Imaging Systems. Nooshin Kiarashi. Department of Electrical and Computer Engineering Duke University. Date: Approved: Loren W. Nolte, Co- Supervisor

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1 Towards Realizing Virtual Clinical Trials for Optimization and Evaluation of Breast Imaging Systems by Nooshin Kiarashi Department of Electrical and Computer Engineering Duke University Date: Approved: Loren W. Nolte, Co- Supervisor Ehsan Samei, Co- Supervisor Joseph Y. Lo, Co- Supervisor William P. Segars Sujata V. Ghate Matthew S. Reynolds Dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Electrical and Computer Engineering in the Graduate School of Duke University 2014

2 ABSTRACT Towards Realizing Virtual Clinical Trials for Optimization and Evaluation of Breast Imaging Systems by Nooshin Kiarashi Department of Electrical and Computer Engineering Duke University Date: Approved: Loren W. Nolte, Co- Supervisor Ehsan Samei, Co- Supervisor Joseph Y. Lo, Co- Supervisor William P. Segars Sujata V. Ghate Matthew S. Reynolds An abstract of a dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Electrical and Computer Engineering in the Graduate School of Duke University 2014

3 Copyright by Nooshin Kiarashi 2014

4 Abstract It is essential that breast cancer be detected at its earliest stages for better prognosis. Advanced imaging techniques and systems are constantly under development and study to improve the screening and detection of breast cancer. Like every technological advancement in medical care, these techniques and systems need to be tested and verified before their clinical translation. What are currently considered the gold standard for justification of clinical translation are clinical trials. Clinical trials are time- consuming, costly, and expose the population to extra irradiation in the case of x- ray imaging. Given the recent advances in computation and modeling, virtual clinical trials can be carefully designed and carried out to inform, orient, or potentially replace clinical trials given adequate validation and credibility. This dissertation elaborates on the design, implementation, and performance analysis of virtual clinical trials, which is made possible through the employment and advancement of sophisticated tools and models. iv

5 Dedication To my fabulous parents, Dr. Nahid Mirhedayati and Dr. Majid Kiarashi, my precious siblings, Ms. Niousha Kiarashi and Mr. Koosha Kiarashi, and my partner in life extraordinaire, Dr. Babak Parkhideh with all my love, gratitude, and respect. v

6 Contents Abstract... iv List of Tables... ix List of Figures... x Acknowledgements... xv 1. Introduction Digital Breast Tomosynthesis: A Concise Overview Abstract Introduction Image Acquisition Reconstruction and Image Handling Clinical Experience and Implementation Advanced Applications Conclusion Development and Application of a Suite of 4D Virtual Breast Phantoms for Optimization and Evaluation of Breast Imaging Systems Abstract Introduction Methods Results Discussion Conclusion vi

7 4. Development of Realistic Physical Breast Phantoms Matched to Virtual Breast Phantoms Based on Human Subject Data Abstract Introduction Methods The Virtual Breast Phantoms Design and Fabrication of the Physical Breast Phantoms Validation of Physical Breast Phantoms Results Discussion Conclusion The Impact of Breast Structure on Lesion Detection in Breast Tomosynthesis Abstract Introduction Methods Population Modeling Lesion Modeling Image Formation Observer Modeling Detection Paradigm Test and Training Datasets Detection Analysis vii

8 Effect of Background Tissue Density Uncertainty Effect of Lesion Uncertainty Effect of Background Tissue Heterogeneity Uncertainty Results Effect of Background Tissue Density Uncertainty Effect of Lesion Uncertainty Effect of Background Tissue Heterogeneity Uncertainty Discussion Conclusion Conclusion and Future Directions Conclusion Future Directions References Biography viii

9 List of Tables Table 1: Fraction of tissue material in the effective tissue- contrast agent- blood mixture for each tissue Table 2: The seven imaging paradigms under comparison applied both in mammography and tomosynthesis, comprising a total of fourteen paradigms Table 3: AUC values for the different detection paradigms. Equalized density categories are denoted by upper and lower bounds on density, d ix

10 List of Figures Figure 1: Diagram of a typical digital breast tomosynthesis system. The x- ray source rotates around the compressed breast within a limited angle range and projection images are formed on the detector. The projection images are then reconstructed into slices through the volume of the breast along the z direction Figure 2: A 62- year- old woman with invasive ductal carcinoma of superior medial right breast. (a) Craniocaudal view conventional digital mammogram demonstrates mass largely obscured by overlying breast parenchyma (arrow). (b) Mediolateral oblique view conventional digital mammogram. Only very subtle architectural distortion visible at site of malignancy (arrow). (c) Craniocaudal projection tomosynthesis image clearly demonstrates round, speculated mass (arrow). (d) Mediolateral oblique projection tomosynthesis image demonstrates subtle but visible irregular mass with associated architectural distortion (arrow) (Reprinted from Academic Radiology, 18/10, Lo JY, Baker JA, Breast tomosynthesis: state- of- the- art and review of the literature, , Copyright 2011, with permission from Elsevier) Figure 3: Axial (top) and coronal (bottom) slices through a 28% dense breast phantom (left) and a 44% dense breast phantom (right). Both phantoms are compressed to 50% of the pendant breast diameter Figure 4: Contrast agent concentration P c,t (t) over time for each type of enhancement pattern Figure 5: A slice through the mid- depth of a (a) 9% dense, (b) 28% dense, and (c) 44% dense breast phantom. Notice the six lesions embedded in the mid- depth shown in dashed circles. The sizes of the phantoms are shown to scale Figure 6: Illustrating the randomized non- overlapping background ROI selection (red, light) in the central region of the breast (blue, dark) for a total of N = 10, 20, 30, and 40 ROIs. Black circles point to the location of the six lesions in the mid- slice of the reconstructed tomosynthesis volume of the 28% dense breast phantom Figure 7: Effect of the total number of ROIs in the background N = 1,, 50 (left), and ROI size (right) on the measured SDNR on a sample phantom Figure 8: A 28% dense breast phantom with lesions at the mid- depth generated at low energy (W/Rh 28 kvp): craniocaudal (CC) mammographic projection (a), and a slice through the mid- depth of the tomosynthesis reconstructed breast volume (b) x

11 Figure 9: Mammographic projection images of a 28% dense breast phantom with lesions following a washout kinetic pattern (Type III) acquired at low- energy (W/Rh 28 kvp) over four time points. The arrows point to the location of the lesions. The images are displayed at such window/level settings to match the backgrounds and help visualize the lesion behavior over time Figure 10: High- energy acquisitions were observed to only be slightly advantageous in contrast- enhanced images (T1). Every other image acquisition paradigm resulted in similar or higher image quality at low- energy. The low- energy and high- energy mammograms of a 28% dense breast phantom are presented here to illustrate this result Figure 11: Comparison of low- energy pre- contrast, post- contrast, temporally subtracted, and dual- energy subtracted simulated mammograms and corresponding central tomosynthesis slices of three breast phantoms. The images were cropped for display so sizes are not to scale Figure 12: Measured SDNR values for various acquisition paradigms applied to the three breast phantoms in mammography (a), and tomosynthesis (b). LE and HE indicate low and high energy, respectively Figure 13: Measured SDNR values for various acquisition paradigms averaged over the three breast phantoms in mammography (a), and tomosynthesis (b). LE and HE indicate low and high energy, respectively Figure 14. Axial and coronal slices through an uncompressed XCAT virtual breast phantom; grey levels show different segmented tissues Figure 15. Glandular equivalency of the sample materials (a) and the estimated attenuation of tissue- equivalent plastic chips (b); attenuation was estimated at 28 kvp with W/Rh. Note the dynamic range of the sample materials, corresponding to 31% glandularity difference Figure 16. Fabricated physical breast phantoms, the Doublet (a) with two materials, and the Singlet (b) with a single material, both in three slabs of 15 mm each Figure 17. The Singlet filled with various near adipose- equivalent filler materials: the whole volume immersed in an oil bath (a), and the bottom slab only filled with half butter/half lard (b), beeswax (c), and the transparent resin (d) xi

12 Figure 18. Mammogram of the Doublet (a) and the empty Singlet (b) acquired with W/Rh at 28 kvp and simulated images generated from the corresponding virtual phantom by incorporating the material properties respectively (c, d) Figure 19. Mammograms of the top, middle, and bottom (left to right) slabs of the Doublet acquired with W/Rh at 28 kvp Figure 20. Slices taken at 30, 20, and 10 mm (left to right) above the detector cover (out of 44 slices total, each 1 mm thick) through the reconstructed volume of the Doublet acquired with W/Rh at 28 kvp Figure 21. Close- up of a characteristic region 13 mm above the detector through the tomosynthesis reconstructed volume of the 15 mm bottom slab of the Singlet with oil (a), butter/lard (b), beeswax (c), and resin (d) fillers. The same region in the Doublet is presented in (e). The characteristic region is highlighted on the Doublet slice image (f). All images were acquired with W/Rh at 28 kvp Figure 22. Full volume mammographic projection through the Singlet with resin filler (a) and the Doublet (b). A slice through the tomosynthesis reconstructed volume of the Singlet with resin filler (c), and the Doublet (d). Corresponding close- up of an analogous region is shown in the bottom row. Imaged with W/Rh at 28 kvp. Comparing the bright vs. dark regions of interest (ROI), the pixel value signal differences were 22.9 (e), 15.1 (f), (g), and 63.5 (h) Figure 23. Microcalcification clusters in mammographic projection of a pure resin slab without anatomy (a), the middle slab of the Singlet filled with resin (b,c), and sandwiched in between the Doublet slabs (d,e), imaged at W/Rh 28 kvp. The detector pixel size is 85 µμm Figure 24. Power- law description of the mammograms of the Doublet (a), and the empty Singlet (b) Figure 25: Middle slice through the 4 cm thick compressed volume of the 20 breast phantoms used in the study. The gray values correspond to different fibroglandular tissue classes based on density. Note the various shapes, sizes, and densities of the phantoms Figure 26: Five lesion models: middle tomosynthesis slice through the lesions in human subject images (top), volume rendering of the generated models (middle), and the three fibroglandular classes after scaling the lesions to fit in a mm bounding box xii

13 Figure 27: The lesion grid with 200 positions 1 cm apart filled with the same lesion model Figure 28: The central projection image of a breast phantom with lesions embedded in its middle depth without (a), and with noise and scatter (b). The middle slice through the reconstructed volume of the same breast phantom without (c), and with noise and scatter (d) Figure 29: Middle slice through adjacent tomosynthesis reconstructed VOIs from one breast, with a lesion model embedded in them (a), and without any lesions (b). Notice that the lesions are invisible in certain VOIs as a result of tissue superposition, noise, and scattering Figure 30: The histogram of the distribution of VOI densities across 2173 VOIs Figure 31. The histogram of log- likelihood ratio in equation (4) under H0 and H1 (a), and the ROC curve for the detector. The AUC is Figure 32: ROC curves for different test density categories in the SKE- BKS paradigm ( ), where the detector is trained on all density categories (a), and the AUC of each curve as a function of density (b). ROC curves for different density categories in the SKE- BKS- DKS paradigm ( ), where the detector is tested and trained on a specific density category (c), and the AUC of each curve as a function of density (d). The change in the density training paradigm increased the AUC by an average of 3.3% in each density category Figure 33: Effect of, total number of VOI realizations included in the test and training datasets, on the stability of AUC values, under the SKE- BKS paradigm ( ), evaluated for every density category Figure 34: ROC curves for the SKE- BKS Across Lesions paradigm ( ) (a) and the SKS- BKS paradigm ( ) (b). ROC curves from the SKE- BKS paradigm ( ) are presented with solid lines in both figures for comparison Figure 35: Middle slice through the tomosynthesis reconstructed volume (a), the corresponding heat map of extracted VOI density (b), the histogram of the log- likelihood ratio under H0 and H1 in each breast as calculated per equation (4) (c), and the ROC curve for each breast (d) of the 20 breast phantoms. Note the substantial detection performance variability across different breasts xiii

14 Figure 36: Tomosynthesis mid- slice (a), VOI density (b), and log- likelihood ratio under H0 and H1 maps per equation (4) (c,d) Figure 37: Distribution of the log- likelihood ratio under H0 (left) and H1 (right) per equation (4) versus density and their corresponding quadratic fits. Dotted vertical lines indicate the density categories with equal number of samples and solid vertical lines at mid- density points indicate standard deviation of the log- likelihoods in the density category xiv

15 Acknowledgements I would like to express my sincere gratitude to my advisors, professor Ehsan Samei, professor Joseph Y. Lo, and professor Loren W. Nolte, to my dissertation committee members, Dr. William P. Segars, Dr. Sujata V. Ghate, and Dr. Matthew S. Reynolds, to the department of electrical and computer engineering, to Duke University, and to the members of Carl E. Ravin advanced imaging laboratories for all the support, vision, and opportunities they provided throughout my tenure at Duke university. I would like to specially thank professor Loren W. Nolte and Dr. Stacy Tantum for their support and input during a turning point in my research career. I would like to acknowledge the sources of funding for my research, the National Institutes of Health, Siemens Healthcare, and the department of electrical and computer engineering at Duke University. I would like to acknowledge Dr. Jered R. Wells for providing the most recent XCAT phantom segmentations, Gregory M. Sturgeon and Kelsey Tarzia for helping with preparing the breast phantoms, Adam C. Nolte for providing the noise and scatter modeling program and helping with the phantom filling experiments, Dr. Yuan Lin for providing the tomosynthesis projection and reconstruction programs, Justin Solomon for providing the lesion- fitting program, Lynda C. Ikejimba for helping with the NPS calculations and contrast experiments, Dr. Baiyu Chen for providing the xv

16 mathematically generated breast phantoms and lesion model, and Dr. Kingshuk Roy Choudhury, Dr. Maciej A. Mazurowski, and Dr. Hilde Bosmans for helpful discussions. Finally, I would like to thank all my family and friends across the globe for their love and support. This dissertation is only a small reflection of the extent of my learning experiences and challenges throughout my tenure at Duke University and I will always remain respectful of every interaction and opportunity that has led to my growth as a person and as a scientist, while hoping to be able to pay my dues and contribute to humanity. xvi

17 1. Introduction Given the recent advances in computation and modeling, virtual clinical trials can be carefully designed and carried out to inform, orient, or potentially replace clinical trials in breast imaging with adequate validation and credibility. In this dissertation, we elaborate on the deployment of advanced tools and models that can be used in the design, implementation, and performance analysis of virtual clinical trials in breast imaging for breast cancer detection. Although most of the efforts were towards x- ray breast imaging, the tools and models can be adapted for application in other breast imaging modalities. Mammography is currently the most widely used tool in the detection and diagnosis of breast cancer. The proven limited sensitivity of mammography due to tissue superposition in a two- dimensional image has motivated the development of alternative three- dimensional imaging systems. The advent of digital detectors facilitated realization of digital breast tomosynthesis systems, which acquire low- dose projection images of the breast from multiple directions to synthesize slices through the volume of the breast parallel to the plane of breast compression. Although still in its clinical infancy, this imaging system has been studied in a multitude of domains. Chapter 2. Digital Breast Tomosynthesis: A Concise Overview, introduces digital breast 1

