Science, Faculty of
Physics and Astronomy, Department of
DSpace
UBCV
Ip, Candice Jia Xin
Master of Science - MSc
University of British Columbia
Luminal water imaging (LWI) is a novel quantitative MRI technique developed to aid with prostate cancer diagnosis. The results of LWI have shown significance in relating its derived parameters to the Gleason score, indicating its usefulness with prostate cancer grading. However, LWI parameters cannot show anatomical information on which radiologists rely for diagnosis. To address the lack of anatomic detail and to allow for LWI to become clinically feasible, a method for enhancing anatomical T2-Weighted (T2W) images with luminal water parametric maps is proposed. In addition to enhancing images, a U-Net model is implemented to automatically segment the prostate region and peripheral zone in T2W images. Results indicate that LWI-enhanced T2W images can provide better image contrast when compared to T2W images alone. Automatic segmentation shows a Dice coefficient score of 91.93% and 75.05% accuracy for the whole-prostate and peripheral zone segmentation, respectively. With automatic segmentation and an LWI enhancement routine, anatomical T2W images can be quickly processed to provide better cancer image diagnostics to radiologists in a clinical setting.
Development of MR Image Analysiswith Machine Learning to EnhanceT2W Images with Luminal WaterImaging for Prostate CancerbyCandice Jia Xin IpB.A.Sc., The University of British Columbia, 2018A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinThe Faculty of Graduate and Postdoctoral Studies(Physics)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)August 2022© Candice Jia Xin Ip 2022The following individuals certify that they have read, and recommend to the Faculty ofGraduate and Postdoctoral Studies for acceptance, the thesis entitled:Development of MR Image Analysis with Machine Learning to EnhanceT2W Images with Luminal Water Imaging for Prostate Cancersubmitted by Candice Jia-Xin Ip in partial fulfillment of the requirements forthe degree of Master of Sciencein PhysicsExamining Committee:Piotr Kozlowski, Associate Professor, Department of Physics and Astronomy, UBCSupervisorStefan Reinsberg, Associate Professor, Department of Physics and Astronomy, UBCSupervisory Committee MemberiiAbstractLuminal water imaging (LWI) is a novel quantitative MRI technique developed to aid withprostate cancer diagnosis. The results of LWI have shown significance in relating its derivedparameters to the Gleason score, indicating its usefulness with prostate cancer grading.However, LWI parameters cannot show anatomical information on which radiologists relyfor diagnosis. To address the lack of anatomic detail and to allow for LWI to becomeclinically feasible, a method for enhancing anatomical T2-Weighted (T2W) images withluminal water parametric maps is proposed. In addition to enhancing images, a U-Netmodel is implemented to automatically segment the prostate region and peripheral zone inT2W images. Results indicate that LWI-enhanced T2W images can provide better imagecontrast when compared to T2W images alone. Automatic segmentation shows a Dicecoefficient score of 91.93 % and 75.05 % accuracy for the whole-prostate and peripheralzone segmentation, respectively. With automatic segmentation and an LWI enhancementroutine, anatomical T2W images can be quickly processed to provide better cancer imagediagnostics to radiologists in a clinical setting.iiiLay SummaryProstate cancer is one of the most commonly diagnosed cancers among men in the world.The current tools for identifying prostate cancer are mainly done by blood testing and tissuesampling. Avoiding these invasive tests can be done with the use of magnetic resonanceimaging (MRI).Luminal water imaging (LWI) is a new magnetic resonance imaging technique for de-tecting prostate cancer; however, it is not yet clinically feasible. This thesis proposes twoprojects that will aid with the process for LWI to become integrated into clinical settings.The first project provides a machine learning model, a computational tool, to avoid pro-hibitively labour-intensive tasks. The second project introduces a way to have LWI becomefamiliar to radiologists yet provide the information from LWI to better detect prostate can-cer by enhancing baseline MR images with LWI. Together, enhanced images can be madequickly and provide more information for detecting prostate cancer.ivPrefaceThe ideas of using Luminal Water Imaging together with T2-weighted images was devel-oped by Dr. Piotr Kozlowski. The raw data used in this study is built upon the work byDr. Shirin Sabouri, who together with Dr. Piotr Kozlowski, developed the luminal waterimaging technique.Analysis scripts to process luminal water imaging data is based on MATLAB and Juliacode written by Dr. Shirin Sabouri, Barry Bohnet, Andrew Yung, and Jonathan Doucette.Image processing and analysis code were carried out by the author. Machine learning mod-els were designed from literature and implemented by the author. Guidance from Dr. SilviaChang informed image analysis and provided ground truth data for machine learning train-ing.The contributions of this thesis led to the following presentation:1. Ip CJX, Chang SD, Sabouri S, Yung A, Reinsberg S, and Kozlowski P. EnhancedT2-weighted images using Luminal Water Imaging and U-Net based segmentation forprostate cancer diagnosis. In Proceedings of the 31st Annual Meeting of ISMRM,England, 2022. Abstract 0823.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixAbbreviations & Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1 Clinical Background of Prostate Cancer . . . . . . . . . . . . . . . . . . . . 32.1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1.2 Prostate Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1.3 Diagnosis and Cancer Grading . . . . . . . . . . . . . . . . . . . . . 42.2 Magnetic Resonance Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2.1 History of MRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2.2 MR Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2.3 Imaging Principals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.3 Luminal Water Imaging for Prostate Cancer . . . . . . . . . . . . . . . . . 132.3.1 T2 Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3.2 MR Pulse Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.3.3 Multi-exponential fitting & NNLS . . . . . . . . . . . . . . . . . . . 142.3.4 Luminal Water Imaging Parameters . . . . . . . . . . . . . . . . . . 162.4 Machine Learning, Deep Learning & Convolutional Neural Networks . . . . 182.4.1 Brief History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.4.2 Convolutional Neural Networks in MRI . . . . . . . . . . . . . . . . 192.4.3 Brief Basics of Deep Learning and Convolutional Neural Networks . 20viTable of Contents3 Prostate Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.2 Methods & Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.2.1 Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.2.2 Network Architecture and Training . . . . . . . . . . . . . . . . . . 323.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.4 Discussion & Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354 Image Augmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.2 Methods & Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.2.1 Images and Data for Augmentation . . . . . . . . . . . . . . . . . . 394.2.2 Equation for Augmentation . . . . . . . . . . . . . . . . . . . . . . . 414.2.3 Image Augmentation Optimization . . . . . . . . . . . . . . . . . . 424.2.4 Analysis of Augmentation Efficacy . . . . . . . . . . . . . . . . . . . 434.2.5 Mapping to High-resolution T2W Images . . . . . . . . . . . . . . . 444.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.3.1 NNLS Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.3.2 Image Augmentation Analysis . . . . . . . . . . . . . . . . . . . . . 454.3.3 High-res Image Augmentation . . . . . . . . . . . . . . . . . . . . . 464.4 Discussion & Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465 Conclusion & Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52AppendicesA Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59A.1 T2 Threshold for LWI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59A.2 MATLAB GUI for Hand-Drawn Prostate ROIs . . . . . . . . . . . . . . . . 60A.3 U-Net Predicted ROIs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61A.4 MATLAB GUI for Deforming ROIs . . . . . . . . . . . . . . . . . . . . . . 61A.5 Image Augmentation Results . . . . . . . . . . . . . . . . . . . . . . . . . . 61viiList of Tables2.1 Description of LWI parameters and their associated symbols. . . . . . . . . 163.1 U-Net performance metrics of full prostate and peripheral zone segmentationon the test datasets. The reported metrics are the average pixel accuracy,average Jaccard index, and average Dice coefficient across the entire testdataset. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.1 PCA values for the various zones in prostate (PZ, TZ, and full prostate zone). 44viiiList of Figures1.1 MRI brain scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1 Prostate zones: axial view. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Histological view of normal human prostate tissue in peripheral zone. . . . . 52.3 Prostate zones: axial view. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.4 Diagram of Zeeman energy splitting for spin 1/2 systems. . . . . . . . . . . 252.5 T1 and T2 Relaxation Curves. . . . . . . . . . . . . . . . . . . . . . . . . . . 252.6 T2-echo Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.7 Seven LWI Parameter Maps. . . . . . . . . . . . . . . . . . . . . . . . . . . 272.8 Deep Learning Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.9 Supervised Learning Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.10 Biases and Weights of a Linear Regression Model . . . . . . . . . . . . . . . 292.11 Convolutional Neural Network . . . . . . . . . . . . . . . . . . . . . . . . . 292.12 Convolutional Kernal Operation . . . . . . . . . . . . . . . . . . . . . . . . 303.1 Prostate Regions-of-Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.2 U-Net Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.3 U-Net Segmented MRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.4 Example Full and PZ Prostate ROIs . . . . . . . . . . . . . . . . . . . . . . 373.5 Effect of γ on Focal Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.6 Outliers in PZ Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . 384.1 Augmented T2W Image with LWF Map . . . . . . . . . . . . . . . . . . . . 394.2 ROI of LWF Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.3 Histology Deformation to T2W Image . . . . . . . . . . . . . . . . . . . . . 424.4 Augmentation Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.5 Difference Map of DECAES Compared with MATLAB NNLS . . . . . . . . 454.6 Image enhancement on the three zones . . . . . . . . . . . . . . . . . . . . . 484.7 Image Augmentation Analysis, w = 0.5 . . . . . . . . . . . . . . . . . . . . 494.8 High Resolution Image Augmentation, w = 0.5 . . . . . . . . . . . . . . . . 50A.1 Histogram of calculated T2 times from 4,700 pixels. . . . . . . . . . . . . . 59A.2 MATLAB GUI for Segmenting ROIs . . . . . . . . . . . . . . . . . . . . . . 60A.3 U-Net Output on Test Dataset . . . . . . . . . . . . . . . . . . . . . . . . . 62A.4 MATLAB GUI for Deforming ROIs . . . . . . . . . . . . . . . . . . . . . . . 66A.5 Augmented Image Analysis Results . . . . . . . . . . . . . . . . . . . . . . . 67ixAbbreviations & SymbolsAlong Area under the long T2 component.Ashort Area under the short T2 component.AFMS Anterior Fibromuscular Stroma.CNN Convolutional Neural Network.CZ Central Zone.DL Deep Learning.gmT2 Geometric mean T2.gmT2, long Geometric mean of long T2 component.gmT2, short Geometric mean of short T2 component.GRASE Gradient-and-Spin Echo.GS Gleason Score.H&E Hematoxylin and Eosin.LWF Luminal Water Fraction.LWI Luminal Water Imaging.ML Machine Learning.mpMRI Mutliparametric MRI.MRI Magnetic Resonance Imaging.MWI Myelin water Imaging.Ncomp Number of T2 components.NE Number of Echoes.xAbbreviations & SymbolsNMR Nuclear Magnetic Resonance.NNLS Non-Negative Least Squares.PCa Prostatic Carcinoma.PZ Peripheral Zone.qMRI Quantitative Magnetic Resonance Imaging.ROI Regions of Interest.SNR Signal-to-Noise Ratio.T2W T2 Weighted Image.TE Echo Time.TR Repetition Time.TRUS Transrectal Ultrasound.TZ Transition Zone.xiAcknowledgements“It’s the sides of the mountain which sustain life, not the top. Here’s where things grow.”