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Design and Evaluation of the Variable-Angle Slant-Hole Collimator for 3D Molecular Breast Imaging

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Title:
Design and Evaluation of the Variable-Angle Slant-Hole Collimator for 3D Molecular Breast Imaging
Creator:
Gopan, Olga
Place of Publication:
[Gainesville, Fla.]
Florida
Publisher:
University of Florida
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Language:
english
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1 online resource (5 p.)

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Biomedical Engineering
Committee Chair:
GILLAND,DAVID R
Committee Co-Chair:
HINTENLANG,DAVID ERIC
Committee Members:
ALLEN,KYLE
HOBERT,JAMES P
Graduation Date:
8/9/2014

Subjects

Subjects / Keywords:
Breasts ( jstor )
Collimators ( jstor )
Geometric angles ( jstor )
Image reconstruction ( jstor )
Imaging ( jstor )
Inhomogeneity ( jstor )
Lesions ( jstor )
Sloping terrain ( jstor )
Spatial resolution ( jstor )
Tumors ( jstor )
Biomedical Engineering -- Dissertations, Academic -- UF
breast -- collimator -- imaging -- spect
Genre:
bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
born-digital ( sobekcm )
Electronic Thesis or Dissertation
Biomedical Engineering thesis, Ph.D.

Notes

Abstract:
Purpose: The purpose of this work is to develop an improved method for 3D molecular imaging of the breast using limited angle SPECT. Methods: The proposed method uses a variable-angle slant-hole (VASH) collimator. Rather than rotate the camera around the breast, the VASH collimator allows limited angle, tomographic acquisition while the detector remains stationary and flush against the compression paddle. This design minimizes object-to-detector distance for high spatial resolution. Theoretical analysis is presented of VASH spatial resolution and sensitivity, including depth-of-interaction (DOI) effects and magnification. The theory is compared with Monte Carlo simulation results for a point source, a breast phantom including a compression paddle and a realistically segmented breast phantom with an inhomogeneous background uptake. A channelized Hotelling observer is applied to the evaluation of VASH using a lesion detection task, and the standard area-under-the-curve (AUC) metric is obtained. Experimental results are presented using a proof-of-concept VASH collimator constructed of brass and used to image a low energy, Am-241 source. Results: The theoretical model of the VASH system showed good agreement with Monte Carlo simulations based on spatial resolution, including DOI effects, and sensitivity. The DOI effect resulted in roughly a 2 mm loss in spatial resolution only in depth dimension; in the other two dimensions the spatial resolution was not affected by DOI. In terms of contrast-to-noise ratio (CNR) and AUC, VASH outperformed a parallel hole SPECT approach. In terms of CNR, VASH outperformed a planar approach when the background inhomogeneity level was greater than 20% and in discerning two overlapping lesions. The difference in VASH and planar AUCs was not statistically significant. The reconstructed images from the proof-of-concept VASH collimator demonstrated the expected image blur in the depth dimension due to limited projection angle effects. Conclusions: The proposed method for breast imaging using limited angle SPECT and VASH collimator demonstrated the potential for superior spatial resolution/sensitivity. In addition, the system design has advantages of simple detector motion, ability to image close to the chest wall and conducive to on-board biopsy and multi-modal imaging with mammography. ( en )
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Thesis (Ph.D.)--University of Florida, 2014.
Local:
Adviser: GILLAND,DAVID R.
Local:
Co-adviser: HINTENLANG,DAVID ERIC.
Statement of Responsibility:
by Olga Gopan.

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Resource Identifier:
969976944 ( OCLC )
Classification:
LD1780 2014 ( lcc )

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DESIGN AND EVALUATION OF THE VARIABLE ANGLE SLANT HOLE COLLIMATOR FOR 3D MOLECULAR BREAST IMAGING By OLGA GOPAN A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE R EQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2014

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2014 Olga Gopan

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To my family

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4 ACKNOWLEDGMENTS I would like to thank my research advisor, David Gilland for the advice and help that he has provided me over the last four years on this project. I would also like to thank the other members of my committee: David Hintenlang, Huabei Jiang, Yunmei Chen, Kyle Allen and James Hobert. The guidance of my committee has been a great help to me in being able to better communicate the results of my research. I would also like to thank all of my friends and family as well as the BME office staff for seeing me through this accomplishment.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 8 LIST OF FIGURES ................................ ................................ ................................ .......... 9 ABSTRACT ................................ ................................ ................................ ................... 12 CHAPTER 1 SPECIFIC AIMS ................................ ................................ ................................ 14 1.1 Specific Aim 1 ................................ ................................ ................................ .. 15 1.2 Specific Aim 2 ................................ ................................ ................................ .. 16 1.3 Specific Aim 3 ................................ ................................ ................................ .. 16 1.4 Specific Aim 4 ................................ ................................ ................................ .. 16 2 BACKGROUND AND SIGNIFICANCE ................................ ............................... 18 2 .1 Mammography ................................ ................................ ................................ 18 2 2 Nuclear Medicine Breast Imaging ................................ ................................ .... 1 9 2.2.1 Radiotracers ................................ ................................ ........................... 19 2.2.2 Scintimammography ................................ ................................ ............... 20 2.2.3 Dedicated Cameras ................................ ................................ ................ 22 2.2.3.1 Molecular breast imaging ................................ ............................ 22 2.2.3.2 Breast specific gamma imaging ................................ ................... 22 2.2.3.3 Advantages and disadvantages ................................ .................. 23 2.2. 4 Dosimetery ................................ ................................ ............................. 24 2.2. 5 Three dimensional Nuclear Medicine Breast Imaing .............................. 2 4 2.2.5.1 Single photon emission computed tomography ........................... 25 2.2. 5 .2 Positron emission tomography and positron emission mammography ................................ ................................ ...................... 25 2.2.5.3 Dual modality breast tomosy nthesis ................................ ............ 26 3 MOLECULAR IMAGING OF THE BREAST USING A VARIABLE_ANGLE SLANT HOLE COLLIMATOR ................................ ................................ ............. 29 3 .1 Introduction ................................ ................................ ................................ ...... 29 3.2 Methods ................................ ................................ ................................ ........... 29 3.2.1 Description of the VASH Collimator ................................ ........................ 29 3 .2.2 Spatial Resolution Analysis ................................ ................................ .... 3 0 3.2. 2 .1 Collimator geometry ................................ ................................ .... 30 3 .2. 2 .2 DOI effect ................................ ................................ .................... 33 3 .2. 2 .3 System spatial reso lution ................................ ............................. 34

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6 3.2 .3 Collimator Sensitivity Analysis ................................ ................................ 34 3 .2. 4 Monte Carlo Simulation Studies ................................ ............................. 35 3.2. 4 .1 Point source study ................................ ................................ ....... 36 3 .2. 4 .2 Simulated breas t phantom study ................................ ................. 37 3. 3 Results ................................ ................................ ................................ ............. 39 3. 3 .1 Point Source Spatial Resolution ................................ ............................. 39 3. 3 1 .1 Planar spatial resolution ................................ .............................. 39 3 3 1.2 Reconstructed spatial reso lution ................................ ................. 40 3 .3.2 Point Source Sensitivity ................................ ................................ .......... 40 3 3 3 Spatial Resolution/Sensitivity Trade off ................................ .................. 41 3 3 4 Simulated Breast Phantom Study ................................ ........................... 42 3. 4 Discussion ................................ ................................ ................................ ....... 4 3 3. 5 Summary and Conclusions ................................ ................................ .............. 45 4 SIMULATION OF AN ANATOMICALLY REALISTIC BREAST PHANTOM WITH INHOMOGENEOUS BACKGROUND UPTAKE ................................ ....... 57 4 .1 Introduction ................................ ................................ ................................ ...... 57 4 .2 Met hods ................................ ................................ ................................ ........... 58 4 .2.1 Modeling the Breast ................................ ................................ ................ 58 4 .2.2 Modeling Compression ................................ ................................ ........... 59 4 .2 .3 Modeling Inhomogeneous Background Uptake ................................ ...... 60 4 .2. 4 Two Tumor Study ................................ ................................ ................... 61 4 3 Results ................................ ................................ ................................ ............. 62 4 3 .1 Homogeneous Background Uptake ................................ ........................ 62 4.3.2 Inhomogeneous Background Uptake ................................ ..................... 62 4 3 3 2D VASH Image ................................ ................................ ..................... 63 4 3 4 Two T umor Study ................................ ................................ ................... 63 4 4 Discussion ................................ ................................ ................................ ....... 64 4.5 Summary and Conclusions ................................ ................................ .............. 65 5 CHANNELIZED HOTELLING OBSERVER IN THE EVALUATION AND COMPARISON OF VASH AND OTHER NUCLEAR MEDICINE BREAST IMAGING M ETHODS ................................ ................................ ......................... 72 5 .1 Introduction ................................ ................................ ................................ ...... 72 5 .2 Methods ................................ ................................ ................................ ........... 73 5 .2.1 Channelized Hotelling Observer Methodology ................................ ....... 73 5 .2. 1 .1 Hotelling observer ................................ ................................ ........ 73 5 .2. 1 .2 Channelized H otelling observer ................................ ................... 74 5 .2. 1 .3 Channel design ................................ ................................ ........... 75 5 .2 2 Monte Carlo Simulation of Test Data ................................ ...................... 75 5 3 Results ................................ ................................ ................................ ............. 77 5 3 .1 ROC Eval uation and Comparison of Methods in the X Y Plane ............. 77 5 .3.2 ROC Evaluation and Comparison of Methods in the X Z Plane ............. 78 5 3 3 Ev aluation at Inhomogeneous Background Uptake s .............................. 79 5 4 Discussion ................................ ................................ ................................ ....... 79

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7 5 .5 Summary and Conclusions ................................ ................................ .............. 81 6 EXPERIMENTAL EVALUATION OF A PROOF OF CONCEPT VASH COLLIMATOR ................................ ................................ ................................ .... 88 6 .1 Introduction ................................ ................................ ................................ ...... 88 6 .2 Methods ................................ ................................ ................................ ........... 88 6 .2.1 Proof of concept VASH Collimator ................................ ......................... 88 6 .2 .2 Mobile Gamma Imaging System ................................ ............................ 89 6 .2. 3 Am 241 Disk Source ................................ ................................ ............... 89 6 .2 .4 Comparison to Monte Carlo Simulations ................................ ................ 90 6 3 Results ................................ ................................ ................................ ............. 91 6 3 .1 Projection Image Results ................................ ................................ ........ 91 6.3.2 R econstructed Image Results ................................ ................................ 91 6 4 Discussion ................................ ................................ ................................ ....... 92 6 .5 Summary and Conclusi ons ................................ ................................ .............. 93 7 CONCLUSIONS AND FUTURE WORK ................................ ............................. 97 APPENDIX M ATLAB CODE FOR DETERMINATION OF CHO TEST STATISTICS .......... 101 LIST OF REFERENCES ................................ ................................ ............................. 104 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 118

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8 LIST OF TABLES Table page 3 1 Image quality metrics at both lesion locations (x y plane) ................................ .. 55 3 2 Image quality metrics at both lesion locations (x z plane) ................................ .. 56 4 1 Composition and density of breast tissue types ................................ .................. 71 4 2 Breast tissue activity concentrations for the simulated phantom ........................ 71 5 1 AUC and SNR for the VASH, planar and PH SPECT methods (x y) .................. 87 5 2 Res ults of tests for statistical significance between various methods ................. 87 5 3 AUC and SNR for the VASH and PH SPECT methods (x z ) .............................. 87

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9 LIST OF FIGURES Figure page 2 1 VA SH collimator in coronal slice with breast outline and compression paddle ... 28 3 1 VASH collimator construction ................................ ................................ ............. 47 3 2 Collimator hole geometry. ................................ ................................ ................... 47 3 3 Computing PSF FWHM for VASH. ................................ ................................ ..... 4 8 3 4 Magnification with VASH. ................................ ................................ ................... 4 8 3 5 The DOI effect for a slant hole collimator. ................................ .......................... 49 3 6 Equation 3 .......................... 49 3 7 Gamma camera and 3D phantom modeled by GATE. ................................ ....... 50 3 8 ROIs used with breast phantom. ................................ ................................ ........ 50 3 9 FWHM in the slant dimension as a function of slant angle. ................................ 51 3 10 PSF profiles for 30 slant angle with DOI effects. ................................ ............... 51 3 11 Reconstructed spatial resolution as a function of iteration number. .................... 52 3 12 Reconstructed point source image in the x z slice plane. ................................ ... 52 3 13 Sensitivity as a function of slant angle. ................................ ............................... 53 3 14 Relative sensitivity for VASH and a fictitious PH collimator that mantains equal spatial resolution with VASH over projection angle. ................................ .. 53 3 15 Normalized c ollimator sensitivity for VASH and PH collimators with equal average spatial resolution over all projection angles. ................................ ......... 54 3 16 Reconstructed breast phantom images (x y plane) and image quality metrics. .. 54 3 17 Reconstructed breast phantom images (x z plane) and image quality metrics. .. 55 3 18 Reducing VASH collimator penetration effects. ................................ .................. 55 4 1 Representational slices of the breast phantom before and after compres sion .. 66 4 2 Reconstructed breast phantom images (x y plane, homogeneous background) and image quality metrics ................................ ............................. 66

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10 4 3 Reconstructed breast phantom images (x y plane, inhomogeneous background (20%)) and image quality metrics ................................ .................. 67 4 4 Reconstructed breast phantom images (x y plane, inhomogeneous background ( 4 0%)) and image quality metrics ................................ .................. 67 4 5 Noise in planar and VASH images plotted as a function of background i nhomogeneity level when TBR = 10:1 ................................ .............................. 68 4 6 CNR in planar and VASH images plotted as a function of background inhomogeneity level when TBR = 10:1 ................................ .............................. 68 4 7 CNR in planar and VASH images plotted as a function of background inhomogeneity level for a range of TBRs ................................ ........................... 69 4 8 A planar image of the breast phantom with two tumors. ................................ ..... 69 4 9 VASH images of the breast phantom with two tumors, 1.5 cm apart. ................. 70 4 10 VASH images of the bre ast phantom with two tumors, 1 cm apart. .................... 70 5 1 Plot of the four frequency channels used in the CHO ................................ ........ 82 5 2 Images of frequency domain channels (top) and spatial domain templat es (bottom) ................................ ................................ ................................ ............. 82 5 3 Flowchart demonstrating the CHO process ................................ ....................... 83 5 4 ROC curves for the VASH, planar and PH SPECT methods using a 2D CHO (x y) ................................ ................................ ................................ ................... 84 5 5 AUC for each of the methods as a f unction of TBR ................................ ........... 84 5 6 AUC for each of the methods as a function of tumor size ................................ .. 85 5 7 ROC curves for the VASH and PH SPECT methods using a 2D CHO (x z) ..... 85 5 8 AUC for the planar and VASH methods plotted as a function of background inhomogeneity level when TBR = 1.5:1 ................................ ............................. 86 5 9 AUC for the planar and VASH methods plotted as a function of background inhomogeneity level when TBR = 2 .5:1 ................................ ............................. 86 6 1 Proof of concept VASH collimator mounted on a compact gamma camera ...... 94 6 2 Illustration of a manually actuated shearing mechanism ................................ ... 94 6 3 Photograph of the mobile imaging system ................................ ......................... 95

