when proper calibration was used, i.e., when the reference phantom had the same diameter as that of the heterogeneous phantom, the errors of the peak absorption coeffi cient recovered relative to the exact value were found to be 1.4% (Figure. 2-10a), 1.2% (Figure. 2-11b), and 2.8% (Figure. 2-12c) for the 50, 75 and 100mm diameter heterogene ous phantom cases, respectively. Whereas when improper calibration was performed, i.e., when the referen ce phantom had different diameter than that of the heterogeneous phantom, such errors are large as 110% and even the target cannot be detected for some of the cases (e.g., see Figs. 3-2b, 3-2c 3-2e and 3-2f). For the 2:1 absorption and

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50 scattering contrast experiments, the errors of the peak scattering coeffi cient compared to the exact value were calculated to be 5.5% (Figure. 3-2j) and 4.1% (Figure. 3-4l) for the 50 and 100mm diameter heterogeneous phantom cases respectively, when proper calibration was applied. Whereas such errors are up to 60% when improper calibration was used. Although the results shown above indicate the dependence of the imag e reconstruction on the size of reference phantom used, the calibration method described here will prove to be useful for clinical studies. For example, in the case of breast imaging, we can build a database based on a series of homogenous phantom measurements wi th a range of dimensions (e.g., from 4 to 11 cm with an increment of 5 mm). Whenever imaging measurements are performed on a particular size of breast, the imaging data obtained can be calibrated with one factor matrix from the database whose reference phantom diameter is equal or closest to th at of the breast under measurement. The calibration method described in this secti on is novel in that it takes advantages of both the pre-processing optimization scheme and the reference homogeneous phantom based method. The homogeneous phantom only based calibration method can remove systematic measurement errors while the pre-processing op timization scheme or model-based calibration methods can reduce the model mismatch errors due to the difference between the photon diffusion model and the physics involved. Thus the new calibration method can remove both types of errors which are resulted from the divi sion of the measured data from the heterogeneous and reference homogeneous phantoms and multiplicat ion of the computed data based on the preprocessing optimization scheme. In sum, in this subsection a new calibra tion method is developed and evaluated by a series of phantom experiments with our newly developed diffuse optical tomography system. We

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51 have shown that when the heterogeneous phant oms of interest and the reference homogeneous phantom have the same dimension, quantitative optical images can be obtained even under the conditions of very low absorption contrast. This study shows that this calibration method is sensitive to the reference phantom size. 3.2 Dual Mesh Method As a finite element based reconstruction me thod, 3D DOT imaging needs a mesh with much more elements and nodes than 2D DOT imaging. For the nonlinear iterative DOT reconstruction, forward computati on needs O(n) multiplications (n is the node number), and the reverse computation needs O(n2) multiplications due to the full matrix property related with the Marquardt and Tikhonov regularization method69. Therefore 3D DOT reconstruction computation burden is undesirable, especially fo r phantoms or tissues of large volumes. The dual mesh method utilizes two separate meshes: one fine mesh for the accurate photon density solution and a coarse mesh for the inverse pro cess to update optical properties. It allows a significant reduction of computati on burden for the problem with a big mesh, thus increasing the overall computational efficiency. In fact, the idea of dual meshing has been implemented in early works in both CW and frequency domains, where this method has been proved to significantly enhance the quality of reconstructed images33. However, these early wo rks did not exploit the potentials of this method in 3D DOT reconstructi on. In this subsection, the dual mesh method is applied in the CW 3D DOT rec onstruction. And the comparison with the single mesh method is made. 3.2.1 Dual Mesh Method There are two meshes used for the dual mesh computation. One is the coarse mesh and the other is the fine mesh. For the cases in this sect ion, the fine mesh is generated by splitting each coarse element into four fine mesh elements with equivalent volume fo r reducing the new mesh

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52 singularity and for simplicity. And the new node i, is created at the centroid of each coarse mesh element, as shown in Figure. 3-6. For the single mesh method, bot h forward and inverse computations are performed in the coarse mesh. The coarse mesh contained 2,241 nodes corresponding to 10,368 linear tetr ahedral elements. And the fine mesh, generated from coarse mesh, contains 12,609 nodes corresponding to 41,472 linear tetr ahedral elements. The dual mesh method for the 2D DOT recons truction is described in detail elsewhere33. The principle of dual mesh algorithm in 3D DOT reconstruction is similar. The forward computation is performed in the fine mesh. The local Lagrangian basis i and j the optical properties D and a in equation are defined in the fine mesh The impact of the dual mesh method on the inverse process app ears during the construction of the Jacobian matrix which is used to update the optical property values. The elements of are composed of th e partial derivatives of the photon density at the observation sites with respect to the values of D and a at each node within the coarse mesh. Considering the impact of the dual meshing, elements of the Jacobian matrix can be written as j i k k D ij (3.5) j i l l ij (3.6) where k and l are the nodes on the coarse mesh, k and l are the basis functions centered on nodes k and l in this mesh, and inner products are still performed over the elements in the fine mesh.

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53 3.2.2 Experiments The phantoms and targets were made of water, Intralipid (as scatterers), Indian Ink (as absorpter) and agers (2%used to solidifying the phantom). Figure 3-7 describes the geometry of the phantom. A homogeneous background phantom ( a =0.005 mm-1 and s =1.0 mm-1) was made at first. Then a cylindrical hole with diam eter of 14 mm was drilled at desired location in the background phantom and the target was put insi de it. At last the hole with the target was refilled with background phantom materials. The location and the opt ical properties of the targets are shown in Table 3-4. For the three phantom ex perimental cases, the optical properties of the target are same ( a =0.02 mm-1 and s =2.8 mm-1) but with different off-center locations (15mm, 10mm, 5mm respectively). These three cas es were performed to investigate lateral resolutions of the target. 3.2.3 Results and Discussion For the dual mesh method, the reconstruction time was about 30 minutes per iteration on a 2.88 GHz PC with 1 Gb of RAM. For the single mesh method, the reconstruction time was about 15 minutes per iteration on the same PC. Reconstructed 3D a and s images for each case are displayed at a series of transverse (coronal) sections perpendicular to axis Z and selected longitudinal (sagittal) sections perpendicular to axis X or axis Y. Quantitative one dimensional (1D) profiles of recovered optical properties alo ng selected transects are also shown for all the cases. Figure. 3-8, Figure. 3-9 and Figure. 3-10 pl ot the reconstructed a images (a-d) and s images (e-h) for case 1 (4:1 a 2.8:1 s contrast, 15 mm off-cen ter), case 2 (4:1 a 2.8:1 s contrast, 10 mm off-cen ter) and case 3 (4:1 a 2.8:1 s contrast, 5 mm off-center) phantom experiments with the dual mesh method (lef t column) and the singl e mesh method (right

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54 column), respectively. Rectangular figures plot recovered images at the sagittal cross section y=0mm and circular figures plot recovered images at the coronal cross section z=2 mm for each case. The color scale bar indicates values of a (a-d) and s (e-h) in mm-1. For all three cases, in the reconstructed a images, the target is detected qua ntitatively, although there are some boundary artifacts in Figs. 3-8c, 3-8d, 3-9c, 9d, 10c and 10d. When the dual mesh method is used we see artifacts in the reconstructed a images (Figs. 3-8c, 3-9c, 3-10c) are less than those in a images (Figs. 3-8d, 3-9d, 3-10d) reconstruc ted with the single mesh method. In the reconstructed s images, with the dual mesh method, the target is different iated quantitatively for all three cases, as shown in figures 3-8e and 3-8g for case 1, figures 3-9e and 3-9g for case 2, figures 3-10e and 3-10g for case 3, while with th e single mesh method, we can see the target shape is deteriorated by artifacts although target s value is close to the exact value, as shown in Figure. 3-8h for case 1, Figure. 3-9h for case 2 and Figure. 3-10h for case 3. Figure 3-11 plots the three-di mensional view of the recons tructed absorption coefficient images (Figs. 3-11a, c, e) in mm-1 and the reconstructed reduced scattering coefficient images (Figs. 3-11b, d, f) in mm-1 for case 1 (Figs. 3-11a, b, 15mm of fset), case 2 (Figs. 3-11c, d, 10mm offset) and case 3 (Figs. 3-11e, f, 5mm offset) using dual mesh method. The showing slices in each figure are crossed at the center of the target. It is clear to s ee that the reconstructed targets are located in the expected positions. Three-dimensional DOT reconstruction for tissu e mimicking phantoms or tissues of large volumes, a mesh with thousands of elements is needed and the computational cost is high. The dual mesh method provides a way to reduce the computational burden w ithout sacrificing the extracted image quality. The results shown in this s ection illustrate the feasibility and potential of the dual mesh method application in CW 3D DOT. We have reported that the dual mesh method

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55 performed very well in two-dimensional DOT rec onstruction for several coarse mesh and fine mesh combinations.33 Here the coarse mesh and the fine mesh are fixed. It is not the purpose of this subsection to study the mesh effects on the 3D DOT reconstruction. One set of coarse mesh and fine mesh is enough to illustrate the dual mesh application in the CW 3D DOT. To date, we have not found any resolution st udies on CW 3D DOT. In frequency domain, Dehghani et. al. have investig ated 3D DOT resolutions and localizations of property heterogeneity24 and good accuracy in localization (w ithin 7 mm of the true position in the worst case) was obtained. While the ac curacy of quantitative imaging is almost 100% of the target values with a priori information regarding the anomaly location, the target absolute value of optical properties is 10% of the expected values without the information. In this section, the target localization error is less than 2 mm with the dual mesh method and less than 4 mm with the single mesh method. The target value erro rs from the reconstructed optical properties a and s images are less than 2.5% and 10.7% with both methods without a priori information The difference is possible due to more measurement of data pairs for our experiments (64 by 64), smaller background phantom size, different 3D DOT algorithm, compared with theirs. In sum, an axial spatial resolution of 5 mm in the CW 3D DOT is achieved with a set of tissue mimicking phantom experiments by using both the dual mesh method and the single mesh method. In addition, for both the high and low contrast anomalies in the turbid media, the dual mesh method has the capability of detecting th em with better image quality and more accurate maximum coefficient values than the single mesh method. 3.3 Source Intensity Optimization Method We have previously demonstrated quantitati ve 3D image reconstruc tion of absorption and scattering images in CW domain using phantom and in vivo experiments.29, 37, 70 While our

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56 results are promising, we intend to improve our 3D imaging capability by developing a method of source intensity optimization. Together with a pre-processing method previously developed for 2D imaging,28 we experimentally show in this pape r that the 3D imaging quality can be significantly enhanced for both absorption and scattering image reconstructions. 3.3.1 Source Intensity Optimization Methods In our reconstruction algorithm, the diffusi on equation is iteratively solved based on a regularized Newtons method in order to update an initially guessed optical property (D and a ) distribution. In addition to the initial optical properties, it is clear that the BC coefficient and the source strength Sk must also be given for the entire solu tion procedure. In fact these initial parameters need to be accurately determined fo r quantitative image reconstructions as illustrated in [28] where we developed a pr eprocessing data optimization sche me for such a purpose. In the following we first describe two previous sour ce calibration methods, uniform source intensity and normalized source intensity, and then introduce the new source optimization method. Uniform source intensity method. In the uniform source inte nsity method, all the source terms, Sk (64 , 2 1 k), are assumed to be the same, i.e., o kS S Thus there are only 4 parameters (, S0, and initial D and a values) that need to be optimized before the reconstruction. In our pre-proce ssing data optimization scheme for determining the four initial parameters, -square errors,2 1 i ) ( i i 2~ M c m, are minimized as a function of the above four parameters, where M is the number of boundary measurements (in this study, M=64), mi is the measured photon density from a give n experimental heter ogeneous medium, and ) c ( ~ i is the computed photon density from a numer ical simulation of a homogeneous medium

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57 with the same geometry as the experimental medium. Given reasonable ranges for the four parameters, the minimum 2 corresponds to the best initia l guess of the four parameters. Normalized unit source intensity method. The second preprocessing method used previously is a normalized unit source calibration method. In this method, the source terms Sk=1 while the measured data at 64 measurement s ites are normalized using the maximum of the 64 measured data for a given source location. Thus using this method we only need to optimize three initial parameters ( and optical properties D and a ), and the normalized measured data must be used for reconstructions. Similarly, square errors, 2 M 1 norm ) c ( norm m 2) ~ ( ) ( i i i, are minimized as a function of the above thre e parameters, where M is the number of boundary measurements (in this study, M=64), norm m) (i is the normalized measured photon density from a given experimental heterogeneous medium, and norm ) c () ~ (i is the normalized computed photon density from a numerical simulation of a homogeneous medium with the same geometry as the experimental medium. The minimum 2 gives the best initial guess of the three parameters. Source intensity optimization method. In the source intensit y optimization method, and initial D and a are optimized first using the norma lized source intensit y method described in the above subsection. Then for each of the 64 excitations, the corresponding source intensity, Sk, is obtained using the similar preprocessing pro cedure described in above two subsections. For each of Sk (k from 1 to 64), square errors, 2 1 M 1 k ) c ( k m 2 k) ~ ( ) ( i i i, are minimized as a function of Sk, where M1 is the number of measurement for each source excitations (in this

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58 study, M1=64), k m) (i indicates the original measur ed photon density from a given experimental heterogeneous medi um for excitation at k, and k ) c () ~ (i is the computed photon density for excitation at k from a numerical simulation of a hom ogeneous medium with the same geometry as the experimental medium and with the D and a obtained in the first step. The optimized source intensity Sk is obtained when 2 k are minimized. Finally a total of 67 initial parameters are searched for full 3D image reconstructions. 3.3.2 Experiments The phantom materials used consisted of Intral ipid as scatterer and India ink as absorber. Agar powder (1-2%) was used to solidify the In tralipid and Indian ink solutions. A single offcenter target was embedded in a homogeneous background phantom in these imaging experiments. Figure 3-12 depicts the geometrical configuration for the test cases under study. One 14 or 9-mm-diameter cylindr ical hole was drilled in the homogeneous background phantom for inclusions of targets with various optical c ontrasts. A cylindrical ta rget (14mm in diameter and 10 mm in height for cases 1-4 and 9 mm in di ameter and 10 mm in height for cases 5-6) was placed into the hole where the rest of the hole was filled with phantom material that was the same as the background. Six experiments with differe nt optical contrast leve ls between the target and background were performed to evaluate the three optimization methods discussed in Section 2. The geometrical information and optical properties used for the target in the 6 experiments are detailed in Table 3-5. The optical properties of the background were the same for all the experiments: a =0.005 mm-1 and s =1.0 mm-1.

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59 3.3.3 Results and Discussion The results presented in this section we re obtained using a 3D mesh with 10386 tetrahedron elements and 2241 nodes. Reconstructed 3D a and s images for each case are displayed at a series of transverse (coronal) sections perpendicular to axis Z and selected longitudinal (sagittal) sections perpendicular to axis X or axis Y. Quantitative 1D profiles of recovered optical properties along selected transects are also shown for some cases. Figure 3-13 shows the reconstructed a images at a selected sagittal and coronal section for case 1 (2:1 a contrast). From Figs. 3-13a and 3-13b, when the uniform source intensity method was used we see that boundary artifacts do minate the images and the target cannot be detected for this relatively low contrast case. The target is detectable with the normalization method (Figs. 3-13c and 3-13d), while we note rela tively strong artifacts in the background. The detection of the target is clea rly improved when the source optimization method was used (Figs. 3-13e and 3-13f), although ther e are still some small artifact s in the background region. Reconstructed a images at a series of cor onal sections for case 2 (4:1 a contrast) are plotted in Figure 3-14. As shown from column 3 in Figure. 3-14, when the uniform source method was used the target cannot be detected at most coronal sections except that at z=-2mm the target was barely visible. For the images obtained by the normalization method (column 2 in Figure. 3-14), the target is resolvable, but with a marked circularly sh aped artifact in the background. Again, when the source optimizatio n method was utilized, th e target is clearly detected with minimal artifacts, as show n from column 1 in Figure. 3-14. Figure 3-15 plots the absorpti on and scattering images recons tructed for case 3. For the a images in this case, the target is differe ntiated successfully from the background with all three methods (Figs. 3-15a-f). However, we can see that the quality of the extracted a images

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60 with the source intensity optimi zation method is still the best (Figs. 3-15a and 3-15d). For example, as shown in Figs. 3-15a and 3-15d, the shape and size of the targ et is better recovered and there are much less artifacts in the background. Forthe s images shown in Figs. 3-15g-o, we note that the uniform source intensity method basi cally fails to detect the target (Figs. 3-15i, l and o). The normalization method has the capability to detect the targ et, but with strong artifacts in the background (Figs. 3-15k and n). In additio n, the recovered target position is shifted towards the center of the background (Figure. 315k). Figures 3-15g, j and m illustrate that the source intensity optimization met hod is capable of reconstructing s images with much better accuracy and with much less artifact s relative to the other two methods. Figures 3-16 and 3-17, respectively, show the recovered absorption and scattering images at a selected sagittal section a nd a series of coronal sections fo r case 4. In this relatively high contrast case, we note that the target is detected for both the a and s images with all three methods (e.g., see the images shown at y=0 and z=2 in Figs. 3-16 and 3-17). However, we can still see that the images with the source intensity optimizatio n method have the best overall quality (column 1 in Figs. 3-16 and 3-17). For the absorption images, we observe that the normalization method (column 2 in Figure. 3-16) gives almost the same quality as the source optimization method, except that it generated more boundary artifacts (see the images at z=-6 in Figure. 3-10). The boundary artif acts in the images from the uniform source intensity method are clearly the strongest such that the target is invisi ble at several cut plan es (e.g., see column 3 at z=6mm in Figure. 3-16). For the scattering im ages shown in Figure. 3-17, we see that the recovered target position is shif ted to the center of the background at severa l cut planes (see the images at z=6mm in Figure. 3-17).

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61 For a more quantitative assessment of the results, Figure 3-18 shows a and s profiles along a transect through the centers of the target and background for the images at y=0mm and z=2mm for the cases 1-4 when the source inte nsity optimization method was used. The dotted line corresponds to the ex act values and the solid line are referred to the extracted optical property values. From Figure.3-18, we calcula ted the relative errors of the recovered a (maximum value) in the target to be 13.0%, 0. 95%, 0.1% and 0.2% for cases 1-4, respectively. The relative errors of the extracted s (maximum value) in the target were found to be 2.0% and 8.8% for cases 3 and 4, respectively. Figure 3-19 plots the absorption images (Fig s. 3-19a and 3-19b) and scattering images (Figs. 3-19c and 3-19d) reconstructed with the source optimization method for case 5 (4:1 a and s contrast) at the section y=0 mm (Figs. 3-19a and 3-19c) and at th e section z=-3 mm. The target is superficial and the closest distance between the target and one fiber bundle is 2 mm. The source intensity at the fibe r bundle obtained with the source optimization method increased by 56% above the average. From figure 3-19 we see that both the scattering images and the absorption images were reconstructed successfully The intensity increase did not appear to degrade the quality of image reconstruction. Figure 3-20 shows the absorption images (Fig s. 3-20a and 3-20b) and scattering images (Figs. 3-20c and 3-20d) reconstructed with the source optimization method for case 6 (4:1 a and s contrast) at the section y=4 mm (Figs. 3-20a and 3-20c) and at th e section z=-6 mm. Again, the target is superfic ial and is embedded between tw o source fiber bundles. The source intensities at these two fibe r bundles increased by 45% and 7.5%, respectively. Both the scattering images and the absorption images were reconstructed successfully while the shape of

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62 the target (Fig 3-20c) was degrad ed because the target was clos e to the bottom of the background phantom. Figures 3-21(a) and 3-21(b) plot the unifo rm source intensity obt ained by the uniform source intensity method (dotted line) and the sour ce intensity distribution obtained by the source intensity optimization method (solid line) from the original measuremen ts of case 4 and the normalized measurements for case 4, respectively. Both the uniform source intensity method and the normalized unit source intensity method assume that all the 64 source intensities are the same. However, the real source in tensity distributions are not unifo rm (the solid line in figure 321) due to the experimental and numerical erro rs. And for case 4, the maximum/minimum ratios are about 3.0 and 1.8 for the original and nor malized data, respectively. The normalization reduced the source intensity maximum/minimum ratio from 3.0 to 1.8 and made the source intensity distribution more uniform. That ma y be the reason why the normalized unit source method is capable of obtaining better images than the uniform source intensity method. Based on the results presented above, it is clearly seen that the source optimization method provides significantly im proved image quality over the existing two source calibration methods. This is not surprising because both th e uniform source intensity and the normalization methods assume that all the 64 source intensitie s are the same, while th e real source intensity distributions are not uniform due to e xperimental errors. We believe that Sks (k from 1 to 64) represent real emitter intensities at the source locations around the phantom surface. The real emitter intensity at one location equals the multiplication of the corresponding laser module output intensity, the source fiber at tenuation and the source fiber-pha ntom coupling coefficient. While detailed evaluation to what extent 3D model can improve DOT imaging over 2D model is beyond the scope of this paper, it is interesting to initially compare the 3D results

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63 presented here with our 2D results obtained previously. We have demonstrated that both a and s images in heterogeneous media can be ex tracted quantitatively using 2D model with appropriate calibration and preprocess methods.31, 71 These 2D images gave similar quantitative accuracy as 3D images presented in this work. One expects that 3D model would provide better accuracy for image reconstruction than 2D model, however. A possible reason for explaining this contradiction is that the volume/ amount of measured data available in the current 3D imaging system may not be enough relative to the num ber of unknown parameters involved in the 3D image reconstructions. It is well known that the source intensity difference among the different source locations significantly degraded the DOT r econstructed image qualities. One way to calibrate the source intensity is that the optical source coupling coefficients and/or the optode positions are reconstructed simultaneously with the image extraction.72-74 Another way is to estimate the coupling coefficients with a homogenous and isotropic phantom before experiments.75-76 In this paper, our method estimated the source intensitie s at the different sour ce locations by a fitting procedure with measured data from an inhomogeneous phantom and simulated data corresponding to a homogeneous model phantom. Th e presented results show that our proposed method can significantly improve the quality of reconstructed images. Combined the methods reported in Refs.72-74 with the source optimizati on method described here may result in further improvement. We plan to evaluate this combined method in future. In sum, we have developed a new source opt imization method in this paper. The imaging results shown indicate that this new me thod can quantitatively improve 3D image reconstructions.

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64 R1 R2 d B A Figure 3-1. Geometry of th e phantom configuration.

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65 (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) Figure 3-2. Reconstructed absorption and scattering images for the 3 cases in Group 1 when each set of imaging data was calibrated with 50mm diam eter homogeneous phantom (left column), 75mm diameter phantom (middle column), a nd 100mm diameter phantom (right column), respectively. (a)-(c): absorption images from the case of target 1. (d)-(f): absorption images from the case of target 2. (g )-(i): absorption images from the case of target 3. (j)-(l): scattering images from the case of target3. The gr ey scale shows the absorption or reduced scattering coefficient value (mm-1), while the axes indicate the spatial dimension (mm). a a a a a a a a a s s s

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66 (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) Figure 3-3 Reconstructed absorption and scattering images for the 3 cases in Group 2 when each set of imaging data was calibrated with 50mm diam eter homogeneous phantom (left column), 75mm diameter phantom (middle column), a nd 100mm diameter phantom (right column), respectively. (a)-(c): absorption images from the case of target 1. (d)-(f): absorption images from the case of target 2. (g )-(i): absorption images from the case of target 3. (j)-(l): scattering images from the case of target 3. The grey scale shows the absorption or reduced scattering coefficient value (mm-1), while the axes indicate the spatial dimension (mm). a a a a a a a a a s s s

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67 (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) Figure 3-4. Reconstructed absorption and scattering images for the 3 cases in Group 3 when each set of imaging data was calibrated with 50mm diam eter homogeneous phantom (left column), 75mm diameter phantom (middle column), a nd 100mm diameter phantom (right column), respectively. (a)-(c): absorption images from the case of target 1. (d)-(f): absorption images from the case of target 2. (g )-(i): absorption images from the case of target 3. (j)-(l): scattering images from the case of target 3. The grey scale shows the absorption or reduced scattering coefficient value (mm-1), while the axes indicate the spatial dimension (mm). a a a a a a a a a s s s

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68 a (mm-1)(a) a (mm-1)(b) Figure 3-5. 1D profile of the absorption coeffici ent along the transect AB (see Figure. 3-1) for the image shown in Figure. 3-2a (a) and for image shown in Figure. 3-2d (b). The dotted and solid lines are, respectively, the exact and rec onstructed absorption coefficient distributions. L1L2L3L4i Figure 3-6. Four fine mesh elements ge nerated from one coarse mesh element.

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69 43 10 10144261X Z Layer 1 Layer 2 Layer 3 Layer 43 6.1 6.1 6.1 AA Offset d Section AA Unit: mm X Y Figure 3-7. Geometry of the tissue mimicking phantom.

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70 Figure 3-8. The a images (a-d) and s images (e-h) reconstructed for case 1 (4:1 a 2.8:1 s contrast, 15 mm off-center) pha ntom experiment with th e dual mesh method (left column) and the single mesh method (righ t column). The rectangular and circular figures are at the cross sections y=0 mm and z=2 mm respectively. The color scale bar indicates values of a (a-d) and s (e-h). ( a ) ( b ) ( c ) ( d ) ( e ) ( f ) ( e ) ( f )

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71 Figure 3-9. The a images (a-d) and s images (e-h) reconstructed for case 2 (4:1 a 2.8:1 s contrast, 10 mm off-center) pha ntom experiment with th e dual mesh method (left column) and the single mesh method (righ t column). The rectangular and circular figures are at the cross sections y=0 mm and z=2 mm respectively. The color scale bar indicates values of a (a-d) and s (e-h). ( a ) ( b ) ( c ) ( d ) ( e ) ( f ) (g) ( h )

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72 Figure 3-10. The a images (a-d) and s images (e-h) reconstructed for case 3 (4:1 a 2.8:1 s contrast, 5 mm off-center) pha ntom experiment with th e dual mesh method (left column) and the single mesh method (righ t column). The rectangular and circular figures are at the cross sections y=0 mm and z=2 mm respectively. The color scale bar indicates values of a (a-d) and s (e-h). ( a ) ( b ) ( c ) ( d ) ( e ) ( f ) (g) ( h )

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73 Figure 3-11. The three-dimensional views of the r econstructed absorption coefficient images (a, c, e) in mm-1 and the reconstructed re duced scattering coefficient images (b, d, f) in mm-1 for case 1 (a, b, 15 mm offset), case 2 (c, d, 10mm offset ) and case 3 (e, f, 10mm offset) respectively using the dual mesh method. In each image, the showing slices are crossed at th e center of the target. ( a ) ( b ) ( c ) ( d ) ( e ) ( f )

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74 Unit: mm 11.25 o Offset d Section AA (case 6) X Y Offset d Section AA (case 1-5) X Y 43 10 1014 4261 X Z Layer 1 Layer 2 Layer 3 Layer 4H 6.1 6.1 6.1 AA Figure 3-12. Geometry of the phantom under study.

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75 Figure 3-13. The absorption images reconstructed for case 1 (2:1 a contrast) with the uniform source intensity method (a, b); the norm alization method (c, d) and the source optimization method (e, f). Column 1 show s that images at y=0 mm plane and Column 2 gives the images at z=0 mm plane. (c) (a) (d) (b) (f) (e)

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76 Figure 3-14. The absorption images reconstructed for case 2 (4:1 a contrast) with the uniform source intensity (column 3); the normali zation method (column 2) and the source optimization method (column 1). z=-2 m m z=2 m m z=-6 m m

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77 Figure 3-15. Reconstructed absorption images (rows 1 and 2) and scattering images (rows 3-5) for case 3 (2:1 a and s contrast) with the uniform so urce intensity (column 3); the normalization method (column 2) and the s ource optimization method (column 1)

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78 (a) (b) (c) (d) (e) (f) (g) (h) (j) (i) (k) (l) (n) (o) (m)

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79 Figure 3-16. The absorption images reconstructed for case 4 (4:1 a and s contrast) with the uniform source intensity (column 3); the normalization method (column 2) and the source optimization method (column 1). z=6 mm z=2 mm z=-6 mm y=0 mm

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80 Figure 3-17. The scattering images reconstructed for case 4 (4:1 a and s contrast) with the uniform source intensity (column 3); the normalization method (column 2) and the source optimization method (column 1). y=0 mm z=2 mm z=-6 mm z=6 mm

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81 Figure 3-18. Recovered a values along a transect through the centers of the target and background for the images at y=0 mm, z=2 mm for case 1 (a), case 2 (b), case 3 (c) and case 4 (e). Reconstructed s values along a transect th rough the centers of the target and background for the images at y=0 mm, z=2 mm for case 3 (d) and case 4 (f). Both the a and s images were reconstructed using the source intensity optimization method. The dotted lines are the exact values and the solid lines indicate the extracted coefficients. (d) (b) (c) (e) (f) (a)

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82 Figure 3-19. The absorption images (a and b) and scattering images (c and d) reconstructed with the source optimization method for case 5 (4:1 a and s contrast) at the section y=0 mm (a and c) and at the section z=-3 mm. (c) (d) (a) (b)

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83 Figure 3-20. The absorption images (a and b) and scattering images (c and d) reconstructed with the source optimization method for case 6 (4:1 a and s contrast) at the section y=4 mm (a and c) and at the section z=-6 mm. Figure 3-21. The source intensity obtained with the uniform sour ce intensity method (dotted line) and the source intensity dist ribution obtained with the s ource intensity optimization method (solid line) from original measured data (a) and the normalized measured data (b) of experiment case 4. (a) (b) (c) (d) (a) (b)

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84 Table 3-1 Optical and geometric parameters used for Group 1 experiments. R2 (mm) D (mm) a (1/mm) s (1/mm) R1 (mm) Target 1 (1.4:1 a contrast) 7.0 9.0 0.007 1.0 Target 2 (2:1 a contrast) 7.0 9.0 0.01 1.0 Target 3 (2:1 a and s contrast) 7.0 9.0 0.01 1.8 Background ( a =0.005 mm-1, s =1.0 mm-1) 25.0 Table 3-2 Optical and geometric parameters used for Group 2 experiments. R2 (mm) D (mm) a (1/mm) s (1/mm) R1 (mm) Target 1 (1.4:1 a contrast) 7.0 11.0 0.007 1.0 Target 2 (2:1 a contrast) 7.0 11.0 0.01 1.0 Target 3 (2:1 a and s contrast) 7.0 11.0 0.01 1.8 Background ( a =0.005 mm-1, s =1.0 mm-1) 37.5 Table 3-3 Optical and geometric parameters used for Group 3 experiments. R2 (mm) D (mm) a (1/mm) s (1/mm) R1 (mm) Target 1 (1.4:1 a contrast) 7.0 21.0 0.007 1.0 Target 2 (2:1 a contrast) 7.0 21.0 0.01 1.0 Target 3 (2:1 a and s contrast) 7.0 21.0 0.01 1.8 Background ( a =0.005 mm-1, s =1.0 mm-1) 50.0

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85 Table 3-4 Optical properties of the phanto m background and the target for all 5 cases. d a (1/mm) s (1/mm) case 1 (4:1 a and s contrast) 15 mm 0.02 2.8 case 2 (4:1 a and s contrast) 10 mm 0.02 2.8 case 3 (4:1 a and s contrast) 5 mm 0.02 2.8 Background ( a =0.005 mm-1, s =1.0 mm-1) Table 3-5 Optical properties of the target and ba ckground used in the six experiments performed. d H a (1/mm) s (1/mm) case 1 (2:1 a contrast) 10 mm 3 mm 0.01 1.0 case 2 (4:1 a contrast) 10 mm 3 mm 0.02 1.0 case 3 (2:1 a and s contrast) 10 mm 3 mm 0.01 1.8 case 4 (4:1 a and s contrast) 5 mm 3 mm 0.02 2.8 case 5 (4:1 a and s contrast) 19 mm 9 mm 0.02 2.8 case 6 (4:1 a and s contrast) 19 mm 12 mm 0.02 2.8 Background ( a =0.005 mm-1, s =1.0 mm-1)

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86 CHAPTER 4 PARTICLE SIZE IMAGING: PHANTOM EXPERIMENTAL STUDIES 4.1 Measurement of Particle Size Distribution and Concentration in Heterogeneous Turbid Media In this section we attempt to establish a method directly based on more rigorous Mie scattering theory for the reconstr uction of particle size distributi on and concentra tion without the limitations existing in the use of the power law. We use both simulations and phantom experiments to validate our met hod. We also describe a new scheme for optimizing the initial parameters needed for reconstructions in MS DOT and a method for calibrating the scattering spectra obtained from phantom experiments. 4.1.1Materials and Methods Two inverse algorithms are required in order to obtain particle size distribution and concentration with MSDOT. The first is a DOT algorithm for the rec overy of spectroscopic scattering images in heterogeneous turbid me dia. Our DOT algorithm, described in detail elsewhere, uses a regularized Newtons method to update an initial optic al property distribution iteratively in order to minimize an object functi on composed of a weighted sum of the squared difference between computed and measured optical data at the medium surface. The computed optical data (i.e., photon inte nsity) is obtained by solving th e photon diffusion equation with finite element method. The second algorithm is one that extracts the particle morphological information using the scattering spectra obtained from the first algorithm described above. It casts the reconstruction as an optimization probl em in which the optimization parameters are coefficients in a probability function such as Gaussian distribution function using a priori assumptions. This inverse algorithm is based on a least squares optimization, where the difference between measured and computed scattering spectra is iteratively minimized by adjusting the optimization parameters under Mie scattering theory.