– Robert M. PirsigFirst and foremost, I would like to express my sincerest gratitude to my supervisor, Dr.Piotr Kozlowski, for his support, patience, and mentorship that made this work possible.He is a kind teacher who allowed me to learn without judgement. I am grateful that he gaveme the freedom to explore different ideas and for the time spent providing me insightfulfeedback and anecdotes on both my research and in life.The same thank you extends to Dr. Stefan Reinsberg, as I was provided informal co-supervision by extension of the lab, which undoubtedly enriched my education and criticalthinking. Another informal supervisor from the lab would be Andrew Yung. A big thanksto these two for their invaluable help with my projects. Their humble ways of teaching andcuriousness are inspiring, and I will always remember their kindness.A special thank you to the current and alumni of the UBC MRI Research Centre: Mon-ica, Michelle, Kirsten, Masha, Annika, Maryam, Barry, and Shirin. This thank you alsoextends to the MRI family at UBC. Learning about MRI with a supportive and welcominggroup has made my learning journey one I am very fond of.I would also like to thank UBC for being my home and community these past severalyears throughout my undergraduate and master’s degree. It’s been a hub where I’ve madedeep connections with fantastic people. With UBC’s infrastructure, I have been able topursue and explore teaching and outreach while fostering my intellectual growth. My MScwould not have been the same without my friends at The (Un)Scientific Method and PhysicsCircle–together, we have built avenues for sharing science.My deepest gratitude for my friends and mentors who have supported me throughout itall, whether it be by providing a helping hand, sharing new perspectives, being a companionon adventures, or reminding me to celebrate life– thank you for being here.Kevin, who has provided unwavering support, patience, and encouragement in my aca-demics and in life, I am truly grateful to have you by my side.And to my family, who have supported me my entire life and I know will continue to doso. Baba, Mama, Michael, and Helen– I’m lucky to have you.xiiChapter 1IntroductionMagnetic resonance imaging (MRI) is a remarkable tool that allows us to see details of ourbrain, musculoskeletal structure, tissues, and much more beyond what our eyes can see.For example, Figure 1.1 shows an example of an MRI depicting the tissue structure of thebrain between the skull. While there are other clinical imaging modalities such as X-ray(including X-ray CT), positron emission tomography (PET), and ultrasound, MRI standsout with being non-invasive and non-ionizing while maintaining good spatial resolution andsuperior tissue contrast [1]. Though, it is worth mentioning that these other imaging toolsalso have their benefits above MRI for various imaging and clinical needs. Today, MRIis an essential clinical and evolving research tool capable of imaging inside our bodies fordiagnosing cancers [2, 3], understanding brain function [4], exploring metabolism [5], andimaging single cell [6].Figure 1.1: A 3D T1 MRI depicting the head where white mat-ter, grey matter, and general brain structure are clearly visible.1.1A 3DT1 MRI of my brain for a spectroscopy study conducted by Alex Ensworth [7]1Chapter 1. IntroductionWhile the MRI tool is mainly known for its use in medicine, the field is interdisciplinaryand diverse. In addition to the prominent scientists, engineers, and mathematicians whohave laid the foundation for MRI to exist today, there are continual contributions fromvarious disciplines in academia and industry who work in uncovering new methods andtechniques to widen the applicability of MRI and allow for new understanding of livingtissues.One of the more novel uses for MRI is to generate quantitative information from scans.MRI is traditionally described as a technique that is typically qualitative in nature. However,the development of quantitative MRI (qMRI) can allow for the extraction of quantitativeestimates (e.g. concentration) of physical properties [8, 9] (e.g. myelin as a fraction ofwater signal or tumour % [10]). There is a vast potential for qMRI to inform clinicians withinformation beyond tissue contrast and with repeatable, accurate, and reliable data acrossand within patients [11]. Nevertheless, work needs to be done in moving qMRI past thepre-clinical stage and become a robust and usable tool for radiologists [9]. As part of thisthesis, we aim to introduce analysis techniques to increase the clinical usability of luminalwater imaging (LWI), a qMRI technique for prostate cancer detection. LWI has shownclinical feasibility and the next step is to include anatomical information that radiologistsrely on. To do so, (computational) image analysis tools are introduced and these tools mayallow a feasible path towards clinical implementation [12].In Chapter 2, background information necessary to understand this work’s context isprovided. It begins with an introduction to prostate cancer that moves into MRI historyand basics, concepts of luminal water imaging, and ends with an overview of deep learningin the context of image segmentation.Chapter 3 outlines how prostate segmentation is performed. By using deep learning,automatic tracing of the prostate is achieved, and the specifics of training, validating, andtesting the algorithm are laid out. Additionally, methods of calculating LWI are comparedand discussed.Chapter 4 moves into the clinical-facing portion of this work. As LWI provides imagesthat lack anatomical information that radiologists rely on to diagnose prostate cancer, mywork attempts to bridge LWI with T2-weighted (T2W) images. We call these augmented(or weighted) T2W images. The equation and the experiments performed to achieve thebest weighting are discussed in this section.Finally, Chapter 5 is the last chapter that mentions a final summary and offers conclud-ing words.2Chapter 2BackgroundThe purpose of this section is to provide the groundwork and context for the results of thisresearch. The first section, Section 2.1, emphasizes prostate cancer’s unfortunate ubiquityand outlines the disease’s current clinical diagnosis and structure. Section 2.2 is used tobriefly outline the classical physics that governs some principles of magnetic resonanceimaging that have been learned from professors, peers, and texts. In Section 2.3, we discussthe technique of Luminal Water Imaging– the imaging methodology upon which this thesisis built. Proceeding to Section 2.4, we motivate the reasons for the ever-growing field ofdeep learning and its use in this thesis while reviewing current algorithms used for imagesegmentation.2.1 Clinical Background of Prostate Cancer2.1.1 MotivationThe motivation for the research in qMRI for prostate cancer is driven by the demand forbetter prostate cancer screening and detection. Prostate cancer is the fifth leading cause ofcancer death and the second most commonly diagnosed cancer among men worldwide [13,14]. The most common type of cancer found in the prostate is adenocarcinoma, a typeof prostatic carcinoma (PCa). Though PCa is a disease that can be effectively treatedwhen diagnosed early on, screening requires invasive measurements involving digital rectalexams, blood tests, and biopsies [15]. However, even after 25 years since the introductionof prostate-specific antigen testing of blood, the method remains a highly debated practicebecause of its tendency to over-diagnose PCa thereby putting stress on both patients andhealthcare systems [16]. Moreover, invasive tests such as biopsies can lead to pain, anxiety,and up to a 5% risk of infections [17]. More accessible and accurate PCa detection anddiagnosis techniques are ultimately needed to reduce PCa morbidity and mortality.2.1.2 Prostate StructureThe prostate is a walnut-shaped gland in the male human pelvis with the primary functionto provide nutrients when developing seminal fluid for the reproductive system. Often,prostate regions are considered in McNeal’s anatomical zones: peripheral zone (PZ), tran-sition zone (TZ), central zone (CZ), and anterior fibromuscular zone [18–20]. Figure 2.1depicts the approximate zone structure from an axial prostate slice.32.1. Clinical Background of Prostate CancerFigure 2.1: A simplified diagram of prostate zones in an axialslice located in the mid gland between the base and apex of theprostate.Prostate tissue comprises both non-glandular and glandular tissue. The anterior fibro-muscular zone is entirely non-glandular and is made of muscle fibres and connective tissue,also known as stroma, whereas glands are present in the PZ, TZ, and CZ [20–22]. Glandswithin the prostate are identified by the organizational structure of secretory cells calledacini connected via ducts [20, 23]. Each unit of acini have secretory cells that form togetheras an epithelium (a structure of cells which line hollow organs and glands) that outlinesand fills a central lumen (a fluid-filled cavity) with prostatic fluid carried by a network ofducts[23–26]. Figure 2.2 shows the microstructure through a microscope image of normalglandular prostate tissue from the PZ stained with hematoxylin and eosin (H&E).2.1.3 Diagnosis and Cancer GradingOver 95% of prostate cancers are adenocarcinoma, indicating that prostate cancer’s highestprevalence is within glandular regions [28]. Of the three glandular regions, roughly 70%-80% of PCAs are found in the PZ, 20%-30% in TZ, and rarely in the CZ [28, 29].The current gold standard method for medically diagnosing PCa is through prostatebiopsies [30]. However, a biopsy is typically only performed if a patient is suspected ofhaving PCa after screening which involves a digital rectal examination and/or a prostate-specific antigen blood test [30, 31]. If a patient returns with a positive screening, theywill be referred to a urologist for a prostate biopsy performed together with transrectalultrasound (TRUS). Interpretation of biopsy is through histopathology, the study of micro-scopic tissues for medical diagnosis. For PCa, current tissue diagnosis is performed throughlight microscopy of H&E stained tissue sections. Since 2014, the accepted and standardizedmethod for reporting histopathology has been with using the Gleason score (GS) [32–35].With Gleason scoring, tumour patterns are separated by the morphology of cancerous tissueas seen in Figure 2.3 to be assigned their GS. The GS is an essential identifier as it is crucialin determining cancer stages [36].The values of the GS are reported as an integer sum of the Gleason primary and sec-ondary pattern, where a pattern (primary or secondary) is assigned an integer value between42.1. Clinical Background of Prostate CancerFigure 2.2: Specimen of human prostatic tissue from normalperipheral zone stained with hematoxylin and eosin with a 20xmagnification for histological examination. Arrows depict theluminal cavities, epithelial secretory cells that provide luminalfluid, and surrounding stroma. Figure used with permissionfrom S. Sabouri[27] ©2017.1 and 5. For example, a Gleason score would be reported as 4 + 3 = 7 for a tissue biopsysample containing such primary and secondary patterns. The lower the number, the moreregular the cell structure appears to normal tissue and vice-versa with higher patterns– thesehave shown a statistically significant correlation with higher cancer stage [38]. Gleason pat-terns 1 and 2 are no longer assigned; thus, only patterns equal or above 3 are included inthe GS [35, 39].MRI has recently been integrated into clinical pipelines for qualitative PCa diagno-sis. The MRI technique used clinically is with the acquisition of multi-parametric MRI(mpMRI) scans that are assessed by radiologists with a standard known as ”Prostate Imag-ing Reporting and Data System” version 2 (PI-RADS V2) [40, 41]. Radiologists are ableto order a suite of MR images during an mpMRI protocol: T2-weighted (T2W), diffusion-weighted (DWI), dynamic contrast-enhanced (DCE), and sometimes proton spectroscopy.From DWI, the apparent diffusion coefficient (ADC) can be calculated for each pixel usingthe Stejskal-Tanner equation [42] thereby creating an ADC map. From DCE, concentrationsof the contrast agents are processed voxel-wise, and a map of the volume transfer constant(Ktrans) can be calculated [43]. The use of mpMRI is often a complementary exam to thestandard PCa tests and biopsies; mpMRI-guided biopsies have shown better efficacy thanTRUS-biopsies and a lower rate of complications [44]. Despite the improvements in PCa52.2. Magnetic Resonance Imagingdiagnosis using mpMRI, some limitations are worth noting: the qualitative nature of thempMRI exam and PI-RADs scoring has lead to inter-observer variability among radiolo-gists, reports of 15-30% of clinically significant tumours are missed due to small tumoursize, and the exam requires the injection of gadolinium-based contrast agents into the pa-tient [43–45]. With MRI being a leading imaging modality for being patient-friendly withhigh tissue-contrast, further investigation in MRI technology and applications may addresscurrent limitations and push MRI to become a mainstream technique for PCa detection.2.2 Magnetic Resonance Imaging2.2.1 History of MRIMRI is a relatively new and expanding field beginning in the 1970s; however, the field isonly made possible through several notable contributions tracing back to over a century ago.Jean-Baptiste Joseph Fourier’s seminal work on infinite series and transformations (nownamed after him as the Fourier Series) published in 1822 [46] provides the mathematicaltools to efficiently generate MR images from signals acquired in the frequency domain.In the 1880s, engineer and inventor Nikola Tesla designed and patented the first rotatingmagnetic field, allowing alternating-current machinery [47]. Tesla’s name is also used as theunit for the magnetic flux density (1 Tesla = 1 Newton/Ampere-meter) alongside the unitof Gauss (1 Gauss = 10−4 T). Then in 1897, Irish physicist and mathematician Sir JosephLarmor wrote down the famous Larmor equation [48]ω = γBo (2.1)describing that the frequency of rotation of any given particle with spin or angular momen-tum, ω, is the product of the strength of an applied magnetic field, Bo, and the gyromagneticratio, γ – a constant specific to each