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11 6 4 Projection images of the source object for 3 different slant angles .................... 95 6 5 Planar images of the experimental (left) and simulated (center) Am 241 source and horizontal profiles (right) ................................ ................................ 96 6 6 Reconstru cted images of the experimental (left) and simulated (center) Am 241 source and horizontal profiles (right) ................................ .......................... 96 6 7 Reconstructed images of the experimental Am 241 source at different iteration numbers ................................ ................................ ............................... 96

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12 Abstract of Disse rtation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy DESIGN AND EVALUATIO N OF THE VARIABLE ANGLE SLANT HOLE COLLIMATOR FOR 3D MOLECULAR BREAS T IMAGING By Olga Gopan August 2014 Chair: David R. Gilland Major: Biomedical Engineering Purpose: The purpose of this work is to develop an improved method for 3D molecular imaging of the breast using limited angle SPECT. Methods: The proposed method uses a variable angle slant hole (VASH) collimator. Rather than rotate the camera around the breast, the VASH collimator allows limited angle, tomographic acquisition while the detector remains stationary and flush against the compression paddle. This d esign minimizes object to detector distance for high spatial resolution. Th eoretical analysis is presented of VASH spatial resolution and sensitivity, including depth of interaction (DOI) effects and magnification. The theory is compared with Monte Carlo simulatio n results for a point source, a breast phantom including a compression paddle and a realistically segmented breast phantom with an inhomogeneous background uptake A channelized Hotelling observer is applied to the evaluation of VASH using a lesi on detection task and the standard area under the curve (AUC) metric is obtained E xperimental results are presented using a proof of concept VASH collimator constructed of brass and used to image a low energy, Am 241 source.

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13 Results: The theoretical mod el of the VASH system showed good agreement with Monte Carlo simulations based on spatial resolution, including DOI effects, and sensitivity. The DOI effect resulted in roughly a 2 mm loss in spatial resolution only in depth dimension; in the other two di mensions the spatial resolution was not affected by DOI. In terms of contrast to noise ratio (CNR) and AUC VASH out performed a parallel hole SPECT approach. In terms of CNR, VASH out performed a planar approach when the background inhomogeneity level was g reater than 20% and in discerning two overlapping lesions The difference in VASH and planar AUCs was not statistically significant The reconstructed images from the proof of concept VASH collimator demonstrated the expected image blur in the depth dimens ion due to limited projection angle effects. Conclusions: The proposed method for breast imaging using limited angle SPECT and VASH collimator demonstrated the potential for superior spatial resolution/sensitivity. In addition, the system design has advan tages of simple detector motion, ability to image close to the chest wall and conducive to on board biopsy and multi modal imaging with mammography.

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14 CHAPTER 1 SPECIFIC AIMS The overall goal of the proposed research is to develop a new high resolution coll imation technique in nuclear medicine breast imaging to enhance the sensitivity and specificity of breast lesion detection. Breast cancer is one of the most common malignancies among women in the United States, and early detection is critical for improved survival probability. X ray mammography (MM) is currently the pr incipal breast imaging modality but suffers from low sensitivity and specificity in patients with dense breasts. In this subset of patients, nuclear medicine imaging of the breast can be use d as an adjunct to MM in the diagnosis of breast diseases. This approach uses a dedicated gamma camera system to image the distribution of 99m Tc sestamibi in the breast. Nuclear medicine breast imaging is minimally affected by breast density and has been s hown to provide superior sensitivity to MM in patients with dense breasts. While nuclear medicine breast imaging has shown promise and potential in the detection of breast cancer, it is unable to detect some small lesions due to low contrast images and th e obscuring of breast lesions radiotracer uptake in overlying, normal structures of the breast Incorporating tomographic imaging methods may improve the accuracy of breast imaging by overcoming the problem of overlapping tissues and may improve image qual ity by offering depth resolution and improved tumor contrast relative to planar imaging. For example, in MM, tomographic imaging has already been achieved through the use of a limited angle computational tomography (CT) method known as digital breast tomo synthesis (DBT). We propose to develop a limited angle emission tomography method to achieve tomographic imaging in nuclear medicine

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15 breast imaging. By acquiring limited angle tomographic images of the breast, this system aims to provide improved spatial resolution, contrast and depth resolution. The system design also facilitates co registration of the nuclear medicine images with DBT and MM images The proposed system promises to achieve these aims through the use of a new high resolution collimator kn own as the variable angle slant hole (VASH) collimator. Instead of being rotated around the patient, a camera equipped with a VASH collimator either remains stationary or is translated laterally. Different projections are acquired when a series of tungst lateral direction. Th is allows the camera to remain close to the breast during imaging and thus to achieve better spatial resolution in the reconstructed images. 1.1 Specific Aim 1 The first aim of this dissertation is t o theoretically analyze the imaging performance of the VASH collimator and to compare the performance both theoretically and with Monte Carlo simulation studies, to other nuclear medicine breast imaging methods Although sla nt hole collimators of various forms have been used for decades, a fundamental analysis of the unique spatial resolution and sensitivity characteristics of these collimators has not been previously presented. Theoretical analysis of the performance of slan t hole collimators in general and the VASH collimator in specific is presented along with the results of Monte Carlo simulation studies. The Monte Carlo studies are used to validate the theoretical analysis and to evaluate the imaging performance of the VA SH collimator with a simple, simulated breast phantom.

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16 1.2 Specific Aim 2 T he second aim of this dissertation is t o design an anatomically realistic breast phantom with inhomogeneous background uptake and use the phantom to evaluate the VASH system in Mon te Carlo simulation studies Superimposed structures from non uniform, normal tissue uptake can create background noise in the images of the breast and reduce the detection accuracy of nuclear medicine breast imaging modalities. Since this background upta ke has been shown to correlate spatially with parenchymal density, evaluation of these modalities would benefit from having a model of a realistically segmented breast with a realistic inhomogeneous background uptake. A breast phantom that is realistically segmented in terms of tissue type and sestamibi uptake was created from previously published data. An inhomogeneous background uptake was simulated by assuming different activity concentrations in the different tissues of the breast. 1.3 Specific Aim 3 T he third aim of this dissertation is t o further evaluate the VASH method for lesion detection using a mathematical model of the human observer, the channelized Hotelling observer (CHO). The CHO arises from statistical decision theory and has been shown to closely model the detection capabilities of human observers. The VASH method was compared to 2D planar imaging of the breast and to a 3D parallel hole single photon emission computed tomography method 1.4 Specific Aim 4 The fourth aim of this dissertatio n is t o build and test a simple prototype system of the VASH collimator A proof of concept VASH collimator was constructed of brass

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17 and designed to image a low energy source. Experimental results from this collimator are prese nted.

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18 CHAPTER 2 BACKGROUND A ND SIGNIFICANCE Except for non melanoma skin cancers, breast cancer is the most common malignancy among women in the United States. In fact, breast cancer accounts for approximately 28% of cancers among American women [1]. Approximately 12% of American wo men have a chance of developing invasive breast cancer at some time over the course of their lives [1]. In 2010, the American Cancer Society (ACS) expected 207,090 new cases of invasive breast cancer and 54,010 new cases of carcinoma in situ to be diagnose d in women in the United States [1]. The ACS also estimated that approximately 39,840 women in the United States would die from breast cancer in 2010, though death rates have been decreasing since 1990 [1]. Amongst other factors, earlier detection of brea st cancer through screening has undoubtedly attributed to these decreases. 2.1 Mammography Mammography (MM) is currently the principal imaging modality for breast cancer screening and detection. It relies on x rays to image the differences in density betw een tumors and the surrounding normal breast tissue The overall sensitivity of MM, defined as the fraction of actually positive cases that are correctly identified as positive at imaging is relatively high, ranging from 71 to 96% [2]. However, the sensit ivity of MM in women with dense or dysplastic breasts is considerably lower. Breast cancers in radiographically dense breasts are not easily detected on a mammogram since the attenuation of the x rays through the tumor is similar to the attenuation of the x rays through the surrounding dense glandular and fibrous tissue. An estimated 25% of women, most of whom are young women, have radiodense breasts [ 3 ]. In these

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19 women, the sensitivity of MM decreases to 68% [ 4 ]. The sensitivity of MM is also significant ly decreased in patients at high risk for breast cancer, in patients with breast prothesis or implants and in patients who had previously undergone radiation therapy, surgery or biopsy [2 ] [ 5]. In addition to its low sensitivity in certain subgroups of wo men, MM has a low specificity in accurately differentiating benign from malignant lesions. Specificity is defined as the fraction of actually negative cases that are correctly identified as negative at imaging The specificity for MM is reported to be as low as 10 to 35% for nonpalpable cancers [ 3 ]. Mammograms of benign and malignant lesions can be similar to each other, so when an abnormality indicative of malignant disease has been identified on a mammogram, the subsequent breast biopsy frequently result s in negative findings. In fact, only 15 to 30% of biopsies result in the diagnosis of cancer [6 ] [ 7]. 2.2 Nuclear Medicine Breast Imaging As a result of the low sensitivity and specificity of MM in patients with radiographically dense breasts [ 8 ], [9] researchers are evaluating other imaging modalities, such as contrast enhanced magnetic resonance imaging [ 10 ] [ 11 ], optical imaging [ 12 ], dedicated CT [ 13 ] [ 14 ] PET [ 15 ] [ 16 ] [ 17 ] and ultrasound, to either replace or serve as an adjunct to MM for b reast cancer detection. One example of a complementary imaging modality is nuclear medicine breast imaging a functional imaging technique that uses a gamma camera to image the activity of an injected radiotracer in the breast. 2.2.1 Radiotracers The r adiotracer is designed to accumulate preferentially in malignant tissues such as cancerous tumors. An ideal radiotracer would exhibit high activity in the tumor,

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20 but no activity within the normal breast tissue or in benign breast lesions [ 18 ] [ 27 ] The rad iotracer that is most commonly used in nuclear medicine breast imaging is 99m Tc sestamibi (Cardiolite or Miraluma; Bristol Myers Squibb Medical Imaging, Inc., Billerica, MA). 99m Tc sestamibi is a small lipo philic cation of technetium, whic h concentrates ap proximately 90% of its activity in the mitochondria [ 18 ]. Initially used in myocardial perfusion imaging, it was approved for nuclear medicine breast imaging by the Food and Drug Administration in 1997 [ 3 ]. Its uptake in breast cancer is determined by seve ral biological factors, including the type, size and grade of the tumor, and depends on regional blood flow, plasma and mitochondrial potential, angiogenesi s and tissue metabolism [ 19 ] [ 22 ] Ano ther commonly used radiopharmaceutical for breast cancer dete ction is 18 F FDG (fluorodeoxyglucose) [ 3 ], and it is primarily used as a radiotracer for positron emission tomograph y 2.2.2 Scintimammography The use of the radiotracer, 99m Tc sestamibi and a conventional gamma camera to image the breast is termed scint imammography (SM). The conventional gamma camera has a large field of view and is designed primarily for whole body imaging. The current procedure guidelines for conventional gamma cameras recommend the use of a high resolution collimator for all lesions a nd the use of an ultrahigh resolution collimator for sub centimeter lesions [ 28 ], [ 29 ]. The injected dose of 99m Tc sestamibi ranges from 20 to 30 mCi (from 740 to 1100 MBq) [ 3 ] [ 23 ]. Images are usually acquired for ten minutes and as soon as five to 15 m inutes after the injection of the radiotracer [ 3 ]. The patient is imaged in either a prone position, with the breast pendulant, or in a supine position [ 30 ].

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21 In the detection of primary breast cancer, SM exhibits an average sensitivity of 84% and specific ity of 86% [ 3], [ 31 ] [ 35 ] SM is also helpful in identifying axillary lymph node involvement in patients with primary breast cancers [ 36 ] [ 37 ]. According to the Society of Nuclear Medicine, 99m Tc sestamibi breast imaging is clinically indicated for certa in subgroups of patients. The s ubgroups of patients that benefit from SM include: Women with m ammographically dense breast tissue The sensitivity of SM in fatty breasts is similar to its sensitivity in dense breasts [ 38 ]. As a result SM has demonstrated the potential to complement MM in women with radio dense breasts [ 39 ] [ 40 ] [ 41 ]. Women with a rchitectural distortions in breast tissue or scarring from prior biopsies, surgery, radiation therapy, chemotherapy or implants [ 3] [ 5 ] [ 31 ] [ 42 ] Women at hi gh risk for breast malignancy Women with indeterminate breast abnormalities Women with q uestionable microcalcifications Women previously diagnosed with breast cancer for i dentifying multicentric, multifocal or bilateral breast cancer Women undergoing preop erative chemotherapy for m onitoring tumor response [3], [ 23 ]. On the other hand, some limitations to SM are : Poor spatial resolution of the gamma camera particularly for imagin g of sub centimeter lesions. T he reported sensitivity of SM for detecting sub centimeter cancers is 35% to 64% [ 34 ] [ 43 ] [ 48 ] Limited ability to depict lesions in the me dial portion of the breast [6] Inability to image the breast in positions comparable to mammography, which makes it difficult to correlate mammographic findings wi th s cintimammographic findings [6] Difficulty in imaging breast tissues proximal to the thoracic wall [ 49 ] due to large inactive area s at the edge of the detector Increased radiation doses as compared to mammography