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87 It is known that an optimized initial optical property distribution is critical for quality image reconstruction using DOT algorithm. We reported an eff ective preprocessing scheme for such purpose previously; however, it requires ti me-consuming computational procedures to obtain the initial parameters needed for image reconstruction at a single wavelength. Clearly this would not be efficient for image reconstructi on at multiple wavelengths in MSDOT. Thus we implemented an algorithm for optimizing initial optical properties based on the following core relationship: c o T TJ ) I J J ( (4.1) where a N a 2 a 1 N 2 1D D D J ) (aD o N o 2 o 1 o, c N c 2 c 1 c, o and c are the observed and calcu lated photon density; D and a are the diffusion and absorption coefficients, respectively; is the update of optical prope rties; N is the number of nodes used in the finite element mesh used; is a regularization parameter and I is an identical matrix. In this algorithm, optimized initial opt ical properties are obtaine d by iteratively solving Eq. (4-1). Since there exist only two variables, it is very fast to reach convergence. Once D is recovered using DOT algorithm, th e reduced scattering spectra can be obtained by the following relati onship for turbid media: D gs3 1 1 (4.2)

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88 where sg 1 is the reduced scattering coefficient a nd g is the average cosine of scattering angles. Following Jiang et al.77-80, the scattering spectra are co rrelated with particle size distribution and concentration through the following relationship under Mie Theory: 0 scat s sdx x f x 2 n x g 1 n x Q 3 g 1 (4.3) where scatQis the scattering efficiency; x is the particle size; n is the refractiv e index of particles; is the particle concentration/volume fraction; f(x) is the particle size distribution. Both scatQ and g can be computed with Mie Theory.81 In Equation (4.3) we have assumed that particles act as independent scatterers without particle-particle intera ction. In order to solve for f(x) and from measured scattering spectra, an inversion of Eq. (4.3) must be obtained. Our numerical inversion is based on a Newton-ty pe iterative scheme through leas t-squares minimization of the objective functional: 10 1j 2 c j s o j s 2 (4.4) where o j s and c j s are the observed and computed reduced scattering coefficients at ten wavelengths, j=1,2,,10 (more wavelengths can be used, depending on the number of wavelength available from the expe rimental system). In the reconstruction, we have assumed a Gaussian particle size distri bution in this study (a priori knowledge about the mode and distribution form of the part icle size are usually available in a practical situation), 2 b 2 2 a x 2e b 2 1 x f where a is the average size of partic les and b is the standard deviation. Substituting above f(x) into Eq. (4.3), we obtain

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89 0 b 2 a x 2 scat s sdx e b 2 1 x 2 n x g 1 n x Q 3 g 12 2 (4.5) Now the particle sizing task becomes to recover three parameters a, b and As described in detail in Refs. 77-78, we have used a comb ined Marquardt-Tikhonov regularization scheme to stabilize the recons truction procedure. 4.1.2 Simulations and experiments Simulations are used to test the sensitivity of particle sizing algorithm to noise effect with reduced scattering coefficients at ten wavelengths (This is the nu mber of wavelength available from our imaging system). Simulated scattering spectra were generated using Eq. (4.5) when the particle size distribution and concentration were given. Particle size distribution and concentration were reconstructe d using the particle sizing algorithm when 0%, 1%, 5%, 10%, and 20% noise was added to the measured scattering spectra, respectively. Phantom experiments were conducted using our ten-wavelength DOT system (638, 673, 690, 733, 775, 808, 840, 915, 922 and 960nm). This newly developed imaging system and its calibration were described in detail elsewhere. Briefly, light from one of the ten laser modules is transmitted to an optical switch, which sequentially passes it to 16 pre-selected points at the surface of the phantom for 2D imaging experiment s. 16x16 measured data is then input into our DOT reconstruction algorithm to generate a 2D cr oss-sectional image of the phantom. Three sets of phantom experiments were conducted to valid ate the overall approach for extracting particle size distribution and concentration using MS DOT. The background phantom materials used consisted of Intralipid as scatterer and India i nk as absorber. Agar powder (1-2%) was used to solidify the Intralipid and Indi a ink solutions. The cylindrical background phantom had a radius of 25mm, an absorption coefficient of 0.005/mm and a reduced scattering coefficient of 1.0/mm. A thin glass tube (9mm in inner diameter, 0.4mm in thickness) containing polystyrene

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90 suspensions (Polysciences, Warrington, PA) wa s embedded off-center in the background solid phantom. Three different types of polystyrene spheres were used in the three experiments: 2.06 m in diameter, 0.02 m in standard deviation and 0.52% in concentration for Case 1; 2.85 m in diameter, 0.14 m in standard deviation and 1.02% in concentration for Case 2; 5.66 m in diameter, 0.30 m in standard deviation and 2.62% in concentration for Case 3. The refractive index of the spheres and their su rrounding aqueous medium are 1.59 and 1.33, respectively. 4.1.3 Results Results from two simulations are displayed in Tables 4-1 and 4-2. From simulation 1 for a particle diameter of 2.855 m, we can see that both the mean size and concentrat ion of particles can be recovered accurately with up to 20% noise ; the relative errors of reconstruction of these two parameters were calculated to be within 3.0 ~ 44.9% and 2.9 ~ 33.3%, respectively, given the noise levels used. We also note that the recove ry of the standard devi ation is quite sensitive to noise effect: the relative error is as large as 100%. From simula tion 2 for a particle diameter of 10.0 m, the relative errors of reconstructed parameters a and are within 0.5 ~ 20.2% and 0.4 ~ 21.8%, respectively, given the noise levels used. Similarly we see that the standard deviation recovery is sensitive to the noise levels and the relative errors is up to 96.6%. Overall the extraction of particle concentration is least sens itive to noise effect. Us ing these reconstructed parameters at different noise levels, we calcu lated the scattering spectra using Eq. (5) for simulation 1 and present them in Figure. 4-1. Phantom data at 10 wavelengths for all thr ee cases were collected, and both absorption and scattering images were recovered at each wavelength using our DOT algorithm (only the scattering images are needed here for particle sizing). Figure 4-2 s hows the reconstructed s

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91 images for Case 2 at 10 diffe rent wavelengths. In particle sizing, both peak and average s values of the target area were used to recove r the particle size distri bution (PSD), f(x), and concentration, We found that best particle sizing was achie ved when the reconstructed peak or average s values calibrated using the optimized initial s values. In this calibration, the subtractions of the mean initial s at 10 wavelengths from each individual initial s value are defined as calibration factors. Then a calibrated s spectrum was obtained by subtracting the calibration factors from the peak or average s values. For all three experimental cases studied, the calibrated s spectra were used to reconstruct the particle size parameters. The mean particle diameter (a), the sta ndard deviation (b) an d the concentration ( ) reconstructed from both the peak and average s values for the three cases are listed in Table 4-3 where the exact parameters from the manuf acture are also given for comparison. We immediately note that both the mean size and concentration are rec overed with good quality, consistent with the simulations. We found the rela tive error of the recons tructed mean particle size is within 8.4% for the three cases examin ed, while the relative error of the recovered concentration is 33.3%, 0.8% and 11.1% for Case s 1, 2 and 3, respectively. Similar to the simulations, the standard deviations were recove red with errors as large as 86.6% (Case 3). When the average s spectra were used, we see that the reconstructed results are generally similar to that with the peak s spectra; however, overall the peak spectra-based reconstruction has better quality. Figure. 4-3 presents the ex act and recovered PSD ( normalized) for the three different polystyrene suspensions when the peak sp ectra were used for reconstruction. In Figure. 4-4, scattering spectra obtained with different me thods for Cases 1 and 3 are shown, in which we

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92 can see that the calibrated spectra match well with the Mie theory fittings using the recovered particle parameters. 4.1.4 Discussion and Conclusions The ultimate goal of our work is to see if we can extract cellular morphological information of breast tissue using MSDOT. The simulations and phantom study presented here represent our first step toward that goal. In our simulations and phantom experiments, the choices of 2, 3, 6 and 10 m polystyrene scatterers were intended to mimic mitochondria and nuclei, the two primary contribut ors to tissue scattering reported in the literature to date.42, 82-83 We have used Mie theory to recover the partic le size distribution and concentration from the scattering spectra obtained using MSDOT at 10 different wavelengths. It is known that Mie theory assumes spherical particle s without particle-par ticle interactions. While these assumptions do not pose problems in our phantom study, they may do so in real tis sue where scatterers generally are not spherical. In terestingly, Mourant et al.82 presented Mie calculations of s in cultured cell suspensions which showed excel lent agreement between the Mie theory and diffusion approximation. In a prior study, we have shown that accurate PSD can be recovered in concentrated TiO2 suspensions where TiO2 particles are not spherical.78-79 In another study, we have demonstrated that the PSD in KCl suspensions can still be well reconstructed when the concentration of KCl particles is as high as 40%.78,80 Thus it is reasonable to believe that the approach described here for pa rticle sizing would provide qual ity results from in vivo data particularly if we focus on the reconstruction of only particle mean size and concentration. In our particle sizing, the refractive indi ces of the polystyrene suspensions and the surrounding medium (water) are important parameters and have been assumed known as a priori. In a clinical situation, we can obtain these information empirically from the literature, or we can

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93 ultimately recover the refractive indices of scatterers as we reconstruct the PSD and concentration. Our phantom results have s hown that the calibration method developed for correcting the initial scattering values is able to provide quality r econstruction of PSD and concentration. However, there is no clear physical explanation about the sp ectra subtraction used in the calibration. We suspect that the spectra subtraction might have reduced the scattering impact of the background medium on the particle suspensions in the target. In addition, we have set the boundary conditions (BC) coefficient as c onstant for all 10 wavelengths in the calibration. We plan to implement a method that can pr ovide optimized wavelength-dependant BC coefficient, which should give be tter initial scat tering spectra. In summary, we have presented an approach for reconstruction of PSD and concentration in heterogeneous turbid media from scat tering spectra measured using MSDOT. Both simulations and phantom results have shown th at the PSD and concentration of polystyrene spheres contained in the target can be reconstr ucted with 10-wavelength da ta available from our current MSDOT system. We expect to apply the a pproach described in th is section to in vivo clinical data obtained from tumor-bearing breasts in the near future. 4.2 Imaging of Particle Size Distribution and Concentratio n in Heterogeneous Turbid Media In this section, we present for the first time images of particle size and concentration using tissue phantom experiments where a targ et is embedded in a scattering medium. The recovered images obtained are quan titative in terms of the target size and shape, and the particle size and concentration in both the target and background media. 4.2.1 Methods and materials The methods were described in above subs ection. Phantom experiments were conducted using our ten-wavelength DOT system (638, 673, 690, 733, 775, 808, 840, 915, 922 and 960nm).

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94 Two sets of phantom experiments were conducte d to demonstrate the overall approach for imaging particle size and concentration usi ng MSDOT. The cylindrical background phantom had a radius of 25mm, an absorption coefficient of 0.005/mm (India ink as absorber) and a reduced scattering coefficient of 1.0/mm (Intralipid as scatterer). A thin glass tube (9mm in inner diameter, 0.4mm in thickness) containing polysty rene suspensions (Polysciences, Warrington, PA) was embedded off-center in the backgr ound solid phantom. Two different types of polystyrene spheres were used in the e xperiments: one had a diameter of 2.06m and a concentration of 0.52%, and th e other had a diameter 5.66 m and a concentration of 2.62%. The refractive index of the spheres and thei r surrounding aqueous medium are 1.59 and 1.33, respectively. 4.2.2 Results and discussion We first performed simulations to evaluate the sensitivity of particle sizing on the number of wavelengths used. Measured s spectra were generated using Eq. (8) with a=2.86 m, b=0.145 m and =1.02% for 10, 20 and 50 wavelengths between 600 and 1000nm, respectively. When 5% noise was added to each set of measured s spectra, we found that the relative errors of recovering th e particle parameters were w ithin 14% using the 10-wavelength spectra, while such errors were as low as 4% when 50-wavelength spectra were used. The Mie theory fittings using the extracted parameters at 10, 20 and 50 wavelengths are shown in Figure. 4-5(a) where the exact spectra are also presente d for comparison. We see that the 10-wavelength spectra are able to provide quantitatively accurate reconstruction. We also performed simulations to test the noise sensitivity when 1, 5, or 10% random noise was added to the 10-wavelength spectra. The relative errors of the recovered parameters (a and ) were calculated to be 3, 14, and 17% for parameter a and 3, 11 and 14% for the parameter However, the recovery of the

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95 standard deviation was sensitive to noise, which had a relative error of 93% when 10% noise was added. A finite element mesh with 634 nodes was us ed for the DOT reconstructions. To show the accuracy of the DOT reconstruction, Figure. 4-5(b) depicts the recovered s spectra at a typical node location in the target area for the 2.06 m polystyrene case, in comparison with the corresponding Mie theory fitting using the extracted particle parameters. And the DOT reconstructed absorption and redu ced scattering images for the 2.06 m polystyrene case for all ten wavelengths are shown in the Figure. 4-6 The recovered mean size and concentration at each node are used for imaging display. Figure. 4-7 pres ents the reconstructed images of particle size and concentration for the 2.06 and 5.66 m polystyrene cases. We immediately note that the particle size and concentration of both the target and backgro und are quantitatively imaged. The reconstructed mean particle size and concentrat ion in the background were found to be within 154.7~155.1nm and 0.92~1.21% for the 2.06 m polystyrene case, and 155.3~155.5nm and 1.17~1.95% for the 5.66 m polystyrene case, compared to 150nm and 1%, the equivalent mean particle size and concentration of the actual Intralipid/Ink background. In the target region, the recovered mean particle sizes ar e in the range of 1.31 to 2.25 m with average value of 1.72 m for the 2.06 m polystyrene case and 3.48 to 5.97 m with average value of 4.62 m for the 5.66 m polystyrene case, while the reconstructed c oncentrations are in the range of 0.48 to 0.87% with average value of 0.65% for the 2.06 m polystyrene case and 1.76 to 2.70% with average value of 2.25% for the 5.66 m polystyrene case. Similar to the simulations, we see that the standard deviation recovery is sensitive to the noise. The maximum relative errors of the extracted standard deviation are up to 67.9% and 84.9% for the 2.06 m and 5.66 m polystyrene case respectively.

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96 It should be noted that while only the recovered s spectra were needed for particle sizing, the absorption images were quantitatively reconstructed for the experimental two cases studied [see Figs. 4-7(a1)-4-7(a10) ; note that the absorption cont rast between the target and background was extremely low in both cases, resu lting in strong artifacts along the boundary]. Others and we have recently shown repeated ex perimental evidence that the cross-talk between a and s images can be minimized using CW based DOT reconstructions, suggesting that future work involving phantom studies with diffe rent levels of absorption in the target are feasible and worthy. In our particle sizing, the refractive indi ces of the polystyrene suspensions and the surrounding medium are important parameters and have been assumed known as a priori. In a clinical situation, we can obtain these informa tion empirically from the literature, or we can ultimately recover the refractive indices of scatterers as we reconstruct the PSD and concentration. In response to the possible perturbation of the glass tube used in the experiments, we have previously shown that such perturbation was insignificant in the image reconstruction84. In this work, we assumed that the scatterers are spherical. But in tissues, while larger scatterers such as nuclei are spherical, th e smaller scatterers such as mitochondria are ellipsoidal. A possible solution to this is to consider a modified Wentzel-Kramers-Brillouin model (WKB) theory for non-spherical particles as described in [63]. Compared with the diffuse reflectance spectroscopy (DRS), our method can image the part icle size and concentration in heterogeneous media whereas DRS can only deal with homogeneous media. In addition, we believe our method can provide more accurate particle sizes and c oncentrations than DRS, because DRS often is based on analytical solutions to the diffusion equation with the as sumption of infinite or semiinfinite media.

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97 In conclusions, we have demonstrated quantitative imaging of particle size and concentration of heterogeneous turbid media using MSDOT. The choices of the 2.06 and 5.66 m polystyrene particles were intended to simulate typical mitochondria and nuclei, respectively. The phantom results presented sugg est that the method desc ribed in this section may be applied for in vivo imaging of tissue morphology, adding more parameters for clinical decision-making. 4.3 Experimental Results from Concentrated Suspensions with Bi-modal Particle Size Distribution A method directly based on more rigorous Mie scattering theory for the reconstruction of particle size distribution and vol ume fraction has already been pr oposed and validated by a set of phantom experiments in the above sections. A si ngle particle size distribution was assumed and the only one kind of particles was used in th e phantom studies. In pure optical spectroscopy studies, it has been shown that scattering sp ectra are correlated with tissue morphology.42, 82-83, 85 These experimental studies had suggested that bo th nuclei and mitochondria contributed to tissue scattering significantly. But it remained uncle ar how much the contribution of nuclei and mitochondria was to the scattering. In this section, two kinds of particles with different diameters and volume fractions were mixed together and their contributions to the sca ttering were studied experi mentally. This section was organized as follows. Subsection 4.3.1 di scussed the experiment system and phantom materials. The experimental results and discus sion were in subsecti on 4.3.2. Finally, the subsection 4.3.3 was about the conclusions. 4.3.1 Experimental system and materials The ten wavelength (638, 673, 690, 733, 775, 808, 840, 915, 922 and 965 nm), the experimental system and its calibration have already been described in detail elsewhere.40, 71 In

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98 this section, two dimensional images were rec onstructed. Only fiber probes of 16 sources and 16 detectors located in one layer were used fo r the 256 measurements at each wavelength. The cylindrical background phantom had a radi us of 25mm, an absorption coefficient of 0.005/mm (India ink as absorber) and a reduced s cattering coefficient of 1.0/mm (Intralipid as scatterer) at wavelength of 808nm. A thin glass tube (9mm in inner diameter, 0.4mm in thickness) containing polystyr ene suspensions (Polysciences Warrington, PA) was embedded off-center in the background solid phantom. Thr ee sets of experiments were performed. The targets were composed of two kinds of polystyrene suspensions and water, as shown in Tables 44, 4-5, and 4-6, respectively. For experiment se t 1, there were 5 cases, with fixed volume fraction 1.255% of polystyrene with diameter of 6 m and decreased volume fraction from 1.255% to 0.05% for polystyrene with diameter of 1 m. For experiment set 2, there were four cases, with fixed volume fraction 0.77% of 1 m polystyrene spheres and volume fraction of 6 m polystyrene spheres reduced from 0.7% to 0.1%. In the 3 cases of experi ment set 3, the volume fraction of 6 m polystyrene spheres was fixed on 1.255% and other kind of polystyrenes spheres had different diameters and volume fraction concen trations for each of 3 cases, as shown in Table 4-6. 4.3.2 Experimental results and discussion For all the 11 experimental cases in the thre e sets, the absorption coefficient image and the reduced scattering coefficient image at each of ten wavelengths were reconstructed using our CW DOT algorithm although only the reduced scattering coefficient images were used for the further particle size and volume fraction extr action. For each case at each wavelength, the preprocess method for searching initial value of absorption coefficient a sand was implemented and the initial valu es corresponding to the global minimum error, which was the

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99 square sum of the difference between the comput ed and measured photon density, resulted in the best reconstruction image quality31. Figure. 4-8 plotted the recons tructed scattering images at nine wavelengths for case 1 in experiment set 1, using the initial values at the global minimum error. However, the boundary coupling coefficient was supposed to be same approximately at all wavelengths due to their same boundary conditi ons. Because of the system noise, the values of corresponding to the global minimum error at the nine wavelengths were not the same. To see how much influences of the values of at different wavelengths on the reconstructed results, we assume the values of at all wavelengths were same and the initial values were chosen when the total initial sear ching error, which was the sum of the initial searching error of all wavelengths, reached the minimum. For the case1 in experiment set 1 (denoted as case1_1 or set1_1), the value of was found to be 0.29 and the reconstructed reduced scattering coefficient images were plotte d in Figure. 4-9. One may see that the image quality was worse than that of Figure. 4-8 since there were more artifacts in Figure. 4-9 because the initial value at each wavelength was not corresponding to the one at the global minimum error. The target region in the scattering images was segmented and the reduced scattering coefficient values of all nodes in the target were averaged. The average values at 10 wavelengths for 5 cases of experiment set 1 were plotted in Figure. 4-10 and Figure. 4-11 The average values in Figure. 4-10 were calculated from the images reconstructed with initial values at global minimum error and in Figure. 4-11 from the imag es reconstructed with the fixed value of at different wavelengths. The point at wavelength 965 nm was ignor ed due to the worst image quality. Only scattering values at nine wavelengt hs were used for further particle size and volume fraction extraction. The extracted scatteri ng spectra in Figure. 4-11 were used for the

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100 further process because they resulted in more stab le results than the spectra in Figure. 4-10. It means that the same value assumption at different wavele ngths was critical for particle size and volume fraction extraction. Fr om both Figure. 4-10 and Figure.4-11, the scattering decreased from case 1 to case 5 as the total particle vol ume fraction decreased. The slopes of the five scattering spectra in Figure.4-11 decreas ed from case1 to case5 as well. Figure. 4-13 and Figure. 4-14 plotted the average values of reduced scattering coefficient in the target at 10 wavelengths fo r experiment set 2 and set 3, resp ectively. All these values were calculated from the images reconstructed with the initial values when the values of at different wavelengths were assumed to be the same. Once ag ain, one could see that the scattering at the tenth wavelength in Figure. 4-12 tu rned out to be abnormal due to the low signal noise ratio at that wavelength and the values at that wavelength were ignored for the further process. In Figure. 4-12, the slope differences among the four scatte ring spectra were easy to see but the scattering level differences were not. One particle size distribution was assumed when the particle size and volume fraction were extracted, although we mixed two different ki nds of particles into th e target. The extracted particle size and volume fraction based on the scattering spectra fr om Figs. 4-11, 4-12 and 4-13 were shown in Tables 4-7, 4-8 and 4-9 for experi ment set 1, set 2 and set 3, respectively. In Table 4-7, the calculated scatte ring ratio was the ratio of th e calculated reduced scattering coefficient of 1 m particles in the glass tube to the total calculated reduced s cattering coefficient from both kinds of particles. The volume fractio n and the particle size distribution were known so that the scattering coefficient was able to be calculated by Eq. (4-3). The volume fraction was referred to as the volume concentration of 1 m particles in the target. Similarly, in Table 4-8, the calculated scattering ratio wa s the ratio of the calculated re duced scattering coefficient of

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101 6 m particles to the total calculated scattering. The volume fraction was referred to as the volume concentration of 6 m particles. In Table 4-9, the calculated scattering ratio was the division of the calculated reduced scattering coefficient of 0.75 m, 0.11 m, 0.075 m particles by the total calculated scattering in the target for each case. And the volume fraction was the volume fraction of 0.75 m, 0.11 m, 0.075 m particles in the glass tube. Figure. 4-14a and 4-15a plotte d the extracted equivalent mean particle diameter versus the calculated reduced scatte ring coefficient ratio of 1 m particles and of 6 m particles for experiment set 1 and set 2, respectively. In both sets, the extracted particle diameter increased almost proportionally as the calculated re duced scattering coe fficient ratio of 6 m particles (the larger particles) increased. In contrary, the extracted particle diam eter decreased almost proportionally as the calculated reduced scattering coefficient ratio of 1 m particles (the smaller particles) decreased. The extracted equivalent particle diameters with respect to the volume fraction of 1 m particles for set1 and the volume fraction of 6 m particles for set 2 were plotted in Figure. 4-14b and 4-15b, respectivel y. For set1, the volume fraction of 6 m particles remains 1.255%. When the volume fraction of 1 m particles increased from 0.05% to 1.255%, the extracted diameter decreased from 3.4 m to 0.7 m. For set 2, the volume fraction of 1 m particles remained 0.77% and when the volume fraction of 6 m increased from 0.1% to 0.7%, the extracted diameter increased from 0.6 m to 1.3 m. For both set1 and set2, the minimum extracted diameter values, such as 0.7 m in case1_1 and 0.6 m in case2_4, were less than the smaller particle diameter 1 m. The possible reason was that th e background particle (Intralipid) diameter around 150 nm may affect the extracted diameter in the target. In the set1 and set2, only two kinds of particles with different diameters of 1 m and 6 m were used. To see how the particle diameter s effected on the extracted equivalent mean

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102 diameter, experiment set 3 was performed. For cases 1_4, 3_1 and 3_2, all of them had one kind of particles with diameter of 6 m, volume fraction of 1.255% and very close calculated scattering ratio of the smalle r particle, 0.24 for case1_4, 0.297 for case3_1 and 0.299 for case3_2. Another kind of particles (with smaller diameter) for them had diameter of 1 m, 0.75 m and 0.11 m and the extracted diameters were 3.2 m, 3.2 m and 1.8 m, respectively. The extracted diameters decreased from 3.2 m to 1.8 m when the smaller particles diameter reduced from 1 m to 0.11 m, provided other conditions we re same. Compared the case3_3 with case1_5, one might obtain the similar conclu sion. These two cases had very close calculated scattering ratio and had the same volume fr action of particles with diameter of 6 m. Another kind of particles had diameter of 1.0 m for case1_5 and 0.064 m for case3_3 and the extracted diameters were 3.4 m and 2.4 m, respectively. For all cases, the equivalent particle volume fraction could not be extracted quantitatively, but it could be obt ained qualitatively. For experiment set1, the true total particle volume fraction was from 1.26% to 2.51% and th e extracted volume fraction was around 0.9%. For experiment set2, the true total particle volume fraction was from 0.87% to 1.47% and the extracted volume fraction was around 0.5%. One might see that the extracted total volume fraction was larger when the true value was bigger. The particles were assumed to be spherical. It was true for the experiments. But the nucleus and the mitochondria in tissues are elli ptical not spherical. Our ultimate goal is the clinical applications. How the spherical assumption affects on the clinical results will be our next research study. In this section, we have assumed that the particle size distribution was Gaussian distribution although we intended to put two different kinds of partic les into the target. It was our

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103 goal to study how each kind of particle affected th e extracted results. Currently, there are only 10 wavelengths available. It is not feasible to assume no size dist ribution mode, as described in reference [78]. We may do so in the future when there are more wavelength measurements available. 4.3.3 Conclusions When there were two kinds of particles with different diameters in the target and only one particle size distribution was assumed in the pa rticle size extraction calculation, the extracted equivalent particle diameter incr eased almost proportionally as the calculated scattering ratio of the bigger particles increased and the calculated scattering ratio of the smaller particles decreased. The extracted diameter was also incr eased with the increment of the volume fraction of bigger particles and the decrement of the vol ume fraction of the smaller particles, but not proportionally. The extracted diamet er decreased when the diameter of one kind of particle in the target decreased and another kind of particle di ameter remained same. The equivalent particle volume fraction could be reconstr ucted qualitatively, but not quant itatively. Finally, the reduced scattering coefficient spectra, obtained when the boundary coupling coefficient was assumed to be constant for each wavelength, resulted in better results than the sp ectra obtained from the initial values corresponding to the global minimum error.

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104 Figure 4-1. Simulated scattering spectra obtained from Mie calcu lation and the fittings based on the recovered particle size distribution and concentration at different noise levels. 10 wavelengths were used in the simulations.

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105 Figure 4-2. Reconstructed scattering images for Case 2 at 10 different wavelengths. (a) at 638 nm (b)at 673 nm, (c)at 690 nm (d) at 733 nm, (e) at 775 nm, (f) at 808 nm, (g) 840 nm, (h) at915 nm, (i) at922 nm and (j) at 965 nm. (a) (b) (c) (d) (e) (f) (g) (j) (i) (h)

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106 Figure 4-3. Normalized exact (solid lines) a nd reconstructed (dashed lines) particle size distribution from phantom measur ements for Cases 1, 2 and 3. Figure 4-4. Experimental scatteri ng spectra obtained with different methods for Case 1 (left) and Case 3 (right). Circles: spect ra from the DOT reconstruction. Diamonds: spectra after calibration. Squares: Mie fitting using the recovered particle parameters. Crosses: calibration factors/spectra.

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107 Figure 4-5. Scattering spectra: (a) The spectra ge nerated by Eq. (5) and the Mie fittings using recovered particle parameters from simula ted data (5% noise) with 10, 20, and 50 wavelengths, respectively. (b) Experimental spectra DOT reconstructed at a typical node in the target area and the correspondi ng Mie fitting using recovered particle parameters for the 2.06 m polystyrene case.

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108 (a1) (a2) (a3) (a4) (a5) (a6) (a7) (a8) (a9) (a10) (b1) (b2) (b3) (b4) (b5) (b6) (b7) (b8) (b9) (b10) Figure 4-6. The DOT reconstructe d absorption images (a1 to a10) and reduced scattering images (b1 to b10) at 10 different wavelengths: a1/b1 at 638nm; a2/b2 at 673nm; a3/b3 at 690nm; a4/b4 at 733nm; a5/b5 at 775nm; a6 /b6 at 808nm; a7/b7 at 840nm; a8/b8 at 915nm; a9/b9 at 922nm and a 10/b10 at 965nm for the 2.06 m polystyrene case for all ten wavelengths.

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109 Figure 4-7. Reconstructed images of mean partic le size (a, c) and concentration (b, d) for the 2.06m (a, b) and 5.66m (c, d) polystyrene cases, respectively. The axes (left and bottom) indicate the spatial scale, in millim eters, whereas the colorful scale (right) records the mean particle size or concen tration, in micrometers or percentage.

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110 Figure 4-8. The reduced scattering coefficient imag es at 9 different wavelengths for experiment set1_1(top row, left) 638 nm, (top row, middle) 673 nm, (top row, right) 690 nm, (middle row, left) 733 nm, (middle row, middle) 775 nm, (middle row, right) 808 nm, (bottom row, left) 840 nm, (bottom row, middle) 915 nm and (bottom row, right) 922 nm. The values were same for all 9 wavelengths.

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111 Figure 4-9. The reduced scattering coefficient imag es at 9 different wavelengths for experiment set1_1: (top row, left) 638 nm, (top row, middle) 673 nm, (top row, right) 690 nm, (middle row, left) 733 nm, (middle row, middle) 775 nm, (middle row, right) 808 nm, (bottom row, left) 840 nm, (bottom row, middle) 915 nm and (bottom row, right) 922 nm. The value for each wavelength is differe nt, obtained from the initial value search program. The global minimum error initial value is selected.

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112 0 0.5 1 1.5 2 2.5 3 6006507007508008509009501000 Wavelength (nm)reduced scattering coefficient (1/mm) set1_1 set1_2 set1_3 set1_4 set1_5 Figure 4-10. Reduced scattering coefficient at 10 wavelengths for 5 cases of experiment set1. Fixed value was applied for each case. 0 0.5 1 1.5 2 2.5 3 3.5 6007008009001000 wavelength (nm)reduced scattering coefficient (1/mm) set1_1 set1_2 set1_3 set1_4 set1_5 Figure 4-11. Reduced scattering coefficient at 10 wavelengths for 5 cases of experiment set1. The value of corresponding to the global minimum error was applied for each case.

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113 0 0.5 1 1.5 2 2.5 3 6007008009001000 wavelength (nm)reduced scattering coefficient (1/mm) set2_1 set2_2 set2_3 set2_4 Figure 4-12. Reduced scattering coefficient at 10 wavelengths for 4 cases of experiment set2. Fixed value was applied for each case. 0 0.5 1 1.5 2 2.5 6006507007508008509009501000 wavelength (nm)reduced scattering coefficient (1/mm) set3_1 set3_2 set3_3 Figure 4-13. Reduced scattering coefficient at 10 wavelengths for 3 cases of experiment set 3. Fixed value was applied for each case.

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114 0 500 1000 1500 2000 2500 3000 3500 4000 00.20.40.60.81 calculated scattering coefficient ratioreconstructed diameter (nm) calculated scattering coefficient ratio of 1u particles calculated scattering coefficient ratio of 6u particles (a) 0 500 1000 1500 2000 2500 3000 3500 4000 00.20.40.60.811.21.4 volume fraction of 1um particles (%)reconstructed diameter (nm) (b) Figure 4-14. The reconstructed diam eter versus (a) the calculated sc attering coefficient ratio of 1 m particles and 6 m particles and (b) the volume fraction of 1 m particles for experiment set 1.

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115 0 200 400 600 800 1000 1200 1400 00.20.40.60.81 calculated scattering coefficient ratioreconstructed diameter (nm) calculated scattering coefficient ratio of 6um particles calculated scattering coefficient ratio of 1um particles (a) 0 200 400 600 800 1000 1200 1400 00.10.20.30.40.50.60.70.8 volume fraction of 6um particlesreconstructed diameter (nm) (b) Figure 4-15. The reconstructed diam eter versus (a) the calculated sc attering coefficient ratio of 1 m particles and 6 m particles and (b) the volume fraction of 1 m particles for experiment set 2.