18 tomosynthesis and elaborates on the state- of- the- art in its applications and performance. This chapter was published in the Imaging in Medicine journal in October Digital breast tomosynthesis with contrast enhancement can provide additional functional information about lesion morphology and kinetics, which in turn may improve lesion identification and characterization. The performance of breast tomosynthesis, either in native or contrast- enhanced mode, is strongly dependent on the structural composition of the breast, which varies significantly among patients. Therefore, breast imaging system and imaging technique optimization should take patient variability into consideration. Furthermore, optimization of imaging techniques that employ contrast agents should include the temporally varying breast composition with respect to the contrast agent uptake kinetics. To these ends, our laboratory at Duke has developed a suite of 4D virtual breast phantoms, which can be used for optimizing and evaluating breast imaging systems by incorporating tissue characteristics. The 4D phantoms are built upon the recently developed extended cardiac torso (XCAT) breast phantoms, which can be representative of a population through the combination of empirical human subject data and mathematical methods. Chapter 3. Development and Application of a Suite of 4D Virtual Breast Phantoms for Optimization and Evaluation of Breast Imaging Systems, introduces the 4D phantoms and presents a simplified example study to compare the performance of fourteen imaging paradigms with and without contrast enhancement, with temporal and dual- energy subtraction, in mammography 2

19 and tomosynthesis, qualitatively and quantitatively using three of the phantoms in the suite. This chapter was published in IEEE Transactions on Medical Imaging journal in July In addition to virtual breast phantoms for simulation studies, physical phantoms are essential for the development, optimization, and evaluation of breast imaging systems. Recognizing the major influence of the anatomical structure of the breast on image quality and clinical performance, such phantoms should ideally reflect the three- dimensional structure of the human breast. Currently, there is no commercially available three- dimensional physical breast phantom that is anthropomorphic in nature. In Chapter 4. Development of Realistic Physical Breast Phantoms Matched to Virtual Breast Phantoms Based on Human Subject Data, we present the development of a new suite of physical breast phantoms based on human data. The phantoms were designed based on the XCAT virtual breast phantoms. The phantoms were fabricated by high- resolution multi- material additive manufacturing technology. Based on the current state- of- the- art in the technology and available materials, two variations were fabricated. The first was a bi- material phantom, the Doublet. The second variation, the Singlet, was fabricated with a single material. It was subsequently filled with candidate near adipose- equivalent materials. Simulated microcalcification clusters were further included in the phantoms. This chapter is submitted for peer- reviewed publication. 3

20 The presented 3D and 4D breast models and the image formation platform are most useful as they can serve as building blocks towards virtual clinical trials. Thus, as a final component of this thesis Chapter 5. The Impact of Breast Structure on Lesion Detection in Breast Tomosynthesis, offers a detection and observer model framework, a doubly composite hypothesis detection theory paradigm with lesion and background known statistically, to characterize the effects of anatomical background tissue density and heterogeneity on the detection of irregular masses in digital breast tomosynthesis. Twenty breast models from the XCAT family were used to extract volumes of interest (VOI) from simulated tomosynthesis images. Anthropomorphic lesions, modeled after human subject tomosynthesis images, were embedded in the VOIs. The sensitivity and specificity analyses indicated that the detection performance is directly related to background tissue density yielding findings consistent with clinical studies. But furthermore, the detection performance was found to be also strongly affected by background tissue heterogeneity. Considering tissue variability can change the outcomes of a study utilizing virtual tools and models in design, optimization, and evaluation of imaging systems and techniques and is hence of crucial importance. The XCAT breast phantoms can address this concern by offering realistic and detailed modeling of tissue variability based on a wide range of human subjects. This chapter is submitted for peer- reviewed publication. 4

21 2. Digital Breast Tomosynthesis: A Concise Overview 2.1 Abstract The proven limited sensitivity of mammography due to tissue superposition in a two- dimensional image has motivated the development of alternative three- dimensional imaging systems with minimal ionizing exposure and relatively low cost. The advent of digital detectors facilitated realization of digital breast tomosynthesis systems, which acquire low- dose projection images of the breast from multiple directions to synthesize slices through the volume of the breast parallel to the plane of the projection images. Although still in its clinical infancy, this imaging system has been studied in a multitude of domains. This concise overview introduces digital breast tomosynthesis and elaborates on the state- of- the- art in its applications and performance. 2.2 Introduction According to the world health organization (WHO), breast cancer is the most common cancer in women both in the developed and the developing world. The incidence of breast cancer is rising in the developing world. Some suggested reasons include increased life expectancy, increased urbanization, and adoption of western 5

22 lifestyle. Although some risk reduction might be achieved with prevention, these strategies cannot eliminate the majority of breast cancers that develop in low- and middle- income countries where breast cancer is diagnosed in very late stages. Therefore, early detection in order for improved breast cancer outcome and prognosis remains the cornerstone of breast cancer control [1]. The recommended early detection strategies are awareness of early symptoms and screening by clinical breast examination in low- and middle- income countries, and mammography in countries with better health infrastructure that can afford a long- term program. WHO, with the support of Komen Foundation, is currently conducting a 5- year breast cancer cost- effectiveness study in 10 low- and middle- income countries. It is expected that the results of this project will contribute to provide evidence for shaping adequate breast cancer policies in less developed countries. Mammography screening is the only screening method that has proven to be effective. It can reduce breast cancer mortality by around 20% in women over 40 years old in high- income countries [2-3]. The American Cancer Society recommends annual screening mammography for women ages 40 and older. While providing the highest spatial resolution, the patients might be called back for further examination due to the limited accuracy and poor image quality of mammography, which also leads to its limited sensitivity and specificity. Unfortunately, the sensitivity of both analog and digital mammography remains as low as 36% 79% depending partly on breast tissue 6

23 density and heterogeneity of tumor growth patterns, with recall rates remaining well above 5% 10% for some practitioners [4-7]. The low sensitivity is caused by breast tissue superposition, which can conceal malignancies. Furthermore, breast tissue superposition can cause false positives, lowering the specificity of mammography to 90%- 98% depending on breast tissue density, and resulting in follow- up imaging, additional radiation exposure, increased expenses, and unnecessary anxiety [4-8]. The clinical work- up can include diagnostic mammography with additional views or magnification, breast ultrasound imaging, breast magnetic resonance (MR) imaging, fine- needle aspiration biopsy, core biopsy, or surgical excisional biopsy. There are also several other established or experimental technologies that could be helpful in reexamining suspicious areas but have not been proven to be a substitute for screening mammography. These technologies include scintimammography [9], thermography [10], electrical impedance imaging (T- scans) [11], positron emission mammography [12], molecular imaging [13], and optical imaging [14]. To overcome the loss of information in the third dimension due to tissue superposition in mammography, new imaging techniques have emerged with the advent of digital detectors [15-17]: dedicated breast computed tomography (CT) [18], and digital breast tomosynthesis [19]. Dedicated breast CT is an imaging technique that provides tomographic images of the breast by scanning the pendant breast during a patient s breath- hold. The technique offers lower spatial resolution and higher contrast 7

24 resolution compared to mammography, presenting challenges for microcalcification detection and axillary tail and chest wall coverage. Currently, there is no dedicated breast CT system available clinically. Digital breast tomosynthesis is an imaging technique that creates cross- sectional images of the breast at mammographic in- plane resolution through limited- angle tomography of the compressed breast. Due to uncertainties that result from the limited angle tomography, the z resolution is distorted and expanded. In- depth reviews of the history and development of tomosynthesis have been published in [20-23]. Digital breast tomosynthesis has the potential to reduce false positives and provide equal or better sensitivity compared to mammography. Currently, there are a number of digital breast tomosynthesis systems available clinically in the world. 2.3 Image Acquisition Digital breast tomosynthesis is a high- resolution limited- angle tomography technique. The original theoretical concept of tomosynthesis was first introduced almost eighty years ago, and the term tomosynthesis was coined in a journal article almost 40 years ago [24-26]. However, since employing digital detectors is necessary in order to effectively implement the theory, digital tomosynthesis has only recently become feasible and developed over the past fifteen years [19]. Digital breast tomosynthesis 8

25 system consists of a rotating x- ray tube that acquires a series of low- dose projections of the compressed breast over a range of angles with a static or moving detector (Figure 1). The low- dose projection images are reconstructed into a semi- tomographic volume of the breast with typically 1 mm thick slices. Tomosynthesis systems use the basic mammography system structure. The patient can be imaged at standing, seated, or lying positions with the breast compressed between the compression paddle and the detector. The applied compression is comparable to mammography. There is, however, some room for a reduction in compression due to the 3D nature of tomosynthesis, compensating for tissue overlap in mammography and resulting in more patient comfort [27]. The radiation dose for a single tomosynthesis exam is comparable to a traditional single mammography exam [20,24]. While the compression paddle and detector cover remain static, the x- ray tube can move with continuous or step- and- shoot motion around the breast to acquire craniocaudal or mediolateral oblique views. Different commercial and prototype systems currently acquire between 11 to 50 projections over a range of 15 to 60 in 5 to 25 seconds. The x- ray tube generates voltages of kvp with tungsten, rhodium, or molybdenum targets coupled with aluminum, silver, rhodium, copper, or titanium filtering. The flat panel digital detectors used for tomosynthesis typically have a faster reading time, minimal detector ghosting and lag, and minimal reduction of detective quantum efficiency at low exposure compared to digital mammography detectors to allow acquisition of several images over 9

26 a short scanning time. These detectors are made of amorphous selenium or amorphous silicon for direct conversion, or cesium iodide for indirect conversion. Since tomosynthesis is a relatively new technique these specifications are subject to change. Detector pixel size currently ranges from 50 µμm to 140 µμm considering detector binning. Reconstructed voxel sizes are typically around 100 µμm 100 µμm 1 mm. However, the 1 mm slice definition in the z direction is not indicative of resolution in that direction. The limited so called z- resolution is caused by limited angle tomography and can be a function of the angular range [28]. Rotation Range! Rotating x-ray source z direction Compression Paddle Breast Digital Detector Figure 1: Diagram of a typical digital breast tomosynthesis system. The x- ray source rotates around the compressed breast within a limited angle range and projection images are formed on the detector. The projection images are then reconstructed into slices through the volume of the breast along the z direction. 10

27 In addition to the commercial and prototype systems explained above, there exist a couple of nontraditional prototype tomosynthesis systems at the moment. One of these prototype tomosynthesis systems employs scanning slit photon counting detectors [29-30]. Advantages of this system include low scatter signal, no electronic noise, high quantum efficiency, and low radiation dose requirements. In addition, a new version of this photon counting detector includes energy resolution, allowing for simultaneous acquisition of two images at low and high energies. Another alternative prototype tomosynthesis system employs multi- beam field emission x- ray source array [31-32] to avoid focal spot blurring due to the x- ray tube motion during acquisition and to potentially shorten total acquisition time. In a recent work [33], the x- ray tube and gantry of a commercial tomosynthesis system (Selenia Dimensions, Hologic, Inc., Bedford, MA) was replaced with a carbon nanotube array with 31 x- ray sources, spanning 370 mm, resulting in an angular coverage of 30. The stationary x- ray source was shown to yield an improved modulation transfer function compared to that with a standard rotating x- ray tube. However, detector readout rate and x- ray tube current and exposure time still need to be addressed to optimize total scan time. 11

28 2.4 Reconstruction and Image Handling Tomosynthesis projection images are reconstructed using filtered backprojection (FBP) [34-35] or iterative algorithms [36]. Most iterative reconstruction techniques are based on other techniques such as the algebraic reconstruction technique (ART) [37], the simultaneous iterative reconstruction technique (SIRT) [38], and the simultaneous algebraic reconstruction technique (SART) [39], and the maximum likelihood expectation maximization (MLEM) reconstruction technique [40], which can provide superior image quality and fewer artifacts compared to FBP [41-42]. However, iterative reconstruction requires several orders of magnitude greater computation time compared to filtered backprojection. There is active research in optimizing reconstruction algorithms to maximize their performance with lower computational cost. The application of graphic processing units (GPU) have also helped significantly reduce the time required for iterative reconstruction. Tomosynthesis is highly susceptible to artifacts due to its nature of limited- angle acquisition [43]. Most common artifacts are the out- of- plane presence of shifted and repeated versions of high- contrast features or ghosting. The other reconstruction artifact, embossed look of high- contrast features, actually sometimes aids in detection. Other artifacts include the blurring of the breast margin into other planes and truncation artifacts close to the edges of the detector. Various new methods and modifications to 12

29 existing reconstruction algorithms have been proposed to reduce or eliminate these artifacts [44-46]. The tomosynthesis reconstructed images can be displayed sequentially as a continuous cine loop or one image at a time controlled manually at the reader'ʹs discretion and preference of image display rate. The readers are allowed to magnify the images to full acquisition resolution. The tomosynthesis projection images can also be available for viewing one by one or in a loop depending on the manufacturer. For microcalcification search, a slab- view has been suggested, improving microcalcification conspicuity by collecting the entire cluster into one slab, rather than having individual microcalcifications spread over several slices [47]. In this view mode, often maximum- intensity projections (MIP) of 5 10 slices are presented [48]. In order to reduce the scan time and patient exposure, in 2011, the C- View TM software was commercially released to reconstruct mammograms from a tomosynthesis dataset synthetically [49]. The Food and Drug Administration (FDA) approved the technique for use in the United States in 2013 [50]. Development of such algorithms, and their clinical evaluations is an active area of research. There are potentially additional viewing modes for tomosynthesis data, including stereoscopy [51] and multi- view stereoscopy [52] among others that await clinical evaluation. Tomosynthesis datasets are significantly larger than mammography datasets. Each projection image in a tomosynthesis scan is equivalent to a mammogram in size. 13

30 Therefore, depending on the number of projection angles, a four- view tomosynthesis dataset can be twenty five times as large as a four- view mammography dataset. Therefore, storage and networking requirements for these large datasets need to be considered in practice. 2.5 Clinical Experience and Implementation Various clinical studies have been devised to evaluate and assess the relative advantages or disadvantages of tomosynthesis to other technologies for screening and diagnosis. Figure 2 illustrates the potential advantage of two- view digital breast tomosynthesis with two- view digital mammography. In a 2007 study, Poplack et al. followed up 98 women with abnormal digital screening mammography with diagnostic film- screen mammography and tomosynthesis [53]. They reported an equivalent or superior image quality for tomosynthesis compared to diagnostic mammography in 89% of the cases, and concluded that had tomosynthesis been used for screening as well, half of these cases would not have been recalled. It should, however, be noted that this study was not properly designed for such inference [54]. In 2008, Good et al. published a pilot study comparing full- field digital mammography (FFDM), 11 low- dose projections acquired for the reconstruction of tomosynthesis images, and the reconstructed digital breast tomosynthesis examinations of 30 subjects read by 9 experts [55]. Although 14

31 observer performance measures were not statistically significant, the authors reported great potentials for tomosynthesis- based breast imaging. In 2008, Andersson et al. published the results of a study they conducted on symptomatic or recalled women in Sweden from 2006 to Their lesion visibility study, within a population of 40 cancers, concluded that cancer visibility in one view tomosynthesis is superior to digital mammography. This indicated the potential of tomosynthesis to increase sensitivity [56]. In 2010, Teertsrtra et al. published the results of a study of 513 women with an abnormal screening mammogram or clinical symptoms in the Netherlands from 2006 to 2007 [57]. They observed that the sensitivity of both techniques for the detection of breast cancer was 92.9%, and the specificity of mammography and tomosynthesis was 86.1% and 84.4%, respectively. They also concluded that tomosynthesis could be used as an additional technique to mammography in patients referred with an abnormal screening mammogram or with clinical symptoms. In 2010, Gennaro et al. published the results of a study of 200 women with at least one breast lesion discovered by mammography and/or ultrasound in Italy from 2007 to 2008 [58]. They concluded that clinical performance of tomosynthesis in one view at the same total dose as standard screen- film mammography is not inferior to digital mammography in two views. In 2013, Skaane et al. published the results of a comparative study of digital mammography alone and digital mammography plus tomosynthesis in women as part of Oslo screening program from 2010 to 2011 [59]. They reported a 27% increase in detection rate for 15