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22 2.2.3 Dedicated Cameras To more effecti vely image the breast, smaller cameras have been introduced to replace the conventional gamma cameras. The compact design of these dedicated cameras improves the imaging geometry and allows a multitude of image orientations [ 50 ] [ 60 ] Dedicated cameras ha ve minimal dead space at the edge of the field of view, enabling the breast to be placed directly on the detector [ 61 ]. As a result, the distance between the breast lesion and the detector is minimized and hence spatial resolution is improved. Dedicated cameras not only offer superior intrinsic spatial resolution but also superior energy resolution [ 62 ] as compared to conventional gamma cameras. 2.2.3.1 Molecular breast imaging One example of nuclear medicine imaging that uses a dedicated gamma camera i nstead of a conventional gamma camera to image the breast is molecular breast imaging (MBI). In particular, MBI uses cadmium zinc telluride ( CZT ) based cameras with small fields of view and high sensitivity collimators to generate planar images of mildly c ompressed breasts [ 49 ] [ 63 ] [ 65 ]. The breast is imaged in a similar orientation to the standard cranio caudal (CC) view used in mammography [ 28 ]. In recent stud ies MBI was shown to detect 92% of all lesions, 86% of lesions smaller than 1 0 m m and 29% of lesions smaller than 5 mm [ 49 ] [ 66 ]. In another study, the addition of MBI to MM improved the detection of node negative breast cancer in dense breasts by 7.5 per 1,000 women screened by MM [ 41 ]. Using dual head dedicated gamma camera system for MBI furt her improved the sensitivity of the approach for all lesion sizes [ 60 ]. 2.2.3.2 Breast specific gamma i maging Another example of a nuclear medicine breast imaging with dedicated gamma camera s is breast specific gamma imaging (BSGI). In this system, the b reast is placed

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23 directly on the detector (NaI(Tl)) of the camera, mildly compressed and imaged in a similar orientation to the standard CC and medio lateral oblique (MLO) views used in MM [7]. BSGI provides superior resolution and sensitivity to SM in det ecting breast cancer, especially for non palpable and sub centimeter lesions [6 ] [ 7]. Retrospective studies with BSGI indicated an excellent overall sensitivity of 96% [ 40 ]. Further studies with BSGI reported sensitivities of 90% for tumors sub centimete r in diameter and 93% for invasive lobular carcinoma [ 40 ] [ 67 ] [ 68 ]. In recent prospective trials, BSGI resulted in a sensitivity of 88.8% and a specificity of 90% for lesions smaller than 1 cm [ 69 ]. 2.2.3.3 Advantages and disadvantages Advantages of BS GI and MBI over SM include: I ncreased flexibility in patient positioning and greater comfort to the patient [7 ] [ 70 ] R educe d image contamination from radiation scattered from th e heart and liver Localization and characterization of focal areas of radiotra cer up take before needle biopsy [7] Better visualization of breast tissue near the thoracic wall [7 ] [ 50 ] Acquisition of a full range of images CC, mediolateral (ML), lateromedial (LM), and oblique (O) without table interference Imp r oved lesion contrast, background uniformity and spatial resolution due to breast compression [7] Acquisition of image s comparable to those in MM (CC and MLO) for better spatial registration and co mparison between the se two modalities Disadvantages of BSGI and MBI include: U nre liability in detecting microcalcifications [ 65 ] Long imaging times Increased radiation doses with the injection of a radiotracer

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24 2.2.4 Dosimetry The radiation dose from the injection of 99m Tc sestamibi in SM, MBI and BSGI is higher than that delivered by a mammogram. Whereas the effective dose from 20 mCi 99m Tc sestamibi is approximately 7.9 mSv, a 2 view bilateral screening mammogram (digital) has an effective dose of only 0. 44 mSv [ 71 ]. Future improvements to MBI can potentially reduce the dose from the injection to 4 mCi or less, yielding effective doses of 1.3 mSv or less [ 62 ]. 2.2. 5 Three d imension al N uclear M edicine B reast I maging Wider application of molecular imaging of the breast, including the potential for use as a screening tool, requires a red uction in radiation dose and improved imaging methods to assure satisfactory image quality at lower dose. One approach to improve image quality is to use tomographic imaging methods, which generally offer improved contrast to noise ratio over planar method s. For x ray breast imaging, limited angle tomography, or digital breast tomosynthesis (DBT), has shown great promise in this regard. This method produces 3D images that provide depth resolution and improved contrast over MM. Recent studies suggest that DB T alone or in combination with full field digital MM improves detection specificity and sensitivity [ 72 ] [ 76 ]. The motivation for developing 3D methods for MBI/BSGI is similar to that for MM. superimposes on tumor uptake, especially in planar images, and reduces detection accuracy. This background uptake, which has been shown to correlate spatially with parenchymal density, can obscure visibility of small, low uptake lesions [ 77 ]. Additional motivation for 3D imaging is to provide improved localization for biopsy and depth

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25 information for more accurate spatial resolution recovery of the depth dependent detector response. 2.2. 5 .1 Single photon emission computed t omography One exa mple of 3D nuclear medicine breast imaging is single photon emission computed tomography (SPECT). In SPECT, the patient is injected with 99m Tc and imaged in either a prone or supine position [ 78 ] [ 79 ]. Compared to 2D nuclear medicine breast imaging metho ds, SPECT has several advantages including : Increased sensitivity when patients are imaged in the supine position [ 80 ] Improved contrast resolution Allows for comparison with MRI images of the breast, which are obtained in comparable positions Improved d etection of lesion s which are obscured in planar images by radiotracer uptake from th e heart or liver Characterization of multicent ric or multifocal lesions D etection of axillary metastases [ 38 ] [ 81 ] Disadvantages include: Reduced specificity when pati ents are imaged in the prone position [ 69] D ifficulties in maintaining close proximity to the breast for high spatial resolution as the camera rotates around the patient [ 38], [ 82 ] [ 83 ] 2.2. 5 .2 Positr on emission t omography and positron emission mammogra phy Another example of 3D nuclear medicine breast imaging is positron emission tomography (PET) [ 8 4] [ 9 1] In PET, the patient is injected with 10 to 20 mCi of FDG and whole body scanners are used to image a supine patient from the base of the skull to th e thighs [ 23 ]. In p osi tron emission mammography (PEM), the field of view is limited to the breast by using dedicated high resolution PET scanners. In this system (PEM

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26 Flex, Naviscan PET Systems, Inc., San Diego, CA) the patient is injected with approxim ately 10 to 15 mCi of FDG, the breast is mildly compressed and tomographic images analogous to those in MM are obtained [ 92 ] [ 9 4] PEM has been shown to have a high sensitivity for detecting breast cancer and excellent specificity of higher than 90% [ 9 3 ] [ 10 0]. 2.2. 5 3 Dual m odality breast t omosynthesis Nuclear medicine imaging can be used in conjunction with anatomically based imaging approaches to provide co registered functional and anatomical images of the breast. I nvestigations are currently underway to evaluate the usefulness of dual modality breast imaging. For example, both a dedicated breast SPECT/CT scanner and a dedicated breast PET/CT scanner are currently under development [ 101 ] [ 103 ]. In both scanners, the patient is imaged in the prone posi tion. However, in these approaches, the addition of CT is questionable since CT alone has low accuracy in breast imaging and results in increased radiation and corresponding radiation induced cancer risks [ 104 ] For this reason, the se methods would benefit from the addition of MM or even DBT (instead of CT) but t he pendant breast approach used in these methods makes co registration with MM or DBT difficult. Furthermore, the pendant breast approach is not conducive to performing biopsy if regions of c oncern are found during imaging. Recently, a dual modality device that combines DBT and limited angle SPECT was developed [ 105 ] [ 106 ]. This system demonstrated improved specificity and positive predictive value compared to DBT alone [ 105 ] [ 106 ] Unlike other du al modality imaging methods [ 101 ] [ 103 ] or even other dedicated breast SPECT imaging methods [ 78 ], [ 79 ] this approach [ 106 ] relies on the use of a flat compression paddle that is also

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27 used in conventional BSGI or MBI. The advantages of using a com pression paddle include reduced attenuation effects, ease of co registration with MM and/or DBT and capability for on board, image guided biopsy if regions of concern are found during imaging. A disadvantage to this system is that, as the gamma camera rotates arou nd the breast, it must be retracted from the breast due to the presence of the compression paddle. The retraction of the gamma camera from the breast degrades the spatial resolution of the system The purpose of this work is to improve on th e limited angle SPECT approach of [ 106 ] by developing a method for 3D molecular imaging of the breast that is designed to improve spatial resolution/sensitivity in an MM or DBT compatible system through the use of a unique collimation technique: the variable angle slant hole (VASH) collimator. Rather than rotate the camera around the breast, the VASH collimator allows limited angle, tomographic acquisition while the detector remains stationary and flush against the compression paddle (Fig. 2 1( A ) and ( B )). This design mi nimizes object distance for high spatial resolution. This collimation technique was originally proposed in 1983 for tomographic imaging of the heart [ 107 ]; however, the advantages of a rotating cardiac SPECT system with complete angular sampling and relati vely close object to detector distance have been preferred. For a gamma camera that is integrated with a MM or DBT system (i.e. utilizing a compression paddle), the limited angle approach has greater potential because of the difficulty in staying close to the object while obtaining complete angular sampling (Fig. 2 1( C )).

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28 A B C Figure 2 1. VASH collimator in coronal slice with breast outline and compression paddle (20 cm width). VASH maintains small object to collimator distance with projection angle compared to paralle l hole collimator (PH). (A) 0 projection, ( B ) 30, ( C ) PH collimator, 30.

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29 CHAPTER 3 MOLECULAR IMAGING OF THE BREAST USING A VARIABLE ANGLE SLANT HOLE COLLIMATOR 1 3.1 Introduction The purpose of this chapter is to evaluate the imagin g performance of the variable angle slant hole ( VASH ) collimator, including the spatial resolution/sensitivity trade off, compared with parallel hole (PH) single photon emission computed tomography ( SPECT ) Theoretical analysis of the performance of a VAS H collimator is presented along with the results of Monte Carlo simulation studies. Although slant hole collimators of various forms have been used for decades, a fundamental analysis of the unique spatial resolution and sensitivity characteristics of the se collimators has not been previously presented. The Monte Carlo studies are used to validate the theoretical analysis and to evaluate the imaging performance of the VASH collimator with a simulated breast phantom. 3.2 Methods 3.2.1 Description of the VASH Collimator The VASH collimator can be constructed of a stack of metal (e.g., tungsten) sheets, each containing an identical array of holes created by photo etching. A parallel hole collimator is created by vertically aligning the holes/septa of the s heets (Fig. 3 1 top). A slant hole collimator is created by shearing the sheets like a deck of cards (Fig. 3 1 bottom). Variable degrees of shearing will create variable slant angles. A simple method for actuating the shearing could involve a series o f wedges, machined for the desired slant angle, that push against the sides of the stack of sheets. We consider the 1 IEEE 2014 Reprinted with minor changes with permission from (O. Gopan, D. Gilland, A. angle slant hole IEEE Trans. Nuc. Sci. vol. 6 1, no. 3, pp. 1143 1152, 2014).

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30 case in which the shearing occurs in only one dimension, creating a variable slant hole configuration within the coronal plane, as illustra ted in Fig. 2 1( B ). We refer to the dimension of the detector plane in the direction of the slant as the slant dimension, and the perpendicular dimension as the non slant dimension. The VASH collimator is intended for use with compact gamma camera systems with active areas of 20 15 cm or 20 20 cm. These detectors are typically composed of either semiconductor materials, such as cadmium zinc telluride (CZT), or arrays of cesium iodide or sodium iodide crystals. For example, one commercially available com pact gamma camera system for breast imaging, the Dilon 6800 system (Dilon Technologies, Newport News, VA, USA), contains a 20 15 cm array of 3 3 mm sodium iodide crystals. 3.2.2 Spatial Resolution Analysis 3.2.2.1 Collimator geometry The standard fo rmula for the spatial resolution of a parallel hole collimator [ 108 ] is used in this analysis: (3 1) where R is the full width at half maximum (FWHM) of the collimator point spread function (PSF), d is the hole diameter, l is the hole length, and b is the object to collimator distance (for simplicity, we disregard the relatively minor effects of effective hole length [ 109 ] and collimator to image plane distance [ 108 ]). Fig. 3 2 ( A ) shows how the collimator hole geometry, namely d/l determines the collimator acceptance angle. Given this angle, the object to image plane distance, l+b determines the extent of the

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31 spread of incident photons on the image plane. The PSF is assumed to be triangular in shape, and so half this extent is e qual the FWHM, or R For the VASH collimator, spatial resolution changes with slant angle due to changes in the collimator hole geometry and the effective object to collimator distance. The hole length has a 1/cos dependence, due to the oblique path through the constant thickness collimator, and the effective object to collimator distance also has a 1/cos dependence due to the oblique path from the object to the collimator face. The hole diameter is affected d ifferently in the non slant and slant dimensions resulting in an anisotropic PSF for non zero In the non slant dimension, the hole diameter is constant with Therefore, the geometry is as that depicted in Fig. 3 2 ( A ) after replacing l /cos for l and b /cos for b This substitution in (3 1) results in the cos factors canceling out, and the spatial resolution in the non slant dimension, R n s is found to be equal to R The effect on spatial resolution from the increase in the effective object to c ollimator distance with is canceled by the increase in hole length, and spatial resolution is constant with in the non slant dimension. In the slant dimension, the effective hole diameter (perpendicular to collimator walls) has a cos dependence (F ig. 3 2 ( B )). As in [ 108 ], the limiting angles of photon acceptance angle can be determined from the geometry of the collimator holes. These limits are represented in Fig. 3 3(A ) as angles B and C. From this figure we observe x=l tan (3 2)

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32 (3 3) Using these formulas for angles B and C and the object to image plane perpendicular distance l+b, we can express the PSF full width based on x 1 and x 2 in Fig. 3 3 ( B ) where: (3 4) (3 5) Substituting (3 2) into (3 4), (3 3) into (3 5), summing the result and dividing by 2 gives the PSF FWHM: (3 6) which simplifies to R as given in (3 1). Thus, in the slant dimension the FWHM on the detect or plane is independent of slant angle and equal to the value at the 0 slant angle. Spatial resolution analysis in the slant dimension is complicated by the fact that the detector plane is oriented obliquely to the path of the incident photons (Fig. 3 2 ( B )). This results in a broadening, or magnification, of the projection image in this dimension, and the width of the measured PSF on the detector plane over estimates the effective PSF width. Fig. 3 4 shows that for both the PH (Fig. 3 4 ( A )) and slant hole (Fig. 3 4 ( B )) cases, the hole geometry determines the acceptance angle of incident photons and the width w of the PSF on the detector plane. For a point source positioned as shown, the shaded region defines the possible location of a backprojected r ay that would arise during reconstruction as a result of a photon detected from the point source. It is the