particle.The origin of the NMR field is attributed to physicist Isidor I. Rabi who was awarded the1944 Nobel Prize in Physics for accurately measuring magnetic moments of atomic nucleiin 1938 [49, 50]. A couple of years later, in 1946, physicists Felix Bloch and Edward Purcellboth independently achieved and reported NMR in condensed matter systems [51–54]. Thetwo shared the 1952 Nobel Prize in Physics, establishing the field of NMR and, therefore,the building blocks of MRI.Several decades later, around 1973, chemist Paul C. Lauterbur and physicist Sir PeterMansfield both independently described the use of magnetic field gradients in NMR [55–57],allowing spatial coordinates to be encoded in the NMR signal. This laid the groundwork forMRI, and their contributions were awarded the 2003 Nobel Prize in Physiology or Medicine.In 1975, Richard Ernst described using the Fourier transform to reconstruct 2D images fromthe phase and frequency encoding of the NMR signals [58]. Using Fourier analysis to ac-celerate MRI reconstruction revolutionized the fields of NMR and MRI, and Ernst wasawarded the 1991 Nobel Prize in Chemistry for his contributions.62.2. Magnetic Resonance ImagingFast forwarding to today, MRI is a widely used tool in clinical practice for noninvasive,in vivo imaging of the human body for diagnostic and assessment purposes. As one ofseveral imaging modalities such as X-ray CT, PET, and ultrasound, it provides the bestsoft-tissue contrast in comparison [59] with the ability to take cross-sectional images. Whileit is an essential tool, it has its shortcomings in being costly and inaccessible due to its com-plexity and hardware requirements [60]. In research, there are several frontiers to innovateand combat its challenges such as developing faster MRI sequences and reconstruction, im-proving MR hardware, imaging new biophysical information, and exploring image analysistechniques.2.2.2 MR PhysicsWhile quantum mechanics is needed to obtain an accurate and rigorous explanation of MRphenomena, we often defer to using classical derivations as it is descriptive enough to de-scribe the behaviour of NMR. This section outlines the basic phenomena of MR and thenmoves toward how a signal is generated and acquired.Nuclear SpinsAtoms with an odd number of protons and/or neutrons possess a non-zero nuclear spinangular momentum and therefore exhibit nuclear magnetic resonance phenomena. Thesenuclei with angular momentum are commonly called spins in MRI. In both NMR and MRI,one of the most commonly used atoms is the hydrogen atom (1H) whose nucleus possesspin. 1H is the most commonly used spin for MR imaging because of its natural abundancein biological specimens in the form of water (H2O), allowing for better SNR; though keepin mind that several other nuclei are also studied for MRI such as phosphorus (31P) andsodium (23Na).The signal of NMR arises from spins’ interactions with two main magnetic fields, namelythe main field (B0) and radiofrequency field (B1).Main Field, B0In a macroscopic view, two effects arise when a body of spins are placed in a constant mag-netic field B0. The first is that a net magnetization moment (M) arises, given the tendencyfor spins to align with B0. Secondly, the spins exhibit a specific resonance frequency knownas the Larmor frequency. It is also worth noting now that typically, B0 defines the z -axisin Cartesian coordinates. The z -axis direction is called the longitudinal direction, while thex-y is called the transverse direction.M can be macroscopically thought of as the sum of the individual dipole momentsµ such that M =∑µ where most µ (but not all) is polarized along z due to B0. Let72.2. Magnetic Resonance Imagingus use an energy argument to describe how dipoles behave and place this polarization inperspective. The potential energy E in a constant field B0 is given byE = −µ ·B = −µzBo. (2.2)Using a little bit of quantum mechanics, we describe that the magnetic dipole momentµ is more specifically characterized by the spin angular momentum vector (S). Giventhe longitudinal alignment of B0, we can discuss these components with respect to thez -direction. Quantum mechanics describes these components as µz = γSz and Sz = ~sz,where ~ is Planck’s constant and sz is the angular momentum quantum number. For asingle proton, the constituent of the 1H nucleus, there only exist two values for sz, either+1/2 or -1/2. Referring back to Equation 2.2, this leads to two possible energy states for aproton in a constant magnetic fieldE = −γ~szBo = ±12γ~Bo (2.3)with an energy separation of∆E = γ~Bo. (2.4)This separation of energy in Equation 2.4 is known as Zeeman energy splitting, as illustratedin Figure 2.4. The two energy levels (the positive and negative energies in Equation 2.3)correspond to two possible orientations of the magnetic moment in the B0 field, knownas either “spin-up” or “spin-down”. In the spin-up state, magnetic moments are alignedparallel to the B0 direction, and in the spin-down state, magnetic moments are antiparallel.For a group of protons, we can count the quantity of spin-up versus spin-down populationsas N+ and N−, respectively. Given the natural tendency for spins to be aligned along theaxis of B0, much like a compass wanting to be aligned with the North pole, the spin-upconfiguration is favoured (lower energy level) and thus implies N+ is larger than N−. Whilethe population of N+ and N− have a certain alignment tendency due to B0, thermal energyeffects also govern their behaviour. From statistical mechanics, the ratio of N+ and N− canbe described by the probability Boltzmann distribution asN−N+= e−∆E/kBT = e−γ~Bo/kBT (2.5)where kB is the Boltzmann’s constant and T is the absolute temperature. A typical ratioof N−N+ for T at room temperature and Bo given a clinical 3 T magnet is about 0.99999342,meaning that only about 6 out of 106 protons in this system would be in the spin-up con-figuration. However, this slight difference in spin configuration gives rise to a measurablenet magnetization in NMR.Coming back to calculating net magnetization along the z -direction, M0, we can ap-proximate for small ∆E/kBT with the following equation:M0 = µ(N+ −N−)≈ µN(∆E2kBT)= Nγ2~2B04kBT(2.6)82.2. Magnetic Resonance Imagingwhere N = N+ + N−. Mo proportionally increases with B0. Hence, collecting data withhigher (magnetic) field strength for NMR machines increases SNR.Precession and Larmor FrequencyThinking about the compass again, we know that when we tip the needle away from North,the needle will oscillate about the direction of North until it settles back to equilibrium.This concept is similar in NMR. A spin has a property known as angular momentum andmomentum is proportional to inertia. Thus, vector M will precesses about the magneticfield B0 when torqued or tipped away from its natural alignment because of the angularmomentum properties of spins. The most frequently used analogy for the precession ofspins, and therefore M , is a spinning top that wobbles about the axis of gravity if it ispushed out of alignment, i.e. the direction of the B0 field in NMR.The frequency is a specific characteristic of the proton and the constant applied magneticfield, known as the Larmor frequency. The Larmor equation,ω0 = γB0 rad/sf0 =γ2piB0 Hz(2.7)describes the resonant frequency of precession where γ is the gyromagnetic ratio, a constantdefined by a particle’s ratio of magnetic moment and angular momentum. For 1H, γ is42.59 MHz/T, and with a 3T scanner, the Larmor frequency would be 127.74 MHz. Spinsthat are ”excited” at their Larmor frequency exhibit resonance, meaning these spins willoscillate and produce a signal when a radiofrequency field B1 is applied and tuned with thisfrequency.Radiofrequency Field, B1, and RelaxationA bulk of spins present in a static B0 field remains in equilibrium with a net magnetizationM aligned along the field’s axis i.e. the z -axis (Mz). However, in order to obtain a signal,tipping of the spins to create precession is required. When tuned to the Larmor frequency,a pulse of oscillating radiofrequency (RF) field, B1, will cause excitation and precession ofthe spins. Effectively, a B1 pulse is applying a torque that tips M to a prescribed angle,with dependence on the strength and duration of B1. In most applications, the RF field,B1, is applied in the transverse plane (x-y plane), which is orthogonal to the main staticfield direction (B0 along the z -dir). The field strength of B1 in clinical MRIs is typically afew microteslas with durations on the order of a few milliseconds.Following excitation, the magnetization will return to its equilibrium state along thestatic B0 field in a manner that provides two measurable relaxation processes: longitudinaland transverse relaxation. These relaxation processes have characteristic times T1 and T2,also known as spin-lattice and spin-spin relaxation times.92.2. Magnetic Resonance ImagingLongitudinal relaxation (also called T1 relaxation, spin-lattice relaxation, or thermalrelaxation) describes the motion for magnetization to return to the z -axis after excitationtowards equilibrium. Equilibrium is achieved by the physical exchange of energy betweennuclei and surrounding particles in the lattice, hence the name of spin-lattice relaxation. T1relaxation behaves according todMz(t)dt= −Mz(t)−M0T1(2.8)where Mo is the original magnitude of magnetization in equilibrium, Mz is the longitudinalmagnetization as a function of time, and T1 is the characteristic relaxation time. Thesolution to this equation gives usMz = M0 + (Mz(0)−M0)e−t/T1 . (2.9)This equation provides a method to calculate T1 if the magnetization signal is acquired. Ifmagnetization is flipped into the transverse plane (i.e. a flip angle of 90◦), Mz(0) will bezero. It is noted that there are external factors which may alter T1 times. For example, sur-rounding magnetic dipoles and random fluctuations increase spin-lattice energy exchangeand reduce T1. In addition, T1 increases as B0 increases since nuclei have less probabilityof interactions with nuclei at the same Larmor frequency at higher field strengths.Transverse relaxation (also called T2 relaxation, T2 decay, or spin-spin relaxation) de-scribes the motion of magnetization in the x-y plane after excitation. Also known as thespin-spin time constant, T2 characterizes the decay of magnetization as it returns to equi-librium in the transverse plane, i.e. a transverse magnetization of zero. T2 decay’s lead-ing cause is spin-spin interactions which disrupt the local magnetic field and broaden themacroscopic resonant (Larmor) frequency causing the dephasing of transverse magnetiza-tion. However, we also mention that there is a T2∗-decay which captures the effects ofstatic field inhomogeneity on transverse relxation. i.e. if B0 or an additional static fieldwere imperfect and inhomogeneous, but present. T2∗ will always be less than or equal toT2. Note that any effect that causes T1 relaxation will also cause T2 relaxation; however,there are additional T2 relaxation processes that end up causing values of T1 ≥ T2. Thebehaviour of T2 relaxation is given bydMxy(t)dt= −Mxy(t)T2(2.10)with solutionMxy = Mxy(0) e−t/T2 . (2.11)where Mxy(0) = Mxy(t = 0).Figure 2.5 shows theoretical relaxation curves for both T1 and T2 relaxations for shortand long characteristic times. Times are usually reported in milliseconds (ms). Given our102.2. Magnetic Resonance Imagingunderstanding of the causes of relaxation, having neighbouring atoms and nuclei with theresonance frequency of the excited spins will promote T1 relaxation (shorten T1) and notaffect T2. Small molecules such as water have a large distribution of motional frequencieswhich poorly matches the Larmor frequency, causing little dephasing and therefore haslong T1 and T2 values. Medium sized molecules such as lipids, have a narrower motionalfrequency which matches the Larmor frequency and the T1 and T2 times are comparativelyshorter as a result. For fixed molecules such as bones, they are ineffective at removingenergy and therefore have long T1 values. However, fixed molecules have the largest localfield variation and therefore have short T2 times. Free, unrestricted water, for example, isconsidered to have long T1 and T2 times with T1 ≈ T2 ≈ 3000 ms at 1.5 T field strength.For fat, T1 times are on the order of 250 ms and 60 ms for T2. For biological tissues, whichare usually partly solid, we tend to see that T1 > T2 (T1 on the order of 1000 ms and T2 onthe order of 1-100 ms).Bloch EquationA fundamental equation in NMR and MRI that describe the dynamics of nuclear magneti-zation is the Bloch equation:dMdt= M × γB − (Mz −M0)zˆT1− Mxxˆ +MyyˆT2. (2.12)The first term, the cross product of magnetization M with the gyromagnetic ratio, γ andstatic field B , describes the precessional behaviour of magnetization– the spins will ro-tate at the Larmor frequency given by Equation 2.7. The following two terms relate tothe relaxation processes described in Equations 2.8 and 2.10. Because the precession isindependent of relaxation, solutions to the Bloch equation can be simplified by transfor-mations to a rotating reference frame and ultimately gives us solutions as in Equation 2.9and Equation 2.11. In all, the Bloch equation allows us to describe the phenomenologicalbehaviour and time-dependence of macroscopic nuclear spin signals in our field to first order.MR Signal AcquisitionOnce M is tipped and is precessing, an RF receiver coil can be placed strategically toobtain the precessing