32 invasive and in situ carcinoma cancers with digital mammography plus tomosynthesis, as well as a 15% decrease in false- positive rates. In 2013, Ciatto et al. published the results of investigating the effect of integrated mammography and tomosynthesis in population breast cancer screening [60]. This comparative study, Screening with Tomosynthesis OR standard Mammography (STORM) trial, recruited 7292 asymptomatic women aged 48 years or older who attended population- based breast cancer screening and reported that integrated mammography and tomosynthesis improves breast- cancer detection and has the potential to reduce false positive recalls. In 2007, Rafferty reported an advantage for mammography in detecting microcalcifications in comparison with tomosynthesis [61]. This might be due to the fact that the microcalcifications are visualized in different planes. As a result, it is suggested that tomosynthesis and mammography may best be used in a complementary way. In 2011, in a study of 100 women Spangler et al. reported mammography to be slightly more sensitive than tomosynthesis for the detection of calcifications [62]. However, since diagnostic performance, as measured by the area under the receiver operating characteristic (ROC) curve, was not significantly different, they envisioned that with improvements in processing algorithms and display, tomosynthesis could potentially be improved for this purpose. In a 2011 study of 119 women, Kopans et al. showed that microcalcifications can be demonstrated with equal or greater clarity on tomosynthesis than on conventional mammography when the detector pixels are not binned [63]. 16

33 Figure 2: A 62- year- old woman with invasive ductal carcinoma of superior medial right breast. (a) Craniocaudal view conventional digital mammogram demonstrates mass largely obscured by overlying breast parenchyma (arrow). (b) Mediolateral oblique view conventional digital mammogram. Only very subtle architectural distortion visible at site of malignancy (arrow). (c) Craniocaudal projection tomosynthesis image clearly demonstrates round, speculated mass (arrow). (d) Mediolateral oblique projection tomosynthesis image demonstrates subtle but visible irregular mass with associated architectural distortion (arrow) (Reprinted from Academic Radiology, 18/10, Lo JY, Baker JA, Breast tomosynthesis: state- of- the- art and review of the literature, , Copyright 2011, with permission from Elsevier). 17

34 As noted earlier, research is ongoing in creating a synthetic mammographic image from a tomosynthesis acquisition. In the only study on this matter [64], Gur et al. reported on an observer study to compare the performance of tomosynthesis combined with either an actual mammogram or a synthetic mammogram and concluded that the synthetic mammogram was not a replacement for the actual mammogram. A number of studies are currently being undertaken to further assess tomosynthesis. For instance, to assess whether tomosynthesis could improve upon digital mammography as a screening tool, particularly in certain groups of women such as those with a family history of breast cancer or those recalled to an assessment clinic following abnormal screening mammography, six centers in United Kingdom are participating in a study, TOMMY trial, to recruit a total of 7000 women undergoing both standard digital mammography and tomosynthesis [65]. The Malmö breast tomosynthesis screening trial is also designed to compare tomosynthesis and mammography as screening tools in terms of the number of cancers detected in women of ages 40 to 74 in Sweden between 2010 and 2016 [66]. There are also studies designed to investigate the effect of number of views available in tomosynthesis and mammography. For instance, Wallis et al. report that two- view tomosynthesis outperforms mammography, but only for readers with least experience [67]. 18

35 It is note worthy that most of these studies acknowledged the potential limiting impacts of observer experience and training in a new technology as well as not fully optimized acquisition and display settings of the prototype units in the outcome of the studies. Smith et al. reported that radiologists with a range of experience demonstrated improved performance using tomosynthesis in combination with digital mammography as measured using recall rate reduction and the area under the ROC curve metrics [68]. Currently tomosynthesis units from a few manufacturers are commercially available in Europe. In the United States, however, only one manufacturer has been approved by the FDA to date. 2.6 Advanced Applications Digital breast tomosynthesis, similar to digital mammography, can benefit from enhanced lesion detectability by incorporating contrast agents. Intravenous iodine- based contrast agents can improve the visibility of areas with high blood perfusion, such as malignancies, when energies above the k- edge of iodine are used for acquisition. Furthermore, contrast agent uptake kinetics patterns of the lesions can be studied if imaging is repeated over the course of a few minutes as the contrast agent propagates throughout the breast. This kinetics information can serve as an additional tool to characterize a potential lesion. Most lesions following a washout or a plateau pattern are 19

36 reported to be suggestive of malignancy, whereas most benign lesions follow constant enhancement patterns [69-70]. The relative advantage of this technique to contrast- enhanced MRI lies in its high in- plane resolution and short acquisition time as well as the considerably lower costs. However, the technique can potentially expose the patient to more ionizing radiation. Contrast- enhanced digital tomosynthesis is extensively studied and continues to be an active area of research [71-72]. To further augment the lesion visibility, post- processing contrast enhancement techniques have been introduced that involve multiple acquisitions before and/or after administration of the contrast agent at one or more energies [73-76]. One contrast enhancement technique is temporal subtraction, which involves acquiring images before and after the administration of the contrast agent and then subtracting them. The principal behind this technique is the fact that after administration of the contrast agent, the areas with most blood infusion show the highest contrast. Hence, when the two images are subtracted most of the anatomy is subtracted out and the malignant lesions that have blood pooling around them will be what remain. Another contrast enhancement technique, dual- energy subtraction, involves acquiring images after the administration of the contrast agent at energies below and above the k- edge of iodine. At the higher energy acquisition, areas with most blood infusion will result in highest attenuation and hence highest contrast. Therefore, if the two images are subtracted, most of the anatomy could cancel out and malignancies could remain visible. Technique 20

37 optimization in contrast- enhanced imaging using physical and virtual phantoms as well as clinical observer studies is an ongoing area of research [77-78]. Although tomosynthesis has only been recently and partly introduced to the clinical practice, some multimodality approached have already been investigated. These approached include the combination of tomosynthesis with electrical impedance tomography for characterization of suspicious lesions [79], and with ultrasound obtaining a co- registered 3D ultrasound image [80]. The combination of morphological information with functional information is also being developed through integrating tomosynthesis with single photon emission computed tomography [81] or with diffuse optical tomography [82]. Phase contrast tomosynthesis in order to enhance feature edges was tested on phantoms and was proved to be promising [83]. Tomosynthesis guided positioning for radiation therapy and interventional biopsy has also been an active area of development [84-85]. Computer aided detection (CAD) of masses in tomosynthesis has been performed employing segmentation and gradient and feature analysis on the projection images, the reconstructed images, or both [86-87]. CAD methods based on information theoretic metrics are also in existence [88-89]. A number of different algorithms have been proposed for automated detection of microcalcification clusters in tomosynthesis images, a task which has proven easier for CAD systems than the detection of masses [90-91]. 21

38 Given the increased risk of cancer in women with denser breasts, there has been attempts in estimating breast density based on tomosynthesis projection and reconstructed images [92-93]. However, it is still unclear whether mammography- based techniques overestimate the density or tomosynthesis- based techniques underestimate the density. 2.7 Conclusion The advent of digital detectors facilitated realization of digital breast tomosynthesis systems, which acquire low- dose projection images of the breast from multiple directions to synthesize slices through the volume of the breast parallel to the plane of the projection images. Although still in its clinical infancy, this imaging system has been studied in a multitude of domains. This concise overview introduced digital breast tomosynthesis and elaborated on the state- of- the- art in its applications and performance. Clearly digital breast tomosynthesis is still in its clinical infancy around the world. Hence, only limited data are available for understanding its advantages and shortcomings. The initial promising clinical results suggest its use as an adjunct to or in combination with digital mammography for screening purposes. Whether tomosynthesis systems could be used as a screening tool or as a diagnostic tool deserves 22

39 further development and investigation. Aside from advancements in hardware, which can potentially facilitate faster, more efficient, and safer acquisition, there needs to be advancements in the post- processing and interpretation arena as well. Development of smart techniques in synthesizing mammograms from tomosynthesis datasets could eventually eliminate the need for a separate mammogram, resulting in faster acquisition and less exposure to the patient. Optimal acquisition protocols and reconstruction techniques for various purposes still need to be determined and examined. Advanced applications have to be tested clinically to justify their proper usage and potential benefits. For translation into wide clinical usage, issues such as reader training, data handling and storage, and assistive CAD tools need to be considered and planned for. Overall, given the current evaluated improvements in sensitivity and specificity over digital mammography, digital breast tomosynthesis is considered an emerging tool in breast imaging with great potential and a bright future. 23

40 3. Development and Application of a Suite of 4D Virtual Breast Phantoms for Optimization and Evaluation of Breast Imaging Systems 3.1 Abstract Mammography is currently the most widely utilized tool for detection and diagnosis of breast cancer. However, in women with dense breast tissue, tissue overlap may obscure lesions and result in reduced sensitivity. Digital breast tomosynthesis can reduce tissue overlap. Furthermore, digital breast tomosynthesis with contrast enhancement can provide additional functional information about lesions, such as morphology and kinetics, which in turn may improve lesion identification and characterization. The performance of these imaging techniques is strongly dependent on the structural composition of the breast, which varies significantly among patients. Therefore, breast imaging system and imaging technique optimization should take patient variability into consideration. Furthermore, optimization of imaging techniques that employ contrast agents should include the temporally varying breast composition with respect to the contrast agent uptake kinetics. To these ends, we have developed a suite of 4D virtual breast phantoms, which can be used for optimizing and evaluating breast imaging systems by incorporating tissue characteristics. The presented 4D phantoms are built upon the recently developed extended cardiac torso (XCAT) breast 24

41 phantoms, which can be representative of a population through the combination of empirical human subject data and mathematical methods. The 4D phantoms are incorporated with the kinetics of contrast agent propagation in different tissues and can realistically model normal breast parenchyma as well as benign and malignant lesions. The realistic modeling of the breast anatomy and contrast agent uptake kinetics presents a new approach in performing simulation studies using truly anthropomorphic models. To demonstrate the utility of the proposed 4D phantoms, we present a simplified example study to compare the performance of fourteen imaging paradigms with and without contrast enhancement, with temporal and dual- energy subtraction, in mammography and tomosynthesis, qualitatively and quantitatively using three of the phantoms in the suite. A ray- tracing algorithm simulates projection images, which are reconstructed with filtered back projection. Dual- energy and temporal subtractions are performed and compared on both mammographic projections and tomosynthesis reconstructed images. A global signal- difference- to- noise ratio (SDNR) is measured and compared for the fourteen imaging paradigms. 3.2 Introduction Breast cancer is the most common cancer among women worldwide. According to the world health organization, early detection remains the cornerstone of breast 25

42 cancer control for better prognosis [1]. Currently, mammography is the most widely utilized tool for screening and diagnosis of breast cancer [94]. However, the sensitivity of mammography is reduced in dense breast tissue, even in the newer technique of digital mammography [95]. Digital breast tomosynthesis has demonstrated the capability to reduce tissue overlap and lesion obscurity by providing depth and morphology information [19]. But even so, there is still a tremendous potential for improvements to the sensitivity and specificity of these imaging modalities via design and use optimization, as well as the incorporation of new contrast mechanisms. Among those, either mammography or digital breast tomosynthesis can make use of contrast agents for high- risk screening and diagnostic purposes. The process of angiogenesis of blood vessels with abnormally increased permeability in tumor development and growth has motivated the application of contrast agents to increase lesion detectability [96]. In the case of x- ray imaging, contrast agents are often iodine- based solutions that are injected to the patient with a volume of about 1 ml per kg patient weight. To further improve lesion visibility, contrast enhancement techniques have been introduced that involve multiple acquisitions at one or more energies before and/or after administration of the contrast agent [74]. There are two different techniques for contrast- enhanced breast imaging to be implemented with x- ray imaging. One technique is temporal subtraction, which involves subtracting images acquired before and after the administration of the contrast agent. The principal behind this technique is that after the 26

43 administration of the contrast agent, the areas with most blood perfusion show the highest contrast. Hence, when the two images are subtracted, most of the anatomy is subtracted out and only the lesions are remained. The other technique, dual- energy subtraction, involves acquiring two images after the administration of the contrast agent at mean beam energies below and above the k- edge of iodine (33.2 kev). After logarithmic transformation, the images are weighted and subtracted, yielding an image with cancelled anatomy and a substantial iodine signal due to the increase in the iodine attenuation at the k- edge. Because of the increased blood flow in tumors and leakage from their highly permeable vessels, malignancies would enhance more relative to surrounding parenchyma. Both techniques can be implemented in mammography or tomosynthesis. As a result of angiogenesis in malignant lesions, contrast agent absorption in malignancies is different from normal tissue. Most of the lesions following a plateau (Type II) or a washout (Type III) contrast kinetic pattern have been reported as malignant, whereas most benign lesions follow a constant enhancement pattern (Type I) [69-70]. Therefore, a combination of morphological features analysis and contrast agent kinetics can provide an augmented technique to characterize lesions. To optimize an imaging system that incorporates contrast agent administration, it is crucial to take into account: 1) the dynamics of contrast agent propagation in the breast tissue and lesions, and 2) the variability of breast composition across the patient population, which can 27

44 significantly change the detectability of lesions. To the best of our knowledge, a breast phantom that possesses these features and can be used for simulations resulting in optimization and evaluation of imaging systems has not yet been developed. There have been a few studies on system optimization for contrast- based breast imaging including clinical trials and simulations; however, most of these studies only rely on either a limited population of patients or an overly simplistic model of the breast [97-101]. This work focuses on the development of a suite of 4D virtual breast phantoms capable of modeling the temporal kinetics of contrast agent propagation in tissue over a wide range of patients. The phantoms were designed to be used as a virtual platform for optimization of the design and the use of both non- contrast and contrast- enhanced breast imaging systems. The phantoms were developed by incorporating contrast agent propagation kinetics into the extended cardiac torso (XCAT) breast phantoms [ ]. The XCAT breast phantoms combine empirical human subject data with the flexibility of mathematical methods to provide a realistic simulation of breast anatomy. They have recently been used with novel transformation methods to generate a large suite of simulated human subject models covering a wide range of patient types [106]. 28

45 3.3 Methods The proposed 4D breast phantoms were developed based on XCAT breast phantoms derived from human subject data. The XCAT phantoms were generated from dedicated breast computed tomography data of several different human subjects by post- processing and segmenting them into skin, adipose tissue, and three classes of fibroglandular tissue according to density, which can be compressed to various thicknesses [ ]. Figure 3 shows axial and coronal slices through compressed volumes of two phantoms with different breast densities (fraction of fibroglandular tissue in the breast volume). These phantoms combine empirical data from real human subjects with the flexibility of mathematical models to include a detailed anatomy and create additional phantoms from different breast data. They are available both in voxelized and mesh formats. 29

46 100% Fibroglandular 67% Fibroglandular 33% Fibroglandular Skin Adipose Figure 3: Axial (top) and coronal (bottom) slices through a 28% dense breast phantom (left) and a 44% dense breast phantom (right). Both phantoms are compressed to 50% of the pendant breast diameter. In order to incorporate the fourth dimension of time into the phantoms, the different tissues in the breast were modified to contain a time- varying fraction of contrast agent- blood mixture as well as the tissue material. In the particular case of x- ray imaging, the phantom tissues are associated with the corresponding attenuation coefficients of their different constituting elements. The effective attenuation coefficient of each tissue T was modeled by µ T,eff (t) = P T µ T + (1! P T )(P c,t (t)µ c + (1! P c,t (t))µ b ), 30