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33 width of this region perpendicular to the backprojected direction, that determines the reconstructed, or effective, spatial resolution. For th e slant hole case, cos The effective FWHM in the slant dimension, considering the magnification effect described above is: (3 7) It is interesting to note that this value for the effective spatial resolution in the slant dimension is equal to the res ult of substituting the dependent hole diameter ( d cos ) hole length ( l /cos ), and object to collimator distance ( b /cos ) for d l and b in the standard formula for the spatial resolution of a PH collimator given in (3 1): (3 8 ) 3.2.2.2 DOI effect Random variability in the depth of interaction (DOI) of the detected photon in the scintillator introduces variability in the positioning of the photon over the detector surface, which contributes to overall spatial resolution loss. A PSF for this effect can be derived based on the probability distribution of photon interaction in the scintillator. Fig. 3 5 shows a slant hole collimator at slant angle the scintillator beneath and a photon that interacts after traveling a distance doi through the crystal. The recorded position of this detected event on the detector plane is (assume = 0 when the photon interacts at the front surface of the s cintillator), which is equal to doi sin Based on exponential attenuation, we can express the probability of a photon interacting within some small distance as a function of doi given the linear attenuation coefficient for the photon in the scintill ator ( ):

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34 (3 9) Now substituting doi = / sin into (3 9) gives: (3 10) We define a point spread function for the DOI effect as: (3 11) Equation 3 11 is plotted in Fig. 3 6 fo r = 10 and 30 con sidering 140 keV photons and a 1 0 mm thick NaI(Tl) scintillator ( = 2.64 cm 1 ), which is used in BSGI systems. PSF DOI is asymmetric and reflects the fact that more photons interact at shallow depths in the scintillator than deep in th e scintillator. The effective width of PSF DOI in terms of its contribution to reconstructed spatial resolution is reduced by a cos factor due to the magnification effect, similar to collimator spatial resolution in the slant dimension. 3.2.2.3 System spa tial resolution The system spatial resolution can be modeled as the convolution of the (3 12) PSF c is defined as a Gaussian function with FWHM equal to R in the non slant dimension or R slant in the slant dimension. PSF int in the slant dimension is reduced in width by a cos factor due to the magnification effect. 3.2.3 Collimator Sensitivity Analysis Collimator point source sensitivity is defined by the solid angle of acceptance of the collimator. The sensitivity is proportional to the square of the hole diameter to length ratio for a PH collimator [ 108 ] [ 109 ]:

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35 (3 13) where K is a constant that depends on hole shape (e.g. hexagonal, circular), and t is the septal thickness. The right term containing t describes the hole packing fraction, and for low energy collimators, a typical value for this term is 0.8. For the VASH collimator, the 1/cos dependence of the hole length imparts a cos 2 factor to the collimator sensitivity. The cos dependence of the hole diameter (in the slant dimension only) imparts an additional cos factor to the sensitivity (excluding hole packing effect). Therefore, a cos 3 factor is required in (3 13) for VASH point source sensitivity in order to model the change in solid acceptance angle with Additionally, the packing fraction decreases with slant angle due to the change in hole diameter in the slant dimension We approximate that effect by replacing d in the packing fraction term with the mean of d in the non slant and slant dimensions. 3.2.4 Monte Carlo Simulation Studies Monte Carlo simulation was used to evaluate the imaging performance of the VASH collim ator and to validate the theoretical analysis. The GATE (Geant4 Application for Tomographic Emission) Monte Carlo code [ 110 ] [ 111 ] was used because of its ability to readily model gamma camera detectors including slant hole collimators. GATE has been ex tensively described and validated in the literature [ 111 ] [ 113 ]. The simulated gamma camera contained 24 cm x 18 cm, 1 cm thick NaI(Tl) scintillator, which is used in BSGI systems. In order to investigate the impact of the DOI effect, we simulated a NaI(T l) crystal both at its natural density (3.67 g/cm 3 ) and at an ultra high density (1x10 10 g/cm 3 ) in which the DOI effect would be negligible. The VASH

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36 collimator consisted of a stack of 128, 0.125 mm thick tungsten sheets (density 19.25 g/cm 3 ). The collim ator had hex shaped holes with hole length ( l ) of 16 mm, hole flat to flat width ( d ) of 1 mm and septal thickness ( t ) of 0.2 mm. The PH collimator for this study was identical to the VASH collimator at 0 slant angle. For all simulations, gamma rays from a 99m Tc source (140 keV) were simulated. An energy resolution of 15% and an intrinsic crystal resolution of 2.0 mm (FWHM) were modeled, and a 15% energy window centered on the photopeak was applied. The electromagnetic processes were simulated, including l ow energy Rayleigh interactions and standard photoelectric and Compton interactions, in the object, collimator and scintillator. The projection images had a matrix size of 128 x 96 pixels and a pixel size of 1.875 mm. 3.2.4.1 Point source study Projectio n images of a point source in air were simulated in order to assess spatial resolution (planar and reconstructed) and point source in air sensitivity. The point source had an activity of 0.37 MBq (10 from the front face of the collimator. Projection data were acquired over a slant angle range of scan time was used (13 hours). Pla nar spatial resolution was assessed in the projection data from 0 to 30. An image profile through the center of the point was obtained, and the FWHM was found using linear interpolation. Since the pixel size was less than one third of the expected FWHM, the half maximum was computed as half of the maximum pixel intensity in the profile.

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37 background to the point source projection data before reconstructing. The background projection data w ere that used in the simulated breast phantom study described in the next section. Before adding the background, point source data were scaled to create a 10:1 object:background ratio. Images were reconstructed using MLEM [ 114 ] considering a range of iter ation stopping points up to 100. In the reconstructed images, profiles through the center of the point in all three dimensions were obtained. The FWHM was obtained for each dimension after subtracting an estimate of the background intensity from the profi le. The background intensity was the average intensity in two, 10 pixel segments, displaced 10 pixels on each side of the peak. The FWHM was obtained from these profiles in the same manner as in the planar case. Point source sensitivity was computed from the projection images by summing the total counts and dividing by scan time. Sensitivity was measured in slant angles from 0 to 30. 3.2.4.2 Simulated breast phantom study A breast phantom was simulated in order to assess reconstructed image quality in a more realistic object, and reconstructed VASH images were compared to PH SPECT and planar images. To model a mildly compressed breast, a semi cylinder was defined with a radius of 8 cm and height of 5.5 cm. Fig. 3 7 shows the breast phantom in a scaled drawing next to the simulated camera. The background activity level was 5.92 kBq/cm 3 (160 nCi/cm 3 ). The breast contained two spherical tumors, both 10 mm in diameter and with a tumor to background activity of 10 to 1. The activity level in the breast pha ntom was representative of clinical Sestamibi breast imaging with an injected dose of 25 mCi, which results in breast activity concentrations from 38 nCi/ml to 176

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38 nCi/ml [ 115 ]. Both tumors were centered in the phantom in the z dimension (perpendicular to the detector face) at a depth from the top breast surface of 2.75 cm. In the x y plane, the first tumor, shown in Fig. 3 7 was placed at the center of the breast ([x,y] = [0 cm, 0 cm]), and the second tumor was placed at the periphery of the breast ([x,y] = [3 cm, 1.5 cm]). The x dimension is the slant dimension of the VASH collimator. The VASH data acquisition was 30, as in the point source study, with the camera positioned as shown in Fig. 3 7 The planar and PH SPECT used a collimator equivalent to V ASH with 0 slant angle. The camera position for the planar images was as shown in Fig. 3 8. The PH SPECT projection images were acquired as illustrated in Fig. 2 1( A ) and 2 1( C ): the camera rotated over 180 from lateral to medial (36 angles) while maint aining contact with the compression paddle (20 cm width) at all angles in order to minimize the object to detector distance. Thus, Fig. 2 1( A ) shows the camera position for planar, VASH at 0 slant angle and PH SPECT at mid orbit. For each method, 10 min ute scan times were used to represent clinical acquisitions. An ensemble of 10 projection datasets were generated in order to compute an ensemble average of the image quality metric, contrast to noise ratio, described below. Both VASH and PH SPECT data w ere reconstructed using MLEM with stopping points of 10, 50 and 100 iterations. MLEM did not include attenuation, scatter or detector response modeling. Linear interpolation was used for the projection and backprojection operations. Contrast to noise rat io (CNR), commonly used to assess signal detectability [ 116 ], was computed in images for each method. Tumor contrast and image noise were measured in each of the 10 ensemble images, then averaged for computing CNR. For

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39 VASH and PH SPECT, a reconstructed s lice (1.875 mm thick) through the center of the tumor was chosen. The tumor activity was obtained using a circular region of interest (ROI) that was centered on the tumor with radius 75% of the true tumor radius. The background activity was obtained using an annular ROI that surrounded the tumor (Fig. 3 8 ( A )). Tumor contrast was defined as (T B)/B, where T and B are the mean counts within the tumor and background ROIs, respectively. Image noise was defined as the standard deviation of the mean counts wit hin tumor size ROIs within the background region in the image. Twelve background ROIs were used as shown in Fig. 3 8 ( B ). CNR was computed for each tumor, then averaged across the two tumors. Tumor contrast, image noise and the ratio, CNR, are reported. 3. 3 Results 3.3.1 Point Source Spatial Resolution 3.3.1.1 Planar spatial resolution Fig. 3 9 shows planar spatial resolution results with and without DOI effect. FWHM in the slant dimension is plotted as a function of slant angle for a point source 5 cm from the collimator. Good agreement between Monte Carlo and theoretical is observed. As expected, the DOI effect causes an increase in the measured FWHM with slant angle. Recall from section 3.2.1.1 that there is a 1/cos magnification in the slant di mension; thus, the effective FWHM in terms of reconstructed spatial resolution is the measured FWHM times cos This is shown for the DOI case in Fig. 3 10 and indicates approximately constant FWHM with slant angle. The shape of the PSF profile from the M onte Carlo results is compared with the theoretical model in Fig. 3 1 0

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40 profiles due to septal penetration are absent in these results, which reflects the fact that the septal thickness (0.2 mm) of the simulated collimator achieves effective collimation. 3.3.1.2 Reconstructed spatial resolution Fig. 3 1 1 shows the reconstructed FWHM as a function of iteration number for all three dimensions with DOI effects (x is the slanting dimension; z is the depth dimension, or perpendicular to the detector face). Also included is the z dimension without DOI effects. The resolution in the x and y dimensions converges quickly, while the resolution in the z dimension (with DOI) steadily decreases but remains l arger than x and y after 100 iterations. At 100 iterations, t he resolution is 5.4, 6.7 and 7.1 mm in the x y and z dimensions, respectively The difference in spatial resolution in the x and y dimensions may be attributed to the anisotropic spatial resolution inherent in the projection images. Comparing the z dimension results with and without the DOI effect shows that this effect accounts for a 2 mm loss in spatial resolution in this dimension (in the x and y dimensions, results with and without DO I were similar). Fig. 3 1 2 shows reconstructed point source images (x z plane) with DOI at 2, 10 and 100 iterations and without DOI at 100 iterations. Evident is the elongated PSF in the z dimension and the reduction of this effect with iteration. Compari ng the 100 iteration images with and without DOI illustrates the impact of this effect on elongating the PSF in the z dimension. 3.3.2 Point Source Sensitivity Fig. 3 1 3 shows the measured point source sensitivity from the Monte Carlo simulation along wit h the theoretical prediction as a function of slant angle. The theoretical curve is the product of collimator sensitivity (3 13), detector efficiency and 37,000 e where is the linear attenuation coefficient

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41 of NaI(Tl) at 140 keV (2.64/cm), and T is the NaI(Tl) thickness (1 cm). Good agreement is observed between the Monte Carlo and theoretical results; differences between t he curves could be partially attributable to approximations in constant K in (3 13). 3.3.3 Spatial Resolution/Sensitivity Trade off The spatial resolution/sensitivity trade off with the VASH approach can be compared with the PH SPECT approach of Fig. 2 1 using the theoretical analysis described above. With VASH, high spatial resolution is maintained over projection angles due to small object to detector distance, but sensitivity decreases due to changes in the hole geometry. With the PH collimator, sensi tivity is constant with projection angle, but spatial resolution worsens due to the greater object to detector distance that is necessary when a compression paddle is being used (Fig. 2 1( C )). One way to compare these approaches on equal grounds is to com pare the collimator sensitivity between VASH and a fictitious PH collimator that changes its hole geometry (i.e. hole length) with projection angle to keep the PH spatial resolution equal with that of the VASH collimator. Fig. 3 1 4 shows the results of th is analysis for the VASH and PH collimators described above. At equal spatial resolution, VASH exhibits substantially improved sensitivity compared with PH; for example, at the 30 angle, the sensitivity for VASH is roughly twice that for PH. For this ana lysis, the VASH spatial resolution was the average of the non slant and slant dimensions and considered intrinsic spatial resolution and DOI effects. For example, at the 30 angle, the effective hole length = 18.5 mm, the effective object to collimator di stance = 57.7 mm, the average spatial resolution = 4.8 mm and the collimator sensitivity ( g ) = 1.17E 4. The PH spatial resolution was computed using (3 1), and b changed with projection angle to keep the detector in contact with the

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42 compression paddle, as in Fig. 2 1. For example, at the 30 angle, b = 93.3 mm, which required hole length l = 27.7 mm to achieve a spatial resolution (including intrinsic) equal to 4.8 mm. This change in hole length resulted in collimator sensitivity ( g ) = 6.12E 5. An alter native approach to compare the resolution/sensitivity trade off between VASH and PH SPECT is to fix the PH collimator hole dimensions to equalize the average spatial resolution over angles 0 through 30 for VASH and PH SPECT ( b = 5 cm). This was achieved for th e PH collimator with l = 22.7 mm, d = 1 mm and t = 0.2 mm. Fig. 3 1 5 shows the resulting normalized sensitivity for the VASH and PH SPECT and the advantage of VASH in this case. 3.3.4 Simulated Breast Phantom Study Fig. 3 1 6 shows the breast phant om images in the x y plane along with the actual phantom object (with breast border shown). Both VASH and PH SPECT were reconstructed using 50 iterations of MLEM. The slice thickness of the VASH and PH SPECT images is 1.875 mm. In terms of tumor contras t, the VASH images were superior to both planar and PH SPECT. The noise was best for the planar image and moderately better for VASH compared to PH SPECT. The lower noise in the planar image is not unexpected given this image contains all counts from the acquisition (compared to single slice images for VASH and PH SPECT) On the other hand, the VASH and PH SPECT images contain only a fraction of the counts of the planar image. Furthermore, there are no superimposed structures from non uniform, normal tiss ue uptake to create background noise. As a result, CNR was best in the planar image, and VASH was superior to PH SPECT of the 3D methods. For VASH and PH SPECT, the same trend in results was observed at lower (10) and higher (100) iteration values.