Mxy signal. The basis for signal acquisition is rooted in Faraday’slaw of induction, where his equation describes how a rotating magnetic field induces anelectromotive force (EMF) or voltage in a circuit. The acquired signal by the RF coil is calledthe free induction decay (FID) signal, which is recorded and used for image reconstruction.Typical magnitudes of the induced EMF are on the order of millivolts and must be amplifiedprior to signal detection. Zooming out to a bigger picture of MR signals, an MR image isa recording of RF signals induced by the body producing super tiny oscillating magneticfluxes to the tune of the Larmor frequency. MR imaging is then essentially mapping theseamplitudes of RF signals to their respective locations in space.112.2. Magnetic Resonance Imaging2.2.3 Imaging PrincipalsWith the basics of NMR under our belt, we know how MR signals are generated, receivedand characterized for a bulk of uniform spins. However, in MRI, we must gather informa-tion in an additional dimension to generate images– this is done by using magnetic fieldgradients. These gradients allow for the localization of certain spins which then are system-atically mapped to spatial coordinates. This technique of using gradients for this purposeis called spatial localization.Slice SelectionTo achieve a 2D MR image, we first must decide the plane of RF signals to capture. Thiscan be considered as taking an image slice, so we must first perform slice selection. Sliceselection exploits linear gradient fields denoted as Gx, Gy, and Gz for gradients in the x,y, and z -direction, respectively. Often, a slice is discussed as a thin ∆z, meaning that theslice (and image) is in the x-y plane. In the simplest case, we can apply a varying linear(gradient) magnetic field in the z-direction, Gz, to the static field B0 during a 90◦ RF pulse.Effectively, this causes the Larmor frequency to vary linearly along z as well. Since the RFpulse only excites spins in a narrow range of frequencies, only a matched slice of spins inthe z -direction can be excited and tipped 90◦ into the transverse plane– thus allowing forslice selection.While there are multiple ways to achieve and optimize a slice selection, only the simplestwas discussed. Following slice selection, the next step is to obtain the RF amplitudes,m(x, y), in the slice.Frequency EncodingIn the simplest 2D MR image example, frequency encoding occurs after slice selection is per-formed. Frequency encoding happens when an additional field gradient is applied duringsignal acquisition. This allows for the decoding of m(x, y) to generate an image. For exam-ples, if frequency encoding was set in the x -axis, there would be an applied gradient field,Gx, in the x -direction after slice selection. During signal acquisition, the spins would havea spatially varying Larmor frequency along that same axis. Proceeding signal acquisition,a Fourier transform (FT) can be used to transform signals from the frequency to spatialdomain. The FT of signal from frequency encoding would give us the 2D projection of theslice’s magnetization in the x -direction. To be able to fully complete spatial localization inall three directions, phase encoding is needed.Phase EncodingContinuing the example of the simple 2D MR image, phase encoding is used prior to fre-quency encoding to obtain spatial localization. Induction signals carry both magnitudeand phase which is unique to MRI when comparing to other imaging modalities. Because122.3. Luminal Water Imaging for Prostate Cancerfrequency encoding is a vector projection rather than a scalar projection, phase encod-ing embeds phase information that resolves m(x, y) in all three directions after a Fouriertransformation. In this simple example, phase encoding also works by applying incrementalamounts of linear gradient fields, Gy, in the y-direction before each frequency encoding toinduce different phases at different y locations.After repeated excitation with frequency and incrementally increasing gradients duringphase encoding, the signal acquired has both magnitude and phase information in the fre-quency domain– this is also known as k-space. K-space images can be directly reconstructedinto a regular, Cartesian image by a 2D FT in the x and y directions.Comments on Spatial Localization and ImagingThe section mentioned above on imaging principles is an extraordinary over-simplificationof how MR images are generated. There are several other techniques and details that go intohow k-space images can be acquired. The interested reader can refer to the classic textbookby Dr. Robert Brown on his book “Magnetic Resonance Imaging: Physical Principles andSequence Design” (also known as the Green Bible) [61] if they wish to learn more.2.3 Luminal Water Imaging for Prostate CancerThe work in this thesis is to further the clinical feasibility of a recently developed quantita-tive MRI technique called Luminal Water Imaging (LWI) for PCa detection and diagnosis,first reported in 2017 by Sabouri et al. [27, 62–64]. The technique is developed to providequantitative information about prostatic tissue structure, specifically luminal space, whichchanges within cancerous tissues.2.3.1 T2 RelaxationLWI measures the T2 decay signal (transverse magnetization signal) of each pixel (or voxel2)in the prostate image. Further processing of the transverse magnetization signal as outlinedin Section 2.3.3 will provide the T2 relaxation times that make up the overall decay signal.Comparing the voxel size of the image to the tissue structures within the prostate, weexpect to gather T2 decay signals from several constituents such as the lumen, stroma,and epithelial cells. The water protons in these varying structures will contribute theirown T2 decay signal, thereby creating a multi-exponential T2 decay signal in each voxel.Equation 2.13 is the model for the T2 decay signal, which describes its multi-exponentialnature:T2 Decay Signal =nT2∑i=1ai e−t/T2,i (2.13)2Note that in this case, a pixel can also be thought of as a thin voxel since each image represents a 4 mmthick slice of the sample (more on the LWI protocol is outlined in Section 2.3.2).132.3. Luminal Water Imaging for Prostate Cancerwhere y(t) is the T2 decay signal as a function of time t, nT2 is the range of exponentialT2 components, ai is the amplitude of the ith component, t is the time, and T2,i is ith T2relaxation time.In LWI, prostate tissue structure is often modelled with two different bodies of water,giving rise to two distinct T2 relaxation times. The shorter T2 is associated with smallerwater compartments such as those in epithelial cells and stroma. The longer T2 is asso-ciated with the water in the luminal compartments. Though in practice, we calculate acontinuous distribution of T2 times instead of sharp peaks/delta functions of T2 times [65],which is discussed in more detail in Section 2.3.3.From previous sections where we outline prostate tissue morphology (Section 2.1), weknow that the structure of lumens change based on the cancer grade. In Figure 2.3, luminalspacing becomes irregular and shrinks as GS increases. Thus, because the long componentof T2 is associated with luminal water compartments, there will be a decrease in the long T2component of pixels in malignant tissue. This hypothesis forms the basis for the LWI MRsignal. From here, a quantifiable parameter–a percentage of the water within the luminalspaces to all other water bodies in a pixel– can be calculated and used to infer prostatetissue’s cancer morphology.2.3.2 MR Pulse SequenceLWI requires the acquisition of the transverse magnetization (T2 relaxation) decay curve.In the original study by Sabouri et al., the protocol is performed on a 3T magnet with amulti-echo acquisition, specifically a 3D gradient-and-spin echo (GRASE) [27], to speed upacquisition time while reducing magnetization transfer effects and phase errors accumulat-ing during multiple gradient-echo readouts [66, 67]. The parameters for the protocol are:repetition time (TR) = 3073 ms, echo time (TE) = 25 ms, number of echoes (NE) = 64,field of view = 240 x 240 x 56 mm2, voxel size = 1 x 1 x 4 mm3, slice thickness 4 mm, scanmatrix size = 240 x 119, flip angle of 90◦, number of averages = 1, SENSE factor = 2, scanduration 673 s [62]. The choice for TE and NE was to optimize the signal-to-noise ratio(SNR), while the choice for TR was decided based on literature findings of a TR to reduceT1 contribution that would affect the signal [63]. Figure 2.6 shows an example of the MRimages captured from each of the 64 echoes.2.3.3 Multi-exponential fitting & NNLSThe T2 distributions are calculated by an iterative fitting algorithm– namely, a non-negativeleast squares (NNLS) algorithm. The algorithm’s purpose is to fit the multi-exponentialmodel as in Equation 2.13 without specifying the number of T2 contributions (nT2) tobe expected in the signal3. From a historical viewpoint, the use of NNLS traces back to3More accurately, an NNLS algorithm will fit to a large number of components (approximately 100,depending on which NNLS algorithm is used) which in comparison to the components expected in LWI(0-3), is on the order of 30-100 times as many.142.3. Luminal Water Imaging for Prostate Canceranother quantitative MRI technique called myelin water imaging (MWI) which found thatusing NNLS was a feasible way to calculate T2 distributions [68]. On the other hand, someother studies model the T2 decay signal as bi-exponential (i.e. nT2 = 2); this leads toa reduction in the computational time to run NNLS, however may lead to less accuratedescriptions and values of the T2 constituents. In some reports, there have been reportedpixels in the prostate that measured three T2 times, likely due to varying sizes of glands orartifacts [27], which would provide different T2 distributions if modelled by a bi-exponential.Below describes how multi-exponential T2 distributions are calculated.First, we can consider the transformation of the acquired T2 decay signal y(t),y(t) =nT2∑i=1ai e−t/T2,i , (2.14)to an exponential basis modelled with the formS(T2) =nT2∑i=1ai δ(T2 − T2,i) (2.15)where S is the signal as a function of different T2 times, a is the amplitude of the i-th T2component (T2,i), and nT2 is the number of T2 components for the acquired signal (y(t)).Since y(t) is assumed to be linear, the modelled signal S(T2) can be written as a system oflinear equations such asSj =nT2∑i=1Aji ai (2.16)where Sj is the expected signal from echo j and Aji the transformation matrix from expo-nential representation with coefficients e−TEj/T2,i from the jth echo time (TE) and ith T2time. In general, the goal is to calculate ai such that the acquired signal can be modelledwhich, in principle, could be done with a pseudo-inverse. However, the introduction ofexperimental data to Equation 2.16 are problematic for calculating exact solutions and cangenerate negative values of ai which are nonphysical. Thus, we defer to NNLS to providephysical constraints in modelling ai.NNLS is used because it constrains non-negative values and can handle a misfit betweenthe acquired and modelled data. The NNLS algorithm iterates the following equation untilai is minimized,argminai≥0 TEN∑j=TEi∣∣∣∣∣∣nT2∑i=1Aji ai − yj∣∣∣∣∣∣2 (2.17)152.3. Luminal Water Imaging for Prostate Cancerwhere yj is the modelled (approximated) decay signal for echo j. Note that the minimumvalue from Equation 2.17 is equivalent to the chi-squared value (χ2), a measure of misfitbetween a simulated and predicted value.Including regularization to the NNLS algorithm is often done and can make the algo-rithm more robust in calculating the T2 distribution, especially in the case for noisy data.Specifically, an L2-norm regularization is utilized [65, 69] to enforce continuity of the T2distribution, thus conforming to the expected physical reality of the distribution [65]. TheNNLS with regularization is presented asargminai≥0 TEN∑j=TEi∣∣∣∣∣∣nT2∑i=1Aji ai − yj∣∣∣∣∣∣2+ µnT2∑i=1a2i (2.18)where µ is an adjustable parameter that effectively increases or decreases χ2 as needed forfitting. Often, χ2 is too low and results in overfitting the data. For MWI applications, theratio of χ2/χ2min is commonly set to 1.02 [65] though for general applications the optimalratio is dependent on the SNR of the data.2.3.4 Luminal Water Imaging ParametersLuminal water imaging generates seven quantities from the T2 distribution calculated fromNNLS. Recall that there is a T2 distribution from each voxel, and in turn, LWI results inproviding seven quantitative images also known as parametric maps. A summary of theparameter description and symbols is shown in Table 2.1. An example image of the sevenLWI parametric maps are shown in 2.7Table 2.1: Description of LWI parameters and their associated symbols.Parameter Symbol DescriptionAshort Area under the short-component of T2 distributionAlong Area under the long-component of T2 distributiongmT2 The geometric mean of the two T2 componentsgmT2,short Geometric mean of the short-component of T2 distributiongmT2,long Geometric mean of the long-component of T2 distributionLWF Luminal water fractionN Number of peaks in the T2 distributionOne of the most telling parameters for prostate morphology is the luminal water fraction(LWF). It is an indirect measurement of the fraction of luminal space in each pixel. Theequation for LWF isLWF =∑T2,maxT2,threshS(T2)∑T2,maxT2,minS(T2)(2.19)162.3. Luminal Water Imaging for Prostate Cancerwhere T2,min and T2,max are the minimum