{"@context":{"@language":"en","Affiliation":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","AggregatedSourceRepository":"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider","Campus":"https:\/\/open.library.ubc.ca\/terms#degreeCampus","Creator":"http:\/\/purl.org\/dc\/terms\/creator","DateAvailable":"http:\/\/purl.org\/dc\/terms\/issued","DateIssued":"http:\/\/purl.org\/dc\/terms\/issued","Degree":"http:\/\/vivoweb.org\/ontology\/core#relatedDegree","DegreeGrantor":"https:\/\/open.library.ubc.ca\/terms#degreeGrantor","Description":"http:\/\/purl.org\/dc\/terms\/description","DigitalResourceOriginalRecord":"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO","FullText":"http:\/\/www.w3.org\/2009\/08\/skos-reference\/skos.html#note","Genre":"http:\/\/www.europeana.eu\/schemas\/edm\/hasType","GraduationDate":"http:\/\/vivoweb.org\/ontology\/core#dateIssued","IsShownAt":"http:\/\/www.europeana.eu\/schemas\/edm\/isShownAt","Language":"http:\/\/purl.org\/dc\/terms\/language","Program":"https:\/\/open.library.ubc.ca\/terms#degreeDiscipline","Provider":"http:\/\/www.europeana.eu\/schemas\/edm\/provider","Publisher":"http:\/\/purl.org\/dc\/terms\/publisher","Rights":"http:\/\/purl.org\/dc\/terms\/rights","RightsURI":"https:\/\/open.library.ubc.ca\/terms#rightsURI","ScholarlyLevel":"https:\/\/open.library.ubc.ca\/terms#scholarLevel","Supervisor":"http:\/\/purl.org\/dc\/terms\/contributor","Title":"http:\/\/purl.org\/dc\/terms\/title","Type":"http:\/\/purl.org\/dc\/terms\/type","URI":"https:\/\/open.library.ubc.ca\/terms#identifierURI","SortDate":"http:\/\/purl.org\/dc\/terms\/date"},"Affiliation":[{"@value":"Science, Faculty of","@language":"en"},{"@value":"Physics and Astronomy, Department of","@language":"en"}],"AggregatedSourceRepository":[{"@value":"DSpace","@language":"en"}],"Campus":[{"@value":"UBCV","@language":"en"}],"Creator":[{"@value":"Sample, Caleb","@language":"en"}],"DateAvailable":[{"@value":"2024-04-04T18:08:02Z","@language":"en"}],"DateIssued":[{"@value":"2024","@language":"en"}],"Degree":[{"@value":"Doctor of Philosophy - PhD","@language":"en"}],"DegreeGrantor":[{"@value":"University of British Columbia","@language":"en"}],"Description":[{"@value":"The complexity of radiotherapy techniques for treating head and neck cancer has significantly advanced over the previous two decades. However, it remains common for patients to finish treatment with a severe loss in salivary function, causing significantly diminished quality of life assessments. The overall goal of research endeavours in this thesis is to develop innovative techniques that lead to better understanding and consideration of salivary glands during head and neck radiotherapy planning. This goal is approached along a multitude of paths using various imaging modalities and treatment planning techniques. \r\n\r\nA method is demonstrated for enhancing prostate specific membrane antigen (PSMA) positron emission tomography (PET) images and intravoxel incoherent motion (IVIM) magnetic resonance imaging (MRI) using neural networks. PSMA PET shows high expression in salivary glands, and its relationship with functional importance can be more accurately assessed after image enhancement. IVIM MRI is a promising diffusion protocol for investigating functional heterogeneity in salivary glands, but suffers from reproducibility issues. Image enhancement methods and a new model-independent approach to quantifying diffusion are shown to improve the utility, and potentially the reproducibility, of IVIM MRI. \r\n\r\nPSMA PET uptake heterogeneity in parotid glands is quantified, demonstrating a consistent bias towards lateroposterior aspects. Uptake patterns are compared with literature-models of subregional parotid gland importance, revealing an anticorrelation between PSMA PET uptake and relative importance. A model is developed for predicting subregional importance using PSMA PET \/ computed tomography (CT) radiomic features. A method for tailoring importance estimates using patient-specific data is presented.\r\n\r\nAn autosegmentation methodology is created for localizing the newly discovered \"tubarial\" salivary glands on CT images. Tubarial glands are only known to be visible on PSMA PET which is not typically acquired for head and neck cancer patients. Therefore a method of localizing the glands on CT images is necessary for tubarial glands to be considered during radiotherapy treatment planning. \r\n\r\nLastly, a technique for translating subregional parotid gland importance data into spatially varying dose constraints during radiotherapy treatment planning is demonstrated. A retrospective planning study showed improvements in predicted salivary output at one year post-radiotherapy using this method.","@language":"en"}],"DigitalResourceOriginalRecord":[{"@value":"https:\/\/circle.library.ubc.ca\/rest\/handle\/2429\/87682?expand=metadata","@language":"en"}],"FullText":[{"@value":"Towards improving radiotherapeutictreatment of the parotid glands: across-modality investigationbyCaleb SampleB.Sc., The University of Northern British Columbia, 2019A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinThe Faculty of Graduate and Postdoctoral Studies(Physics)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)April 2024\u00a9 Caleb Sample 2024The following individuals certify that they have read, and recom-mend to the Faculty of Graduate and Postdoctoral Studies foracceptance, the thesis entitled:Towards improving radiotherapeutic treatment of the parotid glands:a cross-modality investigationsubmitted by Caleb Sample in partial fulfillment of the requirements forthe degree of Doctor of Philosophy in PhysicsExamining CommitteeHaley Clark, Medical Physicist, BC CancerCo-SupervisorStefan Reinsberg, Professor, Physics and Astronomy, UBCCo-SupervisorJonn Wu, Radiation Oncologist, BC CancerSupervisory Committee MemberNancy Ford, Associate Professor, Oral Biological and Medical Sciences, UBCUniversity ExaminerRoger Tam, Associate Professor, Radiology, UBCUniversity ExaminerJoseph O. Deasy, Chair, Medical Physics, Memorial Sloan Kettering CancerCenterExternal ExaminerAdditional Supervisory Committee Members:Alex MacKay, Professor Emeritus, Physics and Astronomy, UBCSupervisory Committee MemberiiAbstractThe complexity of radiotherapy techniques for treating head and neck cancerhas significantly advanced over the previous two decades. However, it re-mains common for patients to finish treatment with a severe loss in salivaryfunction, causing significantly diminished quality of life assessments. Theoverall goal of research endeavours in this thesis is to develop innovativetechniques that lead to better understanding and consideration of salivaryglands during head and neck radiotherapy planning. This goal is approachedalong a multitude of paths using various imaging modalities and treatmentplanning techniques.A method is demonstrated for enhancing prostate specific membraneantigen (PSMA) positron emission tomography (PET) images and intravoxelincoherent motion (IVIM) magnetic resonance imaging (MRI) using neuralnetworks. PSMA PET shows high expression in salivary glands, and itsrelationship with functional importance can be more accurately assessed af-ter image enhancement. IVIM MRI is a promising diffusion protocol forinvestigating functional heterogeneity in salivary glands, but suffers fromreproducibility issues. Image enhancement methods and a new model-independent approach to quantifying diffusion are shown to improve theutility, and potentially the reproducibility, of IVIM MRI.PSMA PET uptake heterogeneity in parotid glands is quantified, demon-strating a consistent bias towards lateroposterior aspects. Uptake patternsare compared with literature-models of subregional parotid gland impor-tance, revealing an anticorrelation between PSMA PET uptake and relativeimportance. A model is developed for predicting subregional importance us-ing PSMA PET \/ computed tomography (CT) radiomic features. A methodfor tailoring importance estimates using patient-specific data is presented.iiiAn autosegmentation methodology is created for localizing the newlydiscovered \u201ctubarial\u201d salivary glands on CT images. Tubarial glands areonly known to be visible on PSMA PET which is not typically acquiredfor head and neck cancer patients. Therefore a method of localizing theglands on CT images is necessary for tubarial glands to be considered duringradiotherapy treatment planning.Lastly, a technique for translating subregional parotid gland importancedata into spatially varying dose constraints during radiotherapy treatmentplanning is demonstrated. A retrospective planning study showed improve-ments in predicted salivary output at one year post-radiotherapy using thismethod.ivLay SummaryHead and neck cancer patients commonly finish radiotherapy with an in-ability to produce saliva, negatively impacting their quality of life. This islargely due to undesirable irradiation of salivary glands during treatment.The aim of this thesis is to develop innovative techniques that lead to betterunderstanding and consideration of salivary glands during head and neckradiotherapy planning. This is done through a variety of approaches, in-cluding medical image deblurring techniques using machine learning, anda new mathematical approach to image analysis that leads to quality im-provements, ultimately allowing the salivary glands to be more accuratelyprobed. We investigate the salivary glands using a recently developed typeof nuclear imaging, and show its usefulness for revealing regions of salivaryglands that are important for saliva production. Important regions must bespared from radiation during cancer treatment, and an effective method fordoing so is also demonstrated.vPrefaceThe overall research goal to improve knowledge and handling of the salivaryglands during head and neck radiotherapy stems from previous research doneat BC Cancer, Vancouver, and is a continuation of efforts by Haley Clark,Jonn Wu, Stephen Thomas, Allan Hovan, and Vitali Moiseenko, duringHaley Clark\u2019s graduate studies at the University of British Columbia andBC Cancer.The PSMA PET \/ CT data used extensively throughout research projectsin this thesis were obtained through a collaboration with nuclear imagingphysicists at BC Cancer Research, Vancouver, including Arman Rahmim,Carlos Uribe, and Franc\u00b8ois Be\u00b4nard. Retrospective studies using this datawere approved by the BC Cancer Agency Research Ethics Board (H21-00518-A001). Arman Rahmim, and Carlos Uribe, Franc\u00b8ois Be\u00b4nard, JonnWu, Haley Clark, and Caleb Sample arrived upon PSMA PET as the modal-ity to analyse salivary glands with. Data was prepared and deidentified byCarlos Uribe.The IVIM MRI clinical study for investigating the parotid glands wasconceived by Stephen Thomas, Haley Clark, Stephen Reinsberg, Jonn Wu,and Caleb Sample. Patient consent and scheduling was managed by JonnWu and Caleb Sample. Image collection was managed by Haley Clark andCaleb Sample. This clinical study was approved by the BC Cancer AgencyResearch Ethics Board (H21-00517).The content of Chapter 5 has been submitted for publication in a peer-reviewed journal. The name of the article is, \u201cNeural blind deconvolution forsimultaneous partial volume correction and super-sampling of PSMA PETimages,\u201d and the co-authors are Caleb Sample, Arman Rahmim, CarlosUribe, Franc\u00b8ois Be\u00b4nard, Jonn Wu, and Haley Clark. The research problem,vianalysis, and write-up were formulated by Caleb Sample. Contributive editswere made by all co-authors.The content of Chapter 6 has been submitted for publication in a peer-reviewed journal. The name of the article is, \u201cImage deblurring and model-independent parameterization for improving IVIMMRI,\u201d and the co-authorsare Caleb Sample, Jonn Wu, and Haley Clark. The research problem, anal-ysis, and write-up were formulated by Caleb Sample. Contributive editswere made by all co-authors. Computational tools used for contouring anddata-sorting were developed by Haley Clark.The content of Chapter 7 has been peer-reviewed and accepted for pub-lication in the Cureus Journal of Medical Science [1]. The name of the ar-ticle is, \u201cDevelopment of a CT-Based autosegmentation model for prostate-specific membrane antigen (PSMA) positron emission tomography-delineatedtubarial glands,\u201d and the co-authors are Caleb Sample, Arman Rahmim,Carlos Uribe, Jonn Wu, and Haley Clark. The research problem, analysis,and write-up were formulated by Caleb Sample. Software for manually con-touring the tubarial glands on PSMA PET images was created by HaleyClark. Contributive edits were made by all co-authors.The content of Chapter 8 has been submitted for publication in a peer-reviewed journal. The name of the article is, \u201cInvestigating heterogeneousPSMA ligand uptake inside parotid glands,\u201d and the co-authors are CalebSample, Arman Rahmim, Carlos Uribe, Franc\u00b8ois Be\u00b4nard, Jonn Wu, andHaley Clark. The research problem came about through discussions withall co-authors. The analysis and write-up were formulated by Caleb Sample.Contributive edits were made by all co-authors.The content of Chapter 9 has been submitted for publication in a peer-reviewed journal. The name of the article is, \u201cPSMA PET as a predictivetool for sub-regional importance estimates in the parotid gland,\u201d and theco-authors are Caleb Sample, Arman Rahmim, Carlos Uribe, Jonn Wu, andHaley Clark. The research problem came about through discussions with allco-authors. The analysis and write-up were formulated by Caleb Sample.Contributive edits were made by all co-authors.The content of Chapter 10 has been peer-reviewed and accepted forviipublication in the Journal of Applied Clinical Medical Physics [2]. The nameof the article is, \u201cIncorporating parotid gland inhomogeneity into head-and-neck treatment optimization through the use of artificial base plans,\u201d and theco-authors are Caleb Sample, Jonn Wu, Steven Thomas, and Haley Clark.The research problem was developed by Haley Clark and Caleb Sample, andcustom software for creating artificial base plans was developed by HaleyClark. The analysis, and write-up was formulated by Caleb Sample, andcontributive edits were made by all co-authors.In all applicable cases, written permission from the Copyright holder wasobtained when materials from other media were reused in this thesis. Fig-ure 2.1 was adapted from the lecture notes of Dr. Qing-San Xiang used inPHYS 542 (MRI physics) at the University of British Columbia. Figure 3.1was adapted with permission of Taylor and Francis Group, LLC, a divisionof Informa plc, from the Handbook of Radiotherapy Physics (Theory andPractice) by Philip Mayles, Alan Nahum, and Jean-Claude Rosenwald [3].Figure 3.2 was reused from with permission from the article, \u201cU-Net: Con-volutional Networks for Biomedical Image Segmentation,\u201d by Olaf Rosse-berger et al.. Figure 4.1 is from the public domain, originally created byHenry Gray. Figure 9.1 was reproduced with permission from, \u201cHeteroge-neous radiotherapy dose-outcomes response,\u201d which was originally publishedin volume 4:035001 of Converg Sci Phys Oncol. (2018) by Clark HD, ThomasSD, Reinsberg SA, Moiseenko VV, Hovan AJ, and Wu JS. Figure 7.2 wasreprinted from Neural Networks, Volume 121, N Ibtehaz and M Sohel Rah-man, \u201dMultiResUNet : Rethinking the U-Net architecture for multimodalbiomedical image segmentation,\u201d Pages 74-87, Copyright 2020, with permis-sion from Elsevier.viiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviiiList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . xxvAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . xxviDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xxviii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Motivation and Objective . . . . . . . . . . . . . . . . . . . . 11.2 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . 2I Introductory Content . . . . . . . . . . . . . . . . . . . . . . 52 Medical Imaging for Radiotherapy . . . . . . . . . . . . . . . 62.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2 Radiography . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2.1 Attenuation Processes . . . . . . . . . . . . . . . . . . 7ix2.2.2 X-Ray Generation . . . . . . . . . . . . . . . . . . . . 82.2.3 X-Ray Detection . . . . . . . . . . . . . . . . . . . . . 92.3 Computed Tomography (CT) . . . . . . . . . . . . . . . . . . 102.3.1 Physical Principles . . . . . . . . . . . . . . . . . . . 102.3.2 Image Collection . . . . . . . . . . . . . . . . . . . . . 102.3.3 Image Reconstruction . . . . . . . . . . . . . . . . . . 122.3.4 Clinical Utility . . . . . . . . . . . . . . . . . . . . . . 132.4 Magnetic Resonance Imaging (MRI) . . . . . . . . . . . . . . 142.4.1 Physical Principals . . . . . . . . . . . . . . . . . . . 142.4.2 T1 and T2 MRI . . . . . . . . . . . . . . . . . . . . . 182.4.3 Spin Echo (SE) and Turbo Spin Echo (TSE) . . . . . 192.4.4 Echo Planar Imaging (EPI) . . . . . . . . . . . . . . . 212.4.5 Diffusion Weighted Imaging (DWI) MRI . . . . . . . 222.4.6 Intravoxel Incoherent Motion (IVIM) MRI . . . . . . 232.4.7 Current Issues with IVIM MRI . . . . . . . . . . . . . 252.4.8 Hardware . . . . . . . . . . . . . . . . . . . . . . . . . 272.4.9 Clinical Utility . . . . . . . . . . . . . . . . . . . . . . 292.5 Positron Emission Tomography (PET) . . . . . . . . . . . . 302.5.1 Physical Principles . . . . . . . . . . . . . . . . . . . 302.5.2 Image Collection . . . . . . . . . . . . . . . . . . . . . 322.5.3 Image Reconstruction . . . . . . . . . . . . . . . . . . 332.5.4 Standard Uptake Values . . . . . . . . . . . . . . . . 332.5.5 Prostate Specific Membrane Antigen (PSMA) PET . 343 Radiotherapy for Head and Neck Cancer Patients . . . . . 363.1 Head and Neck Cancer . . . . . . . . . . . . . . . . . . . . . 363.2 External Beam Radiotherapy . . . . . . . . . . . . . . . . . . 383.2.1 How Does Radiation Treat Cancer? . . . . . . . . . . 383.2.2 History of Radiotherapy . . . . . . . . . . . . . . . . 403.2.3 Radiotherapy for Head and Neck Cancer Treatment . 433.2.4 Radiation With Linear Accelerators (LINACs) . . . 453.2.5 Segmentation of Medical Images for Treatment Plan-ning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48x3.2.6 Semantic Segmentation and U-Net . . . . . . . . . . . 523.2.7 Volume Modulated Arc Therapy (VMAT) . . . . . . 553.2.8 Treatment Planning with Varian Eclipse . . . . . . . 584 The Salivary Glands and Radiotherapy . . . . . . . . . . . . 644.1 Saliva and the Major Salivary Glands . . . . . . . . . . . . . 654.1.1 The Parotid Glands . . . . . . . . . . . . . . . . . . . 664.1.2 The Submandibular Glands . . . . . . . . . . . . . . 694.2 Radiation-Induced Salivary Gland Dysfunction and Xerosto-mia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694.3 Current Dose Guidelines for the Salivary Glands . . . . . . . 724.4 Evidence for a Heterogeneous Dose Response in the SalivaryGlands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734.5 The Tubarial Glands . . . . . . . . . . . . . . . . . . . . . . 77II Research Contributions . . . . . . . . . . . . . . . . . . . . 805 Simultaneous Super-Sampling and Partial Volume Correc-tion of PSMA PET Images . . . . . . . . . . . . . . . . . . . . 815.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 815.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 835.2.1 Data Set . . . . . . . . . . . . . . . . . . . . . . . . . 835.2.2 Overview of Neural Blind Deconvolution . . . . . . . 845.2.3 Model Architecture . . . . . . . . . . . . . . . . . . . 855.2.4 Loss Function and Optimization . . . . . . . . . . . . 875.2.5 Evaluation Metrics . . . . . . . . . . . . . . . . . . . 905.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 915.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1035.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1106 Image Denoising and Model-Independent ParameterizationFor Improving IVIM MRI . . . . . . . . . . . . . . . . . . . . 1116.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 111xi6.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1156.2.1 Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . 1156.2.2 Denoising . . . . . . . . . . . . . . . . . . . . . . . . . 1166.2.3 Evaluating deblurred Images . . . . . . . . . . . . . . 1216.2.4 Extracting Exponential Model Parameters . . . . . . 1236.2.5 Model-independent IVIM parameters . . . . . . . . . 1246.2.6 Comparing Parameters . . . . . . . . . . . . . . . . . 1266.3 Results: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1266.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1376.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1407 An Open Source CT-Autosegmentation Tool for the Tubar-ial Glands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1417.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1417.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1447.2.1 Manual Contouring on PSMA PET images . . . . . . 1447.2.2 Pre-Processing . . . . . . . . . . . . . . . . . . . . . . 1447.2.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 1467.2.4 Model Parameters . . . . . . . . . . . . . . . . . . . . 1487.2.5 Combined Model for Left and Right Tubarial Glands 1487.2.6 Training and Validation . . . . . . . . . . . . . . . . . 1487.2.7 Post-processing . . . . . . . . . . . . . . . . . . . . . 1507.2.8 Model Assessment . . . . . . . . . . . . . . . . . . . . 1507.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1517.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1547.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1598 Investigating Heterogeneous PSMA Ligand Uptake InsideParotid Glands . . . . . . . . . . . . . . . . . . . . . . . . . . . 1618.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1618.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1638.2.1 Cohort and Data Acquisition . . . . . . . . . . . . . . 1638.2.2 Parotid Gland Contouring . . . . . . . . . . . . . . . 163xii8.2.3 Parotid Gland PSMA PET Uptake Analysis . . . . . 1638.2.4 Quantifying the Relationship Between PSMA PETuptake and CT Texture Features . . . . . . . . . . . . 1658.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1688.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1818.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1849 Evaluation of Regional Importance Estimates in the ParotidGlands Using PSMA PET . . . . . . . . . . . . . . . . . . . . 1869.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1869.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1889.2.1 Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . 1889.2.2 Correction of Partial Volume Effects . . . . . . . . . . 1889.2.3 Comparison of PSMA PET with Parotid Gland Im-portance Models . . . . . . . . . . . . . . . . . . . . . 1899.2.4 Development of a predictive Model for parotid glandrelative importance using PSMA PET and CT . . . . 1939.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1989.3.1 Comparison of PSMA PET with Importance Models 1989.3.2 Model Performance for Predicting Parotid Gland Rel-ative Importance . . . . . . . . . . . . . . . . . . . . 2049.3.3 Estimating Deviations of Patient-Specific Importancefrom population Estimates . . . . . . . . . . . . . . . 2049.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2129.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21510 Intra-Parotid Gland Dose Constraints In Radiotherapy Treat-ment Planning Using Artifical Base Plans . . . . . . . . . . 21710.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 21710.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21910.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22710.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23310.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237xiii11 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23811.1 Summary of Scholarly Findings . . . . . . . . . . . . . . . . 23811.2 Further Explorations . . . . . . . . . . . . . . . . . . . . . . 239Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243AppendixA Development of an Automatic Treatment Planning Tool ForUse with Varian Eclipse . . . . . . . . . . . . . . . . . . . . . . 316A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 316A.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318A.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320A.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321xivList of Tables3.1 BC Cancer\u2019s head and neck contour border guidelines. . . . . 505.1 The optimization algorithm for updating network weights topredict deblurred PSMA PET images. . . . . . . . . . . . . . 885.2 Loss Function components used for optimization of Gx(\u03b8x)and Gk(\u03b8k) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 895.3 Blind image quality metrics, CLIP and BRISQUE, for origi-nal (y) and deblurred (x) PSMA PET images . . . . . . . . . 915.4 Spatial distribution of the blur kernel. . . . . . . . . . . . . . 945.5 PSMA PET uptake statistics in CT-defined salivary glandsare summarized using both original and deblurred images. . . 956.1 The optimization algorithm for updating network weights . . 1196.2 Optimization loss function components. . . . . . . . . . . . . 1216.3 Parameter bounds set for IVIM3-NET predictions of expo-nential model parameters. . . . . . . . . . . . . . . . . . . . . 1246.4 Blind image quality metrics, CLIP and BRISQUE are com-pared for original and denoised diffusion MR images . . . . . 1276.5 All IVIM parameter averages and standard deviations insideparotid glands are listed. . . . . . . . . . . . . . . . . . . . . . 1287.1 Tubarial gland model statistics. . . . . . . . . . . . . . . . . . 1527.2 Geometry of predicted and manually contoured tubarial glands.1548.1 Population-level PSMA PET uptake statistics for the parotidand submandibular glands. . . . . . . . . . . . . . . . . . . . 168xv8.2 Shifts from the centre of mass of high uptake regions in theparotid gland. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1708.3 PSMA PET uptake statistics in planar divisions of parotidglands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1718.4 Optimal plane orientation for dividing the parotid gland inhalf. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1758.5 Spearman\u2019s rank correlation coefficient, rs, and the corre-sponding p-value for correlations between PSMA PET andCT images. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1799.1 Models and feature selection (F.S) algorithms, along withtheir corresponding hyper-parameters tested in cross-validation,are shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1979.2 Spearman\u2019s rank correlation coefficients for PSMA PET up-take with Clark\u2019s relative importance estimates. . . . . . . . . 1999.3 Spearman\u2019s rank correlation coefficients for PSMA PET up-take with Han\u2019s relative importance estimates for predictingboth injury, and recovery. . . . . . . . . . . . . . . . . . . . . 2019.4 Comparisons for mean, median, and maximum uptake, in VanLuijk et al.\u2019s critical and non-critical parotid gland subregions.2029.5 PSMA PET uptake in parotid gland subregions correspond-ing to regions of high importance found by Buettner et al. isshown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2039.6 Mean absolute error for each test set of the outer cross val-idation is shown, along with the best performing model andfeature selection algorithm determined during the inner crossvalidation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2059.7 Relative importance of radiomic PSMA PET \/ CT featuresdetermined via principal components analysis for modellingof parotid gland subregion importance. . . . . . . . . . . . . . 20610.1 Mean subregion doses planning with and without artificialbase plans. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228xvi10.2 Stimulated saliva output predictions at one year post-radiotherapyare shown for each plan type. . . . . . . . . . . . . . . . . . . 22810.3 Overlap of PTVs and parotid gland subregions. . . . . . . . . 231A.1 Head-and-neck plan dose constraints and initial optimizationobjective priority applied with Plan n Check. . . . . . . . . . 322A.2 The number of plans passing all dose constraints after N pre-liminary optimization iterations . . . . . . . . . . . . . . . . . 323A.3 Final mean optimization objective priority applied to eachdose constraint with Plan n Check . . . . . . . . . . . . . . . 323xviiList of Figures2.1 Spin echo creation using a refocusing pulse as in CP andCPMG pulse sequences . . . . . . . . . . . . . . . . . . . . . 203.1 TCP curve with and without radiotherapy showing normaltissue complications. . . . . . . . . . . . . . . . . . . . . . . . 443.2 Diagram of the U-Net architecture . . . . . . . . . . . . . . . 533.3 Beams eye view interpreted in Varian Eclipse of a VMATradiation field on a head and neck cancer patient. . . . . . . . 563.4 Varian Eclipse external beam planning window. . . . . . . . . 603.5 Varian Eclipse plan optimization window. . . . . . . . . . . . 624.1 Interior anatomy of the head and neck . . . . . . . . . . . . . 674.2 Clark et al.\u2019s importance estimates in subregions of the parotidgland . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 755.1 The blind deconvolution architecture used for deblurring PSMAPET images . . . . . . . . . . . . . . . . . . . . . . . . . . . . 865.2 A deblurred image and kernel are shown next to the originalPSMA PET image. . . . . . . . . . . . . . . . . . . . . . . . . 925.3 Axial slices intersecting parotid glands and submandibularglands are shown on original and deblurred PSMA PET images. 935.4 Maximum intensity projections of deblurred and original PSMAPET images are shown through the head and neck . . . . . . 965.5 The inner product of recovered PSMA PET blur kernels pre-dicted for all 30 patients is represented by a heat map. . . . . 97xviii5.6 The mean predicted kernel is projected onto the 3 standardpatient planes. . . . . . . . . . . . . . . . . . . . . . . . . . . 985.7 4 variously skewed pseudo-kernels were applied to deblurredimages before re-running the blind deconvolution . . . . . . . 985.8 Supersampling with neural deconvolution is compared withnearest neighbours, linear, quadratic, and cubic interpolation. 995.9 Deblurred and original PSMA PET image slices through parotidglands are shown. . . . . . . . . . . . . . . . . . . . . . . . . . 1005.10 PSMA PET signal across a deblurred and original image arecompared through the parotid glands. . . . . . . . . . . . . . 1015.11 PSMA PET signal across a deblurred and original image arecompared through the parotid glands. . . . . . . . . . . . . . 1025.12 From top to bottom, axial, coronal, and sagittal image slicesare shown for both deblurred (left) and original (right) PSMAPET\/CT fusion images. . . . . . . . . . . . . . . . . . . . . . 1046.1 IVIM deblurring \/ denoising network architecture. . . . . . . 1206.2 The AUC for describing the signal decay curve in IVIM MRI. 1256.3 The average blur kernel predicted for patients is projectedonto the three primary imaging planes. . . . . . . . . . . . . . 1306.4 Denoised and original diffusion image slices with 4 differentb values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1316.5 The neural blind deconvolution denoising process was testedby convolving fixed pseudokernels with previously denoiseddiffusion images before re-starting the denoising process. . . . 1326.6 Axial slices through the parotid gland of denoised and originaldiffusion images with b = 1000 are shown, along with thesignal decay curve of each in a single voxel (indicated in thedenoised image). . . . . . . . . . . . . . . . . . . . . . . . . . 1336.7 Pairwise Spearman\u2019s rank correlation coefficients, rs, betweendose and relative changes in biexponential, triexponential,ADC, and AUC parameters derived from IVIM images aredisplayed for denoised and original images. . . . . . . . . . . . 134xix6.8 Axial slices through the parotid gland of biexponential pa-rameter maps are shown, derived using denoised and originaldiffusion MR images. . . . . . . . . . . . . . . . . . . . . . . . 1356.9 Axial slices through the parotid gland of b = 0 images, andAUC, AUCL, AUCM , andAUCH parameter maps are shown,derived using denoised and original diffusion MR images. . . 1367.1 Overview of the manual tubarial gland contouring process. . . 1457.2 The MultiResUNet architecture . . . . . . . . . . . . . . . . . 1477.3 Combined model training with left and right tubarial glanddata. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1497.4 Autosegmented and manually contoured tubarial glands arecompared. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1537.5 Tubarial gland contours overlayed on PSMA PET images. . . 1558.1 Axial slices of PSMA PET, CT, and two CT texture features. 1668.2 PSMA PET SUVMean across the parotid and submandibularglands. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1698.3 Subregions of high PSMA PET uptake in parotid glands . . . 1728.4 Variability of high-uptake subregions vs. threshold for a rep-resentative patient. . . . . . . . . . . . . . . . . . . . . . . . . 1738.5 PSMA PET uptake statistics in planar divisions of parotidglands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1748.6 The optimal dividing planes for maximizing and minimizingthe difference between SUVMean in halves of the parotid gland 1768.7 Correlation between PSMA PET and CT texture features in12 subregions of the parotid glands. . . . . . . . . . . . . . . 1788.8 Correlations between PSMA PET SUVMean and CT texturefeatures in 18 subregions . . . . . . . . . . . . . . . . . . . . . 1809.1 3D rendering of voxels within a parotid gland correspondingto Clark et al\u2019s relative importance subregions are shown fromtwo angles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190xx9.2 3D rendering of voxels within a parotid gland correspondingto Han et al.\u2019s relative importance subregions are shown fromtwo angles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1919.3 The approximate location of Van Luijk et al.\u2019s critical regionof the parotid gland used for computing uptake statistics isshown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1929.4 For model testing and validation, a double cross validationscheme was employed . . . . . . . . . . . . . . . . . . . . . . 1959.5 Clark\u2019s relative importance versus mean PSMA PET uptakein 18 equal-volume parotid gland subregions, averaged over30 patients. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1999.6 Han\u2019s relative importance versus mean PSMA PET uptakein nine parotid gland subregions, averaged over 30 patients. . 2009.7 Box plot of the mean PSMA PET uptake in critical and non-critical regions of parotid glands, as defined by Van Luijk etal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2019.8 The performance of models and feature selection algorithmsare compared. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2079.9 Model-predicted relative importance estimates for all subre-gions are plotted along with Clark et al.\u2019s importance estimates.2089.10 Patient-specific importance estimtaes in parotid gland subre-gions are compared with population-level estimates. . . . . . 2099.11 Patient-specific parotid subregional importance estimates canbe used to supplement population-level importance estimates 21110.1 Parotid gland subregion labels used for defining dose con-straints. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22110.2 A single parotid gland subregion\u2019s dose response curve is shown.22610.3 Mean subregion doses when planning with and without arti-ficial base plans. . . . . . . . . . . . . . . . . . . . . . . . . . 22910.4 Isodose distribution in the parotid when planning with andwithout base plans. . . . . . . . . . . . . . . . . . . . . . . . . 230xxi10.5 PTV DVHs for plans optimized with various artificial baseplans. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232A.1 Plan n Check\u2019s graphical user interface is shown. . . . . . . . 319A.2 A dose distribution for a head-and-neck VMAT plan createdwith Plan n Check is shown . . . . . . . . . . . . . . . . . . . 324A.3 The scalable DVH viewing panel within Plan n Check is shown.DVHs with customizable axis boundaries are able to be savedinto plan check PDFs produced with Plan n Check. . . . . . . 326xxiiList of AbbreviationsADC Apparent Diffusion Coefficient.BP Base Plan.CBCT Cone Beam CT.CNN Convolutional Neural Network.CT Computed Tomography.DICOM Digital Imaging and Communications in Medicine.DLR Deep Learning Reconstruction.DSC Dice Similarity Coefficient.DVH Dose Volume Histogram.DTI Diffusion Tensor Imaging.DWI Diffusion Weighted Imaging.EPI Echo Planar Imaging.ESAPI Eclipse Scripting Application Programming Interface.FBCT Fan Beam CT.FBP Filtered Back Projection.GLRLM Grey Level Run Length Matrix.xxiiiGLRLML Grey Level Run Length Matrix (Long Run Emphasis).GLRLMS Grey Level Run Length Matrix (Short Run Emphasis).GRAPPA generalized autocalibrating partial parallel acquisition.Gy Gray (Unit of Radiation Dose).HD95 95th Percentile Hausdorff Distance.HPV Human Papillomavirus.HU Hounsfield Units.IR Iterative Reconstruction.IVIM Intravoxel Incoherent Motion.JSC Jaccard Score Coefficient.kBq Kilobecquerel.LINAC Linear Particle Accelerator.MLC Multi-Leaf Collimator.MRI Magnetic Resonance Imaging.NMR Nuclear Magnetic Resonance.OAR Organ-at-Risk.PET Positron Emission Tomography.PSMA Prostate Specific Membrane Antigen.PTV Planning Target Volume.QUANTEC Quantitative Analyses of Normal Tissue Effects in the Clinic.xxivRF Radio Frequency.ROI Region of Interest.SCC Squamous Cell Carcinoma.SE Spin Echo.SNR Signal-to-Noise Ratio.SUV Standard Uptake Value.T Tesla.TE Echo Time.TOF Time-of-Flight.TR Repetition Time.TSE Turbo Spin Echo.VMAT Volume Modulated Arc Therapy.xxvAcknowledgementsFirst of all, I thank Dr. Haley Clark for his mentorship throughout my PhDstudies. I am fortunate and grateful to have been his first graduate student,and this research endeavour was much easier with his patient support, valu-able insight, and computational prowess. His deep knowledge, professionalconduct and passion have inspired me to approach scientific questions withrigour and purposeful intention.I thank Dr. Jonn Wu for his constant support, and willingness to goabove and beyond to help with projects. I also thank Dr. Jonn Wu forfunding my voyages to multiple international conferences. I am inspired byhis patient and thorough correspondence and support, despite his plethoraof clinical responsibilities.I thank Dr. Stefan Reinsberg and Dr. Alex MacKay for their valuableinsight and guidance as supervisory committee members during my PhDstudies.I owe a great thank to Mrs. Rosalie Segal and the late Mr. Joseph Segalfor funding my research studies. I sincerely hope this work leads towardsclinical improvements to head and neck cancer treatment.I thank Dr. Arman Rahmim, Dr. Carlos Uribe, and Dr. Franc\u00b8ois Be\u00b4nardfor collaborating and sharing their extensive knowledge and advice relatedto PSMA PET studies. The PET data they supplied ended up playing acentral role in the research projects of this thesis, and I am very gratefulto have had this opportunity. Data collection was funded by CanadianInstitutes of Health Research (CIHR) Project Grant PJT-162216.Dr. Stephen Thomas and Dr. Stefan Reinsberg contributed to the con-ception and design of the IVIM MRI clinical study, for which I thank them.I thank Dr. Monty Martin, Mindy Dobbs, and the entire MRI staffxxviand radiation oncologists at BC Cancer Vancouver for their patience whilehelping with data collection. I\u2019m grateful for every patient who consented tohaving an extra MRI sequence acquired before and after their radiotherapy.Thank you for your willingness to help during such difficult times.Thank you to Gerald Moran from Siemens Healthcare Limited for anin-kind MRI software loan.I also thank Dr. Kirpal Kohli, the physicists, and physics assistantsat BC Cancer, Surrey for allowing me to access to limited departmentalcomputer resources.I thank my family, especially Sandra Sample, for supporting me duringmy studies. Thank you for believing in me and all of the care packagesthroughout my graduate studies.Thank you Samantha Conte, for shining a light on doctoral drive, andbeing the most supportive partner that anyone could ask for.For the great company kept during long working days at home, I thankmy cats, Billie and Toby.xxviiDedicationI dedicate this work to all those who have and will suffer from cancer.xxviiiChapter 1Introduction1.1 Motivation and ObjectiveIn November of 2023, a government report estimated that 7900 Canadianswere to have been diagnosed with head and neck cancer by the end of the year[4]. Of those diagnosed, 2100 deaths were ultimately expected. Outcomeshave greatly improved for head and neck cancer patients in the last twodecades due to advancements in radiotherapy techniques [5, 6], yet it remainscommon for head and neck cancer patients to be burdened by a severe loss insaliva output following radiotherapy. This leads to significantly diminishedself-assessed quality of life scores [7\u201310], and is largely a result of radiationreceived in salivary glands during radiotherapy. Management of persistent,debilitating side effects is an increasingly important topic as longevity hasgreatly increased for cancer patients [11].The intra-salivary gland dose response is generally not well understood,and modernized dose constraints which account for intra-gland functionalvariability have not seen adoption into clinical protocols. Several analysesof salivary gland functional heterogeneity [12\u201316] have provided evidence for\u201cregional effects\u201d in salivary glands, such that dose to certain subregions dis-proportionately impacts post-radiotherapy outcomes. These findings haveyet to be bridged towards modification of clinical dose constraints for glandsduring radiotherapy treatment planning.The present doctoral thesis started out as a Master of Science thesis,which aimed to incorporate Clark et al.