47 where P T is the mass fraction of the tissue made of tissue T, corresponding to attenuation coefficient µ T and P C,T (t) is the mass fraction of the contrast agent in contrast agent- blood mixture at time t for tissue T, and µ c and µ b are the attenuation coefficients of the contrast agent and blood, respectively. By targeted selection of the fractions over time and material based on previous contrast enhancement studies, these phantoms can represent the flow of contrast agent into the breast tissue [ ]. Combined with the inherent capability of the phantoms to model different patients, changes in the contrast agent- blood fractions may further add to the utility of the phantoms to model different anatomical and physiological representations. The fractions used for various materials in the breast were estimated based on the relative vascularization of various tissues with the same trends reported in the literature [113], but were modified to better illustrate the properties of the phantom. These phantom parameters can be readily modified to reflect other clinical situations. These values are shown in Table 1. Table 1: Fraction of tissue material in the effective tissue- contrast agent- blood mixture for each tissue. Material Adipose Tissue Fibroglandular Tissue Skin Masses P T

48 Assuming that the average weight of a person is 70 kg with 5L of blood, injection of ISOVUE300 (an FDA approved iodine- based contrast agent with 300 mg iodine per ml) with a dosage of 1.5 ml/kg will result in maximum 6.3 g/l iodine concentration in blood. Considering the density of blood (1.06 g/ml) and ISOVUE300 (1.339 g/ml), and a dosage of 1.5 ml per kg of patient weight, the maximum fraction of iodine in iodine- blood mixture amounts to approximately Reasonable temporal enhancement patterns were estimated based on data from magnetic resonance (MR) breast imaging of four patients at four arbitrary time points (T0: pre- contrast, T1, T2, T3: post- contrast) for normal tissue, benign tumors (Type I), and malignant tumors including both plateau (Type II) and washout (Type III) patterns. The estimated values of P c,t (t) based on relative signal intensity for the four different patterns are presented in Figure 4. 32

49 Contrast Agent Fraction in Blood 5 x Normal Tissue Type I Type II Type III 0 T0 T1 T2 T3 Time Figure 4: Contrast agent concentration P c,t (t) over time for each type of enhancement pattern. In order to illustrate the utility of the developed phantoms with realistic breast anatomy and contrast agent uptake kinetics, a simplified example study is presented. The 4D breast phantoms were used to evaluate fourteen mammography and tomosynthesis imaging paradigms listed in Table 2 at clinically relevant spectra. A 9%, a 28%, and a 44% dense (by volume) breast phantom were picked from the available number of breast phantoms for this study to represent a range of the population (Figure 5). Each breast phantom was compressed to 50% of its pendant diameter by applying a mathematical transformation preserving the volume of the breast. Six mathematically generated lesions with a dense center and gradually fading boundaries were then added 33

50 to these phantoms at the mid- depth of the compressed volumes. The same lesion model as in [109] was used. Table 2: The seven imaging paradigms under comparison applied both in mammography and tomosynthesis, comprising a total of fourteen paradigms. Technique Time Energy Non- contrast Single- energy T0 Low- energy High- energy Contrast- enhanced Single- energy T1 Low- energy High- energy Dual- energy T1 High- energy w Low- energy Low- energy Temporal Subtraction T1- T0 High- energy 34

51 A ray- tracing algorithm implemented for a graphic processing unit (GPU) cluster simulated projection images by including an x- ray source spectrum and the geometry of a prototype 1 MAMMOMAT Inspiration tomosynthesis unit (Siemens, Erlangen, Germany). Anode/filter combination of W/Cu with 300 µμm filter thickness at 49 kvp (high- energy: HE) and W/Rh with 50 µμm filter thickness at 28 kvp (low- energy: LE) were used. When operating in tomosynthesis mode, 25 images were acquired over a 50 arc centered at the normal position of the x- ray tube to the detector. A filtered back- projection algorithm based upon previous studies with a cosine filter was then used on a GPU cluster to reconstruct these images into the compressed breast volume with 1 mm slice separation [ ]. A complete simulation framework may also include additional physical aspects of the image formation process such as patient motion, scatter, quantum and electronic noise, image processing, etc. To introduce these new phantoms, this preliminary study demonstrates their use in a simplified environment that did not include these elements. 1 The use of this device for tomosynthesis is preliminary in the US. The safety and effectiveness of the device have not been established. The device is under development and not commercially available in the US, and its future availability cannot be ensured. 35

52 a. b. c. Figure 5: A slice through the mid- depth of a (a) 9% dense, (b) 28% dense, and (c) 44% dense breast phantom. Notice the six lesions embedded in the mid- depth shown in dashed circles. The sizes of the phantoms are shown to scale. Temporal subtraction was performed by subtracting the image at T0 from the image at T1. The dual- energy subtraction was performed by logarithmically subtracting the weighted low- energy image from the high- energy image both at T1. In practice, this can either be achieved through the use of energy selective detectors (e.g., photon counting or dual- layer sensors) or by rapid sequential acquisition of low and high- energy images of the compressed breast. The weight factor was empirically optimized to result in the least contrast between adipose and fibroglandular tissues to reduce the anatomical noise and increase the lesion detectability according to measured signal- difference- to- noise ratio (SDNR) values. A numerical comparison of the fourteen paradigms was made by calculating SDNR as a first- order figure of merit. A circular region of interest (ROI) was selected inside each lesion at half the radius of the lesion. Signal was measured by taking the 36

53 average of the mean values of ROIs in all the lesions. In addition, a number of circular ROIs were selected in the background (internal areas of the breast farther from the edges and excluding the lesions). Assume that the number of ROIs in the background is N. Anatomical noise was measured by taking the average of the mean values of these N ROIs in the background. The difference between the signal and anatomical noise was divided by the standard deviation of the mean values of the ROIs in the background. This process was repeated for every value of N between 1 and the maximum of non- overlapping ROIs that could be fit in the background (50 in the 9% and 28% dense phantoms and 30 in the 44% dense phantom). The calculated SDNR values for N > 20 (steady state) were then averaged and reported (Figure 6). We examined the effect of the size of ROIs in the background and observed that as long as they are larger or equal to the size of the ROIs in the lesions, it has a minimal effect on the stability of the reported SDNR values (Figure 7). Therefore, the area of the ROIs in the background was selected to be 1.5 times the area of the ROIs in the lesions. Instead of the traditional concept of local lesion detectability, this SDNR reflects a global measure of how well lesions can be distinguished from overall anatomical heterogeneity. This measure was devised to address the very different detection paradigm in subtraction imaging, where the lesion often stands out well, but it is challenging to rule out other bright areas that may result from normal anatomy or artifacts. 37

54 N=10 N=20 N=30 N=40 Figure 6: Illustrating the randomized non- overlapping background ROI selection (red, light) in the central region of the breast (blue, dark) for a total of N = 10, 20, 30, and 40 ROIs. Black circles point to the location of the six lesions in the mid- slice of the reconstructed tomosynthesis volume of the 28% dense breast phantom SDNR 10 SDNR Number of ROIs in the Background Background ROI Area / Lesion ROI Area Figure 7: Effect of the total number of ROIs in the background N = 1,, 50 (left), and ROI size (right) on the measured SDNR on a sample phantom. 38

55 3.4 Results To illustrate the quality of simulated mammographic projection and tomosynthesis reconstruction of the phantoms, a 28% dense breast phantom is presented in Figure 8. Notice the distinct structures visible in the slice through the reconstructed volume compared to the more indistinct superposition of all tissue structures in the projection image. Also, notice the advantage of 3D information in lesion visibility in the tomosynthesis reconstructed slice. Both images were generated at the same spectrum. a. b. Figure 8: A 28% dense breast phantom with lesions at the mid- depth generated at low energy (W/Rh 28 kvp): craniocaudal (CC) mammographic projection (a), and a slice through the mid- depth of the tomosynthesis reconstructed breast volume (b). To present the contrast kinetics incorporated in the phantoms, Figure 9 shows simulated mammographic projection images of a 28% dense breast phantom with 39

56 lesions following a washout pattern acquired at low- energy over four time points. Notice how the lesions are most visible at the peak of the contrast at T1. High- energy acquisition seemed to only offer slightly better image quality in contrast- enhanced images (T1). Every other single- energy imaging paradigm under examination seemed to offer better image quality at low- energy. Figure 10 compares the low- energy and high- energy conventional, contrast- enhanced, and temporally subtracted mammograms of a 28% dense breast phantom. T 0 T 1 T 2 T 3 Figure 9: Mammographic projection images of a 28% dense breast phantom with lesions following a washout kinetic pattern (Type III) acquired at low- energy (W/Rh 28 kvp) over four time points. The arrows point to the location of the lesions. The images are displayed at such window/level settings to match the backgrounds and help visualize the lesion behavior over time. 40

57 Low- Energy High- Energy T1 T0 T1 T0 Figure 10: High- energy acquisitions were observed to only be slightly advantageous in contrast- enhanced images (T1). Every other image acquisition paradigm resulted in similar or higher image quality at low- energy. The low- energy and high- energy mammograms of a 28% dense breast phantom are presented here to illustrate this result. 41

58 T1 T0 HE w LE T0 T1 Temporal Subtraction Dual- energy Subtraction Tomo 44% Dense Mammo Tomo 28% Dense Mammo Tomo 9% Dense Mammo Figure 11: Comparison of low- energy pre- contrast, post- contrast, temporally subtracted, and dual- energy subtracted simulated mammograms and corresponding central tomosynthesis slices of three breast phantoms. The images were cropped for display so sizes are not to scale. 42

59 Figure 11 presents the results of the eight paradigms of conventional, contrast- enhanced, temporally subtracted, and dual- energy subtracted mammography and tomosynthesis on a 9% dense, 28% dense, and 44% dense phantom. The results appear to suggest that tomosynthesis can outperform mammography in terms of lesion visibility. Furthermore, it seems that temporal subtraction can be of critical importance to enhance image quality in mammography, whereas in tomosynthesis the contrast- enhanced images (T1) seem to have sufficient image quality. Due to the absorption of contrast agent in normal breast tissue as well as the malignancies, there is more anatomical noise present in dual- energy subtracted images compared to temporally subtracted images. The measured SDNR values for all the examined acquisition paradigms are shown in Figure 12 and Figure 13 for comparison. Temporal subtraction seems to outperform dual- energy subtraction both as visually perceived and as numerically calculated. As presented, compared to low- energy contrast- enhanced acquisition at T1, temporal subtraction on average provided a 7- fold increase in SDNR in mammography and a 4- fold increase in SDNR in tomosynthesis. This can be explained by the fact that in temporal subtraction, the difference is between a contrast- containing image versus the mask image that contains no contrast at all. In comparison, for dual- energy subtraction, both images contain the same amount of contrast agent, and subtraction reflects only the differential absorption of the contrast- agent at two energies. 43

60 The results suggest that in mammography, the performance can generally be expected to be more dependent on the particular anatomy of the breast, as compared to tomosynthesis, possibly due to the 3D nature of tomosynthesis. In mammography, as a result of temporal subtraction, we measured a 10- fold increase in SDNR in a denser breast, compared to about a 4- fold increase in a less dense breast, with respect to low- energy contrast- enhanced mammography at T1. In tomosynthesis on the other hand, about the same 4- fold increase is observed in the three breast phantoms. Both dual- energy subtraction and tomosynthesis are techniques to reduce anatomic noise. The results suggest that in tomosynthesis, dual- energy subtraction may not be as advantageous due to the inherent noise enhancement in dual- energy subtraction; SDNR was decreased on average by 10% compared to low- energy contrast- enhanced acquisition at T1. Conversely, mammography, which does not have the luxury of tomosynthesis s 3D nature, may benefit more from the dual- energy subtraction; SDNR was increased on average by 40% compared to low- energy contrast- enhanced mammography at T1. 44

61 30 25 Mammography Temporal Subtraction 9% 28% 44% Tomosynthesis Temporal Subtraction 9% 28% 44% SDNR Non contrast Contrast enhanced Single energy Dual energy SDNR Non contrast Contrast enhanced Single energy Dual energy LE HE LE HE LE HE DE 0 LE HE LE HE LE HE DE a. b. Figure 12: Measured SDNR values for various acquisition paradigms applied to the three breast phantoms in mammography (a), and tomosynthesis (b). LE and HE indicate low and high energy, respectively. 25 Mammography 25 Tomosynthesis Temporal Subtraction Temporal Subtraction Average SDNR Average SDNR Non contrast Contrast enhanced Single energy Dual energy Non contrast Contrast enhanced Single energy Dual energy LE HE LE HE LE HE DE 0 LE HE LE HE LE HE DE a. b. Figure 13: Measured SDNR values for various acquisition paradigms averaged over the three breast phantoms in mammography (a), and tomosynthesis (b). LE and HE indicate low and high energy, respectively. 45

62 3.5 Discussion In this chapter we presented our development of 4D breast phantoms by incorporating the contrast agent uptake kinetics in various tissues. Realization of these 4D breast phantoms extends upon previous work by including dynamic effects, paving the way to performing several design and optimization studies. Those may include the evaluation of new imaging techniques and technologies, and the evaluation of new reconstruction algorithms. These phantoms provide the ground truth in performing observer studies, enabling creating matched virtual and physical phantoms to be used for system calibration and quality assurance, and eventually to realize virtual clinical trials relevant to dynamic imaging. In order to illustrate the utility of these phantoms, in this work, we presented a first simplified example study where fourteen potential imaging paradigms were selected and simulated by incorporating three breast phantoms representing a range of patients. The paradigms represented a combination of 2D and 3D, conventional and contrast- enhanced, dual- energy and temporal subtraction, and low- and high- energy breast examinations. The paradigms were quantitatively compared in terms of SDNR as a first- order figure of merit. As an additional sanity check, the fully mathematical breast phantom in [109] was also incorporated with the contrast agent uptake kinetics and used 46

63 for comparison. The performance of the fourteen imaging paradigms applied to the 4D mathematical phantom were in agreement with the results of this study. Based on the results of the numerical and qualitative comparisons, 3D imaging is generally expected to result in better detectability. It is also apparent that temporal subtraction outperforms all the other paradigms but it should be noted that these phantom studies essentially represent the ideal situation with perfect compensation of patient motion. Currently, most clinical protocols favor dual- energy subtraction, presumably because temporal subtraction requires longer scan times and is more prone to motion artifacts. The effect of patient motion in these new breast imaging paradigms is a complex issue that has already been reported in previous studies [100]. In fact, it seems necessary to perform temporal subtraction in 2D imaging in order to have comparable performance to 3D paradigms. Dual- energy subtraction seems to be somewhat advantageous but only in 2D imaging. However, the use of optimized spectra based on breast thickness and density can potentially enhance the image quality in dual- energy subtraction. Beam optimization can be carried out using these phantoms. It also seems that in general the performance of 2D paradigms is more dependent on the specific anatomy involved, whereas in 3D imaging the performance is less anatomy- dependent. As an example, the uniformly dense fibroglandular tissue in the 44% dense breast resulted in a higher SDNR calculated for this breast compared to less dense breasts in mammography. Under our global definition, the very dense breast has higher 47