and maximum values of T2 times (20 ms and2000 ms, respectively[62]) and T2,thresh is the threshold for separating the T2 time betweenthe small and large water compartments as discussed in Section 2.3.1. The value for T2,threshis set at 200 ms[62] based on a histogram of the calculated T2 times from 4,700 pixels show-ing the best separation at 200 ms[63]. A figure of the histogram from Sabouri’s thesis canbe found in Appendix A.1.The gmT2 is the geometric mean T2 time within the window of minimum and maximumvalues of T2 times on a logarithmic scale, calculated asgmT2 =∑T2,maxT2,minS(T2) log(T2)∑T2,maxT2,minS(T2). (2.20)The parameters gmT2,short and gmT2,long are defined as the geometric mean T2 time of theshort and long components, respectively. They are calculated asgmT2,short =∑T2,threshT2,minS(T2) log(T2)∑T2,threshT2,minS(T2)(2.21)andgmT2,long =∑T2,maxT2,threshS(T2) log(T2)∑T2,maxT2,threshS(T2). (2.22)Ashort and Along are the calculated areas under the short and long components of the T2distribution and are calculated asAshort =T2,thresh∑T2,minS(T2) (2.23)andAlong =T2,max∑T2,threshS(T2). (2.24)The final quantity is N, a parameter measuring the number of distinct peaks in the T2distribution which can be written asNcomp = # of T2’s. (2.25)In the case of N ≤ 1, the values of gmT2,short and Ashort, or gmT2,long and Along is set tozero depending on which side of T2,thresh the distribution is on [27]. In the case of N= 3, theadditional peak would be added to the contribution of either the short or long componentsand would be averaged geometrically [27].172.4. Machine Learning, Deep Learning & Convolutional Neural Networks2.4 Machine Learning, Deep Learning & ConvolutionalNeural NetworksIt is without a doubt that machine learning (ML) and a further sub-branch, deep learning(DL), have made substantial impacts on the way we interpret and make decisions withinformation.Machine learning encompasses the set of all computer algorithms that attempt to ap-proximate a function by using training data and assuming a model. Deep learning (DL) isa subset of machine learning that has recently seen great use for classifying and segmentingimages in computer vision tasks. Deep learning algorithms make use of artificial neuralnetworks (NN) and contain many more hidden layers to become a “deep” network. In DL,each additional layer progressively extracts higher-level, abstract information from the rawinput. Then in the final layer, a meaningful prediction can be generated. Predictions canonly be generated after the model has been trained. Figure 2.8 depicts a structure of a deeplearning network with 3 layers and 3 nodes in each layer.The main difference between conventional NN and DL models is how features are gen-erated within the network. In NN models, features must be generated by the user i.e.,specifying images and labelling features such as benign or malignant (for a binary classifi-cation example). For DL models, these features can be generated and learned upon. Thisdifference is one of the reasons why the performance of DL methods improves with moredata, unlike linear models such as a simple linear regression.2.4.1 Brief HistoryThe field’s beginnings can be traced back to around the 1950s and 1960s, when psychologistFrank Rosenblatt worked on building machines with the ability to learn, such as identify-ing shapes held before them. Rosenblatt’s machines, also known as perceptrons [70], weremodelled after the biological neuron to perform learning. Though towards the latter end ofthe ’60s, the period known as the artificial intelligence (AI) winter began.Research in AI began to stagnate following a book publication in 1969 by Marvin Min-sky and Seymour Pappert on the mathematical foundations of AI and where perceptronshad difficulties modelling basic logical functions such as the XOR and XNOR [71]. How-ever, around the 1980s, revitalization of the field picked up with Kunihiko Fukushima whoimplemented the first convolutional neural network (CNN) [72], a learning network archi-tecture widely implemented today. Another prominent leader in the field, Yann LeCun,then demonstrated his seminal work with CNN’s (later called LeNet) showing his networkdecoding pictures of house address numbers to digital numbers on computers [73]. However,another AI winter began due to the computer’s lack of computational power at the time.As graphical processing units (GPUs) became more powerful, so did the research andinnovations in AI. In 2012, AI was once again revitalized by Alex Khrisevsky, who demon-182.4. Machine Learning, Deep Learning & Convolutional Neural Networksstrated a CNN known as AlexNet to be able to classify images for the ImageNet LargeScale Visual Recognition Challenge (ILSVRC) [74]. The innovation by Khrisevsky was toimplement CNNs with several GPUs to train a network with 1.2 million images belonging toa thousand unique categories (e.g. coffee mug, border collie, obelisk, etc.). Since AlexNet,AI has exploded in its use in research and industry and while doing so, has founded severalbreakthroughs in many fields. One such field is that in medical imaging with the uses of AIfor MRI.2.4.2 Convolutional Neural Networks in MRIWhile MRI provides several benefits in medicine, including being one of the best spatiallyresolved medical imaging tools, one of the main Achilles heels of the tool is its long acqui-sition times. Part of the AI effort with MRI is focused on decreasing scan time in a myriadof ways. One such method that is extensively researched is training AI to fill in gaps indownsampled k-space for MRI acceleration [75]. Other ways AI is used in MRI are for fastreconstruction for real-time surgical planning [76] and, in the case of this thesis, using AIfor image analysis and segmentation.Specifically for prostate cancer, the increasing use of AI is seen together with the increas-ing use of mpMRI, as mentioned in Section 2.1.3. The mpMRI protocol has led to a growingdemand for experienced radiologists to enable interpretation of these complex scans [77].Part of the complexity of mpMRI stems from the necessity for radiologists to understandthe image’s anatomical, metabolic, and biological context and disease [78]. Hence, AI andspecifically the use of CNNs is a tool whose aim is to distill pertinent information for clini-cians.In the context of LWI, the seven parametric maps produced from a slice of T2 echo, asseen in Figure 2.7, have the prostate region shown while the background is removed. Thisprocess is known as segmentation. The task of segmenting the prostate for several patientsis a tedious task and is well suited for machines and machine learning or AI. Hence, ML-based image segmentation is used in this project to perform segmentation from T2-echoMRI data automatically. The benefit of prostate segmentation is two-fold. The first is thatsegmentation will allow the regions outside the prostate to be nulled. This is especiallyhelpful in LWI since the parameters are specifically designed for prostate tissue and thus,regions outside the prostate will not provide helpful information for PCa detection. Inaddition, LWI lacks anatomical details that radiologists rely upon. Thus, segmentationalso allows merging segmented LWI onto anatomical T2-weighted images. The secondbenefit of segmentation is that several regions can be segmented, such as the peripheraland transition zones, allowing for further analysis in each zone to account for differences intissue morphology.192.4. Machine Learning, Deep Learning & Convolutional Neural Networks2.4.3 Brief Basics of Deep Learning and Convolutional Neural NetworksDeep LearningDeep learning can be thought to run in two modes: a learning mode and a prediction mode.In learning mode, one can think of an algorithm as being pre-mature, and for it to behelpful, it will first need to learn a set of rules. There are three main learning types a DLalgorithm can be built for: unsupervised learning, supervised learning, and semi-supervisedlearning. In supervised learning, a model will be provided the ground truth when learning.Ground truth gives the model an explicit comparison between its prediction and the trueanswer. For example, if we had a picture of flowers and we wanted to group them in termsof their colours, the ground truth would provide a mask that groups like-coloured flowerstogether. If the model predicts an improper grouping, the difference from its prediction andground truth will serve as a way for the model to correct itself. In unsupervised learning,algorithms are not given the ground truth. This allows model to define their own rules. Forexample, using the same example as above, an unsupervised learning may learn to catego-rize the constituents of flower photos based on the number of petals, by petal shape, or bycolour. Semi-supervised learning is a mix of both these two approaches. Once the modelis trained in learning mode, it will be ready to make predictions based on its learned rules.Figure 2.9 shows a schematic of the two modes for a supervised learning model.When building a new model, the available data to teach the model is usually split intothree categories: training, validation, and testing data. When talking about available dataand supervised learning, all data must also have its corresponding ground truth. Trainingand validation data are used to update the model during learning mode. The difference inthe two is that the same training data is used in several iterations of updating the model.In contrast, validation data is used only sparingly to ensure the model learns the correctset of rules on a different set of data. Testing data, however, is only used once the DLmodel is thought to be properly trained. The idea for a DL model is that after training,the model should be able to predict an informed outcome on data it has never seen before.Thus, the testing dataset is reserved only for testing the model and to calculate the model’sperformance. Often, an “80-20” split of the data is implemented where 20% of the data isreserved for testing and the other 80% of is split between training and validating datasetswhich are split another 80% and 20%, respectively.When training a model, there are hyperparameters and model parameters. Hyperpa-rameters configure the model during training; for example, some common hyperpametersare the learning rate, model size, number of epochs, batch size, and number of model pa-rameters. The learning rate determines the step-size during model optimization. The modelsize hyperparameter can vary based on the model type, but based on Figure 2.8, changingthe number of layers and number of nodes changes the model size. The batch size willspecify the number of training samples the model will process before updating. The epochspecifies how often a training dataset will be used to update the model. Hyperparametersare tuned by the user, meaning that a user can vary values for the hyperparameters to202.4. Machine Learning, Deep Learning & Convolutional Neural Networksachieve a better quality model. In contrast, model parameters are internal parameters thatthe model learns itself. Weights and biases are model parameters, where weights connectthe strength of an input to the output of a model and biases are constant offsets.Figure 2.10 shows a simple example of a learning algorithm with weights (m) and biases(b) in the context of a linear regression model. Performing a linear regression on the data(displayed as dots) provides the slope (m) and y-intercept (b) of a line that is optimized tothe provided data. After optimization, the model, y = m ·x+b, can predict future values ofinput ‘X’. Now, if these weights and biases were skewed by outlier data or by other means,it would also mean the model prediction would be less accurate. In the case of (a) in Figure2.10, if we had an input value of X = 0.5, the prediction would provide Y = 2 · 0.5 + 0 = 1,an accurate prediction of what we would expect. On the other hand, model (b) wouldpredict a value of Y = 2.1 · 0.5 + 0.1 = 1.15 which is less accurate. Accuracy and qualityof a model can be improved by tuning hyperparameters. Though, one has to be carefulnot to over-train and overfit a model which can happen by introducing too many modelparameters (too complex of a model) and/or training too long across epoch, batches andlearning rate– when this happens, a model will not be able to generalize to new data verywell.We determine a model’s quality based on its performance on never-seen-before data.Several metrics determine a model’s quality. In the case of binary prediction (e.g. [0 or1] or [‘no’ or ‘yes’]), accuracy is often a leading metric and can be reported as a percentaccuracy, Jaccard index, or Dice coefficient after predicting the entire testing dataset. Thefollowing equations describe how each metric is calculated% Accuracy =TP + TNTP + TN + FP + FNJaccard Index =TPTP + FP + FNDice Coefficient =2 · TP2 · TP + FP + FN(2.26)where TP is true positive, TN is true negative, FP is false positive, and FN is false negativepredictions when compared to ground truth.Convolutional Neural NetworksFigure 2.11 shows a simple convolutional neural network which contains an input layer, aconvolutional layer, pooling layer, a fully connected layer, and an output layer. These layersare some of the core building blocks of deep learning. This thesis discusses the use of CNNsfor image analysis with the structure shown in Figure 2.11; however, in general, CNNs canhave various architectures that can take different forms of