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116 Table 4-1 Reconstructed parameters from simulate d data at different noise levels for simulation 1. Noise Levels Parameter s Exact Reconstructed results and error s 0% 1% 5% 10% 20% Reconstructed1.02%1.05% 1.13%1.16% 1.36% 1.02% Error 0.0%2.9% 10.8%13.7% 33.3% Reconstructed2.85 2.94 3.27 3.36 4.14 a 2.855 Error 0.03%3.0% 14.6%17.6% 44.9% Reconstructed0.14 0.17 0.29 0.01 0.01 b 0.145 Error 0.7%17.9% 100%93.1% 93.1% Table 4-2 Reconstructed parameters from simulate d data at different noise levels for simulation 2. Noise Levels Parameter s Exact Reconstructed results and error s 0% 1% 5% 10% 20% Reconstructed5.0%5.02% 4.89%5.37% 26.4% 5.0% Error 0.0%0.40% 2.20%7.40% 21.8% Reconstructed10.0 10.05 10.0710.74 7.98 a 10.0 Error 0.0%0.50% 0.70%7.40% 20.2% Reconstructed0.30 0.44 0.59 0.043 0.023 b 0.3 Error 0.0%46.7% 96.6%85.7% 92.3% Table 4-3 Reconstructed parameters from expe rimental data using the peak and average scattering spectra of the target area. Cases ParametersExact Reconstructed (Peak) Error (Peak) Reconstructed (Average) Error (Average) 0.52% 0.69% 33.3% 0.75% 44.2% a (um) 2.06 1.96 4.9% 2.40 16.4% Case 1 b (um) 0.02 0.01 50.0% 0.01 67.9% 1.02% 1.01% 0.8% 0.85% 16.6% a (um) 2.85 2.89 1.2% 2.73 4.5% Case 2 b (um) 0.14 0.05 65.6% 0.12 15.2% 2.62% 2.33% 11.1% 2.18% 16.8% a (um) 5.66 5.18 8.4% 5.19 8.2% Case 3 b (um) 0.31 0.04 86.6% 0.05 84.9%

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117 Table 4-4 Target materials of experime nt set 1. The unit of volume is mL. Targets 6 m, 2.51% 1 m, 2.60% water Experiment Sets volume particle volume percent volume particle volume percent volume Total Volume set1-1 4.0 1.255 3.86 1.255 0.14 8.0 set1-2 4.0 1.255 1.54 0.5 2.46 8.0 set1-3 4.0 1.255 0.77 0.25 3.23 8.0 set1-4 4.0 1.255 0.31 0.1 3.69 8.0 set1-5 4.0 1.255 0.15 0.05 3.8 8.0 Table 4-5 Target materials of experime nt set 2. The unit of volume is mL. Targets 1 m, 2.60% 6 m, 2.51% water Experiment Sets volume Particle volume percent volume Particle volume percent volume Total Volume set2-1 0.77 0.25 2.23 0.7 5.0 8.0 set2-2 0.77 0.25 1.12 0.35 6.11 8.0 set2-3 0.77 0.25 0.64 0.2 6.59 8.0 set2-4 0.77 0.25 0.32 0.1 6.91 8.0 Table 4-6 Target materials of experime nt set 3. The unit of volume is mL. Targets 6 m, 2.51% varied diameter water Experiment Set3 volume Particle volume percent diameter Volume Particle volume percent volume Total Volume set3-1 4.0 1.255 0.75 m 0.62 0.2 3.38 8.0 set3-2 4.0 1.255 0.11 m 2.96 1.0 1.04 8.0 set3-3 4.0 1.255 0.064 m 3.95 1.3 0.045 8.0 Table 4-7 Reconstructed results of set1. cases Calculated Scattering ratio Volume ratio (percentage) Extracted total volume percentage Extracted mean diameter ( m) set1_1 0.798 1.255 0.8 700 set1_2 0.613 0.5 0.8 1400 set1_3 0.441 0.25 0.8 1800 set1_4 0.240 0.1 1 3200 set1_5 0.136 0.05 1 3400

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118 Table 4-8 Reconstructed results of set2. cases Calculated Scattering ratio Volume ratio (percentage) Extracted total volume percentage Extracted mean diameter ( m) set2_1 0.414 0.7 0.6 1300 set2_2 0.261 0.35 0.5 1000 set2_3 0.168 0.2 0.5 900 set2_4 0.092 0.1 0.4 600 Table 4-9 Reconstructed results of set3. cases Calculated Scattering ratio Volume ratio (percentage) Extracted total volume percentage Extracted mean diameter ( m) set3_1 0.297 0.2 1.3 3200 set3_2 0.299 1.0 0.9 1800 set3_3 0.156 1.3 1 2400

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119 CHAPTER 5 EX VIVO AND IN VIVO ST UDY OF TUMOR CELL SIZING 5.1 Ex Vivo Study of Tumor Cells The cellular architecture of early cancer cells changes53. These morphological alterations typically include enlargement of the nuclei and increased nuclear density or nuclear crowding. Early tumors are readily treatable if these ce llular alterations can be detected. These early warning signs, however, are thus far detectable only by histological examination of tissues taken out by biopsy. Here we describe a non-invasi ve imaging technique based on multi-spectral diffuse optical tomography (MSDOT) that can image cellular size and crowding. We have tested the potential of this techni que for imaging cellular size and crowding in ex vivo breast tissue. Immediately afte r the mastectomy of the right br east of a 62 years old female with a biopsy confirmed inf iltrating ductal carcinoma ( 3.3.7.0cm), a portion of the breast with the tumors was sectioned transversely into an approximately 1.5 cm thick section using a tissue slicer. From the section, a 3x2cm fresh tissue slice with both tumor and normal tissues was obtained. We then placed this tissue slice in the hole (4x6 cm ) of a 7x10 cm cylindrical solid background phantom composed of agar powder, In tralipid solution and In dia ink for mimicking tissue scattering and absorption (Figure. 5-1a). We furthe r poured liquid phantom (at 39 C) with the same optical properties as the solid phantom into the hole/breast tissue and then cooled down the liquid phantom to 20 C to obtain a full tissue-containing solid phantom for imaging (center in Figure. 5-1b). In Figure. 1b we also see that the multi-channel optic fibers (16 transmitters and 16 receivers) are in gentle contact with the pha ntom. After the optical measurement, a tissue sample from the same tissue slice was taken for histological examination. The microscopic sections of both tumor and normal tissues are sh own in Figs. 5-2a and 5-2b, respectively.

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120 Figs. 5-3a and 5-3b show the recovered ce llular size and crowding or volume fraction images, respectively, where we immediately not e that the tumor, normal tissue and background phantom are readily differentiated. The recovered average size of the sca tteres in the tumor area was calculated to be 5.1 m relative to the average nuclear size of 8.9 m in the tumor region measured from the microscopic sections. This re latively large difference in size makes us to believe that what we reconstructed is most lik ely an effective size of combined nuclear and mitochondria (normally 1~2 m) structure, which gives an expected effective size of approximately 5.0~5.5 m from the microscopic sections. Fr om Figure. 5-3b, we found that the extracted average cellular volume fraction or crowding in the tumor is 17% which is close to the nuclear crowding of 19% estimated fr om the microscopic sections. Our results show that multi-spectral diffuse optical tomography has the potential to image cellular alterations, making it possible fo r detecting precancerous abnormal tissues. 5.2 Morphological Characteristics of Breast Tumors: In-Vivo Study with Multispectral Diffuse Optical Tomography 5.2.1 Methods The three dimensional multispectral (10 wavelengths) imaging system and its calibration were described in chapter 2 and 3. Here onl y two-dimensional image was discussed. And 256 measurement data at 16 detection positions for each of 16 source locations were used for further image reconstruction. Chapter 4 detailed the algorithm of particle size imaging and its validations with numerical simulations and phant om experiments. Briefly, the tissue-mimicking phantom/clinical measurement data at each wa velength were used to obtain the absorption coefficient and reduced scattering coefficient images using our finite element based DOT reconstruction algorithm introduced in subsection 1.5. Then the reconstructed reduced scattering coefficient images at all wavelengths were utili zed to extract the morphological images such as

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121 the mean diameter image and the volume fractio n image of the scatte ring particles using a Levenberg-Marquat inverse procedure. Our clinical trail experiments, performed in the biomedical engineering department of University of Florida, were approved and monito red by the Institute Review Board of University of Florida Health Center. And our clinical trial experiments, performed in physics department, Clemson University, were approved and monitore d by the Institute Review Board of Clemson University. All the patients, taking part in the clinical trial experiments, signed the consent forms. Since the imaging system could only cove r 2 cm slice of a breast, the clinical trial experiments were conducted after the radiologist s showed us which breast was abnormal and the approximate location of the abnormality from th e mammogram films. The imaging results were compared with the mammogram report record ed by the radiologist and the biopsy report recorded by the pathologist. All the cases ha d the mammogram reports. Some clinical cases conducted in Clemson University did not have the biopsy report and all cases conducted in biomedical engineering department of unive rsity of Florida had the biopsy report. 5.2.2 Results 5.2.2.1 Case studies: #1, 2 and 3: Infiltrating ductal carcinomas The NIR diffuse optical tomography imaging was conducted for the right beast of a 52 years old female volunteer with patient ID #G1. The right craniocaudal (CC) and mediolateral oblique (MLO) mammograms for the patient were shown in Figs. 5-4a and 5-4b, respectively. From the mammogram, an ill-defin ed speculated mass was found in the center lateral portion of the right breast, which lay under a marker for the palpable abnormality. BI-RADS category was 4. Sonographic images of the right breast also demonstrated an ill-de fined hypoechoic mass with lobular margins measuring approximately 1.0.6.0 cm in the 9 oclock position corresponding to the abnormality noted in th e mammogram. After biopsy, mastectomy was

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122 performed and the surgery confirmed that the pa tient had an invasive ductal carcinoma in the right breast. Cut surfaces revealed a 1.2 1.2 approximately 1.3 cm retracted and firm nodule of pink-tan tumor tissue in the lower outer quadrant subject to the biopsy site on the skin. The DOT imaging was conducted one week before the biopsy and the mastectomy surgery. The reconstructed redu ced scattering coefficient images at 9 wavelengths from 638nm to 922nm of the examined breast for the patient we re shown in Figs. 5-5a to 5-5i, respectively. The horizontal and vertical axis represented x an d y in mm. The color bar indicated values of reduced scattering coefficients in 1/mm. From a ll the scattering images, one target was detected around 6 oclock while the surgery report indicated the tumor was in the lower outer quadrant, which means the tumor was around 7 oclock. The reduced scattering images at 9 wavelengths were used to extract the scattering particle mean diameter image in micrometer (shown in Figure.5-6a) and the sca ttering particle volume fraction image in percentage (shown in Figure. 56b). From Figure. 5-6a, the maximum diameter in the tumor region was found to be 3.1 m and the average diameters in the tumor and the background were 2.18 m and 0.45 m, respectively. The ratio of the average diameter in the tumor to that in the background was calculated to be 4.84. Sim ilarly, from Figure. 5-6b, the maximum volume fraction in the tumor region was found to be 1.6% and the average volume fractions in the tumor and in the background we re 1.32% and 0.48%. The ratio of the average volume fraction in the tumor to that in the backgr ound was calculated to be 2.75. The target and the background were segmented by the criteria of full width at ha lf maximum (FWHM) at each figure. From both the diameter image and the volume fraction image, the suspicious tumor was located in a small region. This observation was c onsistent with the surgery report which revealed

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123 a 1.2 1.2 approximately 1.3 cm retracted a nd firm nodule of pink-tan tumor tissue in which the tumor was limited in. The second patient (patient ID #G2) was a 50 years old fema le volunteer with palpable abnormality in the right breast. The right cran iocaudal mammogram and the right mediolateral mammogram of the patient were shown in Figur e. 5-7a and 5-7b respectively. From these mammograms, an extremely dense pattern of fibr oglandular tissue, which limits the sensitivity, was identified. There was a 4-5 cm mass-like area in the upper-outer quadrant of the right breast, which correlated to the palpable abnormality. There was no architectural distortion or suspicious calcification. No skin thickening or adenopat hy was noted. The ultras onography of the right breast showed a 3.9 cm heterogeneous hypoe choic mass with some posterior shadowing corresponding to the palpable abnormality locat ed at 10 oclock. And there was an adjacent 9mm similar hypoechoic solid nodule, as we ll as other small nodules. After biopsy, mastectomy surgery was conducted. From the surger y, a white, semi-cystic, semi-solid tumor mass with infiltrative borders was located in the lateral inferior quadrant (6-9 oclock) and measured 4.0 cm from lateral to medial, 4.5 cm from inferior to superior, and 2.4 cm form anterior to deep. The breast parenchyma reveal ed fibrocystic change beneath the areola and nipple, which created a solid tan-white portion of breast tissue, measuring 2.2 3.0 2.5 cm. The NIR DOT imaging of the second patient was conducted two days before the biopsy and surgery. The reconstructed reduced scattering coefficient images at 9 wavelengths from 638nm to 922nm were shown in Figs 5-8a to 5-8i. These images were then used to extract the scattering particle mean diameter and volume fr action images, which were shown in Figs. 5-9a and 5-9b respectively. From the scattering images, one saw that the detected target was not limited in one region. The detected targets were located either in the center or around 10 oclock

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124 of the breast. From the mean diameter image and the volume fraction image shown in Figure. 59, one saw that the detected target were a big one located around the center and around 10 oclock. These findings were consis tent with the surgery report. From Figure. 5-9a, the maximum diameter in the tumor region was found to be 5.3 m and the average diameters in the tumor and in the background were 4.14 m and 0.48 m respectively. The ratio of the average diameter in the tumor to that in the background was calculated to be 8.62. Similarly, from Figure. 5-9b, the maximu m volume fraction in the tumor region was found to be 1.9% and the average volume fractions in the tumor and in the background were 1.7% and 0.56%. The ratio of the average volume fraction in the tumor to that in the background was calculated to be 3.03. The third patient was 50 years old female vol unteer, with patient ID #G8. Unfortunately, we could not obtain the mammogram films because the patient moved to other hospital after the mammogram screening and biopsy were conducted in Shands Hospital where our CO-PI works. The reports of mediolateral oblique mammogram and cranioca udal mammogram of both breasts were obtained. The breasts were composed of ve ry dense fibroglandular tissues, which can limit mammogram sensitivity. In the mammograms, there were no masses or areas of distortion. The mammograms conclusion was Probably benign right mammogram. Benign left mammogram. However, the biopsy report indicated that a duct al carcinoma in situ, non-comedo type, of breast, nuclear grade III is found. The biopsy found there were 2 masses in the left breast, one in the 11 oclock position and one in the retroareolar region. Only the 11 oclock lesion was biopsied. Surgical excision was recommended. Before the biopsy, the NIR DOT imaging e xperiments of the patient left breast were conducted. Because the patient felt pain in the neck during the NIR imaging experiment,

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125 measurements stopped at 7th wavelength. And because the dense breast tissue resulted in low SNR at the shorter wavelengths, the reduced scatte ring coefficient images at 4 wavelengths from 733 nm to 840 nm were reconstructed and shown in Figure. 5-10. Based on the scattering images at 4 wavelengths, the scattering particle mean diameter and volume fraction images were reconstructed and shown in Figs. 5-11a and 5-11 b respectively. From both the scattering images and the morphological images, the detected ta rgets were located around 12 oclock and 3 oclock. There was more than one target, which was consistent with the biopsy report, while the mammogram report indicated that there were no susp icious masses or lesions in the left breast. From Figure. 5-11a, the maximum diameter in the tumor region was found to be 4.8 m and the average diameters in the tu mor and in the background were 3.65 m and 0.31 m respectively. The ratio of the average diameter in the tumor to that in the background was calculated to be 11.77. Similarly, from Figure. 5-11b, the maximum volume fraction in the tumor region was found to be 1.84% and the average volume fractions in the tumor and in the background were 1.61% and 0.64%. Th e ratio of the average volume fr action in the tumor to that in the background was calculated to be 2.51. 5.2.2.2 Case studies: #4, 5 and 6: Benign nodule or mass The fourth patient was a 69 years old female volunteer with patient ID #S5. Figure. 5-12 represented the right breast mediolateral oblique mammogram (a) and the right breast craniocaudal mammogram (b). In the mammogram, a stellate area of archit ectural distortion and asymmetric density had developed in the superi or lateral quadrant, where the patient felt a palpable mass. But the right breast ultrasound examin ation report indicated that in the area of the known mammographic abnormality, no discrete mass was identified. There was some slight shadowing in this area. No biopsy repor t was available for this patient.

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126 The reconstructed absorption coefficient images for the right breast of the patient at 9 wavelengths from 638nm to 922nm (a to i) were shown in Fig 5-13. Horizontal and vertical axis represented x and y in mm, respectively. The color bar indicated the value of absorption coefficient in 1/mm. And the rec onstructed reduced scattering co efficient images at the right breast of the patient at 9 wavele ngths from 638nm to 965nm (a to i) were shown in Figure. 5-14. The color bar indicated the value of the reduced scattering coefficient in 1/mm. Only the reduced scattering coefficient images at 9 wavelengths were used to extract the scattering particle mean diameter image (shown in Figure. 5-15a) and volume fraction image (shown in Figure. 5-15b). In all the absorption coefficient images, the reduced scattering coefficient images and morphological images, only one target around 8 ocl ock is identified, while in the mammogram the abnormality was located around 9 oclock. As shown in Figure. 5-15, the scattering partic le mean diameter increased in the target region while the volume fraction in the target region decreased. From Figure. 5-15a, the maximum diameter in the tumor region was found to be 0.65 m and the average diameters in the tumor and the background were found to be 0.53 m and 0.11 m, respectively. The ratio of the average diameter in the tumor to that in th e background was calculated to be 4.82. Similarly, from Figure. 5-15b, the minimum volume fraction in the tumor region was found to be 0.2% and the average volume fractions in the tumor and in the background were found to be 0.42% and 0.93%. The ratio of the average volume fraction in the tumor to that in the background is calculated to be 0.45. The fifth patient was a 42 years old female volunteer with patient ID #S7. Figure. 5-16 showed the left breast cranioca udal mammogram (a) and the left breast mediolateral oblique mammogram (b). The mammogram report indicated that the nodular density below the scar

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127 marker appeared to press out on the spot comp ression CC view and no persisted nodular density was seen on the roll views. There was reporte dly no palpable mass. The ultrasound report indicated that two smooth lobulated solid nodules were presented in the medial aspect of the left breast at 9:30 oclock. The more anterior nodule measured 5.8 4.8 8.3 mm and the mid left breast nodule measured 6.9 3.6 9. 1 mm. The BI-RADS category is 3. The NIR DOT imaging experiment was c onducted after the mammogram examination. The reconstructed reduced scattering coefficient imag es at 9 wavelengths for the left breast of the patient #S7 were shown in Figure. 5-17. Horizontal and vertical axis represented x and y in mm, respectively. The color bar indicated the value of reduced scattering coefficient in 1/mm. In the scattering images, there were tw o targets located around 6:00 ocl ock and 8 oclock respectively, while the mammogram could not identify any target and the u ltrasound detected two separate nodules positioned around 9:30 oclock. Using the reduced scattering coefficient images the scattering particle mean diameter image (shown in Figure. 5-18a) and volume fr action image (shown in Figure. 5-18b) were reconstructed. The mean diameter image (shown in Figure. 5-18a) had a bi g artifact in the center that was possibly resulted in from the center artifacts in the scatteri ng images 5-17h and 5-17i. The volume fraction image (shown in Figure. 5-18b) identified the targets at the right positions. From Figure. 5-17a, the maximum diameter in the tumor region was found to be 4.7 m and the average diameters in the tumor and the background were 4.15 m and 1.33 m, respectively. The ratio of the average diameter in the tumor to that in the back ground was calculated to be 3.12. Similarly, from Figure. 5-17b, the maximum volume fraction in the tumor region was found to be 1.7% and the average volume fractions in the tumor and in the background were calculated to

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128 be 1.41% and 0.29%. The ratio of the average vo lume fraction in the tumor to that in the background is calculated to be 4.86. The sixth patient was a 60 years old female volunteer with patient ID #S9. Figure. 5-19 showed the mediolateral oblique mammogram (a ) and the mediolateral mammogram (b) of the right breast. The mammogram repor t indicated that small nodular opacity in outer aspect was seen only in single projection on th e exaggerated craniocaudal view of the right breast (the film of the exaggerated CC mammogram was not availa ble) and it had an identical appearance to study one year ago. And a large dominant opac ity was re-demonstrated also unchanged. It measured approximately 1.4 cm in diameter and sit more medially within the lateral aspect of the right breast. The BI-RADS category was 2, benign findings. Ultrasound imaging was not conducted. The NIR DOT imaging experiment was conducted two days after the mammogram screening. The reconstructed reduced scattering co efficient images at 9 wavelengths were shown in Figure. 5-20. Two targets, one at 5 oclock and the other at 11 ocloc k, were identified in almost all the scattering images, which was consistent with the mammogram report indicating two targets, one 4mm in diameter in the outer asp ect and the other 1.4 cm in diameter within the lateral aspect. Using these reduced scattering co efficient images, the sc attering particle mean diameter image (shown in Figure. 5-21a) and volume fraction image (shown in Figure. 5-21b) were reconstructed. The morphological images also identified two target s. From Figure. 5-21a, the maximum diameter in the tumor region was found to be 0.64 m and the average diameters in the tumor and the background were calculated to be 0.53 m and 0.12 m, respectively. The ratio of the average diameter in the tumor to that in the background was calculated to be 4.41. Similarly, from Figure. 5-21b, the maximum volume fraction in the tumor region was found to

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129 be 1.42% and the average volume fractions in th e tumor and in the background were found to be 0.53% and 1.05%. The ratio of the average volume fraction in the tumor to that in the background was calculated to be 0.505. 5.2.2.3 Statistical analysis and pathological co-registration Besides the 6 clinical cases, the clinical experimental m easurements of 7 more benign cases and 1 more malignant tumor case were proc essed. The scattering particle mean diameter and volume fraction for each case were recons tructed. There were 10 benign cases and 4 malignant cases available for the statistical analysis. The peak va lues of the recovered scattering particle mean diameter and volume fraction in th e target region were f ound in the reconstructed mean diameter image and volume fraction imag e for each case. The average values and the standard deviations of the mean diameter and volume fraction for the 10 benign cases and 4 malignant cases were calculated, respectively. Th e calculated results were shown in Figure. 5-22, where the solid bar indicated the malignant cases and the bar with cross pattern represented the benign cases. The average diameter for the malignant tumors was calculated to be 4.325 m with deviation of 1.34 m. And the average volume fraction for malignant tumors was calculated to be 1.7375% with standard deviat ion of 0.65%. Similarly, the av erage diameter for the benign abnormalities was calculated to be 1.3455 m with deviation of 1.43 m. And the average volume fraction for the benign abnormalities was calculated to be 0.658% with standard deviation of 0.51%. The ratio of the average diam eter of malignant tumors to that of benign abnormalities was 4.352/1.345=3.23. Similarly, the ratio of the average volume fraction of malignant tumors to that of beni gn abnormalities was 1.7375%/0.658%=2.64. For each case, the recovered volume fraction versus the recovered diameter was plotted in Figure. 5-23. The square dots indicated the malignant cases and the diamond dots represented the benign cases. It was clear th at all the malignant cases were located in the upright quadrant

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130 and all the benign cases except one were locate d in the downleft quadrant. The exception case was from the patient ID #S7, discussed in a bove subsection. The cente r artifact dominated the reconstructed mean diameter image and the result of that case was deteri orated. The preliminary result showed that the recovered scattering par ticle mean diameter and volume fraction could be the new criteria to differentiate the mali gnant tumors from the benign abnormalities. The microscopic pictures of the tumor cells for patient #G1, #G2 and #G3 were obtained from our cooperated pathologist in the Shands hos pital and they were shown in figure 5-24. All these three pictures were magnified by 400 times. From these pictures, we could find the average diameter and the approximate volume fraction of the cancer cell nucleus and nucleolus. Please node that the nucleus and nucleol us were not spherical. The di ameter of one nucleus was the average of the length and the width. The diamet ero of nucleolus was approximated as 0.2 times the corresponding the nucleus. The volume fraction of the nucleus was 0.667 multiplying the ratio of the area occupied by the nucleus to th e whole area of the section, where 0.667 was the factor considering that we cal culated the 3D volume fraction not the 2D area fraction. The found values were shown in table 5-1. The volume fraction of nucleolus was calculated as (0.2)3=0.008 times the corresponding nucleus vo lume fraction. And these values were compared with average value calculated from the reconstructed diam eter images and volume fraction images for corresponding cases. From the Table 5-1, we found that the relative errors of the reconstructed average diameters for #G1, #G2 and #G8, comp ared to the values of nucleus found from pathological pictures, are 55.3% 6.5% and 31.9%, respectively. Similarly, we found that the extracted average volume fraction, compared to the values found from pathological pictures, are 77.9%, 60.3% and 76.4%, respectively. From the ta ble, we saw that the reconstructed diameters were about 2 times less than the diameters of nucleus for case #G1 and #G8 and the

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131 reconstructed volume fractions were about 3 times less than those of nucleus for all three cases. The reconstructed diameters and volume fraction we re larger than those of the nucleolus and less than those of the nucleus. We coul d conclude that the scattering particles were including both the nucleus and the small particles such as th e nucleolus, mitochondria. We could not see mitochondria in these pictures but their si zes were close to that of nucleolus. In sum, in this subsection, we have st udies 14 clinical cases including 10 benign cases and 4 malignant cases and detailed 6 clinical cases, in which the tumors were identified successfully in both the reconstructed diameter and volume fraction images. The statistical analysis showed that the reconstructed di ameter and volume frac tion may provide new parameters to differentiate the malignant br east tumors from the benign abnormalities while more clinical results were needed to prove it further. By comparison with the pathological pictures, we found that the scatte ring particles were not only th e nucleus but also the smaller particles such as nucleolus and the mitochondria.

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132 Figure 5-1. The microscopic pict ure of (a) the tumor tissue ( 400 time magnificent) and (b) the normal tissue (100 time magnificent). Figure 5-2. Experiment prepar ation: (a) the removed tissue was put inside the background phantom; (b) The tissue was covered with background phantom and examined by the system. (a) (b) (a) (b)

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133 Figure 5-3. Ex-vivo results: (a) The extracted nucleus concentration distribution in the tissue region and the intralipid concentratio n distribution in the background region (percentage), where the color bar indicates the percentage number; (b) The logarithm of extracted nucleus size distribution in the tissue region and the intraplipid size distribution in the background region, where the color bar responses to the logarithm of the diameter in micrometer. (a) (b) Figure 5-4. Mammogram films: (a) Right CC mammogram, (b) Right MLO mammogram for the right breast of a 52 years old patient (patient ID #G1). (a) (b)

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134 (a) (b) (c) (d) (e) (f) (g) (h) (i) Figure 5-5. The constructed scattering images at 9 wavelengths from 638nm to 922nm (figs. a to i) of the examined breast for patient G1. Hori zontal and vertical axis represent x and y respectively. The color bar indicated the valu e of the reduced scattering coefficient in 1/mm. Figure 5-6. The extracted images of particle diam eters (a) and particle volume fraction (b) of the examined breast for patient G1. The colorful ba r in (a) represents the value of particle diameters in micrometer. And the colorful ba r in (b) represents the value of particle volume fraction of percentage. Horizontal and vertical axis represent x and y respectively.

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135 cc MLO Figure 5-7. Mammogram films: (a) CC mammogram, (b) MLO ma mmogram for the right breast of a 50 years old patient.

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136 (a) (b) (c) (d) (e) (f) (g) (h) (i) Figure 5-8. The reconstructed scattering images at 9 wavelengths from 638nm to 922nm (Figs. a to i) of the examined breast for patient #G2. Horizontal axis represents x. The colorful bar indicated the value of the reduced scattering coefficient in 1/mm. Figure 5-9. The extracted images of particle diam eters (a) and particle volume fraction (b) of the examined breast for patient #G2. The colorf ul bar in (a) represents the value of particle diameters in micrometer. And the co lorful bar in (b) repr esents the value of particle volume fracti on of percentage. Horizontal and vertical axis represent x and y respectively.

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137 (a) (b) (c) (d) Figure 5-10. The reconstructed s cattering images at 4 wavelengths from 733nm to 840nm (Figs. a to d) of the examined breast for patient G8 Horizontal and vertical axis represent x and y respectively. The colorful bar indi cated the value of the reduced scattering coefficient in 1/mm. Figure 5-11. The extracted images of particle di ameters (a) and particle volume fraction (b) of the examined breast for patient G8. The colo rful bar in (a) repr esents the value of particle diameters in unit of micrometer. And the colorful bar in (b) represents the value of particle volume frac tion of percentage. Horizontal and vertical axis represent x and y respectively.

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138 (a) (b) Figure 5-12. Mammogram films: (a) MLO and (b) CC mammography of the right breast for patient #S5. (a) (b) (c) (d) (e) (f) (g) (h) (i) Figure 5-13. The reconstructed ab sorption coefficient images for the right breast of the patient #S5 at 9 wavelengths from 638nm to 922nm (a to i). Horizontal and vertical axis represent x and y in mm. re spectively. The color bar indicates the value of the absorption coefficient in 1/mm.

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139 (a) (b) (c) (d) (e) (f) (g) (h) (i) Figure 5-14. The reconstructed s cattering images at the right br east of the patient #S5 at 9 wavelengths from 638nm to 965n m (a to i). The color bar indicated the value of the reduced scattering coefficient in 1/mm. Figure 5-15. The reconstructed particle diamet er image (a) and the particle volume fraction image (b) of the right breast for patient #S5. The colorful bar in (a) represents the value of particle diameters in micr ometer. And the colorful bar in (b) represents the value of particle volume frac tion in percentage.

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140 Figure 5-16. Mammogram films: (a) CC and (b ) MLO mammography of the left breast for patient #S7. (a) (b) (c) (d) (e) (f) (g) (h) (i) Figure 5-17. The reconstructed s cattering images of the examined breast at 9 wavelengths from 638nm to 965nm (a to i) for patient #S7. The color bar indicate d the value of the reduced scattering coefficient in 1/mm. Horiz ontal and vertical axis represent x and y in mm. respectively.

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141 Figure 5-18. The reconstructed particle diamet er image (a) and the particle volume fraction image (b) of the examined breast for patient #S7. The colorful bar in (a) represents the value of particle diameters in micromet er. And the colorful bar in (b) represents the value of particle volume fraction in percentage. RMLO RML Figure 5-19. Mammogram films: (a)RMLO, (b)RML images of the patient #S9.

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142 (a) (b) (c) (d) (e) (f) (g) (h) (i) Figure 5-20. The reconstructed scattering images of the right breast for patient #S9 at 9 wavelengths from 638nm to 965n m (a to i). The color bar indicated the value of the reduced scattering coefficient in 1/mm.

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143 Figure 5-21. The reconstructed particle diamet er image (a) and the particle volume fraction image (b) of the right breast for patient #S9. The colorful bar in (a) represents the value of particle diameters in micrometer. And the colorful bar in (b) represents the value of particle volume fraction in percentage. 4.325 1.7375 1.3455 0.658 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 diameter in micrometer volume fraction in percentage Malignant Benign Figure 5-22. Average values of recovered mean diameter and volume fraction of scattering particles for 8 benign cases and 4 malignant cases, respectively. The deviations are shown in the corresponding bars.

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144 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0123456 diameter in micrometervolume fraction in percentage benign mali g nant Figure 5-23. The peak value of the recovered volume fraction in the target region versus the peak value of mean diameter in the target region. The diamond dots indicate the benign cases and the square dots i ndicate the malignant cases.

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145 (a) (b) (c) Figure 5-24. The pathological microscopic pictures of tumor cells for pati ent #G1 ( shown in a), #G2 (shown in b) and #G3 (shown in c).