64 SDNR due to the relatively more uniform background with less anatomical variability. However, it is expected that by inclusion of more breast phantoms with various densities, such trends could be reversed. Furthermore, the results support the accepted practice that acquisition at conventional mammographic energies generally maintains higher detectability than higher energies [116]; only post- contrast images acquired at higher energies show slight advantage to the lower energies due to the k- edge of iodine. The tomosynthesis scanning can take several seconds during which the contrast agent keeps propagating. The effect of this propagation into the detection performance can only be studied by incorporating finer timing into the uptake kinetics models and spatio- temporal reconstruction algorithms. Similarly, if clinical protocols require multiple views of the affected breast or the imaging of both breasts, then during the time to take these multiple acquisitions, the contrast distribution may change even more. Studying the sensitivity of the results to various uptake kinetics and partial diffusion of contrast agent during the course of a tomosynthesis scan or multiple scans can be worthwhile in future. Although the results were very promising, this simplified example study should further be refined by a number of enhancements before conclusive comparison of the imaging paradigms can be made. First and foremost, a larger number of these 4D phantoms need to be used to enable statistical comparisons. The XCAT breast phantoms currently constitute the state- of- the- art in anthropomorphic breast phantoms. The 48

65 number of available phantoms is currently under expansion, which in turn will capture the wide range of patients. Secondly, the projection images were created by ray tracing through the phantoms, which does not account for scattering and quantum noise. These factors should be incorporated into the simulations to enable a more realistic simulation of image quality and to further bring in the notion of dose in the comparisons. Thirdly, contrast agent uptake kinetics were modeled for normal tissue, benign, and malignant lesions based on patient MR data. The four time points considered in the kinetic patterns were based on MR imaging time stamps. The concentration of iodine in the blood was estimated based on an average population mass. The fraction of iodine in various tissues was modeled based on the relative tissue vasculature and diffusivity. Including finer timing and patient mass dependence can further refine the uptake kinetic patterns. Lastly, the lesion model used was a mathematical rendition of a round lesion with decreasing radial density. More realistic lesion models with spiculations are under development to be used in the future generations of the phantoms. 3.6 Conclusion In this work, a suite of 4D anthropomorphic virtual breast phantoms was developed for optimization and evaluation of contrast- based imaging systems. The human subject- based breast phantoms were supplemented with contrast agent uptake 49

66 kinetics in normal tissue, benign, and malignant lesions, estimated based on patient MR data. In order to demonstrate the utility of the phantom, we employed three prototype breast phantoms to simulate and compare the performance of fourteen clinically relevant imaging paradigms in lesion detection in a demonstration study. While the results are preliminary, further to be refined with Monte Carlo simulations incorporating the addition of quantum noise, scatter, and beam hardening, and further contextualized by the dose and patient variability considerations, they highlight the utility of the phantoms as useful tools for the design and characterization of breast imaging modalities. In future, we aim to increase the number of breast phantoms used to represent a population as well as incorporating more anatomic lesion models and study the sensitivity of the results to contrast agent uptake kinetic patterns. Nevertheless, the present study highlights the dramatic effect of anatomical heterogeneity on image quality, influencing different imaging modalities differently, making a clear indication that homogenous phantoms may lead to misrepresenting characterizations. 50

67 4. Development of Realistic Physical Breast Phantoms Matched to Virtual Breast Phantoms Based on Human Subject Data 4.1 Abstract Physical phantoms are essential for the development, optimization, and evaluation of x- ray breast imaging systems. Recognizing the major effect of anatomy on image quality and clinical performance, such phantoms should ideally reflect the three- dimensional structure of the human breast. Currently, there is no commercially available three- dimensional physical breast phantom that is anthropomorphic. We present the development of a new suite of physical breast phantoms based on human data. The phantoms were designed to match the extended cardiac- torso (XCAT) virtual breast phantoms that were based on dedicated breast computed tomography images of human subjects. The phantoms were fabricated by high- resolution multi- material additive manufacturing (3D printing) technology. The glandular equivalency of the photopolymer materials was measured relative to breast tissue- equivalent plastic materials. Based on the current state- of- the- art in the technology and available materials, two variations were fabricated. The first was a dual- material phantom, the Doublet. Fibroglandular tissue and skin were represented by the most radiographically dense material available; adipose tissue was represented by the least radiographically dense material. The second variation, the Singlet, was fabricated with a single material to 51

68 represent fibroglandular tissue and skin. It was subsequently filled with adipose- equivalent materials including oil, beeswax, and permanent urethane- based polymer. Simulated microcalcification clusters were further included in the phantoms via crushed eggshells. The phantoms were imaged and characterized visually and quantitatively. The mammographic projections and tomosynthesis reconstructed images of the fabricated phantoms yielded realistic breast background. The mammograms of the phantoms demonstrated close correlation with simulated mammographic projection images of the corresponding virtual phantoms. Furthermore, power- law descriptions of the phantom images were in general agreement with real human images. The Singlet approach offered more realistic contrast as compared to the Doublet approach, but at the expense of air bubbles and air pockets that formed during the filling process. The presented physical breast phantoms and their matching virtual breast phantoms offer realistic breast anatomy, patient variability, and ease of use, making them a potential candidate for performing both system quality control testing and virtual clinical trials. 4.2 Introduction Performance of 2D and 3D x- ray breast imaging systems is currently evaluated using uniform phantoms made of tissue- equivalent plastics with embedded test objects [ ]. These uniform phantoms are used for system characterization and for devising 52

69 optimized imaging paradigms [ ]. However, while these phantoms are effective for characterizing the inherent physical properties of an imaging system, they are far from representing realistic breast background, hence significantly underrepresenting the sophistication of diagnostic tasks that should be the basis of medical imaging performance. As such, there is a need to design and implement system evaluation phantoms that more closely represent the clinical reality. In addition, phantoms should ideally reflect realistic breast background in three dimensions to be applicable to both 2D and emerging 3D imaging modalities. A few non- uniform structured phantoms have been developed consisting of random structure generations by mixing materials or spherical objects [ ]. More sophisticated modeling of the breast anatomy has been done in the context of virtual breast phantoms [ ]. Virtual phantoms provide great utility to inform the design of clinical trials or possibly eliminate unnecessary costs and irradiation necessary for such clinical trials by potentially substituting human subjects [ ]. These phantoms broadly fall into one of two categories: rule- based phantoms that are mathematically defined, and phantoms that are based on the anatomy of specific human subjects. Either can provide a strong basis for developing physical phantoms with similar definitions. However, to date, only two groups have translated their virtual breast phantoms into physical form [ ]. 53

70 In this work, we present our physical breast phantoms matched to virtual phantoms based on human subject images. The physical phantoms were fabricated by additive manufacturing following a data conditioning process and material choice considerations. The phantoms were designed to model a realistic breast anatomy with potential to serve as the ground truth for various studies including virtual clinical trials, dosimetry, and comparison of performance across manufacturers and 3D reconstruction techniques. 4.3 Methods The Virtual Breast Phantoms The physical breast phantoms were generated from the extended cardiac- torso (XCAT) virtual breast phantoms [ ]. These phantoms were originally produced by processing and segmenting images from a dedicated breast computed tomography system (UC Davis, Boone et al. [147]) into multiple tissue classes based on glandular density and skin. Glandular density indicates the volume percent of fibrous and glandular tissues in breast tissue. The boundary surfaces of these fibroglandular tissues were then represented as nested meshes [148], which are capable of capturing the complex topology associated with the real human subject data combined with the 54

71 versatility of mathematical methods to produce constructs that are compressible, deformable, scalable, and morphable. These phantoms can also be represented in a conventional voxelized form seen in Figure 14. In this study, two variations of a prototype physical phantom were fabricated in a compressed state from a representative initially uncompressed XCAT virtual breast phantom shown in Figure 14. This virtual phantom was compressed to 4.5 cm, reflecting typical compressed breast thickness, using a mathematical operation preserving the volume, assuming constant mechanical properties for the breast tissues. The final dimensions of the compressed breast were approximately cm. 100% Fibroglandular 67% Fibroglandular 33% Fibroglandular Skin Adipose Figure 14. Axial and coronal slices through an uncompressed XCAT virtual breast phantom; grey levels show different segmented tissues. 55

72 4.3.2 Design and Fabrication of the Physical Breast Phantoms The XCAT virtual phantoms were made into physical phantoms using additive manufacturing or 3D printing, a widely available commercial technology that provides high spatial resolution printing with reasonable cost. Current systems can use two different photopolymer materials in a single build in a layer- by- layer fashion; the photopolymers are jetted at the locations dictated by the input computer- aided design files and cured by ultra- violet rays. The available materials range from rigid to flexible photopolymers. For this study, all samples as well as phantoms were printed via a commercial service that used an Objet500 Connex printer (Stratasys Ltd., Rehovot, Israel). Samples of the available materials (3 mm thick) were first imaged along with breast tissue- equivalent plastic chips (5 mm thick) (CIRS, Norfolk, Virginia, USA) using a prototype mammography/tomosynthesis unit 1 (Siemens MAMMOMAT Inspiration, Erlangen, Germany). Mammography images were acquired at 85 x 85 µμm pixel pitch, and tomosynthesis slice images were also reconstructed to 85 x 85 µμm pixel pitch and 1 mm slice spacing using the manufacturer s default filtered backprojection algorithm [149]. All quantitative analyses were performed on raw pixel/voxel values with no post- processing applied. 1 The use of this device for tomosynthesis is preliminary in the US. The safety and effectiveness of the device have not been established. The device is under development and not commercially available in the US, and its future availability cannot be ensured. 56

73 To measure linear attenuation coefficients, all samples were imaged under mammography (2D) mode using 28 kvp with W/Rh target/filter combination. With those attenuation values, the photopolymer samples were linearly mapped to the glandular density of the known tissue- equivalent chips. As shown in Figure 15, the most radiographically dense material available to the multi- material 3D printers corresponded to 85% glandular tissue. The least radiographically dense material corresponded to 54% glandular tissue. Based on the above analysis, two physical phantom variations were devised. The first phantom, Doublet, was fabricated by simultaneously printing two different materials. The fibroglandular tissue and skin were grouped and represented by the most radiographically dense material available, mimicking 85% glandular tissue. Adipose tissue was represented by one of the least radiographically dense material available, mimicking 61% glandular tissue. Both materials were mechanically flexible plastics. In comparison with real breast tissue where glandular density varies from 0% to 100%, this phantom offered a limited dynamic range of 24% (85% - 61%) glandular density. These materials were also chosen because of their rubber- like qualities, allowing easier handling and compression. 57

74 Glandular Equivalency 100% 80% 60% 40% 20% 0% Estimated Attenuation % 20% 40% 60% 80% 100% Sample Materials Glandular Equivalency of Tissue Chips a. b. Figure 15. Glandular equivalency of the sample materials (a) and the estimated attenuation of tissue- equivalent plastic chips (b); attenuation was estimated at 28 kvp with W/Rh. Note the dynamic range of the sample materials, corresponding to 31% glandularity difference. In order to increase the dynamic range and contrast in comparison with the Doublet, a second phantom, Singlet, was fabricated with a single rigid material mimicking 74% glandular tissue to present the fibroglandular tissue and skin. A rigid plastic was selected for this variation to allow for safer removal of the support material that the 3D printer uses to hold structures in place through the build process. The Singlet was subsequently filled manually with near adipose- equivalent materials, thus providing dynamic range of 74% (74% - 0%). Many materials were investigated including oil, beeswax, and a permanent resin. To allow easier filling and clearing of air pockets, the 45 mm Singlet phantom was printed as three slabs of equal 15 mm 58

75 thickness. To provide consistent comparisons, the Doublet phantom was also printed the same way. This design also allowed the sandwiching of other test objects or instruments at approximately 15 and 30 mm height above the detector cover. For the singlet phantom, the support material was removed by pressure washing. The filler material for the Singlet phantom should ideally have attenuation close to that of adipose tissue, be permanent and easily transportable, and not degrade the printed anatomy upon its insertion. A number of filler materials were tested. The first filler tested was common vegetable oil. The Singlet was carefully immersed in an oil bath to avoid trapping of air bubbles within the complicated structures of the phantom. Not only was this setup potentially very messy and not permanent, but also the surrounding oil added scattering. The next materials tested were butter and lard, which although not permanent, presented a more realistic contrast using a filler of approximate adipose- equivalency. Next, permanent filler options were attempted. Beeswax offered linear attenuation coefficient that was - 0.4% different from the reference adipose- equivalent sample, but the heat required to melt the beeswax (approximately 62 C) resulted in the warping of the phantom as well as the degradation of fine structures. In addition, it was observed that during cooling, beeswax tended to contract, which sometimes resulted in undesirable air gaps at the junctions between adipose and glandular tissues. Finally, a commercially available water simulant based on urethane chemistry ( QuickWater for Silks, Miracle Coatings, Orange County, CA) was 59

76 investigated. Curing within 8 to 10 hours at room temperature into a clear, flexible resin with linear attenuation coefficient that was +0.4% different from the reference adipose- equivalent sample, this option offered key logistical advantages. Simulated microcalcification clusters were further incorporated into the two phantom models. The clusters were created by crushing eggshells into a fine powder. Eggshells are based on calcium carbonate chemistry, which has similar x- ray attenuation properties as calcium oxalate and calcium hydroxyapatite in breast calcifications [150]. Clusters of various grain sizes were imbedded within resin when filling the Singlet and sandwiched in between the Doublet slabs Validation of Physical Breast Phantoms The images of the phantoms, in mammographic and tomographic mode, were visually evaluated to characterize their overall quality in representing breast tissue, and to identify potential artifacts of the fabrication process. To characterize the realism of the tissue heterogeneity, the appearance of the mammographic images of the phantoms were analyzed through a power- law analysis. Power functions were fit to the noise power spectrum (NPS) of the mammograms of the Doublet and the Singlet. The NPS was computed based on 128x128 ROIs extracted from the raw mammograms acquired by the prototype tomosynthesis unit using a W/Rh 28 kvp technique [ ]. 60

77 To examine the correspondence between physical and virtual breast phantoms, mammographic projection images of the matching virtual breast phantoms were simulated. The attenuation properties assigned to the tissues in the virtual breast phantoms were selected based on the estimated glandular density of materials used to fabricate the physical breast phantoms. The same spectrum of W/Rh at 28 kvp as the prototype tomosynthesis unit used for acquiring the images was applied in the simulations. The simulated virtual phantom images were compared with those of actual phantoms in terms of visual fidelity. 4.4 Results The fabricated physical breast phantoms, the Doublet and the Singlet, are shown in Figure 16. Note the realistic appearance of the external breast shape as well as the internal structures of glandular vs. adipose tissue. The anatomy is identical between these two models. 61

78 a. b. Figure 16. Fabricated physical breast phantoms, the Doublet (a) with two materials, and the Singlet (b) with a single material, both in three slabs of 15 mm each. 62

79 The various filler materials for the Singlet are shown in Figure 17. These photographs illustrate the versatility of the Singlet design as it takes on five different fillers. a. b. c. d. Figure 17. The Singlet filled with various near adipose- equivalent filler materials: the whole volume immersed in an oil bath (a), and the bottom slab only filled with half butter/half lard (b), beeswax (c), and the transparent resin (d). Mammograms of the Doublet and the empty Singlet at W/Rh 28 kvp are presented in Figure 18. The phantoms demonstrate patterns resembling the appearance of breast tissue. The simulated mammograms of the Doublet and the Singlet are also presented in Figure 18. One may note the remarkable agreement between the simulated mammograms and the mammograms of the corresponding physical phantoms. 63

80 Doublet Singlet Physical a. b. Simulated c. d. Figure 18. Mammogram of the Doublet (a) and the empty Singlet (b) acquired with W/Rh at 28 kvp and simulated images generated from the corresponding virtual phantom by incorporating the material properties respectively (c, d). 64