input such as text or video data.The input layer is the image’s entry point into the algorithm. Following, is the convo-lutional layer– a core building block of the CNN. In this layer, the input is convolved with212.4. Machine Learning, Deep Learning & Convolutional Neural Networksa smaller matrix called a filter or kernel. A convolution is a mathematical operation of twoinputs (the operation denoted as ∗) that produces an output. In the context of CNNs, theprocess of convolving the input is called an activation, and the output produced is calleda feature map. During activation of 2D images and kernels, the feature map, If , can bedescribed by discrete convolution as the following:If [m,n] = Io[m,n] ∗ k[m,n]=∞∑j=−∞∞∑i=−∞Io[i, j] · k[m− i, n− j] (2.27)where Io is the original image with pixel at locations m and n and k is the kernel. Thebounds of i and j in the sum are bounded by the size of the kernal i.e. for a 3x3 kernel,the bounds will be i ∈ [−1, 1] and j ∈ [−1, 1]. The size of the kernel is user-dependentwith smaller kernels between 1x1 to 3x3 and larger kernels such as 11x11. The kernels inCNNs are learned i.e. they are tuned during training mode. Figure 2.12 shows how specificfeatures such as edges of an image can be highlighted after activation with specific types offilters.Following activation, the feature maps are sent into a pooling layer, where the maps aredown-sampled, which breaks down the image into smaller pieces by some sampling process.The benefit of pooling is in allowing networks to become more generalizable since the res-olution is reduced and less specific information is being used to train the network. Often,max-pooling is employed in CNNs, which gathers the largest pixel value within a specificstride of the feature map, i.e. a stride of 2 would provide a matrix of 2x2 to be max-pooled,and the feature map would be reduced by a factor of 2 in both dimensions of the 2D map.After pooling, the down-sampled feature map is fed into a fully-connected layer. Thisfully-connected layer is a neural network, where each node has a single input for data. Ineach node, the input is put through a non-linear equation, similar to the convolutional acti-vation. The function is called an activation function with learnable weights and biases. Theactivation function needs to be non-linear to allow large multi-layered NN’s to be built4.One of the most commonly used activation functions is the rectified linear unit (ReLU)function; however, there are several other kinds of non-linear functions and is a currentresearch topic since different functions can speed up network training and accuracy. Theoutput from the activation function will result in a probability used for prediction.In training mode, the results of the model’s prediction will be compared to the groundtruth and the metric determining how well the model performed is provided as a valuecalled the loss. The method in which loss is found is by the model’s loss function, alsoknown as a cost function. Commonly used is a mean-squared error fit or cross entropy lossfunction, however there are several loss functions that can be implemented. The results of4If a linear were used, the NN would collapse into a single layer, which would effectively be a simplelinear transform222.4. Machine Learning, Deep Learning & Convolutional Neural Networksthe loss will be back-propagated in the network such that an optimization such as gradientdescent can be performed to update the weights, biases, and kernels to produce a bettermodel. Back-propagation is a mathematical method to share the information of the lossat the output with the previous layers in the model. Once back-propagation is performed,a gradient descent algorithm can be performed which optimizes the weights, biases and/orkernel to minimize the loss in future model predictions. Two main optimization algorithmsare stochastic gradient descent (SGD) or adaptive moment estimation (ADAM). The de-sign of optimization algorithms is a topic that is heavily researched in computer science andmath and not so much in this thesis.232.4. Machine Learning, Deep Learning & Convolutional Neural NetworksFigure 2.3: The original Gleason grading diagram as proposedby Dr. Donald F. Gleason in the 1960s. Reprinted with permis-sion from Springer Nature by Epstein[37] ©2018.242.4. Machine Learning, Deep Learning & Convolutional Neural NetworksFigure 2.4: Diagram of Zeeman energy splitting for spin 1/2systems. Two possible energy states are possible for a protonplaced in an external magnetic field, B0. Populations in thespin-up (sz =12) are counted as N+ with energy E = −12γ~Boand the spin-down (sz = −12) as N− and E = 12γ~Bo. For alarge number of protons, populations N+ and N− depend onthe energy difference, ∆E = γ~Bo, according to the Boltzmanndistribution.Figure 2.5: Diagram of T1 and T2 relaxation curves with exam-ple short and long T1 and T2 times.252.4. Machine Learning, Deep Learning & Convolutional Neural NetworksFigure 2.6: Shown are 64 images corresponding to the 64 echoMR images from a single slice of a patient. The first echo is thetop-left image, the second echo is the image to the right, andit follows this pattern up to the 64th echo image shown in thebottom-right. The sequence used to gather the multi-echo datawas a 3D GRASE sequence. Images shown have the prostateregion segmented with background pixels removed.262.4. Machine Learning, Deep Learning & Convolutional Neural NetworksFigure 2.7: An example of the T2 echo image taken at thefourth echo (100 ms) together with the associated LWI parame-ter maps: number of components (N), geometric mean T2 of thelong component (gmT22), luminal water fraction (LWF), area ofthe first peak (A1), geometric mean T2 of the short component(gmT21), geometric mean T2 of both peaks (gmT2), and areaunder the long component (A2).272.4. Machine Learning, Deep Learning & Convolutional Neural NetworksFigure 2.8: A depiction of a deep learning network with threehidden layers with three nodes each. For example, the inputlayer could be an image and in the hidden layers, a trainednetwork could piece apart hierarchical features (such as edgesor specific contours) to provide an output of whether or notthe image contains what it was trained to identify i.e. prostatezones.Figure 2.9: A depiction of the two modes of a supervised learn-ing model. During training, the model takes in input data andground truth data to learn and update its set of rules. Duringprediction, only input data is provided and the model providesthe prediction based on what it has learned.282.4. Machine Learning, Deep Learning & Convolutional Neural NetworksFigure 2.10: Two images of linear regression models with weight(m) and bias (b) which correspond to the slope and y-interceptof a linear equation. (a) shows a more uniform dataset whereas(b) shows 3 outlier points in its dataset. In green is a prediction(Y) of an input value of X = 0.5. The output of models from (a)and (b) differ and demonstrate the effect of outliers on learnedweights and biases. The model (a) shows a better predictionFigure 2.11: A depiction of a simple convolutional neural net-work (CNN) to perform classification on an input image. (a)Input layer: allows intake of data. (b) Convolutional layer: con-tains filters to identify features that characterize the image in“feature maps” (e.g. red, blue, and yellow blocks). (c) Poolinglayer: downsamples the feature maps. (d) Fully connected layer:connects all feature maps from the previous layer. (e) Outputlayer: provides the result for segmentation or classification.292.4. Machine Learning, Deep Learning & Convolutional Neural NetworksFigure 2.12: Image of the UBC logo convolved with differentkinds of kernels. The first kernel is the identity matrix andreturns the original image. The second is a box blurring kernel,where the image becomes averaged in small regions, causing ablurring of the input image. The third is an edge detectionkernel, where the edges of the input image is highlighted. Inthe fourth and fifth kernel are variations of the Sobel operator,where directional edges are highlighted.30Chapter 3Prostate Segmentation3.1 IntroductionSegmentation of the prostate is one of the two required analysis steps to generate luminalwater imaging enhanced T2-weighted images. The reason being is that LWI lacks anatom-ical detail and has poorly defined LWI values outside the prostate. Thus, by picking outthe prostate region within luminal water images, only the relevant information can be usedto weight anatomical (T2W) images.This section presents a 2D U-Net model tailored for whole prostate and peripheral zonesegmentation from T2-echo MR data.3.2 Methods & Materials3.2.1 DatasetT2-echo data was collected on a 3T MRI scanner with a 3D multi-echo spin echo sequencedeveloped for LWI at the University of British Columbia. The 2D images have a FOV of240 x 240 mm about the prostate with fourteen slices per patient. More specifically, theMR parameters for the scan are: repetition time (TR) = 3073 ms, echo time (TE) = 25ms, number of echos (NE) = 64, FOV = 240 x 240 x 56 mm3, voxel size = 1 x 1 x 4 mm3,scan matrix size = 240 x 119, reconstruction matrix-size = 240 x 240, slice thickness = 4mm, flip angle = 90°, number of averages = 1, sense factor = 1.5, and scan duration = 673seconds [27, 62, 63]. The dataset had 40 patients with 14 slices each, amounting to 560unique images about the prostate location, including the 64 echos of each slice. However,only a subset of the 14 slices contained the prostate; thus, 224 unique images were availablefor splitting among training, validating, and testing data. The data was split with the 80-20rule as outlined in Section 2.4.3 using n = 144 (65%, 27 patients) for training, n = 36 (15%,6 patients) for validating, and n = 44 (20%, 7 patients) for testing data.The ground truth data was generated by outlining each MR image by hand using aMATLAB graphical user interface (GUI) developed for the task. Refer to Appendix A.2 formore information about the GUI. Hand-drawn segmented regions, called regions-of-interest(ROIs), were drawn for the entire prostate and for the peripheral zone. An example of thefull prostate ROI and peripheral zone ROI is shown in Figure 3.1. A total of 224 ROIswere drawn for the entire prostate and another 224 ROIs for the peripheral zone. A trainedradiologist validated a subset of the ROIs to ensure the ROIs were drawn correctly.313.2. Methods & MaterialsFigure 3.1: (A) T2-echo image of a prostate taken for LWI. (B)The corresponding hand-drawn ROIs for the full prostate and(C) the peripheral zone.3.2.2 Network Architecture and TrainingA U-Net model [79] was implemented for prostate segmentation. The network had an inputof a .MAT file containing T2-echo data with the size 240 x 240 x 64, and the output ofthe network was a 240 x 240 binary mask saved as a portable network graphic (PNG) file.Figure 3.2 depicts the architecture used.The first specific choice for the U-Net model was to implement an alpha-balanced focalloss [80] to address the problem of class imbalance. Class imbalance was present in thedataset given the nature of the required task– to predict an ROI. The model is required toperform pixel-wise prediction of either a 0 or 1 in an image that is 240 x 240 (the size of theT2-echo image) where ‘1’ pixels are those inside the ROI and ‘0’ is outside. The equationfor focal loss (ffocal loss) is given byffocal loss = −α(1− pt)γ log(pt) (3.1)pt(p, y) ={− log(p) if y = 1,− log(1− p) if y = 0. (3.2)where α is a selectable hyperparameter of focal loss and is proportional to weighting the‘1’ prediction, γ is the second hyperparameter, and pt is the commonly used binary crossentropy loss function where p is the predicted pixel value and y is the ground truth valueof what the pixel should be.The model training hyperparameters for the full-prostate segmentation and peripheralzone segmentation differed. For the full-prostate ROI segmentation, the model had tunablehyperparameters of the learning rate, batch size, epochs, and the focal loss parameters γand α. A sweep of the focal loss parameters with γ swept between integer values of 2 to8, α swept between [0.05,0.3] in 0.05 steps, learning rates were chosen between 1e-7 to 0.1in increments of 10x, and epochs varied between 50-150 in step sizes of 50. The batch size323.2. Methods & Materialswas kept at 15.The training was implemented in Python 3.0 and performed on two machines: an i7-10875H and an NVIDIA Titan V GPU. For evaluation, pixel accuracy, Jaccard index, andDice coefficients were calculated as per Equation 2.26.333.2.Methods&MaterialsFigure 3.2: Architecture of a U-Net developed for prostate segmentation from T2-echoMR images (64 echoes) taken for luminal water imaging.343.3. Results3.3 ResultsOur model’s best performance was selected based on the Dice score. The metrics for thebest-performing model for segmenting the full prostate and the peripheral zone are shownin Table 3.1. Figure 3.3 shows an example of the prediction for full prostate segmentationand peripheral zone segmentation. A side-by-side comparison of all the predicted ROIstogether with their ground truth is shown in Appendix A.3.The best U-Net model for full prostate segmentation achieved an average Dice coefficientof 91.93% ± 2.6%. The model was trained on the CPU with a learning rate of 1e-4, a batchsize of 2, 50 epochs, γ of 4, and α of 0.1. The total training time was 342.7 minutes.For the peripheral zone segmentation, the best model achieved an average Dice coefficientof 75.07% ± 10.3%. The model was trained on the CUDA platform to allow for parallelcomputation on the GPU. The optimal hyperparameters with a learning rate of 7e-4, batchsize of 15, 100 epochs, γ of 6, and α of 0.1. The total training time was 183.62 minutes.Table 3.1: U-Net performance metrics of full prostate and peripheral zone seg-mentation on the test datasets. The reported metrics are the average pixelaccuracy, average Jaccard index, and average Dice coefficient across the entiretest dataset.SegmentationAverage PixelAccuracy (%)AverageJaccard Index (%)Average DiceCoefficient (%)Full Prostate 99.58 ± 0.13 85.2 ± 4.3 91.93 ± 2.6Peripheral Zone 99.52 ± 0.18 61.1 ± 12.6 75.07 ± 10.33.4 Discussion & ConclusionThe model’s poorer performance in peripheral zone segmentation is not unexpected– thePZ shape is more irregular compared to the full prostate shape when qualitatively examin-ing our patient dataset. Figure 3.4 shows an example of full prostate zone and peripheralzone ROIs on the same MR image and irregularities in PZ are visually more pronouncedthan in the full prostate ROIs. These irregularities makes training more difficult since alarger distribution of PZ shapes needs to be learned. Without tweaking hyperparameters,a method to making PZ ROI segmentation more robust would be to have more trainingdatasets. Though, the tweaking of the hyperparameters reflect the need for more trainingfor the PZ in comparison to the full prostate ROI– the PZ hyperparameters have a largerlearning rate, batch size, epochs, and γ value.The hyperparameter, γ, changes the shape of the loss curve. Figure 3.5 demonstrateshow the curves change for varying γ values. As noted in the paper by Lin et al. presentingfocal loss, as γ increases, the relative losses decrease for well-classified examples [80]. Thus,353.4. Discussion & ConclusionFigure 3.3: Shown are images of hand-drawn ROIs versus U-Net modelpredicted ROIs. To the left is one of the 64 echoes of the T2-echo data.