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146 Table 5-1 Mean diameters and volume fraction of the nucleus and nucleolus found from the microscopic pictures and those of sca ttering particles calculated from the reconstructed images. from microscopic pictures reconstructed nucleus nucleolus cases diameter ( m) volume fraction diameter ( m) volume fraction diameter ( m) volume fraction #G1 4.88 5.89% 0.97 0.047 %2.18 1.32% #G2 4.43 4.29% 0.88 0.034 %4.14 1.70% #G8 5.36 6.84% 1.07 0.054 %3.65 1.61%

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147 CHAPTER 6 SPECTRALLY CONSTRAINED IMAGING OF ABSORPTION CHROMORPHORES AND SCATTERING CONCENTRATION 6.1 Introduction For breast tissue, the major absorption ch romorphores are oxy-hemoglboin (Hbo2), deoxyhemoglobin (Hb), water and lipid.86 Breast tumors have been f ound to have higher Hbo2 and Hb concentrations than the normal tissues.15 The scattering is modeled with a simple power law, which is reasonably accurate for most cases.14, 55 However, the parameters in the power law do not have a clear relationship to the scatterer size and concentration inside tissues. A new model based on Mie theory was proposed for descri bing the scattering inside the tissues.62 Previously, the absorption coefficient and the reduced sc attering coefficient at each wavelength were calculated with DOT and sequentially, the abso rption coefficients at all wavelengths were mapped into the concentrations of Hbo2, Hb, wate r, and lipid using their absorption spectra. The scattering spectra were optimized to find the pa rameters of power law or the scatterers size distribution and volume fractions Recently, Corlu A., et. al., pr oposed to couple the absorption spectra and the power law into the CW DOT reconstruction algorithm to calculate the chromorphore concentrations and the power law pa rameters directly using the measurements at several optimized wavelength simultaneously.55 These authors found that measurements at optimal wavelengths yielded better separation of scattering from absorption and superior separation of one chromophore from the others.55 Srinivasan S. et al.87 have proven that the spectral constraints in the freque ncy domain DOT could provide bett er robustness and stability in the presence of higher level of noise and reduce cross talk be tween chromophore and scattering parameters. Corlu A. et. al. found that the scattering pr efactor a and the scattering power b in the power law were difficult to be separated and th at the scattering power b was fixed and only the

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148 prefactor a was reconstructed when the clinical data were processed39. Instead of the power law, we used the relatively rigorous algorithm in form of an integral for scattering based on Mie theory and we found that it was even more diffi cult to separate the scat terers size distribution and volume fraction when spectra l constraint was applied and the chromophore concentrations, scatterers size and volume fraction were recons tructed simultaneously. In this chapter, we presented a new method to separate the scatte rers size and volume fraction easily and the method was validated by numerical simulation and in vivo clinical experiments. The remainder of this chapter was organized as follows. In section 6.2, the multi-spectral DOT reconstruction algorithms with constraint were introduced, in which there were two different methods, one was the traditional method as described in subsection 6.2.1 and the other was our new proposed method described in subsecti on 6.2.2. In section 6.3, several numerical simulations were performed to validate our new method. In section 6.4, two in vivo clinical experiments were reported and the im aging results were discussed. 6.2 Algorithms 6.2.1 Spectrally Constrained Reconstruction with the Method from Literature In this method, we assume that the tissu e absorption was contri buted by L absorption chromophores with the concentration of Cl for lth chromophore. And the absorption coefficient a could be expressed by L 1 l l l C a (6.1) where l indicates the absorption extin ction coefficient of the lth chromophore at wavelength Following Jiang et al.77-78, the scattering spectra were correlat ed with particle size distribution and concentration through the followi ng relationship under Mie Theory:

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149 0 dx x f x 2 n x g 1 n x scat Q 3 s (6.2) where scatQwas the scattering efficiency; x was the pa rticle size; n was the refractive index of particles; was the particle concentration/volume fraction; f(x) was the particle size distribution. Both scatQ and g could be computed with Mie Theory81 We have assumed a Gaussian particle size distri bution in this study (a priori knowledge about the mode and distribution form of the particle size were usually available in a practical situation), 2 b 2 2 a x e 2 b 2 1 x f where a was the average size of particles and b was the standard deviation, which was fixed to be 1% of a in th is study (the influence of b was relatively small). Instead of reconstructing a and s at each wavelength and sequentially obtaining Cl, a and using the absorption and scattering spectra, a and s were substituted with Cl, a and in the diffusion equation and Cl, a and were reconstructed simultaneously with multi-spectral measurement data using the following equation: a a M C M C 1 C 1 C (6.3) where was the boundary measurements at wavelength was the Jacobian matrix and could be calculated with the following equations: a s 2 3 a s s a s 2 3 s s L 1 l for l a l C a a l C (6.4)

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150 where a and were the Jacobian matrix at each wavelength which could be calculated with the method described by the refere nce [Paulsen and Jiang, 1995], was the diffusion coefficient. From Eq. (6.2), we could obtain 0 dx 2 b 2 2 a x e 2 b 2 1 x 2 n x g 1 n x scat Q 3 s (6.5) and a 0 dx 2 b 2 2 a x e 2 b 2 1 x 2 n x g 1 n x scat Q 3 a s (6.6) Finally, the total system could be expressed as (6.7) where W was the wavelength number of measurements. 6.2.2 Spectrally Constrained Reconstruction with Scatterers Volume Fraction Method In this method, we assume that there were M kinds of particles with different size or diameters inside tissues. For each of them, th e corresponding contributed scattering could be obtained by a L C 1 C W a W W L C W 1 C 2 a 2 2 L C 2 1 C 1 a 1 1 L C 1 1 C W 2 1

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151 M 1 m for 0 dx 2 b 2 2 m a x e 2 b 2 1 x 2 n x g 1 n x scat Q 3 sm (6.8) where b was fixed to be 1% of m a. The total scattering can be calculated by the summation M 1 m sm m s (6.9) where m was the volume fraction of the mth kind of particles. Now it was the m and Cl needed to be reconstructed simultaneously with the following new equation M M 1 1 M C M C 1 C 1 C (6.10) where the Jacobian matrix could be obtained by M 1 m for m s 2 3 m s s m L 1 l for l a l C a a l C (6.11) Finally, substitute Eq. (6.1) into Eq. (6.9), the system equation at all wavelengths could be expressed as (6.12) M 1 L C 1 C W M W 1 W L C W 1 C 2 M 2 1 2 L C 2 1 C 1 M 1 1 1 L C 1 1 C W 2 1

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152 In the above equation, the size of w is M1, each of Jacobain matrix l l C and m m had size of M1N, and each of l C and m had size of N, where N is the node number and M1 was the meas urements per wavelength. 6.3 Numerical Simulations For the following numerical simulation cases the absorption coefficient and reduced scattering coefficient were calculated with Eq. (6.1) and Eq. (6.2) provided the given concentrations of Hbo2, Hb a nd water (ignored the lipid) and the given diameter and volume fraction of particles. The experimental meas urements used for the reconstruction were calculated with the diffusion equation using the finite element method, as described in [69]. 6.3.1 Reconstruction with the Method from Literature For simulation case 1, the cylindrical background had a diameter of 50mm with an offset target of 10mm in diameter. The concentration of Hbo2, Hb and water, the diameter and the volume fraction of particles are 10 M, 8 M, 10 M, 1000 nm and 0.2% in the background and 20 M, 16 M, 20 M, 5000 nm and 2.0% in the target. With the reconstruction method described in section 6.2.1 and measurements at 5 wavelengths (673, 733, 775, 840 and 922), the reconstructed results were shown in Fi gure. 6-1. There was no noise added to the measurement data. The concentration of Hbo2, Hb and water were extracted quantitatively. But the particle diameter image and the particle volume fraction image failed to be reconstructed. In Figure. 6-1d, the volume fraction of the target was reconstructed to be 0.36%, much less than the true value 2.0%. And in Figure. 6-1e, the par ticle diameter of the target was found to be 900 nm, much less than the true value 5000 nm.

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153 In the numerical simulation case 2, we assu me the concentration of Hbo2, Hb and water are same in the background and the targets and only the volume fracti on and the diameter of scattering particles were recons tructed. Figs. 6-2a and 6-2b pl otted the exact values of the particle volume fraction and the particle diameter for both the b ackground and the three targets. These figures also indicated the geometry of the background and the targets. Using the reconstruction method described in section 6.2. 1 and five wavelengths data (673, 733, 775, 840 and 922 nm), the reconstructed particle volume fr action image and the particle diameter image were shown in Figure. 6-2c and 6-2d, respectivel y. There was a significant amount of cross-talks between the reconstructed volume fraction image and diameter image, and the reconstructed values in the targets were far away from the true values. 6.3.2 Reconstruction with the Scattering Volume Fraction Method In the numerical simulation case 3, the absorpti on coefficients at all wavelengths were set to be 0.005mm-1 and only the particle size volume fractio ns were reconstructed. The geometry of the background and the three targ ets were shown in Figure. 6-3a. There were three kinds of particles (150 nm, 1000 nm, 6000 nm in diameters) in both the background and the three targets. The exact particle volume fractions for the back ground and the targets were shown in Table 6-1. The particle size volume fraction images were reconstructed with the method described in subsection 6.2.2. And the reconstructed volume fr action images for the particles with diameters of 150 nm, 1000 nm and 6000 nm were shown in Figs. 6-4a, 6-4b and 6-4c by using measurements at 8 wavelengths and in Figs. 64d, 6-4e and 6-4f by using measurements at 20 wavelengths, respectively. The 8 wavelengths were 638, 673, 690, 733, 775, 808, 840 and 915 nm and the 20 wavelengths were distributed uniformly in the range from 600 nm to 900 nm. With 8 wavelengths, the errors of extracted valu e of the volume fraction we re 2.0 % for target1, 10.0% for target2 and 10.0% for target3. And the reconstructed results were slightly better when

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154 using data at 20 wavelengths. There were slight cross-talks between volume fraction images of 1000 nm particles and 6000 nm particles. That was why there was 10% er ror in the extracted volume fraction values in target 2 and target 3. For the numerical simulation case 4, the ge ometry were shown in Figure. 6-3b and the concentrations of Hbo2, Hb and water, the volume fraction for 1000 nm particles and 6000 nm particles were shown in Table 6-2 for the ba ckground and 5 targets. With the reconstruction method described in subsection 6.2.2 and using m easurement data at 5 wavelengths (673, 733, 775, 840 and 922 nm), the reconstructed concentration and volume fraction images were shown in Figs. 6-5a, 6-5b, 6-5c, 6-5d, 6-5e without nois e added in the data and shown in Figs. 6-5f, 65g, 6-5h, 6-5i, 6-5j when 1.0% random noi se added. These images indicate that the concentrations and the volume fractions were reconstructed quantitatively for both with and without noise. Without noise, the errors of the extracted concentration of Hbo2, Hb and water, the volume fractions of 1000 nm particles and 6000 nm particles were about 2.5%, 2.0%, 1.5%, 3.0% and 5.0%. The cross-talk between the reconstruc ted volume fraction images (Figs. 6-5d and 6-5e) was very slight. The added 1.0% random noise introduced artifacts into the reconstructed images, especially the water con centration image (Figure. 6-5h) and the volume fraction image of 6000nm particles (Figure. 6-5j). The noise made the cross-talk between the volume fraction images worse. The accuracy of the reconstructed water concentration and the reconstructed volume fraction of 6000 nm par ticles was reduced approximately 20% by the noise. In contrary, the reconstructed concentra tion images of Hbo2, Hb and the volume fraction image of 1000 nm particles were not deteriorated by the noise. To see how the selection of sm in Eq. 6.9 affected the reconstructed image quality, numerical simulation case 5 was performed, in which we assumed that targets 4 and 5 were

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155 composed of 150 nm and 5000 nm particles but use the sm from 1000 nm and 6000 nm particles, not from 150 nm and 5000 nm particles, in the recons truction. The images at the bottom row in Figure. 6-5 showed the reconstruc ted results. The water concentration image and the 6000 nm particles volume fraction image we re deteriorated by th e intentional wrongselection of particle diameters in the reconstr uction but they were rec onstructed qua ntitatively although there were some artifacts. The concen tration images of Hbo2 and Hb and the volume fraction image of 1000 nm particles we re reconstructed quantitatively. In sum, the numerical simulation results va lidated the new method, the scatteri ng volume fraction method, with which both the absorption chromophore concentrations and the volume fraction of the scattering partic les were reconstructed successfully and simultaneously while the water concentration image was sensitive to the noise. 6.4 In-Vivo Imaging with the Mola r Absorption from References The experimental system for the clinical study and the system calibrati on were described in reference [40, 71]. The measurement data at five wavelengths of 673, 733, 775, 840 and 922 nm were used for the image reconstructions. Here we assumed that the absorption chromosphores were Hbo2, Hb and water and the scattering pa rticle diameters were 1000 nm (simulating the small particles such as mitichodria) and 6000nm (sim ulating the larger par ticles such as nucleus) in the breast tissue. For the clinical studies here the concentrations of Hbo2, Hb and water, the volume fractions of 1000 nm and 6000 nm diameter particles were reconstructed using the method described in section 6.2.2. The first patient, with patient Id #S28, wa s 58 years old female with a biopsy confirmed multicentric invasive ductal carc inoma at 3 and 9 oclock. The second patient, with patient ID #S5, was a 69 years old female with a benign nodule at 8 oclock. The second patient

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156 mammogram films and report were discussed in subsection 5.2.2.2. The concentration images of Hbo2, Hb and water, and the volume fraction im ages of 1000 nm particle s and 6000 nm particles were shown in Figs. 6-6a, 6-6b, 6-6c, 6-6d and 66e for patient1 and in Figs. 6-6f, 6-6g, 6-6h, 66i and 6-6j for patient2, respectively. For pati ent1, the Hbo2 and water co ncentration images had two targets at correct positions but Hb concentration image onl y identified one target around 3 oclock. For patient2, the Hbo2 and Hb concentrati on images identified the target at the correct position but water concentration image failed to detect the target and only got a circular artifacts. Both of the volume fraction images for patient 1 obtained the targets at 3 and 9 oclock, as shown in Figs. 6-6d and 6-6e. For patient 2, th e target around 8 ocloc k was obvious in both of the reconstructed volume fraction images. Consistent with the numerical simulation case 4, the water concentration image was vulnerable to noise and there was a circular artifact, as shown in Figs. 6-6c and 6-6h. And the volume fraction imag e of 6000 nm particles had more artifact than the volume fraction image of 1000 nm particles. Th e absolute values of the volume fraction of 1000 nm and 6000 nm particles in th e target for patient 1 (malignant tumor) were found to be 1.6% and 4.4%, larger than 0.98% and 2.2% fo r patient 2 (benign tumor). The ratio of the extracted volume fraction of 1000 nm particles to that of 6000 nm par ticles for patient1 was calculated to be 2.75, larger than 2.24 for patient 2. In sum, for both clinical cases, both the absorption chromophore concentration images except the water concentration image and scatte ring particle volume fraction images were reconstructed successfully and the tumors were identified in the correction locations. 6.5 Measurements of Molar Extinction Coefficients In the above sections, the molar extinction coe fficients of Hbo2, Hb and water, used for absorption chromophores reconstruction, were from the literature88-92. However, the system measurement mismatches resulted in the errors and were the possible reasons why the water

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157 images failed to be reconstructed. The molar extinction coefficients measurements were necessary for accurate chromophore imaging. Here we used the human being whole blood (Innovative Research Inc, Sout hfield, MI 48034, USA) solution with blood concentration of 0.6%, 0.8% and 1.0% and Intr alipid concentration 1.0% to measure the molar extinction coefficients of Hbo2 and Hb. The whole blood he moglobin concentration was measured to be 11.3 g/dL using a hemoglobin meter. The hemogl obin concentrations of 0.6%, 0.8% and 1.0% blood solution were calculated to be 45.8 M, 61.7 M and 76.33 M, respectively. The water absorption coefficients at each wavelength were measured using the 1.0% Intralipid solution. The top part of the home-made liquid solution co ntainer was the top part of a drinking water bottle, which holded the bottom part made of Cli ng Wrap (The glad products company, Oakland, CA 94612), as shown in Figure. 6-7. The liquid solu tion container was hung in the center of the ring with a mechanical frame and the fiber probes touched the bottom part of the container, as shown in Figure. 6-8. The Cling Wrap was so th in that its interferences on light propagation could be ignored. When the liquid solution was exposed to air, the hemoglobin was totally oxygenized. The absorption chromorphores were Hbo2 and water. Af ter measurements, several grams yeasts were put into the solution and the container was sealed. One hour later, the oxy-hemoglobin was deoxygenized. The absorption chromophores became Hb and water. Then measurements at each wavelength were made for molar absorption calculation of Hb. Measurements for 1.0% Intralipid solution, Hbo2 and Hb solutions were processed by the algorithms described before. Briefly, for the data at each wavelength of each liquid solution, a preprocessing method was utilized for searchin g the initial values (boundary coefficient optical properties a and s ). The boundary coefficient for all the data were selected as 0.49

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158 for consistency. With the initial values, the reconstructions of absorption and scattering coefficients were performed. The average values of the reconstructed absorption coefficients of all finite element nodes were the solution ab sorption coefficients at the corresponding wavelengths. The tenth wavelength measurements were ignored due to its lowest SNR. The water absorption was calculated at first. The measurement results (the diamond line) were shown in Figure. 6-9. At wavelengths shor ter than 700nm, the measured absorption values were much larger than the values from the literat ure (indicated by the triangle line). At the longer wavelengths, the measured absorption coefficients were close to the values from the literature.8889 The molar extinction coefficients of H bo2 and Hb were calculated by the following equation: C / water soltution M (6.13) where M was the molar extinction coefficient of Hbo2 or Hb in unit of 1/(mm.M) at wavelength soltution was the average value of the recons tructed absorption coefficients of Hbo2 or Hb solution at wavelength in unit of 1/mm, water was the average value of the reconstructed absorption coeffi cients of water at wavelength in unit of 1/mm and C was the molar concentration of the Hbo2 or Hb in unit of M. The measured molar extinction coefficients of Hbo2 and Hb from the solution of three differe nt concentrations were shown in Figure. 6-10 and Figure. 6-11, respectively. The solid line indicates the values from the reference [90-92]. For the Hbo2, the measured molar absorptions at shorter wavelengths were the same as the values from the references, while the largest deviation of the measured value at the longer wavelengths from the reference value was about 25 %. From Figure. 6-11, one could see that the measured molar absorptions at s horter wavelengths were 2 to 3 times smaller than the values

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159 from literature. At longer wavelengths, the meas ured values were close to the values from literature. The measurements for the solutions with different concentrations were very consistent. Finally, the average values of the measured mola r absorptions at three different concentrations were adopted for further image reconstructions. 6.6 Phantom Experiments Four cases of phantom experiments were performed to evaluate the measured water absorption coefficients and the measured mola r extinction coefficients of Hbo2 and Hb. The background of the phantom was made of 0.5% human blood, saline water as absorption chromophores, 1.0% Intralipid as scatterers and 1% agar used to solidify th e cylindrical phantom with diameter of 50 mm. An offset through hole w ith diameter of 9mm was drilled to hold a very thin glass tube, inside which the target liquid solution for each case was put. The target liquid solution was composed of 1.0% Intralipid, salin e water and human blood w ith concentrations of 1.5%, 1.25%, 1.0% and 0.75% for cases 1-4. Th e blood solution with con centrations of 1.5%, 1.25%, 1.0% and 0.75% was calculated to have hemoglobin concentrations of 114.5 M,, 95.41 M, 76.33 M and 57.25 M, respectively. The total hemoglobi n concentration CHbT was defined as the sum of the concentrations of Hbo2 and Hb. And oxygen saturation was referred to as the ratio of CHbo2 to CHbT, where CHbo2 represented the concentration of Hbo2. Using the measured mola r extinction coefficient spectra of Hbo2 and Hb, the measured water absorption spectra and the algorithm described in section 6.2.2, the reconstructed images of total hemoglobin concentra tion, oxygen saturation, the water concentration and scattering par ticle volume fraction for the 4 pha ntom experimental cases were shown in Figure. 6-12. Only one scattering particle size was assu med. So there was one particle volume fraction image for each case, as shown in Figs. 16m-p. Figs. 6-12a-d plotted the

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160 images of CHbT for cases 1-4. The maximum values in the target were found to be 111.0 M, 89.0 M, 80.5 M and 55.5 M and the relative errors were cal culated to be 3.9%, 6.8%, 5.4% and 3.1% for cases1-4, respectively. The oxyge n saturation images, the water concentration images and the volume fraction images for 4 cases were plotted in the second row, third row and forth row in Figure. 6-12. The exact value of oxygen saturation was 1.0 or 100% since the blood solution was exposed to the air. The water con centration was about 99% and the volume fraction of scattering particles was set to be 1.0%. The oxygen saturati on images were deteriorated by the boundary artifacts. The scattering particle volum e fraction images were also deteriorated by artifacts located in the image center. The accur acy of the reconstructed water concentration images were worse compared with other images. In sum, four cases of phantom expe riments with different total hemoglobin concentrations in the target were performed. Th e reconstructed images demonstrated that the total hemoglobin concentrations were extracted accurately, while the oxygen saturation images were deteriorated by the boundary artifacts. 6.7 In-Vivo Imaging with the Measured Molar Extinction Coefficients In this section, five clinical cases were st udied and the clinical experimental data were processed using the measured molar extinction co efficient spectra of Hbo2 and Hb, the measured water absorption spectra and three different re construction methods described in the following paragraphs. In method 1, we assume that the scattering in side the breast tissues were homogeneous and the scattering coefficients at each wavelengt h were selected from the preprocessing method described in section 3.2 and th e scattering coefficient at each wavelength was fixed as initial values. Only the concentrations of absorp tion chromophores Hbo2, Hb and water were reconstructed. The system equa tion 6.12 is modified to be

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161 L C 1 C W L C W 1 C 2, L C 2 1 C 1 L C 1 1 C W 2 1 (6.14) In method 2, we assume that the scatteri ng inside the breast tissues were uniform homogeneous as well. But the uniform scattering coefficient at each wavelength, only one value for all the nodes at one wavelength, was update d as the absorption chromophores Hbo2, Hb and water concentrations at each node were updated in the reconstruction procedure. The system equation was modified to be W 0 D 2 0 D 1 0 D L C 1 C N 1 i W i D 0 0 0 0 0 N 1 i 2 i D 0 0 0 0 N 1 i 1 i D W L C W 1 C 2 L C 2 1 C 1 L C 1 1 C W 2 1 (6.15)

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162 where W 0 D was the diffusion coefficient initial value at wavelength W and was updated each iteration, N 1 i W i Dwas the summation of N Jacobian vectors W i D at wavelength W L C was a vector with size of N and W 0 D was a scalar. In method 3, we assume that there was only one kind of scattering particles and the scattering spectra were calculated with equati on 6.8. Please see the detailed description in subsection 6.2.2. The system equation was written as (6.16) where both L C and 1 are vector with size of N. CASE S5. The patient, with ID #S5, was a 69 y ears old female with a benign nodule at 8 oclock and is the second patient discussed in section 6.4. Her mammogram films and report were discussed in subsection 5.2.2.2. With the measured molar extinction coefficient spectra of Hbo2, Hb and water absorption spectra, the re constructed absorption ch romophore concentration images (a, d, g for Hbo2 concentrations in M, b, e, h for Hb concentrations in M and c, f, I for water concentration in percentage) and scatterers volume fraction image in percentage (j) were shown in Figure. 6-13, using method 1 (1st row), method 2 (2nd row) and method 3 (3rd row). With the molar extin ction coefficient spectra of Hbo2, Hb and the water absorption spectra from literature, the reconstruc ted images of Hbo2, Hb concentrat ions and water concentration were shown in Figure. 6-14. 1 L C 1 C W 1 2 1 1 1 W L C W 1 C 2 L C 2 1 C 1 L C 1 1 C W 2 1

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163 When the molar extinction coefficients from literature were used, the reconstructed water concentration images (Figure. 6-14c with met hod 1, Figure. 6-14.f with method 2) had maximum value larger than 100%. And the Hb concentratio n images (Figure. 6-14b with method 1, Figure. 6-14e with method 2) had more artifacts than th e Hb concentration images (Figure. 6-13b with method 1, Figure. 6-13e with method 2) reconstr ucted with the measured extinction coefficient spectra. The measured molar extinction coefficien t spectra utilization impr oved the reconstructed image quality substantially. In Figure. 6-13, with all three methods, the target was able to be detected in each of concentration images and the sc attering particle volume fracti on image. With method 1, the reconstructed Hbo2, Hb and wate r concentrations shown in Figs. 6-13a, 6-13b and 6-13c were larger than the concentrations reconstructed with method 2 shown in Figs. 6-13d, 6-13e and 613f. Especially the Hbo2 concentration reconstruc ted with method 1 was almost 2 times larger than that reconstructed with method 2. Compared with method 2 and method 3, the reconstructed Hbo2 and Hb concentrations were very close. Bu t the water concentration (Figure. 6-13i) with method 3 was two times less than the water conc entration (Figure. 6-13f ) reconstructed with method 2. CASE S7. The mammogram films and report for patie nt S7 were discussed in subsection 5.2.2.2. Using the measured molar extinction coe fficient spectra of Hbo2, Hb and the measured water absorption spectra, the rec onstructed concentrati on images of Hbo2 (Figs. 6-15a, d, g in M), Hb (Figs. 6-15b, e, h in M) and water (Figs. 6-15c, f, I in percentage) were shown in Figure. 6-15 with method 1 (1st row), method 2 (2nd row) and method 3 (3rd row) for clinical case S7. Figure. 6-16 plotted the concen tration images with method 1 (1st row) and method 2 (2nd row) using the molar extinction coefficient spectra from literature. When the molar extinction

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164 coefficient spectra from literature were used, th e reconstructed water c oncentrations (shown in Figs. 6-16c and 6-16f) were larg er than 100% and the reconstruc ted Hbo2 concentrations (shown in Figs. 6-16a and 6-16d) were almost two times larger than the Hbo2 c oncentrations (shown in Figs. 6-15a and 6-15d) reconstructe d using measured absorption spec tra. The detected target in the images reconstructed with method 2 using the absorption spectra from reference was shifted to the image center, as shown in Figs. 6-16d, e, f. One could see that the measured absorption spectra utilization improve the reconstructe d image quality substantially as well. As shown in Figure. 6-15, the concentra tion images reconstructed with method 1 and method 2 were similar in terms of the target pos ition and the concentration values. When method 3 was applied, the concentration images of Hbo2 and Hb were similar to the images extracted with other two methods. But the water concentra tion was much less than that extracted with method 1 and 2. CASE S28. Figure. 6-17 plotted the reconstruc ted chromophore concentration images (Figs. 6-17a-6-17i) and the scatte ring particle volume fraction im age (Figs. 6-17j) with method 1 (1st row), method 2 (2nd row) and method 3 (3rd row) using the measured extinction coefficient spectra for clinical case S28. With method 1, th e target in Hb concentration image (Figure. 617b) was shifted to the image center and the wate r concentration image (Figure. 6-17c) failed to detect the target and was dominated by the boundary artifacts. With method 3, the water concentration image (Figure. 6-17i) also faile d to detect the target and dominated by the boundary artifacts. With method 2, it was easy to see all the reconstructe d concentration images identified the target successfully. CASE G1. The mammogram films and report for patient case G1 are discussed in subsection 5.2.2.1. Figure. 6-17 plotted the r econstructed chromophore concentration images

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165 (Figs. 6-18a-6-18i) and the scatte ring particle volume fraction im age (Figs. 6-18j) with method 1 (1st row), method 2 (2nd row) and method 3 (3rd row) using the measured extinction coefficient spectra for clinical case G1. The reconstructed concentration images with method 1 (Figs. 6-18ac) and method 2 (Figure. 6-18d-f) were similar in terms of target locations, concentration values and artifacts. With method 3, the reconstructe d Hbo2 concentration image (Figure. 6-18g) and water concentration image (6-18i) have a little b it more artifacts than the images (Figs. 6-18a, c, d and f) extracted with other two methods. CASE G14. Figure. 6-18 plots the reconstructed ch romophore concentration images (Figs. 6-19a-6-19i) and the scattering particle volume fraction image (Figs. 6-19j) with method 1 (1st row), method 2 (2nd row) and method 3 (3rd row) using the measured molar extinction coefficient spectra for clinical case G14. With all three methods, the recons tructed concentration images and scattering particle volume fraction identified th e target successfully, while the reconstructed images with method 3 (Figs. 6-19g and 6-19i) had a little bit more artif acts than the images extracted with other two methods. In sum, 5 clinical cases are st udied with three methods in th is section. Method 2 is best among the three methods, while all 3 methods ca n reconstruct the concentration images and scattering particle volume fraction image su ccessfully. And the measured molar extinction coefficient spectra of Hbo2, Hb and the measured water absorption spectra were critical to the image reconstructions and had improved the image quality substantially.

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166 Figure 6-1. Reconstructed concentration images of Hbo2 (a), Hb (b) and water (c) and images of equivalent diameters (d) and volume frac tion (e) with the method described in subsection 6.2.1. Figure 6-2. The exact images of volume fracti on (a) and diameters (b) and the reconstructed images of volume fraction (c) and diam eters (d) with the method described in subsection 6.2.1 when only the volume frac tion and diameters are reconstructed. (b) (d) (e) (a) (b) (c) (d) (c) (a)

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167 T1 T2 T3 d D Doffset d D Doffset T1 T2 T3 T4 T5 (a) (b) Figure 6-3. The geometry of the numerical simu lations for case 3 (a) and case 4 (b), where D=70 mm, d=20 mm and Doffset=40 mm. Figure 6-4. The reconstructed volume fractions images for 150 nm particles (a, d), 1000 nm particles (b, e) and 6000 nm par ticles (c, f) with data of 8 wavelengths (images from a to c) and with data of 20 wavelengths (from d to f) when only the volume fraction images are reconstructed using the method described in subsection 6.2.2. (a) (b) (c) (d) (e) (f)

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168 Figure 6-5. The reconstructed images of concentr ations of Hbo2, Hb, wate r and volume fractions of 1000 nm particles and 6000 nm particles from leftmost column to rightmost column. The images at the top row and th e middle row were reconstructed without adding noise in the numerical measurement data and with 1% random noise added, respectively. The images at the bottom row were reconstructed with intended wrongselected sizes of particles in the targets. Figure 6-6. The reconstructed concentration images of Hbo2 (a, f), Hb (b, g)j, water (c, h) and volume fraction images of 1000 nm particles (d, i) and 6000 nm particles (e, j) for patient 1 (the top row images from a to e) and for patient 2 (the bottom row images from from f to j). (a) (b) (c) (f) (g) (h) (d) (i) (e) (j) (k) (l) (m) (n) (o) (a) (b) (c) (d) (e) (f) (g) (i) (h) (j)

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169 Figure 6-7. The container for molar absorption measurements. The upper part is the drinking water bottle and the bottom part is composed of Cling Wrap, with 1.0% Intralipid solution inside. Figure 6-8. The liquid solution in side the container is ready for the measurements. The Cling Wrap contacts with fiber probes.

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170 0 0.002 0.004 0.006 0.008 0.01 6007008009001000 wavelength (nm)water absorption (1/mm) water absorption reference data Figure 6-9. The absorption coefficients of water from the reference (triangle) and measurements of Intralipid solution (diamonds). 0 50 100 150 200 250 300 350 6006507007508008509009501000 wavelength (nm)molar absorption (1/mm.M) reference data measurement using 0.6% blood solution measurement using 0.8% blood solution measurement using 1.0% blood solution Figure 6-10. The molar absorption of oxy-hemogl obin from the reference (solid line) and measurements of blood solution with diffe rent concentrations (squares, diamonds, stars).

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171 0 50 100 150 200 250 300 350 6007008009001000 wavelength (nm)molar absorption (1/mm.M) reference data measurement using 0.6% blood solution measurement using 0.8% blood solution measurement using 1.0% blood solution Figure 6-11. The molar absorption of deoxy-hemo globin from the reference (solid line) and measurements of blood solution with diffe rent concentrations (squares, diamonds, stars).