\u2019s [12, 13] parotid gland subre-gional importance estimates into radiotherapy treatment planning. Clark etal.\u2019s [12, 13] importance estimates were derived using historical radiother-apy data, and were not previously incorporated into treatment planning or1cross-examined with medical images and other importance estimates fromthe literature. The present research scope then expanded into a doctoralthesis with a more generalized goal, where all research contributions inthis thesis have been made with the common, ultimate goal ofadvancing knowledge and treatment of the salivary glands for re-ducing the burden of salivary dysfunction and xerostomia for headand neck cancer patients. specific goals of this thesis were to:1. Implement a method of translating Clark et al.\u2019s parotid gland impor-tance estimates into spatially varying dose constraints for radiotherapyplan optimization.2. Evaluate outcome-derived regional importance models for parotid glandsubregions using PSMA PET, and establish uptake trends which maybe related to gland function.3. Demonstrate the utility of PSMA PET for predicting regional impor-tance in the parotid glands4. Develop image deblurring and supersampling methods for PSMA PETimages, so that small regions, such as those within parotid glands, canbe evaluated with less error due to partial volume effects.5. Improve the analytic approach to IVIM MR imaging by implement-ing deblurring and denoising methods, as well as a new approach toanalysing the signal decay curve (signal versus b value).6. Develop a method of segmenting the newly discovered tubarial glands[17] using CT images, so that dose to these regions can be constrainedduring radiotherapy plan optimization.1.2 Thesis OrganizationPart I of this thesis contains introductory material to provide context andsufficient background information for proper appreciation of contributionsmade in Part II. Chapters in Part II were written to be self-contained with2sufficient background information for understanding studies, assuming back-ground knowledge of topics covered in Part I. Due to the broad nature of thisthesis which encompasses a wide array of medical systems and techniques, itwas impossible to microscopically cover all topics without this thesis growingto an overwhelming length. Therefore this introductory section is fairly brieffor any one topic, while providing sufficient material for understanding andmotivation of subsequent content. As machine\/deep learning methodologieshave come to play an integral role in the field of medical physics and dataanalysis in general, elementary knowledge of these topics is assumed, such isthe case for elementary mathematical knowledge. Nonetheless, tools used invarious chapters are properly motivated in background sections in Part II.A particularly important deep learning architecture used in Chapters 5, 6,and 7, is the U-Net architecture, which is specifically described in 3.2.6.Part I consists of Chapters 2, 3, and 4. Chapter 2 introduces med-ical imaging modalities used in Part II\u2019s research contribution. This in-cludes computed tomography (CT), magnetic resonance imaging (MRI), andpositron emission tomography (PET). Physical principles and relevant sub-modalities are introduced. Chapter 3 provides background material relatedto radiotherapy, from its concepts and founding principles, up to modernclinical planning techniques. Chapter 4 covers the salivary glands, providinginformation on the function of different salivary glands, their dose response,and clinical guidelines.Part II includes primary research contributions made during the author\u2019sdoctoral studies. It begins with Chapter 5 which introduces a new methodof simultaneously deblurring and supersampling prostate specific membraneantigen (PSMA) PET images, in an effort to mitigate partial volume effectsfor proper quantitative evaluation of the relatively small parotid glands.Chapter 6 introduces a similar approach for denoising and deblurring IVIMMRI images, whose derived parameters historically suffer from low repro-ducibility throughout the literature [18\u201323]. Furthermore, a new and ef-fective method for simplifying the approach to diffusion parametrization isintroduced.In Chapter 7, a tool is developed for autosegmenting the newly-discovered3tubarial glands [17] using only CT images. Chapter 8 quantifies the hetero-geneity of PSMA PET uptake in the parotid glands. The relationship be-tween parotid gland functionality and PSMA PET uptake is investigated inChapter 9, and a predictive model for importance is developed using PSMAPET\/CT radiomic features.A method for translating Clark et al.\u2019s [12] subregional parotid glandimportance estimates into external beam radiotherapy plan optimization isintroduced in Chapter 10. This method uses artificial \u201cbase plan\u201d dose dis-tributions to effectively steer dose away from highly important regions duringradiotherapy. A tool for automatic planning and application of subregionaldose constraints using a scripting approach is included in the Appendix.The final chapter (11) contains concluding statements and future re-search explorations.4Part IIntroductory Content5Chapter 2Medical Imaging forRadiotherapy2.1 IntroductionThis last century has featured countless monumental accomplishments ofhumanity. Many of these have been related to health care advancementsand our understanding of the human body. Among these, many have beenmade possible by innovative advancements in our ability to visually probethe inside of the human body non-invasively. 69 years lay between thecreation of the first permanent photograph by the french inventor, JosephNice\u00b4phore Nie\u00b4pce [24], and the first x-ray image acquired by the Germanphysicist, William Conrad Ro\u00a8ntgen in 1895. One year later, the first clinicalx-ray image was acquired at Dartmouth college in Hanover, New Hampshirein 1896 [25].It took years for the medical community to properly consider the detri-mental effects of radiation exposure, with the first clinical radiation guide-lines being produced by Ro\u00a8ntgen in 1913, following the death of many radiol-ogists [26]. The ultimate price that many people paid during the pioneeringyears of medical imaging has not been in vain, as it has paved the way for thedevelopment of safe practices and other medical imaging modalities whichhave since allowed countless lives to be saved. To this day, radiography isstill a commonly employed imaging technique in health care.As current abilities to diagnose and treat cancer are dependent on theacquisition of high-quality medical images, it is pertinent to begin the intro-ductory section of this thesis by discussing modern, clinically-used imaging6modalities. While many medical imaging modalities exist, the scope of thischapter is limited to modalities which are relevant to this thesis. Namely,the physical principles and clinical relevancy of radiography, computed to-mography (CT), magnetic resonance imaging (MRI), and positron emissiontomography (PET) are introduced. Only a brief description of their under-lying mechanisms are presented here.2.2 RadiographyAlthough radiography itself is not directly utilised in research analyses inthis thesis, its mechanisms are a prerequisite for understanding the principlesof CT. Radiography, also referred to as x-ray imaging, is the acquisition ofmedical images using high frequency electromagnetic radiation in the x-rayregion of the energy spectrum (0.01 to 10 nm). It is the most commonly usedmedical imaging modality for visualizing internal structures in the body [27].2.2.1 Attenuation ProcessesThe utility of x-rays for visually probing structures within the body is madepossible by the variability of x-ray absorption and scattering rates in differ-ent bodily tissues. The absorption of x-rays in biological tissue is mainlyattributed to the photoelectric effect and Compton scattering.Energy deposition via the photoelectric effect is the primary providerof contrast in x-ray images of the body. The photoelectric effect, initiallydescribed by Albert Einstein in his famous 1905 paper [28] for which he laterwon the Nobel Prize, is the complete absorption of a photon, or quantumof electromagnetic radiation, by electrons bound to atomic nuclei withinmaterials. In this context, light behaves as a bundle of individual particleswhose entire energy is transferred to electrons upon colliding. This causesthe emission of photoelectrons within the material, with energies given byE = h\u03bd \u2212 \u03a6, where h is Plank\u2019s constant, \u03bd is the frequency of the photon,and \u03a6 is the binding energy of the electron.Different materials have different characteristic electron binding energy7levels, and experience a sharply increased probability of photon absorptionwhen these electron binding energy levels are just barely exceeded by thephoton energy. The probability of photon absorption is also proportional tospatial density, and the cube of the material\u2019s atomic number [27]. 60% ofbone by weight is made up of the inorganic chemical, hydroxyapatite [29],which is itself composed of nearly 40% calcium and 18% phosphorus [30].Therefore, bone has a much higher average atomic number than organic softtissue, and furthermore is more dense, resulting in much higher absorptionin bone than in soft tissue. The photoelectric effect is the primary cause ofphoton attenuation in soft tissue up to energies of approximately 30 keV,whereafter the Compton effect begins to dominate.Compton scattering, also known as the Compton effect, is another promi-nent energy transfer mechanism for x-ray photons in biological tissue. Thisinvolves the partial transfer of an incident photon\u2019s energy to loosely boundvalence electrons, resulting in the emission of an electron, as well as a scat-tered, lower energy photon. Compton scattering is independent of atomicnumber, but does depend on electron density, and the number of valenceelectrons [31].By adjusting the photon energy, the relative contributions of the twomentioned processes to the total attenuation of photos can be modified. Theradiographic photon energy must be optimized to maximize contrast andtissue penetration in tissue while minimizing exposure to ionizing radiation.Ultimately, an image is formed by passing x-rays through an object, andcapturing the resultant \u201cshadow\u201d on a detector.2.2.2 X-Ray GenerationThe production of x-rays for radiographic imaging involves accelerating elec-trons and converting their kinetic energy to electromagnetic energy (x-rays).This conventionally occurs inside a glass vacuum chamber called an x-raytube, where electrons are accelerated from a cathode filament towards ametal anode block. To achieve this, a current is first applied to the cath-ode, causing it to heat up and release electrons via thermionic emission [32].8This forms an electron cloud around the filament. A generator then appliesa high voltage between the cathode and anode, with the anode being con-nected to the positive side of the circuit. This causes electrons to acceleratetowards the anode. The electron beam is shaped and steered towards thethe focal spot of the anode by a negatively charged focusing cup surroundingthe filament. The anode is typically made of Tungsten [33], and x-rays areprimarily generated by bremsstrahlung, or \u201cbraking radiation,\u201d where thecreation of electromagnetic radiation accompanies the deceleration of elec-trons near atomic nuclei. Electrons can also collide with bound electronswithin the anode, removing them from their bound state. This is accom-panied by the generation of \u201ccharacteristic x-rays\u201d, where other electronstransition from higher energy states to fill the newly created vacancy. Theradiation spectrum generated by these processes is continuous, and is definedby the peak kilovoltage (kVp), applied between the cathode and anode.2.2.3 X-Ray DetectionImages are acquired by placing objects of interest between the x-ray tubeand an x-ray detector. Conventional analog radiography using film, as in-troduced by Ro\u00a8ntgen in the late 19th century, is still a commonly employedtechnique. x-ray film consists of a transparent base that is coated on eachside with an emulsion gelatin layer containing silver halide crystals. Uponexposure, the halide is ionized, releasing an electron which is then trappedwithin crystal defects. These trapped electrons attract and reduce silverions, whose presence forms the final image upon development [34].The use of film for clinical radiography has been gradually phased out bysolid state flat panel detectors. Digital images can be acquired by convertingx-rays directly to electric charge (direct detection) or first to visible light andthen charge (indirect detection). Indirect detection consists of a scintillatormaterial spread over an amorphous silicon array of thin film transistors(TFTs) [35]. The light created by x-rays striking the scintillator material isthen converted to an electrical signal using photodiodes. Generated signalsalong the array are then amplified and used to construct a digital image.9Direct detectors convert x-rays directly to electrons, eliminating the needfor a scintillator. Direct flat panel detectors use photoconductors, such asamorphous selenium, to convert x-rays to electrons via the photoelectriceffect [36]. A voltage is applied across the conductor to attract electronstowards a TFT array, which converts electrons to a signal within each pixel.This signal is amplified and used to construct a final image.2.3 Computed Tomography (CT)2.3.1 Physical PrinciplesCT, otherwise known as computed axial tomography (CAT), is a methodof reconstructing cross-sectional image slices from a collection of x-ray im-age projections acquired at different angles to the object of interest. Theunderlying mathematical concept that CT exploits is the Radon transform[37]. CT imaging employs the inverse of the Radon transform to transformthe data collected from an angular series of x-ray projections through anobject (line integrals) into a unified axial image slice. The Radon transformwas first described in 1917 by the Austrian mathematician, Johann Radon.50 years later, in 1967, an English electrical engineer named Sir GodfreyHounsfield invented the first functioning CT scanner [38]. 4 years later, thefirst CT scanner for clinical use was adopted [38].CT acquisition can be broken into two steps: image collection, and imagereconstruction.2.3.2 Image CollectionThe scanner hardware necessary for CT acquisition is considerably morerobust than what is required for plain radiography. In order for image pro-jections to be acquired from all angles along a series of axial planes definedover the length of patient bodies, intricate systems have been developed.The fundamental components of a stand-alone fan-beam CT (FBCT)scanner include a gantry and a movable couch. The gantry is a rotating,donut shaped frame that houses an x-ray generator and detector on opposite10sides of its bore (donut hole). Objects to be imaged lie on the couch, which isa motorized platform that can move in and out of the bore. This motorizedrelative motion of the couch and bore allows multiple axial slices to beacquired without pausing to manually shift the object of interest betweenslices.X-rays are generated by an x-ray tube, as in radiography. However,effective heat dissipation from the anode becomes an increasingly prominentissue in CT imaging due to the necessarily longer scan time required foracquiring multiple slices and angles. Traditionally, an x-ray tube equippedwith a rotating anode disc is used to spread the resultant heat over a largersurface area throughout the duration of the scan. This technology wasgreatly improved upon by the development of the rotating envelope tube inthe early 2000s [39], which connects the anode with the outer wall of thetube\u2019s housing while rotating the entire tube around the anode. A collimatoris used filter out the penumbra of the beam before it travels across the gantry.The collimator gives the beam it\u2019s characteristic \u201cfan\u201d shape.Modern CT scanners typically employ x-ray detectors that use indirectconversion, requiring a scintillator. These indirect detectors operate by thesame principles described in the radiography section. Modern detectorstypically consist of multiple pixel rows, allowing multiple image slices to beacquired simultaneously (multislice CT). Data can be acquired in a typi-cal \u201cstep-and-shoot\u201d fashion, where the couch sequentially moves throughthe bore while intermittently stopping for image acquisition, or via \u201chelicalCT,\u201d where the gantry and couch move simulaneously to create a helicallyshaped acquisition path. Helical CT offers reductions in image artifacts andhigher efficiency compared to step-and-shoot CT, and has become the mostcommon standard-of-care clinical acquisition method for CT [40]. BC Can-cer employs helical CT and a custom beam energy for optimal head andneck contrast iwhen acquiring radiotherapy planning CT images for headand neck cancer patients.Currently, a hot research topic is the development of photon-countingCT, which employs direct-conversion x-ray detectors that record energy-dependent signals from individual photons. Photon counting CT has demon-11strated an ability to improve spatial resolution, and reduce noise and arti-facts [41].In addition to stand-alone, FBCT, there exists Cone Beam CT (CBCT),which makes use of conic, diverging beams to acquire 2-dimensional pro-jection images, rather than slices. This allows for the reconstruction of 3Danatomical images after a single rotation around the patient. CBCT gen-erally requires significantly lower radiation exposure levels than traditionalFBCT. Modern linear accelerators used for radiotherapy are often equippedwith CBCTs, allowing for increased accuracy of anatomical localization, andreal-time motion tracking [42].2.3.3 Image ReconstructionThe raw image projections acquired during the CT scan time would havelimited utility if not for sophisticated reconstruction algorithms used to as-semble final image slices. The goal of image reconstruction is to take theprojection data, which represents the total beam attenuation between the x-ray tube and the detector, and determine the attenuation coefficient withina grid of pixels spanning the image plane. These attenuation coefficientsare typically measured in Hounsfield Units (HUs), which are scaled atten-uation coefficients corresponding to the Beer-Lambert law [43]. While thetechnical details of commercially available CT reconstruction algorithms areproprietary [44], and optimization of CT reconstruction algorithms remainsan active area of research, reconstruction techniques can be broadly cat-egorized into three main methodologies: filtered back projection (FBP),iterative reconstruction (IR), and deep learning reconstruction (DLR).FBP is the traditional CT reconstruction technique [44], and consists oftwo steps: filtering and back projection. After collecting an angular seriesof image projections for a given slice (forward projection), the image slice isfirst estimated by simply spreading each projection quantity over all pixelsbetween the detector and the source, at each angle. This is called backprojection. This in itself provides an estimate of the final image; however,it is blurry, and tends to concentrate in the center of the image slice. To12control for these adverse effects, appropriate filtering of the projected datais necessary. A common approach to filtering is to apply a ramp filter toFourier transformed data, suppressing low frequency components in the data[45].Another approach to image reconstruction is to use iterative algorithms,where a series of image estimates are successively modified until a stoppingcriteria is met. This approach is called iterative reconstruction (IR), andits basic procedure is straightforward. An initial estimate is first generatedfrom the projection data using FBP or other methods. Simulated projectionsof the image estimate are then calculated using forward projection. Thesesimulated projections are then compared with real projections detected bythe scanner, and a correction term is calculated accordingly. Finally, theinitial image estimate is updated using the correction term, and the cyclerepeats. Compared to FBP, IR tends to provide better image quality interms of reductions in noise and unwanted image artifacts [44].From 2018 onwards, deep learning reconstruction (DLR) techniques havebeen demonstrated to provide accurate, detailed, and low-noise image esti-mates, while reducing radiation dose by up to 71% [46]. DLR uses artificialneural network architectures to estimate images from the scanner\u2019s collectedprojection data. Modern approaches to DLR can be categorized into directand indirect methodologies. Direct DLR predicts final image estimates di-rectly from the raw projection data, while indirect DLR continues to useFBP or IR while optimizing projection and\/or image data with neural net-works. DLR commonly employs convolutional neural networks (CNNs), suchas wavelet based U-Net [47] or residual encoder-decoders [48]. Non-CNN ap-proaches have also proven their efficacy, with general-adversarial networks[49] and transformer based networks [50] also having demonstrated utility.2.3.4 Clinical UtilityCT scans provide detailed images in all regions of the body, and are clinicallyacquired for many different circumstances. Like radiography, CT providesexcellent contrast between tissues of different density and atomic number13(i.e. bone and soft tissue). Furthermore, it has improved soft tissue contrast,illuminating detailed spatial information in image slices, rather than theprojections acquired by radiography.Most relevant to this work is the standard-of-care usage of CT for ra-diotherapy treatment planning [51]. CT is used in this context for threeprimary purposes. First, CT is used to localize tumour volumes for accu-rate dose delivery during treatment. Second, healthy organs at risk (OARs)are localized for optimal avoidance of dose to these regions. Lastly, the at-tenuation coefficients within each image voxel are used to create an electrondensity map of tissue in the body, to be used for dose calculations dur-ing treatment plan optimization. Scan parameters tend to remain largelyunaltered from patient-to-patient on radiotherapy CT scanners, to avoidresultant dosimetric uncertainty during treatment planning [52].Head and neck radiotherapy planning CTs in this study used a helicalCT acquisition protocol with beam parameters set for optimal head andneck contrast (kVp: 120, exposure time per gantry rotation: 1.7 s).2.4 Magnetic Resonance Imaging (MRI)2.4.1 Physical PrincipalsMRI is a medical imaging technique that measures localized chemical prop-erties in objects by exploiting interactions between nuclear spins and mag-netic fields. The nuclear spin is an intrinsic, quantized angular momentumproperty of nuclei which does not correspond to physical rotation [53].The physical process serving as the backbone of MRI is nuclear magneticresonance (NMR), as first discovered by the American physicist, Isidor Rabi,in 1938 [54], for which he won the Nobel Prize in Physics in 1944. NMRwas first described as a method of measuring the nuclear magnetic momentsof chemical mixture components, and was demonstrated to detect the res-onance peaks of Li and Cl constituents in LiCl. The basic concept is asfollows. First expose a material of interest to a sufficiently strong, homoge-neous magnetic field in order to decouple nuclear spins from neighbouring14spins and chemical rotations. Let the strong homogenous field be along thelongitudinal direction. Then, if a small oscillating magnetic field is appliedat a right angle to the strong field (in the transverse plane), with a frequencymatching the Larmor precessional frequency of constituent nuclei, nuclearspins will have a heightened transition probability for re-orienting to thetransverse plane. An induction coil can be oriented at a right angle to thestrong magnetic field and used to detect signals generated by precessing spinmagnetization vectors which have been rotated towards the transverse plane.In NMR spectroscopy, this process is used to infer chemical constituents ofsubstances, based on the variation in excitation signals acquired at differentprecessional frequencies, which correspond to constituent Larmor Frequen-cies.Initial experiments to observe resonance effects in condensed matter werecarried out by two independent groups in 1945 to 1946, Bloch\u2019s and Purcell\u2019s[55\u201357]. Purcell\u2019s group at Harvard [57] detected the resonant absorptionfrequency of protons in paraffin. This was done by first generating a ra-diofrequency (RF) magnetic field in a coil coupled with a resonant cavity,and placing it within and a strong homogeneous magnetic field, with the coilaxis oriented orthogonally to the field. The coil was filled with paraffin, andthe homogeneous field was varied until a significant reduction in the outputsignal from the coil was observed. This reduction corresponded to resonanceabsorption of protons in the paraffin. This method of inferring resonanceabsorption from a loss in the input RF signal is sometimes referred to as the\u201cabsorption method.\u201dBloch\u2019s group at Stanford University measured the resonance absorptionof protons in both water and paraffin by detecting an induction signal in areceiver coil oriented orthogonally to both the strong homogeneous field andthe RF transmitting coil [55, 56]. This method of detection is sometimesreferred to as the \u201cinduction method\u201d and is the dominant form of signaldetection used in modern NMR technology. In 1952, Dr. Edward MillsPurcell and Dr. Felix Bloch shared the Nobel Prize in Physics for \u201ctheirdevelopment of new methods for nuclear magnetic precision measurementsand discoveries in connection therewith.\u201d15This process works when nuclei have non-zero spin (j \u0338= 0) and thus anon-zero magnetic moment, m\u20d7, such as in 1H, 19F, or 23Na. The majorityof modern MRI sequences are tuned to excite 1H atoms, as they are presentin high concentrations throughout biological tissue.The strong, homogeneous field used in NMR is commonly referred to asthe B\u20d70 field, whose direction is traditionally made to define the z\u20d7-axis of aCartesian coordinate system. Transmission and receiver coils are orientedfor signals in the (x\u20d7, y\u20d7) plane. Individual nuclear magnetic moments alongthe z-axis can only be measured to have one of two values (m\u20d7 = \u00b1\u03b3\u210f\/2),where \u03b3 is the gyromagnetic ratio of the nucleus and \u210f is the reduced Plankconstant. The low and high energy states are oriented parallel and anti-parallel to B\u20d70, respectively. These energy states obey a simple equation,E = \u2212m\u20d7 \u00b7 B\u20d70. (2.1)When thermal equilibrium has been reached, the ratio of nuclei to be foundin either state is governed by the Boltzmann distribution of energy stateoccupancy probabilities. This yields a low-to-high energy state ratio ofe\u2206E\/kT \u2248 1.00001 for protons with a a temperature of 300 K in a magneticfield strength of 1.5 T. The combination of individual nuclear magnetizationvectors results in a macroscopic magnetization per unit volume of, M\u20d70. Thephysical manipulation and measuring of M\u20d70 is what makes MRI possible.As M\u20d70 is proportional to B\u20d70, higher magnetic field strengths result in highersignals.Upon the application of a transverse radio frequency (RF) magnetic field(B1) matching the Larmor frequency of1H (42.58 MHz \/ T), the macroscopicmagnetization M\u20d70 rotates towards the transverse plane, and a signal can bedetected. This signal is usually detected via induction, as mentioned. How-ever, this simple strategy results in only a single signal which corresponds tothe total magnetization of the object being imaged, and signal localizationtechniques are required if an image is to be created.The American chemist, Paul Lauterbur, is credited with first publishingNMR signal localization techniques for imaging in his 1973 Nature publi-16cation [58]. In 2003, Lauterbur received the Nobel Prize in Physiology orMedicine with Sir Peter Mansfield for their \u201cdiscoveries concerning magneticresonance imaging.\u201d Modern signal localization for acquiring 2-dimensionalmagnetic resonance images is typically accomplished using slice selectiongradients as well as frequency and phase encoding techniques to encode thespatial location of signal in the frequency domain.Slice selection is a method of confining resonance to 2-dimensional slicesby perturbing the homogeneous B\u20d70 field with a linear gradient field, whichresults in the Larmor frequency of nuclei becoming a function of positionalong the gradient\u2019s direction. The orientation of the linear gradient fieldis arbitrary, allowing for slice selection in alterable directions to be possi-ble. Specific signal slices are excited by applying radiofrequency pulses forwhich the bandwidth determines the slice thickness and the main frequencydetermines the spatial location. The resultant planar signal can then beindirectly localized via signal encoding in the frequency domain.While it is possible to apply two additional orthogonal slice selectiongradients to confine signal to within a single voxel, it is advantageous to in-stead encode the 2-dimensional spatial location of constituent signals withinthe selected slice according to the frequency and phase of the magnetizationvector in each voxel. Afterwards, a Fourier transform can be applied to theacquired data matrix to obtain a spatial image. Theses processes are referreto as frequency and phase encoding.Frequency encoding involves the application of a field gradient that ren-ders the Larmor frequency position-dependent across the selected slice. Theacquired signal as a function of time can then be Fourier transformed toobtain the signal as a function of frequency. The frequency is directly map-pable to spatial rows within the image, and as a result this process can beused to localize signal to rows within the selected slice. These rows cor-respond to vector projections of the magnetization vector along the givenrow. By convention, the signal phase is not considered as a function of timewhich maps to frequency space, but rather a function of spatial frequencywhich maps to spatial location.The signal is finally localized to within single voxels with phase encoding.17As signal in rows determined via frequency encoding corresponds to vectorprojections rather than scalar projections, the basic principle behind phaseencoding is that the magnitude of the magnetization vector in each pixelacross each row can be determined if many different projections are acquiredwith different relative phases between pixel magnetization vectors. Thephase is made position dependent across rows using short field gradientpulses. If signal from N pixels is to be differentiated across each row, thenN phase encodings are needed, spaced evenly across a phase cycle. Thedistribution of phases across each spatial row is cyclical upon phase encodingand defines the field of view as the distance needed to complete a single phasecycle. The phase encoding in the acquisition of each row is dependent on theapplication time and strength of the phase encoding gradient, but is morecommonly referred to in terms of spatial frequency, such as was mentionedfor the case of frequency encoding. The phase of the complex signal canthen be written as ikx, which is convenient notation for application of a2-dimensional Fourier transform. The spatial frequency space is referred toas k-space, and corresponds to the raw acquisition matrix. 2-dimensionalspatial images are obtained upon Fourier transforming the data matrix.2.4.2 T1 and T2 MRIThe Larmor precession of an excited spin ensemble characterized by itsmacroscopic magnetization, M\u20d70, will invariably undergo dephasing of con-stituent spins due to magnetic field perturbations caused by neighbouringspins [59]. After the application of an RF pulse to rotate M\u20d70 into thetransverse plane, this dephasing phenomenon results in exponential, \u201cfreeinduction decay\u201d (FID) of detectable signals in the transverse plane, whichis characterized by the so-called T2 time (e\u2212t\/T2). In practice, the observedT2 time is corrupted due to inhomogeneities in B\u20d70, and the observed decayconstant is called T2\u2217. Detected transverse signals will also simultaneouslydecay due to relaxation of spin states back towards the longitudinal direc-tion.In addition to spatially localizing the MR signal, it can be further tuned18to suit various applications by varying the strength and timing of RF pulses,gradients, and signal collection. MRI images are typically classified intothree types based on their primary source of image contrast. Sequencestuned to provide high contrast between different longitudinal (along B\u20d70)relaxation times of the magnetization vector, M\u20d70, are called T1-weightedimages. On the other hand, T2-weighted images primarily convey differencesin the transverse (orthogonal to z\u20d7) relaxation time. T1-weighted imagesenhance fatty tissue while suppressing water tissue, and T2-weighted imagesenhance the signal of water [60]. If an image\u2019s primary source of contrastis proton density rather than magnetic properties, then the image is protondensity (PD)-weighted.The combination and timing of gradients, RF pulses, and signal collec-tion used during a scan is referred to as the MRI pulse sequence. MRI pulsesequences are highly optimized and nuanced, with many different versionsbeing used clinically and for research purposes. Most relevant to the workin this thesis are the turbo spin echo (TSE), echo-planar imaging (EPI),diffusion, and Intravoxel Incoherent Motion IVIM sequences.2.4.3 Spin Echo (SE) and Turbo Spin Echo (TSE)The concept of spin-echos (SE) was first published in 1950 by the Ameri-can physicist, Erwin Hahn [59] as a method of rephasing signals that havedephased due to field inhomogeneities. In other words, this method allowsthe \u201ctrue\u201d T2 signal decay constant to be measured instead of T2\u2217. Spinecho sequences consist of an initial RF pulse to rotate M\u20d70 into the trans-verse plane, followed by a \u201crefocusing\u201d RF pulse for rephasing signals thathave dispersed due to field inhomogeneities. Basically, the refocusing pulsereverses the dephasing direction of constituent nuclear spins, effectively un-doing inhomogeneity-induced dephasing so that spins reconverge. Americanphysicists, Herman Carr and Edward Purcell, further optimized spin echosequences by demonstrating optimal rephasing with a 180\u25e6 refocusing pulse[61]. This version of spin-echo acquisition is called a CP sequence, and it wasfurther modified by Meiboom and Gill to yield the CPMG pulse sequence19[62]. The process of spin-echo creation using a CP and CPMG refocusingpulse is shown in Fig 2.1. Multiple refocusing pulses can be applied during asingle sequence, creating multiple spin echos, called an echo train. If the timebetween the initial RF pulse and the 180\u25e6 pulse is defined as t = TE\/2, thenthe signals will experience maximal rephasing at t = TE. TE is called theecho time, and is an important tunable parameter for spin-echo sequences.The signal is collected in a receiver coil at t = TE. The time between ex-citation pulses (to tilt M\u20d70 into the transverse plane) is called the repetitiontime (TR).Figure 2.1: Spin echo creation using a refocusing pulse as in CP and CPMGpulse sequences is illustrated from a frame of reference rotating at the macro-scopic magnetization\u2019s Larmor frequency. At time t = 0, the macroscopicmagnetization, M\u20d70, has been rotated into the transverse plane using a 90\u25e6RF pulse. At t = T\u2212, the constituent spins of M\u20d70 have partially dephaseddue to local field perturbations, resulting in lesser signal. At t = T, a 180\u25e6refocusing pulse is applied. The difference between CP and CPMG pulsesequences lie in the axis about which the magnetization is flipped. In eithercase, the direction of dephasing is reversed, resulting in the gradual rephas-ing seen at t = T+ and the formation of a rephased \u201cecho\u201d signal at t = 2T.These images were adapted with permission from Qing-San Xiang, LectureNotes, PHYS 542 class at University of British Columbia.Turbo Spin Echo (TSE), also known as fast spin echo (FSE) or rapid20acquisition with relaxation enhancement (RARE) MRI [63, 64], is a methodof increasing the acquisition speed of SE images, first published by a teamof German scientists in 1986. The basic method of TSE is to apply varyingphase encoding gradients before each echo in the echo train. This allowsmultiple rows of the raw k-space image to be acquired in the time normallytaken for one. The \u201cturbo factor\u201d of TSE sequences is the number of dif-ferent phase encoded echo signals acquired after each excitation pulse. Thismethod of acceleration yields great improvements in acquisition speed, andhas resulted in conventional SE being largely replaced by TSE sequences inclinical and research applications [65].2.4.4 Echo Planar Imaging (EPI)Echo Planar Imaging (EPI) is a rapid form of MRI acquisition where all ofk-space can be sampled within 20-100 ms [66]. Its concept was first pub-lished by the British Physicist and Nobel Laureate, Sir Peter Mansfield, in1977 [67]. As in SE sequences, EPI includes an excitation pulse, followedby a refocusing pulse. Afterwards, EPI applies oscillating frequency encod-ing gradients, forming a train of gradient echos [68]. Each gradient echocorresponds to a different line in k-space. Modern phase encoding pulsesoccur between each gradient echo [69], allowing all lines in k-space to besampled within a single TR. This method is referred to as single-shot EPI,while multi-shot EPI divides the signal readout throughout multiple TRs.Multi-shot EPI has been shown to reduce off-resonance distortions due tomagnetic field inhomogeneities [70], but can heighten ghost artifacts [71] dueto phase corruption [72].The rapid application of gradient pulses demanded by EPI requires highperformance hardware, and advancements in gradient technology since the1990s have significantly increased the clinical viability of EPI [73]. EPI offersgreat advantages in the form of not only faster image acquisition but also aresultant reduction in motion artifacts [66]. An added benefit of fast imageacquisition with EPI is its allowance for high temporal resolution in im-ages, finding applications in functional MRI (fMRI) and diffusion weighted21imaging (DWI) [74].2.4.5 Diffusion Weighted Imaging (DWI) MRIWhile previously discussed sequences provide image contrast through dif-ferences in proton density, T1 relaxation, and T2 relaxation, the contrastin diffusion-weighted imaging (DWI) is due to molecular motion. In vivomotion of water molecules results from bulk flow of fluid and imperfectBrownian motion that has been variously obstructed by microscopic tissuestructures. In the context of in Vivo imaging, \u201crestricted diffusion\u201d is aterm used to describe the diffusive behaviour of water molecules whose freemotion has been impeded by surrounding tissue. The roots of DWI traceback to to 1965, with the introduction of time-dependent pulsed gradientsby American and British physicists, Edward Stejskal and John Tanner [75].Their proposed method involves the application of short, identical gradi-ent pulses before and after applying the 180\u25e6 refocusing pulse as used inSE and EPI sequences. In theory, these symmetric gradients have oppo-site effects on the phase of molecules at rest, leaving the signal unchangedfor stationary molecules. However, molecules in motion experience unevenphase shifting by the two gradients. This causes regions with higher levelsof molecular motion to have lower signal, appearing darker on reconstructedimages compared to relatively stagnant regions.The strength and timing of these diffusion gradients are characterizedby diffusion \u201cb-values\u201d:b = \u03b32G2\u03b42(T\u2212 \u03b4\/3) (2.2)where \u03b3 is the gyromagnetic ratio of a proton, G is the rate of change ofthe gradient field, T is the delay between gradients and \u03b4 is the durationof each gradient [76]. Starting from the Bloch equations [55], Stejskal andTanner derived the relationship between signal attenuation and diffusion bvalue within a homogeneous