81 Figure 19 depicts the individual mammograms of the three slabs of the Doublet. Note the different appearance of different layers of breast parenchyma. Figure 19. Mammograms of the top, middle, and bottom (left to right) slabs of the Doublet acquired with W/Rh at 28 kvp. Tomosynthesis filtered back- projection reconstructed slices of the Doublet at various depths can be seen in Figure 20. The structures of glandular tissue in the adipose background can be appreciated in these images despite the reduced contrast difference between the two materials. 65

82 Figure 20. Slices taken at 30, 20, and 10 mm (left to right) above the detector cover (out of 44 slices total, each 1 mm thick) through the reconstructed volume of the Doublet acquired with W/Rh at 28 kvp. For the same tomosynthesis slice, Figure 21 shows an analogous region of only the bottom slab of the Singlet filled with each of the tested filler materials. The characteristics of each material are highlighted in Figure 21. The butter/lard created a substantial number of small air pockets, the beeswax left air gaps around the edges when it contracted upon cooling, and the resin produced air bubbles. The resin approach was repeated several times using different filling techniques, but always resulted in some amount of undesirable air bubbles. 66

83 a. b. e. c. d. f. Figure 21. Close- up of a characteristic region 13 mm above the detector through the tomosynthesis reconstructed volume of the 15 mm bottom slab of the Singlet with oil (a), butter/lard (b), beeswax (c), and resin (d) fillers. The same region in the Doublet is presented in (e). The characteristic region is highlighted on the Doublet slice image (f). All images were acquired with W/Rh at 28 kvp. Figure 22 compares mammography and tomosynthesis reconstructed images of the full- volume of the Singlet with resin filler and those of the Doublet. Note the greater subject contrast of the Singlet in both mammography and tomosynthesis images as figuratively measured by the difference between representative analogous bright and dark regions. 67

84 a. b. c. d. e. f. g. h. Figure 22. Full volume mammographic projection through the Singlet with resin filler (a) and the Doublet (b). A slice through the tomosynthesis reconstructed volume of the Singlet with resin filler (c), and the Doublet (d). Corresponding close- up of an analogous region is shown in the bottom row. Imaged with W/Rh at 28 kvp. Comparing the bright vs. dark regions of interest (ROI), the pixel value signal differences were 22.9 (e), 15.1 (f), (g), and 63.5 (h). Figure 23 showcases the mammographic appearance of micro calcifications and the wide range of possibilities of calcification sizes and morphology representing many possible morphological simulations. 68

85 a. b. c. d. e. Figure 23. Microcalcification clusters in mammographic projection of a pure resin slab without anatomy (a), the middle slab of the Singlet filled with resin (b,c), and sandwiched in between the Doublet slabs (d,e), imaged at W/Rh 28 kvp. The detector pixel size is 85 µμm. The power- law description of the mammograms of the Doublet and the empty Singlet, fit to various reported range of spatial frequencies in the literature [ ], are shown in Figure 24. It is seen that the Doublet complies with the reported exponent in the literature for mammographic backgrounds in a narrower frequency range, while the Singlet does so over a wider range. This can be explained by the more significant presence of high frequency components in the Singlet, that more closely correspond with mammographic structures. 69

86 NNPS (mm 2 ) NNPS (mm 2 ) power power fit fit NNPS NNPS data data = = R 2 = R = NNPS (mm 2 ) power fit NNPS data = R 2 = Spatial Frequency (cycles/mm) Spatial Frequency (cycles/mm) Spatial Frequency (cycles/mm) a. b. Figure 24. Power- law description of the mammograms of the Doublet (a), and the empty Singlet (b). 4.5 Discussion There is a need for structured and realistic phantoms for both system quality assurance testing and development and optimization of imaging systems. The available phantoms, commercial or reported in the literature, have tried to address the needs for anthropomorphism in phantoms as well as presence of 3D structures. However, no prior work has generated physical phantoms directly from human subject data at high resolution. In this work, we demonstrated that it is possible to develop physical breast phantoms directly based on human subject images. The XCAT virtual breast phantoms were translated into physical breast phantoms through 3D printing. According to the current technological capabilities, two variations were fabricated based on the same 70

87 matching virtual breast phantom: the Doublet phantom was fabricated from two materials, and the Singlet was fabricated with a single material and subsequently filled with various near adipose- equivalent materials. The physical phantoms demonstrated realistic looking breast anatomy in both 2D and 3D images. The power- law description of the mammograms of the physical phantoms was in good accordance with real human mammograms [ ]. It has been shown previously that the exponent is approximately 3 in real human mammograms and that the lesions will be detectable at smaller sizes for mammogram regions with smaller power- law exponents. It should be noted that power- law similarities do not completely assure anthropomorphic quality; it is possible to have phantoms with desired power- law property but low anthropomorphism. However, our approach is unique because the Singlet and Doublet phantoms are designed to closely reproduce the anatomy of actual human subjects based on which they were modeled. The correspondence between physical and virtual phantoms makes our approach suitable for purposes where the ground truth of the physical phantom is required, such as reconstruction algorithm evaluations and cross- platform comparisons. The simulated mammograms of the virtual phantoms showed great agreement with the mammograms of the physical phantoms. It should be noted, however, that in the case of the Singlet, due to the single material nature of the phantom, isolated islands of fibroglandular structure were excluded in the mesh model. Some fine structures further 71

88 did not endure the support material removal process. These small differences between the physical and the virtual phantoms may need to be reduced in future developments. Additionally, we demonstrated the inclusion of realistic microcalcification clusters of various sizes and morphology in the phantoms. The microcalcifications can be cured permanently within the resin filler, or sandwiched in a thin sheet as an insert. Like many other manually produced phantoms, these clusters cannot be reproduced or controlled. They also lack the inherent match to a gold standard virtual phantom. However, for the clusters implemented in a thin sheet, one may create gold standard maps using high resolution optical scanning. The Doublet was fabricated with the two commercially available materials that offered highest radiographic contrast. However, that corresponded to only 24% difference in glandularity, whereas the real breast tissues vary between 0 to 100% glandularity. As a result, the current version of the Doublet images has limited dynamic range and contrast. The field of 3D printing is undergoing dramatic and rapid advancements. When more materials become available in the future, the dynamic range and contrast can be improved. But in spite of contrast limitation, the Doublet offers the key advantage of being an all in one design where the phantom (in whole or sub- sections) can be fabricated simultaneously in one pass. The plastic material is firm but flexible, and the exterior is shaped like a human breast, so the phantom can be compressed without scratching the paddle or detector cover. 72

89 Compared to the Doublet, the Singlet showed potential for improved dynamic range and contrast. Comparing signal differences within the same region, the Singlet approach consistently offers an improved dynamic range and better contrast between adipose and glandular tissue. However, due to the complexity of its structure, air pockets and bubbles of various sizes were trapped inside. These early prototypes were produced in our labs with minimal professional equipment or experience with materials science; it is anticipated that commercial phantom manufacturers would be able to overcome some of these limitations. For example, performing the filling procedure in a pressure tank or vacuum chamber may alleviate this problem. Furthermore, adipose- equivalent resins can be synthesized to be used as the filler [155]. For both the Singlet and Doublet approach, the result is a fabricated, permanent phantom. In particular, there are no liquid components that are contraindicated for use around sensitive electronic equipment. Although all imaging in this study was performed using one vendor, in practice these phantoms can be imaged on any mammography or tomosynthesis system. The current state- of- the- art in additive manufacturing allows printing with two different materials at a time. Hence, the range of tissue densities in the virtual phantom were binary thresholded into just two simple classes for fibroglandular vs. adipose tissue. This resulted in the loss of some of the finer fibroglandular structures and eliminated the marbling effects created by the multiple fibroglandular classes. We are 73

90 currently exploring the capability of the printers in mixing various materials to reintroduce the intermediary fibroglandular classes into the physical phantoms. In the future, we envision expanding the number of models available by creating more matching virtual and physical phantoms to be used for various studies requiring a representation of the population. In ongoing work, we are expanding the number of virtual phantoms to over a hundred, representing a large library of anatomical variation in a full range of breast sizes and densities [156]. We have also developed techniques that can morph or recombine features of a finite number of human subjects, thus creating many more pseudo- independent variations [135]. For physics quality control (QC) purposes, various test structures such as simple lesions and resolution patterns can be embedded into either approach. Furthermore, lesion models based on algorithmic or human subject data may be embedded in the phantoms [ ]. 4.6 Conclusion This work presented one of the first matched physical and virtual breast phantoms based on human subject data. The mammographic projections and tomosynthesis reconstructed slices of the fabricated physical phantoms offered realistic anatomical breast anatomy. This 3D physical breast phantom was directly based on actual human subject anatomy. Work is under progress to explore different materials to 74

91 enhance the dynamic range and contrast of the phantom images and to add to the diversity of the fabricated phantoms using the many available XCAT virtual phantoms. We envision fabricating phantoms including QC test structures and lesions as well. The extended family of fabricated phantoms may pave the way to virtual clinical trials in the future. 75

92 5. The Impact of Breast Structure on Lesion Detection in Breast Tomosynthesis 5.1 Abstract Given the recent advances in computation and modeling, virtual clinical trials can be carefully designed and carried out to inform, orient, or potentially replace clinical trials given adequate validation and credibility. In this study, we elaborate on the employment and advancement of the sophisticated tools and models that can be used in the design, implementation, and performance analysis of virtual clinical trials. The focus of this study was to demonstrate the capability of these tools and models through characterization of the effect of background tissue density and heterogeneity on the detection of irregular masses in digital breast tomosynthesis. Twenty breast phantoms from the extended cardiac- torso (XCAT) family, which are generated based on dedicated breast computed tomography of human subjects, were used to extract a total of 2173 volumes of interest (VOI) from simulated tomosynthesis images through ray- tracing, noise and scatter modeling, and filtered back- projection reconstruction. Five different lesions, modeled after human subject tomosynthesis images, were embedded in the breast phantoms to create a set of VOIs with and without lesions. Effects of background tissue density and heterogeneity on the detection of the lesions were studied by implementing a doubly composite hypothesis signal detection theory 76

93 paradigm with location known exactly, lesion known exactly or statistically, and background known statistically. The performance of the detectors were evaluated under several situations of interest via receiver operating characteristic curves (ROC). The results indicated that the detection performance is directly related to background tissue density; under the lesion known exactly and background known statistically paradigm, the performance as measured by the area under the curve (AUC) deteriorated by 36% as density was increased 266 folds, yielding findings consistent with clinical studies. Training and testing the detector in a given density category resulted in an average 3.3% improvement in the AUC values. The detection performance varied substantially across the twenty breasts, with AUC ranging from almost one to 0.5. Furthermore, the log- likelihood ratio under H1 and the log- likelihood ratio under H0 seemed to be affected by background tissue density and heterogeneity differently; background tissue density affected the log- likelihood ratio under H1 slightly more than background tissue heterogeneity, while background tissue heterogeneity affected the log- likelihood ratio under H0 4.5 times as much as background tissue density. Considering background tissue variability can change the outcomes of a study utilizing virtual tools and models in design, optimization, and evaluation of imaging systems and techniques and is hence of crucial importance. The XCAT breast phantoms can address this concern by offering realistic and detailed modeling of background tissue variability based on a wide range of human subjects. 77

94 5.2 Introduction It is essential that breast cancer be detected at its earliest stages for better prognosis. Advanced imaging techniques and systems are constantly under development and examination to improve the screening and diagnosis of breast cancer. More recently, with the advent of digital x- ray detectors, three- dimensional imaging of the breast has been made possible. Digital breast tomosynthesis and dedicated breast computed tomography (CT) are two promising three- dimensional modalities that are rapidly growing. Like most technological advancements in medical care, these techniques and systems need to be tested and verified before their clinical translation. What are currently considered the gold standard for justification of clinical translation are clinical trials. Clinical trials are time- consuming, costly, and may expose the population to extra radiation in the case of x- ray imaging. Given the recent advances in computation and modeling, virtual clinical trials can be carefully designed and carried out to inform, orient, or potentially replace clinical trials given adequate validation and credibility. With the ultimate goal of improved cancer detection with breast imaging, it is imperative to understand the detection process and employ this knowledge in design and optimization of better equipment and techniques. Several simulation studies have been carried out in the past to address the performance of a real or a model observer 78

95 under different circumstances [ ]. The seminal work of Burgess et al. in [169, 170] enabled relevant simulation of breast tissue in mammograms with power- law descriptions of the power spectra to be used in observer studies. These studies mainly investigated the effects of various factors in the performance of a real or a model observer in the detection of cancer in mammograms. They quantified the effects of lesion size, shape, and location, background tissue density and variation, as well as system geometry, noise, resolution, and radiation dose on lesion detection in mammograms [ ]. New studies have tried to extend such analyses to three- dimensional modalities using simulation platforms [ ]. These studies have reported that system performance varies dramatically in the presence of background variability. Given the three- dimensional nature of the breast and these modalities, the importance of employment of realistic breast models with three- dimensional structure in these studies is evident [ ]. Realistic modeling of lesions and image formation are other important factors that need to be addressed. It is also evident that modeling real observers should be done as accurately as possible to accelerate virtual clinical trials by moving from signal known exactly paradigms to more complicated observer models with signal and background uncertainty, and incorporation of volumetric data as investigated in [ , ]. In this study, we elaborate on the employment and advancement of the sophisticated tools and models that were developed in previous studies [ ] and 79

96 can potentially be used in the design, implementation, and performance analysis of a virtual clinical trial. One attribute of uncertain background tissue is its average density, the volume fraction of fibroglandular tissue, which can be considered as a first order statistic. The background tissue average density is referred to as background tissue density for simplicity hereafter. But that is only one aspect; the spatial distribution and texture of the background tissue, referred to as heterogeneity hereafter, is also an important attribute, which reflects higher order statistics. The focus of this study is to demonstrate the utility of these tools and models through characterization of the effect of background tissue density and heterogeneity on the detection of irregular masses in digital breast tomosynthesis. This was made possible through modeling the population, the imaging system, and the observers. The population was represented via several virtual breast phantoms from the extended cardiac- torso (XCAT) family [ ], with lesion models extracted from human subject tomosynthesis images. The geometry, spectrum, and noise and scatter characteristics of the imaging system were modeled after a prototype tomosynthesis imaging system to simulate the image formation chain. Finally, a doubly composite hypothesis signal detection theory paradigm was devised and implemented to evaluate and characterize the performance of observers in signal known exactly or statistically and background known statistically detection paradigms. The implemented detection paradigm, a Bayesian ideal observer, took advantage of the volumetric data available in tomosynthesis images, incorporated both lesion and 80

97 background uncertainty in decision- making, and used an optimal decision metric with the help of Monte Carlo integration techniques. 5.3 Methods Detecting a lesion in tomosynthesis images can be modeled as classifying a given volume of interest (VOI) as corresponding to only background tissue or to background tissue plus a lesion. This detection task is confounded by three factors: background tissue variation masking the lesion in images, background tissue variation creating an illusion of a lesion in the images, and the presence of system quantum noise, scattering, and other physical artifacts of the system hindering the detection of a lesion. It is therefore important to consider all of these factors when studying the lesion detection. An additional confounding factor which is not considered in this work is rotational, translational, or scale variation between lesion templates and the observed tissue. This detection/classification problem can be formulated in terms of a hypothesis test, where the null hypothesis indicates the sole presence of noisy and uncertain background tissue, and the alternative hypothesis indicates the presence of a lesion in noisy and uncertain background tissue in a VOI in the tomosynthesis image set. In other words, the detector, emulating a radiologist reader, is trying to decide whether a VOI in tomosynthesis images contains a lesion or it is simply normal breast tissue. The readers 81