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172 Figure 6-12. Reconstructed images of total hemoglobin concentrations (1st row) in unit of M, oxygen saturation (2nd row), water concentration (3rd row) in percentage and scatterers volume fraction (4th row) in percentage of phantom experiments case 1 (1st column from left to right)), case 2 (2nd column), case 3 (3rd column) and case 4 (4th column). (m) (o) (p) (n) (k) (l) (j) (i) ( e ) ( f ) ( g ) ( h ) ( a ) ( b ) ( c ) ( d )

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173 Figure 6-13. Chromophores concentration imag es (a, d, g for Hbo2 concentrations in M, b, e, h for Hb concentrations in M and c, f, I for water concentration in percentage) and scatterers volume fraction image in percen tage (j) reconstructed with the measured molar spectra, using method 1 (1st row), method 2 (2nd row) and method 3 (3rd row) for clinical case S5. Figure 6-14. For clinical case S5, chromophor es concentration images (a, d for Hbo2 concentrations in M, b, e for Hb concentrations in M and c, f for water concentration in percentage) reconstructed with the molar spectra from reference, using method 1 (1st row) and method 2 (2nd row) for clinical case S5. ( a ) ( b ) ( c ) ( e ) ( d ) ( f ) ( f ) ( g ) ( h ) ( j ) ( i ) ( a ) ( d ) ( e ) ( c ) ( b )

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174 Figure 6-15. For clinical case S7, chromophores concentration images (a, d, g for Hbo2 concentrations in M, b, e, h for Hb concentrations in M and c, f, I for water concentration in percentage) and scatterers volume fracti on image in percentage (j) reconstructed with the measured molar spectra, using method 1 (1st row), method 2 (2nd row) and method 3 (3rd row). Figure 6-16. For clinical case S7, chromophor es concentration images (a, d for Hbo2 concentrations in M, b, e for Hb concentrations in M and c, f for water concentration in percentage) reconstructed with the molar spectra from reference, using method 1 (1st row) and method 2 (2nd row). ( c ) ( a ) ( b ) ( d ) ( j ) ( i ) ( g ) ( h ) ( f ) ( e ) ( a ) ( f ) ( e ) ( d ) ( c ) ( b )

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175 Figure 6-17. For clinical case S28, chromophores concentration images (a, d, g for Hbo2 concentrations in M, b, e, h for Hb concentrations in M and c, f, I for water concentration in percentage) and scatterers volume fracti on image in percentage (j) reconstructed with the measured molar spectra, using method 1 (1st row), method 2 (2nd row) and method 3 (3rd row). ( a ) ( b ) ( d ) ( g ) ( h ) ( e ) ( c ) ( f ) ( i ) ( j )

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176 Figure 6-18. For clinical case G1, chromophores concentration images (a, d, g for Hbo2 concentrations in M, b, e, h for Hb concentrations in M and c, f, I for water concentration in percentage) and scatterers volume fracti on image in percentage (j) reconstructed with the measured molar spectra, using method 1 (1st row), method 2 (2nd row) and method 3 (3rd row). ( a ) ( h ) ( j ) ( i ) ( f ) ( e ) ( d ) ( c ) ( b ) ( g )

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177 Figure 6-19. For clinical case G14, Chromophor es concentration images (a, d, g for Hbo2 concentrations in M, b, e, h for Hb concentrations in M and c, f, I for water concentration in percentage) and scatterers volume fracti on image in percentage (j) reconstructed with the measured molar spectra, using method 1 (1st row), method 2 (2nd row) and method 3 (3rd row). ( a ) ( b ) ( c ) ( d ) ( e ) ( f ) ( g ) ( h ) ( i ) ( j )

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178 Table 6-1 Volume fraction of different partic les in the background and the three targets for numerical simulation case 3. Volume fraction of different particles Regions Diameter of 150 nmDiameter of 1000 nm Diameter of 60000 nm Background 0.25% 0.25% 0.5% Target 1 0.5% 0.5% 1.0% Target 2 0.5% 0.5% 1.0% Target 3 0.5% 0.5% 1.0% Table 6-2 Concentrations of the absorption chro morphores and Volume fractions particles for numerical simulation case4. Concentrations of absorption chromophores ( M) Volume fraction of different partilces Regions Hbo2 Hb water Diameter of 1000 nm Diameter of 60000 nm Background 10.0 10.0 18.0 0.25% 0.5% Target 1 20.0 10.0 18.0 0.25% 0.5% Target 2 10.0 20.0 18.0 0.25% 0.5% Target 3 10.0 10.0 36.0 0.25% 0.5% Target 4 10.0 10.0 18.0 0.375% 0.5% Target 5 10.0 10.0 18.0 0.25% 1.0%

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179 CHAPTER 7 CONCLUSIONS AND FUTURE STUDIES 7.1 Conclusions This dissertation has explored the abilities of diffuse opti cal tomography to detect the breast tumors from both the hardware and the algo rithm aspects. In general, both the tissue-like phantom experimental results and the clinical trial experimental results show that DOT is very promising to identify the breast abnormalities. The unique features of DOT, functional imaging and morphological imaging, allows DOT to detect the tumors when the tumors are at early stages. The continue-wave imaging system played a key role in this st udy. All the tissue-like phantom experiments and clini cal trial experiments are cond ucted with the system. The quantitative imaging results proved that the sy stem is very robust. Furthermore, the LABVIEW controller provides a very friendly interface and makes the instrument easy to be operated. Especially the application of gain controller and optical switch make the instrument running automatically whenever the patient breast is in good position. Both the dual mesh method and the source in tensity optimization method can improve the 3D DOT image quality substantially, as shown by the tissue-like phantom experimental results in chapter 3. These results also show the robustness and the accuracy of our 3D DOT algorithm. The target with absorption contrast as low as 1. 4 times can be identified. The spatial resolution of 5mm in the lateral direction is achieved. Sma ller spatial resolution may be obtained if higher contrast targets are used. The morphological imaging, including the sc attering particle mean diameter imaging and the scattering particle volume fraction imag ing, is first proposed by us. The morphological images are extracted from the reduced scatte ring images at different wavelengths. The

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180 morphological imaging has the possibilities to prove doctors with nucleus size and nucleus crowding non-invasively. The tissue-like phantom results in chapter 4 show that the reconstructed diameter is larger if there are relative more scattering particles with larger diameters. This conclusion may se rve as criteria for our further cl inical results of morphological images. Experimental data for 10 benign clinical cases and 4 malignant cases are processed to obtain the morphological images. These preliminar y results show that the estimated maximum diameter and volume fraction in the malignant tu mor region are 3.23 and 2.64 times as large as that in the benign abnormality region, respectiv ely. The reconstructed diameter and volume fraction could be the new criteria to differen tiate the malignant tumors from the benign abnormalities, although more clinical results are n eeded to further prove the ratio number. By comparison with the pathological pictures, we fi nd that the scattering particles are not only the nucleus but also the smalle r particles such as nucle olus and the mitochondria. Spectrally constrained DOT imaging is s upposed to provide better accuracy compared with the two steps imaging method, in which the absorption coefficients and scattering coefficients are obtained at first and then these coefficients are fitting to extract the absorption chromophore concentrations and scattering parameters. The spect rally constrained DOT imaging method is proposed by Corlu et al at first. However, the scat tering parameter a and b in the power law are difficult to be obt ained simultaneously. A new method, namely scatterers volume fraction method, is proposed, in which the sc attering equation is linear ized. With this new method, both the concentration images of Hbo2, Hb and water and the volume fraction images of scattering particles with differe nt diameters can be imaged simultaneously. The method is validated by numerical simulations and clinical results.

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181 The measured molar absorption extincti on coefficients of Hbo2 and Hb and the absorption spectra of water are di fferent with those in the litera ture at some wavelengths. When the measured absorption spectra for Hbo2, Hb and water are utilized, the reconstructed image quality is improved substantially in terms of targ et locations, concentratio n values and artifacts, especially for the water concentration image. 7.2 Future Studies 7.2.1 Imaging System and Calibrations The potentials of DOT imaging are deterior ated by the artifacts. The artifacts are caused by many reasons, such as experimental system noise, computational errors, modeling errors, detection and source fiber coupling errors, et c. The calibration met hod, source intensity optimization method, dual mesh method and sp ectrally constraint reconstruction method discussed in the above chapters are used to reduce the reconstruc ted image artifacts. Computational calibration method,72-75 in which the coupling coefficients are updated at the same time as the optical propert ies are updated in the reconstruction, may further eliminate the artifacts. A recent study show that the difference in data for multiple wavelength pairs, instead of the absolute measurements at the wavelengths, is used to reconstruct absolute absorption chromophore concentrations and the im age quality is improved substantially.93 While the DOT image quality, especially for clinical cases, is acceptable, more efforts are needed to further eliminate the artifacts because the artifacts may resu lt in unnecessary biopsy if one day the optical imaging modality serves as the routine breast cancer screening. There are only 10 laser modules with diffe rent wavelengths from 638 nm to 965 nm in our experimental system. The measurements at more wavelengths should provide more robust and more accurate results of morphological a nd functional imaging using the multi-spectral

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182 DOT. Next generation of our expe rimental system should have more laser modules or have a laser with the adjustable wavelengths. The current system can not image the whole breast one time and only cover 2 cm slice each imaging time, while the whole breast can be imaged one slice after another by adjusting the patient vertical positions using the hydraulic pump in the system. Further modifications of the fiber buddle interface are needed to image the whole breast one imaging time. 7.2.2 Multi-modality Imaging One of the major drawbacks of the DOT imagi ng is its low spatial resolution. One way to overcome the drawback is using other imaging modality such as MRI, ultrasound, X-ray to enhance the spatial resolution. This tec hnology is called multi-modality imaging. The combination of high spatial resolution MRI im aging and high contrast DOT imaging in frequency domain has been inve stigated and the DOT imaging qua lity has been improved using the co-registered MRI imaging guided structural information.94 The study of coregistered tomographic x-ray and optical breast imaging has been performed recently and the pilot clinical results have been shown.95 A study has shown that targets of 2-3mm in diameter embedded inside a cylindrical background phantom with 5cm in diameter could be reconstructed quantitatively in terms of the positions and opt ical properties using the ultrasound guided finite element based DOT imaging modality.96 Combination of two imagi ng modalities could integrate their strengths and avoid one or two weakness of an individual modality.97 7.2.3 Scattering Theory We have assumed that the scattering particles such as nucleus or mitichondra inside the breast are spherical due to the utilization of MIE theory. But the real shape of the scattering particles is nonspherical. Advan ced scattering theories are need ed to describe the scattering behaviors of the nonspherical par ticles. So far, there are no acc urate and robust mathematical

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183 models to describe the light scatteri ng properties of complex structures.98 Recent progress in reduced-order expressions for th e total scattering cro ss section spectra of nonspherical particles provides a possible way to solve the problem.99 Another method to study the scattering of complex structures is finite -difference time-domain modeling.100 7.2.4 Clinical Studies The ultimate goal of this dissertation and our study is to detect the breast tumors and differentiate the malignant tumors from the benign abnormalities. The hardware improvements, system calibration methods and new algorithms in troduced in this disser tation serve the goal. The clinical trial experiments play a key role to validate our methods The phantom experiments of 3D DOT has been done. However, clinical results of 3D DOT imaging are needed to further show the abilitie s and promises of our 3D DOT for breast cancer detection since the real breast cancer imaging is a 3D problem. The preliminary clinical studies in chapter 5 shows that the reconstructed diameter and volume fraction could be the new cr iteria to differentiate the malignant tumors from the benign abnormalities based on the results of 14 clinical cases However, more clinical results are needed to further prove the conclusion. The co-registration of optical imaging with ot her methods such as biopsy and surgery is important but difficult. We have compared our reconstructed diamet er imaging and volume fraction with the pathological pictures taken from the tumor samples in the target area. But we dont know the exact location of the samples corr esponding to the reconstructed images because there are no good ways to record sample locations in the real breast during the surgery (we only know the approximate location) and the breasts ar e soft and easy to deform. A better way to do the co-registration should be proposed in the future clinical studies.

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PAGE 192

192 BIOGRAPHICAL SKETCH Changqing Li was born on August 21, 1973 in Xingyang, Henan Province, China. He earned his B.S. in the Mechanical and Electrical Engineering from the No rthwestern Polytechnic University, Xian China in 1995. He earned hi s M.E. in Engineering Mechanics from the Tsinghua University, Beijing, China in 1998. And he earned his M.S. in Electrical Engineering from Clemson University, SC in 2002. He entered the PhD program in the physics department, Clemson in 2002 and transferred to the biomedical engineering department, University of Florida at the beginning of 2005.


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BREAST CANCER DETECTION WITH DIFFUSE OPTICAL TOMOGRAPHY


By

CHANGQING LI













A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2006































Copyright 2006

by

Changqing Li









ACKNOWLEDGMENTS

First, I would like to thank Professor Huabei Jiang, for his continuous support, trusts and

precious advice during my study for the Ph.D. Professor Jiang is well-known in the Hield of

optical tomography. His views and understandings on the research subj ects are exceptional. As a

professor, although his schedule is very tight, he is always available to help me on my research

whenever I have frustrations. What I have learned and experienced in Professor Jiang's lab will

definitely benefit my future career and life.

Secondly, my thanks go to my academic committee members: Dr. William Ditto, Dr.

Mingzhou Ding, Dr. Sihong Song. Their comments and suggestions were very helpful to my

study and research. Their valuable time spent on reading my dissertation is highly appreciated.

Thirdly, I would like to thank Dr. Steven Grobmyer, an assistant professor in the surgery

department of University of Florida. As our clinical research partner, Dr. Grobmyer helps us to

recruit many breast cancer patients. And I would like to thank the research scientist in our lab,

Dr. Qizhi Zhang, for his help on both my study and my research. I also thank Dr. Zhen Yuan for

his help on the algorithm development. Dr. Qiang Wang's suggestions on the experiments were

always impressive. Miss Lin Chen, a graduate student in our lab, gave me lots of help in

performing the clinical trial experiments. So did Dr. Xiaoping Liang. Their help is highly

appreciated.

Fourthly, thanks got to my wife, Pan Sheng, for her support. Without her support and

encouragement, I could not have gotten through my graduate study. And thanks go to my lovely

son, Jonathan Li, for giving me so many excellent memories and happiness.

At last, thanks to NIH for the Einancial support on the breast cancer imaging proj ect.












TABLE OF CONTENTS


page

ACKNOWLEDGMENTS .............. ...............3.....


LIST OF TABLES ................ ...............7............ ....


LIST OF FIGURES .............. ...............8.....


AB S TRAC T ............._. .......... ..............._ 14...


CHAPTER


1 INTRODUCTION ................. ...............16.......... ......


1.1 Breast Cancer Facts .............. ...............16....
1.2 History of Optical Imaging ................. ...............16...............
1.3 Optical Imaging of the Breast ................. ...............17..............
1.4 Optical Diffusion Theory............... ...............23.
1.5 DOT Reconstruction Algorithm .............. ...............26....
1.5.1 Forward Solution Procedure............... ...............2
1.5.2 Inverse Solution Procedure............... ...............2


2 DOT IMAGING SYSTEM AND ITS CALIBRATION ......____ ........ ...............30O


2. 1 DOT Imaging System ........._................._._. ...............30..
2.1.3 Source/detector Fiber Optic Probe .............. ...............31....
2. 1.4 Detection Unit .............. ...............32....
2.1.5 Gain Control .............. .. ...... ................3
2.1.6 Detector Sensitivity and Dynamic Range............... ...............34.
2. 1.7 Stability ................ .........__ ...............34...
2.1.8 DC Offset/Noise Reduction............... ...............3
2. 1.9 Data Acquisition Unit ............_ ..... ..__ ...............35
2.1.10 System Timing............... ...............36.
2.2 DOT Imaging System Operation ............_ ..... ..__ ...............36.


3 SYSTEM CALIBRATION AND DOT ALGORITHM REFINEMENTS ............................45


3.1 System Calibration................. ..................4
3.1.1 Image Reconstruction Algorithm .............. ...............45....
3.1.2 Calibration M ethod ................... ......... ...............46.....
3.1.3 Experimental Methods and Materials............... ...............4
3.1.4 Results and Discussion ................. ...............48..............
3.2 Dual M esh M ethod ................. ...............51.......... ....
3.2. 1 Dual M esh M ethod ................. ...............51...............
3.2.2 Experiments ................. ...............53........... ....
3.2.3 Results and Discussion ................. ...............53........... ...












3.3 Source Intensity Optimization Method............... ...............55.
3.3.1 Source Intensity Optimization Methods .............. ...............56....
3.3.2 Experiments ........._.. ..... ._ ...............58....
3.3.3 Results and Discussion ........._.._ ..... .___ ...............59...


4 PARTICLE SIZE IMAGING: PHANTOM EXPERIMENTAL STUDIES ..........................86


4. 1 Measurement of Particle Size Distribution and Concentration in Heterogeneous
Turbid M edia......................... ............8
4.1.1Materials and Methods ................... ...............8
4. 1.2 Simulations and experiments ................. ...............89...............
4.1.3 Results ............... ... ...............90
4. 1.4 Discussion and Conclusions ................. .......... ... ...... ..................9
4.2 Imaging of Particle Size Distribution and Concentration in Heterogeneous Turbid
Media .............. .........................9
4.2.1 Methods and materials............... ...............9
4.2.2 Results and discussion ................... .. ......... .............. ..... ...............9
4.3 Experimental Results from Concentrated Suspensions with Bi-modal Particle Size
Distribution .............. ....... .. .. ... .........9
4.3.1 Experimental system and materials ................ ...............97..............
4.3.2 Experimental results and discussion ................. ...............98........... .
4.3.3 Conclusions .............. ...............103....


5 EX VIVO AND IN VIVO STUDY OF TUMOR CELL SIZING ................. ................. 119


5.1 Ex Vivo Study of Tumor Cells .............. .... .............. ............. ...............19
5.2 Morphological Characteristics of Breast Tumors: In-Vivo Study with Multispectral
Diffuse Optical Tomography .............. ...............120....
5.2. 1 M ethods ................ ...............120...............
5.2.2 R results ........ ............... ......... ................12
5.2.2. 1 Case studies: #1, 2 and 3: Infiltrating ductal carcinomas........................... 121
5.2.2.2 Case studies: #4, 5 and 6: Benign nodule or mass .................. ...............125
5.2.2.3 Statistical analysis and pathological co-registration ................. ...............129

6 SPECTRALLY CONSTRAINED IMAGING OF ABSORPTION
CHROMORPHORES AND SCATTERING CONCENTRATION .............. ..............147


6. 1 Introducti on ............ ..... ._ ...............147..
6.2 Algorithm s .............. ......_ ...._ .... ..... ......... .. .........4
6.2.1 Spectrally Constrained Reconstruction with the Method from Literature ...........148
6.2.2 Spectrally Constrained Reconstruction with Scatterer's Volume Fraction
M ethod ................ ...............150......... ......
6.3 Numerical Simulations ........................ .. ........ .. ........15
6.3.1 Reconstruction with the Method from Literature.................... .......................152
6.3.2 Reconstruction with the Scattering Volume Fraction Method ................... ..........153
6.4 In-Vivo Imaging with the Molar Absorption from References ............_.. ..............155
6.5 Measurements of Molar Extinction Coefficients ......____ ..... ... .__ ..........._....156












6.6 Phantom Experiments ................. .. .......... ... .. .. ........... ...... .........5
6.7 In-Vivo Imaging with the Measured Molar Extinction Coeffieients ................... ...........160


7 CONCLUSIONS AND FUTURE STUDIES............... ...............179


7.1 Conclusions............... ..............17
7.2 Future Studies .............. .. .........__ ......._ ............18
7.2.1 Imaging System and Calibrations............... .............18
7.2.2 Multi-modality Imaging .............. ...............182....
7.2.3 Scattering Theory .............. ...............182....
7.2.4 Clinical Studies............... ...............183


LIST OF REFERENCES ............. ...... ._ ...............184...


BIOGRAPHICAL SKETCH ............. ......___ ...............192...











LIST OF TABLES


Table page

3-1 Optical and geometric parameters used for Group 1 experiments ................. ................. 84

3-2 Optical and geometric parameters used for Group 2 experiments ................. ................. 84

3-3 Optical and geometric parameters used for Group 3 experiments ................. ................. 84

3-4 Optical properties of the phantom background and the target for all 5 cases. ................... 85

3-5 Optical properties of the target and background used in the six experiments
perform ed. .............. ...............85....

4-1 Reconstructed parameters from simulated data at different noise levels for simulation
1............... ...............116...

4-2 Reconstructed parameters from simulated data at different noise levels for simulation
2............... ...............116...

4-3 Reconstructed parameters from experimental data using the peak and average
scattering spectra of the target area. ........._._. ...._... ...............116..

4-4 Target materials of experiment set 1. The unit of volume is mL. ........._.._... ................1 17

4-5 Target materials of experiment set 2. The unit of volume is mL. ........._.._... ................1 17

4-6 Target materials of experiment set 3. The unit of volume is mL. ........._.._... ................1 17

4-7 Reconstructed results of setl. ........._.._.._ ...............117......_....

4-8 Reconstructed results of set2. ..........._ ..... .__ ...............118..

4-9 Reconstructed results of set3. ........._.._.._ ...............118......_....

5-1 Mean diameters and volume fraction of the nucleus and nucleolus found from the
microscopic pictures and those of scattering particles calculated from the
reconstructed images ................. ...............146....._._. .....

6-1 Volume fraction of different particles in the background and the three targets for
numerical simulation case 3 ................. ...............178........ ....

6-2 Concentrations of the absorption chromorphores and Volume fractions particles for
numerical simulation case4............... ...............178.










LIST OF FIGURES


Figure page

2-1 Schematic of the experimental system ........__......... __ .........__ ....__......37

2-2 Photographs of the experimental system. .......__......... __ ................. ....__..38

2-3 Optical switch (a) Schematic and (b) photograph............... ...............3

2-4 Photographs of the ring structure ...._... ....._. ................. ......._............_..40

2-5 Internal and external connections of a silicon photodiode S8754. ............. ...................40

2-6 Diagram of mounting configuration for one sensor. ......____ ... ....._ ................41

2-7 The detection board: (a) Schematic;(b) layout ................. ...............42........... ..

2-8 Flow chart of a detector gain controller. .............. ...............43....

2-9 The control panel of the DOT imaging system ................. ...............43........... .

2-10 The LABVIEW control panel of the DOT imaging system. ................ ............. .......44

3-1 Geometry of the phantom configuration ................. ...............64...............

3-2 Reconstructed absorption and scattering images for the 3 cases in Group 1. ....................65

3-3 Reconstructed absorption and scattering images for the 3 cases in Group 2. ........._.._.......66

3-4 Reconstructed absorption and scattering images for the 3 cases in Group 3 ........._.._........67

3-5 1D profile of the absorption coefficient along the transect AB (see Figure. 3-1) for
the image shown in Figure. 3-2a (a) and for image shown in Figure. 3-2d (b).. ...............68

3-6 Four fine mesh elements generated from one coarse mesh element ................. ...............68

3-7 Geometry of the tissue mimicking phantom ................. ...............69........... ..

3-8 The C1a images (a-d) and C's images (e-h) reconstructed for case 1 (4:1 Ca, 2.8:1

C's contrast, 15 mm off-center) phantom experiment. ............... ......... ................. 70

3-9 The C1a images (a-d) and C's images (e-h) reconstructed for case 2 (4:1 Ca, 2.8:1

C's contrast, 10 mm off-center) phantom experiment. ............. ...............71.....

3-10 The C1a images (a-d) and C's images (e-h) reconstructed for case 3 (4:1 Ca, 2.8:1

C's contrast, 5 mm off-center) phantom experiment .............. ...............72....










3-11 The three-dimensional views of the reconstructed absorption coefficient images (a, c,
e) in mm-1 and the reconstructed reduced scattering coefficient images (b, d, f) ..............73

3-12 Geometry of the phantom under study ................. ...............74........... ..

3-13 The absorption images reconstructed for case 1 (2:1 C1a contrast). ................. ...............75

3-14 The absorption images reconstructed for case 2 (4:1 C1a contrast) ........._...... ........._.....76

3-15 Reconstructed absorption images (rows 1 and 2) and scattering images (rows 3-5) for
case 3 (2:1 C1 and C's contrast) .............. ...............77....

3-16 The absorption images reconstructed for case 4 (4:1 C1a and C's contrast). ................... ....79

3-17 The scattering images reconstructed for case 4 (4:1 C1a and C's contrast). ........................80

3-18 Recovered C1a values along a transect through the centers of the target and
background for the images at y=0 mm, z=2 mm.. ............ ...............81.....

3-19 The absorption images (a and b) and scattering images (c and d) reconstructed with
the source optimization method for case 5 (4:1 C1a and C's contrast) ............... ...............82

3-20 The absorption images (a and b) and scattering images (c and d) reconstructed with
the source optimization method for case 6. ............. ...............83.....

3-21 The source intensity obtained with the uniform source intensity method and the
source intensity distribution obtained with the source intensity optimization method......83

4-1 Simulated scattering spectra obtained from Mie calculation and the fittings based on
the recovered particle size distribution and concentration at different noise levels. .......104

4-2 Reconstructed scattering images for Case 2 at 10 different wavelengths............._.._.. .....105

4-3 Normalized exact (solid lines) and reconstructed (dashed lines) particle size
distribution from phantom measurements for Cases 1, 2 and 3............... ..................106

4-4 Experimental scattering spectra obtained with different methods for Case 1 (left) and
Case 3 (right) ................. ...............106................

4-5 Scattering spectra: (a) The spectra generated by Eq. (5) and the Mie fittings using
recovered particle parameters from simulated data. ............. ...............107....

4-6 The DOT reconstructed absorption images (al to al0) and reduced scattering images
(b l to bl0) at 10 different wavelengths. ....__. ...._.._ ........_..... .........0










4-7 Reconstructed images of mean particle size (a, c) and concentration (b, d) for the
2.06pLm (a, b) and 5.66sLm (c, d) polystyrene cases, respectively. .............. ... ........._....109

4-8 The reduced scattering coefficient images at 9 different wavelengths for experiment
set1 1. ............. ...............110...

4-9 The reduced scattering coefficient images at 9 different wavelengths for experiment
setl_1. The global minimum error initial value is selected ................. .........__ ......111

4-10 Reduced scattering coefficient at 10 wavelengths for 5 cases of experiment setl.
Fixed a value was applied for each case. ....__ ......_____ .......___ .........12

4-11 Reduced scattering coefficient at 10 wavelengths for 5 cases of experiment setl. The
value of a corresponding to the global minimum error was applied for each case. ......112

4-12 Reduced scattering coefficient at 10 wavelengths for 4 cases of experiment set2.
Fixed a value was applied for each case. ......___ .... ... ._ ....................1

4-13 Reduced scattering coefficient at 10 wavelengths for 3 cases of experiment set 3.
Fixed a value was applied for each case. ....._____ .... ... .__ .......... ........13

4-14 The reconstructed diameter versus (a) the calculated scattering coefficient ratio of 1
Cpm particles and 6 Cpm particles and (b) the volume fraction of 1 Cpm particles for
experiment set 1. ..........._.._ ...............114....._ ......

4-15 The reconstructed diameter versus (a) the calculated scattering coefficient ratio of 1
Cpm particles and 6 Cpm particles and (b) the volume fraction of 1 Cpm particles for
experiment set 2. ..........._.._ ...............115....._ ......

5-1 The microscopic picture of(a) the tumor tissue (400 time magnificent) and (b) the
normal tissue (100 time magnificent). ............. ...............132....

5-2 Experiment preparation: (a) the removed tissue was put inside the background
phantom; (b) The tissue was covered with background phantom and examined by the
system ............. ...............132....

5-3 Ex-vivo results: (a) The extracted nucleus concentration distribution in the tissue
region and the intralipid concentration distribution in the background region................133

5-4 Mammogram films: (a) Right CC mammogram, (b) Right MLO mammogram for the
right breast of a 52 years old patient (patient ID #Gl). ................. .................133

5-5 The constructed scattering images at 9 wavelengths from 63 8nm to 922nm (figs. a to
i) of the examined breast for patient Gl ......__ ......____ .......__ .........13

5-6 The extracted images of particle diameters (a) and particle volume fraction (b) of the
examined breast for patient Gl............................ ........134










5-7 Mammogram films: (a) CC mammogram, (b) MLO mammogram for the right breast
of a 50 years old patient. ........................... ........135

5-8 The reconstructed scattering images at 9 wavelengths from 63 8nm to 922nm (Figs. a
to i) of the examined breast for patient #G2. ............. .....__ ....._ .............136

5-9 The extracted images of particle diameters (a) and particle volume fraction (b) of the
examined breast for patient #G2.. ............ ...............136.....

5-10 The reconstructed scattering images at 4 wavelengths from 733nm to 840nm (Figs. a
to d) of the examined breast for patient G8. ......_.._.._ ......_. ...._.._._.........3

5-11 The extracted images of particle diameters (a) and particle volume fraction (b) of the
examined breast for patient G8.. ............ ...............137.....

5-12 Mammogram films: (a) MLO and (b) CC mammography of the right breast for
patient #S5. ............. ...............138....

5-13 The reconstructed absorption coefficient images for the right breast of the patient
#S5 at 9 wavelengths from 63 8nm to 922nm (a to i). ......___ ........._ ..............13 8

5-14 The reconstructed scattering images at the right breast of the patient #S5 at 9
wavelengths from 63 8nm to 965nm (a to i). ....__ ......_____ ..... ...__ .........3

5-16 Mammogram films: (a) CC and (b) MLO mammography of the left breast for patient
# S7. ............. ...............140....

5-17 The reconstructed scattering images of the examined breast at 9 wavelengths from
63 8nm to 965nm (a to i) for patient #S7. ......___ .... ..___ ...............14

5-18 The reconstructed particle diameter image (a) and the particle volume fraction image
(b) of the examined breast for patient #S7. ....__ ......_____ .......___ .........14

5-19 Mammogram films: (a)RMLO, (b)RML images of the patient #S9. .............. .... ...........141

5-20 The reconstructed scattering images of the right breast for patient #S9 at 9
wavelengths from 63 8nm to 965nm (a to i). ....__ ......_____ ..... ...__ .........4

5-21 The reconstructed particle diameter image (a) and the particle volume fraction image
(b) of the right breast for patient #S9. ................ ...._ ...............143...

5-22 Average values of recovered mean diameter and volume fraction of scattering
particles for 8 benign cases and 4 malignant cases, respectively .............. ..................143

5-23 The peak value of the recovered volume fraction in the target region versus the peak
value of mean diameter in the target region ................. ...............144......___..

5-24 The pathological microscopic pictures of tumor cells for patient #G1 ( shown in a),
#G2 (shown in b) and #G3 (shown in c)............... ...............145..










6-1 Reconstructed concentration images of Hbo2 (a), Hb (b) and water (c) and images of
equivalent diameters (d) and volume fraction (e) ....._.__._ ... .... ._ .........._.......166

6-2 The exact images of volume fraction (a) and diameters (b) and the reconstructed
images of volume fraction (c) and diameters (d) with the method described in
subsection 6.2. 1 when only the volume fraction and diameters are reconstructed. .........166

6-3 The geometry of the numerical simulations for case 3 (a) and case 4 (b), where D=70
mm, d=20 mm and Doffset=40 mm............... ...............167..

6-4 The reconstructed volume fractions images for 150 nm particles (a, d), 1000 nm
particles (b, e) and 6000 nm particles (c, f) .............. ...............167....

6-5 The reconstructed images of concentrations of Hbo2, Hb, water and volume fractions
of 1000 nm particles and 6000 nm particles from leftmost column to rightmost
column............... ...............168

6-6 The reconstructed concentration images ofHbo2 (a, f), Hb (b, glj, water (c, h) and
volume fraction images of 1000 nm particles (d, i) and 6000 nm particles (e, j) for
patient 1 and for patient 2 .............. ...............168....

6-7 The container for molar absorption measurements. The upper part is the drinking
water bottle and the bottom part is composed of Cling Wrap .............. .................... 169

6-8 The liquid solution inside the container is ready for the measurements. The Cling
Wrap contacts with fiber probes. ............. ...............169....

6-9 The absorption coefficients of water from the reference (triangle) and measurements
of Intralipid solution (diamonds). ................ .......... ......... ........ ............170

6-10 The molar absorption of oxy-hemoglobin from the reference (solid line) and
measurements of blood solution with different concentrations ................. ................170

6-11 The molar absorption of deoxy-hemoglobin from the reference (solid line) and
measurements of blood solution with different concentrations ........._..._.. ........_..._......171

6-12 Reconstructed images of total hemoglobin concentrations (1st row) in unit of CLM,
oxygen saturation (2nd row), water concentration (3rd row) in percentage and
scatterers volume fraction (4th row) in percentage of phantom experiments ........._.._......172

6-13 Chromophores concentration images and scatterers' volume fraction image in
percentage (j) reconstructed with the measured molar spectra, using method 1 (1st
row), method 2 (2nd row) and method 3 (3rd TOW) for clinical case S5 ................... .........173

6-14 For clinical case S5, chromophores concentration images reconstructed with the
molar spectra from reference, using method 1 (1st row) and method 2 (2nd TOW) foT
clinical case S5............... ...............173..









6-15 For clinical case S7, chromophores concentration images and scatterers' volume
fraction image in percentage (j) reconstructed with the measured molar spectra, using
method 1 (1st row), method 2 (2nd row) and method 3 (3rd row) .............. ...................174

6-16 For clinical case S7, chromophores concentration images reconstructed with the
molar spectra from reference, using method 1 (1st row) and method 2 (2nd row)............174

6-17 For clinical case S28, chromophores concentration images and scatterers' volume
fraction image in percentage (j) reconstructed with the measured molar spectra, using
method 1 (1st row), method 2 (2nd row) and method 3 (3rd row) .............. ...................175

6-18 For clinical case Gl, chromophores concentration images and scatterers' volume
fraction image in percentage (j) reconstructed with the measured molar spectra, using
method 1 (1st row), method 2 (2nd row) and method 3 (3rd row) .............. ...................176

6-19 For clinical case Gl4, Chromophores concentration images and scatterers' volume
fraction image in percentage (j) reconstructed with the measured molar spectra, using
method 1 (1st row), method 2 (2nd row) and method 3 (3rd row) .............. ...................177









Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

BREAST CANCER DETECTION WITH DIFFUSE OPTICAL TOMOGRAPHY

By

Changqing Li

December 2006

Chair: Huabei Jiang
Maj or Department: Biomedical Engineering

Diffuse optical tomography (DOT) is emerging as a potential imaging technique for breast

cancer detection. Compared with the routine x-ray mammography which gives only the

structural images of breast tissue, DOT provides not only the structural information, but also the

functional images including oxyhemoglobin, deoxyhemoglobin, lipid and water content as well

as the morphological images including nucleus size and volume fraction. The goal of this thesis

study is to obtain these structural, functional and morphological contents of breast tissue using a

multi-spectral DOT reconstruction approach. This study involves imaging hardware

implementation and software development necessary for achieving the goal. The imaging system

and reconstruction software implemented are tested and evaluated using extensive simulations,

tissue-like phantom experiments and in vivo clinical studies.

A compact diffuse optical tomography system, specifically designed for breast imaging, is

constructed. The system consists of 64 silicon photodiode detectors, 64 excitation points, and 10

diode lasers in the near-infrared region, allowing multi-spectral, three-dimensional optical

imaging of breast tissue. The system performance and optimization through a calibration

procedure are detailed. The system is evaluated using tissue-like phantom and clinical

experiments. Quantitative 2D and 3D images of absorption and reduced scattering coefficients









are obtained from these experimental data. Two methods, dual mesh method and source intensity

optimization method, are implemented for improved 3D DOT reconstructions and validated by

tissue-like phantom experiments.

Reconstruction algorithms for obtaining tissue morphological images are described.

Quantitative images are successfully reconstructed in terms of the size, location and tissue

morphology of target from both tissue phantom and in vivo data. Initial clinical results show that

the scattering particle size and volume fraction at cellular level are potential new parameters that

could be used for differentiating malignant from benign lesions.

A new method, namely spectrally constrained DOT, is also developed to directly

reconstruct tissue chromophore concentrations and volume fraction of scattering particles

simultaneously. The absorption extinction coefficient spectra of oxy-hemoglobin, deoxy-

hemoglobin as well as the absorption spectrum of water are measured using a mixture of human

blood and Intralipid solution with the imaging system developed. The quality of the

reconstructed images is improved substantially when the measured spectra are utilized, compared

with that of the images recovered with the spectra obtained from the literature.