liquid sample:S(b)\/S(0) = e\u2212b\u00b7D (2.3)22where S(b) is the signal acquired with diffusion gradients characterized bythe given b value, and D is the self-diffusion coefficient of protons [77]. Selfdiffusion is the random, Brownian motion of molecules in a fluid, as describedby Einstein in one of his famous manuscripts written at a Swiss patent officein 1905 [78].Diffusion gradients can be applied in any direction, allowing the re-stricted diffusion of water molecules to be described in tensor form, as indiffusion tensor imaging (DTI) [79]. There are many different ways of ac-quiring diffusion-weighted MRI. Most importantly for this thesis, is what\u2019sknown as intravoxel incoherent motion (IVIM) MRI. For IVIM MRI, sig-nals are typically acquired using at least 3 diffusion gradients in differentdirections, and then combined into a single image by taking the geometricmean, S = \u03a0ni Si, where n is the number of directions used. Due to timeand motion artifact issues, IVIM, DTI and other diffusion-weighted MRIsequences were not clinically relevant until MRI hardware advancements inthe late 1980s made EPI a feasible sequence for clinical use [80, 81]. In recentyears, improvements in parallel imaging techniques have greatly improvedthe overall quality of EPI sequences available for DWI.2.4.6 Intravoxel Incoherent Motion (IVIM) MRIAs IVIM MRI is the most prominent MRI sequence used in the researchcontributions of this thesis, this section is slightly more extensive than thoseof previously described techniques.Dr. Denis Le Bihan, a French physicist and physician, has been instru-mental in the formulation of modern diffusion imaging techniques, includ-ing IVIM MRI. IVIM is defined as \u201ctranslational movements which withina given voxel and during the measurement time present a distribution ofspeeds in orientation and\/or amplitude\u201d [82], and Le Bihan first introduceda method of quantifying these in Vivo motions using Stejskal and Tanner\u2019sdiffusion gradient method in 1986 [83]. This paper introduced the con-cept of an \u201capparent diffusion coefficient\u201d (ADC). The ADC quantifies thecombined motion due to real diffusion (random molecular motion) and the23randomly oriented microcirculation of blood in capillary beds. By acquiringsignals using multiple diffusion b-values, the ADC can be determined usingthe equation,S(b)\/S(0) = e\u2212ADC\u00b7b (2.4)which is analagous to Stejskal and Tanner\u2019s in Vitro diffusion equation dis-cussed in the previous section [75]. The ADC is a useful and simple metricfor describing the signal decay curve in Vivo; however, it is not mathemati-cally derived to model real diffusion, and is only a method of approximatingthe biological mechanisms responsible for the observed signal decay seenwith increasing diffusion b-values. An important difference between Stejkaland Tanner\u2019s and Le Bihan\u2019s diffusion equations is that Stejkal and Tanner\u2019sdiffusion equation (2.3) comes from directly solving the Bloch equations [55]for the magnetization vector, M\u20d70, as a function of time, while Le Bihan\u2019sapplication of this equation to in Vivo motion is an approximation. Themost useful way to interpret the ADC may be to think of it as no more thana parameter for approximating the in Vivo signal vs. b-value curve as anexponential decay curve.In 1988, Le Bihan introduced a method of hypothetically separating theADC into its constituent components arising from diffusion and perfusion(also called \u201cpseudodiffusion\u201d) [84]. This is done by fitting a biexponentialmodel to the signal vs. b-value decay curve, in the formS(b)\/S(0) = f e\u2212b\u00b7D\u2217+ (1\u2212 f)e\u2212b\u00b7D (2.5)where D\u2217 is the so-called pseudodiffusion coefficient and f is the pseudod-iffusion fraction (or often called the perfusion fraction). The interpretationis that the measured signal decay curve in each voxel is a result of f \u00d7 100%microcirculation in capillaries and ((1\u2212 f)\u00d7 100%) regular diffusion.While Le Bihan\u2019s initial studies solved for the ADC and biexponentialparameters analytically using two and three distinct b-values, respectively,modern techniques typically acquire at least 10 b-values and then fit modelsusing various techniques, such as non-linear regression, Bayesian regression,and machine learning approaches. Based on estimates for blood flow speed24in capillaries and the mean length of straight capillary segments in-betweendirection changes, D\u2217 was estimated by Le Bihan to be approximately 10times larger than typically diffusion coefficients [82]. This explains the ob-served deviation of the signal decay curve from exponential behaviour in thelow b-value regime (\u2248 b < 250), whereas signal in higher b-value regions isprimarily (\u2248 90%) impacted by tissue diffusion [82].Reproducibility of the pseudodiffusion coefficient, D\u2217, remains a long-standing issue, while ADC and D have proven to have higher stability [18\u201323]. Furthermore, f and D\u2217 have been shown to have inferior reproducibilityto D; however, f has also been shown to be useful for predicting age innervous tissue [85, 86].In recent years, the literature has seen a shift towards adoption of atriexponential model [87\u201392] of the formS(b)\/S(0) = f1 e\u2212b\u00b7D\u22171 + f2 e\u2212b\u00b7D\u22172 + (1\u2212 f1 \u2212 f2) e\u2212b\u00b7D. (2.6)Unsurprisingly, model-fit uncertainty can be reduced by introducing an ex-tra exponential term [88\u201392]; however, it remains to be seen whether theseparameters are reproducible or have any practical physiological interpreta-tion.The concept of modelling in Vivo flow with exponential models is basedon the assumption of free, Gaussian diffusion, mixed with perfusion processesthat can be well-modeled as Gaussian processes. However, it is known thatdiffusion in tissues cannot be accurately modeled as Gaussian processes [93].Tissue boundaries preventing free molecular flow in Vivo fail to be accountedfor in these models. Many different models have been suggested to amelio-rate this discrepancy [94\u2013101]. Despite these attempts, simple exponentialmodels continue with widespread use in modern clinical studies using IVIMMRI.2.4.7 Current Issues with IVIM MRIIt is uncertain whether attempts to separate diffusion from perfusion areeffective, as it has been reported that fitting a mono-exponential function,25S(b)\/S(0) = (1\u2212f) e\u2212b\u00b7D is more reliable than a bi-exponential fit for differ-entiating pathological grades of esophageal squamous cell carcinoma (ESCC)[23]. Heightened measurement error of signal at low b-values [102, 103] leadsto sub-optimal conditions for estimating perfusion effects, and estimation ofADC in low b-value regions has shown poor reproducibility [104]. Noise-levels have also been shown to greatly impact parameter estimates [105].IVIM voxel maps typically display high variation, so individual voxels ofIVIM images are averaged over regions-of-interest (ROIs). This issue is ex-acerbated by partial volume effects (PVEs) from various tissue types andbleed-in from neighbouring voxels.Poor reproducibility of perfusion-related parameters could be partiallyexplained by over-simplification of physiological processes inherent in sim-ple exponential models, as it has been shown that the optimal choice ofmodel is dependent on tissue type [106]. It is without doubt that, in real-ity, each image voxel containing biological tissue will encompass a complexarrangement of micro-structures, all having various perfusion fractions andmolecular motion properties. Kuai et al [87] used simulated data with 2-5perfusion components in an exponential model to show that the variance off and D\u2217 tend to increase as the number of perfusion components increases,or the difference between pseudodiffusion components increases.Reproducibility of IVIM parameters is also impacted by a lack of stan-dardization for voxel sizes and b-value distributions, which several studieshave attempted to optimize [107\u2013112]. Variation in voxel size is certainto impact multi-exponential model fits. For example, suppose there existsIVIM images with a voxel size of 2 x 2 x 2 mm3 and it is fitted with abi-exponential model. Suppose that image is then re-acquired with voxelsof size 1 x 1 x 1 mm3 and again modeled with a bi-exponential fit. By com-paring the two images, it is clear that the original image had been modellingocto-exponential components with a bi-exponential function. Averaging theparameters from the smaller voxels over the larger ones will, in general, yielddifferent parameters than those of larger voxels.Above all, the goal of applying various signal-decay models to IVIMdata is to describe the signal decay curve, which is the fundamental distri-26bution that quantifies motion within image voxels. Bi- and tri-exponentialparameters are particularly enticing for describing diffusion as they appearto have clear physiological interpretations. However, there is no consensusthat f is correlated with blood vessel density [105, 113, 114], and the abil-ity of parameters to be interpreted physiologically is generally unimportantfor practical applications. There is furthermore no consensus for what theoptimal IVIM model for describing the signal decay curve is, with manyinconsistent versions being recommended [99\u2013101, 115, 116].2.4.8 HardwareClinical MRI scanners have continually improved since their conception.New technologies developed in fields such as material science, computer sci-ence, engineering, and data processing, have been rapidly incorporated intoMRI architectures [117]. In recent years, an exciting development has beenthe merging of MR with PET [118] and radiotherapeutic systems [119],which has required many new hardware considerations. To accurately de-scribe all the state-of-the-art components which constitute a modern MRIscanner would require a series of books, and therefore this section aims todescribe only the basic components and mechanisms at play in an open-boreMRI scanner.Most modern clinical scanners supply static magnetic field strengths of1.5 Teslas (T) or 3 T; however, MRI field strengths of up to 11.7 T have beencommissioned [120] for human use. Field strengths for animal research scan-ners have currently reached 21.1 T [121]. For comparison, these strengthsare all over 10,000 times the strength of the earth\u2019s magnetic field. Creationof these strong, homogeneous fields requires intricate engineering which isthe main reason that MR scanners are so expensive [122]. The majorityof modern scanners with open bore designs generate magnetic fields usingsuperconductive solenoids. Typically, noibium-titanium (NbTi) is the con-ductor used, which becomes superconductive below a critical temperature of9.4 K. Maintaining superconductive wires at temperatures below this criticaltemperature requires high refrigeration and installation costs [123]. Super-27conductive wires are typically cooled using liquid helium within a cryostat.Liquid helium is a non-renewable resource, and sustainability concerns haveled to great improvements in MRI cooling designs, with modern designs suchas the Phillips BlueSeal 1.5 T requiring less than one Litre of liquid Helium,compared to conventional cryostats, which required 1500-2000 Litres of liq-uid Helium as well as refills [124].The magnetic field is fine-tuned for high homogeneity using passive andsuperconductive shims, such that local deviations are kept to within 10parts per million over a spherical diameter of 45-50 cm [125]. Shims are alsolocated within the cryostat.Modern MRI scanners require gradient coils capable of producing highmagnetic field strengths and slew rates (on\/off speeds). Many advancementshave been made in coil design, leading to reductions in Eddy currents, im-provements in gradient linearity, reduced switching times, and higher effi-ciency [126]. MR scanners include separate gradient coils oriented for pro-duction of gradients in the x\u20d7, y\u20d7, and z\u20d7 directions. Modern gradient coilsgenerate gradient fields by applying current through distributed windingpatterns made in large copper cylinders [126]. These designs have been andcontinue to be optimized using a variety of techniques.MRI scanners have built-in RF coils for transmitting RF pulses and re-ceiving signals. Most modern scanners use separate transmitting and receiv-ing coils, although single coils are still used in some scanners. The separationof transmitting and receiver coils allows transmission and receiving coil de-signs to be separately optimized for their specific needs. The performanceof the RF coil is the most important determinant of optimal signal-to-noiseratio (SNR) in an MRI scanner [127]. First generation receiver coils hadsingle-coil designs that could only receive one dimension of the rotatingmagnetization vector. These have been made obsolete by quadrature se-tups, where two orthogonal coils detect the rotating magnetization vectorin orthogonal transverse directions [128]. RF coil design was significantlyimproved with the introduction of phase-array technology by an Americangroup, Roemer et al. [129] in 1990. This boosted SNR and spatial resolu-tion by allowing simultaneous acquisition of signal from multiple coils that28are arranged for minimal mutual induction effects [129]. Phased array coilsallow parallel imaging techniques to be employed, such as generalized auto-calibrating partial parallel acquisition (GRAPPA), which greatly increasesthe speed of acquisition [130].2.4.9 Clinical UtilityMRI revolutionized head and neck imaging for cancer patients and haslargely replaced CT as the modality of choice for investigating tumour vol-umes [131]. This is a result of its much higher soft tissue contrast whichallows the differentiation of tumour volumes from surrounding tissue withmuch greater accuracy than possible using CT. Furthermore, using MRIrather than CT for imaging the head-and-neck region circumvents the com-mon issue of image artifact formation due to dental hardware and the densecortical bone of the mandible, skull base, and shoulders.Spin echo sequences are fundamental, work-horse sequences in MRI imag-ing, and are commonly used for obtaining T1, T2, and proton densityweighted diagnostic images of tumour volumes in cancer patients. Fat\/waterinterfaces in the extracranial head-and-neck region are important features fordefining anatomical regions, and as a result, T1 weightings, which provideexcellent fatty-tissue contrast, are used in the vast majority of extracra-nial head-and-neck acquisitions [131]. Since the 1990s, it has also becomecommon for patients to be injected with a Gadolinium contrast agent priorto image acquisition [132]. This greatly improves soft tissue contrast bylowering T1 values in the blood, but this could be made obsolete with thepopularization of PET\/MR [133].EPI is usually employed in DWI \/ IVIM sequences, which are commonlyadded to standard imaging protocols for head-and-neck cancer patients [134].This is often limited to acquiring DWI with two different b-values for fittingthe ADC [135], such is the case at BC Cancer, Vancouver. The ADC hasbeen shown to be beneficial for tumour and detection of nodal metastases[134].292.5 Positron Emission Tomography (PET)2.5.1 Physical PrinciplesPositron Emission Tomography (PET) is an imaging modality that measuresphysiological activity by detecting the radioactive decay of positron-emittingtracers (radiotracers) that have been intravenously injected into the body.It is currently the most specific and sensitive method for detecting in Vivometabolic interactions and pathways [136]. This specificity is made possiblethrough the development of specified radiotracers for different applications.Different radiotracers have characteristic, well-known half-lives which indi-cate the time it takes for half of the radiotracer to decay. The primary decaymechanism of PET radiotracers is \u03b2+ decay. \u03b2+ decay is the physical phe-nomenon whereby a proton spontaneously decays into a neutron, a positron,and an electron neutrino (p\u2192 n+ e+ + \u03bde).PET has an interesting history, beginning with the prediction of posi-tively charged electrons (positrons) by the English physicist Paul Dirac inhis pivotal 1928 manuscript, \u201cthe quantum theory of the electron\u201d [137, 138].The positron is the antiparticle of the electron, and is identical to the elec-tron in all respects other than the sign of its charge. The existence ofpositrons (detected as cosmic rays) was then verified experimentally byAmerican physicist, Carl Anderson, in 1932 [139]. When positrons andelectrons collide, their respective masses are entirely converted to electro-magnetic energy in the form of two photons of energy 511 keV. This is calledannihilation, and is the fundamental physical process harnessed by PET tocreate images. The two photons that arise from the annihilation of thepositron with an electron are emitted in opposite directions and detected ondifferent detectors situated around the object of interest. If the two photonsare detected within a very short time interval, called the time coincidencewindow (TCW), a \u201ccoincidence event\u201d is recorded, and the time differencebetween the detection of each photon is used to approximate the origin of thetwo photons where the positron annhilation occurred (time-of-flight (TOF)PET).The development of radiotracers began with the invention of the cy-30clotron around 1930 at the University of California, Berkeley [140]. The firstdevice for localizing radiotracer activity in Vivo was presented in 1953 byAmerican physicists Gordon Brownell and William Sweet, who used 64Cuand 75As to emit positrons, which annihilated with electrons in tissue tocreate detectable photons. PET systems have evolved greatly since thisinvention, and modern scanners having tens of thousands of individual de-tectors built in [141]. The development of PET was then greatly boosted bythe invention of CT imaging and subsequent innovative CT reconstructionalgorithms.Many different radiotracers have been developed for PET imaging. Cur-rently, the most commonly used radiotracer is 18fluoro-deoxyglucose (18F-FDG) [142]. This molecule behaves similarly to glucose in the body, exceptthat it is not metabolised like glucose. This makes it an especially usefulradiotracer for cancer staging due to the upregulation of glucose metabolismin cancer cells [143], which results in cancer cells having increased accumu-lation of radiotracers over time. 18F decays into 18O with a half life of 110minutes [144], with 96.9% of the decay being due to \u03b2+, and the rest due toelectron capture [145].The resolution of PET images is limited by the distribution of lengthstravelled by positrons before annihilating with electrons. The probabil-ity of positron-electron annihilation is higher for particles at rest, so thepositron typically travels through tissue, losing energy through scatteringand coulomb interactions, before eventually annhilating with an electron.This distance travelled before annihilation is called the positron range. Forexample, positrons emitted through the \u03b2+ decay of 18F have a mean andmaximum initial kinetic energy of 0.25 MeV and 0.63 MeV, which correspondto mean and maximum positron ranges of 0.6 mm and 2.5 mm, respectively[144]. Even if the origin of detected coincident photons is precisely deter-mined, the positron origin remains uncertain and limits spatial resolution ofPET. [146].PET resolution is further limited by non-colinearity uncertainty of pho-tons, which describes the deviation of emitted photons from perfect 180\u25e6separation. This uncertainty arises from the uncertain speed of positrons31at the time of decay, as well as possible scattering of photons before detec-tion. The uncertainty of the positron range following \u03b2+ decay is usuallythe dominant form of uncertainty in PET imaging [147].2.5.2 Image CollectionThe large-scale components of a PET scanner are very similar to those ofCT scanners, and indeed, PET and CT images are often acquired on thesame scanner, known as a PET \/ CT scanner. Patients lie on a movablecouch which glides into a donut-shaped gantry filled with detector rings foracquiring images. The physical processes and detection methods used forPET and CT are of course, very different.Before images can be acquired, patients must be first intravenously in-jected with radiotracers, typically in the arm [148]. Patients then wait for aset amount of time before acquisition, according to recommended guidelinesfor each specific radiotracer. For example, the recommended delay timeafter 18F-FDG injection is approximately 60 minutes [148].Most PET detectors include a large axial range of detectors, to increasethe amount of response lines along which positron decays can be detected[149]. The outside layer of a PET detector consists of scintillator crystals,which produce visible light using the energy of incident gamma-rays de-tected. Resultant visible light pulses then excite many photocathode elec-trons via the photoelectric effect within photomultiplier tubes, creating asignal which is then amplified and digitized. In recent years, advancementsin PET detectors have led to the increased adoption of silicon photomul-tipliers (SiPMs) in place of photomultiplier tubes, which provide a varietyof advantages including high count rates and reduced sensitivity to mag-netic fields, which is an important characteristic in PET \/ MRI applications[150, 151]. The majority of new commercially available PET scanners in-clude lutetium-based scintillators and SiPMs detectors.Modern clinical PET scans usually include detector rings with an axialrange of 16-30 cm, requiring patients to be scanned in 8-10 overlapping bedpositions [152]. However, there are many different detector designs available32and new techniques continue to be developed.2.5.3 Image ReconstructionModern time-of-flight (TOF) PET allows the photon emission point to belocalized with high precision, using the time difference between detected,coincident photons [153]. TOF PET was first adopted into practical use inthe early 1980s [154, 155], and is now the standard practice for reconstruc-tion. Modern PET scanners most commonly use iterative reconstructionalgorithms based on the ordered subsets maximization (OSEM) algorithm[156]. To mitigate image noise, the OSEM algorithm is often followed byapplication of various smoothing filters [157].It is necessary to correct for tissue attenuation during reconstruction ofPET images. Indeed, the attenuation of emitted photons in biological tissuebefore detection is the most detrimental physical factor to the overall qualityof PET images [158]. In PET\/CT systems, CT images are used to obtainelectron density maps throughout the tissue which can be used to correctfor attenuation. In PET\/MRI systems, segmentation of MRI regions isgenerally used for attenuation correction, as MRI signals cannot be directlylinked with electron density [159]. Many attenuation correction algorithmsexist, including recent developments of deep learning-based algorithms [160,161].2.5.4 Standard Uptake ValuesA great advantage of PET imaging over other modalities like CT and MRIis its utility for quantitative imaging and theranostics (a combination oftherapeutic and diagnosic purposes). This is possible due to the nature ofthe PET signal, which originates from radiotracers which display selectiveuptake in Vivo according to different physiological processes. The inten-sity of each image voxel is then directly proportional to the voxel\u2019s relativeradioactivity, which itself is proportional to some physiological event.A unique calibration factor is determined for individual PET scannersand radiotracers that converts voxel intensity to radiation activity in units33of kilobecquerels per millilitre (kBq \/ mL). One Becquerel corresponds toone decay per second. The measured activity in patient tissue is inverselyproportional to patient size, and so the activity is most often scaled to\u201cstandard uptake values\u201d (SUVs) [162]. The formula for obtaining SUVs isSUV =AC\/W(2.7)where A is the measured activity in a voxel, C is the decay-corrected amountof radiotracer injected in kBq, and W is the patient\u2019s weight in grams. SUVsare made to be unitless by approximating 1 mL of tissue to have a massof exactly 1 g throughout the body. This method of normalization basedon weight is sometimes referred to as SUVs normalized by body weight(SUVBW), as there are other methods of normalization. One of these othermethods, which has gained popularity in recent years, is to normalize activ-ity by lean body mass (SUVLBM) [163], which has been shown to performbetter by reducing mass-dependent estimation bias [164]. Normalizing SUVsby body surface area (SUVBSA) has also been demonstrated to reduce esti-mation bias [165]. Various methods of estimating lean body mass and bodysurface area exist.2.5.5 Prostate Specific Membrane Antigen (PSMA) PETThe most relevant PET radiotracer to this thesis targets the prostate spe-cific membrane antigen (PSMA). The PSMA is a type 2 integral membraneprotein that is expressed in all forms of prostate tissue, including carcinoma[166]. It has been shown to have enzymatic activity, acting as a glutamate-preferring carboxypeptidase [167, 168]; however, the impact of these func-tions on prostate and other types of tissues is unclear [169, 170]. PSMAis an excellent target for imaging prostate cancer due to its high relativeabundance on prostate cancer cells, which increases in proportion to thestage and grade of tumours [171]. In addition to its expression in prostatetissue, PSMA expression has been reported in tumours within various otherregions of the body, such as the breast, colon, rectum, and bladder [171\u201334175]. PSMA is furthermore expressed on membranes of astrocyte cells inthe central nervous system [176].Many different PSMA ligands have been developed for PET imaging[177]. The one used to acquire PSMA PET images analysed in this thesisis 18F-DCFPyL. 18F-DCFPyL has proven to be safe, sensitive, and effectivefor localization of prostate cancer [178]. The development of 18F-DCFPyLand other effective PSMA ligands have paved the way for PSMA PET tobecome a common standard-of-care imaging procedure for prostate cancerpatients.The reason that PSMA PET is relevant to this thesis is that PSMA lig-and radiotracers developed for PSMA PET imaging have demonstrated highphysiological uptake in the salivary glands, as well as the lacrimal glands,liver, spleen, kidneys, and colon [179]. PSMA PET was furthermore usedby Valstar et al. in 2021 [17] to discover previously undocumented bilateralsalivary glands in the posterior nasopharynx, the \u201ctubarial glands.\u201d It isunclear whether uptake in non-prostate tissue is mediated by the expressionof PSMA in these tissues, or if PSMA ligand uptake is a result of other phys-iological mechanisms [179]. There is mounting evidence that PSMA liganduptake in salivary glands is linked to functional capacity [180\u2013183], whichmotivated the investigation of PSMA ligand uptake within salivary glandsin this thesis.35Chapter 3Radiotherapy for Head andNeck Cancer Patients3.1 Head and Neck CancerHead and neck cancer describes a broad group of cancer sites located inregions throughout the neck including the lips, oral cavity, nasopharynx,pharynx, larynx, and salivary glands. Cancer sites in the brain, esophagus,thryoid, and skin of the head and neck are not classified as head and neckcancers. The overwhelming majority of head and neck cancers spread fromsquamous cells that line mucosal surfaces, and are hence classified as squa-mous cell carcinomas (SCC) [184]. The remaining types mostly fall into thecategory of salivary gland carcinomas [185]. When SCCs in the head andneck spread, it is almost always spread locally and to the lymph nodes [186].As of 2020, 6 % of global cancer diagnoses were categorized as head andneck cancer [187, 188]. According to Canadian Cancer Statistics 2022 [4],approximately 7500 Canadians were diagnosed with head and neck cancerin 2023, resulting in 2100 mortalities. Of these mortalities, nearly threeout of four will be men. Over 70 percent of head and neck cancer patientsare over the age of 65 and 50 percent are over 70 [189, 190]. Incidenceand mortality rates of head and neck cancers vary significantly throughoutdifferent geographic regions worldwide [191].Tobacco use is a major risk factor for head and neck cancer [192]. Bypooling data from 19 international studies from 1971 to 2007, it was deter-mined that cigar or pipe smoking increased the risk of head and neck cancerby odds ratios of 3.39 and 3.71, respectively [193]. Cigarette smoking has36been estimated to increase the risk of head and neck SCC by 10 times, withthe risk increasing in proportion to dose of smoke inhaled [185]. Alcohol isanother important risk factor for head and neck SCC, being a contributingcause of 75 % of cases as of 1988. While alcohol is an independent risk factorfor head and neck SCC, it is particularly catalytic of carcinogenic damagedue to tobacco usage [194]. An increasing prevalence of tobacco use andalcohol consumption in developing nations has contributed to the incidenceof head and neck SCCs having predicted annual increases of 30 percent by2030 [195].The incidence of head and neck cancers in patients under the age of 45has increased sharply in the last two decades due to a rise in oropharyngealcancers caused by the human papillomavirus (HPV) [185, 196]. This form oforopharyngeal cancer is clinically distinct from non-HPV related carcinomas[197], and has also contributed to the increasing incidence of head and neckSCCs seen globally [195]. The primary risk factors for HPV-positive headand neck SCCs are related to sexual behaviour while HPV-negative headand neck SCCs are primarily associated with alcohol and tobacco usage[198]. Survival outcomes for patients with HPV-positive head and neckSCCs are much better than for patients with HPV-negative head and neckSCCs [199\u2013201]. Prevalence rates of HPV are lower in non-oropharyngealversus oropharyngeal cancer patients, but it is unknown whether a laggingeffect will lead to a future rise in non-oropharyngeal head and neck cancersdue to the rising prevalence of HPV [196, 202].Common symptoms of head and neck cancer include the presence ofan irregular mass in the neck, difficulties and pain while swallowing, earpain, hoarseness, oral or oropharyngeal pain, and weight loss [192]. It iscommon for head and neck cancer to be discovered incidentally by dentistsand primary care physicians, and patients are then referred for examinationby an otolaryngologist (physicians specializing in the head and neck region).Patients are then sent for imaging to aid in staging. PET\/CT is a commonlyused modality for staging primary and nodal tumours in the head and neck[203]. The PET\/CT used for staging is typically followed up with contrast-enhanced CT and\/or MRI for more accurate localization of cancerous regions37for staging and treatment planning. Patients who receive both contrast-enhanced CT and MRI most often have primary tumours in the oral cavityand\/or oropharyngeal [192].Head and neck cancers are known for being complicated. The largenumber of organs in close proximity within the head and neck makes it par-ticularly challenging to design treatment plans for head and neck cancerswhich target tumours while preserving the functionality of healthy organs[204]. It is therefore recommended that head and neck patients receivecare at high-volume centres with expertise, that can offer a multi-modalityapproach [205]. External beam radiotherapy is a central component of treat-ment plans for most head and neck cancer patients [192], with 80 percentof head and neck cancer patients receiving some form of radiotherapy asof 2018 [206]. Chemotherapy is often prescribed in conjunction with radio-therapy, and surgical removal of tumour regions is also an option for somepatients.There is significant inter-institutional variation in treatment policies forhead and neck cancer [207]. The general goal is to maximize tumour con-trol while minimizing collateral dose to OARs. If treatment includes radio-therapy, dose prescribed by the radiation oncologist is dependent on manyfactors, including the extent and location of primary tumour volumes andneck lymphadenopathy, previously received radiotherapy dose levels, andwhether there is curative intent.3.2 External Beam Radiotherapy3.2.1 How Does Radiation Treat Cancer?The effects of ionizing radiation, as used to treat cancer via radiotherapy,have been a topic of interest since the discovery of x-rays in 1895. in Vivo,the most toxic method by which ionizing radiation damages cells is throughdirect damage of deoxyribonucleic acid (DNA) strands [208]. A particularlydevastating event for the life of a cell is the occurrence of single-strand breaksof DNA molecules in close proximity, resulting in double-strand breaks,38whereby the molecule undergoes complete separation. Subsequent cellularrepair mechanisms for double strand breaks of DNA molecules often lead tomutations which ultimately result in cell death [209]. The direct damageof DNA caused by ionizing radiation was first confirmed by the Americangeneticist Karl Sax in 1938 [210]. Another pathway along which ionizingradiation damages DNA is called \u201cindirect\u201d damage. Indirect damage isa result of free radicals, radical ions, and excited molecular states createdthrough interactions with incident ionizing radiation, which ultimately leadsto DNA damage. The largest source of indirect damage in Vivo is free rad-ical formation in water [208]. Subsequent reactive oxygen species then leadto single strand breaks of DNA, as well as base pair deletions and oxidizedDNA bases [209]. These effects can normally be repaired by cellular re-pair mechanisms; however, when many events occur simultaneously, doublestrand breaks often arise during repair, leading to cell death [209]. Linearenergy transfer rates of ionizing radiation are proportional to the extent ofcellular death due to both indirect and direct damage of DNA.The question then becomes, \u201chow can cancer be treated with radiationwithout killing all of the patient\u2019s healthy cells?\u201d Without a deeper under-standing of differential effects of radiation on tumours and normal tissue, itmay be especially surprising that primitive techniques, which deposited dosein broad, approximate regions around tumours, had any success whatsoever.While these effects are highly detailed and require great lengths to properlyconvey, the ultimate reality is that cancer cells generally have heightenedradiosensitivity, meaning that they are more prone to cell death via radia-tion damage than surrounding normal cells. This is largely due to the rapidproliferation of cancer cells, making it more probable for cancer cells to befound in a replicative phase of their cell cycle than normal cells. Cells in areplicative phase of their cycle are more prone to radiation damage, hencetheir heightened dose sensitivity [3]. Another fundamental method of selec-tively targeting cancer cells during radiotherapy is the use of fractionateddose delivery schemes. Fractionation involves delivering a prescribed doseto a patient in many small increments, or fractions. This is beneficial forseveral reasons. [211]. First of all, it allows cancerous cells to cycle through39various replicative stages, making it more likely for dose to eventually tar-get them during their most radiosensitive phase (cells are more sensitiveduring active replication in G2 and M phases). Fractionation also allowstime for tumour cells to reoxygenate, which heightens radiosensitivity [212].Fractionation also gives normal cells an opportunity to enact cell reparationmechanisms between fractions. Modern modulated treatment techniques,to be discussed in a subsequent section (3.2.7), further differentiate the im-pact of radiotherapy on tumours and healthy tissue by allowing tumours tobe selectively targeted with much higher dose conformality than previouslypossible [213].Ionizing radiation can be classified as either directly or indirectly ion-izing, based on the nature of the radiating particles. Uncharged particleslike photons that make up ultraviolet and x-ray radiation are examples ofindirectly ionizing particles. The majority of ionizations caused by theseparticles are a result of secondary ionizations that occur after the incidentparticle\u2019s energy has been transferred to electrons via the photoelectric orCompton effect. Neutron beams are another example of indirectly ionizingradiation. On the other hand, charged particles such as electrons or protonsare directly ionizing, because they directly ionize molecules via coulomb in-teractions. Modern external beam radiotherapy generally uses either mega-voltage photons or electron beams. Megavoltage photons penetrate deeperinto tissue and are therefore beneficial for treating tumours that are deepwithin the body. In general, electrons are useful for treating lesions near thesurface of skin.3.2.2 History of RadiotherapyRadiotherapy has been a continually evolving practice for treating cancersince shortly after the discovery of x-rays by the German physicist WilhelmRo\u00a8ntgen in 1895. Within a year, over 1000 scientific articles and 50 bookswere published on the subject [214], and the first therapeutic use of x-raysfor treating pathologic lesions was documented by American physician andmanufacturer of vacuum tubes, Emil Grubbe\u00b4 [215]. After the discovery of40radium, extracted from uraninite by the Polish-French and French physicists,Marie and Pierre Curie, in 1898 [216], Marie Curie and the French engineerHenri Becquerel reported on the physiological effects of radium exposure[217] in 1901. Shortly after, they donated some of their material to St LouisHospital, Paris for medical applications, and the first disease treated wascutaneous lupus [218]. In subsequent years, x-ray therapy for cancer wasfailing, and attempts were made to treat cancer by directly applying radiumslabs to lesions [218]. Treatment techniques were further advanced withthe adoption of Radon therapy, which allowed radiation dose to be bettercontrolled. In these early years, the efficacy of radiotherapy was often dismaland fiercely debated, and according to a 1915 debate in the United StatesSenate, many doctors believed the curability of cancer using radiation was\u201cdelusional\u201d [219]. Haphazard attempts at treating a wide range of ailmentscontinued until the end of the 1920s, when the benefits of delivering dose infractionated schemes were shown by the French physician, Henri Coutard[220, 221]. Coutard was the first scientist to adopt an organized approach toradiotherapy, resulting in the first reported curative treatments of laryngealcancer, for which he published 5-year survivorship statistics [222]. Anotherimportant achievement of the late 1920s was the invention of the Geiger-Mu\u00a8ller tube by the german physicists Hans Geiger and Walther Mu\u00a8ller in1928, which rapidly attained wide usage for quantifying medical radiation.The period from 1930 to the early 1950\u2019s is known as the \u201corthovoltageera\u201d of radiotherapy [223]. During this period, external beam treatments (asopposed to radium brachytherapy) evolved with the development of super-voltage x-ray tubes that could deliver beam energies of 50 - 200 kVp [223].Orthovoltage radiotherapy found success for lesions close to the surface ofthe skin, but could not penetrate far enough into tissue to treat deep lesionswithout burning the skin [224]. Orthovoltage x-ray beams deposit the ma-jority of their dose within the first few millimetres of patients\u2019 skin and dosefalls off rapidly at further depths [225].A major innovation was to come in 1951, at the University of Saskatchewanin Saskatoon, Canada, with the world\u2019s first calibrated Cobalt-60 megavolt-age therapy unit being put into clinical use. Cobalt-60 is a radioactive41isotope of Cobalt that is synthesized in nuclear reactors via neutron activa-tion, where nuclei of Cobalt atoms are bombarded with neutrons, resultingin temporary absorption of neutrons into unstable bound nuclear states thateventually undergo \u03b2-decay to an excited Nickel-60 isotope governed by ahalf-life of 5.272 years. The primary decay pathway of excited Nickel-60isotopes is by emission of two photons of energies 1.17 and 1.33 MeV. Theseare the photons that are used therapeutically during Cobalt-60 radiother-apy. The long half life of Cobalt-60, along with the high energy of itsemitted photons, made it a prime candidate for clinical practice. Cobalt-60treatment units are quite simple, including Cobalt-60 sources inside largelead-filled containers, with some sort of \u201con-off\u201d mechanism for moving thesource in\/out of a collimated window through which patients are exposed.The megavoltage photons emitted through the decay of Cobalt-60 allow formuch deeper penetration of radiation into tissue than possible with ortho-voltage units. The maximum dose occurs at a depth of approximately 0.5 cmin water equivalent tissue, and measured doses fall to 50% of the maximumat a depth of approximately 12 cm [226]. Treatment of cancer using usingCobalt-60 units