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43 Fig. 3 1 7 is similar in format to Fig. 3 1 6 but for the x z slice plane (z dimension is vertical; the planar image is not relevant). The z dimension blurring of the VASH images is apparent. The image quality metrics in this slice plane follow the same trend a s in the x y plane: VASH exhibits superior tumor contrast and comparable image noise, which translates to superior CNR. The VASH images exhibit non uniform intensity within the uniform activity background region, which could be due to a combination of att enuation and limited angle effects. Table s 3 1 and 3 2 summarize the results of the breast phantom study for both tumors. The computation time on a Linux workstation with dual 2.4 GHz AMD Opteron 200 processors was approximately 4.5 seconds per MLEM iterat ion. 3.4 Discussion The contrast, noise and CNR results presented here for VASH, planar and PH SPECT are relevant to breast imaging using a compression paddle. Other camera trajectories (and other choices of paddle size) may shift the nature of the resul ts. The results may also be affected by the use of resolution recovery methods incorporated into the iterative reconstruction [ 117 ], which have shown effectiveness in other breast emission tomosynthesis systems [ 118 ]. Furthermore, projection images in this study were reconstructed using a basic MLEM reconstruction method that did not include attenuation correction, system PSF modeling or scatter correction. The inclusion of these corrections into the reconstruction method will be the focus of future work an d may also shift the nature of the results, particularly the spatial resolution sensitivity tradeoffs as presented above. The collimator design described in this chapter is a theoretical design, and fabrication of the VASH collimator will undoubtedly meet with challenges. A mechanism

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44 for precisely aligning and moving the sheets during the acquisition may be expensive and not justify potential gain in image quality over rotating camera systems. Several viable designs are conceivable for the mechanism that actuates the slanting. In one design, the slanting is accomplished by a ball screw driven linear actuator coupled to a pair of paddles, which press on the lateral sides of the tungsten sheets. With a high torque, servo motor driven ball screw actuator in a precision feedback control loop, this approach allows a nearly continuous range of angles. At large slant angles, however, off axis forces imposed on the sliding sheets by the paddles will limit the effectiveness of this mechanism. More robust and accu rate mechanisms are readily conceivable, for example, electro mechanical placement of guide wedges, which can eliminate off axis forces. Although superior in precision and accuracy, these mechanisms limit the available slant angles to a finite and predeter mined set. While the tungsten sheets are manufactured with a smooth finish and low coefficient of friction, methods to reduce friction may be advantageous, for example, with coatings and polish. The VASH approach obviates the need to rotate the camera arou nd the object to achieve tomographic imaging. However, imaging a fixed field of view over a range of slant angles expands the x (lateral) dimension over which the detector must be positioned. This can be achieved either by translating the detector later ally with slant angle or by using a larger detector in the lateral dimension. The latter is advantageous from the standpoint of mechanical simplicity but incurs greater detector costs. Over a slant angle range of 30, a fixed object point 6 cm from the detector surface projects onto the detector over a lateral range of approximately 3.5 cm; thus, a 7 cm wider detector would be required with the stationary detector approach.

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45 The shearing distance the distance each sheet must translate relative to adjacen t sheets to achieve the desired slant angle depends on the sheet thickness: shearing distance equals the sheet thickness times the tangent of the slant angle. A design under consideration uses 0.2 mm sheet thickness, which results in 0.12 mm shearing dist ance for 30 slant angle. The shearing distance must be less than the collimator septal thickness to prevent gaps in the collimator walls that allow penetration for certain photon paths. Fig. 3 1 8 ( A ) illustrates this effect for a 30 slant angle and a shee t thickness that is twice the size of the septa thickness. This effect can be mitigated by either decreasing sheet thickness or increasing septa thickness. Alternatively, a slight variability can be introduced into collimator hole diameter, for example, b y making every other hole 10% narrower than the others. This is easily accomplished with photo etching and will have minimal effect on collimator spatial resolution. As Fig. 3 1 8 ( B ) shows, this restores proper collimation. 3.5 Summary and Conclusions Th is chapter evaluates a method for limited angle, breast SPECT imaging using a VASH collimator. The method has several attractive features: 1. The distance from the detector to the breast is minimized for high spatial resolution. 2. There is no detector orbiting motion necessary for reduced mechanical complication and cost. 3. The detector can be readily positioned adjacent to the chest wall for imaging this critical region. 4. The system is conducive to on board biopsy. 5. The system is conducive to multi modal image co registration with MM or DBT.

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46 The theoretical model of the VASH system showed good agreement with Monte Carlo simulations in terms of point source spatial resolution, including DOI effects, and sensitivity. For 140 keV photons and a NaI(Tl) scintillator, t he DOI effect resulted in roughly a 2 mm loss in spatial resolution only in the z or depth, dimension. In the simulated breast phantom study, the VASH approach out performed PH SPECT in terms of CNR in reconstructed images when a compression paddle was u sed. Based on the results of this study, we conclude that the VASH collimator approach with limited angle tomography offers the potential for improved image quality in molecular imaging of the breast.

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47 Figure 3 1 VASH collimator construction. (t op) without slanting, (bottom) with slanting. Drawings on right show a magnified, cut out section of collimator. A B Figure 3 2 Collimator hole geometry: ( A ) parall el hole collimator and (B) VASH collimator in the slant dimension.

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48 A B Figure 3 3 Computing PSF FWHM for VASH: ( A ) VASH hole geometry and limiting angles B and C. ( B ) PSF wid th. A B Figure 3 4 Magnification with VASH. ( A ) PH collimator, ( B ) VASH collimator.

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49 Figure 3 5 The DOI effect for a slant hole collimator. Figur e 3 6 Equation 3 1 1 plotted as a function of for = 10 and 30.

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50 Figure 3 7 Gamma camera and 3D phantom modeled by GATE. A B Figure 3 8 ROIs used with breast phantom for ( A ) tumor contrast and ( B ) CNR.

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51 Figure 3 9 FWHM in the slant dimension as a function of slant angle with and without DOI effect for theoretical (Th) and Monte Carlo (MC) results. Also shown is MC with DOI corrected for magnification (MC (DOI) cos ). Figure 3 1 0 PSF profiles for 30 slant angle with DOI eff ects.

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52 Figure 3 1 1 Reconstructed spatial resolution as a function of iteration number. Figure 3 12 Reconstructed point source image in the x z slice plane. The position with respect to the point source is shown (not to scale).

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53 Figur e 3 1 3 Sensitivity as a function of slant angle. Figure 3 1 4 Relative sensitivity for VASH and a fictitious PH collimator that maintains equal spatial resolution with VASH over projection angle.

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54 Fig ure 3 1 5 Normalized collimator sensitivity f or VASH and PH collimator s with equ al average spatial resolution over all projection angles. Figure 3 1 6 Reconstructed breast phant om images (x y plane) and image quality metrics (averaged over 10 ensembl e images at both lesion locations).

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55 Figure 3 1 7 Reconstructed breast phant om images (x z plane) and image quality metrics (averaged over 10 ensemble im ages at both lesion locations). A B Figure 3 1 8 Reducing VASH collimator penetration effects. Table 3 1. Image quality metrics at both lesi on locations (x y plane). CNR VASH Tumor 1 8.14 0.64 0.43 0.05 18.73 Tumor 2 7.44 0.83 0.44 0.12 16.87 PH SPECT Tumor 1 4.26 1.54 0.57 0.11 7.49 Tumor 2 3.64 0.86 0.54 0.01 6.71 Plana r Tumor 1 0.94 0.12 0.03 0.01 32.41 Tumor 2 0.97 0.14 0.04 0.01 28.76

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56 Table 3 2. Image quality metrics at both lesion locations (x z plane). CNR VASH Tumor 1 7.17 1.31 0.41 0.07 17.49 Tumor 2 5.4 9 1.25 0.44 0.04 12.46 PH SPECT Tumor 1 2.93 0.44 0.42 0.02 6.98 Tumor 2 3.71 0.61 0.40 0.05 9.25

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57 CHAPTER 4 SIMULATION OF AN ANATOMICALLY REALISTIC BREAST PHANTOM WITH INHOMOGENEOUS BACKGROUND UPTAKE 4.1 Introduction A prelimi nary method for 3D molecular imaging of the breast has been developed by our lab and has shown promising results (Chapter 3). Our previous work considered a simulated breast phantom with homogeneous background uptake ; however, evaluation of the VASH system and other breast imaging modalities would benefit from having a model of the breast with a realistic inhomogeneous background uptake [ 65 ]. Several computerized 3D breast phantoms have been created to date, based either on mathematical models or voxelizati on of real patient data. Computerized breast phantoms based on mathematical models are simplistic and provide an unrealistic model of the complex 3D anatomy of the breast. Furthermore, they are frequently limited in use to a single modality, usually mammog raphy and cannot be used for other applications such as molecular imaging of the breast [ 119 ] [ 124 ]. One phantom that is frequently used in nuclear medicine imaging research and that is realistic in representing the human anatomy is the four dimensional ( 4D) NURBS based cardiac torso (NCAT) phantom. However, the female breast in the NCAT phantom is modeled using only a simple outer surface and does not include any detailed anatomical structures [ 125 ] [ 128 ]. Another example of a computerized 3D breast phant om is based on voxelization of actual subject data and therefore offers realistic segmentation of the breast into its respective tissues (either adipose or glandular) [ 129 ] [ 131 ]. This type of computerized breast phantom is of great interest in our work si nce it will allow us to simulate an inhomogeneous background uptake by assuming differences in sestamibi uptake in the different tissues of the breast.

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58 The goal of the work described in this chapter is to create a voxelized breast phantom with realistic i nhomogeneous background uptake s by assuming a variety of activity concentrations in the different breast tissue types based on data available in the literature [ 115 ]. We will consider these phantoms in our evaluation and comparison of the VASH, PH SPECT an d planar imaging systems. 4.2 Methods Monte Carlo calculations were performed with the GATE (Geant4 Application for Tomographic Emission) Monte Carlo code [ 110 111 ]. The parameters of the simulated gamma camera system are listed in section 3 .2.4 The tumo r was simulated by modeling a centrally located, 10 mm diameter sphere with tumor to background activity ratios (TBR) ranging from 2.5:1 to 10:1. The acquisition protocol for each of the methods (VASH, PH SPECT and planar) is described in section 3 .2.4.2 For further comparison, slices of the 3D VASH image were summed together to create a 2D VASH image of the simulated breast phantom. 4.2.1 Modeling the B reast To approximate a realistically segmented breast, a phantom was created using an anatomically real istic MRI derived numerical breast phantom from previously published work [ 132 ]. The phantom contained a 3D grid of cubic voxels, where each voxel was initially 0.5 mm x 0.5 mm x 0.5 mm. The chosen phantom (ID 012304) was also classified according to its r adiographic density, defined by the American College of Radiology, as very dense breast (>75% glandular) [ 133 ]. This phantom was chosen because molecular imaging of the breast is particularly useful in women with radiographically dense breasts. This phant om was originally comprised of seven tissue types that differed in their dielectric properties: three classes of glandular tissue, three

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59 classes of adipose tissue and a transitional tissue, which had dielectric properties transitioning between glandular an d adipose tissue. For our study, voxels containing any of the three classes of adipose or glandular tissue were set to one tissue type (either adipose or glandular), with the density and composition shown in Table 4 1. The transitional tissue was approxim ated in the phantom as being a mixture of the two tissue types, with a mass fraction of 50% adipose tissue and 50% glandular tissue. 4.2.2 Modeling C ompression The original phantom was derived from a series of images of patients in a prone position and, c onsequently modeled an uncompressed breast. To model a compressed breast, we used a simple algorithm to simulate compression the breast was assumed to have constant volume and was compressed in one dimension (z) and elongated in the other two dimensions (x and y), on a voxel by voxel basis. This compression model did not assume compression with a paddle. If we assume that the voxel is compressed in the z dimension by a given factor, then the voxel needs to be extended in the x and y dimensions by one ov er the square root of the factor to ma intain the same volume. In mammography, the typical range of compressed breast thickness is from 5 to 7 cm [ 134 ]. The thickness of the simulated breast phantom before compression was 13.1 cm; hence, to model a breast c ompressed to a thickness of 5.5 cm, which falls within this typical range, the breast was compressed to approximately 60% of its original thickness In mammography, the compression plates induce a large body strain on the breast in the direction of compres sion. This strain can be greater than 50% and is very likely to reach 70% or 80% [ 135 ] [ 136 ]; therefore, the 60% strain assumed in the present study was clinically relevant.

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60 Each voxel in the phantom was compressed in the z dimension by a factor of 0.42 a nd extended in the x and y dimensions by a factor of 1.54. When describing a voxelized phantom in GATE, the code allows the user to specify the voxel size. To model an uncompressed phantom, the voxel size would remain 0.5 mm x 0.5 mm x 0.5 mm. To model th e compressed phantom, the voxel size would change to 0.77 mm x 0.77 mm x 0.21 mm. Even though the size of the voxel would change, the information contained in the voxel (material or activity concentration) would remain the same. Figure 4 1 shows representa tional slices of the phantom before and after compression. 4.2.3 Modeling I nhomogeneous B ackground U ptake To simulate inhomogeneous background uptake of sestamibi in the breast, different activity concentrations were assumed in the adipose, glandular and transitional breast tissues. An initial study to quantify sestamibi uptake as a function of tissue type found the mean uptake in glandular and adipose tissues ( standard deviation) to be 0.12 ( 0.39 ) and 0.11 ( 0.37 ) 3 respectively [ 115 ]. For each of the subjects in the study one breast was imaged using a SPECT CT system. The resulting CT images of the breast were first segmented into adipose and glandular tissues and then registered to the SPECT images For e ach patient, t he mean activity concentration and standard deviation were measured for the adipose, glandular and total breast tissues from the SPECT data using the CT based segmentation The va lues reported above correspond to the overall average activity concentration ( standard deviation) across the patient cohort. In the present study ac tivity concentrations ranging from 0.0877 to 0.1755 3 were assumed for adipose tissue, activity concentrations ranging from 0.1755 3 were assumed for glandular tissue and an activity concentration

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61 equal to the mean of these two concen 3 ) was assumed for the transitional tissue (see Table 4 2). These values fell within the standard deviations of the previously published mean concentrations and corresponded to differences ranging from 0% (homogeneous) to 100% in upt ake between adipose and glandular tissues. The percentage difference in uptake between these two tissues w as defined as: (4 1 ) and was used to define the level of background inhomogeneity. Contrast, noise and contrast to noise rat io ( CNR ) were computed in images for each of the methods. The methodology used to compute these image quality metrics is described in section 3 .2.4.2 Both VASH and PH SPECT were reconstructed using 50 iterations of MLEM. The slice thickness of the VASH a nd PH SPECT images wa s 1.875 mm. 4.2.4 Two Tumor Study To test the advantage and capability of tomosynthesis, tests were done using a phantom with two lesions that overlapped in the x y slice but not in the z dimension. Initially, t wo 10 mm tumors with TB R of 10:1 were placed at the center of the breast in the x y plane ([x,y]=[0 cm, 0 cm]), but at different depths in the z dimension. One tumor was placed at a depth of 1.5 cm from the top breast surface, and the other tumor was placed at depth s of 3.5 cm a nd 4 cm from the top breast surface, with an edge to edge distance of 1 cm and 1.5 cm between the tumors. Planar and VASH images of this phantom were acquired and compared.