CHAPTER 1
INTTRODUCTION

1.1 Breast Cancer Facts

The American Cancer Society estimates that 211,240 women will be diagnosed with

invasive breast cancer, as well as approximately an additional 58,490 women will be diagnosed

with in situ breast cancer, and 40,410 women will die of cancer of the breast in 2005. Only lung

cancer accounts for more cancer deaths in women. Based on rates from 2000-2002, 13.22% of

women born today will be diagnosed with cancer of the breast at some time during their lifetime.

This number can also be expressed as 1 in 8 women will be diagnosed with cancer of the breast

during their lifetime.l

1.2 History of Optical Imaging

Breast cancer is caused by the cancer cells, which are characterized by the uncontrolled

division and the ability to invade into the normal tissues and spread to the whole body. The stage

before the spreading is called in situ, meaning that the tumor is happened locally and is not

invasive. When a tumor or a lump is palpable in the breast, it is usually one centimetre in size

and contains one million cells approximately. It is estimated that a lump of this size may take one

to five years to be developed. The cancer may metastasize, or spread to other tissues by

lymphatics or blood during the development period. The earlier the cancer is detected, the lower

risk for patients to have it spread and the higher probability to have it cured. Optical imaging

allows the possibility of earlier breast cancer detection due to its unique feature of functional

imaging. Furthermore, the physical examination has only 20% to 30% specificity for lesion

detections. And annual mammography screening provides higher specificity and sensitivity of

breast lesion detection. However, the patients are under risk with exposure to x-ray radiations









frequently. The non-ionized optical imaging can be used to screen the breasts frequently without

any side effects.

Earlier time, optical imaging was called transillumination or diaphanography, in which the

white light cast on a breast directly and the shadow of the breast was reviewed.2 This technology

was further improved by using the red light and near infrared (wavelength from 600 nm to 800

nm) since the photons at these wavelengths could penetrate deeper into the breast.3 However, the

clinical trail results of the improved transillumination showed that the method failed to detect

tumors less than 2cm inside the breast due to the dominated scattering.4- This is unacceptable for

the breast screening since the screening resolution is required to be a few millimeters at least.

The optical imaging for breast cancer detection has made substantial progress recently

due to the improved mathematical models of optical transportation, much more powerful

computation tools, and advanced measurement technologies. The mathematical models are

introduced in subsection 1.4. The models are solved by the finite element method, differential

method or other methods. All these methods need heavy computation. The powerful and cheap

computer makes the heavy computation possible and feasible for many scholars. With the

progress in electronics, there are many advanced optical measurement tools available, such as

photomultiplier tube (PMT), photodiodes, CCD. These tools measure the photon flying time, the

amplitude and phase of high frequency modulated light or the light intensity of continue-wave

light. These accurate measurements allow a good quality of optical imaging.

1.3 Optical Imaging of the Breast

Optical imaging attracts more and more scholars because of its unique features. At first, it

is non-ionized. There are no side effects for the optical breast imaging. So the patient can do

breast screening frequently. Secondly, compared with other methods, the cost of optical imaging

is lower. Thirdly, optical imaging is efficient to differentiate between the soft tissues because the










optical absorption is proportional to the concentrations of hemoglobin, water and lipid in the

tissues. Finally, optical imaging is both a functional and morphological imaging method. It is

able to image the concentrations of oxy-hemoglobin, deoxy-hemoglobin, water and lipid of the

examined tissues using the optical absorption spectra. And it is also able to obtain the particle

(such as nucleus) size distribution and density in the tissues using the scattering spectra. This

special feature makes the optical imaging a possible method to detect the breast cancer earlier

than other methods such as mammography, ultrasound, MRI and PET. Mammography is the

most widely accepted method for breast cancer screening. Despite its advantages, mammography

has a high false positive rate because it can not differentiate the benign and malignant tumors

efficiently. And mammography makes the patient expose to the x-ray radiation. As an adjunct to

the mammography, the breast ultrasound is used to determine whether a lump is filled with fluid

or solid mass. Ultrasound works well for dense breasts. Ultrasound breast imaging is still under

investigation for further improvements. Current breast MRI clinical applications include the

evaluation of the extent of cancer in breast before surgery, imaging the breast with silicone

augmentation and evaluating the extent of chest wall to assist the surgery. Breast MRI is more

expensive than mammography, ultrasound and optical imaging. Positron emission tomography

(PET) of breast can determine whether a tumor is malignant or benign. But its spatial resolution

is very low. And PET is also very expensive.

Optical breast imaging method is based on the fact that the optical properties of diseased

and normal breast tissues are different.6-1 At NIR wavelength, the absorption in carcinoma is

significantly higher than in adj acent uninvolved tissues. The difference between diseased and

normal tissues is as high as 100% in the near infrared region due to the increased hemoglobin









concentration in tumor.8 It was also reported that there was a four-fold increase in blood volume

in diseased breast compared to the normal tissue due to the increased blood vessels and size."l

Although the mechanisms of photon propagation in breast tissues have not been

understood completely, pilot in vivo measurements of endogenous optical properties and

endogenous tumor contrast have been reported.12-2 The reported results were promising. For

example, Gu et al.12 TepOrted that cysts ranging from 1-4 cm in diameter can be quantitatively

imaged. Cysts can be differentiated from solid breast tumors because cysts generally demonstrate

lower absorption and scattering coefficients compared with the surrounding normal tissue,

whereas solid tumors show concurrent higher absorption and scattering related to the normal

tissue. The use of exogenous contrast agents has also studies.23 For example, Indocyanine green

(ICG) was demonstrated to enhance breast tumor contrast in vivo.23 All the reported results

suggest that the optical imaging is a potential diagnostic method.

So far, several groups including our own have developed reconstruction algorithms for

optical image reconstructions in frequency domain24-26, time domain27 and CW domain28-31, Of in

a hybrid (frequency/continuous-wave) domain.32 We are interested in the CW domain DOT due

to its simple hardware implementation compared with the frequency and time domain DOT.

While we and other groups have shown that the CW method could extract the absorption

coefficient and the reduced scattering coefficient images quantitatively two- and three-

dimensionally using tissue mimicking phantoms and in vivo tissues at the specific

wavelengths,28,30,32 it is still a very challenging problem to obtain the quantitative images at the

wavelengths in the region from 600 nm to 1000 nm due to the worse signal noise ratio at both the

short and long wavelengths such as 600 nm and 1000 nm. Because the spectroscopy in the whole

region is needed in order to extract the optical scatterers' size and volume fraction, it is necessary









to further improve our current algorithm by using methods such as the dual mesh method,32-34

and source intensity optimization.35

We built our first generation DOT system using single photomultiplier tube (PMT)

detection.28 Even though it was extremely slow, it allowed us to obtain the first successful 2D

and 3D optical imaging of in vivo breast tissue based on CW approaches.36-37 Recently we

developed the second generation optical imaging system using 16 PMTs and 3 wavelengths.38

Significant in vivo breast imaging results have been generated from this second generation

machinel2 while active clinical studies are still on-going using this system. In order to acquire the

functional and morphology images, 3 wavelengths are not enough and more laser modules at

different wavelengths are needed.39-4 A new system with 10 wavelengths which are capable of

fast data collection is needed.

When light propagates through mammalian tissues, the scatterers are cell organelles of

various sizes, such as nucleus and mitochondria, which have higher refractive index than the

surrounding cytoplasm.41 Perelman et al. have shown that light singly backscattered from an

epithelial layer of tissue such as the skin has a wavelength-dependent periodic pattern.42 They

found that the periodicity of the pattern increased with nuclear size and the amplitude of the

periodic signal was related with the density of nucleus. After analyzing the periodic pattern, the

nucleus size and density could be extracted. However, the periodic pattern was overwhelmed by

the diffuse background or by the multiple scattered lights since the backscattered light is only a

small portion of the scattered light. One way to overcome the problem is to use a model to

mathematically describe the single backscattered light. But this method has to be remodeled for

different tissues under investigation which is inconvenient.42 Another robust approach, also

proposed by Backman et al., is to use polarized light to differentiate the single scattered light









from multiple scattered light background.43 It was reported that the initially polarized light lost

its polarization after scattered propagation in turbid media such as biological tissues.44-46 In

contrast, the single backscattered light kept its polarization.47 After subtracting the unpolarized

light, the polarized component of the backscattered light from the epithelial layer of the tissue

was obtained. An alternative approach to differentiate the backscattering from background is to

utilize a probe geometry that optimizes the detection of single scattered light.48 It was

demonstrated that the single optical fiber approach was highly sensitive to the light backscattered

from layered superficial tissues.

Cells have complicated structures and the organelles inside a cell vary in size from a

tenth of micron to 10 microns. All the organelles contribute to the scattering which complicates

the cell scattering phenomena. With fiber-optic, polarized elastic-scattering spectroscopy

techniques, Mourant et al. estimated that the average scatterer radius in tissue was from 0.5 to 1.0

CL m, which is much smaller than the nucleus.49 Using the polarized light spectroscopy, the

particle size distribution in mammal cells was measured and the results suggested that small

particles (possibly the mitochondria) contribute most to the scattering. However, other

subcellular structures, such as the nucleoli and the nucleus, may also contribute significantly.5o

Backman et al. demonstrated that the spectrum of the single backscattering component was

capable of providing the cell nuclei size distribution, which means the single backscattering was

dominated by the nucleus."

Scattering spectra in multi-spectral disuse optical tomography (MSDOT) have been

relatively less explored. This is hampered largely by the strong crosstalk between absorption and

scattering contrasts that occurred in earlier DOT reconstructions, which was reduced/eliminated

only recently by various image enhancement schemes.31,52 In puTO Optical spectroscopy studies as









described above, it has been shown that scattering spectra are correlated with tissue morphology.

These experimental studies have suggested that both nuclei and mitochondria contribute to tissue

scattering significantly. On the other hand, it is well known in pathology that tumor cells/nuclei

are considerably enlarged relative to normal ones.53 Thus significant clinical value would be

resulted from the exploration of scattering spectra in MSDOT. Thus far scattering spectra in

MSDOT have been studied with a simple power law,54-55 which was originated from

spectroscopy studies with homogeneous media.56-59 The advantages of the power law are its

simplicity and reasonable accuracy under certain conditions. The disadvantage is that the

constants in the power law have no clear physical meanings and that particle size distribution and

concentration cannot be directly obtained from this empirical relationship.

Currently, two noninvasive optical imaging methods are used to measure particle size

distribution. One is the light scattering spectroscopy (LSS),60 in which polarized light was

delivered to the epithelial tissue and the single backscattering light that kept the polarization was

analyzed to extract the morphological features and the refractive index of the scatterers. This

method is limited primarily to superficial surface imaging. The other one, which we are trying to

further develop, is a tomographic imaging method based on multi-spectral diffuse optical

tomography,61-62 in which the tomographic scattering images of tissue at multiple wavelengths

were obtained with diffuse optical tomography and the scattering spectra were then used to

extract the scatterer' s size information with a Mie theory based reconstruction method. To utilize

the Mie theory for particle/nucleus sizing, several assumptions are generally made: particles are

spherical; no particle-particle interactions exist; and the photon diffusion equation is valid which

means that light scattering is much larger than the absorption. While the reasonable results have

been obtained based on above assumptions,61-62 we plan to investigate them further to see









whether better results could be extracted if more complicated models such as Wentzel-Kramers-

Brillouin (WKB) model was applied.63

Conventionally, two separate sequential steps are deployed to calculate the functional

images. At first, the absorption images at different wavelengths are reconstructed by DOT. Then

the contributions to the absorption images from each tissue chromophore are calculated."

Recently, a new approach for extracting the tissue chromophores is that tissue chromophore

concentrations and Mie scattering factors are reconstructed directly by exploiting the spectral

priori information.'" Corlu et al. show that the new method works very well in the CW domain

with the linear inverse method to update the parameters iteratively. While the chromophore

concentration image quality is improved substantially due to the reduction of the reconstructed

parameters by exploiting a priori spectral constrained technique, the cross talk between the

scattering parameters a and b limited its applications. The new method applications to our

nonlinear iterative DOT algorithm will also be investigated in this dissertation to determine

whether image quality could be further improved.

1.4 Optical Diffusion Theory

Boltzmann transport equation describes incoherent photon propagation through highly

scattering media such as tissue. The equation in time domain is written as


-+ *V+ t 2 (,,t =s rJ 0, '(,',td+q(,,t)(3.1)


where $(r, i', t) is the radiance [W/(cm2 Sr)] at position i, at time t, propagating along the unit

vector & Clrt/) = ta (is CL(i) is the transport cross section at position 2 Ca (i) and Cs (i), the

absorption and scattering coefficients, are the inverse of the absorption and scattering mean free

path respectively. c is the speed of light in the medium. The function 0(i, 8') is the probability









density function over all solid angels of the change in photon propagation direction from & to 8'

due to an elastic scattering event which satisfies the condition: 1471 0$, ifsd = 1. q(i, 2, t) is the

photon power generated at position i along direction & This equation reflects the energy

conservation in the medium. However, the equation often must be simplified to be

mathematically manageable. One way to simplify it is to expand the equation with spherical

harmonics and truncate the series at the Nth term, namely PN approximation. Thus the quantities

in equation 3.1 can be expressed as


$(,,t= L 2L +1 2LmtYm( (3.2)
L m=-L 4x:


m3 L 2L +1 233
q(r, s, t)= 1 Lm2,tYC(B 33
L m=-L 4x:

2 1
0,'= 2L + 2n L"oPL(cos6) (3.4)









P1 approximation is obtained when N=1 from the PN approximation. After simplification,

the following equations are obtained:


1 8+ 0t 2 ~,t T2 )=M 2@? )+00, 2 )(3.5)
c 8t


-- Rt (2 ^T2,t) o~(i, t) = 01Rs (E)^T(, t) + 81(i, t) (3.6)
c- 8t









where


@(i, t) = 90.0 (i, t) is the


photon fluence,


J(?, t) = -~Y gy_1P t) wiz (r, t)X gy_(? ) l ?,t Y (,t the photon flux.


The P1 approximation can be further simplified by making the following assumptions:


= 0, q l= 0. (3.7)


The approximation, namely diffuse approximation, is usually justified only if the scattering

coefficient is much lager than the absorption coefficient in order to satisfy the first assumption,


= 0. The second assumption, fly = 0, means that the photon source is isotropic. The diffuse


approximation leads to the following equation, namely diffusion equation, in the time domain

V D(2)VO(i t) + Cla e(i t) + 1 ?,t = 90 (i, t), (3.8)
c 8t

or in the frequency domain


-V D()V O(2,w+)a ,0;,)'~;)= cl0(ra), (3.9)

or in the continue wave domain

V D(i)VO(i)+ CRa 9(-) 0 (i) (3.10)

whee D2)=1 ,is the diffusion coefficient, CMs= (1-01)CLs the reduced scattering
whee ~i)=3 M~sa + s1


coefficient and q0 i)= 40,0(i) the isotropic source.

In infinite homogeneous media, the solution to the diffusion equation can be obtained

through the Green function method. However, for realistic finite homo- or hetero-geneous media

such as tissue, the boundary effects/conditions must be accounted for.









1.5 DOT Reconstruction Algorithm


There are two procedures involved in the DOT image reconstruction. The first one is the

forward solution procedure, in which the distribution of light in the medium of interest is

predicted. The second one, the inverse solution procedure, is used to iteratively update the

initially guessed optical property distribution of the medium through an optimization method

such as Newton method by minimizing the squared difference between the data computed from

the diffusion equation and measured around the surface of the medium.

1.5.1 Forward Solution Procedure

Since an analytical solution to the Boltzmann transport or the diffusion equation is not

available in a realistic situation, numerical methods must be used for most cases. Finite element

method (FEM) is a natural choice because it can be used to solve the diffusion equation in

inhomogeneous media with an arbitrary geometry, although other numerical methods such as

finite difference method64, f1nite volume method65 and boundary element method66 have been

used in DOT. The FEM applications in DOT have been discussed in details elsewhere686. Here

we follow Paulsen and Jiang69 and briefly describe the FEM method in the CW DOT.

Using the finite element discretization, the stead-state photon diffuse equation coupled

with the type III boundary conditions, DVO fi = ae, can be transformed into the following

matrix form

[A1@}= (b}, (3.11)

where a is the BC coefficient related to the internal reflection at the boundary; the elements of

matrix [Ai] are a, = -DVQI VO, Ms 30,) where ( ) indicates integration over the problem


domain; (b} is -(Sm,) + af O j$,$,ds S =S,8(r -r,,) where S,, is the source strength and









6(r ro) is the Dirac delta function for a source at ro; ; M is the number of boundary nodes; $2

and 5, are locally spatially varying Lagrangian basis functions at nodes i and j, respectively. The

vector (OJ= [@1,02---> N] is the photon density.

Four critical parameters (the BC coefficient c, the source strength So, and the initial guess

ofD and C1a) should be accurately determined by a preprocessing data optimization scheme for

the forward computation. We assume all the source intensities are the same and equal to So. The

pre-processing data optimization scheme for determining the four initial parameters is discussed


in detail elsew-here [Nic and Jiang, 2000]. Briefly, X -square errors, X2 m )~ mj,]c)ar


minimized as the function of the above four parameters, where Ml is the number of boundary

measurements (for example M1=64x64), @m") is the measured photon density from a given


experimental heterogeneous medium, and i') is the computed photon density from a numerical

simulation of a homogeneous medium with the same geometry as the experimental medium.

Given reasonable ranges for the four parameters, the minimum X2 COrresponds to the best initial

guess of the four parameters.

1.5.2 Inverse Solution Procedure

An example of inverse solution procedure is given here based on Taylor expansion or

Newton method. We assume that the computed and/or the measured O are analytic functions of

D and R ,, and that D and C1, are independent parameters. O then can be Taylor expanded about

an assumed (D, C1a) distribution, which is a perturbation away from some other distribution,


(D, jRa,), and the expansion is expressed as,









@D,0a)=E O(,0) AD+- a + --- (3.12)


where AD = D D and AC1a = C1a Cia If the assumed optical property distribution is close to

the true one, the high order items in the expansion can be neglected and we obtain

JAX = Yo Ye (3.13)

where

SY, dY, au, au, au, au,
8Do 8D2 8DK d80al d80a2 d80aL

8?2 dY2 u2 au2 u2 au2
dD1 dD2 dDK d80al d80a2 d80aL
J = (3.14)





8Do 8D2 8DK d80al d80a2 d80aL


AZ= ADI AD2 --- ADK Ral. Ra2L RaL T (3.15)


Yo= ~ 10 9 --- Yvlo (3.16)


'Yc=Y Ic IF Ic-- (3.17)

and Yio and Vic are observed and calculated data for i=1,2,...M measurements, Dk foT

k=1,2,...,K and C1al for l=1,2,...,L are the reconstruction optical parameters. In order for

equation 3.13 invertible, regularization method is used and expressed as


JTJ+1 A)X = JT 90 qc (3.18)









where I is the identity matrix with the size of 2Nx2N, N is the node number of the finite element

mesh, h is the regularization parameter, JT is the transposed Jocabian matrix, AX is the updating

vector defined by equation 3.15.









CHAPTER 2
DOT IMAGING SYSTEM AND ITS CALIBRATION

2.1 DOT Imaging System

The imaging system is schematically shown in Figure 2-1. Light beams from ten laser

modules are transmitted to the optical switch, which sequentially passes one of the beams to 64

pre-selected points at the surface of the phantom or breast via source fiber bundles. The ring

structure or fiber optic/tissue interface holds the 64 source and 64 detection fiber bundles. Light

from the 64 detection fiber bundles are sensed by the detection units, which convert the light

intensity into voltage signals. The computer collects the signals through a data acquisition board.

The DC motor near the ring is used to adjust the diameter of the ring. Two CCD cameras are

mounted underneath the ring to monitor the contact between the tissue and fiber optics. Figures

2-2a and 2-2b show photograph of the entire imaging system where we can see that all the

optical and electronic components are housed under the exam table. The individual components

are detailed below.

2.1.1 10-wavelength Laser System

10 fiber-coupled laser modules at different wavelengths are used as CW laser sources.

Each laser module is a compact integrated package of laser driver, thermoelectric cooler and

temperature controller. The output power can be set from zero to maximum by adjusting the

output control voltage from 0 to 5 volts. The pigtail fibers are 100um in diameter and have a

numerical aperture (NA) of 0.22. Table 2-1 gives more detailed information about these laser

modules.

2.1.2 Optical Switch

A programmable 10x64 optical switch (GP700-4-1, Dicon Fiberoptics, Richmond, CA),

controlled by a LABVIEW program through RS-232 remote interface, is used to deliver light









from lasers to the source fiber bundles. The configuration diagram and photograph of the optical

switch are shown in Figures 2-3a and 2-3b, respectively. Inside the optical switch, there is a dual

switch that works in tandem to deliver light to the target. The function of the left switch is to

choose the wavelength and the other to select the source fibers. 100 Clm fibers with FC

connectors inside the optical switch, connected to the pig-tail fibers from the 10 laser modules,

are used for light receiving/coupling. The insertion loss and back reflection are in the range from

0.56 to 1.15 dB and from -30.20 to -23.80 dB, respectively. The maximum crosstalk between any

two channels is -80 dB. The laser output passes through the optical switch via 100um-diameter

fibers, and is then coupled to 1mm-diameter source fiber bundles.

2.1.3 Source/detector Fiber Optic Probe

Figures 2-4a and 2-4b show photographs of the source/detector fiber optic array. It

consists of a diameter-adjustable cone-shaped frustum containing four planes/rings of fiber optic

bundles (RoMack, Williamsburg, VA). In each plane/ring, 16 detector fiber bundles (2.0 mm in

diameter) are arranged equally spaced around the annulus with another 16 source fiber bundles

(1.0mm in diameter) interspersed between the detector bundles. This fiber-optic/tissue interface

was custom designed and constructed with high precision. The synchronized radial motion of

fibers is realized through mechanical fingers that are driven by a DC motor. The diameter of the

fiber array can be adjusted between 4.0 and 15.0 cm to fit different breast sizes. The height of the

four-layer fiber array covers 2.0 cm.

The fiber optic probe is mounted right below an aperture on the exam table. During a

clinical imaging measurement, the patient places her breast through the aperture so that the

breast comes in contact with the fiber optic array. While the four-layer fiber optics is good

enough to image the tissue volume for most cases in which we are currently interested, different










vertical positioning can be realized through the vertical translation of the ring. The position of

the four planes/rings of fiber optic bundles is extended up intentionally. This allows the fiber

optic probe to be positioned close to the patient' s chest wall if necessary.

2.1.4 Detection Unit

Low noise light sensors, silicon photodiodes (S8745, Hamamatsu, Bridgewater, NJ) are

chosen for low level light measurement. Each sensor, integrated into a small package, consists of

a large area silicon photodiode (D i), an operation amplifier, a feed back resistance (Rf = 1 G0)

and a capacitance (Cf = 5pF), as shown in Figure 2-5. The external feed back resistors, Rfl, Rf2

and Rf3, are used to adjust the feedback gain. By controlling the relay (8LO2-05-01, COTO

Technology) switches (switch 1, switch 2 and switch 3), the sensor gain can be set to one of four

gains gainn, gain, gain2 and gain3. The gain switching is discussed in detail in section 4.B

below.

Four detection boards are made with 16 sensors mounted on each board. There are 64

sensors totally in the detection unit, which receive light intensities delivered from the 64

detection fiber bundles simultaneously. Figure 2-6 shows the diagram of mounting configuration

for one sensor as well as the coupling between the detection fiber bundle and the silicon window

of the sensor. The ten pins of each sensor are easy to be bent/broken. To protect the pins, one

piece of plastic is used to hold the sensor and the plastic is attached to the circuit board to insure

that there is no relative movement between the plastic and the circuit board once the pins are

soldered on the circuit board. The plastic also isolates the circuit board from the grounded

aluminum box, which shields any external electric/magnetic noises.

Figure 2-7a shows the schematic of a circuit board we designed. The 4-16 decoder is used

to select the sensors. A four-bit digital signal from the computer is sent to the decoder directly.









Once a sensor is selected, the external feedback resistors are connected with pin4 and pin6 such

that the gain is adjusted by the "gain switch controller", whose function is to reduce the gain

whenever the output is saturated and to increase the gain whenever the output is below 0.2 V.

The controller sends the gain status (digital signal) to the computer. The signal output from the

inverting amplifier is subsequently sent to a low-pass filter with a cutoff frequency of 10 KHz.

Finally, the output signal from the low-pass filter, is sent to the A/D board. The A/D board

collects only one output at a time from each time. The whole detection unit has four detection

boards, hence four channels of data can be acquired at the same periods and 16 times of data

collection are needed for all the 64 detection channels. Figure 2.7b shows the layout of the

detection board, which is designed by the ORCAD.

2.1.5 Gain Control

When all the three gain switches are off, the detector gain is set to maximum (gainO).

Whenever one of the switches is on, the other two must be off. The gain ratio, gainO: gainl:

gain2: gain3, is 27000:900:30:1.

Figure 2-8 is a schematic, showing how the three switches are controlled. Once the

output voltage is larger than 9.9V, the controller switches the gain to next level and the voltage is

reduced by a factor of 30 to the level of 0.33V, shown by arrows 2, 4, and 6. Whenever the

output voltage is less than 0.2V, the gain is switched to upper level and the voltage is amplified

by a factor of 30, shown by arrows 1, 3, and 5. The hysteresis loop makes the controller

insensitive to small signal fluctuations.

All the detector gains are set to gain initially. Most signal levels are between 0.2 and

9.9V, and the signal-to-noise ratio (SNR) is as high as 200:1 since the background noise

measured in dark room is around 1 mV. But for a very large size phantom or breast tissue (e.g.,










larger than 10 cm), the minimum output is as small as 20mV at gainO. The SNR is then

deteriorated to 20:1 in this case.

2.1.6 Detector Sensitivity and Dynamic Range

According to the data sheet of S8745 provided by Hamamatsu, photon sensitivity (S) of

the detector is 0.3V/nW at 673 nm. Using a laser module of 673 nm and neutral density (ND)

filters, the photon sensitivity of a representative photodiode sensor is measured. With a power

meter, optical signal directed to the sensor is measured at different levels of laser input. Photon

sensitivity for one detector at gain 0 (maximum gain), gain 1, gain 2 and gain 3 (minimum gain)

is 0.23V/nW, 7.7V/uW, 0.257V/uW and 8.5V/mW, respectively. At gain 0, there are no

externally connected resistors and the photon sensitivity is approximately equal to that provided

by the manufacture data sheet. The slight difference is due to the loss occurred in the fiber

coupling.

The maximum output voltage of a detector unit is 9.9V while the minimum output voltage

or the electronic noise level is ImV. At gain 3, the maximum detectable optical intensity is

9.9V Imi-
= 1.164mW. At gain 0, the noise equivalent intensity is = 4.34pW Thus
8.5V/lmW 0.231'/nW

the dynamic range can be calculated to be 2.682x10 .

2.1.7 Stability

For testing the stability, one laser module and one detector are chosen randomly. Laser

beam with a power of 40 mw is sent to the optical switch, then to a 5 cm diameter phantom

through one source fiber bundle. The diffused light delivered by a detector fiber bundle is

measured by a photodiode detector. The data points are acquired every 10 seconds and the output

voltage is normalized. The measurement fluctuation is less than 0.5%.









2.1.8 DC Offset/Noise Reduction

The DC offset came from the preamplifier and the low pass filters deteriorates the system

performance. Before each experiment, the DC offset of each detection channel is collected. The

setup is the same as that for experiments except the laser sources were off. The maximum offset

is below 1mV.

Both optical and electronic noises exist in the system. Optical noises are from the laser

modules and ambient environment. Electronic noises come from the electrical power grounding,

fluctuation of power supply, electromagnetic disturbance, digital grounding of the computer,

preamplifier in the photodiodes, operational amplifier offset, and resistance variation in the

resistors. Since the experiments are performed in a dark room, influence from environmental

light can be eliminated. To remove the remaining noises, the following routine methods are

applied: low pass filers at a cutoff frequency of 1 KHz, a sealed aluminum box for each

detection unit, a Tantalum capacitor to remove the power supply fluctuation and other standard

techniques.

2.1.9 Data Acquisition Unit

The data acquisition unit is composed of PCI-DAS603 5 and PCI-DDAO8/12

(Measurement Computing, Middleboro, Massachusetts). PCI-DAS6035 is a 16-bit resolution

A/D board with a maximum ADC rate of 200 KS/s. It has 8 differential channels, four of them

are used currently (one for each board). The digital I/O ports of PCI-DDAO8/12 are configured

as two 8255 mode 0 emulations, each consisting of four ports: port A (8 bits), port B (8 bits),

port C high (4 bits), and port C low (4 bits). These digital I/O lines either send digital signal to

the decoder or receive the gain status from the boards. A LABVIEW program controls the

operation of the data acquisition unit.









2.1.10 System Timing

When the gain of a sensor is set to gain0, the cutoff frequency of operational amplifier

equals 32 Hz. To increase signal quality, 150 ms settling time used before the signal is converted

by the A/D board when the sensor gain is set to gainO. Most sensors need to be set at gain0 for

large size phantoms or tissues due to the associated small SNR. For each illumination position,

the detection unit needs 2.4 seconds to collect all the data. The optical switch operates at the

speed of 330 ms per switching action. Thus for 64 illumination and 64 detection positions, the

total data acquisition time is about 2.9 minutes per wavelength. For a ten-wavelength

measurement, the data collection time adds up to 29 minutes.

2.2 DOT Imaging System Operation

Before the imaging experiment, the system should be powered for half an hour for warm

up. Figure 2-9 shows the power buttons of the system. Usually, the optical switch is powered at

first, then the computer, and at last the laser modules. The switching power supply for the

computer will affect the boot of the optical switch if the computer is powered before the optical

switch.

Since our imaging system can only cover 2 cm slice of a breast at one imaging time, doctor

has to tell us which breast of the patient has problems and the approximate location of the

abnormality in the breast from the mammography films. When the patient comes, the consent

form must be read and signed by the patient. The examined breast is positioned in correct

location by the operator.

Figure 2-10 shows the LABVIEW control panel of the imaging system. Operator changes

the output data fie names, one for voltage signals and the other for gain stages of corresponding

voltage signals. Then the number of detection layers and the number of laser modules are

selected from the control panel. At last, the system runs automatically for the data acquisition.










The collected data will be calibrated and then used for the DOT image reconstruction using our

finite element based algorithms.


Computer

Figure 2-1. Schematic of the experimental system.


















































(b)

Figure 2-2. Photographs of the experimental system.






38










OUTPUT

1
2

















63
64


10








2
1

INPUT


3 (a)


3 (b)


Figure 2-3. Optical switch (a) Schematic and (b) photograph.
































(a) (b)
Figure 2-4. Photographs of the ring structure.


switch3 Rf3


switch2 Rf2


Pin 6 switch1l Rfl
Rf 1G


Cf 1 5 PF I






.Pre Amplifier
I PhotcDoe


Iteqrn~al. Conn~cti.;gx __ __ _





Figure 2-5. Internal and external connections of a silicon photodiode S8754.


Pin 4



RL










Detection
Fiber Bundle


Alunninunt Fiber
Holder


Screw


~Pla ric


1111


( irc~uir liourd~t


k*.uni-


Figure 2-6. Diagram of mounting configuration for one sensor.






































Pin 4


switch chl6


Figure 2-7. The detection board: (a) Schematic;(b) layout.










Voltage


10 V
9.9 V


in 3




0.3 V


Power


1.164 mW


Figure 2-8. Flow chart of a detector gain controller.


Figure 2-9. The control panel of the DOT imaging system.






















































-1 -
I.1 1 .. J ; 6 1 II, ] I I1 I I~ 4 1


I I.


DATA ACQUISITION, PROCESSING and WRITING TO FILES

output file path (dialog if empty)
::\clinic~test_dc.dat I laser number| Source Pointsl
1... .-1e., l II 1,,..51 1. 1 ,1.84 source points



output waveforml
gain file path (dialog if empty) -l~
::\clinic~testqgain.clat


function (open:0)


append to fie? (newu file F) _:



~ Ill..- 11 1 4 r. 1I O II I. I

gain waveforml
output



~ji~:i r~_II


Figure 2-10. The LABVIEW control panel of the DOT imaging system.


I4









CHAPTER 3
SYSTEM CALIBRATION AND DOT ALGORITHM REFINEMENTS

3.1 System Calibration

We describe a new calibration method that takes advantages of both the reference

phantom based method and the data optimization scheme we developed. Various phantom

experiments are performed using our newly developed silicon photodiodes-based DOT system in

order to evaluate the calibration method. The dependence of the calibration method on phantom

size and optical properties is also studied systemically. The results show that our new method

can significantly improve the quality of quantitative absorption and scattering imaging even

under the condition of very low ab sorption contrast.