continues to this day, most notably in developing nations[227].Cobalt-60 units have gradually phased out from modern treatment cen-tres since the invention of compact linear particle accelerators (LINACs) inthe 1950s. The rollout of LINAC technology in North America began with a6 MeV unit created by Varian Associates and the American physicist HenryKaplan in 1956 [228]. The basic concept of LINAC technology is to accel-erate electrons to megavoltage energies which can then be used to treat topatients, either directly or indirectly by first converting electrons to mega-voltage photons. The LINAC began to see widespread clinical adoption inthe late 1960s as the technology continued to improve [228]. To this day,LINACs remain the primary method of radiation production for medicalapplications at modern sites, and the technology will be discussed furtherin the following section (3.2.4).423.2.3 Radiotherapy for Head and Neck Cancer TreatmentRadiotherapy plays a central role in the treatment of head and neck cancerpatients, in both a curative and palliative sense. In curative treatment plansfor head and neck patients, radiotherapy is normally delivered in fractionsof 1.8 - 2 Gy for 5 days a week, up to a total dose of 66 - 74 Gy to primarytumour sites [192]. However, radiotherapy prescribed following surgery orwith palliative intent often delivers a lower cumulative dose [192].Radiotherapy prescribing and planning is a complicated optimizationproblem, where the goal is to maximize the tumour control probability(TCP) while minimizing the normal tissue complication probability (NTCP).Radiation-induced cell death is a stochastic process [229, 230], and thereforeTCP models are statistical in nature. Currently, a Poisson distribution isoften used to model the probability of n out of n0 cancerous cells surviving atreatment dose. The TCP corresponds to n = 0, and is given by the equationTCP = P (0) = e\u2212n0\u00b7S , where S is the probability of a single cell surviving[3]. For in Vivo applications, n0 is very large and S is small (n0 \u2248 10\u22129 for1 cm3 of cancerous tissue and S \u2248 0.1 for a radiation dose of 2 Gray (Gy))[230\u2013232]. Radiation dose is commonly measured by the Gray, where oneGy = one Joule per kilogram.An important statistical equation for modelling the probability of a singlecell surviving the entire course of treatment, is the linear quadratic model,S = e\u2212\u03b1D\u2212\u03b2GD2 . The interpretation of all these parameters is outside thescope of this work, but in short, parameters are dependent on a wide arrayof factors related to cell damage mechanisms, radiation energy, time inter-vals between treatment, dose rate, oxygenation, concurrent chemotherapy,etc [230]. These parameters are derived experimentally from in Vivo andin Vitro survival curves, and are then used to guide clinical prescriptionpractices.The tumour control probability (TCP) follows a sigmoid curve, as shownin part (a) of Figure 3.1. Chemotherapy provides a well-known therapeuticgain to radiotherapy, as seen in part (a) of Figure 3.1 [3, 233, 234]. However,chemotherapy is also known to commonly increase normal tissue complica-43tions, as shown in (b). A common approach to controlling chemotherapylevels is to identify the dose which, when combined with chemotherapy, leadsto the same probability of normal tissue complications as with radiotherapyalone (points A and B in the graphs). The fact that B is higher than Aon the left curve indicates that there has indeed been a therapeutic gain.Commonly used chemotherapy drugs in concurrence with radiotherapy atBC Cancer are cisplatin and carboplatin.Figure 3.1: The tumour control probability (TCP) follows a sigmoid curve,as shown in part (a). The therapeutic gain of adding chemotherapy (drug)is seen, allowing TCP to be achieved at lower overall dose levels, as in(a). However, chemotherapy is also known to commonly increase normaltissue complications, as shown in (b). A common approach to control-ling chemotherapy levels is to identify the dose which, when combined withchemotherapy, leads to the same probability of normal tissue complicationsas with radiotherapy alone (points A and B in the graphs). The fact thatB is higher than A on the left curve indicates that there has indeed been atherapeutic gain. Copyright 2007 From Handbook of Radiotherapy Physics(Theory and Practice) by Philip Mayles, Alan Nahum, and Jean-ClaudeRosenwald. Reproduced by permission of Taylor and Francis Group, LLC,a division of Informa plc.The foundation of modern radiotherapy practices is based on mentionedradiobiological models, which are used to prescribe specific therapeutic dose44levels to different targets. A typical clinical workflow includes the establish-ment of dose constraints and objectives by a radiation oncologist who thencollaborates with medical physicists and dosimetrists to develop a treatmentplan that meets objectives as best as possible while respecting all constraints.In the head and neck, it is common to have a dose of approximately 70 Gyprescribed to primary \u201chigh risk\u201d tumour volumes, a dose of 63 Gy pre-scribed to \u201cintermediate-risk\u201d regions around the primary tumour volume,and a dose of approximately 56 Gy prescribed to \u201clow-risk\u201d regions encom-passing the lymph nodes [235]. At BC Cancer, current clinical constraintsrequire at least 95 % of tumour volumes (extended by a margin) to be cov-ered by at least 98 % of their respective prescription dose. This is expressedas V95% \u2265 98%. There are also maximum dose constraints that must not beexceeded within critical nervous tissue.Side effects of radiotherapy for head and neck cancer patients can belong-lasting or even permanent, including difficulty swallowing, speaking,general oral discomfort\/pain, and a host of other issues [206]. The subjectivesensation of a dry mouth, called xerostomia, is a common side effect for headand neck radiotherapy patients, which leads to a significant diminishmentin self-assessed quality of life [7\u201310]. All original research contributions inthis thesis have been made with the common, ultimate goal of reducing theburden of xerostomia for head and neck radiotherapy patients. More detailsrelating to xerostomia are included in Chapter 4 which covers the salivaryglands.3.2.4 Radiation With Linear Accelerators (LINACs)The LINAC is the most commonly used treatment unit for external beamradiotherapy in modern times. It is the primary device for external beamradiotherapy at BC Cancer, used for treatment planning in Chapter 10.Rather than relying on a radioactive source for delivering dose, LINACs areused to accerate electrons from rest up to relativistic speeds correspondingto megavoltage energies. There are many highly-optimized components thatmake up a LINAC, and even entire graduate courses on the topic can only45survey the internal mechanisms. This section therefore settles to describeprimary LINAC components and their basic principles, leaving out manyfine details.The main component of a LINAC is the waveguide. The waveguide isused to accelerate electrons and it does so using an ingenious method. Sinceit is infeasible to accelerate electrons to megavoltage energies using a linearpotential difference along a reasonable length without resultant dialectricbreakdown, waveguides circumvent this issue by accelerating electrons withoscillating, radiofrequency (RF) microwave fields. The concept of usingresonant microwave cavities to accelerate electrons was published in 1938by William Hansen at Stanford University [236]. A waveguide consists of alinear series of resonant cavities within which a standing RF wave is formed.The RF oscillations are timed so precisely that electrons travelling alongthe waveguide are always subjected to a forward-accelerating potential whiletraversing the series of cavities. This accelerates electrons to megavoltageenergies (very close to the speed of light) while travelling distances on theorder of one metre.The war effort during World War 2 then demanded the production ofmegavoltage microwaves for the purposes of radar systems, and two sys-tems were developed in 1939 [228]. The first system, the magnetron, wasdeveloped in Europe. The magnetron is a self-oscillator, capable of pro-ducing high energy microwaves using a DC power supply [237]. It createsmicrowaves by accelerating electrons, in the presence of a magnetic field, ra-dially outwards from a central cathode filament to a concentric anode shellwhich contains a series of resonant cavities that produce microwave radia-tion in response to the accelerating electrons. The second system is calledthe klystron, and was produced in the United States by the Varian broth-ers [238]. While the magnetron generates microwave radiation directly, theklystron acts as an amplifier of low power microwave input. Both types of RFgenerators are still used and coupled with waveguides in modern LINACs,but magnetrons are mainly limited to low power LINACs [239].A waveguide, coupled with an RF generator, forms the apparatus forelectron acceleration needed for radiotherapy. The next required component46is an electron source. For this an electron gun is coupled to one end ofthe waveguide, from which emitted electrons will be accelerated towards theother end. The electron gun releases electrons thermionically from a cathodeas in an x-ray tube. The RF acceleration of electrons in the waveguidesrequires high peak power outage which is attained by operating the LINACin a pulsed repetitive mode [240]. This pulsed power is managed usinga pulse modulator which supplies high voltage pulses on the order of amillisecond to the electron gun and microwave source [3]. The microwavesource is either a magnetron itself, or a separate source coupled to a klystron.The electron beam must be carefully focused and steered along the cen-tral axis of the waveguide, and this is achieved using a collection of steeringcoils (usually Helmholtz coils [3]). Steering coils are also used to controlthe electron beam upon its exit from the waveguide where it enters the so-called \u201cbending magnet,\u201d which is used to curve the beam towards the finaltreatment head aperture. Many different bending magnet designs exist.If the final intention is to operate the unit in electron beam mode, thenelectrons simply exit the treatment head towards the patient. If, however,a photon beam is desired, then a high-density target is placed in the line ofthe electron beam, to create photons via bremsstrahlung emission as in anx-ray tube. The target is generally made of tungsten. A circular primarycollimator is located directly after the target to attenuate unnecessary edgesof the beam. A flattening filter is then optionally inserted in the way ofthe photon beam to reshape it to to a more radially uniform profile. Thetungsten target and flattening filter are motorized so they can be moved inand out of the beam by remote control.To give final, customized shape to radiation beams, the treatment headincludes a series of secondary collimators, and multi-leaf collimators (MLCs).Different collimation designs exist, such as Varian\u2019s, which generally hastwo subsequent secondary collimators in the beam\u2019s path, each consistingof a pair of high-density metal slabs. These can open and close towardsthe central axis of the radiation beam, allowing the beam to be reshapedinto arbitrary rectangular shapes. Finally, the MLCs are used to furthercustomize the beam shape. These include a series of long, adjacent metal47(usually tungsten) leaves that can move in and out of the radiation beamindependently. This allows the final beam shape to be highly customized.The first commercially available MLCs became available in the 1990s [3],and have since played a crucial role in advancing radiotherapy techniques,to the great benefit of cancer patients.The treatment head, through which radiation exits towards patients, ison one end of a \u201cC\u201d-shaped gantry, which is capable of rotating by 360\u25e6 alonga horizontal axis that is in-line with the treatment couch. Head and neckcancer patients typically lie supine on the treatment couch. On the oppositeend of the C-shaped gantry is an electronic portal imaging device (EPID)for reading-out the radiation beam for alignment and verification purposes.Some LINACs, such as the Varian TrueBeam [241], come equipped with acone beam CT, set up at a right angle to the radiation beam and throughthe isocentre (the centre of the circle defined by gantry rotation).3.2.5 Segmentation of Medical Images for TreatmentPlanningAfter discussing how radiation beams are created for radiotherapy, and be-fore discussing modern treatment planning techniques, an important stepthat cannot be left out. This is the act of segmenting regions-of-interest(ROIs) on medical images so that the locations of tumour boundaries andhealthy OARs are precisely known. This is an important task for radiother-apy treatment planning because these segmented ROIs are used to guide theprecise dose delivery systems used during treatment.ROIs are often segmented on each axial slice of an image series, resultingin a set of parallel plane contours to describe each region. Structures out-lined on medical images are therefore often called \u201ccontours.\u201d Traditionallythis is done manually, requiring expert knowledge to accurately define vari-ous anatomical regions. It is quite time-consuming [242], in fact being oneof the most time consuming tasks in the clinical workflow of radiotherapytreatment planning [243].Currently, CT is the image modality used at BC Cancer for defining pa-48tient geometries for radiotherapy treatment planning. Planning CT imagesare acquired on a CT simulator, which is essentially a CT scanner that hasbeen set up to match the couch and positioning of the treatment LINAC.During the CT simulation, the patient is set up using the same immobi-lization and support devices used during treatment on the LINAC. Thisalignment of geometries allows the position of target volumes and OARs tobe known during treatment on the LINAC, provided the patient is iden-tically set-up on the treatment couch. Furthermore, patient tattoos andphotographs are acquired to assist with replicating patient setup.Guidelines for contouring specific OARs vary across institutions, anda number of different approaches to parotid gland contouring having beenpublished [244\u2013246]. For example, BC Cancer\u2019s guidelines for defining bor-ders of the parotid glands, submandibular glands, and oral cavity, are shownin Table 3.1.49Table 3.1: BC Cancer\u2019s clinical guidelines for defining the borders of the parotid glands, submandibular glands,and oral cavity. This figure was used with permission from Haley Clark\u2019s PhD thesis at the University of BritishColumbia, 2017: Assessment of spatially inhomogeneous intra-organ radiation dose response in salivary glands[13]Structure Border StructuresParotid Anterior Masseter muscle, Ramus of mandiblePosterior Sternocleidomastoid muscle, Digastrics muscle posterior bellySuperior Zygomatic ArchInferior Fascia between Sternocleidomastoid muscle and MandibleMedial Styloid Process, Medial Pterygoid muscleLateral (open)Submandibular Anterior Platysma musclePosterior Sternocleidomastoid muscleSuperior Mandible, Mastoid processInferior Diagastric muscles, Epiglottis, LaryngopharynxHyoid bone, Tongue, OropharynxLateral Platysma muscle, MandibleOral Cavity Teeth, MandiblePosterior Laryngopharynx (communicates with Oropharynx)Superior Palate (hard, soft)Inferior Tongue, Mucosa, Geniohyloid and Mylohyoid musclesHyoid bone, Teeth, MandibleLateral Teeth, Mandible50Contouring tumour volumes requires sequential extension of border mar-gins to account for various types of uncertainty, and can be described as fol-lows. First, the visible tumour regions are contoured as gross target volumes(GTVs). For head and neck cancers, each GTV margin is then extendedoutwards (usually by 5 mm at BC Cancer) to encapsulate regions of micro-scopic spread surrounding tumours. Resultant structures are called clinicaltarget volumes (CTVs). Another margin is then applied to account for setuperror (5 mm at BC Cancer), which yields planning target volumes (PTVs).Manual contouring of CT images is prone to various types of discrep-ancies and uncertainties [13]. First of all, there are discrepancies across in-stitutions, due to differences in established contouring guidelines, training,and expertise [247\u2013249]. Furthermore, there is well-documented variation incontouring between observers within single institutions [250\u2013255]. To makematters even worse, there is significant intra-observer variation in contour-ing [256\u2013259], partially explained by lapses in concentration and uncertaintyin defining edges [3]. Inaccurate contours that do not reflect the true dimen-sions of ROIs will result in inferior dose sparing of OARs and suboptimaltreatment of target volumes.Motivated by the high time requirement and uncertainty of manual im-age contouring, automation techniques for medical image segmentation (au-tosegmentation) have become a popular area of research and developmentin recent years. In fact, autosegmentation is one of the most active areas ofresearch in computer vision [260]. According to literature publications, con-touring a full set of head and neck OARs takes approximately three hours[261\u2013265].Autosegmentation has been shown effective for reducing both inter-observervariability and time taken for contouring head and neck OARs [261]. Au-tomation techniques have advanced significantly since the introduction of theU-Net deep learning architecture by the German computer scientist, OlafRonnenberger in 2015 [266]. The U-Net architecture has been so importantin advancing image segmentation algorithms, that it is worth describingbriefly. The U-Net architecture is also relevant to the research contribu-tions of this thesis, as we employ a derivative model, MultiResUNet [267],51for auto-segmentation of PSMA PET defined tubarial glands on registeredCT images (Chapter 7). A U-Net style architecture is also used within theneural blind deconvolution methodology employed in Chapters 5 and 6.3.2.6 Semantic Segmentation and U-NetU-Net is a neural network architecture that built off of Long et al.\u2019s \u201cfullyconvolutional network\u201d for carrying out the task of semantic segmentation[268]. Semantic segmentation is an image classification task that locally clas-sifies each pixel within an image. In the context of medical image segmenta-tion, for which U-Net was originally developed, image pixels are classified asbeing located inside or outside of various ROIs. These pixel classificationscan then be post-processed to produce final ROI contour sets for treatmentplanning.U-Net is a type of feed-forward convolutional neural network [269]. Aconvolutional neural network is a popular deep learning architecture thatwas originally inspired by the arrangement of neurons in the visual cor-tex of the human brain [270]. The concept stems from the invention ofthe \u201cneocognitron\u201d by the Japanese electrical engineer Kunihiko Fukushimain 1980 [271]. These networks pass input data through multiple layers ofconvolutions, transposed convolutions, max-pooling operations, activationfunctions [272], and other functions to extract hierarchical features from thedata. Deep convolutional networks encode location and semantics in a local-to-global hierachy [268], where location refers to the \u201dwhere\u201d and semanticsrefers to the \u201cwhat.\u201d Before the development of U-Net, convolutional neu-ral networks were mostly limited to whole-image classification tasks (i.e \u201cisthere a bus in this image?\u201d). Convolutional neural networks have provenparticularly useful for image classification tasks, including semantic segmen-tation.The U-Net architecture can be broken into 2 feed-forward sections calledan encoder and decoder, each forming opposite sides of a \u201cU\u201d shape. Theencoder is a contracting path, where features are extracted through a se-ries of 3 \u00d7 3 convolutions, activation functions, and 2 \u00d7 2 max-pooling op-52Figure 3.2: The U-Net architecture is shown using input images of size572x572. Blue boxes correspond to multi-channel feature maps, with thenumber of channels indicated on top. The image size throughout the networkis indicated at the lower edge of boxes. White boxes indicate copied featuremaps. This figure belongs to, and was reused from the article, \u201cU-Net: Con-volutional Networks for Biomedical Image Segmentation,\u201d with permissionfrom, Olaf Ronneberger (https:\/\/doi.org\/10.48550\/arXiv.1505.04597).53erations with a stride of 2 [273] which decrease image spatial dimensionswhile increasing the number of image channels. The decoder is an expansivepath, which increases the spatial dimensions back to the original size whiledecreasing the channel count through a series of 2 \u00d7 2 transposed convo-lutions, 3 \u00d7 3 convolutions, and activation functions. The original U-Netarchitecture used rectified linear units (ReLU) [274] as activation functions,which remain common in currently developed neural network architectures.ReLU functions add non-linearity to network architectures by outputtingReLU(x) = max(0, x). Alternatives to ReLU activation functions includeleaky ReLU [275], exponential linear units (ELU) [276], adaptive piecewiselinear units [277], and many others [278]. To address degradation loss [279]as data propagates through the network, \u201cskip connections\u201d are used to con-catenate decoder and encoder features in corresponding network layers. Adiagram of the U-Net architecture is shown in Figure 3.2. All in all, imagesare fed into the network which outputs a mask image, classifying each pixelas inside or outside of a given ROI. The collection of pixels constituting agiven ROI are referred to as the ROI\u2019s mask.U-Net is typically trained using a supervised learning approach. Su-pervised learning for semantic segmentation is a machine learning approachwhereby networks or models are trained to output datasets of \u201dground truth\u201dmanually contoured masks from their corresponding input images. The basicapproach can be broken into two basic steps:1. back-propagate the gradient of a loss function (minimizing differencebetween output and ground truth images) sequentially through net-work weightings of the model.2. Update model weights using some form of gradient descent algorithm.In this manner, networks adapt their weights to recognize importantinput features for predicting ground truth masks. A common approach toupdating networks weights is ADAM optimization [280]. Network training isa computationally expensive task which is greatly accelerated by propagat-ing through network gradients on graphics processing units (GPUs) rather54than central processing units (CPUs). GPUs provide parallelism and wereinitially designed to accelerate graphic and imaging processing calculationsbefore becoming more generalized computing devices. Developers can utiliseGPU parallelism through computational libraries such as NVIDIA\u2019s Com-pute Unified Device Architecture (CUDA) which are used by deep learningframeworks such as PyTorch [281] and TensorFlow [282].Deep learning model performance scales with the size of training datasets,mostly by mitigating overfitting issues via data generalization [283]. A pri-mary and challenging focus of innovation in deep learning architectures is theimprovement of model generalizability. Generalizability refers to how wella model performs on previously unseen data [284]. Methods for boostinggeneralizability include batch normalization [285], dropout regularization[286], and transfer learning [287]. Another common approach is to augmentthe dataset by applying various geometric transformations to the originaldataset [283, 288, 289].The development of U-Net was a major step forward for image seg-mentation algorithms, sparking many derivative models in the literature.Commercial autosegmentation software for medical images has recently seenadoption into clinical usage, such as LIMBUS AI [290], which is currentlylicenced for used at BC Cancer, Surrey.3.2.7 Volume Modulated Arc Therapy (VMAT)Over the past few decades, radiotherapy techniques have greatly improvedthrough a series of iterative adjustments. A particularly important im-provement came with the development of Volume Modulated Arc Therapy(VMAT) in 2007 by Karl Otto at BC Cancer, Vancouver [291], which builtoff of Intensity Modulated Arc Therapy (IMAT) which had been inventedin 1995 by Cedric Yu [292]. VMAT is a LINAC radiation delivery techniquethat allows the simultaneous variation of gantry rotation, dose rate, andMLC leaves. Optimizing these degrees of freedom together allows highlyconformal dose distributions to be created, as compared to those of con-ventional radiotherapy or static Intensity Modulated Radiotherapy (IMRT)55[293]. IMRT and IMAT conventionally work by first optimizing radiationfluence maps and then sequencing MLC leaf motions accordingly, therebynot granting free-reign to beam aperture shape. It is common for VMATplans to be optimized using 2 (or sometimes more) rotations of the gantrywith differing collimator angles, further enhancing beam shaping abilities.VMAT is currently used as the standard-of-care approach to head and neckradiotherapy at BC Cancer, and is also the common standard-of-care usedworldwide. Double arc VMAT for treatment of head and neck cancer hasproven to outperform its predecessor, 7-9 field IMRT, in terms of increaseddose target conformality, lower mean dose levels in OARs, less beam-ontime, and less time required [294\u2013296]. The transition from conventionalradiotherapy to IMRT resulted in improved sparing of salivary function dueto higher dose conformality [297]. VMAT has led to even better dose confor-mality, further reducing mean dose levels received in parotid glands duringradiotherapy [298].Figure 3.3: A beams eye view of a VMAT radiation field incident on a headand neck cancer patient is shown along with select ROIs, as interpreted inVarian Eclipse. The radiation field is defined by the secondary collimatorsof the LINAC, while the jagged, yellow bars inside correspond to the MLCleaves, with provide further beam aperature customization.VMAT optimization is an \u201cinverse planning\u201d method, meaning thathardware parameters are optimized to achieve a desired dose distribution.56This is in contrast to traditional \u201cforward planning\u201d techniques, which startwith a given hardware configuration and determine the resultant dose distri-bution. Optimization proceeds by approximating the continuous rotationalfield created by the gantry as a discrete set of static field control points,whose cumulative dose constitutes the final dose distribution. Within eachfield, the location of all ROIs is known because the LINAC geometry matchesthe geometry of contours obtained during the CT simulation. An examplebeams-eye-view of a radiation field incident on a patient showing 3D con-tours rendered in Varian Eclipse is shown in Figure 3.3. Optimized dosedistributions and LINAC treatment parameters are guided by dose-volumeconstraints that are input by a treatment planner in the planning system.This is discussed further in the following section.The computational procedure for optimizing VMAT plans involves com-plicated algorithms, but the basic steps can be simply summarized as follows:1. Establish an optimal dose distribution to strive towards (ie. prescrip-tion dose in target volumes, 0 elsewhere).2. Define the physical treatment field\/arc\/couch geometries, and initial-ize LINAC parameters to be optimized, such as MLC leaf positionsand monitor units delivered around the arc.3. use a dose calculation algorithm to accurately determine the dose dis-tribution throughout the patient with the current LINAC parameters.4. Calculate the output of an objective cost function, which diminishesas the current dose distribution approaches the optimal distribution.5. Execute an optimization algorithm that adjusts LINAC parametersbased on back-propagated objective cost function gradients.6. Repeat from step 3 until an end criteria is met.VMAT optimization typically uses a multi-resolution approach, where addi-tional control points at gantry angles between existing angles are iterativelyinserted into the calculations. At BC Cancer, a commonly used optimiza-tion algorithm is the photon optimizer (PO) algorithm [299] which built off57of the dose volume optimizer (DVO) and progressive resolution optimizer(PRO) [300]. A commonly used dose calculation method is the AnalyticalAnisotropic Algorithm (AAA) [301].3.2.8 Treatment Planning with Varian EclipseThe treatment planning software used with Varian LINACs is called VarianEclipse. As Varian LINACs are employed at BC Cancer, Varian Eclipse isused in these research contributions of this thesis. The basic methods andtools for external beam treatment planning in Varian Eclipse are discussedin this section, to give context to treatment planning strategies used in laterchapters.All forms of patient data, such as images, contours, and dose prescrip-tions, are managed and loaded into Eclipse using Varian\u2019s ARIA\u00ae oncologyinformation system. ARIA\u00ae is an electronic health records system that actsas an in-between server for managing patient data across multiple systems.It allows images of various modalities and other data to be uploaded to acentral server directly from their respective platforms, and then loaded intoa variety of different applications, one of them being Varian Eclipse. Imagefiles and structure sets are stored as Digital Imaging and Communications inMedicine (DICOM) files. Data pertaining to optimized radiotherapy plansmade in Varian Eclipse, such as dose distributions and linac parameters, arealso exported to ARIA as DICOM files.The basic graphical interface of the external beam planning window inVarian Eclipse is shown in Fig 3.4. Eclipse provides a visual interface forevaluating dose distributions throughout a patient\u2019s anatomy using isodosemaps overlayed with CT images and contoured ROIs, as well as dose vol-ume histograms (DVHs). After all images and other treatment data havebeen loaded into Eclipse, treatment planning begins with the definition ofradiation fields geometries. In the case of head and neck VMAT, this in-cludes defining the quantity and geometries of arcs used, the couch position,and the position and angle of secondary collimators for shaping the beamaperture. These fields define how the patient will be exposed to the radia-58tion beam during treatment, and limits the final dose distribution achievableafter optimization of MLC leaf motion and dose rates.59Figure 3.4: The external beam planning window in Varian Eclipse is shown. Dose volume histograms for variousregions of interest are displayed in the top right box, and three planar slices of an anonymized head and neckpatient\u2019s CT images with contoured regions are shown in the other boxes.60The next step is to input dose constraints and objectives to be consideredduring optimization. These constraints are defined for each ROI in termsof either the mean dose, or points of constraint along the DVH curve. Toboost normal tissue dose sparing [302\u2013304], there is also a normal tissue ob-jective (NTO), which is an adjustable function of falloff versus distance fromtarget volumes. The optimizer window in Eclipse, used for evaluating andmodifying dose constraints while optimizing plans, is shown in Figure 3.5.Optimization proceeds through multiple levels of resolution as discussed inthe previous section, ultimately converging towards a final treatment planand dose distribution, which can then be evaluated by radiation oncologistsand medical physicists.DVHs are central to dose level quantification for defining dose constraintsin ROIs, so it is necessary to briefly describe their form before proceeding.A dose volume histogram is a 2-dimensional curve with dose on the x-axisand the volume of an ROI on the y-axis. Dose levels are divided equallyinto a number of discrete bins, from zero up to the prescription dose, andthen the volume of the given ROI receiving a dose within each respectivebin is plotted. This yields a differential DVH (dDVH). Oftentimes, a morepractical way to describe the DVH is with the cumulative sum of dDVH val-ues taken from right to left on the x-axis, resulting in a so-called cumulativeDVH, which will be simply referred to as a DVH from here on out. ExampleDVH curves are seen in the top right of Fig 3.4. The DVH describes thedistribution of dose within ROIs much more thoroughly than single metricslike the mean and median, and different points along the curve can be usedto define dose objectives\/constraints. These points can be defined in termsof the volume receiving at least a certain dose level (Vdose %), or the dosereceived by at least a certain volume (Dvolume %).As previously mentioned in 3.2.3, a constraint used on target volumesat BC Cancer is V95% \u2265 98%. Along with target constraints, clinical doseobjectives in terms of DVH values exist for the large variety of OARs en-countered in the head and neck. Dose constraints for the salivary glandswill be covered further in the following chapter.61Figure 3.5: The external beam plan optimization window within Varian Eclipse is shown. On the left, dose volumeconstraints are manually updated to converge towards an optimal dose distribution. The dose volume histogramsin the centre are dynamic, corresponding to dose volume calculations using currently optimized MLC leaf positionsand monitor unit rates. The current dose distribution can be seen on the right, with customizable isodose linesfor viewing specific dose levels. As indicated by the progress bars on the bottom, optimization is currently at theforth multi-resolution level.62Although the treatment planner\u2019s role in creating radiotherapy plans issimple in principle, it generally requires extensive fine-tuning for generationof optimal plans for each patient [305, 306]. Perhaps the most challengingaspect of the planning process is the uncertainty of the best attainable dosedistribution for each patient. There is currently wide-spread interest in de-veloping, and implementing into the clinic, data-driven planning techniquesusing historical data, which is a strategy referred to as knowledge-based-planning [307\u2013310]. The general goal of these methods are to use deep neuralnetworks, or other algorithms, to guide the optimization of dose distribu-tions on a patient-specific basis. A major commercially used product forknowledge based planning is Varian\u2019s RapidPlan\u00ae, which has seen growingimplementation in clinical head and neck planning in recent years [311\u2013314].An advantage of implementing knowledge-based planning methods is thatthese methods can be continually improved using more data, and promisesto reduce the uncertainty seen in treatment plan quality within and betweeninstitutions [305, 315, 316].Along with knowledge-based planning, there has been growing interestin automation techniques for streamlining tedious aspects of treatment plan-ning [305, 306, 317\u2013321]. The ability of planners to implement automationtechniques within Varian Eclipse was greatly facilitated by the release of theEclipse Scripting Application Programming Interface (ESAPI) with version11 of Varian Eclipse [322]. ESAPI is an application programming inter-face (API) built into Varian Eclipse, that allows users to write and run C#scripts and compiled DLL programs that operate on and manipulate patientdata that has been loaded from ARIA in Eclipse. ESAPI provides a set offunctions for interacting with data such ROI contours, radiation fields, doseconstraints, and optimization settings. ESAPI was used to develop a pro-gram, \u201cPlan n Check\u201d for sub-segmentation of ROI dose constraints andautomation of VMAT planning \/ Verification for standard head and neck \/nasopharynx patients, as reported on in Chapter A.63Chapter 4The Salivary Glands andRadiotherapyThe production of saliva (approximately 0.5 - 1.5 L per day per person [323])is something that most of us probably take for granted, until inhibitory is-sues are encountered. As previously mentioned, salivary dysfunction andxerostomia (common side effects for head and neck radiotherapy patients) isassociated with a significant reductions in self-assessed quality of life scores[7\u201310], and for radiotherapy patients is largely caused by dose to the salivaryglands. Even with modern modulated therapies such as VMAT, it remainscommon for salivary glands to receive large doses during radiotherapy, dueto close proximity of tumours. Matters are made more difficult through tar-get volume boundaries being extended outwards to eliminate microscopicspread and account for setup uncertainty [324]. The research contributionsof this work were largely motivated by the desire to improve patient out-comes regarding saliva production and xerostomia, so it is prudent to brieflydiscuss the basic anatomy and physiology of the major salivary glands. Thischapter also contains information about xerostomia and salivary dysfunctionfor head and neck radiotherapy patients, as well as currently recommendedclinical dose constraints for the glands. To further motivate research con-tributions, current knowledge pertaining to the heterogeneity of the intra-salivary gland dose response is discussed, as well as the newly discovered,potential OAR, the tubarial glands [325].644.1 Saliva and the Major Salivary GlandsSaliva plays a number of physiological roles and are found in a wide array ofanimal classes. The physiological benefit of saliva derives from its liquid na-ture, as well as its specific molecular make-up [326, 327]. While the extentof salivary knowledge shared in Canadian high school biology curricula isusually limited to the fact that saliva plays a the crucial role in the digestivesystem (by aiding in the hydrolysis of starch into (ultimately) glucose via\u03b1-amylase [328])), the action of saliva goes much further. Saliva is crucialfor hydrating mucosal tissue in the mouth, clearing cellular debris and foodremnants, buffering the oral pH, tasting, digesting certain lipids, preventingdental wear during chewing, forming boli for swallowing, preventing toothdemineralization, and providing antimicrobial support to prevent infectionsand heal wounds [326, 328\u2013330]). The role saliva plays in tasting is not to beoverlooked, as our sensation of taste guides our dietary decisions and facili-tates other physiological processes [331, 332]. Saliva also contains abundant,biologically active proteins whose physiological functions remain unknown[333, 334]. The final composition of saliva is approximately 99 % water [335].The parenchyma of salivary glands contain secretory units called \u201cend-pieces,\u201d which connect to the oral cavity through ducts. These endpieces canbe divided into three categories: mucous, serous, or seromucous, which de-scribe their types of secretions. Mucous secretions are characterized by thepresence of mucins, which are glycoproteins with carbohydrate tails. Mucinsgenerally contain negatively charged functional groups that increase the vis-cosity of the saliva. Serous secretions are much more watery, due to theabsence of mucins, but do contain many other proteins. Mucous secretorycells have an elongated, columnar shape, while serous cells are pyramidal.Seromucous endpieces contain a combination of serous and mucous secretorycells. Secretory cells empty their secretions into intercalated ducts, whichlead to striated ducts, which lead to excretory ducts that ultimately de-posit saliva into the oral cavity. Ducts vary by the type of cells lining theirsurfaces, and some ductal regions actively modify the ionic composition ofsaliva [326]. Furthermore, ductal cells add numerous proteins to saliva, ren-65dering the fluid hypotonic through removal of sodium ions and addition ofpotassium and bicarbonate ions [323, 326].The secretion of saliva is facilitated by contracting myoepithelial cellsthat border the secretory cells. Blood vessels around these cells dilate tomeet the demands of salivary production [336] and nerves mediate the var-ious functions throughout the salivary glands. Secretory cells are furtherlined by an extracellular matrix, immune cells, stromal cells, and myofi-broblasts [337]. Saliva secretion is primarily conducted by the autonomicnervous system.Salivary glands are divided into two main categories: the major sali-vary glands, and the minor salivary glands. The major glands include theparotid, submandibular, and sublingual glands, which are surrounded bydense connective tissue capsules and produce 92-95 % of total saliva output[323]. The number of minor salivary glands is on the order of 1000, andthey are found all around the oral cavity. Minor salivary gland secretionsare primarily mucosal, aiding in lubrication of the mucous membrane of theoral cavity [335]. A diagram of the major salivary glands is shown in Fig-ure 4.1. The anatomy of the parotid and submandibular glands are brieflydiscussed here, with an emphasis on the parotid gland, as it is the glandmost considered in this thesis.4.1.1 The Parotid GlandsOut of the three major salivary