(A) shows the hand-drawn full prostate ROI for the same T2-echo imagewhere (B) is the U-Net predicted segmentation. (C) shows the hand-drawn PZ zone ROI and (D) the U-Net model predicted ROI.we can bias our model using focal loss to identify less commonly seen ROI shapes such thatit can be robust to both standard and rarer shapes. This trend is seen in the optimal choiceof α of PZ versus full prostate segmentation as the optimal model for PZ took a larger αthan the latter model. As PZ has more irregularities in its shape across all training andvalidating datasets, it would benefit to weight unexpected examples more heavily to becomea more robust and generalizable model.Figure 3.6 shows an example where the PZ segmentation shows an artifact of pixelsoutside of the ROI. The frequency of these island pixels were more common in PZ than infull prostate segmentation, indicating that the PZ model will benefit from training diverseshapes of PZ ROIs. In addition to more diverse training datasets, there are future possibil-ities of researching loss functions that may manage the problem of islands. Perceptual loss,introduced by Johnson et al. in 2016 used often for style-transfer, shows a loss functioncapable of capturing high-level differences such as pixel groupings rather than per-pixellosses [81]. The current loss function implemented does not differentiate loss from an incor-rect pixel far away from the ROI and an incorrect pixel near to the ROI. Perceptual losscould potentially address this problem as it could be tailored to increase its penalizationfor further island-like pixels from the ideal ROI.363.4. Discussion & ConclusionFigure 3.4: Images of paired full and PZ prostate ROIsdemonstrating the eccentric shapes that can be present.The PZ has more exaggerated differences when comparedwith the full prostate ROI for the same MR slice and pa-tient.With the advancement of ML-based ROI segmentation of prostate regions in MRI, twothings are made possible: increased efficiency in workflow for the laborious segmentationtask and the possibility for automatic enhancement of T2W images with LWI. Enhancementof T2W images is discussed in the following chapter.373.4. Discussion & ConclusionFigure 3.5: One of two hyperparameters of focal loss: α andγ. α is kept constant, and different values of γ are presented.Based on the plotted graph, as γ increases, the relative lossvalue decreases towards well classified examples. Thus, byincreasing γ, a model undergoing training will reduce itsbias towards well classified cases.Figure 3.6: Outlier pixels shown in a PZ segmentation.Comparing U-Net ROIs from full prostate segmented ROIs,PZ had higher incidences of outlier pixels.38Chapter 4Image Augmentation4.1 IntroductionWhile luminal water imaging (LWI) shows significant results in correlating with the Glea-son score, it lacks anatomical information that radiologists rely on during prostate cancerdiagnoses. Thus, a method in weighting anatomical images with LWI maps is proposed.When the LWI map weights an anatomical MR image, we call them augmented images.Figure 4.1 shows an example of an augmented T2W image.Figure 4.1: (a) a histological slice of the prostate, outliningGleason scores of 3+3 and 4+3 tumours with correspondingT2W image (b). Image (c) shows an augmented T2W imagewith the luminal water fraction map. Highlighted arrowsindicate the increased image contrast where the 3+3 and4+3 tumours are present.4.2 Methods & MaterialsAugmentation and analysis were performed in Python 3.0. Enlarging ROIs from 240 x 240to 512 x 512 was performed in MATLAB.4.2.1 Images and Data for AugmentationThree types of images are required for image augmentation. The first is the anatomicalimage, the second is the quantitative image map (LWI maps), and the third is the ROI394.2. Methods & Materialsmasking image. To verify the efficacy of image augmentation, correlated histology slicesregistered to T2W images are used in analyzing augmented images.Anatomical ImageThe anatomical image used in the investigation of image augmentation are T2-weighted(T2W) images collected by Dr. Sabouri in the LWI study [27]. Though, any anatomicalimage could be used.The first anatomical images are T2W images of size 240 x 240, selected to be at echo =4 which with TE = 80 ms, matches the effective echo time of high-resolution T2W image.The details on the multi-echo MR acquisition method to obtain the T2W image is discussedin Section 3.2.1. In addition to the 240 x 240 T2W images, a high-spatial-resolution T2Wimage (high-res T2W) was captured.The high-res T2W was taken for each patient and for all the same slices as the T2-echodata using a multi-section turbo spin-echo sequence. The high-res images are acquired witha TR = 1851 ms, TE = 80 ms, number of echoes = 1, FOV = 140 x 140 x 72 mm2 mmvoxel size = 0.3 x 0.3 x 4 mm3, imaging matrix size = 288 x288, reconstruction matrix size= 512 x 512, slice thickness = 4 mm, flip angle = 90°, number of averages = 3, and imagingduration = 285 seconds[27].Luminal Water Imaging MapsSeven luminal water imaging maps can be generated from T2-echo data by gathering theT2 distributions from an NNLS fitting and calculating the maps as discussed in Section2.3.3 and 2.3.4. Figure 2.7 shows an example of all 7 maps and the corresponding T2Wimage. Two types of NNLS algorithms were explored: an in-house developed MATLABscript[27, 82] and DECAES[69]. When using DECAES, only six of the seven LWI mapswere calculated: Ashort, gmT2, gmT2,short, gmT2,long, LWF, and N. Alongwas not calculatedwhen using DECAES as it was not an extracted parameter from the DECAES algorithm.The multi-echo T2 data is the same data as outlined in Section 3.2.1.In addition to the quantitative parameter maps, principal component analysis (PCA)was performed to generate a new map that used all LWI parameters from the MATLABNNLS. PCA values were calculated using the LWI parameters of each pixel in the full-prostate ROI for all valid patient datasets. PCA was implemented in Python using thesklearn library. The coefficients calculated from the PCA analysis were then used to createa new image, weighted by LWI parameters. This was achieved by taking the dot product ofthe PCA components with the 7 LWI parameters for each pixel, thereby generating a newimage.404.2. Methods & MaterialsROI MaskThe ROI masks are the segmented PZ and full-prostate regions as discussed in Chapter 3.The masks are of size 240 x 240 and are generated by modifying the PNG format of theROI image to a boolean array such that the mask has pixels with a ‘1’ for inside the ROIand ‘0’ otherwise. The boolean format is helpful since element-wise multiplication with theT2W image (240 x 240) will mask every pixel outside the ROI as ‘0’ and inside the ROIthe values of the original T2W pixel value. For example, Figure 4.2 demonstrates the useof the ROI. The TZ was the full ROI subtracted by the PZ ROI.Figure 4.2: The first image shows the luminal water frac-tion map, one of the seven LWI parameters. Outside theprostate region, the LWF map has unusable values. Byperforming an element-wise multiplication of the LWF mapwith the ROI boolean mask, all regions outside the ROI areset to zero.Correlated HistologyIn the patient population of the LWI study by Dr. Sabouri, each patient underwent radicalprostatectomy after MR data was collected. The excised prostate specimens allowed forhistological examination by pathologists who evaluated slides of the specimen and assignedGS. Dr. Sabouri provided the deformable registration of histologic slices to the multi-echoT2 slices [63] which is used in the analysis of enhanced images. Figure 4.3 shows thehistologically-defined regions deformed onto its corresponding 240 x 240 T2W image.4.2.2 Equation for AugmentationAn equation was developed for weighting T2W anatomical images with LWI parametermaps. Equation 4.1 shows how the augmented image, IA is generated.IA = frescale (fnorm (I0 · fw (IPW)) · w + I0 · (1− w)) , (4.1)414.2. Methods & MaterialsFigure 4.3: (a) Histologically examined slice with its corre-sponding T2W image in (b). Outlines of the GS in histologywere registered to MR images and seen in image (b). AnMR image with GS masks with scores 3+3 and 3+4 andthe PZ and full prostate segmentation outline.where I0 is the anatomical image normalized to the maximum and minimum pixel intensityvalues within the ROI and IPW is one of seven LWI parametric map already element-wisemultiplied with an ROI and standardized to values in the ROI, and w is a weighting valuescaled from 0 to 1. Function fw performs functional weighting on image IPW and is discussedin more detail in the next section, Section 4.2.3, fnorm maps all values between [0, 1], andfrescale maps the new image to the relative maximum and minimum intensities found inthe original I0 image. Figure 4.4 demonstrates Equation 4.1 graphically. The augmentedimages were then saved as .PNG format.4.2.3 Image Augmentation OptimizationImage augmentation can vary based on the selection of parameters in Equation 4.1. Thus,(computational) experiments were performed with varying parameters to investigate theeffect of augmentation on image contrast. This included sweeping w between 0 and 1 byincrements of 0.25, sweeping through all 7 LWI maps for IPW, and testing two weightingfunctions for fw. The two weighting functions were hyperbolic tan and sigmoid function.Since fw acts on IPW, an ROI-specific parameter map that has been standardized, theoutcome after a hyperbolic tan function will map values of IPW to a scale of [−1, 1] and thesigmoid function to a scale of [0, 1] astanh(x) =ex − e−xex + e−xsigmoid(x) =11 + e−x.