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62 4.3 Results 4.3.1 Homogeneous Background Uptake Fig. 4 2 shows images of the brea st phantom with a homogeneous activity background (0% background inhomogeneity level) and high TBR ( 10:1) in the x y plane. The expected phantom image is also shown. In terms of tumor contrast, the 3D VASH images are superior to both the planar and PH SPE CT images. In ter ms of noise, the 3D VASH images are slightly better than the PH SPECT images, but noise is best for the planar image. As a result, CNR is also best in the planar image; however, of the 3D methods, VASH is superior to PH SPECT in terms of CNR. 4.3.2 Inhomogeneous Background Uptake Fig. 4 3 and 4 4 are similar in format to Fig. 4 2 but for a phantom with an inhomogeneous background uptake (20% and 40% background inhomogeneity levels, respectively). The contrast and noise for this phantom fo llow the same trend as for the phantom with the homogeneous background: VASH exhibits superior tumor contrast to both the planar and PH SPECT images and superior image noise and CNR to the PH SPECT image. However, while image noise is still best for the pl anar image, VASH images now exhibit comparable CNR to the planar images when the inhomogeneity level is 20% and superior CNR when the inhomogeneity level is 40%. Fig. 4 5 and 4 6 show noise and CNR in planar and VASH images plotted as a function of backgr ound inhomogeneity level when TBR = 10:1. In planar images, as the inhomogeneity level increases, the contrast remains the same, noise increases, and CNR decreases. In VASH images, as the inhomogeneity level increases, contrast stays constant and there is little to no effect on noise and CNR As a result, w hen the inhomogeneity level is higher than 20%, the VASH approach exhibits superior CNR to

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63 the planar approach. In both the planar and VASH images, the same trend in results is observed at lower values o f TBR (see Fig. 4 7). 4.3.3 2D VASH Image At all levels of background inhomogenei ty (Fig. 4 2, 4 3 and 4 4) the 2D VASH images exhibit comparable contrast to the planar images. However, since there is more noise in the 2D VASH images than in the planar i mag es, the 2D VASH images exhibit inferior CNR to the pl anar images. They also exhibit inferior CNR to the 3D VASH images. Since the 2D VASH image contains the same counts from the acquisition as the planar image, it is not clear to us why the 2D VASH imag e is not as good as the planar image in terms of noise and CNR This will be the subject of future studies. 4.3.4 Two Tumor Study We have shown that, while the detection properties of VASH are superior to those of PH SPECT, they are either inferior or, at best, comparable to those of the planar method for clinically realistic inhomogeneity levels of 20% or less [ 115 ]. The advantage of the VASH method over the planar method lies in its ability to provide depth information. Fig. 4 8 shows a planar image of t he breast phantom with two tumors that overlap in the x y plane but are spaced 1.5 cm apart in the z dimension. Even though two tumors are present in the phantom, only one tumor can be discerned in the image. Fig. 4 9 show s VASH images of the same phantom in the x z (coronal) and y z (sagittal) planes, along with vertical profiles through the center of the tumors. Two separate tumors can easily be discerned, either visually in the images or as two peaks in the pr ofiles. In addition, Figure 4 10 shows VASH i mages of the same phantom, but with tumors spaced 1 cm apart. At this 1 cm separation, the two tumors are also resolvable.

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64 4.4 Discussion In this work we evaluated the VASH design using a breast phantom with both homogeneous and inhomogeneous background activitie s and compared VASH to both planar and PH SPECT methods. The breast phantom in the present work was based on voxelization of actual subject data. Voxelized breast phantoms offer realistic segmentation of breast tissue; however, they are modeled af ter a single breast and do not represent the variability that is present in the patient population. Phantoms based on breasts of other patients vary in size, density and tissue distribution and may shift the nature of the results reported in this chapter. Furthermore, the current model used a simple compression algorithm that did not realistically deform the model and did not take into consideration the material and mechanical properties of the different breast tissues. To more realistically simulate the de formation of breast tissue under compression, finite element methods can be implemented [ 134 ] [ 135 ]. In finite element analysis, either a 2D surface mesh or a 3D volume mesh of the breast is generated from segmented breast images. Each of the mesh nodes i n the mesh are assigned the material and mechanical properties that define how the tissue will react to the mechanical loading exerted by the compression paddles. This mesh can then be used to simulate breast compression under certain loading conditions by 1) applying a prescribed uniaxial strain to the breast through a contact problem with rigid plates and 2) evaluating the displacement induced in the other dimensions in response to this strain [ 134 ] [ 135 ]. Finite element analysis will be the subject of f uture studies. To simulate a breast with an inhomogeneous background uptake, different activity concentrations were assumed for adipose, glandular and transitional tissues. The difference in uptake between adipose and glandular tissues ranged from 0%

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65 (homo genous background uptake) to 100%. However, an initial study to quantify sestamibi uptake as a function of tissue type found no preferential uptake of sestamibi by adipose or glandular tissues [ 115 ], with the largest reported difference in uptake between a dipose and glandular tissues equal to about 23%. In this initial quantification, only four subjects were included in the detailed segmentation analysis, while approxim ately 30 subjects are necessary to achieve a 95% confidence in total breast quantificatio n results [ 115 ]. Consequently, f urther studies are needed to provide greater confidence in the expected mean sestamibi uptake in different tissue types, and the results of these studies may shift the nature of our conclusions. 4.5 Summary and Conclusions A breast phantom with realistic inhomogeneous background uptake was developed for this work. The phantom was based on voxelization of real subject data and was used in the evaluation of the VASH method compared to planar and PH SPECT approaches. Differenti ating sestamibi uptake in the adipose and glandular tissues of the phantom created more background noise in the planar images and reduced the detection accuracy of this approach As a result CNR was better in the VASH images compared to the planar images for background inhomogeneity levels greater than 20%. Furthermore, the VASH method out performed the planar method in discerning two lesions that overlapped in the x y plane but not in the z dimension.

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66 Transaxial (x y) Coronal (x z) Sagittal (y z) Befor e Compression After Compression Figure 4 1. Representational slices of the breast phantom before and after compression. The breast was compressed to approximately 60% of its original thickness, which is typical in mammography. The compressi on model did not assume compression between plates. Figure 4 2. Reconstructed br east phantom images (x y plane, homogeneous background) and image quality metrics (aver aged over 10 ensemble images ).

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67 Figure 4 3. Reconstructed breast phantom images (x y plane, in homogeneous background (20%) ) and image quality met rics (averaged over 10 ensemble images ). Figure 4 4. Reconstructed breast phantom images (x y plane, in homogeneous background (40%) ) and image quality met rics (averaged over 10 ensemble images ).

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68 Figure 4 5. Noise in planar and VASH images plotted as a function of background inhomogeneity level when TBR = 10:1 Figure 4 6. CNR in planar and VASH images plotted as a function of background inhomogeneity level when TBR = 10:1

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69 F igure 4 7. CNR in planar and VASH images plotted as a function of background inhomogeneity level for a range of TBRs Figure 4 8. A planar image of the breast phantom with t wo tumors that overlap in the x y plane but not in the z dimension.

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70 x z (Co ronal) y z (Sagittal) Figure 4 9. VASH images of the breast phantom with two tumors, 1.5 cm apart in the z dimension along with vertical profiles through the center of the tumors. x z (Coronal) y z (Sagittal) Figure 4 10. VASH ima ges of the breast phantom with two tumors, 1 cm apart in the z dimension along with vertical profiles through the center of the tumors.

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71 Table 4 1. Composition and density of breast tissue types. Tissue Density (g/cm 3 ) Mass fraction (%) O C H N S Na P Cl Ca Adipose 1.02 52.7 33.2 10.6 3.0 0.2 0.1 0.1 0.1 0.0 Glandular 0.92 22.9 64.0 12.0 0.8 0.0 0.0 0.2 0.0 0.1 Table 4 2. Breast tissue activity concentrations for the simulated phantom. 3 ) Uptake difference (%) Adipose Glandular Transitional 0 0.1755 0.1755 0.1755 10 0.1667 0.1843 0.1755 20 0.1579 0.1931 0.1755 30 0.1492 0.2018 0.1755 40 0.1404 0.2106 0.1755 50 0.1316 0.2194 0.175 5 60 0.1228 0.2281 0.1755 70 0.1141 0.2369 0.1755 80 0.1053 0.2457 0.1755 90 0.0965 0.2545 0.1755 100 0.0877 0.2632 0.1755

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72 CHAPTER 5 CHANNELIZED HOTELLING OBSERVER IN THE EVALUATION AND COMPARISON OF VASH AND OTHER NUCLEAR MEDI CINE BREAST IMAGING METHODS 5.1 Introduction A preliminary method for 3D molecular imaging of the breast has been developed by our lab and has shown promising results ( c hapter s 3 and 4 ). Pixel CNR, as used in our previous work, was used to evaluate the VA SH, PH SPECT and planar method s over only one tumor size. Evaluations of each method would benefit from using a task specific metric, rather than the simple CNR, and from being done over a range of tumor sizes. Receiver operating characteristics (ROC) stud ies using human observers have proved useful for evaluating and comparing the detection properties of imaging systems [ 137 ]. Since these studies entail the participation of multiple human observers, they can be time consuming to conduct, so an emerging alt ernative to human observer studies is the use of computational model observers [ 138 ]. These model observers are especially useful in preliminary evaluations or if a large amount of methods are to be evaluated. A variety of model observers has been proposed [ 139 ], an example of which is the channelized Hotelling observer (CHO) that was proposed by Myers and Barrett in 1987 [ 140 ]. The method models the human visual system and has been shown to provide good correlation with human observer performance, even in relatively difficult detection tasks involving both correlated noise and random backgrounds [ 140 ]. The goal of the work described in this chapter is to evaluate the VASH method in terms of lesion detection compared to the planar and PH SPECT methods using the CHO method For the VASH and PH SPECT methods, the CHO will be applied to the 2D slice image through the center of the lesion.

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73 5.2 Methods 5.2.1 Channelized Hotelling Observer Methodology This study was based on a binary classification task for cla ssifying images of the simulated breast phantom as either normal (lesion is absent) or abnormal (lesion is present). In a binary classification task, two hypotheses exist for a given image: H 0 signal absent (e.g., lesion is absent) and H 1 signal present (e.g., lesion is present): (5 1) In (5 1), image vector f represents either a projection image or a 2D slice of a reconstructed image, b is the image vector of the background, n is a vector of the noise generated during the image acquisition, and s is the image vector of the the lesion (or signal object). For an image that is N x x N y in dimension, the vector f is M x 1 in dimension, where M = N x x N y The task we consider is a signal known exactly (SKE) task, meaning that the obser ver has full knowledge of the lesion location beforehand. 5.2.1.1 Hotelling o bserver Different computational observers exist, but the Hotelling o bserver (HO) is the optimal linear observer when the signal to noise ratio (SNR) is used as the figure of meri t since the HO maximizes the SNR. The HO SNR is calculated by first applying a template w (a vector with dimension equal to that of f) to an image vector f to produce a scalar value of the test statistic : (5 2) The test statisti c represents the likelihood that a lesion is present in the image corresponding to the given f and can be compared to a decision threshold to classify the image as either normal or abnormal. The means and variances of for a given class

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74 H 1 (signal pr esent) or H 0 (signal absent) can be used to calculate the HO SNR, which can be used as an image quality figure of merit: (5 3) The area under the ROC curve (AUC) is related to SNR by: (5 4) To estimate th e template w in equation 5 2 the HO methodology involves covariance matrix calculation and inversion : (5 5) The covariance matrix K is given by: (5 6) where n and m are the number of signal present and s ignal absent images, respectively, and and are the means of the signal present and signal absent images, respectively. To prevent bias, sets of training images are used to generate the template w and sets of testing images are used to calculate the test statistics 5.2.1.2 Channelized Hotelling o bserver To reduce the dimensionality of the HO computation, a channelized H otelling observer, or CHO, can be used. The CHO processes the image using a number of frequency channels or bands, based on the fact that humans are sensitive only to the total power in a series of frequency bands or channels rather than to individual frequencies. To apply the channels, image vectors are multiplied with a series of

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75 channel template image vectors, where each vector has dimensions eq ual to that of the image vector ( M x 1 ). Assuming a total of L channels u the i th channel response v i is given by: (5 7) where i = 1 : L Stacking the channel responses together results in a channelized data vector v : (5 8) The CHO uses the channelized data vector v instead of the image vector f to estimate the template w (equations 5 5 and 5 6 ) and to calculate the test statistics (equation 5 2 ) 5.2.1.3 Channel design To describe the set of channels u four rotationally symmetric frequency bands or channels were chosen. The start and width of the first channel were both 1/64 (or 0.015625) cycles per pixel. The pixel size was 1.875 mm. These channels have been shown to correlate well with human observe rs [ 141 ]. Fig. 5 1 shows a plot of the four channels. For each frequency band, spatial domain templates were calculated by taking the inverse F ourier transform of the frequency domain channels. The central 32 x 32 pixels of the resulting spatial domain tem plates were extracted. Fig. 5 2 shows the images of the four frequency domain channels and their respective spatial domain templates. The CHO process is further summarized in Fig. 5 3. 5.2.2 Monte Carlo Simulation of Test Data Three nuclear medicine breas t imaging methods were evaluated and compared using the CHO : our 3D VASH method, a 2D planar imaging method and a 3D PH