glands, the research of this thesis mostlyconsiders the parotid glands. They are the largest salivary glands, situatedbelow and in front of each ear and at the back of the mouth. They are re-sponsible for producing at least 50 % of stimulated saliva [335]. Stimulationof salivary output is a result of both chemical and mechanical processes,and can also be influenced by pain or discomfort [338]. Secretion can bestimulated by chewing, the presence of food in the stomach, sight or odourof food, and hunger; and is inhibited by violent muscular activity and eroticmotion [338]. The parotid glands primarily produce watery, serous salivafrom serous secretory cells which contain high concentrations of \u03b1-amylase.66Figure 4.1: Interior anatomy of the head and neck is shown, featuringthe major salivary glands: the parotid, submandibular, and the sublingualglands. Contributed by Wikimedia Commons, Henry Gray (Public Domain)67The parotid glands are bound inferiorly by the sternocleidomastoid mus-cle, posteriorly by the sternocleidomastoid muscle and the ramus of themandible, anteriorly by the masseter muscle, and superiorly by the zygo-matic arch. They connect with the oral cavity near the second upper molarcrown via the Stensen\u2019s duct, which is approximately 5 cm in length andpierces the buccinator muscle [326, 339]. The Stensen\u2019s duct connects to theanterior side of the gland, and runs superficial to the masseter muscle. Forthe sake of classifying surgical procedures, the parotid gland is divided intotwo regions: the superficial and deep lobes. The deep lobe lies medial to thefacial nerve and between the mastoid process and mandibular ramus [340].Blood supply in the parotid gland is from the external carotid artery,which passes through the posteromedial aspect of the gland, before bifurcat-ing into the maxillary and superficial temporal arteries, which exit towardssuperior aspects. The superficial temporal artery also gives rise to the trans-verse facial artery, which supplies blood to the gland and Stensen\u2019s duct.Sometimes, the posterior auricular artery branches off from the externalcarotid inside inferior aspect of the parotid gland. The superficial temporaland maxillary veins form the retromandibular vein, which passes through thegland vertically before exiting through the caudal-posterior aspect. Thereis a high density of lymph nodes surrounding the parotid glands.The parotid glands have parasympathetic innervation pathways for ionand saliva secretion, and sympathetic innervation for protein secretion andmaintaining blood flow in the glands [341]. Innvervation stems from theglossopharyngeal nerve, which synapses with the otic ganglion. Nerve signalsalso pass through the auriculotemporal nerve. Sympathetic signals alsoderive from the sympathetic plexus of the carotid sheath.The presence of salivary tissue outside of the major glands, oral cavity,pharynx, and upper airways, is a common phenomenon called heterotopiaand is often seen in the lymph nodes around the parotid glands [337]. Fur-thermore, 21-69% of cadaveric cases [342\u2013346] have found a small \u201caccessoryparotid\u201d gland in close association or anterior to the Stensen\u2019s duct, detachedfrom the main parotid gland [347]. It is generally the size of a pea to a kid-ney bean, and has a mean distance of 0.6 cm from the parotid gland [342].68Tumours found in the accessory parotid glands are approximately twice aslikely to be malignant as tumours found in the parotid glands [342, 345, 348].4.1.2 The Submandibular GlandsThe submandibular glands are the second largest pair of salivary glands andare responsible for secreting approximately two thirds of unstimulated saliva[335]. However, the saliva contribution from the parotid glands dominatesupon stimulation [349]. They are located beneath the mandible in the sub-mandibular triangles, just below the floor of the mouth. Their acini areprimarily composed of serous secretory cells, with approximately 10 percentof acini being mucosal [323]. The capsule of the submandibular gland is apart of the superficial layer of the deep cervical fascia. The submandibulargland is separated into superficial and deep lobes (like the parotid gland),divided by the mylohyoid muscle. It drains through the floor of the oral cav-ity via the Wharton\u2019s duct, which has a length of approximately 5 cm [350].Submandibular blood supply derives from the facial nerve, and innervationis directed through the submandibular ganglion.4.2 Radiation-Induced Salivary GlandDysfunction and XerostomiaThe parotid glands are highly sensitive to dose, having been found to ex-perience a 60 % decline in saliva output after one week of conventionalradiotherapy [351]. Xerostomia is one of the most commonly reported sideeffects of head and neck radiotherapy patients [335].The morphology and imaging characteristics of the parotid glands areknown to undergo radiotherapy-induced changes [352, 353]. The volume ofparotid glands decrease after radiotherapy in proportion to the mean dosereceived in the glands [354]. One study found that 10 patients receivinga mean dose of 41.5 Gy in the parotid glands in 35 fractions experienced39.4 % reduction in volume size (p < 0.02) [352]. These same patients alsodemonstrated a significant reduction in CT Hounsfield units after radiother-69apy (p < 0.05), which was strongly correlated with saliva output (p < 0.01).A decrease in CT Hounsfield units within parotid glands was confirmed inanother study [355]. A similar volume change was reported in an additionalstudy (44%) [356]. The rapid and severe observed changes in parotid glandvolume and position during radiotherapy presents challenges, as this motionis not conventionally accounted for during the course of treatment. Onestudy on 15 patients using adaptive planning with weekly CT simulationsfor recalculating dose distributions, found that 60 % of parotid glands wereoverdosed by an average of 4 Gy, and the overall mean dose had been signif-icantly underestimated [357]. Smaller parotid gland volumes have also beenfound to correlate significantly with post-treatment xerostomia scores [358].The volume of submandibular glands have been found to shrink and moveupwards after radiotherapy [354].The loss in salivary output experienced by head and neck cancer patientsafter radiotherapy is well-known. A study at BC Cancer collected stimulatedsaliva output measurements from 102 head and neck cancer patients before,three months post-radiotherapy, and one year post-radiotherapy [359]. Themedian early and late loss respectively was 72% and 56 % of baseline. Inanother study, a cohort of 52 head and neck cancer patients receiving conven-tional radiotherapy had stimulated salivary flow rate measurements takenbefore and after treatment [360]. After six weeks of therapy, measurementshad fallen from 0.31 mL per minute to 0.14 mL \/ minute, which recoveredto 0.19 mL \/ minute after 12 months. At five years post - radiotherapy,the average flow rate had risen to 0.25 mL \/ minute [360]. Stimulated flowrate measurements were also collected in another study on 222 head andneck cancer patients before and one year after receiving either IMRT orconventional radiotherapy [361]. They defined a complication to be a post-treatment flow rate of less than 25 % of the pre-treatment measurement, andfound that 50 % of patients experience a complication at a TD50 of 40Gy.Stimulated salivary measurements were acquired before and after treatmentfor 117 head and neck radiotherapy patients in another study, which foundthat complete recovery can be achieved if the mean dose in at least one glandis kept below 26 Gy [362]. Another study assessed parotid gland function70in 39 head and neck radiotherapy patients using salivary gland scintigraphybefore and at six months after radiotherapy [363]. They found that themean dose in glands should be kept below 20 Gy to preserve function.While the parotid glands are decidedly the most important salivaryglands to save during radiotherapy, and form the basis for clinical guide-lines involving salivary glands [13, 364], the health of submandibular glandsbefore and after radiotherapy is not to be overlooked, as they produce themajority of unstimulated saliva. A loss in submandibular function is alsoknown to induce xerostomia [297]. One study on 36 head and neck patientstreated with IMRT took stimulated and unstimulated saliva measurementsbefore and after radiotherapy, where half of these patients had one sub-mandibular gland spared from high dose levels. After 12 months, the cohortwith one submandibular spared had a mean unstimulated salivary output of60 percent of baseline, while the other cohort had an output of 25 percentof baseline [297]. Another study by Murthy et al. [365] measured sub-mandibular gland functionality before and after radiotherapy using salivarygland scintigraphy and found that the TD50 for less than 45% of baselineexcretion at one and two years post-radiotherapy was 36 Gy and 44 Gy,respectively. TD50 is the dose that predicts toxicity in 50 percent of pa-tients. Murdoch-Kinch et al. [366] collected stimulated and unstimulatedsubmandibular flow rates before and after radiotherapy found that salivaoutput decreased exponentially with dose up to 39 Gy, where it plateauednear zero.Dose to salivary glands is not the only variable predictive of late oral dis-comfort. Dose levels in pharyngeal constrictor muscles and the supraglotticlarynx have been directly associated with late dysphagia [261, 367\u2013369].While saliva-related side effects may seem a trivial burden in exchangefor cancer, it is important to keep in mind that reductions in unstimulatedand stimulated saliva output, leading to xerostomia, significantly reducesperceived quality of life [370].714.3 Current Dose Guidelines for the SalivaryGlandsClinical dose constraints for OARs at BC Cancer are based on recommenda-tions from the Quantitative Analyses of Normal Tissue Effects in the Clinic(QUANTEC) guidelines [371]. The QUANTEC guidelines were developedthrough a comprehensive analysis of available dose volume and outcome datafor various OARs. The objective was to define clinically useful, standardizedrecommendations [372]. It\u2019s important to note that the QUANTEC guide-lines were designed using DVH data, and therefore do not include spatialinformation related to the dose reponse in OARs [372]. Furthermore, theygenerally do not consider fractionation schemes or chemotherapy prescrip-tions.The QUANTEC group\u2019s recommended dose constraint for the parotidglands is to keep the mean dose in both glands below 25 Gy, or to keep thedose in one gland below 20 Gy [373]. This recommendation is based on re-ducing the probability of long term xerostomia, defined as a stimulated salivaoutput of less than 25 percent of baseline at 12 months post-radiotherapy[373]. In 2012, Moiseenko et al. at BC Cancer [374] sought to validate theserecommendations, as well as a recommendation by Ortholan et al. [375]to limit the volume of the glands receiving more than 40 Gy to less thanone third. They assessed whole mouth stimulated saliva in 66 head andneck patients before and after radiotherapy, and found that the QUANTECguidelines were effective for predicting late xerostomia. Otholan et al.\u2019s rec-ommendation was also effective, but had a lower negative predictive valuethan the QUANTEC criteria.As mentioned, BC Cancer\u2019s current parotid gland dose guidelines arebased on the QUANTEC criteria. For both parotid and submandibularglands, the objective is to limit the whole mean dose to at least one of theglands to 20 Gy, or else limit the mean dose of both to 25 Gy. Planning fornasopharynx cancers is particularly challenging due to the close proximityof tumours to critical OARs, and BC Cancer\u2019s recommended guideline inthis case is to limit parotid and submandibular gland mean doses to 30 Gy.72It is common for the submandibular glands to be entirely engulphed bylow-risk nodal tissue which is considered a target volume to be irradiated forlimiting cancerous spread. In these cases, the submandibular glands cannotpossibly meet clinical objectives. This is partially why developing spatiallyvariant dose constraints for parotid glands is of higher priority than devel-oping constraints for submandibular glands. Even with extensive knowledgeof regional importance in submandibulars, as analysed by Clark et al. [13],important regions often cannot be spared as submandibular glands often-times require tumoricidal doses during treatment. Surgical relocation ofsubmandibular glands from high radiation fields prior to radiotherapy hasbeen shown to effectively reduce late xerostomia [376, 377]. Of course, thisis often not a practical course of action due to time and booking constraints.4.4 Evidence for a Heterogeneous Dose Responsein the Salivary GlandsWhile the clinical adoption of whole-mean parotid gland dose constraintshas been shown to reduce the incidence of post-treatment xerostomia [373,374, 378], it fails to account for any possible heterogeneity of the dose re-sponse within the glands. A whole-mean dose constraint may be suitable foran OAR which exhibits purely parallel functionality, but is very problematicfor organs with serial functional mechanisms. An organ has a parallel archi-tecture if damage to one of its subregions does not cause damage to otherregions, while a serial architecture is one where damage to a single subre-gion can result in a loss of function throughout the entire organ. Parotidshave been treated as parallel organs since the inception of radiotherapy [13].The justification for this treatment has been the predictivity of toxic effectsfrom whole mean dose [379], despite this dose response showing high levelsof noise.The current use of DVHs for defining dose constraints inherently ignoresany possible spatial inhomogeneity of the dose response within OARs. Theassumption of spatially homogeneous functional burden within the parotid73glands has been widely criticized by radiobiologists [380\u2013382]. Even be-fore the QUANTEC group developed their clinical recommendations for theparotid gland, evidence for subregional heterogeneity had been published[375, 383\u2013385]. While modulated therapies have improved dose-sparing toparotid glands, there is a need for better-informed dose constraints that canbe used during plan optimization. At a glance, a glaring \u201dnext-step\u201d forcreating modernized treatment planning techniques is to design spatiallyvarying dose constraints within OARs that depend on local functional im-portance (with respect to the health of the whole OAR). Before this is done,the varying dose response within different OARs must be investigated.It is thought that spatially heterogeneous distributions of parenchymawithin OARs results in spatially heterogeneous dose responses [386] Re-cently, an effort by Clark et al. at BC Cancer quantified the heterogeneityof the dose response within parotid glands [12]. They partitioned contralat-eral parotid glands for a single cohort of 332 patients into 2, 3, 4, 18, and 96equal volume subregions and derived the relative importance of each frommean dose regressors using random forests and conditional inference trees.For each patient, the contralateral parotid gland was defined as the gland re-ceiving the lowest mean dose. Parotid gland structure sets and dose profileswere used to calculate the mean dose to various subregions, and outcomeswere described using stimulated saliva output at 1-yr post-radiotherapy andself- assessed xerostomia questionnaires. For 18 subregions, the most impor-tant subregion (caudal\u2013anterior) had a relative importance of 3.85 times theexpected result for a homogenous parotid gland. The least important sub-region exhibited virtually no importance. Important regions of the parotidgland tended towards the caudal-anterior aspect of the gland, with the mostimportant region situated at the caudal-most, anterior-most, middle aspectof the gland (Figure 4.2).74Figure 4.2: Clark et al.\u2019s relative importance estimates in 18 and 96 equal-volume subregions are shown. Axialsubregions are represented as single slices for visual purposes [12]. \u00a9IOP Publishing. This illustration is from\u201cHeterogeneous radiotherapy dose-outcomes response\u201d which was originally published in volume 4:035001 of Con-verg Sci Phys Oncol. (2018) by Clark HD, Thomas SD, Reinsberg SA, Moiseenko VV, Hovan AJ, and Wu JS.Reproduced with permission. All rights reserved.75In another relative importance investigation study, Han et al. [16] as-sessed the relative importance of nine parotid gland subregions for predictinginjury (\u2265 grade 2 xerostomia at six months post-radiotherapy) and recovery(\u2265 grade 2 xerostomia at six months post-radiotherapy, followed by < grade2 xerostomia at 18 months post-radiotherapy). Subregions were defined byfirst applying a 3 mm margin to whole parotid glands, then dividing glandsinto three 120\u25e6 radial sectors (anterior, medial, posterior), then further di-viding these sectors along the inferior-superior axis into three equal-lengthregions. Han et al. [16] determined the relative importance of nine dose-volume statistics in 10% volume increments from D10 (Minimum dose to10% volume) to D90 (Minimum dose to 90% volume) in each subregion.They found that lower dose levels were more important for predicting re-covery than initial injury, and regions of high relative importance tendedtowards the middle portion of the gland relative to the inferior-superiordirection.Van Luijk et al. [15] analysed the relationship between stimulated salivaand radiotherapeutic dose levels, locating \u201ccritical\u201d regions within parotidglands that are highly predictive of salivary outcome at one year post ra-diotherapy. The study did not specify a generalized, algorithmically re-producible location of critical regions; however, it is stated to be in closeproximity of the Stensen\u2019s duct, adjacent to the dorsal side of the mandible.This critical region was found to contain high concentrations of stem cells,whose preservation is critical for the gland\u2019s ability to repair itself followingradiotherapy. Regions of high stem cell density were determined accordingto the expression of c-Kit+ cell surface markers [387]. A recent clinical trialthat tested the ability of dose-sparing in critical regions to preserve parotidgland function found no significant preservation of function [388].Buettner et al. [14] evaluated the predictive ability of various dose \u201cmo-ments\u201d in a regression model for post-treatment xerostomia in 63 head-and-neck cancer patients, treated with either IMRT or conventional radiotherapy.Important variables included mean dose to the superficial lobe, skewness ofdose in the cranial-caudal direction within the deep and superficial lobe,and relative concentration of dose in the caudal-medial region of the deep76lobe. While the parotid glands were only segmented into superficial anddeep lobes, dose moments calculated within these regions correspond to ge-ometrical dose distributions and thus revealed the spatial variance of thedose response throughout the gland. Buettner et al. found the superficialand the deep lobe to be of high relative importance, with high importanceconcentrating slightly towards caudal regions. The caudal-medial subregionof the deep lobe was predicted to be of high importance.The models of Clark et al., Han et al., Van Luijk et al., and Buettner etal. are cross-examined with PSMA PET uptake in Chapter 9. Clark et al.\u2019smodel is used \/ analysed the most throughout the research contributions inthis thesis, as it has numerous advantages over other models. One majoradvantage that Clark et al.\u2019s and Han et al.\u2019s models have over Van Luijket al.\u2019s and Buettner et al.\u2019s is that they create well-defined, calculablesubregions throughout the gland that can be easily segmented on a patient-to-patient basis. This behaviour lends itself well to the practical purposeof defining and applying regional dose constraints corresponding to relativeimportance. Clark et al.\u2019s model has the added advantage over Han etal.\u2019s that subregions are of equal volume. This feature of subregions, alongwith reports on the linear dose response of the glands [389], allows derivedimportance values for subregions to be interpreted as regional criticality forpredicting late salivary dysfunction [12]. Of course, Clark et al.\u2019s modelis also convenient for further investigating as it was derived at BC Cancerusing institutional data.4.5 The Tubarial GlandsIt\u2019s not often the case that a scientific discovery will attract sufficient atten-tion for major news coverage. However, an interesting finding by a team ofDutch physicians and scientists, Valstar et al. [17] in 2021 was significantenough to appear in a CNN article [390, 391]. This was the discovery of the\u201ctubarial glands.\u201dUpon evaluating PSMA PET uptake in the head and neck region ofprostate and urethral cancer patients, Valstar et al. noticed a consistent77pattern of high bilateral uptake in the posterior nasopharynx. Uptake levelsin these regions were similar to those found in the major salivary glands, andthe regions did not correspond to any known anatomical feature expectedto have distinguished uptake [17, 392, 393]. Since PSMA ligands in humansalivary gland specimens are expressed on the epithelium of acinar glandularcells [394], it was hypothesized that these newly found regions of high uptakecould have functional importance for saliva production [17].Valstar et al. then formulated a comprehensive analysis which retrospec-tively evaluated PSMA PET uptake in 100 consecutively scanned prostateor urethral cancer patients, performed a human cadaver study (n=2), andtested the correlation of late xerostomia with dose in these regions. All 100PSMA PET scans demonstrated clear bilateral uptake regions in the poste-rior nasopharynx, with an average height of 4 cm. Uptake levels were foundsimilar to those in the sublingual glands, and higher than levels in minor sali-vary glands of the palate [17]. The human cadavers revealed aggregations ofprimarily mucosal salivary tissue, with several macroscopic drainage ductsvisible. Glands extended from the pharyngeal wall to the Rosenmu\u00a8ller\u2019sfossa. They furthermore reported T2 MRI signals in these regions that wereconsistent with sublingual gland signals. They found dose in these regionsto be predictive of post-treatment xerostomia, independently from dose inparotid glands.Upon these findings, they named these regions the tubarial glands, andpublished the potential benefit of treating these glands as a new OAR inradiotherapy treatment planning. The existence of tubarial glands is notwithout contention. Bikker and Vissink [395] argue that these glands shouldnot yet be termed \u201csalivary glands,\u201d as they do not contribute to oral fluidin the oral cavity, and the histopathology suggests they are a collection ofminor glands rather than single major glands. In a reply to comments,Valstar et al. [396] respond by noting that there is no evidence that thetubarial glands do not contribute to the oral fluid, that saliva is not strictlydefined, and that all fluids contributing to the mixture in the oral cavity canbe called saliva. Furthermore, they claim that the excretory duct openings oftubarial glands are macroscopically visible, and the major and minor gland78classification system is limited. In another response to the original article[397], it is argued that there is no hard evidence for the existence of thetubarial glands, as neither PSMA PET\/CT nor histology can prove theirexistence. The authors responded [396] by noting that they did not claimthe existence of the glands based on either of these methods of discovery,but rather convey that the tubarial gland tissue has not previously beenconsidered as salivary gland tissue but may need to be considered as anOAR for radiotherapy.The reception to the tubarial gland findings has not been entirely nega-tive, and some have written follow up review articles to support the originalfindings [398]. Based on the consistent high uptake seen in 100 consecu-tively acquired PSMA PET images, the human cadaver study, and the doseresponse findings, it appears prudent to treat the tubarial glands as OARsfor head and neck radiotherapy planning. Unfortunately, this finding hasnot yet seen wide-spread clinical consideration.79Part IIResearch Contributions80Chapter 5SimultaneousSuper-Sampling and PartialVolume Correction of PSMAPET Images5.1 IntroductionProstate-specific membrane antigen (PSMA) positron emission tomog-raphy (PET) is an imaging modality typically used for the detection ofprostate cancer [399]. For these purposes, one side effect is the accumu-lation of PSMA ligands in salivary and lacrimal gland tissue, resulting inunwanted dose to these regions [400\u2013402]. However, this can be exploitedfor PSMA PET to identify intra-salivary gland parenchyma, which is anarea of active research in the context of radiotherapy treatment planning[12, 14, 15].Quantifying uptake statistics in the relatively small size of salivary glandsis difficult, due to partial volume effects (PVEs) associated with the intrinsi-cally low resolution of PET imaging [403], which is typically over 5 mm [404].PVEs in PET images primarily correspond to spill-over between image vox-The content of this chapter has been submitted for publication in a peer-reviewedjournal. The name of the article is, \u201cNeural blind deconvolution for simultaneous partialvolume correction and super-sampling of PSMA PET images,\u201d and the co-authors areCaleb Sample, Arman Rahmim, Carlos Uribe, Franc\u00b8ois Be\u00b4nard, Jonn Wu, and HaleyClark.81els due to the positron range and point-spread function of the scanner [405].Patient motion, and poisson-distributed noise due to low photon counts,further exacerbates blur in PET images. While official SNMMI guidelinesrecommend using the maximum standard uptake value (SUVmax) in sin-gle voxels for uptake metrics [406], maximum uptake values are affected by\u201cspill-in\u201d from neighbouring voxels and would be expected to differ if PVEscould be mitigated.There have been attempts to mitigate partial volume effects in PETimages using analytical methods [405, 407\u2013410], with most traditional ap-proaches involving estimation of the point spread function. These methodsare not applicable in the case of collaborative studies involving multiplescanners, or where the point spread function is unknown.The ill-posed problem of simultaneously estimating the theoretical \u201cde-blurred\u201d image, x, along with the spread-function or blur kernel, k, fromthe original image y, is referred to as blind deconvolution.y = x \u2217 k (5.1)Traditional maximum a posteriori (MAP)-based methods require estima-tions for the prior distributions of the kernel and deblurred image and specialoptimization techniques to avoid convergence towards a trivial solution.MAP-based methods are governed by the equation(k,x) = argmaxk,xPr(k,x|y) = argmaxk,xPr(y|k|x)Pr(x)Pr(k) (5.2)where Pr(y|k|x) is the fidelity term likelihood and Pr(x) and Pr(k) arethe priors of the deblurred image and blur kernel, respectively. Many priormodels have been suggested [411\u2013416], but are generally hand-crafted andinsufficient for accurate modelling of x and k [417].In 2020, Ren et al. [417] developed \u201cneural blind deconvolution\u201d for es-timating the deblurred image and blur kernel from 2D natural images usingtwo neural networks which are optimized simultaneously, as opposed to tra-ditional MAP-based methods which generally employ alternating optimiza-82tion to avoid a trivial solution[417]. This is a self-supervised deep learningmethod that does not involve a separate training set, but instead learns topredict deblurred images independently for each image. Neural blind de-convolution out-performed other traditional methods based on prediction\u2019speak signal-to-noise ratio, SSIM, and error ratio.In this work, we build off of the development of 2D neural blind decon-volution [417, 418], implementing changes to the network architecture andoptimization procedures for suitability with 3D PSMA PET medical images.We also incorporate supersampling to enhance spatial resolution.5.2 Methods5.2.1 Data SetFull-body [18F]DCFPyL PSMA PET\/CT images were de-identified for 30previous prostate cancer patients (Mean Age 68, Age Range 45-81; meanweight: 90 kg, weight range 52 kg-128 kg). Patients had been scanned, twohours following intravenous injection, from the thighs to the top of the skullon a GE Discovery MI (DMI) scanner. The mean and standard deviation ofthe injected dose was 310 \u00b1 66 MBq (minimum: 182 MBq, maximum: 442MBq). PET images were reconstructed using VPFXS (OSEM with time-of-flight and point spread function corrections) (number of iterations\/subsetsunknown, pixel spacing: 2.73\/3.16 mm, slice thickness: 2.8\/3.02 mm). Thescan duration was 180 s per bed position. For appropriate comparison ofvoxel values between patients, patient images were all resampled to a slicethickness of 2.8 and pixel spacing of 2.73 using linear interpolation. HelicalCT scans were acquired on the same scanner (kVP: 120, pixel spacing: 0.98mm, slice thickness: 3.75 mm).Images were cropped to within 6 slices below the bottom of the sub-mandibular glands and 6 slices above the top of the parotid glands. Crop-ping was employed to avoid exceeding time constraints and the 6 GB mem-ory of the NVIDIA GeForce GTX 1060 GPU used for training. RegisteredCT images were used for delineating parotid and submandibular glands for83calculating uptake statistics. Limbus AI [419] was used for preliminary auto-segmentation of the glands on CT images, which were then manually refinedby a single senior Radiation Oncologist, Jonn Wu. Images were scaled sothat voxels ranged between [0,1] prior to deblurring, and afterwards rescaledto standard uptake values normalized by lean body mass (SUVlbm). Leanbody mass was estimated from patient weight and height using the Humeformula [420].5.2.2 Overview of Neural Blind DeconvolutionThe method of neural blind deconvolution as first demonstrated by Renet al. [417] estimates a \u201cdeblurred\u201d version, x, of an actual image, y, bytraining neural networks on a case-specific basis. Specifically, two neuralnetworks, Gx and Gk are trained to predict x, and a blur kernel, k, whoseconvolution together yields a close estimate of the original image, y. Theuse of neural networks for image prediction was motivated by the work ofUlyanov et al. on deep image priors [421]:Gx(\u03b8x) = x , Gk(\u03b8k) = k , y = x \u2217 k (5.3)where \u03b8x and \u03b8k represent trainable model parameters of Gx and Gk, respec-tively. The following implicit constraints exist on network outputs which aresatisfied automatically due to the networks\u2019 architectures.0 \u2264 Gx(\u03b8x) \u2264 1 , Gk(\u03b8k) \u2265 0 ,\u2211iGk(\u03b8k)i = 1 (5.4)Previously, [417] [418] such networks were trained using a loss function in-cluding a mean squared error (MSE) fidelity term along with regularizationterms, R(x,k), wherex,k = argminx,k||x \u2217 k \u2212 y||22 +R(x,k) (5.5)The mathematical formulation of our problem differs slightly as we haveadapted Gx to yield an output image, x which is twice as large as y in each84dimension to accomplish supersampling. Our x is then linearly downsam-pled to the original image size, x\u2193, before being convolved with the kernel.Furthermore, we incorporate a component of mean absolute error into ourloss function\u2019s fidelity term.x,k = argminx,k||x\u2193 \u2217 k \u2212 y||22 + ||x\u2193 \u2217 k \u2212 y||1 +R(x,k) (5.6)This can be written in terms of the model parameters \u03b8x and \u03b8k as\u03b8x, \u03b8k = arg min\u03b8x,\u03b8k||Gx(\u03b8x)\u2193\u2217Gk(\u03b8k)\u2212y||22+||Gx(\u03b8x)\u2193\u2217Gk(\u03b8k)\u2212y||1+R(Gx(\u03b8x), Gk(\u03b8k))(5.7)which can then be optimized via backpropagation of loss gradients.5.2.3 Model ArchitectureNeural blind deconvolution was originally demonstrated on 2D images usinga \u201cU-Net\u201d[422]-style, symmetric, multiscale, autoencoder network for Gxand a shallow fully-connected network for Gk. We built off of this method-ology while implementing some notable changes to optimize model perfor-mance on PSMA PET images. A schematic diagram of the network designis shown in Figure 5.1.Gx ArchitectureAll operations involving Gx were adapted for use with 3D images. Thenetwork includes only 3 layers in the encoder-decoder series (as opposed to 5in Ren et al.\u2019s implementation) [417]. A decrease in network layers is justifiedby the low resolution of PET images, which requires a smaller receptive fieldthan needed for high-resolution images to localize edge features [423]. Anadditional layer was added to the end of the decoder section, including anupsampling operation, and double convolution, to output a final x twice aslarge in each dimension as the original input. This design allows x to besimultaneously supersampled and deblurred within the blind deconvolutionprocess.85Figure 5.1: The blind deconvolution architecture used for deblurring PSMAPET images. Gx is an asymmetric, convolutional auto-encoder network forpredicting the deblurred image, x, and Gk is a fully-connected network forpredicting the blur kernel, k. The convolution of x and k is trained to matchthe original image by using back-propagated model gradients from the lossfunction for iterative optimization.Rather than iteratively increasing channels towards deeper regions ofthe encoder and decoder, we found that reversing the design such that thechannel count decreases towards inward regions of the network producedfavourable results. For each double convolution, the first convolution de-creases the image size via a stride of 2. We included a high number of skipconnection channels (64), as it was found to improve prediction accuracy.Furthermore, we scaled the final sigmoid layer used in previous versionsof neural blind deconvolution [417, 418], as a regular sigmoid constrains thex to have the same maximum value as y. This is not necessarily true, norexpected for the case of partial volume effect correction. We therefore scaledthe final layer by 3\/2.86Gk ArchitectureGk is a single layer perceptron, whose architecture Ren et al. [417] found tooutperform the auto-encoder style design of Gx for the case of predicting thekernel. Model input is a 1-dimensional vector of length 3375, which is fedthrough a fully connected layer with 16,875 nodes, to an output of length3375 which is passed through a SoftMax operation before being reshapedinto a 15 \u00d7 15 \u00d7 15 3D kernel image. The softmax function ensures thatkernel voxels sum to unity, and has the form:\u03c3(ki) =ezi\u22113375j=1 ezj(5.8)5.2.4 Loss Function and OptimizationThe main optimization procedure consisted of 5000 iterations broken into3 stages, stage 1: 0 \u2264 step <300, stage 2: 300 \u2264 step <2000, stage 3:2000 \u2264 step <3500, stage 4: step \u2265 3500. 5000 iterations was chosen asit had been used in previous neural blind deonvolution methods, and fur-thermore because we found this number of iterations to be sufficient for thetraining loss to level out. We implemented a multi-scale pre-training pro-cedure similar to the method recommended by Kotera et al. [418]. Thisinvolves initially training Gx and Gk to predict x and k using 2\u00d7 down-sampled PSMA PET images, which are then upsampled by\u221a2 and usedas input for a second round of pre-training. The output is then upsampledback to the original size to serve as inputs for the regular training stage.We modify the procedure further such that after every upsampling duringpre-training, the models, Gx and Gk are trained to predict their own inputsfor 100 iterations, which was sufficient to allow training in the next scale tobegin by predicting upsampled versions of the predictions in the previouslayer. The size of k varies with the size of x, such that three kernel sizesare used, 7 \u00d7 7 \u00d7 7, 10 \u00d7 10 \u00d7 10, and the original size 15 \u00d7 15 \u00d7 15. Forthe downsampled pre-training of x and k, 1000 iterations were used in eachstage. This number of iterations was chosen to allow the pre-training imageto approximately converge to its final estimate. The initial input vector for87Table 5.1: The optimization algorithm for updating network weights to pre-dict deblurred PSMA PET images. This algorithm builds off of Ren et al.