3.1.1 Image Reconstruction Algorithm

An iterative finite element based algorithm, previously described in details elsewhere, iS

used for our image reconstruction of absorption and reduced scattering coefficients. Briefly, the

stead-state photon diffuse equation

V ~r)O~r)- R (rO~r)= -~r)(3.1)

coupled with Type III boundary conditions, DVO fi = ae, is transformed into the following

matrix form of

[A]@}= (b}, (3.2)

by the finite element discretization, where O(r) is the photon density, Cla(r) is the absorption

coefficient; D(r) is the diffusion coefficient which can be written as D(r) = 1/3[C1, (r)+ C1 (r)]

where Cl (r) is the reduced scattering coefficient; S = S,8(r r,), is used where S, is the source

strength and 8(r r,,) is the Dirac delta function for a source at r,; ri is the unit normal vector

for the boundary surface; a is the BC coefficient related to the internal reflection at the









boundary; the elements of matrix [A] are a, = DV53 V5, I- Ra 30,) where ( ) indicates


integration over the problem domain; (b} is -(S4,) + afC O~ j4,4 ds; M is the number of


boundary nodes; 4, and 5, are locally spatially varying Lagrangian basis functions at nodes i

and j, respectively. Four critical parameters (the BC coefficient a, the source strength So, and

the initial guess of D and C1a) can be accurately determined by a preprocessing data optimization

scheme28. Then a regularized Newton's method is used to update the initially guessed optical

property (D and C1a) distribution iteratively in order to minimize an obj ect function composed of

a weighted sum of the squared difference between computed and measured optical data at the

medium surface.

The pre-processing data optimization scheme for determining the four initial parameters is


discussed in detail elsewhere28. Briefly, X -square errors, X2 m) _j" (c)i are minimized


as the function of the above four parameters, where Ml is the number of boundary

measurements, O m) is the measured photon density from a given experimental heterogeneous

medium, and O,'"' is the computed photon density from a numerical simulation of a

homogeneous medium with the same geometry as the experimental medium. Given reasonable

ranges for the four parameters, the minimum X2 COrresponds to the best initial guess of the four

parameters.

3.1.2 Calibration Method

We present the calibration method here and provide further discussion about the method

in subsection below. For a 2D imaging experiment, the calibration procedure is described by the

following six steps:









A. Make a homogeneous phantom that has the same diameter as the heterogeneous phantom

of interest.

B. Perform experiments with the homogeneous phantom. For 2D imaging experiments, there

are 16 transmitters and 16 receivers. Obtain a set of measured data D,, where i is the transmitter

number from 1 to 16 and j is the receiver number from 1 to 16. For each source i, light intensities

from the 16 detectors are normalized.

C. Find the initial values of absorption coefficient Ca, reduced scattering coefficient C's and

the boundary conditions coefficient a using D, These initial parameters are required by our

nonlinear iterative algorithm and can be found using the pre-processing method briefly described

in Subsection 2. 1 above.

D. Generate a 2D finite element mesh with the same diameter as the phantom. Using a unit

source intensity for the 16 illuminated positions, the 2D photon propagation is simulated with the

optical properties Ca,~ C1s and the boundary conditions coefficient a identified in Step C. This


creates a new set of data Dij from the simulation.

E.Obtain a factor matrix J)I using the following equation


fij = Dij / Dij i, j = 1...16 (3.3)

F.Multiply f, by the data set (E, ) from the heterogeneous phantom to get the final data set for

image reconstruction:


EU Ajlyi, j= 1... 16 (3.4)









3.1.3 Experimental Methods and Materials

This system has been described in detail in subsection 2. 1. The phantom materials used

consisted of Intralipid as scatterer and India ink as absorber. Agar powder (1-2%) was used to

solidify the Intralipid and Indian ink solutions. A single off-center target was embedded in a

homogeneous background phantom in these imaging experiments. Figure 3-1 depicts the

geometrical configuration for the test cases under study. One 14-mm-diameter cylindrical hole

was drilled in the homogeneous background phantom for inclusions of the target with various

optical contrasts. Three groups of experiments were performed to evaluate the calibration

method. The three groups each contained three experiments with different phantom diameters

and different levels of contrast in the target. The optical properties and geometry properties used

in Groups 1 to 3 experiments are detailed in tables 3-1 to 3-3. The optical properties of the

background phantoms for groups 1 to 3 are the same: ya=0.005 mm-l and C1's=1.0 mml

3.1.4 Results and Discussion

Figs. 3-2 to 3-4 present the reconstructed absorption and reduced scattering images from

Groups 1, 2 and 3 experiments, respectively, where each set of imaging data was calibrated with

the homogeneous phantom measurements from reference 1 (50mm diameter; left column),

reference 2 (75mm diameter; middle column), and reference 3 (100mm diameter; right column),

respectively. We can see that the best image quality is achieved when both the imaging and

reference phantoms have the same dimension (see left column in Figure. 3-2, middle column in

Figure. 3-3 and right column in Figure. 3-4). Under this situation, the recovered absorption and

scattering images are quantitatively accurate in terms of the location, size and optical properties

of the target. The reconstruction of the background is overall of high quality without any artifacts

for smaller dimension cases and with minimal slight artifacts for larger dimension cases. In










particular, the very low absorption target is quantitatively resolved for all three background

dimensions (Figure. 3-2a, Figure. 3-3b and Figure. 3-4c), which was impossible previously.

Figure. 3-5 shows the one-dimensional (lD) profile of the absorption coefficient along the

transect AB (see Figure. 3-1) for the images shown in Figs. 3-2a and 3-2d. This demonstrates a

close quantitative examination of the selected images. Other cases have similar quality.

When the imaging data were calibrated using homogeneous phantom measurements

having different dimension than the heterogeneous phantom of interest, the quality of the

recovered images is clearly degraded (Figs. 3-2 to 3-4). These degradations are generally shown

as a ring-pattern artifact (Figs. 3-2b and 3-2e; Figs. 3-4b, 4-4d and 3-4e) or a few millimeters

shifting of the target toward the center of the background (Figs. 3-2c and 3-2f; Figs. 3-3a and 3-

3d). It is interesting that there is no target shifting for all cases with the phantom of 100mm

diameter. In general, the target is clearly detectable for most cases and the reconstruction is

quantitative except for two cases with 100mm diameter phantom (Figs. 3-4j and 3-4k) where the

recovered value of the reduced scattering coefficient is incorrect.

Quantitatively the improvement in image reconstruction with proper calibration is

striking. For example, for the 1.4: 1 absorption contrast experiments, when proper calibration was

used, i.e., when the reference phantom had the same diameter as that of the heterogeneous

phantom, the errors of the peak absorption coefficient recovered relative to the exact value were

found to be 1.4% (Figure. 2-10a), 1.2% (Figure. 2-11b), and 2.8% (Figure. 2-12c) for the 50, 75

and 100mm diameter heterogeneous phantom cases, respectively. Whereas when improper

calibration was performed, i.e., when the reference phantom had different diameter than that of

the heterogeneous phantom, such errors are large as 110% and even the target cannot be detected

for some of the cases (e.g., see Figs. 3-2b, 3-2c, 3-2e and 3-2f). For the 2:1 absorption and










scattering contrast experiments, the errors of the peak scattering coefficient compared to the

exact value were calculated to be 5.5% (Figure. 3-2j) and 4. 1% (Figure. 3-41) for the 50 and

100mm diameter heterogeneous phantom cases, respectively, when proper calibration was

applied. Whereas such errors are up to 60% when improper calibration was used.

Although the results shown above indicate the dependence of the image reconstruction on

the size of reference phantom used, the calibration method described here will prove to be useful

for clinical studies. For example, in the case of breast imaging, we can build a database based on

a series of homogenous phantom measurements with a range of dimensions (e.g., from 4 to 1 1

cm with an increment of 5 mm). Whenever imaging measurements are performed on a particular

size of breast, the imaging data obtained can be calibrated with one factor matrix from the

database whose reference phantom diameter is equal or closest to that of the breast under

measurement.

The calibration method described in this section is novel in that it takes advantages of

both the pre-processing optimization scheme and the reference homogeneous phantom based

method. The homogeneous phantom only based calibration method can remove systematic

measurement errors while the pre-processing optimization scheme or model-based calibration

methods can reduce the model mismatch errors due to the difference between the photon

diffusion model and the physics involved. Thus the new calibration method can remove both

types of errors which are resulted from the division of the measured data from the heterogeneous

and reference homogeneous phantoms and multiplication of the computed data based on the pre-

processing optimization scheme.

In sum, in this subsection a new calibration method is developed and evaluated by a

series of phantom experiments with our newly developed diffuse optical tomography system. We









have shown that when the heterogeneous phantoms of interest and the reference homogeneous

phantom have the same dimension, quantitative optical images can be obtained even under the

conditions of very low absorption contrast. This study shows that this calibration method is

sensitive to the reference phantom size.

3.2 Dual Mesh Method

As a Einite element based reconstruction method, 3D DOT imaging needs a mesh with

much more elements and nodes than 2D DOT imaging. For the nonlinear iterative DOT

reconstruction, forward computation needs O(n) multiplications (n is the node number), and the

reverse computation needs O(n2) multiplications due to the full matrix property related with the

Marquardt and Tikhonov regularization method69. Therefore 3D DOT reconstructionn

computation burden is undesirable, especially for phantoms or tissues of large volumes. The dual

mesh method utilizes two separate meshes: one Eine mesh for the accurate photon density

solution and a coarse mesh for the inverse process to update optical properties. It allows a

significant reduction of computation burden for the problem with a big mesh, thus increasing the

overall computational efficiency. In fact, the idea of dual meshing has been implemented in early

works in both CW and frequency domains, where this method has been proved to significantly

enhance the quality of reconstructed imageS33. However, these early works did not exploit the

potentials of this method in 3D DOT reconstructionn. In this subsection, the dual mesh method is

applied in the CW 3D DOT reconstructionn. And the comparison with the single mesh method is

made.

3.2.1 Dual Mesh Method

There are two meshes used for the dual mesh computation. One is the coarse mesh and the

other is the fine mesh. For the cases in this section, the Eine mesh is generated by splitting each

coarse element into four fine mesh elements with equivalent volume for reducing the new mesh









singularity and for simplicity. And the new node i, is created at the centroid of each coarse mesh

element, as shown in Figure. 3-6. For the single mesh method, both forward and inverse

computations are performed in the coarse mesh. The coarse mesh contained 2,241 nodes

corresponding to 10,368 linear tetrahedral elements. And the Eine mesh, generated from coarse

mesh, contains 12,609 nodes corresponding to 41,472 linear tetrahedral elements.

The dual mesh method for the 2D DOT reconstruction is described in detail elsewhere33

The principle of dual mesh algorithm in 3D DOT reconstruction is similar. The forward

computation is performed in the Eine mesh. The local Lagrangian basis 4, and 5,, the optical

properties D and C1a in equation are defined in the fine mesh. The impact of the dual mesh method

on the inverse process appears during the construction of the Jacobian matrix [S], which is used

to update the optical property values. The elements of [S] are composed of the partial derivatives

of the photon density at the observation sites with respect to the values of D and C1a at each node

within the coarse mesh. Considering the impact of the dual meshing, elements of the Jacobian

matrix can be written as




dij _'EkVmi *Vmj (3.5)




where k and I are the nodes on the coarse mesh, 'Fk and 'F, are the basis functions centered on

nodes k and I in this mesh, and inner products are still performed over the elements in the Eine

mesh.









3.2.2 Experiments

The phantoms and targets were made of water, Intralipid (as scatterers), Indian Ink (as

absorpter) and agers (2%, used to solidifying the phantom). Figure 3-7 describes the geometry

of the phantom. A homogeneous background phantom ( C1,=0.005 mm-l and C1's=1.0 mm l) was

made at first. Then a cylindrical hole with diameter of 14 mm was drilled at desired location in

the background phantom and the target was put inside it. At last the hole with the target was

refilled with background phantom materials. The location and the optical properties of the targets

are shown in Table 3-4. For the three phantom experimental cases, the optical properties of the

target are same (C1,=0.02 mm-l and C1's=2.8 mm- ) but with different off-center locations

(15mm, 10mm, 5mm respectively). These three cases were performed to investigate lateral

resolutions of the target.

3.2.3 Results and Discussion

For the dual mesh method, the reconstruction time was about 30 minutes per iteration on a

2.88 GHz PC with 1 Gb of RAM. For the single mesh method, the reconstruction time was about

15 minutes per iteration on the same PC. Reconstructed 3D C1a and C's images for each case are

displayed at a series of transverse (coronal) sections perpendicular to axis Z and selected

longitudinal sagittall) sections perpendicular to axis X or axis Y. Quantitative one dimensional

(lD) profiles of recovered optical properties along selected transects are also shown for all the

cases.

Figure. 3-8, Figure. 3-9 and Figure. 3-10 plot the reconstructed C1a images (a-d) and C's

images (e-h) for case 1 (4:1 Ca,, 2.8:1 C's contrast, 15 mm off-center), case 2 (4:1 Ca,, 2.8:1 C's

contrast, 10 mm off-center) and case 3 (4:1 Ca, 2.8:1 C's contrast, 5 mm off-center) phantom

experiments with the dual mesh method (left column) and the single mesh method (right









column), respectively. Rectangular figures plot recovered images at the sagittal cross section

y=0mm and circular figures plot recovered images at the coronal cross section z=2 mm for each

case. The color scale bar indicates values of C1a (a-d) and C's (e-h) in mm l. For all three cases,

in the reconstructed C1a images, the target is detected quantitatively, although there are some

boundary artifacts in Figs. 3-8c, 3-8d, 3-9c, 9d, 10c and 10d. When the dual mesh method is used

we see artifacts in the reconstructed C1a images (Figs. 3-8c, 3-9c, 3-10c) are less than those in

Cia images (Figs. 3-8d, 3-9d, 3-10d) reconstructed with the single mesh method. In the

reconstructed Cl's images, with the dual mesh method, the target is differentiated quantitatively

for all three cases, as shown in figures 3-8e and 3-8g for case 1, figures 3-9e and 3-9g for case 2,

figures 3-10e and 3-10g for case 3, while with the single mesh method, we can see the target

shape is deteriorated by artifacts although target C's value is close to the exact value, as shown in

Figure. 3-8h for case 1, Figure. 3-9h for case 2 and Figure. 3-10h for case 3.

Figure 3-11 plots the three-dimensional view of the reconstructed absorption coefficient

images (Figs. 3-11a, c, e) in mm-l and the reconstructed reduced scattering coefficient images

(Figs. 3-11b, d, f) in mml for case 1 (Figs. 3-11a, b, 15mm offset), case 2 (Figs. 3-11c, d, 10mm

offset) and case 3 (Figs. 3-11e, f, 5mm offset) using dual mesh method. The showing slices in

each figure are crossed at the center of the target. It is clear to see that the reconstructed targets

are located in the expected positions.

Three-dimensional DOT reconstruction for tissue mimicking phantoms or tissues of large

volumes, a mesh with thousands of elements is needed and the computational cost is high. The

dual mesh method provides a way to reduce the computational burden without sacrificing the

extracted image quality. The results shown in this section illustrate the feasibility and potential of

the dual mesh method application in CW 3D DOT. We have reported that the dual mesh method









performed very well in two-dimensional DOT reconstruction for several coarse mesh and fine

mesh combinations.33 Here the coarse mesh and the fine mesh are fixed. It is not the purpose of

this subsection to study the mesh effects on the 3D DOT reconstruction. One set of coarse mesh

and fine mesh is enough to illustrate the dual mesh application in the CW 3D DOT.

To date, we have not found any resolution studies on CW 3D DOT. In frequency domain,

Dehghani et. al. have investigated 3D DOT resolutions and localizations of property

heterogeneity24 and good accuracy in localization (within 7 mm of the true position in the worst

case) was obtained. While the accuracy of quantitative imaging is almost 100% of the target

values with a priori information regarding the anomaly location, the target absolute value of

optical properties is 10% of the expected values without the information. In this section, the

target localization error is less than 2 mm with the dual mesh method and less than 4 mm with

the single mesh method. The target value errors from the reconstructed optical properties C1, and

C's images are less than 2.5% and 10.7% with both methods without a pzriori information. The

difference is possible due to more measurement of data pairs for our experiments (64 by 64),

smaller background phantom size, different 3D DOT algorithm, compared with theirs.

In sum, an axial spatial resolution of 5 mm in the CW 3D DOT is achieved with a set of

tissue mimicking phantom experiments by using both the dual mesh method and the single mesh

method. In addition, for both the high and low contrast anomalies in the turbid media, the dual

mesh method has the capability of detecting them with better image quality and more accurate

maximum coefficient values than the single mesh method.

3.3 Source Intensity Optimization Method

We have previously demonstrated quantitative 3D image reconstructionn of absorption and

scattering images in CW domain using phantom and in vivo experiments.29, 37, 70 While our









results are promising, we intend to improve our 3D imaging capability by developing a method

of source intensity optimization. Together with a pre-processing method previously developed

for 2D imaging,28 we experimentally show in this paper that the 3D imaging quality can be

significantly enhanced for both absorption and scattering image reconstructions.

3.3.1 Source Intensity Optimization Methods

In our reconstruction algorithm, the diffusion equation is iteratively solved based on a

regularized Newton's method in order to update an initially guessed optical property (D and C1a)

distribution. In addition to the initial optical properties, it is clear that the BC coefficient a and

the source strength Sk must also be given for the entire solution procedure. In fact these initial

parameters need to be accurately determined for quantitative image reconstructions as illustrated

in [28] where we developed a preprocessing data optimization scheme for such a purpose. In the

following we first describe two previous source calibration methods, uniform source intensity

and normalized source intensity, and then introduce the new source optimization method.

Uniform source intensity method. In the uniform source intensity method, all the source

terms, Sk (k = 1,2,- ,64), are assumed to be the same, i.e., Sk = So Thus there are only 4

parameters (u, So, and initial D and C1, values) that need to be optimized before the

reconstr-uction. In our pre-processing data optimization scheme for determining the four initial


parameters, X -square errors, X = ", _di~ cj ,] ar minmiized as a function of the above


four parameters, where M is the number of boundary measurements (in this study, M=64x64),

O m) is the measured photon density from a given experimental heterogeneous medium, and

Oi" is the computed photon density from a numerical simulation of a homogeneous medium









with the same geometry as the experimental medium. Given reasonable ranges for the four

parameters, the minimum X2 COrresponds to the best initial guess of the four parameters.

Normalized unit source intensity method. The second preprocessing method used

previously is a normalized unit source calibration method. In this method, the source terms Sk 1

while the measured data at 64 measurement sites are normalized using the maximum of the 64

measured data for a given source location. Thus, using this method we only need to optimize

three initial parameters (a and optical properties D and C1a), and the normalized measured data


must be used for reconstructions. Similarly, square errors, XZ 2 m~))nor(m _))norm
i=1

are minimized as a function of the above three parameters, where M is the number of boundary

measurements (in this study, M=64x64), (O m))nor is the normalized measured photon density


from a given experimental heterogeneous medium, and (Oi )norm is the normalized computed

photon density from a numerical simulation of a homogeneous medium with the same geometry

as the experimental medium. The minimum X2 giVCS the best initial guess of the three

parameters.

Source intensity optimization method. In the source intensity optimization method, oc

and initial D and C1, are optimized first using the normalized source intensity method described

in the above subsection. Then for each of the 64 excitations, the corresponding source intensity,

Sk, iS Obtained using the similar preprocessing procedure described in above two sub sections. For


each of Sk from 1 to 64), sqluareerrors, Xk2 cml k cm!k ,, are minimizedas a
i=1

function of Sk, where Ml is the number of measurement for each source excitations (in this










study, M1=64), (O, m)k indicates the original measured photon density from a given


experimental heterogeneous medium for excitation at k, and (Oi ))k is the computed photon

density for excitation at k from a numerical simulation of a homogeneous medium with the same

geometry as the experimental medium and with the ot,D and C1, obtained in the first step. The


optimized source intensity Sk is Obtained when Xk,2 are minimized. Finally a total of 67 initial

parameters are searched for full 3D image reconstructions.

3.3.2 Experiments

The phantom materials used consisted of Intralipid as scatterer and India ink as absorber.

Agar powder (1-2%) was used to solidify the Intralipid and Indian ink solutions. A single off-

center target was embedded in a homogeneous background phantom in these imaging

experiments. Figure 3-12 depicts the geometrical configuration for the test cases under study.

One 14 or 9-mm-diameter cylindrical hole was drilled in the homogeneous background phantom

for inclusions of targets with various optical contrasts. A cylindrical target (14mm in diameter

and 10 mm in height for cases 1-4 and 9 mm in diameter and 10 mm in height for cases 5-6) was

placed into the hole where the rest of the hole was filled with phantom material that was the

same as the background. Six experiments with different optical contrast levels between the target

and background were performed to evaluate the three optimization methods discussed in Section

2. The geometrical information and optical properties used for the target in the 6 experiments are

detailed in Table 3-5. The optical properties of the background were the same for all the

experiments: Cla=0.005 mm-l and C1;=1.0 mml









3.3.3 Results and Discussion

The results presented in this section were obtained using a 3D mesh with 10386

tetrahedron elements and 2241 nodes. Reconstructed 3D C1a and C1; images for each case are

displayed at a series of transverse (coronal) sections perpendicular to axis Z and selected

longitudinal sagittall) sections perpendicular to axis X or axis Y. Quantitative 1D profiles of

recovered optical properties along selected transects are also shown for some cases.

Figure 3-13 shows the reconstructed C1a images at a selected sagittal and coronal section

for case 1 (2: 1 C1a contrast). From Figs. 3-13a and 3-13b, when the uniform source intensity

method was used we see that boundary artifacts dominate the images and the target cannot be

detected for this relatively low contrast case. The target is detectable with the normalization

method (Figs. 3-13c and 3-13d), while we note relatively strong artifacts in the background. The

detection of the target is clearly improved when the source optimization method was used (Figs.

3-13e and 3-13f), although there are still some small artifacts in the background region.

Reconstructed C1a images at a series of coronal sections for case 2 (4:1 C1a contrast) are

plotted in Figure 3-14. As shown from column 3 in Figure. 3-14, when the uniform source

method was used the target cannot be detected at most coronal sections except that at z=-2mm

the target was barely visible. For the images obtained by the normalization method (column 2 in

Figure. 3-14), the target is resolvable, but with a marked circularly shaped artifact in the

background. Again, when the source optimization method was utilized, the target is clearly

detected with minimal artifacts, as shown from column 1 in Figure. 3-14.

Figure 3-15 plots the absorption and scattering images reconstructed for case 3. For the

C1a images in this case, the target is differentiated successfully from the background with all

three methods (Figs. 3-15a-f). However, we can see that the quality of the extracted C1a images









with the source intensity optimization method is still the best (Figs. 3-15a and 3-15d). For

example, as shown in Figs. 3-15a and 3-15d, the shape and size of the target is better recovered

and there are much less artifacts in the background. Forthe C1l images shown in Figs. 3-15g-o,

we note that the uniform source intensity method basically fails to detect the target (Figs. 3-15i, I

and o). The normalization method has the capability to detect the target, but with strong artifacts

in the background (Figs. 3-15k and n). In addition, the recovered target position is shifted

towards the center of the background (Figure. 3-15k). Figures 3-15g, j and m illustrate that the

source intensity optimization method is capable of reconstructing Gif images with much better

accuracy and with much less artifacts relative to the other two methods.

Figures 3-16 and 3-17, respectively, show the recovered absorption and scattering images

at a selected sagittal section and a series of coronal sections for case 4. In this relatively high

contrast case, we note that the target is detected for both the C1a and C1; images with all three

methods (e.g., see the images shown at y=0 and z=2 in Figs. 3-16 and 3-17). However, we can

still see that the images with the source intensity optimization method have the best overall

quality (column 1 in Figs. 3-16 and 3-17). For the absorption images, we observe that the

normalization method (column 2 in Figure. 3-16) gives almost the same quality as the source

optimization method, except that it generated more boundary artifacts (see the images at z=-6 in

Figure. 3-10). The boundary artifacts in the images from the uniform source intensity method

are clearly the strongest such that the target is invisible at several cut planes (e.g., see column 3

at z=6mm in Figure. 3-16). For the scattering images shown in Figure. 3-17, we see that the

recovered target position is shifted to the center of the background at several cut planes (see the

images at z=6mm in Figure. 3-17).









For a more quantitative assessment of the results, Figure 3-18 shows C1a and C1(profiles

along a transect through the centers of the target and background for the images at y=0mm and

z=2mm for the cases 1-4 when the source intensity optimization method was used. The dotted

line corresponds to the exact values and the solid line are referred to the extracted optical

property values. From Figure.3-18, we calculated the relative errors of the recovered C1a

(maximum value) in the target to be 13.0%, 0.95%, 0. 1% and 0.2% for cases 1-4, respectively.

The relative errors of the extracted Gif (maximum value) in the target were found to be 2.0% and

8.8% for cases 3 and 4, respectively.

Figure 3-19 plots the absorption images (Figs. 3-19a and 3-19b) and scattering images

(Figs. 3-19c and 3-19d) reconstructed with the source optimization method for case 5 (4: 1

Cia and C's contrast) at the section y=0 mm (Figs. 3-19a and 3-19c) and at the section z=-3 mm.

The target is superficial and the closest distance between the target and one fiber bundle is 2 mm.

The source intensity at the fiber bundle obtained with the source optimization method increased

by 56% above the average. From figure 3-19 we see that both the scattering images and the

absorption images were reconstructed successfully. The intensity increase did not appear to

degrade the quality of image reconstruction.

Figure 3-20 shows the absorption images (Figs. 3-20a and 3-20b) and scattering images

(Figs. 3-20c and 3-20d) reconstructed with the source optimization method for case 6 (4:1

Cia and C's contrast) at the section y=4 mm (Figs. 3-20a and 3-20c) and at the section z=-6 mm.

Again, the target is superficial and is embedded between two source fiber bundles. The source

intensities at these two fiber bundles increased by 45% and 7.5%, respectively. Both the

scattering images and the absorption images were reconstructed successfully while the shape of









the target (Fig 3-20c) was degraded because the target was close to the bottom of the background

phantom .

Figures 3-21(a) and 3-21(b) plot the uniform source intensity obtained by the uniform

source intensity method (dotted line) and the source intensity distribution obtained by the source

intensity optimization method (solid line) from the original measurements of case 4 and the

normalized measurements for case 4, respectively. Both the uniform source intensity method and

the normalized unit source intensity method assume that all the 64 source intensities are the

same. However, the real source intensity distributions are not uniform (the solid line in Eigure 3-

21) due to the experimental and numerical errors. And for case 4, the maximum/minimum ratios

are about 3.0 and 1.8 for the original and normalized data, respectively. The normalization

reduced the source intensity maximum/minimum ratio from 3.0 to 1.8 and made the source

intensity distribution more uniform. That may be the reason why the normalized unit source

method is capable of obtaining better images than the uniform source intensity method.

Based on the results presented above, it is clearly seen that the source optimization

method provides significantly improved image quality over the existing two source calibration

methods. This is not surprising because both the uniform source intensity and the normalization

methods assume that all the 64 source intensities are the same, while the real source intensity

distributions are not uniform due to experimental errors. We believe that Sk's (k from 1 to 64)

represent real emitter intensities at the source locations around the phantom surface. The real

emitter intensity at one location equals the multiplication of the corresponding laser module

output intensity, the source fiber attenuation and the source fiber-phantom coupling coefficient.

While detailed evaluation to what extent 3D model can improve DOT imaging over 2D

model is beyond the scope of this paper, it is interesting to initially compare the 3D results










presented here with our 2D results obtained previously. We have demonstrated that both C1a and

C1l images in heterogeneous media can be extracted quantitatively using 2D model with

appropriate calibration and preprocess methods.31, 71 These 2D images gave similar quantitative

accuracy as 3D images presented in this work. One expects that 3D model would provide better

accuracy for image reconstruction than 2D model, however. A possible reason for explaining this

contradiction is that the volume/amount of measured data available in the current 3D imaging

system may not be enough relative to the number of unknown parameters involved in the 3D

image reconstructions.

It is well known that the source intensity difference among the different source locations

significantly degraded the DOT reconstructed image qualities. One way to calibrate the source

intensity is that the optical source coupling coefficients and/or the optode positions are

reconstructed simultaneously with the image extraction.72-74 Another way is to estimate the

coupling coefficients with a homogenous and isotropic phantom before experiments.75-76 In this

paper, our method estimated the source intensities at the different source locations by a fitting

procedure with measured data from an inhomogeneous phantom and simulated data

corresponding to a homogeneous model phantom. The presented results show that our proposed

method can significantly improve the quality of reconstructed images. Combined the methods

reported in Refs.72-74 with the source optimization method described here may result in further

improvement. We plan to evaluate this combined method in future.

In sum, we have developed a new source optimization method in this paper. The imaging

results shown indicate that this new method can quantitatively improve 3D image

reconstructions.






















A ____________ ___ -~~---~ B



'I









Figure 3-1. Geometry of the phantom configuration.



















200 4


2x 1


10. 10 10 10- 1



-10 -10-.. -10

.goiii- 6;ii;;i' -202-04
-20 -10 0 10 20 -20 -10 0 10~l 20 -20 -10 0 10 20

(d) (e) (f)
(1 0 I x 10 Jlx1
20 11 20 1

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10 151





-20 -10) 0 10 20 -20 -10 0 10 20 -20 -101 0 10 20
X (mm) X~m x(mm)
(g) (h) (i)

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-2009-0 0- -20

-20 -10 0 10 20 -20 -101 0 10 20 -20 -101 0 10 20
x(m)x(mm) x (mm)
(j) (k) (1)
Figur 3-.Rcntuce bopioanscatrn imge fo h 3cssin ru hnahsto
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40 -20 0 rj 20 40 40 -20 0 ~ 20 40 40 -20 0 ~ 20 40

(j) (k) (1)
Figure 3-3. Reconstructed absorption and scattering images for the 3 cases in Group 2 when each set of
imaging data was calibrated with 50mm diameter homogeneous phantom (left column),
75mm diameter phantom (middle column), and 100mm diameter phantom (right column),
respectively. (a)-(c): absorption images from the case of target 1. (d)-(f): absorption images
from the case of target 2. (g)-(i): absorption images from the case of target 3. (j)-(1):
scattering images from the case of target 3. The grey scale shores the absorption or reduced
scattering coefficient value (mm '), while the axes indicate the spatial dimension (mm).


-20 5 20
lp -3 .-3





-20 -20 i

1,-0 10 r~
0o 03 o a o t o a

6 -10 -10

-20 -20 5
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-30 -3 4 o
40 -20 0 20 40 40 -20 0 20 60


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-30


20 -02 0



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20
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-20
-30
0 -20


x (mm)
(e)


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X (mm)
(d)


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-20
-30
40 -20 0 20 40
x (mm)
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40 -20 0 20 40

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Figure 3-4. Reconstructed absorption and scattering images for the 3 cases in Group 3 when each set of
imaging data was calibrated with 50mm diameter homogeneous phantom (left column),
75mm diameter phantom (middle column), and 100mm diameter phantom (right column),
respectively. (a)-(c): absorption images from the case of target 1. (d)-(f): absorption images
from the case of target 2. (g)-(i): absorption images from the case of target 3. (j)-(1):
scattering images from the case of target 3. The grey scale shores the absorption or reduced
scattering coefficient value (mm '), while the axes indicate the spatial dimension (mm).


J





IIra

s.r


rrlO
50 i~i ~J~IIII~F




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,r


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so
0.8 _











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Figure 3-5. 1D profile of the absorption coefficient along the transect AB (see Figure. 3-1) for
the image shown in Figure. 3-2a (a) and for image shown in Figure. 3-2d (b). The
dotted and solid lines are, respectively, the exact and reconstructed absorption
coefficient distributions.


Figure 3-6. Four fine mesh elements generated from one coarse mesh element.








Section AA


X'1 7




Unit: mm


Figure 3-7. Geometry of the tissue mimicking phantom.


Layer 1-
SLyrLayer:
A Layer
























-20 0
X (mm)


(b) n







20

ao .004


-20 0
X (mm)


20


10



-10

-20

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-20 0
X (mm)


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x (mm)


30: 30 1

20 20 25









-30. -30:
-20 0 20 -20 0 20
X (m m)
Figure 3-8. The C1a images (a-d) and C's images (e-h) reconstructed for case 1 (4:1 Ca, 2.8:1

C's contrast, 15 mm off-center) phantom experiment with the dual mesh method (left
column) and the single mesh method (right column). The rectangular and circular
figures are at the cross sections y=0 mm and z=2 mm respectively. The color scale
bar indicates values of C1a (a-d) and C's (e-h).


(a) o.ess




20 .m
.0*4





















0 005









02~


10


-20 0
X (mm)


x 10





6
4







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0.8


10


N


-20 0
X (mm)


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122.5
1.5


1.5


-20 0 20 -20 0 20
X (mm) X (mm)

Figure 3-9. The C1a images (a-d) and C's images (e-h) reconstructed for case 2 (4:1 Ca, 2.8:1

C's contrast, 10 mm off-center) phantom experiment with the dual mesh method (left
column) and the single mesh method (right column). The rectangular and circular
figures are at the cross sections y=0 mm and z=2 mm respectively. The color scale
bar indicates values of C1a (a-d) and C's (e-h).


(a)








-20 0 20
x (mm)















I I


0
X (mm)


.016
.014
; O012


-20 0
X (mm)


-20 0
X (mm)


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-10


-20 0
X (mm)


-20 0
x (mm)


30 \ 30 I

20 l.5 20



-20 1 -0

-30. i -30.