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76 SPECT method. The gamma camera system was simulated as described in section 3.2.4 and an anatomically realistic breast phantom was simu lated as described in section 4.2 The acquisition protocols for each of the methods are also described in section 3.2.4.2 Tumors were simulated by modeling four centrally located spheres of different diameters (2.5 mm, 5 mm, 7.5 mm, 10 mm), each of which had six different TBRs, or tumor to background activity ratios (1.5:1, 2:1, 2.5:1, 5:1, 7.5:1, 10 :1), for a total of 24 tumors. Images of the breast phantom without any tumors were acquired to create a signal absent image. Images of each of the 24 differe nt tumors were acquired and then a dded to the signal absent image to create signal present images. Relatively high count, low noise projection data were acquired by allowing the simulations to run for 20 minutes for each projection until noise in the proje ction data was low ( 10% ). N oise was defined as the standard deviation of all counts within a region of interest (defined within the background activity of the breast phantom) divided by the mean of the counts. In order to simulate the increased noise that results from clinical acquisition times (10 minutes) used to generate lower count data from this high count data [ 142 ]. This technique involved replacing each pixel value in the high count data with a sample from a binomi al distribution with number of trials n equal to the high count pixel value and probability of success p equal to the desired scale factor. The count thinning approach was used to scale the high count projection data by factors of 0.5 for the planar approa ch (1 projection image) 0.0385 for the VASH approach (13 projection images) and 0.0139 for the PH SPECT approach (36 projection images) so that the total acquisition time of each approach was 10 minutes. projection data w as

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77 12% for the planar approach, 44% for the VASH approach and 77% for the PH SPECT approach. For each approach, these values of noise were comparable to the noise measured in clinical count images that were not count thinned For each of the 24 signal pre sent images, 26 count thinned images were generated, for a total of 624 signal present images 312 testing and 312 training images. For the signal absent image, 624 count thinned images were generated for a total of 624 signal absent images 312 testing and 312 training images. The slice covering the centroid voxel of the lesion region was cropped to the channel template size (32 x 32), with the centroid voxel at the center of the cropped image. Images were evaluated in terms of the CHO SNR and AUC. A co de was written in the MATLAB (R2012b) language to calculate to test statistics for a set of input images. The ROCKIT software package developed at the University of Chicago [ 137 ] was then used to calculate the AUC for each method from the respective test s tatistics The SNR was calculated from the AUC using equation 5 4. The ROCKIT software package was also used to estimate individual ROC curves for each method and to compare the ROC curves of each of the methods. The AUCs for each of the methods were also compared and tested for statistical significance. A difference in AUCs was deemed statistically significant if the p value was less than 0.05. 5.3 Results 5.3.1 ROC Evaluation and Comparison of Methods in the X Y Plane Fig. 5 4 shows the ROC curves gener ated using a CHO applied to the x y slice for each of the metho ds and assuming a phantom with homogeneous background uptake The AUCs for each of the methods and the respective SNRs are listed in Table 5 1. The ROC curve for the planar method stays above t he other curves in all areas of

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78 the plot, representing superior values of AUC and SNR and, hence, superior detection. Of the 3D methods, the VASH curve stays above the PH SPECT curve in all areas of the plot. Table 5 2 compares the various pairs of method s using the ROCKIT code. This table indicates that the rankings of these methods are planar>VASH>PH SPECT. The differences between VASH as compared to PH SPECT are statistically significant, so we can conclude that the detection characteristics of the VASH and PH SPECT methods differ in the x y slice. However, the difference between VASH as compared to planar is not statistically significant at the p=0.05 level, so we cannot conclude that the detection characteristics of these methods differ. Fig. 5 5 and 5 6 show the results found by testing the CHO at different levels of TBR and tumor size. The figure shows that, for all methods, the AUC increases as both the TBR and tumor size is increased. In both plots, the planar images show superior AUC to the VASH an d PH SPECT images, and, of the 3D methods, the VASH images show superior AUC to the PH SPECT images. 5.3.2 ROC Evaluation and Comparison of Methods in the X Z Plane Fig. 5 7 shows the ROC curves generated using a CHO applied to the x z slice for each of t he 3D methods. The AUCs for each of the methods and the respective SNRs are listed in Table 5 3. The VASH curve stays slightly above the PH SPECT curve in all areas of the plot, resulting in comparable values of AUC and SNR. The p value calculated from the correlated bivariate chi square test statistic was 0.8792; as a result, we cannot conclude that the detection characteristics of the VASH and PH SPECT methods differ in the x z slice.

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79 5.3.3 Evaluation at Inhomogeneous Background Uptakes Fig. 5 8 shows th e AUC for the planar and VASH methods as a function of background inhomogeneity level when TBR = 1.5:1. At this TBR, the AUC of the planar method decreases with increasing inhom ogeneity level. This decrease is not unexpected due to the increase in image no ise depicted in Fig. 4 5. At other TBRs, there is little to no decrease of AUC with increasing inhomogeneity level. For example, Fig. 5 9 shows the planar and VASH AUC when TBR = 2.5:1. At this TBR, there is no change in planar AUC with inhomogeneity. F or the VASH approach, the AUC stays constant as a function of inhomogeneity level at all values of tested TBR. For all combinations of TBR and inhomogeneity level, the planar images show superior AUC to the VASH images; however, at the lowest level of TBR (1.5:1), the planar AUC begins to approach the VASH AUC as the inhomogeneity level increases. Consequently, when imaging very low contrast tumors in increasingly inhomogeneous backgrounds, the detection properties of the VASH method begin to approach those of the planar method. 5.4 Discussion In this chapter we evaluated the VASH method compared to the planar and PH SPECT methods in terms of lesion detection using the CHO method When the background uptake in the phantom was homogeneous, the results of the CHO study agree d with the CNR results from Chapter 4 the planar method wa s superior to the VASH and PH SPECT methods, and, of the 3D methods, VASH wa s superior to PH SPECT. However, when the background uptake wa s inhomogeneous, the results of the CHO st udy contradict ed the CNR results. For background inhomogeneity levels of more than 20%, the VASH approach was superior to the planar approach in terms of CNR ; however, it was inferior to the planar approach in terms of the CHO AUC Hence, we do

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80 not show im proved lesion detection using the VASH approach at increasing inhomogeneity levels, despite the improved image CNR. Hence, claiming improved pixel CNR alone does not necessarily imply improved lesion detection in VASH images. Furthermore, the CHO was insen sitive to background inhomogeneity, which casts doubt on how accurately the CHO models humans. We would expect humans to be sensitive to background inhomogeneity; however, human observer studies are needed to determine if humans are, in reality, sensitive to background inhomogeneity. Human observer studies are also needed to determine if the current model observer matches human observers for this set of images and, if not, if other model observers would further improve the fit with human data. Evaluation of each of these methods with other model observers may change the nature of the results. In the present work, each of the methods was evaluated using a 2D CHO. For the 3D imaging methods (VASH and PH SPECT), image quality in the depth dimension was evalu ated by applying the CHO to a coronal slice through the lesion. The 2D CHO methodology is useful in comparing VASH and PH SPECT to planar and other 2D imaging methods. However, when comparing the 3D methods amongst themselves, a 3D CHO may also be used. Th e 3D CHO models are multi slice models, built as a sequence of a 2D CHO and 1D HO, where the CHO is used to calculate a vector of metrics for each slice in the planar view and the HO is used to calculate the final scalar statistic of the model [ 143 ] Evalu ating VASH with a 3D CHO will be the subject of future studies. Each of the methods was evaluated using model observers which performed a binary detection task known as a signal known exactly (SKE) task, where the lesion

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81 locations are known beforehand. In reality, lesion locations are not known beforehand, so model observers which perform both lesion localization and detection may provide a greater degree of clinical realism. One way of extending the models used in SKE tasks from binary detection tasks to l ocalization detection tasks is through the use of scanning models, in which a multiclass observer examines every possible lesion location in an image. These multiclass observers have been shown to correlate well with human obs ervers in SPECT LROC studies [ 144 ]. 5.5 Summary and Conclusions This chapter evaluates a novel method for 3D molecular imaging (VASH) using an anatomically realistic breast phantom and the CHO methodology. The VASH approach out performed the PH SPECT approach in terms of the AUC. Whil e the AUC of the VASH method was inferior to that of the planar method, the difference in AUCs was not statistically significant, so we cannot conclude that the detection properties of the VASH and planar methods differ. Also, for highly inhomogeneous back grounds and very low contrast tumors, the AUC of the planar method began to approach the AUC of the VASH method.

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82 Figure 5 1. Plot of the four frequency channels used in the CHO. Figure 5 2 Images of frequency domain channels (to p) and spatial domain templates (bottom)

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83 Figure 5 3. Flowchart demonstrating the CHO process.

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84 Figure 5 4 ROC curves for the VASH, planar and PH SPECT methods using a 2D CHO (x y) Each of the methods was evaluated using a phantom with a homogene ous background uptake and over a range of TBRs and tumor sizes. Figure 5 5. AUC for each of the methods as a function of TBR and assuming a phantom with a homogeneous background uptake As expected, the AUC is approximately 0.5 when TBR = 1:1.

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85 Fig ure 5 6 AUC for each of the methods as a function of tumor size and assuming a phantom with a homogeneous background uptake Figure 5 7 ROC curves for the VASH and PH SPECT methods using a 2D CHO (x z).

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86 Figure 5 8. AUC for the planar and VASH methods plotted as a functi on of background inhomogeneity level when TBR = 1.5:1. Figure 5 9 AUC for the planar and VASH methods plotted as a functi on of background inhomogeneity level when TBR = 2.5:1.

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87 Table 5 1. AUC and SNR for the VASH, planar and PH SPECT methods (x y) VASH Planar PH SPECT AUC 0.82 0.85 0.75 SNR 1.3 1.47 0.94 Table 5 2. Results of t ests for s tatistical s ignificance between v arious m ethods (x y) Method 1 Method 2 AUC1 AUC2 p value Statistica lly Significant Planar VASH 0.0279 0.271 No Planar PH SPECT 0.1026 <0.0001 Yes VASH PH SPECT 0.0719 0.0044 Yes Table 5 3. AUC and SNR for the VASH and PH SPECT methods (x z) VASH PH SPECT AUC 0.8 2 0.81 SNR 1. 28 1.22

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88 C HAPTER 6 EXPERIMENTAL EVALUATION OF A PROOF OF CONCEPT VASH COLLIMATOR 6.1 Introduction Even though Monte Carlo simulations as used in our previous work, are increasingly used in nuclear medicine imaging to assist in the design of new medical imaging dev ices for emission tomography, questions can be raised about how closely the simulations approximate the real system. For this reason, we ultimately wish to build a prototype gamma breast imager incorporating the novel VASH collimator design and evaluate th e imaging performance of the device. In this chapter, initial experimental results are presented using a proof of concept VASH collimator constructed of brass and used to image a low energy source. 6.2 Methods 6.2.1 Proof of concept VASH Collimator A pro of of concept VASH collimator was constructed for experimental evaluation. The primary purpose of the prototype VASH collimator study was to investigate the effects of limited angle acquisition (30) on reconstructed image quality with a slant hole colli mator. In order to reduce costs, the collimator was made of brass and designed to image low energy emitters (Fig. 6 1). The collimator consisted of 16, 0.81 mm thick brass plates with machine drilled round holes, which created a hole length of 13.0 mm. The holes were 2 mm diameter with 1 mm septal thickness. The hole packing fraction of the proof of concept VASH collimator was smaller than that of a typical low energy collimator ( approximately 0.8) because the VASH collimator was made of brass and requir ed a larger septal thickne ss to reduce septal penetration

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89 A simple method for shearing the plates involved manually placing aluminum wedges on the lateral sides of the stack of plates (Fig. 6 1). As illustrated in Figure 6 2, a pair of precision ground, angle guide blocks (gray) was used to create each of the established VASH collimator angles. Each pair of blocks was identical and had a level, vertical side and an angled side. First, the blocks were inserted within the collimator housing and properly po sitioned using grooves at the bottom of the housing (Figure 6 2 (top)). Afterwards, the plates were sheared so that the edges of the plates contacted the angled side of the blocks, causing the angle of the holes to match the angle of the block (Figure 6 2 (bottom)). An adjustable screw attached to the level side of the block was used to fix the block in its position. A total of 12 aluminum wedges (or 6 wedge pairs) were used to achieve the 13 angular positions. The wedge pairs were accurately machined to ac hieve the desired slant angle. 6.2.2 Mobile Gamma Imaging System The collimator was adapted to an existing compact, mobile gamma imaging system previously developed at the University of Florida [ 145 ] [ 146 ]. Each detector in the mobile gamma imaging syste m has an area of approximately 25 x 25 cm 2 and is mounted on a mobile gantry system with a detachable computer and electronics rack (Figure 6 3). Furthermore, the detectors consist of pixilated NaI(Tl) ( 5.0 x 5.0 x 12.5 mm 3 with 5.5 mm pitch). The photo multiplier tube (PMT) readout uses position sensitive PMTs with high rate four analog outputs arranged in a 4 x 4 array for each detector to form the 25 x 25 cm 2 active detector area. 6.2.3 Am 241 Disk Source A small disk source (approx. 20 mm in diamete r and 1 mm in thickness) of Am 241, which has a primary photon emission energy of 60 keV, was imaged using a slant

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90 angle range of 30 and 13 slant angles (5 increments). Since the disk source was encapsulated in a planchet, it was impossible to accurate ly measure its diameter or thickness. Furthermore, the source exhibi ted signs of damage where areas of the foil were scratched out; hence, the active area of the source may actually be less than what The source was positioned directly on the collimator surface with the disk face parallel with the collimator surface. Projection data were acquired with approximately 20,000 counts per angle. Images were reconstructed by the MLEM algorithm described in C hapter 3 using 100 iterations. The voxel size of the reconstructed image was 5.6 x 5.6 x 5.6 mm. 6.2.4 Comparison to Monte Carlo Simulations For comparison, the GATE Monte Carlo code was used to simulate the prototype VASH collimator, mobile gamma camera detector and Am 241 disk source. The simulated VASH collimator was composed of brass, which was assumed to be a mixture of 30% zinc and 70% copper, with a density of 8.4 g/cm 3 The simulated gamma camera contained a 25 cm x 25 cm, 1.25 cm thick, continuous NaI(Tl) scintillator, since the version of GATE used in this study (version 5.0.0_p01) did not have the capability to model pixilated detectors. The source was modeled as a cylinder of radius = 10 mm, sitioned directly on the simulated collimator surface. Images were acquired with the same acquisition protocol and with approxim ately the same number of counts per angle as in the experiments and then compared to their experimental counterparts.