\u2019sproposed joint optimization algorithm [417] and implements modificationssuggested by Kotera et al. [418].Network Optimization AlgorithmInput: Original PSMA PET image, yOutput: Deblurred PSMA PET image, x, and blur kernel, kPre-training1. Downsample y to 1\/2 resolution2. Initialize input zx from uniform distribution to match size of y3. Initialize zk as size 7\u00d7 7\u00d7 7 Gaussian kernel with standard deviation of two voxels4. for i = 1 to 1000:5. x = Gix(zx)6. k = Gik(zk)7. Compute loss and back-propagate gradients8. Update Gix and Gik using the ADAM optimizer [280]9. x = G1000x (zx), k = G1000k (zk)10. Upsample k by 11\/7 and downsample x by a factor of\u221a211. Downsample y by\u221a2 to match new convolution size12. zx = x , zk = k13. Repeat steps 4 through 9.14. Upsample k by 15\/11 and downsample x by a factor of\u221a215. zx = x , zk = kMain Training16. for i = 1 to 5000:17. x = Gix(zx)18. k = Gik(zk)19. Compute loss and back-propagate gradients20. Update Gix and Gik using the ADAM optimizer [280]21. x = G5000x (zx), k = G5000k (zk)Gk was a Gaussian Kernel with a standard deviation of two voxels, and theinitial input vector for Gx was a pseudorandom-generated array, sampledfrom a uniform distribution. The loss function components for each stageare summarized in Table 1. The parameters of Gx and Gk were updatedusing the ADAM optimizer [280].It was previously reported by [418] that adopting a total variation (TV)loss term biases outputs towards a trivial solution during the initial stagesof training, but improves image quality as predictions near the final, correctsolution. We experienced similar findings, and therefore implemented a TVloss term only after the first 2000 iterations. After the first 3500 iterations,88Table 5.2: Loss Function components used for optimization of Gx(\u03b8x) andGk(\u03b8k). To guide training during the first 300 optimization steps, the Struc-tural Similarity Index Measure (SSIM) is minimized between the deblurredimage x\u2193 and the registered CT\u2019s texture map. Conditions are invoked onthe kernel estimate until the final 1500 steps of optimization. TV loss isintroduced after the first 2000 steps, to avoid convergence towards a trivialsolution.0 \u2264 step <300 300 \u2264 step <2000 2000 \u2264 step <3500 step \u2265 3500MSE + MAE MSE + MAE MSE + MAE SSIMCT Texture SSIM Kernel MSE Kernel MSE TVKernel MSE TVthe fidelity term of the loss function transitions from a combination of MSEand MAE to the structural similarity index metric, which was also found toboost performance during final stages [418].During the first 300 iterations of training, we employ registered com-puted tomography (CT) images to provide anatomical guidance. This isimplemented by including a SSIM loss term involving x and a CT texturemap of the grey level run length matrix (GLRLM) with a long run emphasis,computed with pyradiomics [424]. We opted to use the texture map as op-posed to the regular CT image as CT texture maps have been demonstratedto have a closer correlation with PSMA PET uptake [425] than standardimages. CT guidance is used to steer outputs towards the correct solutionduring the the first 300 steps of training before being dropped, to preventcompetition with the fidelity term as outputs move closer towards final esti-mates. A previous study using traditional MAP-based blind deconvolutionof PET images demonstrated the utility of magnetic resonance images forguiding optimization [426\u2013428].A cumbersome challenge in performing a blind deconvolution is avoidinga trivial solution, x \u2217 k = x \u2217 \u03b4 = y [429\u2013431]. It is therefore necessary toimpose regularization on kernel predictions. Previously, [417, 418] appliedan \u21132 norm constraint to the kernel to avoid convergence to a delta function.We also applied an \u21132 norm term; however, we only penalized kernel valueslarger than 0.7, to avoid a trivial solution while not penalizing small- tomid-range values in the kernel.895.2.5 Evaluation MetricsAs our model was developed on true diagnostic PSMA PET images, groundtruth deblurred images are not available, and we therefore adopted a varietyof strategies and metrics for evaluating the quality of predicted deblurredimages and the model\u2019s ability to predict accurate blur kernels.We compare two quantitative blind image quality metrics between xand y. First of all, we compare images via the Blind\/Referenceless ImageSpatial Quality Evaluator (BRISQUE) score [432], which varies between 0and 100, indicating the lowest and highest possible quality, respectively.Secondly, we compare images using the Contrastive Language-Image Pre-training (CLIP) metric [433] which varies between 0 and 1. BRISQUE takesan input image and computes a set of features using the distribution ofintensity and relationships between neighbouring voxels. It then predictsits image quality from its predicted deviation from a natural, undistortedimage. CLIP is a multi-modal (language and vision) neural network trainedwith millions of image\/text pairs. The model can be used for predicting bothimage quality and image caption quality. The clip network predicts imagequality by ranking the applied captions \u201cgood photo\u201d and \u201cbad photo\u201d.CLIP was compared with numerous other quality metrics and was found toperform second to only BRISQUE.To validate the model\u2019s ability to accurately recover the blur kernel,rather than arbitrary or semi-random shapes imposed by the loss func-tion\/optimization, we generated four types of \u201cpseudokernels\u201d and con-volved them with predicted deblurred images, which were then fed backinto the blind deconvolution model. We could then test the models abilityto predict a kernel by comparing the newly predicted kernels with pseu-dokernels. Ideally, the model would predict the pseudokernel as the blurkernel, and thus they would be exactly the same. The generated pseudoker-nel shapes included a regular gaussian, and 3 gaussians skewed in either thex, y, and z direction. The similarity between pre-constructed and predictedpseudokernels was measured by taking the inner product of normalized ker-nel images.90The theoretical blur kernel of PET images has a component resultingfrom the point spread function of the scanner, as well as other limitations andpatient motion. Since all PET images were acquired on the same scanner,with the same image collection protocol, it is expected that predicted blurkernels should have high inter-patient similarity, Kernels were comparedbetween patients quantitatively by taking the inner product of normalizedkernel images.5.3 ResultsFor the two tested blind image quality metrics, BRISQUE and CLIP, de-blurred images out-ranked original images upsampled using nearest-neighbours,linear, quadratic, and cubic interpolation. These results are summarized inTable 6.4.Table 5.3: Blind image quality metrics, CLIP and BRISQUE are comparedfor original (y) and deblurred (x) PSMA PET images. For appropriate com-parison, y was upsampled by 2 in each dimension to match the size of x.In the first column, y is upsampled using nearest neighbours interpolationto remain visually identical. We also compared the quality of y when up-sampled using linear, quadratic and cubic interpolation (y\u21911 ,y\u21912 ,y\u21913). Forboth BRISQUE and CLIP, larger values indicate higher quality. The rangeof possible CLIP and BRISQUE values are over the interval [0,1] and [0,100]respectively.Original Polynomial Interpolation Proposed Methody y\u21911 y\u21912 y\u21913 xCLIP 0.19\u00b1 0.03 0.33\u00b1 0.05 0.32\u00b1 0.05 0.32\u00b1 0.05 0.39\u00b1 0.04BRISQUE 75.8\u00b1 8.1 89.6\u00b1 5.4 85.0\u00b1 6.3 84.8\u00b1 6.32 90.5\u00b1 7.591Figure 5.2: A: a deblurred maximum intensity projection image and B: axial projection of the predicted kernelare shown, along with C: the maximum intensity projection of the convolution of the deblurred image and kernel,which is trained to match D: the original image, on the right. The inferior aspect of the tubarial glands are visiblebetween the parotid glands.92A maximum intensity projection of x, k, x \u2217 k, and y are shown for asingle patient in Figure 5.2 and visual comparisons of original and deblurredPET image slices including parotid glands and submandibular glands areshown for 3 different patients in Figure 5.3. Maximum intensity projectionimages are shown through the head and neck in Figure 5.4.Figure 5.3: Axial slices intersecting parotid glands (left) and submandibularglands (right) for 3 different patients are shown on original and deblurredimages.Predicted blur kernels displayed low inter-patient variability, having amean inner product between different patients of 0.73. A heat-map of allinter-patient inner products is found in Figure 5.5.Projections of the mean predicted kernel onto the three standard carte-sian planes are found in Figure 6.3. Predicted kernels were found to bemostly symmetric, with small deviations in skewness found from patient-to-patient. The distribution of the kernel in various patient directions is93summarized in Table 5.4, with maximum variation found in the anterior-posterior direction. Kernels were found to display a centred peak, whichrapidly fell off to less than 0.01 when two voxels from the center in anydirection.The mean absolute difference of the total activity found within all voxelsof original and deblurred images varied by less than 0.05 \u00b1 0.07%. Thepredicted blurred image, x \u2217 k, and the original image, y, had a MAE andMSE of 0.013\u00b1 0.004 SUVlbm and 0.003\u00b1 0.001 SUVlbm, respectively.Table 5.4: The fraction of the kernel contained within a plane oriented ineach Cartesian direction and intersecting the center of the kernel image,averaged over all patients. For example, the average blur kernel has a sumof 0.52 anterior to the center point.Anterior Posterior Superior Inferior Left Right0.52\u00b1 0.07 0.48\u00b1 0.07 0.49\u00b1 0.05 0.51\u00b1 0.05 0.51\u00b1 0.05 0.49\u00b1 0.05Pseudokernels applied to deblurred PET images were predicted well,with mean inner products of predicted and generated pseudokernels above0.90 for each of the 4 types of pseudokernel applied (regular Gaussian, andskewed Gaussian along 3 patient axes). These results are displayed in Fig-ure 5.7.Deblurred images appeared to be visually sharper than original images.Since x is double the size of y, we upsampled y using nearest-neighbours,linear, quadratic, and cubic interpolation for comparison\u2019s sake. Side byside images are found in Figure 5.8.Deblurred and original images of parotid glands are shown in axial, coro-nal and sagittal plane slices in Figure 5.9.Cohort uptake statistics within CT-defined salivary glands, calculatedusing both original and deblurred images, are listed in Table 5.5. Maximumuptake values in both parotid and submandibular glands were significantlyhigher in deblurred images (p < 0.01), and mean uptake values were insignif-icantly higher. Uptake plots are shown over corresponding lines throughparotid and submandibular glands in Figures 5.10 and 5.11. The gradientof uptake from 0.5 SUVlbm to the full width at half-maximum (FWHM)94Table 5.5: PSMA PET uptake statistics in CT-defined salivary glands aresummarized using both original and deblurred images.Parotid SubmandibularOriginal Deblurred p-value Original Deblurred p-valueSUVmax 16.2\u00b1 4.6 21.0\u00b1 6.2 p < 0.001 15.9\u00b1 3.9 20.2\u00b1 5.2 p < 0.001SUVmean 7.1\u00b1 1.9 6.7\u00b1 1.8 p < 0.001 7.1\u00b1 1.8 7.8\u00b1 2.2 p < 0.00195Figure 5.4: Maximum intensity projections of deblurred (left) and original(right) PSMA PET images are shown through the head and neck in theaxial (top), coronal (middle) and sagittal (bottom) planes.96Figure 5.5: The inner product of recovered blur kernels predicted for all 30patients is represented by a heat map. Blur kernels for PET images arecaused by both scanner limitations as well as patient motion, so kernels areexpected to be similar, but not identical. Diagonal elements are all equal tounity by definition. The mean inner product, excluding the diagonal terms,is 0.73.97Figure 5.6: The mean predicted kernel is projected onto the 3 standardpatient planes. The predicted blur kernel was found to be mostly symmetric.Figure 5.7: To validate the model\u2019s ability to predict accurate blur kernels,4 variously skewed pseudo-kernels were applied to deblurred images beforere-running the blind deconvolution. Generated pseudo-kernels (k\u2217, left) andtheir corresponding predicted kernel (k, right) are shown in separate rowsfor each of the 4 pseudo-kernel shapes, in axial, coronal, and sagittal imageslices. The dot-product of normalized kernels, k\u2217 \u00b7 k, was used to assesskernel similarity.98Figure 5.8: Predicted deblurred images, x are twice the original resolution,and we therefore tested whether perceived improvements in image qual-ity were only due to the size difference by up-sampling the original imageusing nearest neighbours, linear, quadratic, and cubic interpolation. Thedeblurred image (right) appeared to have the best quality.99Figure 5.9: PSMA PET image slices through parotid glands are shown in theaxial (top), coronal (middle) and sagittal (bottom) planes, in both original(left) and deblurred (right) images.100Figure 5.10: An axial slice through the original (left) and deblurred (right)PSMA PET images, intersecting the parotid glands is shown, along with ared line whose corresponding uptake plot is shown below. The deblurredimages are found to have smaller partial volume effects, as demonstrated bya more rapid ascent to the full width at half maximum, as shown on lateraledges. In this case, the rise to FWHM was twice as steep in the deblurredimages.101Figure 5.11: An axial slice through the original (left) and deblurred (right)PSMA PET images, intersecting the submandibular glands is shown, alongwith a red line whose corresponding uptake plot is shown below. The de-blurred images are found to have smaller partial volume effects, as demon-strated by a more rapid ascent to the full width at half maximum, as shownon lateral edges. In this case, the rise to FWHM was more than twice assteep in the deblurred images.102is approximately twice as steep for deblurred images than their originalcounter-parts. The deblurred images display internal heterogeneity withinparotid and submandibular glands that appears unresolved in original im-ages. Axial, coronal and sagittal slices of fusion PET\/CT images are shownfor both deblurred and original images in Figure 5.12.5.4 DiscussionBased on blind image quality metrics and visual appearance, neural blind de-convolution helped mitigate PVEs and improve overall image quality. Qual-ity improvements were a demonstrated result of the blind deconvolutionprocess, and not only standard upsampling, as shown by comparing resultswith original images upsampled using various polynomial interpolation or-ders. The intrinsically low spatial resolution of PET imaging, and conse-quent PVEs [434], render PVE correction a necessary task when quantifyinguptake in small image regions. Furthermore, PVE correction of PET im-ages has been shown to increase the statistical significance of correlationsbetween uptake bio-markers and various clinical endpoints and prognosticindices [435\u2013439].Predicted blur kernels were consistent with anticipated sizes and shapes,being small (generally no more than 3 voxels across in any direction withvalues larger than 0.01) and mostly symmetric. By observing uptake fall-offat body borders in original images, it appears that PVEs cause small spill-out to distances larger than one voxel, but neural blind deconvolution cannotdetect such small blur components. For model validation, it was essentialthat predicted kernels shared similarities between patients. The low but non-zero inter-patient variability of predicted kernels was as expected, which canbe considered to be an unknown combination of the point spread function,scanner limitations, patient motion and other artifacts.An advantage of neural blind deconvolution over traditional blind decon-volution methods [440] for mitigating PVEs in PET images is that it doesnot require prior assumptions of the PSF to be imposed. A review of var-ious blind deconvolution algorithms (excluding neural blind deconvolution)103Figure 5.12: From top to bottom, axial, coronal, and sagittal image slicesare shown for both deblurred (left) and original (right) PSMA PET\/CTfusion images.104applied to natural images [441] found that the shift-invariant assumption forthe blur kernel is often incorrect, which possibly explains a portion of thevariance seen in predicted kernels. The proposed method assumes a uniformblur kernel, such that the image can be modelled as y = x \u2217 k. However,it is known that PET image blur is dependent on radial distance from theisocentre (radial astigmatism) [147, 442], so this methodology could likelybe improved by modifying the training algorithm to incorporate a spatiallyvarying kernel. However, due to the static nature of the PET scanner, itis likely that this variance is less pronounced here than in cases of naturalimage acquisition using hand-held devices.The model\u2019s capacity to predict pseudokernels convolved with previouslydeblurred images validated its ability to predict various kernel shapes ratherthan simply Gaussian shapes. All generated pseudokernel shapes were pre-dicted with high accuracy, but it is notable that the highest accuracy (meaninner product = 0.98) was found for pseudokernel\u2019s that were stretched ontoprimarily one axial slice, and all kernel\u2019s stretched onto primarily one axiswere predicted with a higher accuracy than the symmetric Gaussian kernel.This may be due to the slightly larger slice spacing than pixel spacing (ratioof 1.025), as it is unclear what mechanism in the model architecture wouldresult in increased predictive power of axially flattened kernels.This deblurring methodology for PSMA PET requires further explo-ration. A phantom study would be useful to quantify improvements inboundary delineation upon deblurring. Due to the nature of this unsuper-vised deblurring algorithm, it is difficult to assess physical improvementsin in Vivo PSMA PET uptake. As discussed, we did quantify the model\u2019sability to accurately predict blur \u201cpseudokernels,\u201d and found that kernelpredictions across patients had similar patterns. These findings, along withimprovements in blind image quality metrics, BRISQUE and CLIP, andsharpened ROI uptake boundaries do support this methods ability to im-prove image quality. It is particularly important to further explore the affectof deblurring on the SUVmax in lesions. Partial volume correction in smallregions of high uptake leads to increased maximum uptake values whichmust be considered when deblurred and original images are compared.105Previous approaches to super-resolution of PSMA PET images typicallyseek to reconstruct images of standard quality using lower than standarddoses [443\u2013446]. These methods use supervised learning to train models topredict known\u201cground truth\u201d high resolution images from their lower reso-lution counterparts. Other approaches acquire standard images at multiplepoints of view and attempt to reconstruct single images of supersampledresolution [447]. In contrast, the present approach seeks to supersample re-constructed images of standard quality to higher than standard resolution,using self-supervised learning. Therefore, ground truth images do not ex-ist in the present study for a direct comparison of real and predicted highresolution images. We therefore relied on assessing improvements in blindimage quality metrics, and testing kernel similarity between patients andthe model\u2019s ability to accurately predict pseudokernels.To directly compare the present method with previous supersamplingtechniques [443\u2013446], a potential study could acquire both low and highresolution PSMA PET images, and then apply the present method to thelow resolution images. The acquired \u201chigh resolution\u201d images could thenbe compared with predicted values. This allows for direct quantification ofsupersampling quality.The performance of neural blind deconvolution on 2D natural imageswas previously found to out-perform other deblurring approaches [417, 418].A fundamental difference between applying deblurring approaches to PETimages vs natural images is that \u2018still\u2019 natural images can typically be takenas ground-truth images, while \u2019still\u2019 PSMA PET images have intrinsic blur.This makes it especially challenging to assess deblurring approaches ap-plied to PET images. It was not possible to directly assess the accuracy ofpredicted blur kernels, as true blur kernels are unknown, and can only beestimated from the scanner\u2019s point spread function, which is a source of un-certainty that burdens traditional blind deconvolution a posteriori analyses.A great advantage of self-supervised learning over supervised learningdeep learning algorithms is that a large training set is unnecessary. This isespecially important in the case of PSMA PET deblurring, PSMA PET iscostly [448], making it difficult to acquire large datasets. A self-supervised106approach to super-resolution of PET images using generative adversarialnetworks [449] has had demonstrated success, despite its use of 2D ratherthan 3D convolutions.While in the traditional U-Net architecture as well as previous neuralblind deconvolution studies, the channel count increases towards deeper re-gions of the encoder and decoder [417, 418, 422], we discovered that largerchannel counts towards outside regions of the network, decreasing towardsthe bottom of the encoder and decoder, performed most accurately. Fur-thermore, including a large number of skip connection channels (64 each)greatly improved performance. This is likely due to increased high-levelfeature extraction at the top of the network allowing for ultimately betterimage reconstruction, along with bottle-necking in deeper regions leadingto improved learning of important features [450]. Our modelling power waslimited by time and GPU resources, and we were unable to test whetherscaling all channel counts further could improve results. The model code isavailable for download online [451].Image quality appeared higher within the high uptake regions of salivaryglands as well as other low uptake regions. Before adopting the combinationof MAE and MSE used in the loss function, we used only MSE as in previousliterature[417, 418], but found that this lent itself poorly to the highly skeweddistribution of PSMA PET uptake. Adding in MAE allowed appropriatepenalization of discrepancy in lower-uptake regions, leading to higher overallquality. We found that decreasing the number of autoencoder layers in Gxfrom 5 to 4 or 3 had no perceived affect on the model\u2019s predictive power, andopened up GPU memory for more channels to be added to the remaininglayers. We experimented with various numbers of hidden layers and channelcounts in Gk and found that a single layer with 5 times the number ofchannels in the flattened kernel image worked best.PET imaging suffers from intrinsically low resolution, resulting in appar-ent partial volume effects. We have demonstrated neural blind deconvolu-tion to be a viable post-reconstruction method for mitigating these effects.As opposed to traditional maximum a posteriori methods for estimatingdeblurred images, neural blind deconvolution allows for simultaneous es-107timation of x and k without convergence towards a trivial solution. Wehave built off of previously demonstrated 2D natural image architectures[417, 418] to create a suitable architecture for 3D PET images. Inclusionof the CT texture map for steering optimization during early stages helpedguide training towards a centered kernel, as opposed to an off-centered ker-nel and deblurred image, which when convolved, predict a centered imagefor comparison with the original image. Use of CT images for guiding blinddeconvolution relies on accurate image registration. The GLRLM with along-run emphasis was used rather than the original CT im age, due to itslower contrast which matches PSMA PET better, and due to our previousfindings which demonstrated a strong correlation between PSMA PET up-take and the CT GLRLM [425]. Initially, a joint entropy loss function wasused rather than SSIM, however, this relies on voxel-binning which causesproblems during gradient calculation for back-propagation. Regularizationof the kernel was necessary for avoiding a trivial solution. However, once aMSE penalty was applied to kernel values greater than 0.7, the model con-verged to non-trivial solutions for all patients. Maximum kernel values weregenerally less than 0.4, so our kernel constraint did not arbitrarily constrainthe maximum value found in predicted kernels to a set value.This analysis was performed on a dataset of previously reconstructed im-ages, without access to raw scanner data. VPFXS had been previously cho-sen for clinical image reconstruction over BSREM\/Q.Clear [452, 453] for con-sistency across scanners (which did not all have access to BSREM\/Q.Clearreconstruction algorithms). The voxel size is an important acquisition pa-rameter whose modification is sure to affect model performance. The de-pendence of model performance on voxel size would make for an interestingfuture study. Many other acquisition and model parameters can be fur-ther fine-tuned for optimal performance. Future studies seeking to enhancePSMA PET with neural blind deconvolution should maintain a consistentvoxel size across patients for the sake of comparison.PSMA PET uptake is heavily biased towards the salivary glands thanother regions in the head and neck, as seen in figures. A previous studyhas demonstrated heterogeneous uptake of PSMA-PET in parotid glands108[425], and mitigating partial volume effects using neural blind deconvolu-tion appears to make this effect more pronounced. The tubarial glands [17]appeared with greater definition in deblurred images, as two distinct regionsof high uptake. Maximum uptake regions were better localized in deblurredimages, resulting in increased overall maximum values, as well as slight in-creases in whole-gland means. These results are too be expected, due tomitigated spill-out and spill-in of voxel values around maximum values, andspill-out near gland edges. The total activity in original and deblurred im-ages remained constant, which was necessary in the context of PET imaging.Originally, we included a separate total activity constraint in the loss func-tion, but found this redundant since our fidelity term accomplished thisgoal.Supersampling during neural blind deconvolution is not limited to doublescaling, and the demonstrated model architecture can easily be amended foraccommodating additional resizing. Furthermore, the methodology couldbe adapted for kernels to be first convolved with deblurred images beforedownsampling to compute the fidelity loss. Our methodology was limitedby time and computation resources.Deblurring and supersampling PSMA PET images was motivated bythe challenge of quantifying uptake in small spatial regions of images, suchas the salivary glands, where partial volume effects become increasinglyproblematic. Prostate specific membrane antigen (PSMA) positron emissiontomography (PET) has high ligand accumulation in the parotid glands [400\u2013402], and has been suggested to relate to whole-gland functionality [180\u2013182]. Heterogeneity of PSMA PET uptake trends in salivary glands can beanalysed with greater fine detail brought out by deblurring \/ supersampling.PSMA PET has the unique potential to quantitatively investigate salivarygland physiology, which could potentially lead to better understanding oftheir functionality as relevant for radiotherapy treatment planning.PSMA PET is primarily used for detecting and staging prostate can-cer, and deblurring\/supersampling with neural blind deconvolution couldimprove fine detail in small lesions, leading to better localization. Thismethodology has the potential to improve target localization for treatment109planning and reduce the rate of false negative lesion detection. Greater lo-calization ability will lead to better estimation of lesion volumes and bettermonitoring of treatment outcomes. Further retrospective in Vivo or phan-tom studies are needed to validate this methodology before it can be used toenhance clinical scans. Use of SUVmean over SUVmax will likely be necessaryfor characterising regions of interest as super-resolution algorithms continueto develop and gain clinical confidence, as thdenoie SUVmax is more sensitiveto partial volume effects in small regions.5.5 ConclusionIn this work, we have adapted neural blind deconvolution for simultaneousPVE correction and supersampling of 3D PSMA PET images. PVE correc-tion allows for fine detail recovery within the imaging field, such as uptakepatterns within salivary glands. Leveraging the power of deep learning with-out the need for a large training data set or prior probabilistic assumptions,makes neural blind deconvolution a powerful PVE correction method. Ourresults demonstrate improvements in quality metrics of deblurred imagesover other commonly used supersampling techniques. The model code isavailable online for further studies [451].110Chapter 6Image Denoising andModel-IndependentParameterization ForImproving IVIM MRI6.1 IntroductionIntravoxel Incoherent Motion (IVIM) Magnetic Resonance Imaging (MRI)is a diffusion imaging technique which quantifies the translational motion ofmolecules within imaging voxels [454]. This translational motion is due tothe random diffusion of water molecules within tissue, as well as perfusioneffects. These translational motions are inferred by analyzing signal decay ineach voxel as a function of applied diffusion gradient strengths (b-values). LeBihan first introduced a method of quantifying these in vivo motions usingStejskal and Tanner\u2019s [75] diffusion gradient method in 1986 [83]. This paperintroduced the concept of an \u201capparent diffusion coefficient\u201d (ADC). Thepseudodiffusion coefficient quantifies the combined effects of real diffusiondue to random molecular motion and the randomly oriented microcirculationof blood in capillary beds. By acquiring signals using multiple diffusion b-The content of this chapter has been submitted for publication in a peer-reviewedjournal. The name of the article is, \u201cImage deblurring and model-independent parameter-ization for improving IVIM MRI,\u201d and the co-authors are Caleb Sample, Jonn Wu, andHaley Clark.111values, the ADC can be determined using the equation,S(b)\/S(0) = e\u2212ADC\u00b7b (6.1)which is analagous to Stejkal and Tanner\u2019s in vitro diffusion equation for astill liquid, S(b)\/S(0) = e\u2212D\u00b7b [75], where D is the self-diffusion coefficient ofthe liquid. The ADC is a simple metric for describing the signal decay curvein vivo; however, it does not model real diffusion, and is only a method ofapproximating the biological mechanisms responsible for the observed signaldecay seen with increasing diffusion b-values. An important difference isthat Stejskal and Tanner\u2019s diffusion equation comes from directly solvingthe Bloch equations [55] for the magnetization vector, M\u20d70, as a function oftime, while Le Bihan\u2019s application of this equation to in vivo motion is anapproximation based on this derivation. The most useful way to interpretthe ADC is to think of it as simply a parameter for approximating the invivo signal versus b-value curve as an exponential decay curve.It is theorised that contributions of diffusion and perfusion motion tothe signal decay can be disentangled by fitting appropriate models to thesignal decay curve in each voxel, as originally posed by Le Bihan in 1988[455]. This operates by modelling the collective perfusion of blood throughmicrocapillaries as a \u201cpseudodiffusion\u201d process, with a pseudodiffusion coef-ficient, D\u2217. D\u2217 is typically on the order of 10 times larger than D [454], andtherefore, the signal decay is largely attributed to perfusion at low b-values,and diffusion at high b-values [456]. A common approach for separatingdiffusion and pseudodiffusion in practice is to apply a biexponential signaldecay model to the data,S(b)\/S(0) = f e\u2212b\u00b7D\u2217+ (1\u2212 f) e\u2212b\u00b7D (6.2)where f denotes the fraction of the signal decay attributed to pseudodiffusionwithin a voxel.Reproducibility of the pseudodiffusion coefficient remains a long-standingissue while D and ADC have been shown to exhibit higher stability [18\u201323].112f and D\u2217 have been shown to have inferior reproducibility to D; however, fhas been shown to be empirically useful for predicting age in nervous tissue[85, 86].In recent years, the literature has seen a shift towards adoption of atriexponential model [87\u201392] of the formS(b)\/S(0) = f1 e\u2212b\u00b7D\u22172 + f2 e\u2212b\u00b7D\u22172 + (1\u2212 f1 \u2212 f2) e\u2212b\u00b7D (6.3)Model-fit uncertainty can be reduced by introducing an extra exponentialterm [88\u201392]; however, it remains to be seen whether these parameters arereproducible or have practical physiological interpretations.It is uncertain whether attempts to separate diffusion from perfusion areeffective, as it has been reported that fitting a mono-exponential function,S(b)\/S(0) = (1\u2212f) e\u2212b\u00b7D is more reliable than a bi-exponential fit for differ-entiating pathological grades of esophageal squamous cell carcinoma (ESCC)[23]. Heightened measurement error of signal at low b-values [102, 103] leadsto sub-optimal conditions for estimating perfusion effects, and estimation ofADC in low b-value regions has shown poor reproducibility [104]. Noise-levels have also been shown to greatly impact parameter estimates [105].Poor reproducibility of perfusion-related parameters could be partiallyexplained by over-simplification of physiological processes inherent in sim-ple exponential models, as it has been shown that the optimal choice ofmodel is dependent on tissue type [106]. It is without doubt that, in reality,each imaging voxel containing biological tissue will encompass a complexarrangement of micro-structures, all having various perfusion fractions andmolecular motion. Kuai et al [87] used simulated data with 2-5 perfusioncomponents to show that the variance of f and D\u2217 tend to increase as thenumber of perfusion components increases, or the difference between pseu-dodiffusion components increases.Reproducibility of IVIM parameters is also impacted by a lack of stan-dardization for voxel sizes and b-value distributions, which several studieshave attempted to optimize [107\u2013112]. Variation in voxel size is certainto impact multi-exponential model fits. For example, suppose there exists113IVIM images with a voxel size of 2 x 2 x 2 mm3 and it is fitted with abi-exponential model. That image is then immediately re-acquired withvoxels of size 1 x 1 x 1 mm3 and again modeled with a bi-exponential fit.By comparing the two images, it is clear that the original image had beenmodelling octo-exponential components with a bi-exponential function. Av-eraging the parameters from the smaller voxels over the larger ones will, ingeneral, yield different parameters than those of larger voxels exactly paired.Voxel-by-voxel analysis of IVIM images is difficult due to uncertainty, andparameters are therefore averaged over regions-of-interest (ROIs). This issueis exacerbated by partial volume effects (PVEs) from various tissue typesand bleed-in from neighbouring voxels.The goal of applying various signal-decay models to IVIM data is todescribe the signal decay curve, which in turn, quantifies microscopic fluidmotion within tissue. Bi- and tri-exponential parameters are particularlyenticing as they appear to have a clear physiological interpretation. How-ever, there is no consensus that f is correlated with blood vessel density[105, 113, 114], and the ability of parameters to be interpreted physiologi-cally is generally unimportant for practical applications. There is further-more no consensus on the optimal IVIMmodel for describing the signal decaycurve, with many alternative versions being recommended [99\u2013101, 115, 116].IVIM parameters tend to be used to construct models for predictingvarious clinical end-points, without being directly interpreted. While modelcomplexity has risen since the conception of IVIM MRI, the overall goalremains simple: to best describe the signal decay curve. We hypothesizethat describing the signal decay curve without imposing any specific modelsonto the data will lead to higher reproducibility, and better modelling ofoutcomes.The purpose of this study is to introduce two methods for improvingIVIM MRI efficacy and reproducibility. First, to improve image quality andreduce the effect of image aberrations on parameter estimates, we apply a de-noising algorithm to each patient\u2019s diffusion images prior to model-fitting.Second, we introduce several model-independent parameters for quantify-ing the signal decay curve of IVIM MRI images, and compare them to114bi-exponential, tri-exponential, and ADC parameters.6.2 Methods6.2.1 DatasetThis study was approved by the BC Cancer Agency Research Ethics Board(H21-00517), and written, informed consent was obtained from all patients.The inclusion criteria for recruitment were: (1) a diagnosis of nasopharynx,base-of-tongue, or tonsil cancer to be treated with external beam radio-therapy; (2) expected to receive dose in parotid glands during treatment;(3) scheduled to have MR images acquired prior to radiotherapy and at 3months following the last treatment day. IVIM MR images encompassingthe parotid glands were acquired during routine clinical appointments for 12head-and-neck cancer patients prior to radiotherapy (Age: 35-78Y, average:60.4 ; sex: 11M, 1F). Of these, 5 had follow-up images acquired at 3 monthspost-RT (Age: 49-78Y, average: 59.3 ; sex: 5M, 1F). 4 of these 5 patientsreceived weekly chemotherapy concurrent with radiotherapy (three patients:weekly 40 mg\/m2 cisplatin, one patient: weekly 20-40 mg\/m2 per week and240 mg carboplatin).Images were acquired on a 1.5 T Magnetom Sola scanner (SiemensHealthineers) with an echo planar imaging sequence (EPI). Diffusion weightedimages were acquired with a voxel size of 1.6 x 1.6 x (3.4-3.9) mm3. Thisslight inter-patient variation in slice thickness was imposed to encompassparotid glands within 32 slices while maximizing the signal-to-noise ratio(SNR). The repetition time (TR) and echo time (TE) were 4900 ms and105 ms, with a flip angle of 90\u25e6. Images were acquired for 16 b-values (0,20, 30, 40, 50, 60, 70, 80, 90, 100, 120, 150, 250, 400, 800, 1000). Thesevalues were chosen to follow recommendations for effectively separating per-fusion parameters [457, 458], typically with a partition margin around 50s\/mm2 [109]. Signals were acquired in 6 directions, spanning the 3 princi-pal Cartesian axes and their vectors. Two signal averages were computedin each direction. Signals from various directions were combined by taking115the geometric mean [459].Parotid glands were manually contoured by a graduate physics studenton clinical T1 images. These images were acquired with a turbo spin-echo(TSE) sequence (TR: 564 ms, TE: 20 ms, flip angle: 148\u25e6). T1 images wereacquired with a voxel size of 0.6 x 0.6 x 3 mm.DICOM planning CTs, radiotherapy dose and planning structure set filesused for external beam radiotherapy treatment planning were exported fromVarian Eclipse (Varian Medical Systems, Inc.) for computing dose statisticsinside parotid glands. Whole-mean parotid gland dose levels were calculatedwithin computed tomography (CT) contours, manually defined by a single,senior clinical radiation oncologist.6.2.2 DenoisingTo mitigate the influence of partial volume and other blurring effects onIVIM parameter estimates, images were denoised using neural blind de-convolution. Blind deconvolution is the ill-posed mathematical problem ofestimating hypothetical denoised images, x, and their associated blur ker-nel, k, which convolve to yield the original image, y = x \u2217 k. This methodis particularly useful in situations where spatial resolution and precision ofsignal localization is low, hence many studies have attempted to employ itfor positron emission tomography (PET) [405, 407\u2013409, 460]. Neural blinddeconvolution is the method of solving this problem using neural networkswhich are simultaneously optimized to predict x and k. It was originallyimplemented by Ren et al. [417] in 2020 and applied to images from a2-dimensional natural image database, and then significantly improved byKotera et al. [418] in 2021. Neural blind deconvolution is an unsupervisedlearning methodology which trains and predicts on a case-by-case basis,without the requirement of a separate training set with ground truth im-ages.Neural blind deconvolution was adapted for 3-dimensional prostate spe-cific membrane antigen (PSMA) positron emission tomography (PET) in2023, while incorporating simultaneous super-sampling into the method-116ology [461]. It was shown to improve blind image quality metrics, andstrengthen correlations between PSMA PET uptake and sub-regional im-portance estimates in the parotid gland for predicting post-radiotherapyxerostomia (subjective dry mouth) [462].Here we further build off of this methodology for suitability with IVIMMRI. First of all, we adapt the network to handle 4-dimensional input im-ages (b, x, y, z), composed of 3-dimensional images for all b-values stacked.Images were normalized as x\u2192 x\u2212\u00b5body\u03c3body , where \u00b5body and \u03c3body are the meanand standard deviation of signal in body voxels. The network architecturewas maintained to predict a single kernel, such that a single blur kernel waspredicted using all b-value images for each patient.The traditional neural blind convolution architecture [417, 418, 461, 462]consists of a symmetric convolutional auto-encoder network, Gx, for predict-ing the denoised image, x, and a fully connected network, Gk for predictingthe flattened kernel, k. While the decoder architecture of Gx was previ-ously modifed to super-sample PSMA PET images [461], we omitted super-sampling for IVIM images.As the traditional formulation of the blind deconvolution problem, y =x \u2217 k, accounts for bleeding of voxel signals, it does not account for back-ground noise. As MRI signals contain rician noise [463], we modified themathematical formulation of the problem to include a noise term:y = x \u2217 k + \u03b4 (6.4)This required the introduction of an additional symmetric convolutionalauto-encoder network, G\u03b4, for predicting the noise term \u03b4. The networksused are thus,Gx(\u03b8x) = x , G\u03b4(\u03b8\u03b4) = \u03b4 , Gk(\u03b8k) = k , y = x \u2217 k + \u03b4. (6.5)where \u03b8x, \u03b8\u03b4 and \u03b8k represent trainable model parameters of Gx, G\u03b4 and Gk,respectively. The following implicit constraints exist on network outputs117which are satisfied automatically.0 \u2264 Gx(\u03b8x) , Gk(\u03b8k) \u2265 0 ,\u2211iGk(\u03b8k)i = 1. (6.6)The optimization problem can be written in terms of the model parameters\u03b8x, \u03b8\u03b4 and \u03b8k as\u03b8x, \u03b8k, \u03b8\u03b4 = arg min\u03b8x,\u03b8k,\u03b8\u03b4||Gx(\u03b8x) \u2217Gk(\u03b8k)+G\u03b4(\u03b8\u03b4)\u2212y||22+R(Gx(\u03b8x), Gk(\u03b8k)).(6.7)The full architecture is summarized visually in Figure 6.1.Optimization was performed using a single NVIDIA GeForce GTX 1060GPU and a 2.8GHz Intel CoreTM i5-8400 CPU. As neural blind decon-volution is a computationally expensive procedure, further exacerbated bystacking multiple b-value images, images were cropped to extend at least 5voxels outside of parotid gland borders in all 3 cartesian directions. This wasperformed separately for the left and right parotid glands, such that neuralblind deconvolution was performed separately for each gland. Decreasingthe image size in this manner was necessary to limit GPU memory usage.A multi-scale optimization procedure was implemented, as recommendedfor neural blind deconvolution by Kotera et al. [418] and recently imple-mented for PET denoising in Chapter 5. This involved pre-training net-works using images that were first down-sampled by a factor of 2, thenup-sampling final outputs by\u221a2 before performing a second round of pre-training. After these two pre-training rounds, the outputs, Gx, Gk, and G\u03b4,are used as initial inputs for the regular training procedure. An 11x11x11kernel was used, which was down-sampled to 5x5x5, and then 7x7x7 duringpre-training stages. The algorithm for updating network weights to predictdenoised diffusion images is summarized in Table 6.1The regular training procedure consisted of 5000 iterations, as in pre-vious implementations. This was split into two stages, with two differentloss functions. These stages and their corresponding loss terms are sum-marized in Table 6.2. It is necessary to include regularization terms in theloss function to avoid convergence to a trivial solution (k becomes a unit118Table 6.1: The optimization algorithm for updating network weights to pre-dict deblurred PSMA PET images. This algorithm builds off of Ren et al.