98 are usually trained by studying images of numerous cases and their corresponding pathological appearance. For each modality, the readers have practically formed a training library of statistically known background tissue variations with and without lesions. In the case of tomosynthesis, the readers have access to slices through the reconstructed volume of a compressed breast, which they can scroll through, look in cine, or look at their maximum intensity projection rendering. In this study, we considered the detector to have access to the tomosynthesis reconstructed slices in a VOI, forming such a training library. The following subsections elaborate the design and implementation of this detection paradigm and its performance analysis Population Modeling The XCAT breast phantoms were generated through processing and segmenting dedicated breast CT images of a large number of human subjects [ ]. These phantoms combine empirical data with the flexibility of mathematical techniques, making the phantoms a great candidate for performing simulation studies. A group of 20 different breast phantoms from the XCAT family were selected to represent a wide range of the population with different shapes, sizes, and densities (volume fraction of fibroglandular tissue). These models consisted of three fibroglandular classes based on density as well as adipose tissue. Each fibroglandular class was considered to be a 82

99 mixture of fibroglandular tissue and adipose tissue. For example, a 90% dense tissue was defined as 90% fibroglandular and 10% adipose tissue by volume. These phantoms are available in both voxelized and mesh formats and can be compressed to various thicknesses. The mesh models for these breast phantoms were compressed to 4 cm thickness in the craniocaudal direction using a simplistic mathematical technique, which preserved the volume of the breast by spreading the tissues in the perpendicular directions to the compression direction. Figure 25 shows the middle axial slice through the 4 cm thick compressed volume of the 20 breast phantoms. The gray values correspond to different fibroglandular tissue classes based on density. The various anatomical distribution of the tissues, the different shapes, sizes, and densities of the breasts can be appreciated in this figure. 83

100 Figure 25: Middle slice through the 4 cm thick compressed volume of the 20 breast phantoms used in the study. The gray values correspond to different fibroglandular tissue classes based on density. Note the various shapes, sizes, and densities of the phantoms Lesion Modeling The lesion models for this study were generated from the tomosynthesis images of five biopsy- proven malignant lesions from five different human subjects. To create the lesion models these images were segmented manually in three dimensions to serve 84

101 as a mask to inform the fitting of a mathematical volume with a Gaussian edge profile to the images based on the techniques in [193]. The finer sampling of the space when fitting a mathematical volume, leads to finer modeling of the irregularities at the cost of computational resources. These models were then thresholded into three fibroglandular tissue classes to correspond with the breast phantoms. For the purposes of this study, the lesions were scaled in three dimensions to be bound in a mm cube and were limited to irregular masses. Figure 26 depicts the middle slice through the tomosynthesis images of the human subjects and the corresponding models generated based on them. It should be noted that in the process of lesion segmentation, the inherent image properties of the tomosynthesis system were included in the lesion definition. A grid with 200 positions 1 cm apart was designed to embed a lesion in the central depth of each breast phantom. This arrangement was designed to take advantage of as much of the breast volume as possible. Clearly not all breasts were large enough to accommodate the potential 200 lesion locations. Only locations falling within the uniformly compressed 4 cm thick region of each breast were used. Figure 27 depicts the lesion grid with one of the five lesion models in all of its 200 positions. Using this technique, a total of 2173 grid positions were identified for lesion placement within the 20 breast phantoms. Lesions, if present, were embedded in the geometric center of each grid position. 85

102 Figure 26: Five lesion models: middle tomosynthesis slice through the lesions in human subject images (top), volume rendering of the generated models (middle), and the three fibroglandular classes after scaling the lesions to fit in a mm bounding box. Figure 27: The lesion grid with 200 positions 1 cm apart filled with the same lesion model. 86

103 5.3.3 Image Formation The geometry, spectrum, and physical characteristics of a prototype tomosynthesis unit 1 (Siemens MAMMOMAT Inspiration, Erlangen, Germany) were used to simulate the tomosynthesis images. Twenty- five projection images spanning a 45 arc were simulated by ray tracing through the mesh models of the breast phantoms, implemented on a GPU cluster. A conventional mammographic spectrum with W/Rh at 30 kvp was used for generating the projection images. Pixels were 4x4 binned to 340 µμm size to limit computational complexity. Considering the spatial extent of the imaging features, this process was expected to have negligible effects on the results. Noise and scatter were simulated and added to the projection images based on measurements done on the prototype tomosynthesis system. The scatter contribution was generated by convolution of the system point spread function (PSF) with the primary image. The PSF of the system was approximated as a function of breast thickness [194]. The scatter contribution was then added to the primary image via a weighted summation based on empirically measured scatter- to- primary ratio for various compressed thicknesses and acquisition energies. The noise magnitude as a function of pixel value and the noise power spectrum (NPS) were estimated based on a 50% 1 The use of this device for tomosynthesis is preliminary in the US. The safety and effectiveness of the device have not been established. The device is under development and not commercially available in the US, and its future availability cannot be ensured. 87

104 glandular, 4 cm uniform phantom (CIRS Inc., Norfolk, VA). To add the noise to the projection images, a Gaussian noise map was created and filtered by the shape of the NPS curve. This map was then multiplied by an intensity- to- noise magnitude map defined by the measured trends to give the overall noise pattern [195]. The magnitude of the added noise corresponded with a typical tube current of 100 mas, corresponding to an average glandular dose of 1 mgy. A classic filtered back- projection algorithm with a cosine filter implemented on a GPU cluster was used to reconstruct the tomosynthesis slices at 1 mm slice spacing and 340 µμm in- plane resolution. To estimate the noise in the tomosynthesis reconstructed images, a requirement of our likelihood ratio calculations, projection images of a uniform phantom were simulated with added noise and scatter and reconstructed. The first order probability density function of the reconstructed noise was found to correspond to a zero- mean Gaussian noise, but presumed not to be white. Figure 28 shows simulated projection and reconstructed images of a breast phantom with various lesions embedded in its middle depth, with and without simulated noise and scatter. 88

105 a. b. c. d. Figure 28: The central projection image of a breast phantom with lesions embedded in its middle depth without (a), and with noise and scatter (b). The middle slice through the reconstructed volume of the same breast phantom without (c), and with noise and scatter (d) Observer Modeling Detection Paradigm It is commonly known that dense parenchymal background tissue may obscure lesions leading to degradation in lesion detection [ ]. At the same time, parenchymal tissue has been postulated to mimic lesions leading to high number of false positives. In this study, we aimed to quantify the impact of background tissue heterogeneity and put that in comparison with background tissue density. As such, we 89

106 evaluated the dependence of detection performance to both background tissue density and heterogeneity. The detection/classification problem can be formulated as a doubly composite signal detection theory paradigm where the null hypothesis indicates the sole presence of noisy and uncertain background tissue in a VOI in tomosynthesis images, and the alternative hypothesis indicates the presence of a lesion in noisy and uncertain background tissue in the VOI in tomosynthesis images. The optimum detector for this situation forms the likelihood ratio, which incorporates the uncertainties in an optimal way. In the context of observer modeling, the likelihood ratio detector is sometimes called a Bayesian ideal observer since it provides an upper bound in detection performance when the inherent uncertainties of the data are optimally taken into account. Note that noise refers to the aggregate deteriorating effects of system quantum noise, scatter, and other physical characteristics on reconstructed tomosynthesis images. Noise was modeled as an additive zero- mean white Gaussian noise with a standard deviation estimated from the images. The uncertainty of the background tissue was modeled directly by using a library of several realizations of VOIs in tomosynthesis reconstructed images of background tissue. The detector is presented with a VOI in reconstructed tomosynthesis images and processes the information so as to decide whether there is a lesion in the VOI or if it is solely background tissue. Each VOI has K voxels. The detector has access to N 90

107 different realizations of a VOI of this size in its training dataset, which represents the uncertainty in the background tissue variations. is the set of these N background S 0 tissue- only VOIs. The detector also has access to a copy of each VOI from S 0 with a given lesion model, l, embedded in the same background tissue, for all lesion models 1 S 1,,L l =1,, L. is the set of these L! N VOIs. Therefore, the detector training dataset consists of S 0 1! S 1,,L. The detector classifies a vectorized test VOI x v = (x v,1,, x v,k ) as belonging to either hypothesis, H 0 : x v = s 0 i + n, s 0 i = (s 0 i,1,,s 0 i,k ), i =1,,N, s 0 i! S 0 or H 1 : x v = s 1 i (l)+ n, s 1 i(l) = (s 1 1 i,1 (l),,s i,k (l)), i =1,,N, l =1,, L, s 1 1 i (l)! S 1,,L (1) where n = (n 1,, n K ), n i ~ N(0,! ) represents the noise. The fact that background tissue can vary significantly introduces uncertainty in both hypotheses. Furthermore, the lesion model embedded in the VOIs can introduce additional uncertainty. This doubly composite signal detection theory problem can be tackled by computing the likelihood ratio for a test VOI and comparing it against a threshold to make a decision. It is well known that likelihood ratio detectors are optimum for a wide variety of criteria. As a result, the receiver operating characteristic curves (ROC) using this optimal approach provide a realistic upper bound on the detection performance as a function of the 91

108 uncertainties in both the lesion and the background. Equation (2) shows the derivation of the likelihood ratio,! v, for a given test VOI, x v, for the doubly composite hypothesis signal detection theory problem; namely where there is background uncertainty present under both hypotheses, and lesion uncertainty under the alternative hypothesis. In particular, the likelihood ratio is formulated to incorporate quite directly the uncertain background information. It should be noted that the lesion location was assumed to be fixed, at the center of every VOI, and thus the effect of rotation, translation, and scale of the lesion templates on detection was not evaluated in this work. The VOIs in the training dataset were assumed to be equiprobable: p(s 0 i H 0 ) = 1 N, p(s 1 i (l) H 1 ) = 1,i =1,, N,l =1,, L LN. The last step in deriving this form of the likelihood ratio is to use a Monte Carlo integration to approximate the integrals. This results in a form of the likelihood ratio that uses the available realizations of a VOI in the training dataset [201]. It was also assumed that the training dataset does not include the exact background tissue as in the test VOI, with or without a lesion embedded in it. The likelihood ratio calculation as presented, goes beyond simple cross- correlation calculation by including energy terms in both its numerator and denominator. 92

109 ( ) ( ) =! v = p x H v 1 p x v H 0 = = = = = " L " L l=1 s 1 1 (l),s 1 i (l)!s 1 v (l) " L s N 1 (l) l=1 s 1 1 (l),s 1 i (l)!s 1 v (l) ( ) " p( x v H 1, s 1 i (l)).p s 1 i (l) H 1.ds 1 i ( l).dl s N 0 " s 1 0,s i 0!s v 0 0 p( x v H 0, s i ).p s 0 0 ( i H 0 ).ds i K " # p( x v, j H 1, s 1 i ( l j=1( ))).p ( s 1 i (l) H 1 ).ds 1 i ( l).dl s N 1 (l) s N 0 " s 1 0,s i 0!s v 0 l=1 s 1 1 (l),s 1 i (l)!s 1 v (l) L " K 0 # p( x v, j H 0, s j=1( i )).p s 0 0 ( i H 0 ).ds i % % 1 2!" exp $ x $ s 1 2 (( ' K ' ( v, j i, j ( l) ) ** " '# j=1 ' 2! 2 **.p ( s 1 i (l) H 1 ).ds 1 i ( l).dl & & )) 0 1 2!" exp $ x 0 2 s N % % (( ' K ' ( v, j $ s i, j) ** '# j=1 ' 2! 2 **.p s 0 0 " ( i H 0 ).ds i s 0 1,s 0 0 i!s v & & )) s N 1 (l) s N 1 (l) " l=1 s 1 1 (l),s 1 i (l)!s 1 v (l) L " l=1 % ' ' ' & L + l=1 N + i=1 i!v % ' ' & % ' ' & s N 0 " s 1 0,s i 0!s v 0 + K j=1 + ( ( )) % exp $ x $ s 1 ' v, j i, j l ' 2! 2 & % exp $ x $ s 0 K ' v, j i, j j=1 ' 2! 2 & ( ) % % exp $ x $ s 1 2 (( ( ' K ' ( v, j i, j ( l) ) ** * 1 ' + j=1' 2! 2 ** *. & & )) * LN.dl ) % % exp $ x $ s 0 2 (( N ' K ' ( v, j i, j) ** ' j=1' 2! 2 ** N & & )) i=1 i!v % % % exp $ x $ s 1 2 (( ( ' N ' K ' ( v, j i, j ( l) ) ** * ' + ' + j=1' 2! 2 ** * ' i=1 & & ) & ) * i!v ). % % L exp $ x 0 2 (( N ' K ' ( v, j $ s i, j ) ** + ' + j=1' 2! 2 ** & & )) i=1 i!v 2 2 (( ** **.p ( s 1 i (l) H 1 ).ds 1 i ( l).dl )) (( ** **.p ( s 0 i H 0 ).ds 0 i )) (2) 93

110 The likelihood ratio is calculated for every VOI in the test dataset. Using the same test dataset as the training dataset results in optimal decision making. After obtaining the probability density function of the likelihood ratio under each hypothesis, one can use equation (3) in the traditional way to obtain the ROC, or the resultant area under the curve (AUC), as the detection performance metric. The following shows the decision rule based on a threshold,!, and the resulting probability of detection, P D, P F and the probability of false alarm, :! v H 1 > H 0! < ", P = p D "! H 1 (!)d!, P F = " p! H0 (!)d!. " "! (3) Test and Training Datasets Two different sets of tomosynthesis images were generated to constitute the test and training data under the two hypotheses. Under H0, from the images of the 20 breast phantoms, without inclusion of any lesions, 2173 VOIs of dimensions cm were extracted at the locations that fall within the uniformly 4 cm thick region of each breast. These VOIs constituted S 0 with N = Under H1 on the other hand, tomosynthesis images were generated with the inclusion of a lesion grid. A set of 2173 VOIs of the same 94

111 dimensions was extracted from the same locations as in S 0 per each of the five lesion models. As a result, a total of VOIs were generated. Different subsets of these VOIs could be used to constitute data for problems with different hypotheses for S 1 l H0 and H1. The subscript in specifies the lesion model(s) used in the VOIs in the set; for instance S 1 1 consists of 2173 VOIs with lesion model 1 embedded in them, and S 1 2,3,4,5 consists of the 2173 VOIs with lesion model 2 embedded in them, the 2173 VOIs with lesion model 3 embedded in them, etc.: constituting VOIs in total. In theory, the elements of S 0 and S 1 may not be contaminated by noise or scatter. However, in practice, such images are unavailable. As a result, all VOI realizations in S 0 and S 1 included noise and scatter. Figure 29 shows sample VOIs from one breast under both hypotheses. The test and training datasets were used in a leave- one- out fashion, meaning that the particular background realization under test was excluded from the training dataset to mimic real practice more closely. The density of every VOI was calculated from the corresponding cm region in the voxelized breast phantom as a fraction of fibroglandular tissue in the volume. Figure 30 shows the distribution of the VOI density across the 2173 VOIs. The mean VOI density per breast for the 20 breast phantoms was 0.23, in a range of 0.02 to

112 a. b. Figure 29: Middle slice through adjacent tomosynthesis reconstructed VOIs from one breast, with a lesion model embedded in them (a), and without any lesions (b). Notice that the lesions are invisible in certain VOIs as a result of tissue superposition, noise, and scattering. Figure 30: The histogram of the distribution of VOI densities across 2173 VOIs. 96