-20 0 20 -20 0 20
X (mm)
Figure 3-10. The C1a images (a-d) and C's images (e-h) reconstructed for case 3 (4:1 Ca, 2.8:1

C's contrast, 5 mm off-center) phantom experiment with the dual mesh method (left
column) and the single mesh method (right column). The rectangular and circular
figures are at the cross sections y=0 mm and z=2 mm respectively. The color scale
bar indicates values of C1a (a-d) and C's (e-h).


x 10












x10


(a) .a




N 0.1 N
-100.0 -10
m~~ 0006
-20 0 20 -20
X (mm) 0 004


10

1. -0
















.02
(a)
absorption 1.018
.016
.014
U.012

-20 ..1

20 20 0os

0.004






absorption .2

0.018
0.016



0 0
i=0 ...... '
20 0.0
20 y .004







absorption .2


.2

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scattering


-10 -20
-20 /0
0 20 20


N 0 -
-10 G
















11 *


1rl


~


-2


.5


20


(f)

scattering .







0 0 200.


Figure 3-1 1. The three-dimensional views of the reconstructed absorption coefficient images (a,
c, e) in mm-1 and the reconstructed reduced scattering coefficient images (b, d, f) in
mml for case 1 (a, b, 15 mm offset), case 2 (c, d, 10mm offset) and case 3 (e, f,
10mm offset) respectively using the dual mesh method. In each image, the showing
slices are crossed at the center of the target.


(b) .


(d) 2

scattering .




-2 0























A Layer -i "-" -- -- A




1 ~43

Section AA Section AA
(case 1-5) (case 6)










Of





Offset d


Unit: mm
Figure 3-12. Geometry of the phantom under study.












(a) (b)








-20 0 20
-220 20

x(c) 1 a (d) a




-20 0 20
X (mm))

(C>-2 x~0 mo) 20~









210 0 20 /2
K (mm) 2 -
-20 0 20
x (mm)



opimzaio mthd(e, ) Coolum 1f shw thtimgs ty0 m lnn



Column~~~~~~~1 2 ie h iae tz= mpae





x005


I


x00




14





0:
-2


z=2 mm









z=-2 mm


-20 x mm 20


-0 x (mom)


441

x00


-20 0)
M (mm)


-20) 0 20 -20 0 20 -20) 0 20
X (mml x (mm) X Imm)
Figure 3-14. The absorption images reconstructed for case 2 (4:1 C1a contrast) with the uniform
source intensity (column 3); the normalization method (column 2) and the source
optimization method (column 1).


x10



z=-6 mm









Figure 3-15. Reconstructed absorption images (rows 1 and 2) and scattering images (rows 3-5)
for case 3 (2:1 C1a and C's contrast) with the uniform source intensity (column 3); the
normalization method (column 2) and the source optimization method (column 1)


















E
E


:i




jo
drJ
1,
F
E
~I
.l(j
3ij


x (mm)


-0 X (mm)


Sx (mm)


xo 1/ < 1
ri)(e IIIo Ir ( C




5 30



-0 X (mn) X mom)


-20 x m 20


-0 x (mm)


(i)







-20 X(m) 20 0


-2V
0x (mn)


-2- O o
0x (mm)


-20 x Am 20


ill


-20 x (m) o


IIIn so (o)




20.



-20 x(mom) 20 -0 x (m) a


4 10




(c) '


a









(3


x la
(a) a






3


(g) lt (h)



08


-20 x mm 20 o d


ao ) j0 Il 30o (1)~






rooa


(m) a












x(D


x(mml


x*



B'
ii: ~
:r
~ L
-20 O 2P
r(mml


,,

uls

/oass
"' xlr'n~

r% r
RI~P~ar~~

I""'
I'! I""'
;I ull
"II C ~pg~
i ri
*.
:I
-0~01
Z~POZO
x)D







~I
:: 20
Slnml


z= 6 mm


olr~
nm
OA01

x*




E:''


z= -6 mm f


-20 0mm 20


z. so.]


Figure 3-16. The absorption images reconstructed for case 4 (4:1 C1a and C's contrast) with the
uniform source intensity (column 3); the normalization method (column 2) and the
source optimization method (column 1).


y=0 mm rI ~

-20r P 20 1 20 0 20 ,,





























y=0 mm


-20 0 20 20 4 0 20
X mmJ x(mm]


-201 20


z= 2 mm E





;I







z= -6 mm


ii] :i I1
*(lnml


520 1' 20




a' o







10 IDI r

aC ~ ~ rl i


rl P 29
X(mm)


i] O 20
x(mm)


ii] :i h
Ilmilr


Figure 3-17. The scattering images reconstructed for case 4 (4:1 C1a and C's contrast) with the

uniform source intensity (column 3); the normalization method (column 2) and the

source optimization method (column 1).


z= 6 mm r 0

rn-10

20 0 20


- 210 .

20 Xm)













.,X 109


-20 -10 x (nm) in 2o


Figure 3-18. Recovered C1a values along a transect through the centers of the target and
background for the images at y=0 mm, z=2 mm for case 1 (a), case 2 (b), case 3 (c)
and case 4 (e). Reconstructed C's values along a transect through the centers of the
target and background for the images at y=0 mm, z=2 mm for case 3 (d) and case 4
(f). Both the C1a and Cl's images were reconstructed using the source intensity
optimization method. The dotted lines are the exact values and the solid lines indicate
the extracted coefficients.


C----------


-20 -lo x (Am)












x 10

620



14 2



-20 0 20 4 -0 ,gg
X (m m) 2
-20 0 20
X (mm)



(c) .. (d) .

202




0 0 1.6


-20 0 20 1 2
X (mm) -0
-20 0 20
x (mm)


Figure 3-19. The absorption images (a and b) and scattering images (c and d) reconstructed with
the source optimization method for case 5 (4:1 C1a and y's contrast) at the section y=0

mm (a and c) and at the section z=-3 mm.
















15


0 10 p
f0.01
10 5 -10

-20 0 20 2 00
X (mm) o
-30
-20 x mm 20




(c) so (d) 2



60 80



-10r~ -101.

-20 0 201-21
x (mm) oJs
-30.
-20 0 20
x (mm)
Figure 3-20. The absorption images (a and b) and scattering images (c and d) reconstructed with
the source optimization method for case 6 (4:1 ya and y's contrast) at the section y=4

mm (a and c) and at the section z=-6 mm.






(a) (b)
3. 10 3

3 Unform stouse nt tonor rce Intensity
~ Surc Itenit Opimraton ~ Nomeiz25c

.....*2
v01. _I. L o_1~
8-'-I 1IIIrlY15




0 20 40 60 0 20 40 60
Detectors Detectors


Figure 3-21. The source intensity obtained with the uniform source intensity method (dotted line)
and the source intensity distribution obtained with the source intensity optimization
method (solid line) from original measured data (a) and the normalized measured data
(b) of experiment case 4.











Table 3-1 Optical and geometric parameters used for Group, 1 experiments.
R2 D Cia Cls R1
(mm) (mm) (1/mm) (1/mm) (mm)
Target 1
7.0 9.0 0.007 1.0
(1.4: 1 Cia contrast)
Background
Target 2 7. .1 10 (Ra =0.005 mm 25.0
(2:1 Cia contrast) ,1 _,0mml
Target 3
7.0 9.0 0.01 1.8
(2:1 Cia and Cl's contrast)



Table 3-2 Optical and geometric parameters used for Group 2 experiments.
R2 D Cia Cls R1
(mm) (mm) (1/mm) (1/mm) (mm)
Target 1
7.0 11.0 0.007 1.0
(1.4: 1 Cia contrast)
Background
Target 27. 110 01 10 (Ra,=0.005 mm 37.5
(2:1 Cia contrast) _
C1' =1.0 mm l)
Target 3
7.0 11.0 0.01 1.8
(2:1 Cia and Cl's contrast)




Table 3-3 Optical and geometric parameters used for Group 3 experiments.
R2 D Cia Cls R1
(mm) (mm) (1/mm) (1/mm) (mm)
Target 1
7.0 21.0 0.007 1.0
(1.4: 1 Cia contrast)
Background
Target 27. 210 01 10 (Ra,=0.005 mm 50.0
(2:1 Cia contrast) _
C1' =1.0 mm l)
Target 3
7.0 21.0 0.01 1.8
(2:1 Cia and Cl's contrast)










Table 3-4 Optical properties of the phantom background and the target for all 5 cases.
d Ra Cls
(1/mm) (1/mm)
case 1
15 mm 0.02 2.8
(4:1 Cia and C's contrast)
Background
case 210 mm 0.02 2.8 (a005m
(4:1 Cia and Cl's contrast) ,_
C1$ =1.0 mm l)
case 3
(4:1 Cia and Cl's contrast) 5mm 022.


Table 3-5 Optical properties of the target and background used in the six experiments performed.

d H as
(1/mm) (1/mm)
case 1
(21 a onrat) 10 mm 3 mm 0.01 1.0
(4:1 Cia contrast) 10m3mm.210
case 3


(2:1 Cia and 10 mm 3 mm 0.01 1.8
p's contrast) Background
case 4 (1a =0.005
(4:1 Ci "nd-1
(41 a nd5 mm 3 mm 0.02 2.8 m
C' -1.0
C's contrast)s
case 5 mm )>
(4:1 Cia and 19 mm 9 mm 0.02 2.8
C's contrast)
case 6
(4:1 Cia and 19 mm 12 mm 0.02 2.8
C's contrast)









CHAPTER 4
PARTICLE SIZE IMAGING: PHANTOM EXPERIMENTAL STUDIES

4.1 Measurement of Particle Size Distribution and Concentration in Heterogeneous Turbid
Media

In this section we attempt to establish a method directly based on more rigorous Mie

scattering theory for the reconstruction of particle size distribution and concentration without the

limitations existing in the use of the power law. We use both simulations and phantom

experiments to validate our method. We also describe a new scheme for optimizing the initial

parameters needed for reconstructions in MSDOT and a method for calibrating the scattering

spectra obtained from phantom experiments.

4.1.1Materials and Methods

Two inverse algorithms are required in order to obtain particle size distribution and

concentration with MSDOT. The first is a DOT algorithm for the recovery of spectroscopic

scattering images in heterogeneous turbid media. Our DOT algorithm, described in detail

elsewhere, uses a regularized Newton's method to update an initial optical property distribution

iteratively in order to minimize an obj ect function composed of a weighted sum of the squared

difference between computed and measured optical data at the medium surface. The computed

optical data (i.e., photon intensity) is obtained by solving the photon diffusion equation with

Einite element method. The second algorithm is one that extracts the particle morphological

information using the scattering spectra obtained from the first algorithm described above. It

casts the reconstructionn as an optimization problem in which the optimization parameters are

coefficients in a probability function such as Gaussian distribution function using a priori

assumptions. This inverse algorithm is based on a least squares optimization, where the

difference between measured and computed scattering spectra is iteratively minimized by

adjusting the optimization parameters under Mie scattering theory.









It is known that an optimized initial optical property distribution is critical for quality

image reconstruction using DOT algorithm. We reported an effective preprocessing scheme for

such purpose previously; however, it requires time-consuming computational procedures to

obtain the initial parameters needed for image reconstruction at a single wavelength. Clearly this

would not be efficient for image reconstruction at multiple wavelengths in MSDOT. Thus we

implemented an algorithm for optimizing initial optical properties based on the following core

relationship:

(J TJ +pl)AX = J'~o e') (4.1)

where




80 802 ~oc
J=< D 8a >, A g (AD,Agrr), ~O 2 2





00 and Oc are the observed and calculated photon density; D and au are the diffusion and

absorption coefficients, respectively; Ag is the update of optical properties; N is the number of

nodes used in the finite element mesh used; p is a regularization parameter and I is an identical

matrix. In this algorithm, optimized initial optical properties are obtained by iteratively solving

Eq. (4-1). Since there exist only two variables, it is very fast to reach convergence.

Once D(h) is recovered using DOT algorithm, the reduced scattering spectra can be

obtained by the following relationship for turbid media:


(1- gp, ()= 1(4.2)
3D(A1)









where (1- g)CLs is the reduced scattering coefficient and g is the average cosine of scattering

angles. Following Jiang et al.77-so, the scattering spectra are correlated with particle size

distribution and concentration through the following relationship under Mie Theory:


(1g)s )=9 )=.3set~~n11-~xn,) f (x)dx (4.3)


where Qscat is the scattering efficiency; x is the particle size; n is the refractive index of particles;

Sis the particle concentration/volume fraction; f(x) is the particle size distribution. Both Qscat

and g can be computed with Mie Theory.8 In Equation (4.3) we have assumed that particles act

as independent scatterers without particle-particle interaction. In order to solve for f(x) and $

from measured scattering spectra, an inversion of Eq. (4.3) must be obtained. Our numerical

inversion is based on a Newton-type iterative scheme through least-squares minimization of the

obj ective functional:





where (b )S and (4 )~ are the observed and computed reduced scattering coefficients at ten

wavelengths, j= h,,2 h,,... 10 (mOre wavelengths can be used, depending on the number of

wavelength available from the experimental system). In the reconstruction, we have assumed a

Gaussian particle size distribution in this study (a priori knowledge about the mode and

distribution form of the particle size are usually available in a practical situation),

(x-a)2
f~x) 1 e2b2 where a is the average size of particles and b is the standard deviation.


Substituting above f(x) into Eq. (4.3), we obtain










e ~ ~ ~ 3 seat:()= iU. (x, n, h)[1 gx, n, 1)l 1 "
(1-~~~~~ g)s(1 p() dx (4.5)
2x ~ b

Now the particle sizing task becomes to recover three parameters a, b and # As described

in detail in Refs. 77-78, we have used a combined Marquardt-Tikhonov regularization scheme to

stabilize the reconstruction procedure.

4.1.2 Simulations and experiments

Simulations are used to test the sensitivity of particle sizing algorithm to noise effect with

reduced scattering coefficients at ten wavelengths (This is the number of wavelength available

from our imaging system). Simulated scattering spectra were generated using Eq. (4.5) when the

particle size distribution and concentration were given. Particle size distribution and

concentration were reconstructed using the particle sizing algorithm when 0%, 1%, 5%, 10%,

and 20% noise was added to the "measured" scattering spectra, respectively.

Phantom experiments were conducted using our ten-wavelength DOT system (63 8, 673,

690, 733, 775, 808, 840, 915, 922 and 960nm). This newly developed imaging system and its

calibration were described in detail elsewhere. Briefly, light from one of the ten laser modules is

transmitted to an optical switch, which sequentially passes it to 16 pre-selected points at the

surface of the phantom for 2D imaging experiments. 16xl6 measured data is then input into our

DOT reconstruction algorithm to generate a 2D cross-sectional image of the phantom. Three sets

of phantom experiments were conducted to validate the overall approach for extracting particle

size distribution and concentration using MSDOT. The background phantom materials used

consisted of Intralipid as scatterer and India ink as absorber. Agar powder (1-2%) was used to

solidify the Intralipid and India ink solutions. The cylindrical background phantom had a radius

of 25mm, an absorption coefficient of 0.005/mm and a reduced scattering coefficient of 1.0/mm.

A thin glass tube (9mm in inner diameter, 0.4mm in thickness) containing polystyrene










suspensions (Polysciences, Warrington, PA) was embedded off-center in the background solid

phantom. Three different types of polystyrene spheres were used in the three experiments:

2.06 pum in diameter, 0.02 pum in standard deviation and 0.52% in concentration for Case 1;

2.85 pum in diameter, 0. 14 pum in standard deviation and 1.02% in concentration for Case 2;

5.66 pum in diameter, 0.30 pum in standard deviation and 2.62% in concentration for Case 3. The

refractive index of the spheres and their surrounding aqueous medium are 1.59 and 1.33,

respectively.

4.1.3 Results

Results from two simulations are displayed in Tables 4-1 and 4-2. From simulation 1 for

a particle diameter of 2.855Cpm, we can see that both the mean size and concentration of particles

can be recovered accurately with up to 20% noise; the relative errors of reconstruction of these

two parameters were calculated to be within 3.0 ~ 44.9% and 2.9 ~ 33.3%, respectively, given

the noise levels used. We also note that the recovery of the standard deviation is quite sensitive

to noise effect: the relative error is as large as 100%. From simulation 2 for a particle diameter of

10.0plm, the relative errors of reconstructed parameters a and $ are within 0.5 ~ 20.2% and 0.4 ~

21.8%, respectively, given the noise levels used. Similarly we see that the standard deviation

recovery is sensitive to the noise levels and the relative errors is up to 96.6%. Overall the

extraction of particle concentration is least sensitive to noise effect. Using these reconstructed

parameters at different noise levels, we calculated the scattering spectra using Eq. (5) for

simulation 1 and present them in Figure. 4-1.

Phantom data at 10 wavelengths for all three cases were collected, and both absorption

and scattering images were recovered at each wavelength using our DOT algorithm (only the

scattering images are needed here for particle sizing). Figure 4-2 shows the reconstructed p'~










images for Case 2 at 10 different wavelengths. In particle sizing, both peak and average C1l

values of the target area were used to recover the particle size distribution (PSD), f(x), and

concentration, O .

We found that best particle sizing was achieved when the reconstructed peak or average

C1l values calibrated using the optimized initial Cl values. In this calibration, the subtractions of

the mean initial C1 at 10 wavelengths from each individual initial C1 value are defined as

calibration factors. Then a calibrated C1l spectrum was obtained by subtracting the calibration

factors from the peak or average C1 values. For all three experimental cases studied, the

calibrated C1l spectra were used to reconstruct the particle size parameters.

The mean particle diameter (a), the standard deviation (b) and the concentration (0)

reconstructed from both the peak and average Cl values for the three cases are listed in Table 4-3

where the exact parameters from the manufacture are also given for comparison. We

immediately note that both the mean size and concentration are recovered with good quality,

consistent with the simulations. We found the relative error of the reconstructed mean particle

size is within 8.4% for the three cases examined, while the relative error of the recovered

concentration is 33.3%, 0.8% and 11.1% for Cases 1, 2 and 3, respectively. Similar to the

simulations, the standard deviations were recovered with errors as large as 86.6% (Case 3).

When the average C1 spectra were used, we see that the reconstructed results are generally

similar to that with the peak C1l spectra; however, overall the peak spectra-based reconstruction

has better quality. Figure. 4-3 presents the exact and recovered PSD (normalized) for the three

different polystyrene suspensions when the peak spectra were used for reconstruction. In Figure.

4-4, scattering spectra obtained with different methods for Cases 1 and 3 are shown, in which we









can see that the calibrated spectra match well with the Mie theory fittings using the recovered

particle parameters.

4.1.4 Discussion and Conclusions

The ultimate goal of our work is to see if we can extract cellular morphological

information of breast tissue using MSDOT. The simulations and phantom study presented here

represent our first step toward that goal. In our simulations and phantom experiments, the

choices of 2, 3, 6 and 10Clm polystyrene scatterers were intended to mimic mitochondria and

nuclei, the two primary contributors to tissue scattering reported mn the literature to date.42 28

We have used Mie theory to recover the particle size distribution and concentration from the

scattering spectra obtained using MSDOT at 10 different wavelengths. It is known that Mie

theory assumes spherical particles without particle-particle interactions. While these assumptions

do not pose problems in our phantom study, they may do so in real tissue where scatterers

generally are not spherical. Interestingly, Mourant et al.82 preSented Mie calculations of C1 in

cultured cell suspensions which showed excellent agreement between the Mie theory and

diffusion approximation. In a prior study, we have shown that accurate PSD can be recovered in

concentrated TiO2 Suspensions where TiO2 particles are not spherical.7-7 In another study, we

have demonstrated that the PSD in KCl suspensions can still be well reconstructed when the

concentration of KCl particles is as high as 40%.7s,so Thus it is reasonable to believe that the

approach described here for particle sizing would provide quality results from in vivo data

particularly if we focus on the reconstruction of only particle mean size and concentration.

In our particle sizing, the refractive indices of the polystyrene suspensions and the

surrounding medium (water) are important parameters and have been assumed known as a priori.

In a clinical situation, we can obtain these information empirically from the literature, or we can









ultimately recover the refractive indices of scatterers as we reconstruct the PSD and

concentration. Our phantom results have shown that the calibration method developed for

correcting the initial scattering values is able to provide quality reconstruction of PSD and

concentration. However, there is no clear physical explanation about the spectra subtraction used

in the calibration. We suspect that the spectra subtraction might have reduced the scattering

impact of the background medium on the particle suspensions in the target. In addition, we have

set the boundary conditions (BC) coefficient as constant for all 10 wavelengths in the calibration.

We plan to implement a method that can provide optimized wavelength-dependant BC

coefficient, which should give better initial scattering spectra.

In summary, we have presented an approach for reconstruction of PSD and concentration

in heterogeneous turbid media from scattering spectra measured using MSDOT. Both

simulations and phantom results have shown that the PSD and concentration of polystyrene

spheres contained in the target can be reconstructed with 10-wavelength data available from our

current MSDOT system. We expect to apply the approach described in this section to in vivo

clinical data obtained from tumor-bearing breasts in the near future.

4.2 Imaging of Particle Size Distribution and Concentration in Heterogeneous Turbid
Media

In this section, we present for the first time images of particle size and concentration

using tissue phantom experiments where a target is embedded in a scattering medium. The

recovered images obtained are quantitative in terms of the target size and shape, and the particle

size and concentration in both the target and background media.

4.2.1 Methods and materials

The methods were described in above subsection. Phantom experiments were conducted

using our ten-wavelength DOT system (638, 673, 690, 733, 775, 808, 840, 915, 922 and 960nm).









Two sets of phantom experiments were conducted to demonstrate the overall approach for

imaging particle size and concentration using MSDOT. The cylindrical background phantom had

a radius of 25mm, an absorption coefficient of 0.005/mm (India ink as absorber) and a reduced

scattering coefficient of 1.0/mm (Intralipid as scatterer). A thin glass tube (9mm in inner

diameter, 0.4mm in thickness) containing polystyrene suspensions (Polysciences, Warrington,

PA) was embedded off-center in the background solid phantom. Two different types of

polystyrene spheres were used in the experiments: one had a diameter of 2.06 ctm and a

concentration of 0.52%, and the other had a diameter 5.66 ctm and a concentration of 2.62%.

The refractive index of the spheres and their surrounding aqueous medium are 1.59 and 1.33,

respectively.

4.2.2 Results and discussion

We first performed simulations to evaluate the sensitivity of particle sizing on the number

of wavelengths used. "Measured" cL~ spectra were generated using Eq. (8) with a=2.86 Cpm,

b=0. 145 Cpm and 4 =1.02% for 10, 20 and 50 wavelengths between 600 and 1000nm,

respectively. When 5% noise was added to each set of "measured" cL~ spectra, we found that the

relative errors of recovering the particle parameters were within 14% using the 10O-wavelength

spectra, while such errors were as low as 4% when 50-wavelength spectra were used. The Mie

theory fittings using the extracted parameters at 10, 20 and 50 wavelengths are shown in Figure.

4-5(a) where the exact spectra are also presented for comparison. We see that the 10-wavelength

spectra are able to provide quantitatively accurate reconstruction. We also performed simulations

to test the noise sensitivity when 1, 5, or 10% random noise was added to the 10-wavelength

spectra. The relative errors of the recovered parameters (a and 4) were calculated to be 3, 14,

and 17% for parameter a and 3, 11 and 14% for the parameter 4 However, the recovery of the










standard deviation was sensitive to noise, which had a relative error of 93% when 10% noise was

added.

A finite element mesh with 634 nodes was used for the DOT reconstructions. To show

the accuracy of the DOT reconstruction, Figure. 4-5(b) depicts the recovered C's spectra at a

typical node location in the target area for the 2.06 Cpm polystyrene case, in comparison with the

corresponding Mie theory fitting using the extracted particle parameters. And the DOT

reconstructed absorption and reduced scattering images for the 2.06 clm polystyrene case for all

ten wavelengths are shown in the Figure. 4-6. The recovered mean size and concentration at each

node are used for imaging display. Figure. 4-7 presents the reconstructed images of particle size

and concentration for the 2.06 and 5.66 ctm polystyrene cases. We immediately note that the

particle size and concentration of both the target and background are quantitatively imaged. The

reconstructed mean particle size and concentration in the background were found to be within

154.7~155.1nm and 0.92~1.21% for the 2.06 ctm polystyrene case, and 155.3~155.5nm and

1.17~1.95% for the 5.66 ctm polystyrene case, compared to 150nm and 1%, the equivalent mean

particle size and concentration of the actual Intralipid/Ink background. In the target region, the

recovered mean particle sizes are in the range of 1.31 to 2.25 cpm with average value of 1.72 ctm

for the 2.06 ctm polystyrene case and 3.48 to 5.97 CLm with average value of 4.62 ctm for the

5.66 ctm polystyrene case, while the reconstructed concentrations are in the range of 0.48 to

0.87% with average value of 0.65% for the 2.06 ctm polystyrene case and 1.76 to 2.70% with

average value of 2.25% for the 5.66 ctm polystyrene case. Similar to the simulations, we see that

the standard deviation recovery is sensitive to the noise. The maximum relative errors of the

extracted standard deviation are up to 67.9% and 84.9% for the 2.06 ctm and 5.66 ctm polystyrene

case respectively.










It should be noted that while only the recovered C's spectra were needed for particle

sizing, the absorption images were quantitatively reconstructed for the experimental two cases

studied [see Figs. 4-7(al)-4-7(al0); note that the absorption contrast between the target and

background was extremely low in both cases, resulting in strong artifacts along the boundary].

Others and we have recently shown repeated experimental evidence that the cross-talk between

CL, and CL's images can be minimized using CW based DOT reconstructions, suggesting that

future work involving phantom studies with different levels of absorption in the target are

feasible and worthy.

In our particle sizing, the refractive indices of the polystyrene suspensions and the

surrounding medium are important parameters and have been assumed known as a priori. In a

clinical situation, we can obtain these information empirically from the literature, or we can

ultimately recover the refractive indices of scatterers as we reconstruct the PSD and

concentration. In response to the possible perturbation of the glass tube used in the experiments,

we have previously shown that such perturbation was insignificant in the image reconstruction

In this work, we assumed that the scatterers are spherical. But in tissues, while larger scatterers

such as nuclei are spherical, the smaller scatterers such as mitochondria are ellipsoidal. A

possible solution to this is to consider a modified Wentzel-Kramers-Brillouin model (WKB)

theory for non-spherical particles as described in [63]. Compared with the diffuse reflectance

spectroscopy (DRS), our method can image the particle size and concentration in heterogeneous

media whereas DRS can only deal with homogeneous media. In addition, we believe our method

can provide more accurate particle sizes and concentrations than DRS, because DRS often is

based on analytical solutions to the diffusion equation with the assumption of infinite or semi-

infinite media.









In conclusions, we have demonstrated quantitative imaging of particle size and

concentration of heterogeneous turbid media using MSDOT. The choices of the 2.06 and 5.66

Csm polystyrene particles were intended to simulate typical mitochondria and nuclei,

respectively. The phantom results presented suggest that the method described in this section

may be applied for in vivo imaging of tissue morphology, adding more parameters for clinical

deci sion-making.

4.3 Experimental Results from Concentrated Suspensions with Bi-modal Particle Size
Distribution

A method directly based on more rigorous Mie scattering theory for the reconstruction of

particle size distribution and volume fraction has already been proposed and validated by a set of

phantom experiments in the above sections. A single particle size distribution was assumed and

the only one kind of particles was used in the phantom studies. In pure optical spectroscopy

studies, it has been shown that scattering spectra are correlated with tissue morphology.42, 82-83, 85

These experimental studies had suggested that both nuclei and mitochondria contributed to tissue

scattering significantly. But it remained unclear how much the contribution of nuclei and

mitochondria was to the scattering.

In this section, two kinds of particles with different diameters and volume fractions were

mixed together and their contributions to the scattering were studied experimentally. This section

was organized as follows. Subsection 4.3.1 discussed the experiment system and phantom

materials. The experimental results and discussion were in subsection 4.3.2. Finally, the

subsection 4.3.3 was about the conclusions.

4.3.1 Experimental system and materials

The ten wavelength (638, 673, 690, 733, 775, 808, 840, 915, 922 and 965 nm), the

experimental system and its calibration have already been described in detail elsewhere.40, 71 I









this section, two dimensional images were reconstructed. Only fiber probes of 16 sources and 16

detectors located in one layer were used for the 256 measurements at each wavelength.

The cylindrical background phantom had a radius of 25mm, an absorption coefficient of

0.005/mm (India ink as absorber) and a reduced scattering coefficient of 1.0/mm (Intralipid as

scatterer) at wavelength of 808nm. A thin glass tube (9mm in inner diameter, 0.4mm in

thickness) containing polystyrene suspensions (Polysciences, Warrington, PA) was embedded

off-center in the background solid phantom. Three sets of experiments were performed. The

targets were composed of two kinds of polystyrene suspensions and water, as shown in Tables 4-

4, 4-5, and 4-6, respectively. For experiment set 1, there were 5 cases, with fixed volume fraction

1.255% of polystyrene with diameter of 6Cpm and decreased volume fraction from 1.255% to

0.05% for polystyrene with diameter of 1lym. For experiment set 2, there were four cases, with

fixed volume fraction 0.77% of 1lym polystyrene spheres and volume fraction of 6Cpm

polystyrene spheres reduced from 0.7% to 0. 1%. In the 3 cases of experiment set 3, the volume

fraction of 6Cpm polystyrene spheres was fixed on 1.255% and other kind of polystyrenes spheres

had different diameters and volume fraction concentrations for each of 3 cases, as shown in

Table 4-6.

4.3.2 Experimental results and discussion

For all the 11 experimental cases in the three sets, the absorption coefficient image and the

reduced scattering coefficient image at each of ten wavelengths were reconstructed using our

CW DOT algorithm although only the reduced scattering coefficient images were used for the

further particle size and volume fraction extraction. For each case at each wavelength, the

preprocess method for searching initial value of absorption coefficient cta, CLs(1) and a was

implemented and the initial values corresponding to the global minimum error, which was the










square sum of the difference between the computed and measured photon density, resulted in the

best reconstruction image quality31. Figure. 4-8 plotted the reconstructed scattering images at

nine wavelengths for case 1 in experiment set 1, using the initial values at the global minimum

error. However, the boundary coupling coefficient a was supposed to be same approximately at

all wavelengths due to their same boundary conditions. Because of the system noise, the values

of a corresponding to the global minimum error at the nine wavelengths were not the same.

To see how much influences of the values of a at different wavelengths on the

reconstructed results, we assume the values of a at all wavelengths were same and the initial

values were chosen when the total initial searching error, which was the sum of the initial

searching error of all wavelengths, reached the minimum. For the casel in experiment set 1

(denoted as casel_1 or setl_1), the value of a was found to be 0.29 and the reconstructed

reduced scattering coefficient images were plotted in Figure. 4-9. One may see that the image

quality was worse than that of Figure. 4-8 since there were more artifacts in Figure. 4-9 because

the initial value at each wavelength was not corresponding to the one at the global minimum

error.

The target region in the scattering images was segmented and the reduced scattering

coefficient values of all nodes in the target were averaged. The average values at 10 wavelengths

for 5 cases of experiment set 1 were plotted in Figure. 4-10 and Figure. 4-11 The average values

in Figure. 4-10 were calculated from the images reconstructed with initial values at global

minimum error and in Figure. 4-11 from the images reconstructed with the fixed value of a at

different wavelengths. The point at wavelength 965 nm was ignored due to the worst image

quality. Only scattering values at nine wavelengths were used for further particle size and

volume fraction extraction. The extracted scattering spectra in Figure. 4-11 were used for the










further process because they resulted in more stable results than the spectra in Figure. 4-10. It

means that the same a value assumption at different wavelengths was critical for particle size

and volume fraction extraction. From both Figure. 4-10 and Figure.4-11, the scattering decreased

from case 1 to case 5 as the total particle volume fraction decreased. The slopes of the five

scattering spectra in Figure.4-11 decreased from casel to case5 as well.

Figure. 4-13 and Figure. 4-14 plotted the average values of reduced scattering coefficient

in the target at 10 wavelengths for experiment set 2 and set 3, respectively. All these values were

calculated from the images reconstructed with the initial values when the values of a at different

wavelengths were assumed to be the same. Once again, one could see that the scattering at the

tenth wavelength in Figure. 4-12 turned out to be abnormal due to the low signal noise ratio at

that wavelength and the values at that wavelength were ignored for the further process. In Figure.

4-12, the slope differences among the four scattering spectra were easy to see but the scattering

level differences were not.

One particle size distribution was assumed when the particle size and volume fraction

were extracted, although we mixed two different kinds of particles into the target. The extracted

particle size and volume fraction based on the scattering spectra from Figs. 4-11, 4-12 and 4-13

were shown in Tables 4-7, 4-8 and 4-9 for experiment set 1, set 2 and set 3, respectively. In

Table 4-7, the calculated scattering ratio was the ratio of the calculated reduced scattering

coefficient of 1 Cpm particles in the glass tube to the total calculated reduced scattering coefficient

from both kinds of particles. The volume fraction and the particle size distribution were known

so that the scattering coefficient was able to be calculated by Eq. (4-3). The volume fraction was

referred to as the volume concentration of 1 Cpm particles in the target. Similarly, in Table 4-8,

the calculated scattering ratio was the ratio of the calculated reduced scattering coefficient of