\u2019sproposed joint optimization algorithm [417] and implements modificationssuggested by Kotera et al. [418].Diffusion Denoising AlgorithmInput: Original 4D (b, z, y, x) image, yOutput: Deblurred 4D (b, z, y, x)image, x, 4D (b, z, y, x) noise image, \u03b4, and 3D blur kernel, kPre-training1. Downsample spatial dimensions of y to 1\/2 resolution2. Initialize zx, z\u03b4 from uniform distribution to match size of y3. Initialize zk as size 5\u00d7 5\u00d7 5 Gaussian kernel with standard deviation of one voxel4. for i = 1 to 1000:5. x = Gix(zx)6. k = Gik(zk)7. \u03b4 = Gi\u03b4(z\u03b4)8. Compute loss and back-propagate gradients9. Update Gix, Gi\u03b4 and Gik using the ADAM optimizer [280]10. x = G1000x (zx), k = G1000k (zk), \u03b4 = G1000\u03b4 (z\u03b4)11. Upsample k by 7\/5 and upsample spatial dimensions of x and \u03b4 by a factor of\u221a212. Downsample spatial dimensions of y by\u221a2 to match new convolution size13. zx = x, z\u03b4 = \u03b4, zk = k14. Repeat steps 4 through 10.15. Upsample k by 11\/7 and upsample spatial dimensions of x and \u03b4 by a factor of\u221a216. zx = x, z\u03b4 = \u03b4, zk = kMain Training17. for i = 1 to 5000:18. x = Gix(zx)19. k = Gik(zk)20. \u03b4 = Gi\u03b4(z\u03b4)21. Compute loss and back-propagate gradients22. Update Gix, Gi\u03b4 and Gik using the ADAM optimizer [280]23. x = G5000x (zx), k = G5000k (zk), \u03b4 = G1000\u03b4 (z\u03b4)impulse). Therefore, the mean squared error (MSE) of kernel values above0.7 were penalized. We only penalized values above this cutoff to avoid atrivial solution while still allowing small contributions from neighbouringvoxels to go unpenalized. We furthermore penalized the MSE of noise vox-els above \u00b5\u03b4 + \u03c3\u03b4, where \u00b5\u03b4 and \u03c3\u03b4 are the mean and standard deviation ofthe normalized original image voxels located outside of the body. A totalvariation (TV) loss term for x was included after the 3500th iteration, asthis has been shown to improve results when employed in later stages of op-timization [418]. Furthermore, our fidelity loss function switched from MSE119Figure 6.1: The blind deconvolution architecture used for deblurring IVIMimages is illustrated. Gx and G\u03b4 are symmetric, convolutional auto-encodernetworks for predicting the deblurred image, x, and its additive noise contri-butions, \u03b4. Gk is a fully-connected network for predicting the blur kernel, k.The fidelity loss term used in optimization compares the original image withx \u2217 k + \u03b4 by using back-propagated model gradients from the loss functionfor iterative optimization.120to the structural similarity index metric (SSIM) after the 3500th iteration,as recommended [418] for improving final image quality.Table 6.2: Optimization consisted of 5000 iterations, split into 3 stages, eachhaving a different loss function. Up to the 3500th iteration, the fidelity lossfunction was mean squared error (MSE). The structural similarity indexmetric (SSIM) was used in remaining iterations. In all iterations, a kerneland noise regularization term were included. The MSE of kernel values werepenalized to avoid convergence to the trivial solution. The MSE of noisevalues above \u00b5\u03b4+\u03c3\u03b4, where \u00b5\u03b4 and \u03c3\u03b4 are the mean and standard deviationof the normalized original image voxels located outside of the body. Finally,the total variation (TV) between denoised image voxels was penalized afterthe 3500th iteration, as it has been shown to improve results when employedin later stages of optimization [418]Iteration<3500 Iteration \u2265 3500Fidelity Term MSE SSIMRegularization Terms 1. Kernel 1. Kernel2. Noise 2. Noise3. TV6.2.3 Evaluating deblurred ImagesAs neural blind deconvolution is an unsupervised training methodology,ground truth images were not used for direct evaluation of denoised images.We compared image quality between denoised and original IVIM images interms of two blind image quality metrics. The Blind\/Referenceless ImageSpatial Quality Evaluator (BRISQUE) [432] and Contrastive Language Im-age Pre-training (CLIP) [433] score were evaluated. BRISQUE ranks imagequality on a scale between 0 and 100 based on a series of features derivedfrom various signal intensity and distribution statistics. These features areused to predict the deviation of the input image from a natural, undistortedimage. CLIP uses a language\/vision neural network trained using millions ofnatural image\/caption pairs to assess either image quality or caption qual-ity. We furthermore assessed the quality of IVIM parameter maps predictedusing original and denoised images in terms of BRISQUE and CLIP metrics.121We furthermore assessed the similarity between predicted kernels amongstpatients. As all patient images were acquired on the same scanner, predictedblur kernels were expected to be similar. As the blur kernel contains com-ponents due to both scanner uncertainty, as well as patient motion, weanticipated predicted blur kernels to be similar, yet nonidentical, betweenpatients. We compared blur kernels quantitatively by computing the innerproduct between normalized kernels.To ensure the model\u2019s ability for predicting accurate blur kernels, weemployed the same strategy used for evaluating neural blind deconvolutionfor PSMA PET images [461]. This involves generating artificial kernels, con-volving them with previously denoised images, then re-starting the neuralblind deconvolution process. The objective is then to test how accuratelypseudokernels can be predicted, measured using the inner product betweengenerated and predicted pseudokernels. Four types of pseudokernels weregenerated: a regular Gaussian with a standard deviation of 1 voxel in eachdirection, and three oblong Gaussians, each having a standard deviationtruncated by a factor of three in one of the three Cartesian directions. Pseu-dokernels were all normalized to a unit sum.Original and denoised images were further compared in terms of theirpractical ability for model-building. Beginning with the hypothesis thatIVIM parameters are related to histological features within imaging voxels,we tested the ability of radiotherapy dose levels to predict changes in IVIMparameters following treatment. This was assessed in two different ways.First of all, Spearman\u2019s rank correlation coefficient (rs) was compared be-tween the whole-mean dose and relative changes in mean IVIM parameterswithin each parotid gland (Pf\u2212PiPi), where Pi and Pf are the parametersbefore and after radiotherapy).The dose response of parameters were further analysed using a multipleregression analysis. Post-radiotherapy parameters were used as dependentvariables while pre-radiotherapy parameters and mean dose levels servedas two independent variables. The best-fit slope with respect to dose wasthen compared between parameters. For comparison\u2019s sake, slopes werecalculated with respect to parameters that had been normalized to statis-122tical Z-values, with statistics derived using pre-radiotherapy voxels withineach patient\u2019s parotid glands. Images were normalized to statistical Z-valuerather than by the maximum image voxel, as it was found that maximumvalues tended to substantially exceed average values within parotid glands,leading to compression of voxel values.6.2.4 Extracting Exponential Model ParametersTo serve as a basis of comparison for newly derived, model-independentIVIM parameters, we extracted ADC, bi-exponential, and tri-exponentialparameter maps for all patients. Voxel-wise parameter fitting was per-formed using IVIM3-NET models [464], trained for each model type usingall acquired original and denoised IVIM images. Voxels were first filteredto exclude voxels located outside the body from training. This resulted inapproximately 3.6 million training voxels. Voxels for each b-value were nor-malized to signals acquired with b = 0. IVIM3-NET hyper-parameters weretuned according to previously derived optimal values [464]. Models consistof fully-connected networks with 2 hidden layers, which take normalizedsignal versus b-value arrays as input, and predict the appropriate numberof parameters for each model. Each layer consists of a linear function, anexponential linear unit (ELU) activation function [276], and batch normal-ization. Sigmoid functions were used to constrain parameter predictionswithin boundaries chosen to over-encompass anticipated ranges (Table6.3).Network weights were then optimized via back-propagation using a batchsize of 256 and an ADAM optimizer [280].To mediate the effect of image noise at S(b = 0) affecting all normalizedmeasurements acquired at other b-values, IVIM3-NET models were also usedto simultaneously predict S(b = 0) along with other model parameters. Thiswas shown to improve fit results in a previous study [464]. Hence, the lossterm is of the form,L =(S(b)S\u02c60\u2212 S\u02c6(b))2(6.8)where S(b) is the actual signal in a given voxel, and S\u02c60 and S\u02c6(b) are model123predictions. For example, a bi-exponential model outputs S\u02c60, f , D\u2217 and D,which yield S\u02c6(b) = fe\u2212b\u00b7D\u2217 + (1\u2212 f)e\u2212b\u00b7DTable 6.3: Parameter bounds set for IVIM3-NET predictions of exponentialmodel parameters. Bounds were set to over-encompass anticipated param-eter ranges, in order to compensate for diminishing gradients at sigmoidasymptotes [465]Model Parameter Lower Bound Upper BoundBi-exponential D (mm2\/s) 7\u00d7 10\u22125 4\u00d7 10\u22123D\u2217 (mm2\/s) 2\u00d7 10\u22123 0.15f 0 0.5Tri-exponential D (mm2\/s) 7\u00d7 10\u22125 4\u00d7 10\u22123D\u22171(mm2\/s) 3\u00d7 10\u22123 2\u00d7 10\u22122D\u22172(mm2\/s) 2\u00d7 10\u22122 0.7f1 0 0.5f2 0 0.5ADC ADC(mm2\/s) 7\u00d7 10\u22125 5\u00d7 10\u221236.2.5 Model-independent IVIM parametersTo describe the signal decay curve without imposing specific mathematicalmodels onto the data, we define the area under the curve (AUC) parameter.The AUC captures the general fall-off of signal with increasing b-value, andcan be equivalently described as the integral of S(b)\/S(0). The anticipatedrelationship between AUC and exponential parameters can be found byintegrating over exponential functions between b = 0 to b = 1000. For theADC model,AUC =\u222b 10000SADC(b)SADC(0)db =1ADC[1\u2212 e\u2212ADC\u00b71000] . (6.9)AUC and ADC are thus inversely proportional. For the biexponentialmodel,AUC =\u222b 10000Sbi(b)Sbi(0)db =fD\u2217[1\u2212 e\u22121000\u00b7D\u2217]+1\u2212 fD[1\u2212 e\u22121000\u00b7D] (6.10)124. AUC decreases with increasing D, and is roughly independent of D\u2217assuming D\u2217 \u2248 10D, and f small). For the triexponential model,AUC =\u222b 10000Stri(b)Stri(0)db =f1D\u22171[1\u2212 e\u22121000\u00b7D\u22171]+f2D\u22172[1\u2212 e\u22121000\u00b7D\u22172]+1\u2212 f1 \u2212 f2D[1\u2212 e\u22121000\u00b7D] .(6.11)AUC is roughly independent of D\u22171 and D\u22172 (assuming D\u2217i \u2248 10D and fismall, i \u2208 {1, 2}).The AUC was calculated for each voxel using a middle Riemann sum.The AUC was furthermore calculated in 3 subsets of b-values, defining alow-, middle-, and high-range AUC (AUCl, AUCm, AUCh, respectively).The ranges were defined as:\u2022 Low: b \u2264 120\u2022 Medium: 120 \u2264 b \u2264 400\u2022 High: 400 \u2264 b \u2264 1000The method of calculating AUC, AUCl, AUCm, and AUCh using middleRiemann sums is shown graphically in Figure 6.2.Figure 6.2: AUC parameters were calculated using middle Riemann sums.On the left, the AUC within a single voxel is calculated graphically. Ina separate voxel on the right, AUCL, AUCM , and AUCH are calculated(yellow, rose, blue), which sum to the regular AUC.1256.2.6 Comparing ParametersWhole-mean parameters were computed within all parotid glands. To com-pare functional utility of AUC parameters with exponential model parame-ters, we employed several strategies. First of all, we included AUC parame-ters in the previously mentioned dose-response comparison of IVIM param-eters in parotid glands. This allowed the practical utility of parameters foruse in dose response studies to be analysed, based on the hypothesis thatparameter statistics are related to tissue composition and characteristics ata histological level.We further tested the relative importance of IVIM parameters in captur-ing the variance of the dataset by evaluating contributions to the primaryprincipal component obtained through singular value decomposition. Theprimary principal component is the optimal linear combination of all inputfeatures for describing the maximum variation in the data. This was com-puted by first creating a 2-dimensional array, where each row represents asingle voxel in an image and each column represents a given feature. Voxelswithin the body in all cropped images were included as rows in this array.All biexponential, triexponential, ADC, and AUC features were included ascolumns. This yielded an m\u00d713 matrix for which the singular value decom-position was computed. The squared projection of the primary principalcomponent on each of the 13 parameters was then calculated and plotted.6.3 Results:Neural blind deconvolution for denoising diffusion MR images appeared toeffectively suppress random noise while enhancing fine detail within images.This improvement is supported quantitatively by an increase in blind imagequality metrics, BRISQUE and CLIP for denoised images (Table 6.4).Predicted blur kernels were similar among all patients, having a meaninter-patient inner product of 0.88 \u00b1 0.10. Furthermore, each patient hadtwo predicted kernels (for diffusion images cropped over the left and rightparotid, separately) whose mean inner product was 0.97\u00b1 0.02. Projections126Table 6.4: Blind image quality metrics, CLIP and BRISQUE are comparedfor original (y) and denoised (x) diffusion MR images. Results were averagedover all slices and b-values. The significance of the difference was testedusing a paired t-test.Denoised Original SignificanceBRISQUE 36.4\u00b1 7.8 14.6\u00b1 6.9 p < 0.001CLIP 0.37\u00b1 0.03 0.35\u00b1 0.03 p < 0.001of the mean predicted kernel are shown in Fig 6.3. Kernel voxels were mainlyconfined to within axial planes, with the highest variance in the anterior-posterior direction. The general shape of pseudokernels was predicted usingneural blind deconvolution; however, it can be seen that predicted kernelvoxels were mostly confined to within one voxel of the centre value (Fig 6.5).Axial slices of denoised and original diffusion images corresponding toseveral different b-values are contrasted in Fig 6.4. Image denoising resultedin significantly (p < 0.001) more monotonically decreasing signal versusb-value curves, as shown in Fig 6.6. This was assessed by first taking Spear-man\u2019s rank correlation coefficient, rs, between signal and b-values, averagedover all voxels within body tissue. A paired t-test was then used to assessdifferences between correlations in denoised and original images. rs was\u22120.80\u00b1 0.31 in denoised images and \u22120.60\u00b1 0.29 in original images.ADC, biexponential, triexponential, and all AUC parameter statisticsin parotid glands are summarized in Table 6.5.127Table 6.5: All IVIM parameter averages and standard deviations inside parotid glands are listed. Averages werecalculated over parotid glands from pre-radiotherapy (pre-RT) and post-RT scans separately, along with thesignificance of their difference. Results are calculated using both denoised and original images. Lastly, the finalcolumn lists the significance of differences between denoised and original values before radiotherapy. Significancevalues were determined using a paired t-test.Denoised Images Original ImagesParameter Pre-RT Post-RT p-value Pre-RT Post-RT p-value p-value (Deblur versus Orig)ADC (\u00d710\u22123mm2\/s) 1.23\u00b1 0.37 1.98\u00b1 0.20 <0.001 1.27\u00b1 0.36 1.96\u00b1 20 <0.001 > 0.05D (biexponential, \u00d710\u22124mm2\/s) 4.8\u00b1 1.1 6.6\u00b1 1.2 <0.01 4.7\u00b1 1.2 6.5\u00b1 1.2 <0.01 <0.001D\u2217 (biexponential, \u00d710\u22122mm2\/s) 1.6\u00b1 0.8 1.1\u00b1 0.2 > 0.05 2.2\u00b1 0.9 1.4\u00b1 0.4 <0.01 <0.001f (biexponential) 0.25\u00b1 0.04 0.32\u00b1 0.03 <0.001 0.26\u00b1 0.03 0.32\u00b1 0.03 <0.001 <0.001D (Triexponential, \u00d710\u22124mm2\/s) 4.6\u00b1 1.1 6.3\u00b1 1.1 <0.001 4.5\u00b1 1.2 6.3\u00b1 1.1 <0.001 <0.001D\u22171 (Triexponential, \u00d710\u22123mm2\/s) 6.2\u00b1 0.9 5.2\u00b1 0.6 > 0.05 6.9\u00b1 1.0 6.1\u00b1 0.7 <0.01 <0.001f1 (triexponential) 0.20\u00b1 0.04 0.27\u00b1 0.03 <0.001 0.20\u00b1 0.03 0.26\u00b1 0.03 <0.001 p<0.001D\u22172 (Triexponential, \u00d710\u22121mm2\/s) 0.70\u00b1 0.30 0.55\u00b1 0.3 > 0.05 1.3\u00b1 0.3 0.9\u00b1 0.3 > 0.05 p < 0.001f2 (Triexponential) 0.04\u00b1 0.01 0.03\u00b1 0.01 > 0.05 0.06\u00b1 0.01 0.042\u00b1 0.001 < 0.01 p < 0.001AUC (s\/mm2) 652\u00b1 41 587\u00b1 32 < 0.001 642\u00b1 39 580\u00b1 32 < 0.001 p < 0.001AUCL (s\/mm2) 108\u00b1 2.4 108\u00b1 2.4 > 0.05 105\u00b1 1.6 107\u00b1 1.7 > 0.05 p < 0.001AUCM (s\/mm2) 205\u00b1 8.7 191\u00b1 9.0 <0.01 201\u00b1 7.7 189\u00b1 7.6 <0.01 p < 0.001AUCH (s\/mm2) 443\u00b1 39.4 382\u00b1 28 <0.01 437\u00b1 37 378\u00b1 29 <0.01 p < 0.001128Image denoising was found to strengthen correlations between whole-mean parotid dose levels and changes in IVIM parameters (Fig 6.7). Changesin AUC, AUCM , and AUCH and ADC had the strongest correlations withmean dose levels. Correlations between dose and AUC parameters wereparticular strong in denoised images. Regression slopes for changes in pa-rameters versus dose are also shown in Fig 6.7. Changes in ADC had thehighest slope with respect to dose in both denoised and original images.AUC, AUCM , AUCH , D\u22172, f , and Dbiexp had similarly high dose slopes,while D\u2217biexp, Dtriexp, D\u22171, f1, f2, and AUCL had lower slopes. Fig 6.7 alsoshows the relative contribution of each parameter to the first principal com-ponent obtained via the SVD analysis. AUC, AUCH and ADC capturedthe highest proportion of variance in the data, with f1 also capturing arelatively high proportion of the variance. Pairwise correlations between allparameter combinations are displayed in Fig 6.7. AUC, AUCM , and AUCHwere highly correlated with one another, and also with ADC, D (biexponen-tial and triexponential), f , and f1, while AUCL was most correlated withf2 and D\u22171.AUC parameter maps derived using denoised and original diffusion im-ages are shown in Fig 6.8. Parameter maps of biexponential parameterscorresponding to the same slice are shown in Fig 6.9.129Figure 6.3: The average blur kernel predicted for patients is projected onto the three primary imaging planes. Thekernel was mostly confined to axial planes, which was expected due to elongation of voxels in the superior-inferiordirection (slice thickness > 2\u00d7 axial slice pixel spacing). The kernel had a greater spread in the anterior-posteriordirection than the left-right direction.130Figure 6.4: Axial slices through parotid glands of denoised (left) and original(right) diffusion images at 4 different b-values are shown. Denoising appearsto effectively suppress noise while enhancing fine detail within images. Herein particular, the posterior region of the parotid gland becomes discernibleonly upon denoising.131Figure 6.5: The neural blind deconvolution denoising process was testedby convolving fixed pseudokernels with previously denoised diffusion imagesbefore restarting the denoising process. Four pseudokernels, including aregular Gaussian, as well as a Gaussian elongated in each of the 3 primaryimage axes, were applied.132Figure 6.6: Axial slices through the parotid gland of denoised and original diffusion images with b = 1000 areshown, along with the signal decay curve of each in a single voxel (indicated in the denoised image). Signalvalues were normalized to statistical Z-values within the body. Denoising appears to suppress random noise whileilluminating fine detail within images. The loss function used during image denoising did not impose a decreasein signal value with increasing b-value, yet signal values in denoised images appear to naturally decrease moremonotonically and more smoothly than in original images.133Figure 6.7: Pairwise Spearman\u2019s rank correlation coefficients, rs, betweendose and relative changes in biexponential, triexponential, ADC, and AUCparameters derived from IVIM images are displayed (top) for denoised andoriginal images (left and right). Best-fit regression slopes of parameters ver-sus dose are shown underneath in green. The singular value decomposition(SVD) of the data was computed, and the relative variance captured by eachparameter in the first principal component was plotted (bottom).134Figure 6.8: Axial slices through the parotid gland of biexponential parameter maps are shown, derived usingdenoised (top) and original (bottom) diffusion MR images. Axial b = 0, AUC, AUCL, AUCM , and AUCH imageslices derived from denoised (top) and original (bottom) are shown.135Figure 6.9: Axial slices through the parotid gland of biexponential modelparameter maps are shown, derived using denoised (top) and original (bot-tom) diffusion MR images.1366.4 DiscussionThere is high variability of derived IVIM MRI parameters in the literature.The proposed model-independent parameter, the AUC, proved to be an ef-fective parameter for characterizing the signal decay versus b-value curve.In terms of stand-alone model-building potential, AUC parameters maybe more effective than traditional IVIM parameters for predicting variousclinical outcomes, based on their high correlations with radiotherapy doselevels and high contributions to the primary principal component of the totaldataset. Changes in the AUC, AUCM and AUCH following radiotherapywere more correlated with dose than diffusion coefficients derived from ex-ponential models. Furthermore, changes in the ADC following radiotherapywere more correlated with dose than diffusion coefficients derived from biex-ponential and triexponential models. Perfusion fractions for biexponentialand triexponential models, f and f1, were more correlated with dose thantheir corresponding model\u2019s diffusion coefficient, D.Neural blind deconvolution for denoising IVIM MRI prior to parameterfitting proved to be effective. Denoising enhanced fine detail in images whilesuppressing noise, resulting in higher blind image quality metrics, BRISQUEand CLIP [432, 433]. denoising resulted in higher correlations between doseand IVIM parameter values, especially with AUC, AUCM , and AUCH .This suggests that denoising may be beneficial for future studies seekingto use IVIM imaging to assess radiotherapy-induced tissue damage. AUCvalues significantly decreased following radiotherapy. AUCL was found to bethe least effective AUC variant, possibly due to the low amount of datasetvariability it accounted for, and its lower correlation with dose comparedwith other AUC variants. This is similar to the limited functional utility ofpseudodiffusion coefficients, which also describe the behaviour of the signaldecay curve in the low b-value regime.In both denoised and original images, the newly proposed Area Underthe Curve (AUC) of the normalized signal decay curve, and the AUC in thehigh b-value region (AUCH) captured the largest proportion of the variance.The ADC captured a higher proportion of the variance than the diffusion137coefficients of biexponential and triexponential models. Perfusion fractions,f (biexponential) and f1 (triexponential) captured a higher proportion ofthe variance than diffusion or pseudodiffusion coefficients. Pseudodiffusioncoefficients and AUCL constituted a particularly low proportion of the data\u2019svariance. These variables are less correlated with other variables, as seen inthe correlations grid.The results of this study suggest that within our dataset, AUC param-eters and the ADC are the most effective IVIM parameters for modellingdose-related outcomes. However, this study included a small number of pa-tients having post-radiotherapy data, rendering our dose response quantitiesprone to uncertainty. Further validation is needed to assess the efficacy ofAUC parameters and neural blind deconvolution for improving the practicalutility of IVIM imaging. It appears that denoising images could improve pa-rameter reproducibility, but more work is required for this to be confirmed.Predicted blur kernels were highly similar between patients, and kernelspredicted for images encompassing the left and right parotid gland of eachpatient were nearly identical (mean inner product: 0.97 \u00b1 0.02). Predictedkernels were mainly confined to axial planes, which is expected, due tothe axial elongation of the voxel geometry used in this study. To avoidconvergence towards a trivial solution, where the kernel becomes a deltafunction, a regularization term penalizing the MSE of kernel values above0.7 was included. Previous neural blind deconvolution studies have simplyapplied MSE to all kernel voxels [417, 418], but we only penalized voxelswith values above a given cutoff in order to allow small contributions fromneighbouring voxels to go entirely unpenalized.This method successfully approximated the general shape of all fourpseudokernel types, albeit with truncation at the edges. Predictions weremostly confined to within one voxel of the center value. This indicates thatdenoising is effective for mitigating cross-talk between neighbouring vox-els, but does not account for non-neighbouring voxel interactions. Similartruncation is reported for PSMA PET images [461]; however, voxels appearslightly more centralized in this study. This may be partially explained bythe smaller kernel size employed in this study. As we were anticipating a rel-138atively small deblur kernel for IVIM MRI images (due to generally sharperMR images than PET), while also considering memory constraints, we de-creased the kernel size to 11x11x11 from the 15x15x15 size used for PSMAPET [461, 462]. Overall, this denoising process appears to be effective forcorrecting cross-talk between neighbouring voxels, but more distant effectsare not accounted for.Parameters obtained from denoised and original images had similar pop-ulation means and standard deviations, but paired t-tests between valuesfound all parameters to be significantly different, except for the ADC. AUCvalues tended to be slightly higher in denoised images than original im-ages, although differences did not exceed one standard deviation. In allcases, differences in parameters following radiotherapy followed the sametrend. Mean ADC values agreed with those previously reported in the lit-erature [466\u2013468]. D and D\u2217 were lower than previously reported values[456, 468, 469], both before and after radiotherapy. However, D and D\u2217were within a standard deviation of the mean values reported by Kimuraet al. [468]. Furthermore, diffusion coefficients increased after radiotherapywith similar proportions to those found previously [456]. f within parotidglands was lower than values reported by Zhou et al. [456] and Beckert etal. [469] but smaller than values reported by Kimura et al. [468].It is not uncommon for IVIM parameters reported in the literature to bein conflict [108], which was the motivation for this work. For example, thesignificant variability of reported IVIM parameters in the liver has createddifficulties establishing normal, baseline perfusion parameters [470]. The lowSNR associated with echo-planar imaging is likely a significant contributor tothese issues. Disregarding time constraints, a spin echo sequence may lead tomuch greater reliability in parameter estimates. Variations in SNR betweenscanners used in different studies has been reported to affect parameterestimates [106, 470]. Variability of b-value distributions [471] and voxel sizesalso contribute to variability among parameter estimates in the literature.The intrinsically low SNR of echo planar imaging sequences used forIVIM imaging makes denoising an important endeavour. Incorporating anoise term into the neural blind deconvolution methodology allowed for cor-139rections of non-negative, scanner related noise to be corrected for. Noisesuppression after denoising is clearly visible in voxels located outside ofbody regions (Fig 6.4). A notable result is the increased monotonicity ofthe signal decay curve found after image denoising (Fig 6.6). It is expectedthat increasing diffusion gradient strength should result in strictly decreas-ing signal acquisition; however, this expectation was not enforced in the lossfunction used for optimization. This perceivable suppression of noise in thedecay curve seems to validate the denoising process.Characterizing the signal decay curvenon-parametrically can be advan-tageous, as it has the potential to improve the utility and reproducibility ofIVIM parameters without presuming the underlying mathematical model.While it is more desirable in theory to have physically interpretable pa-rameters, it has not proven to be practical for IVIM imaging. The AUCand its sub-quantities are only one method of describing the signal decaycurve. While this study affirms their utility, there remains room for furtherexploration and validation of other model-independent parameters. Futurestudies can continue to improve upon this methodology using the code avail-able online [451].6.5 ConclusionCharacterizing the signal decay curve using model-independent metrics, suchas the the AUC parameters, and denoising images prior to parameter estima-tion, could improve reproducibility and the practical utility of IVIM imag-ing for developing outcome-predictive models. IVIM parameters have shownsubstantial variability throughout the literature. A shift in the methodol-ogy for characterizing the signal decay curve offers a potential solution tomitigate this inconsistency.140Chapter 7An Open SourceCT-Autosegmentation Toolfor the Tubarial Glands7.1 IntroductionAs previously addressed, a challenging aspect of creating high-quality ra-diotherapy treatment plans is providing tumoricidal doses to target volumeswhile simultaneously sparing normal tissue. This is a multi-criteria opti-mization problem requiring oncologists to make trade-offs between tumordose coverage and normal tissue irradiation. This is especially true duringthe creation of treatment plans for head and neck cancer patients, wheresalivary glands often abut or overlap with target volumes [472]. It is com-mon for saliva production in post-therapy head and neck patients to beseverely impaired [473] as a result of salivary gland irradiation. This resultsin a subjective condition called xerostomia, or self-reported \u201cdry mouth.\u201dXerostomia and hyposalivation are known to severely impact the quality oflife by hindering or eliminating the ability to speak, chew, taste, or swal-low [7] and may cause oral infections, dental caries, and other oral sequelaeThe content of this chapter has been peer-reviewed and accepted for publication inthe Cureus Journal of Medical Science [1]. The name of the article is, \u201cDevelopmentof a CT-Based autosegmentation model for prostate-specific membrane antigen (PSMA)positron emission tomography-delineated tubarial glands,\u201d and the co-authors are CalebSample, Arman Rahmim, Carlos Uribe, Jonn Wu, and Haley Clark.141[8\u201310]. Irradiation of parotid glands has been found to be the greatest riskfactor for xerostomia following treatment [474].To achieve satisfactory organ sparing during radiotherapy, treatmentplanning workflows must include methods for defining the patient\u2019s geome-try and anatomy via medical imaging and image segmentation. Typically,computed tomography (CT) is used for the delineation of organs at risk(OARs).Advances in machine learning techniques have made possible automaticsegmentation (autosegmentation) of objects in images, most commonly usingconvolutional neural networks (CNNs). The quality of autosegmentation al-gorithms significantly improved with the development of the U-Net architec-ture [266] in 2015, which allowed for clinical adoption of auto-segmentationsoftware for contouring regions of interest (ROIs) to become a viable real-ity [419]. U-Net is a CNN architecture divided into a contraction path forextracting features (encoder) and an expansion path for constructing maskimages using these extracted features (decoder). The encoder iterativelyreduces the image size and increases the number of channels by means of aseries of double 3\u00d7 3 convolutions with numerous kernels, and intermittentactivation functions such as rectified linear units (ReLU) [274] as well asmax-pooling operations. A symmetric decoder then upsamples images backto their original size while reducing the number of channels using a seriesof transposed convolutions, 3 \u00d7 3 convolutions, and activation functions.Lastly, in what are called skip connections, the output of each activationfunction within the encoder is concatenated with the output of a transposedconvolution in the decoder at a symmetric level within the pipeline. See3.2.5 for more information on U-Net.In modern times, it is perhaps taken for granted that the anatomy ofthe human body has been scrupulously studied to a level where all relevantOARs are understood and considered during radiotherapy plan optimiza-tion. However, an unaccounted-for pair of bilateral salivary glands in theposterior nasopharynx region was discovered in early 2021 [17] and has beennamed the tubarial glands. This discovery was made by observing full-bodyprostate-specific membrane antigen (PSMA) positron emission tomography142(PET) and CT images. PSMA PET involves the injection of a radiotracer,which binds to the PSMA, a transmembrane protein specific to prostatecells including carcinoma. This radiotracer is also found to have an affin-ity for salivary and lacrimal gland tissue, rendering PSMA PET a viablemethod of delineating salivary glands in addition to the prostate. Referto Section 2.5.5 for more information about PSMA PET. While viewingfull-body PSMA PET images, it was noticed that radiotracer uptake in theposterior nasopharynx region resembled uptake observed in major salivaryglands [17]. The finding was confirmed by observing PSMA PET imagesfor 100 consecutively scanned patients and with a human cadaver study.The average length of the glands was found to be approximately 4 cm. Thesame group also retrospectively assessed the correlation between tubarialgland mean dose during radiotherapy and post-treatment xerostomia after12 months, finding a significant correlation (p = 0.007) [17]. Refer back toSection 4.5 for more on the tubarial glands. Based on these findings, con-sidering the tubarial glands as OARs in radiotherapy plan optimization isworth considering, and appears to have high potential for improving headand neck patient outcomes.As previously mentioned, the existence of the tubarial glands as majorsalivary glands is not without debate [395\u2013397], and this contention wouldbe best settled through experimentation, by testing the impact of treatingtubarial glands as OARs during radiotherapy plan optimization. A logicalnext step in assessing the impact of the dose on these glands is to carry out aclinical study, comparing patient outcomes for plans created with and with-out tubarial gland dose constraints. However, segmentation of the tubarialglands currently requires PSMA PET, which is costly and not routinelyacquired for head and neck patients.The aim of this work is to develop an autosegmentation model for thetubarial glands that requires only CT images. This will allow automaticcontouring of glands without requiring PSMA PET images or changes toexisting clinical imaging workflows. The ability to contour tubarial glandswith only CT images allows the role of tubarial glands in radiotherapy tobe further analysed.1437.2 Methods7.2.1 Manual Contouring on PSMA PET imagesRegistered [18F]DCFPyL PSMA PET and radiotherapy treatment planningCT images for a small cohort of prostate cancer patients (n = 30, age: 68\u00b1 13, weight: 90 kg \u00b1 38 kg) having previously received treatment werecollected for model training. DICOMautomaton [475] was used for manualsegmentation and Digital Imaging and Communications in Medicine (DI-COM) file export of tubarial gland structures using PSMA PET images.As absolute PSMA PET uptake varies from patient to patient, images werenormalized to standard uptake values based on body weight (SUVbw). Alower threshold of SUVbw = 1 was applied to PET images to approximatethe location of tubarial glands borders. The right and left tubarial glandswere then manually contoured slice by slice around the threshold-definedperimeters and the resulting structures were exported as DICOM files.7.2.2 Pre-ProcessingAn open-source program for autosegmentation of medical images, Organo-genesis [476], was developed and used for pre-processing, model training, andpost-processing of CT-predicted tubarial gland structures. Organogenesis iswritten in the Python programming language and its neural network modelsrely on the PyTorch package [281]. Data were preprocessed to create sepa-rate binary mask images for the right and left tubarial glands correspondingto each CT slice. CT images were normalized and PyTorch data loaderswere initialized for randomly iterating through the dataset during training.The process of using PSMA PET images to create tubarial gland masksfor CT images is illustrated in Figure 7.1. The dataset was augmented byapplying random elastic and perspective transformations included in theAlbumentations Python library [477].144Figure 7.1: Overview of the manual tubarial gland contouring process. (A)PSMA PET image voxels are converted to SUVbw. (B) A threshold is ap-plied to images to illuminate tubarial gland perimeters. (C) Tubarial glandsare contoured according to the threshold-defined perimeter. (D) CT andPET images are registered so that PET-derived contours and CT imagesuse the same coordinate system. (E) Binary masks for each CT slice arecreated (1 inside the gland, 0 outside). (F) For visualization, the tubarialgland masks are shown overlayed with their corresponding location on theCT image (not used for training).1457.2.3 ModelThe MultiResUNet architecture [267] was chosen for model development inthis study. MultiResUNet is a deep learning architecture and was intro-duced in 2020 by Ibtehaz and Rahman as a potential successor to the U-Netarchitecture [266]. Ibtehaz and Rahman made two major modifications tothe U-Net architecture.The first modification was the substitution of \u201cMultiRes\u201d blocks in placeof double 3\u00d7 3 convolutions throughout the decoder and encoder paths. U-Net\u2019s double convolution routines were shown to resemble a single 5 \u00d7 5convolution [478]. MultiRes blocks effectively enable feature learning atmultiple resolutions by applying a series of three 3\u00d7 3 convolutions in placeof each double convolution used in U-Net. MultiRes blocks were inspired by\u201cInception Blocks\u201d from the Inception architecture [479] and emulate theeffect of applying parallel 3 \u00d7 3, 5 \u00d7 5 and 7 \u00d7 7 convolutions for multi-resolution analyses. Avoiding parallel convolutions within networks is im-portant for memory considerations. To further avoid memory issues, thenumber of filters in successive convolutions is gradually increased ratherthan held constant. Residual \u201dskip\u201d connections were also added after thefirst and second convolution in each block.The other major innovation of MultiResUNet is the use of \u201cRes paths\u201din place of skip connections. Whereas skip connections directly concate-nate encoder and decoder outputs at successive corresponding levels of theencoder and decoder paths, Res paths first pass encoder output through aseries of convolutions and residual connections to avoid negative effects thatmay arise from concatenating high and low level features. The convolutionsequences are said to reduce the \u201csemantic gap\u201d do to encoder features be-ing of lower level than decoder features. The semantic gap reduces towardsdeep layers of the encoder and decoder. A diagram of the MultiResUnetarchitecture is shown in Figure 7.2.A two-dimensional (2D) MultiResUNet implementation was used, suchthat individual image slices are used as model input. Upon reviewing theliterature to compare the performance of OAR segmentation models using146Figure 7.2: The MultiResUNet architecture [267]. The double convolutionallayers used in the U-Net architecture were replaced with MultiRes blocks,and Res paths were used instead of plain skip connections. The structureof a MultiRes block and Res path are shown below. Reprinted from NeuralNetworks, Volume 121, N Ibtehaz and M Sohel Rahman, \u201dMultiResUNet: Rethinking the U-Net architecture for multimodal biomedical image seg-mentation,\u201d Pages 74-87, Copyright 2020, with permission from Elsevier.1472D and three-dimensional (3D) U-Net [480, 481], it was found that 2D U-Net often performs as well or better than 3D U-Net, and we, therefore,hypothesized that repeating model training with a 3D-architecture wouldnot be significantly beneficial for the present study.7.2.4 Model ParametersModels were trained through 20 epochs using a batch size of one and alearning rate of 0.001. These parameters were transferred from values ob-tained during prior experimentation with other head and neck OAR modelsin Organogenesis [476]. The batch size was limited to avoid memory con-straints. A binary cross entropy loss function was used for gradient calcula-tions and model parameters were updated using an Adam optimizer [280].Models were trained using a 6 GB NVIDIA GeForce GTX 1060 (NVIDIACorporation, Santa Clara, California) graphics processing unit (GPU).7.2.5 Combined Model for Left and Right Tubarial GlandsTo maximize the training power of our limited available dataset, the bilateralsymmetry of the tubarial glands was exploited to pool the right tubarial andleft tubarial datasets into a combined dataset after first reflecting the lefttubarial CT images and masks about the patient\u2019s posterior-anterior axis.This procedure effectively doubles the size of the right tubarial dataset, andthe combined dataset can then be used to train a single model