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91 6.3 Resul ts 6.3.1 Projection Image Results Fig. 6 4 shows the projection images of the Am 241 disk source using the proof of concept VASH collimator at three different angles of slant. Fig. 6 5 shows planar images of the disk source at 0 slant acquired from both the experiments and Monte Carlo simulations. Fig. 6 5 also compares the horizontal image profiles through the center of the disk source. Since the face of the disk source is parallel with the collimator face, the planar images show the expected circular i mage intensity. Compared to the experimental image and profile, the simulated image and profile are slightly wider. Since the disk source used in the experiments exhibits signs of damage where areas of the foil are scratched out, the active area of the sou rce may actually be less than what was measured and used in the simulations, accounting for the differences in image size and profile width between experiment and simulation. 6.3.2 Reconstructed Image Results Fig. 6 6 shows the reconstructed images and im age profiles in the x y (top) and x z (bottom) slices planes. Since x y plane is parallel with the disk face, the expected image intensity is similar to the planar image, and this is observed in the figure. The x z plane shows the degree of depth informat ion. In this plane, the source object in the z dimension (vertical) is effectively an impulse function. Consequently, the full width at half maximum (FWHM) of a profile through the center of the source should yield the degree of spatial resolution in the z dimension. The FWHM in this direction was approximately 10 mm. The figure reveals the blurring in the image in this dimension due to limited angle effects. The large voxel size of the reconstructed image may also account for the distortion of the disk ima ge in this dimension. The low intensity tails can

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92 be seen in the image profile, although this effect is not readily observed in the image. Experimental and simulated images of the disk source in the x z plane are comparable to each other. The slightly nar rower profile from the experiment occurs since the disk source is most likely thinner than the 1 mm approximated in the simulations. Figure 6 7 shows the reconstructed image of the disk source at different iterations. At low iteration numbers, there is sub stantial streaking in the z direction which reduces as the iteration number increases. 6.4 Discussion The primary purpose of the prototype VASH collimator study was to investigate the effects of limited angle acquisition (30) on reconstructed image qual ity with a slant hole collimator. This study differs in several aspects from the context of a VASH collimator intended for clinical imaging. This camera/collimator does not provide the high spatial resolution capability expected of a dedicated clinical bre ast imager. The collimator hole dimensions were chosen to meet a spatial resolution target (~10 mm at 50 mm distance) and to achieve effective collimation for low energy photons (~60 keV) by standard PH collimator design formulas [ 109 ]. Also, the 60 keV p hotons of Am 241 do not produce the same degree of DOI effects (see section 3 .2.2.2 ) as the 140 keV photons of Tc 99m. Finally, the frictional effects of the smaller brass plates likely differ from that of larger tungsten plates. Results from the experime ntal study were compared to results from a Monte Carlo simulation that mimicked the experimental setup. Slight differences were noted between the experiment and simulations and were probably due to unavoidable differences in simulating the real system with the Monte Carlo code. First, the material composition and density of the brass that was used to construct the prototype VASH

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93 collimator were not known and may have been different from those that were assumed in the simulation. Second, a continuous scintil lator was modeled for the simulation instead of the actual pixilated one, since the version of GATE that was used for this study was not capable of modeling pixilated detectors. Last, since the Am 241 disk source was encapsulated in a planchet, it was impo ssible to accurately measure its diameter or thickness. The estimates of the dimensions that were made (and that were used in the simulation) may not have reflected the actual dimensions of the source. Furthermore, damage to the source in the form of scrat ches to the Am 241 foil me ant that the activity of the source was not uniformly distributed and may have actually been 6.5 Summary and Conclusions A proof of concept VASH collimator was constructed for low energy imaging, and reconstructed images from this system demonstrated the expected image blur in the depth dimension due to limited projection angle (30) effects. The experimental results were found to be comparable to Monte Carlo simulations of this system. Initial results support the concept that a VASH col limator can be readily constructed, but further studies are warranted.

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94 Figure 6 1. Proof of concept VASH collimator mounted on a compact gamma camera. Shown on the collimator surface are the aluminum guide wedges that adjust the collimator slant angle Figure 6 2. Illustration of a manually actuated shearing mechanism.

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95 Figure 6 3. Photograph of the mobile imaging system (Photograph courtesy of M. T. for a bedside IEEE Trans. Nuc. Sci. vol. 57, pp. 206 213, 2010, Page 1, Figure 1 ) Figure 6 4. Projection images of the source object for 3 different slant angles ( 30, 0 and +30).

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96 Figure 6 5. Planar images of the experimental (left) and simulated (center) Am 241 source and horizontal profiles (right). Figure 6 6. Reconstructed images of the experimental (left) and simulated (center) Am 241 source and profiles (right). Top: x y plane (horizontal profile through the center of the object); Bottom: x z plane (vertical profile through the center of the object). Figure 6 7. Reconstructed images of the experimental Am 241 source at different iteration numbers.

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97 CHAPTER 7 CONCLUSIONS AND FUTURE WORK This dissertation investig ated a novel collimation technique for 3D molecular imaging of the breast, called the variable angle slant hole (VASH) collimator. Rather than rotate the camera around the breast, the VASH collimator allows limited angle, tomographic acquisition while the detector remains stationary and flush against the compression paddle. As a result, the distance from the detector to the breast is minimized for high spatial resolution. Other advantages of the VASH approach include reduced attenuation effects, ease of co registration with MM and/or DBT and capability for on board, image guided biopsy if regions of concern are found during imaging. Furthermore, there is no detector orbiting motion necessary for reduced mechanical complication and cost, and the detector can be readily positioned adjacent to the chest wall for imaging this critical region. In Chapter 3, a fundamental theoretical analysis of the unique spatial resolution and sensitivity characteristics of the VASH collimator was presented. Monte Carlo studies were used to validate the theoretical analysis and to evaluate the imaging performance of the VASH collimator with a simulated breast phantom. It was found that the theoretical model of the VASH system showed good agreement with Monte Carlo simulations in terms of point source spatial resolution, including DOI effects, and sensitivity. For 140 keV photons and a NaI(Tl) scintillator, the DOI effect resulted in roughly a 2 mm loss in spatial resolution only in the z or depth, dimension. In the simulated br east phantom study, the VASH approach out performed PH SPECT in terms of CNR in reconstructed images when a compression paddle was used. However, the planar images exhibited better CNR than both the VASH and PH SPECT

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98 images. Since the breast phantom was s imulated with a homogeneous background, there were no superimposed structures from non uniform, normal tissue uptake to create background noise in the planar images and reduce the detection accuracy of this modality. The goal of the work described in Chap ter 4 was to create a voxelized breast phantom with realistic inhomogeneous backgrounds by assuming a variety of activity concentrations in the different breast tissue types based on data available in the literature. It was found that differentiating sesta mibi uptake in the adipose and glandular tissues of the phantom created planar and, to a lesser degree, VASH images with increased noise and reduced CNR. Compared to planar images, VASH images exhibited superior CNR for uptake differences greater than 20%. However, an initial study to quantify sestamibi uptake as a function of tissue type found no preferential uptake of sestamibi by adipose or glandular tissues [ 115 ], with the largest reported difference in uptake between adipose and glandular tissues equal to about 23%. At these clinically relevant levels of uptake differentiation, planar images still exhibit superior CNR to VASH. Furthermore, the VASH method outperformed the planar method in discerning two lesions that overlapped in the x y plane but not i n the z dimension. As mentioned in Chapter 4 the phantom was modeled after a single breast and, as a result, was not representative of the variability present in the patient population. A future area of investigation is to evaluate and compare these meth ods with phantoms that vary in size, density and tissue distribution. Furthermore, the current model used a simple compression algorithm that did not realistically deform the model and did not take into consideration the material and mechanical properties of the

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99 different breast tissues. To more realistically simulate the deformation of breast tissue under compression, finite element methods can be implemented T he goal of the work described in Chapter 5 was to evaluate the detection characteristics of the VASH method in terms of lesion detection compared to the planar and PH SPECT methods. A 2D channelized Hotelling observer was used to evaluate reconstructed images from each of the methods on a central slice through the lesion. It was found that the VASH a pproach out performed the PH SPECT approach in terms of the AUC, and the differences in detection between the VASH and planar methods were not statistically significant. One interesting result of this study is that, as the background inhomogeneity level in creases, the AUC of the VASH methods stay constant and the AUC of the planar method only decrease s for very low contrast tumors. Superimposed structures from non uniform, normal tissue uptake create background noise in planar and, to a lesser degree, VASH images, and the presence of this noise in the image affects the ability of the computational model observer to detect low contrast lesions, especially in planar images. As a result, when imaging very low contrast tumors (TBR = 1.5:1) in increasingly inhomo geneous background, the detection properties of the VASH method begin to approach those of the planar method. A further area of investigation is to use a 3D CHO model to evaluate the detection properties of the VASH method compared to the PH SPECT method. The current CHO model can also be extended from a simple binary det ection task (where the location of all lesions is known beforehand) to a more clinically realistic localization detection task through the use of a scanning model, in which the observer exa mines every possible lesion location in an image.

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100 In Chapter 6 initial experimental results were presented using a proof of concept VASH collimator constructed of brass and used to image a low energy source. Reconstructed images from this system demonstra ted the expected image blur in the depth dimension due to limited projection angle (30) effects. The experimental results were found to be comparable to Monte Carlo simulations of this system. Initial results support the concept that a VASH collimator ca n be readily constructed; however, further studies with a dedicated clinical breast imager capable of imaging 99m Tc at high spatial resolutions are warranted. Based on the results of this dissertation, we conclude that the VASH collimator approach with lim ited angle tomography offers the potential for improved image quality in molecular imaging of the breast.

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101 APPENDIX MATLAB CODE FOR DETERMINATION OF CHO TEST STATISTICS %Specify size (m_dim_image x n_dim_image) of original 2D image. m_dim_image=128; n_di m_image=96; %Specify number of singal present (signal absent) images used for testing %(training). image_number= 312 ; %Specify size (m_dim_template x n_dim_template) of original spatial domain %template. m_dim_template=64; n_dim_template=64; %Spec ify size (m_dim x n_dim) of final spatial domain template. The central %m_dim x n_dim pixels of the original template will be extracted. The 2D %image will also be cropped to this template size, with the centroid voxel %of the lesion region at the center o f the cropped image. m_dim=32; n_dim=32; %Step 1: Generate frequency channels and spatial domain templates x=linspace( 0.5,0.5,(m_dim_template+1)); x(end)=[]; y=linspace( 0.5,0.5,(n_dim_template+1)); y(end)=[]; [xx,yy]=meshgrid(x,y); r=sqrt(xx.^2 + y y.^2); u=zeros(m_dim_template,n_dim_template); %Generate four rotationally symmetric frequency bands or channels. The start %and width of the first channel were both 1/64 cycles per pixel. for k=1:4 for i=1:m_dim_template for j=1:n_dim_temp late if r(i,j)>(2*(2^(k 1))/64) u(i,j)=0; elseif r(i,j)<((2^(k 1))/64) u(i,j)=0; else u(i,j)=1;

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102 end end end U=circshift(ifft2(circshift(u, [ m_d im_template/2 n_dim_template/2])), [m_dim_template/2 n_dim_template/2]); %Extract central o_dim x p_dim pixels of the resulting template. for m=1:m_dim for n=1:n_dim UU(m,n)=U(m+(m_dim_template m_dim)/2,n+(n_dim_template n_dim)/2); end end W(:,k)=UU(:); end size=size(W); %Step 2: Open 2D images, crop them to template size and channelize them. v_sp_test=zeros(image_number,size(2)); v_sp_train=zeros(image_number,size(2)); v_sa_test=zeros(image_number,si ze(2)); v_sa_train=zeros(image_number,size(2)); for i = 1:image_number sp_test = sprintf( 'SP/test/%d.rec' i); fid=fopen(sp_test); a1=fread(fid,[m_dim_image n_dim_image], 'float' ); fclose(fid); sp_train = sprintf( 'SP/train/%d.rec' i); fid=fopen(sp_train); a2=fread(fid,[m_dim_image n_dim_image], 'float' ); fclose(fid); sa_test = sprintf( 'SA/test/%d.rec' i); fid=fopen(sa_test); a3=fread(fid,[m_dim_image n_dim_image], 'float' ); fclose(fid); sa_train = sprintf( 'SA/train/%d.rec' i); fid=fopen(sa_train); a4=fread(fid,[m_dim_image n_dim_image], 'float' ); fclose(fid);

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103 %The 2D image needs to be cropped to the template size, with the centroid %voxel of the lesion region at the center of the crop ped image. In this %case, the centroid voxel is located at the center of the original image. for m=1:m_dim for n=1:n_dim A1(m,n)=a1(m+(m_dim_image m_dim)/2,n+(n_dim_image n_dim)/2); A2(m,n)=a2(m+(m_dim_image m_dim)/2,n +(n_dim_image n_dim)/2); A3(m,n)=a3(m+(m_dim_image m_dim)/2,n+(n_dim_image n_dim)/2); A4(m,n)=a4(m+(m_dim_image m_dim)/2,n+(n_dim_image n_dim)/2); end end %Images need to be channelized. v_sp_test(i,:)=A1(:)'*W; v_sp_train(i,:)=A2(:)'*W; v_sa_test(i,:)=A3(:)'*W; v_sa_train(i,:)=A4(:)'*W; fclose( 'all' ); end %Step 3: Calculate and display the CHO SNR and AUC. Save the test %statistics for signal absent and signal present images for use in the % ROCKIT program. sig_test=mean(v_sp_test) mean(v_sa_test); K=(cov(v_sp_test)+cov(v_sa_test))/2; w_hot=inv(K)*sig_test(:); lambda_sp=v_sp_train*w_hot; lambda_sa=v_sa_train*w_hot; SNR=sqrt(((mean(lambda_sp) mean(lambda_sa)).^2) / (.5*var(lambda_sp) + .5* var(lambda_sa))) AUC = .5+.5*erf(SNR/2) fid = fopen( 'sp.txt' 'wt' ); fprintf(fid, '%0.10f \ n' ,lambda_sp.'); fclose(fid); fid = fopen( 'sa.txt' 'wt' ); fprintf(fid, '%0.10f \ n' ,lambda_sa.'); fclose(fid);

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118 BIOGRAPHICAL SKETCH Olga Gopan was born in Moscow, Russia. She moved to the United States of America in 1993 and grew up in Wisconsin. She earned a B achelor of Arts in Mathematics and a B achelor of Applied Science in Physics from Northwe stern University in 2007, a Master of Science in Radiological Physics from Wayne State University in 2009 and a Doctor of Philosophy from University of Florida (UF) in 2014. After graduating from UF, she will begin working as a medical physics resident at Universi ty of Washi ngton in Seattle, WA.