113 5.3.5 Detection Analysis There are a number of interesting and different detection situations that merit investigation. To evaluate the detection performance of the detector, an ROC curve was generated from the likelihood ratios calculated for each test VOI based on a variant of equation (2) suited to the situation under investigation. First, the performance of the detector was evaluated under a lesion known exactly and background known statistically situation. It should be noted that the knowledge of the lesion is in the form of tomosynthesis images of the lesion in various background tissue realizations, which already includes effects of tissue superposition and tomosynthesis artifacts. In other words although the lesion embedded in the VOIs is considered known exactly, its appearance in tomosynthesis images can vary depending on the background tissue it is embedded in. The detector was both trained and tested on S 0! S 1 1 in a leave- one- out fashion. The optimal likelihood ratio for this paradigm was calculated as! v = N ( i=1 i)v " exp $ $ # N ( i=1 i)v K ( j=1 " exp $ $ # ( ( )) "! x! s 1 $ v, j i, j 1 $ 2" 2 # K ( j=1 ( ) "! x! s 0 $ v, j i, j $ 2" 2 # 2 2 %% '' '' &&, N = 2173, K = %% '' '' && (4) 97

114 The histogram of the log- likelihood ratios under each hypothesis were also generated for further visualization of their underlying relationship Effect of Background Tissue Density Uncertainty To study the effect of background tissue density on detection performance, the 2173 background realizations were divided into five categories based on the density of the VOI, denoted by d(!). The density categories were selected so that there was equal number of VOIs in each category. The category bounds were specified by d m, m =1,, 5. The effect of background tissue density uncertainty was evaluated in two different paradigms. Note that under both paradigms, the detector had to classify a test VOI in a given density category as either background- only, or background plus a known lesion. The background was only known statistically Signal Known Exactly- Background Known Statistically (SKE- BKS): First, it was assumed that the detector is trained in all density categories but is tested in a certain density category. The likelihood ratio was calculated based on equation (4) with S 0! S 1 1 as the training dataset, and {s 0 i, s 1 i (1) i! D m }, D m = {i d m " d(s 0 i ) < d m+1,i =1,, N}, m =1,, 5 as the test datasets. Under this paradigm, the effect of the number of realizations included in the test and 98

115 training datasets, 89! N! 2173, was examined on the detection performance in every density category Signal Known Exactly- Background Known Statistically- Density Known Statistically (SKE- BKS- DKS): Next, it was assumed that the detector knows the background tissue density category of the test VOI, but not its particular background tissue density, which is the underlying uncertainty. The detector was both tested and trained in a specific density category: {s 0 i, s 1 i (1) i! D m }, D m = {i d m " d(s 0 i ) < d m+1,i =1,, N}, m =1,, 5. The optimal likelihood ratio for this paradigm was calculated as! v!dm = ) i!d m i*v ) i!d m i*v # exp % % $ K ) j=1 # exp % % $ ( ( )) # " x " s 1 % v, j i, j 1 % 2" 2 $ K ) j=1 ( ) # " x " s 0 % v, j i, j % 2" 2 $ 2 2 && (( (( '', K = 9251, m =1,, 5. && (( (( '' (5) This paradigm examined the effect of background tissue uncertainty with the knowledge of background tissue density category on detection performance. 99

116 Effect of Lesion Uncertainty To characterize the effect of lesion uncertainty on detection performance, two different paradigms were considered. Note that under both paradigms, the detector had to classify a test VOI in a given density category as either background- only, or background plus a lesion. The background was only known statistically Signal Known Exactly- Background Known Statistically- Across Lesions (SKE- BKS Across Lesions): First, it was assumed that the detector exactly knows the lesion; this situation was implemented for every one of the five lesion models. The detector was trained in S 0 1! S l, and tested in {s 0 i, s 1 i (l) i! D m }, D m = {i d m " d(s 0 i ) < d m+1,i =1,, N}, m =1,, 5. This paradigm examines the effect of lesion variability on detection performance. The optimal likelihood ratio for this paradigm was calculated as! v!dm = N ) i=1 i*v # exp % % $ N ) i=1 i*v K ) j=1 # exp % % $ ( ( )) # " x " s 1 % v, j i, j l % 2" 2 $ K ) j=1 ( ) # " x " s 0 % v, j i, j % 2" 2 $ 2 2 && (( (( '', N = 2173, K = 9251, m =1,, 5. && (( (( '' (6) 100

117 Signal Known Statistically- Background Known Statistically (SKS- BKS): Next, the detector was assumed to only have a statistical knowledge of the lesion in the sense that it is trained with a finite number of similar lesion possibilities. The detector was tested in {s 0 i, s 1 i (1) i! D m }, D m = {i d m " d(s 0 i ) < d m+1,i =1,, N}, m =1,, 5, while trained in S 0! S 1 2,3,4,5. The likelihood ratio was calculated as! v!dm = L ) l=2 # # # exp " x 1 2 && & % N K % % ( v, j " s i, j ( l) ) (( ( % ) %)% 2" 2 (( ( % i=1 j=1 $ $ ' $ ' ( i*v ', L = 5, N = 2173, K = 9251, m =1,, 5. # # 4 exp " x 0 2 && N K % % ( v, j " s i, j ) (( ) %)% 2" 2 (( j=1 $ $ '' i=1 i*v (7) The purpose of this paradigm was to examine the effect of lesion uncertainty in addition to background uncertainty when the detector is trained with several lesion models but tested on a new lesion model Effect of Background Tissue Heterogeneity Uncertainty Up to this point, the data collected from 20 breasts were combined to evaluate the detection performance. To evaluate the detection performance in an individual 101

118 breast, the lesion known exactly, background known statistically paradigm was selected for each VOI and the detector assumed the VOIs for a given breast were statistically independent. The log- likelihood ratios calculated as in equation (4) under H0 and H1 corresponding only to the VOIs in a given breast were used to create an ROC curve for each breast. The trends in log- likelihood ratio under H0 and H1 at the 2173 VOI locations across the 20 breast phantoms were compared with the trends in background tissue density to examine the contribution of background tissue density and heterogeneity to detection performance. This was done as an effort to characterize the underlying information content in image data that can lead to true positive and false positive lesion identification in eventual observer experimentation. It is in that context that this manuscript used the terms log- likelihood ratio under H0 and the log- likelihood ratio under H1 to characterize the effect of uncertainty in the background tissue density and heterogeneity. 102

119 5.4 Results Effect of Background Tissue Density Uncertainty Figure 31 shows the histogram of the log- likelihood ratio per equation (4) under each hypothesis with test and training datasets S 0! S 1 1. The corresponding ROC curve is also shown. The detector is faced with background uncertainty, has no detailed knowledge of the background density, and the lesion is considered known exactly. Under the same conditions, the ROC curves were generated for each density category separately to evaluate the effect of density uncertainty on the detection performance in each density category in the SKE- BKS paradigm ( ), Figure 32- a,b. In this case, it is seen that the AUC was decreased by 2%, 6%, 13% and 20% as density was increased between 0, 0.005, 0.049, 0.142, 0.332, and 1.0 (density category bounds) respectively. In other words, the detection performance deteriorated as the density increased. With the test and training datasets divided into the five density categories in the SKE- BKS- DKS paradigm ( ), the effect of more detailed knowledge of the density category on detection performance, and the AUC, are presented in Figure 32- c,d. The results suggest that the knowledge of the density category, improves the performance of 103

120 the detector by an average of 3.4% increase in the AUC in each density category, compared to the SKE- BKS paradigm ( ). Under the paradigm of training on all density categories, the SKE- BKS paradigm ( ), the effect of varying the number of VOIs included in the test and training datasets on the AUC was studied to ensure the stability of the above findings. The results are presented in Figure 33. Note that when different values were used, the number of VOIs in each density category were not necessarily equalized. It appears that a minimum of four hundred independent VOIs needed to be included in the training dataset for the results to approach the steady state. The concordance of these results with the common knowledge can serve as a validation of the tools and models used in this study for possible application in virtual clinical trials. Beyond the subjective validation, the results show the impact of background tissue density in the presence of background uncertainty in quantitative terms. 104

121 H 0 18 H Histogram Histogram Log likelihood Ratio 1 a Log likelihood Ratio P D b. Figure 31. The histogram of log- likelihood ratio in equation (4) under H0 and H1 (a), and the ROC curve for the detector. The AUC is P F 105

122 P D 0.5 AUC <= Density < <= Density < <= Density < <= Density < <= Density < P F 1 a. b Density P D 0.5 AUC <= Density < <= Density < <= Density < <= Density < <= Density < P F Density c. d. Figure 32: ROC curves for different test density categories in the SKE- BKS paradigm ( ), where the detector is trained on all density categories (a), and the AUC of each curve as a function of density (b). ROC curves for different density categories in the SKE- BKS- DKS paradigm ( ), where the detector is tested and trained on a specific density category (c), and the AUC of each curve as a function of density (d). The change in the density training paradigm increased the AUC by an average of 3.3% in each density category. 106

123 AUC <= Density < <= Density < <= Density < <= Density < <= Density < number of VOIs Figure 33: Effect of N, total number of VOI realizations included in the test and training datasets, on the stability of AUC values, under the SKE- BKS paradigm ( ), evaluated for every density category Effect of Lesion Uncertainty Having assured that enough VOI realizations were used in the training dataset, the effect of lesion uncertainty on detection performance was evaluated. First, the effect of lesion variability was examined on the detection performance in the SKE- BKS Across Lesions paradigm ( ). The use of the five lesion models led to similar performance in terms of density dependence. The ROC curves corresponding to these paradigms are shown in Figure 34- (a). The AUC dropped by 1.3%, 4.8%, 12.1%, and 23.3% on average as the density was increased between 0, 0.005, 0.049, 0.142, 0.332, and 107

124 1.0 respectively, for the five lesion models. The AUC varied between 1.2% to 8.4% across the lesion models in the same density category. Greater background density led to an average AUC of 0.625±0.013 over the five lesion models, which indicates the closeness to an almost chance performance. Next, the ROC curves for the case of lesion and background known statistically in the SKS- BKS paradigm ( ) are shown in Figure 34- (b) in each density category. The AUC dropped between 2.8% to 7.9% in the same density categories in comparison with the SKE- BKS paradigm ( ). These results are in accordance with the expectation that not knowing the exact characteristics of the lesion can make the detection harder. This last paradigm can be considered to be a preliminary result closer to a situation for a radiologist reader; the radiologist has seen many sample lesions, certainly more than the four training examples used in this work, but as in this work not the exact lesion, which may be present in the patient under test. Table 3 shows the AUC values for each of these paradigms. 108

125 P D Lesion 1, 0<= Density < Lesion 1, <= Density < Lesion 1, <= Density <0.142 Lesion 1, 0.142<= Density <0.332 Lesion 1, 0.332<= Density <1 Lesion 2, 0<= Density < Lesion 2, <= Density < Lesion 2, <= Density <0.142 Lesion 2, 0.142<= Density <0.332 Lesion 2, 0.332<= Density <1 Lesion 3, 0<= Density < Lesion 3, <= Density < Lesion 3, <= Density <0.142 Lesion 3, 0.142<= Density <0.332 Lesion 3, 0.332<= Density <1 Lesion 4, 0<= Density < Lesion 4, <= Density < Lesion 4, <= Density <0.142 Lesion 4, 0.142<= Density <0.332 Lesion 4, 0.332<= Density <1 Lesion 5, 0<= Density < Lesion 5, <= Density < Lesion 5, <= Density <0.142 Lesion 5, 0.142<= Density <0.332 Lesion 5, 0.332<= Density < P F P D Same, 0<= Density < Same, <= Density < Same, <= Density <0.142 Same, 0.142<= Density <0.332 Same, 0.332<= Density <1 Rest, 0<= Density < Rest, <= Density < Rest, <= Density <0.142 Rest, 0.142<= Density <0.332 Rest, 0.332<= Density < P F a. b. Figure 34: ROC curves for the SKE- BKS Across Lesions paradigm ( ) (a) and the SKS- BKS paradigm ( ) (b). ROC curves from the SKE- BKS paradigm ( ) are presented with solid lines in both figures for comparison. Table 3: AUC values for the different detection paradigms. Equalized density categories are denoted by upper and lower bounds on density, d. Paradigm 0 d< d< d< d< d<1 SKE- BKS ( ) SKE- BKS- DKS ( ) SKE- BKS Lesion 2 ( ) SKE- BKS Lesion 3 ( ) SKE- BKS Lesion 4 ( ) SKE- BKS Lesion 5 ( ) SKS- BKS ( )

126 5.4.3 Effect of Background Tissue Heterogeneity Uncertainty Recall that in equation (4), the same test and training datasets, S 0! S 1 1, were used to calculate the log- likelihood ratio under H0 and H1 for every VOI location. The histogram of the log- likelihood ratio under H0 and H1 corresponding to the VOIs from each breast is shown in Figure 35- c. The log- likelihood ratios under H0 and H1 along with their corresponding probability density functions were used to generate ROC curves for each breast for comprehensive performance analysis. These ROC curves are shown in Figure 35- d. It should be noted that the likelihood ratio in equation (4) is not necessarily an optimum metric for an individual breast, since it does not take into account the spatial dependencies and structure across VOIs in a breast. It seems that the detection performance varies substantially across different breasts and that it tends to be closely related to the breast density. To further visualize the location- wise dependence of detection performance within every breast, Figure 36 aims to visualize the correspondence between background tissue density, background tissue heterogeneity, the log- likelihood ratio under H0, and the log- likelihood ratio under H1 at every VOI location across the 20 breast phantoms. First, the middle slice through the tomosynthesis reconstructed volume of every breast is presented for reference. Next, a heat map is generated for every breast to depict the VOI density at various locations throughout the breast. The 110

127 corresponding log- likelihood ratio under H0 and log- likelihood ratio under H1 at the VOI locations as calculated per equation (4) are presented in the form of two heat maps with the same scale. Comparing the same VOI location across the middle tomosynthesis slice and the heat maps suggests that in general the log- likelihood ratio under H0 follows the density trend and the log- likelihood ratio under H1 follows the opposite density trend; generally the log- likelihood ratio under H0 is higher where the density is higher and the log- likelihood ratio under H1 is higher where the density is lower. However, there are several locations for which the reverse is observed. This is not too surprising since it is the uncertain heterogeneity of the background that is being modeled using actual realizations of real tomosynthesis reconstructed images, for which the density is just one parameter that only partially characterizes the uncertainty in the background. 111

128 a. b P F H 0 Histogram P D P D P D P D P D 0 0 P F P F P F P F P D P D P D P D P D 0 0 P F P F P F P F P F P D P D P D P D P D 0 0 P F P F P F P F P F H 1 P D P D P D P D P D Log likelihood Ratio 0 0 P F P F P F P F P F 1 c. d. Figure 35: Middle slice through the tomosynthesis reconstructed volume (a), the corresponding heat map of extracted VOI density (b), the histogram of the log- likelihood ratio under H0 and H1 in each breast as calculated per equation (4) (c), and the ROC curve for each breast (d) of the 20 breast phantoms. Note the substantial detection performance variability across different breasts. 112

129 a. b. c. d. Figure 36: Tomosynthesis mid- slice (a), VOI density (b), and log- likelihood ratio under H0 and H1 maps per equation (4) (c,d). Figure 37 shows a scatter plot of the log- likelihood ratio under H0 and the log- likelihood ratio under H1 against density across all VOIs. The data suggest that the relationship between density and the log- likelihood ratio under H0 or H1 is not linear and can rather be approximated by a quadratic fit. As a result of density variation from 0 to 1, the quadratic fit to the log- likelihood ratio under H0 varied by 3.36 and the 113