(4.2)424.2. Methods & MaterialsFigure 4.4: Demonstration of the function used to augmentimages. The augmented image, IA, requires the originalanatomical image, I0, normalized to values within the user-defined ROI and parameter-weighting image, IPW, stan-dardized to values within the user-defined ROI. w will de-termine how much weighting of the parameter maps will bein the final image. Three functions, fw, fnorm, and frescalecorrespond to the weighting, normalization, and rescalingfunctions respectively.4.2.4 Analysis of Augmentation EfficacyImage augmentation was evaluated against the original anatomical T2W image based ontwo kinds of analysis: a histogram overlap (OVL) and area under the curve (AUC) anal-ysis. OVL and AUC metrics were measured for an individual slice and were most usefulwhen comparing the two metrics of a T2W image and an augmented image. Both the pe-ripheral zone and transition zone were analyzed and OVL and AUC metrics were calculated.OVL provides a decimal value between [0,1] for how separable benign versus malignantpixels are based on pixel intensity. OVL is based on comparing histograms of benign andmalignant pixel intensities in PZ or TZ with histogram binning based on Sturge’s rule [83].The registered histology defines malignant pixels in the MR image; the number of malig-nant histograms for an image is based on how many distinct Gleason scores are defined.The OVL value is the percentage overlap of one of the malignant histogram’s to the benignhistogram. Thus, as OVL increases, the worse the separability of benign and malignantpixels and vice versa for a decrease in OVL.AUC provides a decimal value between [0,1] as another method to characterize be-nign and malignant separability based on pixel intensity. Receiver operator characteristics(ROC) were calculated on pixel intensity values normalized to the maximum intensity inthe ROI with ground truths from registered histology. The normalized pixel intensities wereused as the probability for measuring malignancy within the ROI, i.e. a pixel intensity of1 was mapped as positive for malignancy. Thus, for parameters LWF, gmT2, gmT2,short,434.3. ResultsAlong, and N, their values were inverted prior to calculating ROC since they were foundto negatively correlate to malignancy [62]. The AUC was then calculated from the ROCcurves and reported.4.2.5 Mapping to High-resolution T2W ImagesGiven the availability of high-res T2W images (512 x 512), the LWI map (240 x 240) andweighting were enlarged to generate high-res augmented images while performing the anal-ysis on the 240 x 240 augmented images. A MATLAB GUI was developed to perform ROIdeformation from the 240 x 240 image to the corresponding 512 x 512 T2W image. TheGUI allowed for translation and enlargement, which is discussed further in Appendix A.4.A total of 224 high-res T2W images were processed to generate 224 high-res augmentedT2W images in .PNG format.The high-res augmented images were also reformatted to DICOM files and will be re-viewed by a radiologist in future research to investigate the augmented T2W’s effect inidentifying tumours.4.3 ResultsPCA ComponentsThe PCA component values were found and are reported in Table 4.1. These values werethen used to generate a new quantitative map for augmenting images.Table 4.1: PCA values for the various zones in prostate (PZ, TZ, and fullprostate zone).Segmentation PZ TZ Full ProstateAshort -0.4797 -0.4510 -0.4857LWF 0.4956 0.5176 0.5080N -0.0478 0.0954 0.0264gmT2 0.4478 0.4221 0.4233gmT2,short 0.2610 0.2315 0.2271gmT2,long 0.0942 0.1464 0.13814.3.1 NNLS AlgorithmsWhen comparing the speed in calculating the T2 distribution via NNLS between the MAT-LAB (in-house) versus Julia (DECAES) implementation, the DECAES algorithm was fasterby a factor of 59.5 times. The average time to process a single T2-echo slice with 64 echoeswas 60.1 seconds with DECAES and 3572.4 seconds (59.54 minutes) for MATLAB. When444.3. Resultscomparing the outcomes of the luminal water fraction maps, the average difference betweenthe two maps for the LWF map across all 244 slices was 0.0533. Figure 4.5 shows an exampledifference map between the two algorithms for a single slice.Figure 4.5: A single slice from a patient’s LWF map is shown. The left-most image is the LWF map generated by the DECAES NNLS algorithmand the middle image shows the LWF map from the MATLAB NNLSalgorithm. The rightmost image shows the pixel-wise difference betweenthe two maps. The maximum difference in this slice for LWF was 0.1716and the average difference was 0.024741.4.3.2 Image Augmentation AnalysisShown here is the analysis for a single slice where the augmentation experiments sweptvalues of the weights w, weighting functions fw, and parameter images IPW. Results of allOVL and AUC values for the slice can be found in Appendix A.5. The augmented imagesgenerated for the full prostate, PZ, and TZ regions by the parameter maps with the bestAUC metrics are shown in Figure 4.6.Within the PZ, AUC metrics for all parameters maps for GS 4+3 except gmT2,longandAshort and w = 1 for gmT2,short show better separability of malignancy when compared withthe original T2W image. OVL metrics showed that all parameters except for N providedbetter separability than the original T2W, even at varying weights. Of the GS 4+3 region,AUC and OVL showed several combinations of w, IPW, and fw that performed better thanthe original T2W image by the AUC and OVL metric. For GS 3+3, fewer combinationsprovided better OVL metrics. Only PCA and LWF augmented images at high weightingsprovided better separability. On the other hand, AUC reported better separability of ma-lignancy with mostly all parameter weightings.OVL reported better separability within the TZ using gmT2, gmT2,long, and N at higherweightings. When using AUC, PCA, LWF, gmT2, and gmT2,short showed better separabil-ity at higher weightings and Along with lower weightings.454.4. Discussion & ConclusionSimilar trends to the PZ analysis were found when analyzing the full prostate.Figure 4.7 shows the augmented image result of a single slice with w = 0.5 for the PZusing LWF parameter map as IPW.4.3.3 High-res Image AugmentationFigure 4.8 shows the high-res T2W image and the associated augmented images for aweighting of w = 0.75. Only qualitative assessments of the images were performed.4.4 Discussion & ConclusionUsing OVL and AUC as metrics for measuring benign-to-malignant separation aided withfinding the best parameters for image augmentation at high GS. Separability of benign-to-malignant regions for lower GS such as the GS 3+3 showed little to no benefit fromaugmentation using the OVL metric. However, qualitatively assessing the image showedvisible changes that could be beneficial for identifying malignant regions. In contrast, AUCprovided values that reflected changes in the augmented image from the original imageand thus, showed that AUC may be a more sensitive metric for discerning malignancy. Inaddition, OVL and AUC are susceptible to image artifacts since they read absolute pixelintensity. Artifacts that change pixel intensities, such as gradient field artifacts, will distortthe values calculated.For high GS, parameter-weighted image augmentation on anatomical T2W images hasshown better image contrast in distinguishing malignant and benign pixels with respect tousing OVL and AUC. Of the parameter weightings that provide the best contrast, gmT2,LWF, gmT2,short and PCA provided relatively consistent improvement in cancer separabil-ity when augmenting the T2W image in all zones. It is also noted that higher weightingsof the parameter maps were preferred for TZ and full prostate; however, it was found thatas weighting increases, anatomical details of the T2W image decrease.When qualitatively assessing the TZ image, whether the image was augmented or not,the tissues were more heterogeneous with varying pixel intensities compared to PZ. In gen-eral, the TZ is a region that is exclusive to having benign prostatic hyperplasia (BPH)–theenlargement of tissue cells but the growth is not necessarily cancerous. Due to this changein tissue structure, regions of BPH will present differently from ‘normal’ tissue in the MRimage, even though the region is considered benign. This heterogeneity would affect thecontrast of both T2W and augmented images and may change the effectiveness OVL andAUC analysis in this region. Together with TZ segmentation, future development for analternate image enhancement in the TZ region specifically can be implemented to overcomethe heterogeneous reading of benign tissue.464.4. Discussion & ConclusionThe exploration of using DECAES or a MATLAB NNLS script provided results in show-ing the decreased computation time required to analyze NNLS. The error maps generatedbetween the two algorithms were small, at a scale of a few percent differences. With thereduction in computation time, important options are opened, such as having real-time LWIanalysis after the MR sequence is taken at the hospital.Given the various factors that can be modified when augmenting an image and thelimits of using OVL and AUC metrics, a qualitative assessment remains one of the quickestmethods to evaluate its efficacy. Using high-res 512 x 512 images, gmT2, LWF, gmT2,and PCA provide some of the most natural-looking images with fewer discontinuities in theimage intensity, which may or may not be preferable to radiologists. In all, the developmentof augmented images may be helpful for qualitative assessment by radiologists. Furtherinvestigation and studies with radiologists are needed to assess if and which parameter-weighted augmented images provide helpful information for diagnosing tumour extent andlocation.474.4. Discussion & ConclusionFigure 4.6: Image augmentation was performed on the full prostate,PZ, and TZ regions with all available parameter maps. (a) depictsthe registered histology to an MR image with GS 3+4 and 4+3 tu-mours present in both the PZ and TZ. (b) shows the enhanced imageon the entire prostate with a weighting of w = 0.5. (c) shows the en-hanced images on the PZ with weighting of w = 0.75. (d) shows theenhanced images on the TZ with weighting of w = 1. The process ofanalyzing.484.4. Discussion & ConclusionFigure 4.7: Image augmentation performed and analyzed for a singleslice in the PZ where the two Gleason scores are present, 3+4 and4+3. A weighting value of w = 0.5 is shown in the figures. Boththe tanh and sigmoid functions, fw, are shown. The lefmost columnof images shows the PZ region of the LWF map, below it is thesegmented T2W image with the GS and zones outlined. The secondcolumn shows the T2W image and the corresponding histogramsand AUC curves. The third column shows the augmented imageusing the tanh weighting function and corresponding analyses. Thelast column shows the augmented image using a sigmoid weightingfunction and corresponding analyses.494.4. Discussion & ConclusionFigure 4.8: Image augmentation performed on high-res T2W imageswith a weighting factor of 0.75. Parameter weighted images (origi-nally 240 x 240 pixels) were deformed by translation and enlargementto fit the 512 x 512 image size. Shown on the top left is the 240 x240 image with the associated GS mapped onto the image. To theright is the original high-res T2W image. Following images are theaugmented images with the associated parameter noted in the image.50Chapter 5Conclusion & Future WorkThe research presented was made with the goals to increase accessibility for prostate cancerdiagnosis and diagnostic accuracy. Pushing forward the utility of luminal water imagingaddresses both of these goals. Specifically, in the scope of this thesis, tools were developedto increase the efficiency of LWI and to make LWI clinically feasible. This is done by usingLWI parameters to augment anatomical T2W images.The outcome of augmenting T2W anatomical images with certain LWI parameters mapsprovides radiologists with a method to evaluate T2W images with increased intensity con-trast tailored to identify malignant tissue. 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The distribution of T2 shows a separation at200 ms, providing insight to an optimal T2,thresh between thetwo bodies of water modelled in a pixel of the prostate gland.The short-component (blue) and long-component (orange) T2has a double Gaussian-fitted function shown as solid lines. Fig-ure used with permission from S. Sabouri[27] ©2017.59A.2. MATLAB GUI for Hand-Drawn Prostate ROIsA.2 MATLAB GUI for Hand-Drawn Prostate ROIsMATLAB 2022a was used to develop the hand-drawn segmented regions of interests (ROIs).The app can be found at the following Github link: GUI for segmenting masks. Revisionsto the Github page will be made to provide a tutorial-like scheme, or an outline of how touse app.A total of 224 ROIs were developed for the full prostate and another 224 ROIs for theperipheral zone. These ROIs were used as the ground truth in developing a deep learningmodel for automatic segmentation of the full prostate and peripheral zone.Key features of the app is the ability to load pre-existing ROIs and insert them aspolygon objects such that they have move-able points. When exporting, the polygon isconverted to a black-and-white portable network graphic (PNG) image that can be usedreadily for viewing or further analysis.Figure A.2: A GUI was developed in MATLAB’s AppDesignerto enable hand-drawn regions of interests on an image. Depictedis an example of drawing the ROI of a full prostate on slice 7 of14.60A.3. U-Net Predicted ROIsA.3 U-Net Predicted ROIsThe results of the ROI prediction by U-Net is shown in Figure A.3.A.4 MATLAB GUI for Deforming ROIsA MATLAB GUI for performing translation and expansion of an ROI can be found at theGithub link here: GUI for Deforming ROIs. A screenshot of the GUI is shown in Figure A.4.Revisions to the Github page will be made to provide a tutorial-like scheme, or an outlineof how to use app.A.5 Image Augmentation ResultsImage augmentation analysis was generated using code written in Python (uploaded toGithub: Code for image augmentation analysis). The results are shown in Figure A.5.61A.5. Image Augmentation ResultsFigure A.3: Shown is the full test dataset with each column showingthe reference MR image, PZ ground truth ROI, predicted PZ ROI, fullprostate ground truth ROI, predicted full prostate ROI. Each row showsa particular patient slice.62A.5. Image Augmentation Results63A.5. Image Augmentation Results64A.5. Image Augmentation Results65A.5. Image Augmentation ResultsFigure A.4: A GUI was developed in MATLAB’s AppDe-signer to enable the deformation of an ROI from a lowerresolution image (240 x 240) to a higher resolution image(512 x 512). Depicted is an example deformation occurringat slice 7 of the patient.66A.5. Image Augmentation ResultsFigure A.5: Results of OVL and AUC for a single slicewith 7 parameter-weighted images with various weightingsswept from [0.25, 0.5, 0.7, 1.0], tanh and sigmoid weightingfunctions, and within the PZ, TZ, and full prostate zones.67A.5. Image Augmentation Results68A.5. Image Augmentation Results69A.5. Image Augmentation Results70
Thesis/Dissertation
eng
Physics
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Kozlowski, Piotr
Development of MR image analysis with machine learning to enhance T2W images with luminal water imaging for prostate cancer
Text