for pre-dicting tubarial glands. When predicting right tubarial glands, CT imagesare fed straight into the model to obtain right tubarial masks. When pre-dicting left tubarial glands, CT images must be first reflected about theposterior-anterior axis. Similarly, the model output must be reflected aboutthe posterior-anterior axis, to generate a final left tubarial mask. This pro-cedure is summarized visually in Figure 7.37.2.6 Training and ValidationTo assess the generalized performance of the model, a recommended [482]five-fold cross-validation approach was used for model training and evalua-148Figure 7.3: How a model for predicting tubarial glands on the right sideof the body can be used for predicting left tubarial glands is illustrated.On the top row, the process for predicting a right tubarial gland is shown.In this case, a CT image slice (R.A) is input directly to the model, and aright tubarial predicted mask is generated (R.B). In this case, the mask isoverlayed with the CT image for better visualization. On the bottom row,the process for predicting a left tubarial gland is shown. Before the originalCT image (L.A) can be input into the model, it must first be flipped laterally(L.B). The mask generated by the model (L.C) must then be flipped laterally(L.D) to create the left tubarial gland mask image.149tion. Five-fold cross-validation divides the dataset into five disjoint subsets,each containing six validation patients. For each validation set, the remain-ing 24 patients would become the respective training set. Within each of thefive folds, separate models were trained with each training set and validatedwith the respective validation set. In this manner, five models were trainedfor both the left and right tubarial glands, which were all validated withindependent validation sets. Model statistics were averaged over the fivefolds.7.2.7 Post-processingModel output is in the form of image masks for each CT slice, which aresubsequently subjected to a sigmoid function, and then binarized via thresh-olding to form a mask. The threshold varies according to the predictiveconfidence and was determined iteratively for each fold by minimizing theDice similarity coefficient (DSC). Linear interpolation was used to correctfor any \u201cgap\u201d slices where certain slices had no predicted mask but maskswere predicted for slices directly above and below. The Canny edge de-tection algorithm [483] was used to detect pixels containing tubarial edgesin predicted mask images, which were then used to create tubarial contourarrays defined using the patient geometry from the CT metadata. Model-predicted tubarial gland contours were exported as DICOM radiotherapystructure set (RTSTRUCT) files.7.2.8 Model AssessmentTo gauge model performance, the DSC, 95th percentile Hausdorff distance(HD95), and Jaccard similarity coefficient (JSC) were determined on thevalidation set of each fold. The DSC quantifies the precision and recall ofa model and when applied to Boolean data, is defined using the number oftrue positive (TP), false positive (FP), and false negative (FN) predictions.DSC =2TP2TP + FN+ FP(7.1)150The Hausdorff distance is a maximin function, defined as the maximumdistance from any point in one set to the nearest point in the other set (the95th percentile of the distances is used to eliminate the impact of a verysmall subset of outliers). The JSC compares the similarity between two setsby taking the ratio of the intersection to the union.JSC(A,B) =A \u2229BA \u222aB (7.2)The effective length and radius of predicted tubarial glands were calculatedto compare manually contoured and autosegmented gland sizes. The lengthwas measured along the axial direction, and the gland radius was definedas the 90th percentile image slice radius, treating the contoured area fromeach image slice as a perfect circle.r = P90\u221aA\/\u03c0 (7.3)Differences between measurements of manually contoured and autoseg-mented glands were assessed using a paired t-test.The effective length and radius of predicted tubarial glands were calcu-lated to compare manually contoured and autosegmented gland sizes. Thelength was measured along the axial direction, and the gland radius was de-fined as the 90th percentile image slice radius, treating the contoured areafrom each image slice as a perfect circle.7.3 ResultsTable 7.1 includes the DSC, HD95, and JSC statistics over cross-validationsets. Predicted contours qualitatively conformed well to the general shapeand size of manually contoured tubarial glands, as shown in Figure 7.4 withisolated contours and in Figure 7.5 with contours overlayed on PSMA PETimages.151Table 7.1: Organogenesis models for the tubarial glands are assessed over afive-fold cross-validation with the Dice similarity coefficient (DSC), 95th per-centile Hausdorff distance (HD95), and Jaccard similarity coefficient (JSC).Mean and standard deviations over the five folds are included.Performance Statistics Cross Validation AverageDSC 0.64\u00b1 0.03HD95 7.9\u00b1 2.0 mmJSC 0.48\u00b1 0.03152Figure 7.4: Manually contoured and auto-segmented tubarial glands are shown for three validation patients froma front-facing coronal perspective. The right glands are shown in blue and the left glands are shown in red.153The length and radii of manually contoured and model-predicted tubarialglands are summarized in Table 7.2. The mean lengths calculated for man-ually contoured tubarial glands in this study were approximately 4.5 cm.Autosegmented lengths were insignificantly (Table 7.2) larger than manu-ally contoured lengths, with a mean length of 4.95\u00b1 0.98 cm. The averageradius of manually delineated tubarial glands was 8.5 \u00b1 1.1 mm, while theradius of autosegmented glands was slightly larger at 9.3\u00b1 1.3 mm.Table 7.2: Mean and standard deviation radius and length are shown formanually contoured and model-predicted tubarial glands (averaged over thefive folds). The significance of the difference between statistics for manuallycontoured and model-predicted glands, calculated using a paired t-test, isincluded.Tubarial Type Mean Radius (mm) Mean Length (mm)Manually contoured 8.5\u00b1 1.1 45.7\u00b1 8.5Autosegmented 9.3\u00b1 1.3 49.5\u00b1 9.8Significance of Difference p < 0.02 p = 0.11Using commodity hardware, autosegmentation models created for thetubarial gland predicted contours and generated RTSTRUCT DICOM filesfor each patient in approximately one minute when utilizing an NVIDIAGeForce GTX 1060 (6 GB) GPU and 10 minutes when running strictly onan Intel Core i7-10700 (2.9 GHz; Intel Corporation, Santa Clara, California)central processing unit (CPU).7.4 DiscussionWith ground-truth anatomical structures defined using PSMA PET images,a model for automatic segmentation of tubarial glands using only CT imageshas been developed. The current state of the model allows for an estimationof tubarial gland locations within CT images that can be used for headand neck radiotherapy plan optimization. Use of this model for tubarialgland segmentation prior to radiotherapy requires low human effort and hasthe potential to positively impact patient outcomes if dose constraints areapplied to these regions, as it has been determined that dose to tubarial154Figure 7.5: Manually contoured and auto-segmented tubarial glands areshown overlayed with PSMA PET images. (A) Coronal slice of manuallycontoured glands from the anterior direction. (B) Sagittal slice of manuallycontoured left tubarial gland from the patient\u2019s left-hand side. (C) Coronalslice of auto-segmented glands from the anterior direction. (D) Sagittal sliceof auto-segmented left tubarial gland from the patient\u2019s left-hand side.155glands is a strong predictor of clinical toxicity [17]. The autosegmentationprogram, Organogenesis, is available as open source code, and the model canbe improved upon by institutions having access to further PSMA PET\/CTdata.The DSC and HD95 between autosegmented and manually segmentedtubarial gland structures in this work were lower than values reported usingstate-of-the-art models for parotid glands [482]. This is not unexpected, andit is important to remember that tubarial gland models in this work weretrained using a very limited dataset. The aim of this work is not to presenta model with conformity statistics competitive with those of state-of-the-art OAR autosegmentation models for head and neck OARs trained withplentiful data, but rather to implement an initial CT-based autosegmenta-tion model for the tubarial glands, which can be iteratively improved upon,collaboratively. The cost of PSMA PET is prohibitive compared with CT,making it difficult to obtain large datasets for training. PET boundaries arealso difficult to assess, making it difficult to create high-resolution tubarialgland contours.While the current state of the model is inadequate for highly precisequantification of dose levels in the glands, due to its imperfect localization ofgland borders, it is still useful for approximating dose and would be effectivefor constraining dose to the general region of tubarial glands. Optimistically,institutions that have access to PSMA PET data will use the same techniqueused here to contour tubarial glands using PSMA PET and continue to trainthe existing model, improving its performance.The tubarial glands were found to have high inter-patient variability inlength and radius, and our dataset was not sufficiently large for our modelsto learn all predictive features on CT images for generalized model perfor-mance. The variance observed may be partially explained by the use ofSUVbw - defined tubarial gland borders, as SUVbw values have a knowndependence on patient mass [484]. The caudal (inferior) portion of manu-ally delineated and auto-segmented glands was found to exhibit a narrowcolumnar shape, which was found to extend much further inferiorly in somepatients than in others. The discrepancy in the lengths of auto-segmented156and manually contoured tubarial glands may be partially explained by modelbias for contouring these lower caudal regions (bias for false positive overfalse negative prediction error).Mean lengths calculated for manually contoured tubarial glands in thisstudy were approximately 5 mm larger than previously observed values [17].This is likely due to the choice of the threshold used for delineating theglands. Furthermore, the caudal region of the glands exhibits a thin, elon-gated, stem-like shape, which may reasonably not be fully included in theirlength calculation. Sample statistics of our small dataset may also deviatefrom population statistics.In choosing the threshold for defining the boundary of tubarial glands,we observed that voxels in the head and neck region having a SUVbw greaterthan one were primarily limited to the regions of major salivary and tubarialglands, and only found sparsely outside these glands. Furthermore, SUVbwgradients along the perimeters of the glands were steep enough for smallchanges in the threshold to have little effect on gland definition. Theseobservations made SUVbw = 1 a suitable threshold for defining the tubarialglands. Glands were segmented manually around thresholded regions toavoid anomalous border definitions going unnoticed.The 90th percentile slice width was chosen to define the gland width asit is close to the maximum width but more robust to noise associated withmaximum value in a sample distribution. Widths of manually contouredtubarial glands were slightly smaller than autosegmented widths. This hasstatistical significance (Table 7.2), but the discrepancy is less than 1 mm,which is less than a single PET voxel and likely clinically insignificant.Model performance was limited by the small cohort of 30 patients usedfor developing the models, which made it a challenge to decide the mosteffective way of splitting the data for training, validation, and testing. It iscommon for a certain percentage of data to be set aside as an independenttraining set that can be used for assessing model performance after training.This is most important if different predictive models are to be compared onthe validation sets used for cross-validation. After consideration of allocatinga small portion of our data to an independent test set, we decided the benefit157of having a final set for assessing model performance would be outweighedby the decrease in size of our training set, as well as the questionable validityof such a small test set for assessing performance. A test set would havebeen required had we used our validation set to tune model architecturesand hyperparameters, but for the purposes of this study, it was not a viableoption.Model performance is a function of chosen model hyperparameters, whichhave not been extensively fine-tuned using this dataset. It was infeasible forparameters to be fine-tuned in this study due to computational and timelimitations. Our training rate was less than 15 epochs per day, requiringover a week to train all five folds of the cross-validation. Performing nestedcross-validation [482] for iterating over permutations of hyperparameterswould require months of computation (with our resources), which could notpossibly be carried out for this study.Tubarial gland boundaries are invisible on CT images, and the imagingspace around the the glands has high inter-patient variability. While themodel successfully extracted relevant features for learning the approximateregion of tubarial glands, it is unable to predict glands with highly accurateconformity due to the high variability of glands contoured with PSMA PET.One challenge of training deep learning models is the requirement of verylarge datasets for generalized accuracy [485]. Even using a larger trainingset, it will be a challenge for the model to learn CT image features thatcorrelate with PSMA PET uptake in the tubarial glands, which is used todefine ground truth image masks.Models for the segmentation of medical image structures are typicallytrained using much larger training sets, resulting in higher-level perfor-mance. While it may be argued that deep learning architectures are moreappropriate for larger data sets, the use of deep learning is advantageouscompared to other machine learning methods in this context due to theability of deep learning model performance to scale with data. Althoughthe dataset used for training this model was relatively small, a U-Net-basedarchitecture was chosen such that the model can be incrementally improvedupon as more data becomes available. The full Organogenesis program in-158cluding the tubarial gland model is available online so that groups havingadditional PSMA-PET\/CT data can continue training for improved modelperformance.Dose in the tubarial glands has been correlated with post-treatment xe-rostomia [17]. The multicollinearity between parotid and tubarial gland dosefor predicting xerostomia makes it difficult to predict an independent doseresponse of the tubarial glands, but it is possible that the lack of aware-ness around the presence of the tubarial glands has resulted in a missingvariable, which could now be used to reduce the apparent uncertainty insalivary dose response. The dose response of the parotid glands has a highdegree of inter-patient variability [486], and we suspect tubarial glands toshare this variability. Given the similar PSMA-PET uptake of tubarial andparotid glands, as well as the previously demonstrated correlation betweentubarial gland dose and xerostomia, it seems prudent to adopt parotid doseconstraints for the tubarial glands until more specific guidelines becomeavailable.As previously discussed (Chapter 7), the existence of the tubarial glandsis currently up for debate. A clinical study to test the benefit of consideringthe tubarial glands as OARs during radiotherapy treatment planning couldhelp resolve the lack of consensus on the role of these glands in radiotherapy.The autosegmentation model developed here is freely available in Organo-genesis, make this possible. Clinically derived, empirical evidence suggestingthat dose to tubarial glands is predictive of salivary outcomes would be aconvincing motivator for adopting tubarial glands as standard OARs.7.5 ConclusionIn conclusion, we have developed a CT-based autosegmentation model forthe newly discovered tubarial glands. PSMA-PET was used to create groundtruth tubarial gland masks which were registered with corresponding CT im-ages prior to training. A MultiResUNet architecture was trained to predicttubarial gland masks using CT only. All autosegmentation software hasbeen made open-source on GitHub including trained tubarial gland mod-159els, amongst auto-segmentation models for other OARs. Including tubarialglands in the optimization process of head and neck radiotherapy has thepotential to improve patient outcomes with minimal effort, though furtherwork is required to quantify these benefits. Organogenesis can be used toquantify dose in the region of the tubarial glands for further evaluation andplanning. The software for using this model is freely available and featurescross-platform compatibility.160Chapter 8Investigating HeterogeneousPSMA Ligand Uptake InsideParotid Glands8.1 IntroductionProstate-specific membrane antigen (PSMA) positron emission tomography(PET) is an imaging procedure primarily used for detecting prostate can-cer [399], which quantifies the expression of the PSMA, which is found onprostate cancer cells, using radiolabeled PSMA ligands. These PSMA lig-ands also accumulate in the major salivary and lacrimal glands [487\u2013489], bya process postulated to be at-least partially unrelated to PSMA-mediateduptake [490]. While salivary gland uptake is undesirable for the purposes ofradioligand therapy for prostate cancer patients, it renders PSMA PET apotentially useful quantitative imaging modality for salivary glands.Klein-Nulent et al. [180] hypothesized that uptake of the PSMA ligandin salivary glands is associated with the functional capacity of the glands,based on two findings. First, they noted that xerostomia (subjective drymouth) is a common side effect of 177Lu-PSMA treatment, which may bedue to the uptake and cell loss in functional regions of the gland. Secondly,The content of this chapter has been submitted for publication in a peer-reviewedjournal. The name of the article is, \u201cInvestigating heterogeneous PSMA ligand uptakeinside parotid glands,\u201d and the co-authors are Caleb Sample, Arman Rahmim, CarlosUribe, Franc\u00b8ois Be\u00b4nard, Jonn Wu, and Haley Clark.16168Ga-PSMA uptake is significantly lower in irradiated submandibular glandsthan normal glands [491]. In another study, supporting PSMA PET\u2019s utilityfor assessing salivary gland functionality, Zhao et al. [181, 492] showedthat 68Ga-PSMA-11 PET\/CT is an effective supplement to salivary glandscintigraphy, which is a nuclear imaging method use to clinically evaluatesalivary gland function. Furthermore, prior 131I-radionuclide therapy hasbeen found to significantly decrease PSMA PET uptake in salivary glands,with a high degree of inter- and intra-patient variability [182].Assuming salivary gland functionality and PSMA PET uptake in theglands are correlated, then in principle, both inter-and intra-patient vari-ability in uptake could provide valuable insight into the functional anatomyof the glands. Several independent analyses have shown head-and neck can-cer patients to have variable intra-parotid therapeutic-dose responses duringradiotherapy [12, 13, 15, 375, 383, 493, 494]. It remains unclear whetherPSMA PET \/ computed tomography (CT) has utility for assessing intra-parotid gland anatomical variability for the purposes of radiotherapy plan-ning. Intra-patient PSMA ligand uptake in salivary glands has been reportedas homogeneous [180]. This is a reasonable qualitative description of uptakein the glands, as they tend to appear visually homogeneous when viewedwith a default window\/level for a full-body PET\/CT image. However, uponviewing several PSMA PET images of prostate cancer patients with varyingwindows and levels, we were able to detect an asymmetric trend for uptakein the parotid glands, where regions of high uptake were biased towards thelateral and posterior portions of the gland. Uptake in the submandibularglands did appear to be homogeneous.In this retrospective study of [18F]DCFPyL PSMA PET images of 30prostate cancer patients, we first seek to assess the spatial heterogeneityof uptake within the parotid glands, with the motive of quantifying noveltrends with future applications in improving parotid gland radiotherapydose constraints. To make our findings practically useful, we also test fora correlation between intra-parotid PSMA PET uptake and CT radiomictexture features to assess whether CT could potentially be used as a low-cost proxy when PSMA PET imaging is not available.1628.2 Methods8.2.1 Cohort and Data AcquisitionThis retrospective study was approved by an institutional review board.Full-body [18F]DCFPyL PSMA PET\/CT images were de-identified for 30previous prostate cancer patients who had previously consented to the useof their data for research studies (Mean Age 68, Age Range 45-81; meanweight: 90 kg, weight range 52 kg-128 kg). Patients were scanned, twohours following intravenous injection, from the thighs to the top of the skullon a GE Discovery MI (DMI) scanner. PET images were reconstructed usingVPFXS (OSEM with TOF and PSF corrections) (pixel spacing: 2.73-3.16mm, slice thickness: 2.8-3.02 mm). Helical CT scans were acquired on thesame scanner (kVP: 120, pixel spacing: 0.98 mm, slice thickness: 3.75 mm).To avoid imposing interpolation methods, voxel sizes were not resampled.8.2.2 Parotid Gland ContouringCT images were used for contouring parotid and submandibular glands.This consisted of two steps, where Limbus AI [419] was first used for auto-segmentation of the glands, which were then manually refined by a singlesenior radiation oncologist, Jonn Wu. Unless stated otherwise, all reportedresults are defined within these CT-defined regions.8.2.3 Parotid Gland PSMA PET Uptake AnalysisThe analysis was performed using custom software written in the Pythonprogramming language. Standard Uptake Values (SUVs) in PET Imageswere normalized by lean body mass (SUVlbm) where lean body mass wasestimated for each patient using the Hume formula [420]. For the remain-der of this article, for brevity, SUV should be interpreted as SUVlbm. BothSUVmean and SUVmax were included in the results as relevant metrics in-side various regions of interest (ROIs). For the investigation of intra-glanduptake, right and left gland statistics were pooled whilst respecting the cen-tral axis of symmetry, meaning that a \u201cmedial-lateral\u201d direction was used163rather than simply \u201cleft-right\u201d. In the first part of the analysis, we deter-mined typical SUV cohort statistics within the parotid and submandibularglands, as well as within the superficial and deep lobes of the parotid gland,with the latter not previously reported in the literature. Superficial anddeep lobes were contoured by dividing the whole-parotid gland contoursaccording to the standard procedure outlined by Zhang et al. [495]. Tovisualize the extent of population-level spatial uptake asymmetry along themedial-lateral and anterior-posterior directions in the parotid glands andsymmetry in the submandibular glands, as seen in our initial patient-specificinspection, PSMA PET uptake in both glands was plotted as a function oflateral and posterior displacement from the gland\u2019s center of mass. This dis-placement was recorded as a fraction of the gland\u2019s maximum half width ineach direction (medial-lateral or anterior-posterior). Sturges\u2019 rule using theaverage number of voxels within glands was used to determine the optimalnumber of displacement bins for creating a histogram of uptake vs. displace-ment (N Bins = log2 n + 1, where n is the average number of voxels ). TheSUVmean in each patient\u2019s left and right parotid gland was found in each dis-placement bin, and finally, SUVmean in each displacement bin was averagedover all glands and patients to yield SUVMean. We then analyzed how re-gions of high PSMA PET uptake in the parotid gland are distributed, usingvarious lower thresholds for defining said regions. Thresholds were chosenas combinations of SUVmean (\u00b5) and the standard deviation, \u03c3, within thewhole gland. The average displacement of various high-uptake regions fromthe whole parotid gland center of mass is reported. Next, we performeda sub-region analysis where parotid glands were divided by parallel planesinto four sub-segments of equal volume. This was done separately along eachCartesian direction, resulting in a total of 12 subregions. Subsegmentationwas performed such that the \u2018slab volume\u2019 of each subregion (total planararea multiplied by the image slice thickness) [13] was equal to within an er-ror tolerance of 0.01 % in each region. SUVMean and SUVMax (averaged overall patients) were then computed in each sub-region. We then determinedthe optimal planes for dividing the parotid gland in half to either maximizeor minimize the difference between SUVMean and SUVMax between halves.164Planes were defined by their normal vectors in spherical coordinates, withthe zenith direction corresponding to the patient\u2019s superior direction, andthe azimuthal angle of 0\u25e6 being defined in the lateral direction and initiallyincreasing towards the posterior direction. Azimuthal and polar angle com-binations were used to define the planes, using azimuthal angles between 0and 180 degrees (increments of 15 degrees) and polar angles between 0 and90 degrees (increments of 10 degrees). This resulted in a total of 120 cuttingplanes being tested. The dividing plane always passed through the parotidgland\u2019s center of mass, and uptake statistics were calculated separately forvoxels below and above the plane.8.2.4 Quantifying the Relationship Between PSMA PETuptake and CT Texture FeaturesWe evaluated the correlation between PSMA PET uptake in various sub-regions of the parotid glands with regular CT Hounsfield units (HUs) as wellas two CT texture feature map images. Texture features computed includedthe Grey Level Run Length Matrix (GLRLM) with a short (GLRLMS)and long (GLRLML) run length emphasis. Only two texture features wereevaluated to reduce the likelihood of false discoveries from multiple featuretesting. An axial slice containing the parotid glands is shown for PSMAPET, GLRLML, GLRLMS, and regular CT in Figure 8.1.165Figure 8.1: Axial slices of PSMA PET, CT, and two CT texture features: the Grey Level Run Length Matrix,with a long and short run emphasis (GLRLML and GLRLMS), are shown. Slices intersect the parotid glands.166The GLRLM was chosen for this study as it is a standard texture met-ric, but there are many other features which could have been tested. TheGLRLM is an extraction of high order statistical texture features from im-ages [496], which quantifies the distribution of consecutive voxels having thesame discretized grey level. It is represented as separate 2-dimensional ma-trices calculated along various angles throughout an ROI, where the (i, j)thelement represents the number of runs with grey level: i, and length: j. Asingle value is then obtained for each ROI by averaging over all elements andangles, where the GLRLMS weights runs by the inverse square of the runlength, while the GLRLML weights runs by the square of the run length. Wechose to calculate both long-run and short-run versions of the GLRLM be-cause we were unsure which quantity would be more suitable for comparingwith PSMA PET. Voxel-wise feature maps can be calculated by specifyinga kernel size which defines a region around each voxel for computing theGLRLM.Features maps were calculated using the pyradiomics library [424] usinga 5 \u00d7 5 masked kernel. The masked kernel is used to exclude voxels out-side of parotid glands from contributing to run lengths). Grey levels werediscretized, which is required for tractability of feature selection [497, 498].The number of discrete bings used was determined by Sturges\u2019 rule [499]with the average number of voxels in each gland. Feature maps were calcu-lated on regular CTs after constraining their maximum values to 1000 HU,to lower the effect of artifacts on grey-level discretization.The correlation of PSMA PET uptake with CT images and texture fea-tures was tested between SUVMean and CT HUs, GLRLML and GLRLMS,corresponding to values calculated in the 12 sub-regions considered in thesub-region analysis as well as the superficial and deep lobes, making a totalof 14 sub-regions. The correlation was assessed using Spearman\u2019s rank cor-relation coefficient, rs and its corresponding p-value. Sub-region values werenormalized as fractional deviations from the whole-gland mean. Lastly, aBenjamini\u2013Hockberg (BH) false discovery correction was performed, as out-lined by Rahmim et al. [500].To add confidence to findings, correlations were then re-tested between167PSMA PET uptake and CT texture features within 18 non-overlapping,equal-volume sub-regions of parotid glands, as defined by Clark et al. [501].Correlations between both normalized and absolute sub-regional values werecomputed. Lastly, we tested the correlation between whole-gland SUVmean,GLRLML and GLRLMS.8.3 ResultsPSMA PET uptake statistics are reported in Table 8.1 for parotid and sub-mandibular glands, as well as the superficial and deep lobes of the parotidgland. Whole gland statistics agreed with those reported in the literature[180, 502]. SUVMean and SUVMax in the superficial lobe were significantlyhigher than in the deep lobe (p < 0.001). SUVMean in submandibular glandsappeared mostly homogeneous, while parotid glands had increased SUVMeanand SUVMax in posterior and lateral regions (p < 0.001) as shown in Fig-ure 8.2Table 8.1: Population-level PSMA PET uptake statistics (n=60) are shownfor the parotid and submandibular glands, as well as the superficial anddeep lobes of the parotid gland.Region of Interest SUVMean SUVMaxParotid Whole 6.2\u00b1 1.7 15.5\u00b1 4.5Left 6.2\u00b1 1.7 15.7\u00b1 4.5Right 6.1\u00b1 1.7 15.3\u00b1 4.5Deep Lobe 5.0\u00b1 1.7 12.7\u00b1 3.3Superficial Lobe 6.5\u00b1 1.9 15.4\u00b1 4.4Submandibular Whole 6.5\u00b1 1.9 15.3\u00b1 3.3Left 6.5\u00b1 1.9 15.1\u00b1 3.7Right 6.6\u00b1 1.8 15.4\u00b1 3.8Thresholded sub-regions of high uptake in parotid glands tended to besituated laterally, posteriorly, and superiorly from the centre of mass. Theshift in the highest-uptake region from the centre of mass was most pro-nounced in the lateral direction (Table 8.2). A sub-region with threshold\u00b5+ 3\u03c32 is shown inside a left and right parotid for a representative patient in168Figure 8.2: PSMA PET SUVMean in regions shifted along the medial-lateral(top) and anterior-posterior (bottom) directions in the parotid (left) andsubmandibular (right) glands. Displacements are expressed relative to themaximum half width of the gland in the appropriate direction. For example,a shift of \u201c1\u201d or \u201d-1\u201d from the centre of mass in the medial direction wouldbe right along the medial or lateral border, respectively.169Figure 8.3. How the geometry of sub-regions vary as the threshold increasesis shown for another representative patient in Figure 8.4.Table 8.2: Shift from the whole gland\u2019s center of mass, for regions of highPSMA PET uptake. Shifts are listed as fractions of the half width along therespective patient axis. For example. A shift of 0 means the high uptakeregion\u2019s center of mass is in perfect alignment with that of the whole gland,while a value of 1 means the center of mass is shifted to the furthest edge ofthe gland. High-uptake regions are defined with a lower threshold in termsof \u00b5 and \u03c3, the mean and standard deviation within the whole parotid gland.High-Uptake Shift from centre of mass (fraction of half-width)Region ThresholdLateral Posterior Superior\u00b5 0.06\u00b1 0.09 0.08\u00b1 0.09 0.03\u00b1 0.07\u00b5\u00b1 \u03c3 0.22\u00b1 0.13 0.11\u00b1 0.11 0.03\u00b1 0.10\u00b5\u00b1 3\u03c32 0.33\u00b1 0.15 0.10\u00b1 0.16 0.04\u00b1 0.18\u00b5\u00b1 2\u03c3 0.41\u00b1 0.24 0.03\u00b1 0.30 0.08\u00b1 0.30Uptake statistics in equal-volume subregions of the parotid gland areshown in Table 8.3 and visualized in Figure 8.5. SUVMean varied greatlybetween subregions, with regions of highest uptake for the three cuttingplanes being the two lateral-most sub-regions for the sagittal plane, theposterior subregion for the coronal plane, and the middle-superior regionfor the transverse plane. SUVMean in the two lateral-most sub-regions ofthe gland differed insignificantly from each other (paired t(59) = 0.14,p > 0.88) but were 45 % higher than the medial-most sub-region (pairedt(59) = 8.0, p < 0.001). Out of all 60 parotids examined, 50 SUVmax werefound in the lateral half of the gland, with 30 found in the lateral-mostsub-region. SUVMean in the posterior-most sub-region of the gland was 42% higher than the anterior-most sub-region (paired t(59) = 7.5, p < 0.001).SUVMean was highest in the two interior subregions when cut transversely,with the middle-superior subregion being 6 % larger than the middle-inferiorsubregion (t(59) = 5.3, p < 0.001). The SUVMax varied with the same trendas the SUVMean for the sagittal and transverse divisions but was found tobe much more homogeneous than SUVMean for the coronal divisions.170Table 8.3: PSMA PET uptake statistics. Statistics are shown in subre-gions created by dividing parotid glands with parallel planes into four equal-volume regions. This is done separately with sagittal, coronal, and trans-verse cutting planes. The final column includes the number of times thewhole gland\u2019s maximum uptake voxel was found in the respective region.Cutting Plane Subregion SUVMean SUVMax ContainsSUVmaxWhole (n=60)Sagittal Lateral 7.1\u00b1 2.3 15.2\u00b1 4.5 30Middle-Lateral 7.1\u00b1 2.1 14.6\u00b1 4.2 20Middle-Medial 6.1\u00b1 1.8 13.9\u00b1 3.8 5Medial 4.9\u00b1 1.5 12.9\u00b1 3.3 5Coronal Posterior 7.2\u00b1 2.3 14.7\u00b1 4.2 13Middle-Posterior 6.8\u00b1 1.9 14.9\u00b1 4.2 18Middle-Anterior 6.0\u00b1 1.6 14.6\u00b1 4.2 12Anterior 5.1\u00b1 1.8 14.4\u00b1 4.5 17Transverse Inferior 5.4\u00b1 1.6 14.0\u00b1 4.2 9Middle-Inferior 6.7\u00b1 1.9 14.7\u00b1 4.3 13Middle-Superior 7.1\u00b1 2.1 14.9\u00b1 4.5 20Superior 5.9\u00b1 1.8 14.8\u00b1 4.4 18171Figure 8.3: A subregion of high PSMA PET uptake (pink), defined using alower threshold of \u00b5 \u00b1 3\u03c32 inside the left and right parotid gland (cyan) fora representative patient. \u00b5 and \u03c3 are the mean and standard deviation ofuptake in the whole parotid.172Figure 8.4: Variability of high-uptake subregions vs. threshold for a repre-sentative patient. Thresholds are defined in terms of the mean and standarddeviation of uptake in the whole parotid gland, \u00b5 and \u03c3. The region of high-est uptake tends towards the lateral and posterior (and somewhat superior)portions of the gland.173Figure 8.5: SUVMean for sub-regions defined by dividing the parotid into four equal-volume regions with parallelplanes along each Cartesian direction. The regions of highest uptake for the three cutting planes were the posteriorsub-region for the coronal plane cuts (left), the two lateral-most sub-regions for the sagittal plane (middle), andthe middle-superior region for the transverse plane (right).174The optimal dividing planes for maximizing or minimizing the differencebetween SUVMean and SUVMax in halves of the parotid gland are sum-marized in Table 8.4. The results are visualized for the maximum andminimum separation of SUVMean in Figure 8.6. The maximum separationof SUVMean occurred with a division plane defined by its normal vector,(\u03d5, \u03b8) = (135\u25e6, 90\u25e6), which is a diagonal split separating the posterolat-eral and anteromedial aspects of parotid glands. The posterolateral sub-region\u2019s SUVMean was 41 % higher than the anteromedial region (pairedt(59) = 9.5, p < 0.001). The maximum separation of SUVMax occurred witha similar plane vector, (\u03d5, \u03b8) = (165\u25e6, 80\u25e6), with the lateral-most subregion\u2019sSUVMax being 12 % higher (paired t(59) = 7.7, p < 0.001).Table 8.4: Optimal plane orientation for dividing the parotid gland inhalf. Orientations were selected to maximize and minimize the differencein SUVMean and SUVMax between halves. Uptake statistics on either side ofthe dividing plane are also provided (i.e. the quantity being minimized andmaximized). Planes are defined in spherical coordinates, with the zenith di-rection in the patient\u2019s superior direction, and the azimuthal angle, \u03d5, being0 in the medial direction, and increasing towards the posterior direction.Division Type Chopping Plane (\u03d5, \u03b8) SUVAbove SUVBelowSUVMean Largest Difference (135\u25e6, 90\u25e6) 5.0\u00b1 1.5 7.4\u00b1 2.3Smallest Difference (45\u25e6, 70\u25e6) 6.1\u00b1 1.8 6.2\u00b1 1.8SUVMax Largest Difference (165\u25e6, 80\u25e6) 13.7\u00b1 3.5 15.3\u00b1 4.4Smallest Difference (30\u25e6, 40\u25e6) 14.9\u00b1 4.2 14.9\u00b1 4.4175Figure 8.6: The optimal dividing planes for maximizing (left) and minimizing (right) the difference betweenSUVMean in halves of the parotid gland. Planes are defined in spherical coordinates, with the zenith directionin the patient\u2019s superior direction, and the azimuthal angle, \u03d5, being 0 in the medial direction, and increasingtowards the posterior direction.176In the 14 analysis sub-regions (4 planar divisions in each Cartesian di-rection and superficial\/deep lobes), the spatial distribution of SUVMean wasstrongly correlated with the GLRLML (rs = 0.93, p < 0.001) and stronglyanti-correlated with the GLRLMS (rs = 0.94, p < 0.001). SUVMean wasnot correlated with CT image HUs. These results are shown in Figure 8.7.Correlations of PSMA PET uptake with GLRLML and GLRLMS remainedsignificant (p < 0.001) following a BH false discovery correction. Correla-tions remained strong after recalculating correlations of uptake and texturefeatures within Clark et al.\u2019s [12] 18 equal-volume subregions described inthe methods (p < 0.001). Correlations and corresponding significance valuesare summarized in Table 8.5. Correlations were approximately unchangedwhen calculating with either absolute uptake\/GLRLM values or values nor-malized to whole-mean statistics. Whole-gland SUVmean was insignificantlycorrelated with GLRLML and GLRLMS. These results are summarized inFigure 8.8.177Figure 8.7: The spatial distribution of SUVMean was found to be stronglycorrelated with the GLRLML (left) and strongly anti-correlated with theGLRLMS (right). Correlations were tested using means calculated in 14sub-regions of parotid glands, represented as normalized differences fromwhole gland statistics.178Table 8.5: Spearman\u2019s rank correlation coefficient, rs, and the correspondingp-value for correlations between PSMA PET and CT images. PSMA PETand CT Grey Level Run Length Matrices with long and short run lengthemphases (GLRLML and GLRLMS) were significantly correlated, whereasraw PSMA PET and regular CT HUs were not correlated. Correlations werecalculated using mean uptake values in either the 14 subregions mentionedin the methods, or Clark et al.\u2019s 18 subregions [12].Image Pair rs p-value14 subregions PET& GLRLML 0.93 p < 0.001PET& GLRLMS -0.94 p < 0.001PET & CT -0.20 > 0.4818 subregions PET& GLRLML 0.90 p < 0.001PET& GLRLMS -0.74 p < 0.001179Figure 8.8: Correlations between PSMA PET SUVMean and the GLRLML(left) and the GLRLMS (right) were significant when calculated using statis-tics in 18 non-overlapping, equal volume sub-regions of parotid glands. Cor-relations were tested using absolute (top) and relative (middle) statisticsinside sub-regions. We also tested the correlation between whole-glandSUVMean and CT texture features, over the 60 parotid glands in the dataset.The whole gland PSMA PET and GLRLM were not significantly correlated.1808.4 DiscussionSpatial heterogeneity of [18F]DCFPyL PSMA PET uptake in the parotidglands has been demonstrated and quantified in well-defined regions. Wholegland statistics agreed with those reported in the literature [180, 503]. Thesubmandibular gland\u2019s relatively homogeneous uptake (Figure 8.2) and thefact that PET images were attenuation corrected reassured us that regionaltrends were not simply due to the lateral\/posterior regions of glands beingcloser to the skin surface, or partial volume effects.In general, SUVMean and SUVMax were found to be highest in subregionstowards the lateral, posterior, and middle-superior portions of the parotidglands. This was demonstrated by examining sub-regions of the gland de-fined using SUV thresholds and planar divisions. SUVMean was found toincrease in an approximately linear fashion from the anterior to the poste-rior portion of the gland (Figure 8.5). SUVMax did not display as strong ofa trend (Table 8.3). This can be explained by the higher noise associatedwith a single voxel than the average over a region. In the medial to lat-eral direction, the SUVMean and SUVMax was significantly higher in the twolateral-most sub-regions than the two medial-most subregions. The uptakewas found to be more centrally localized in the inferior-superior direction,with the highest uptake in the middle-superior region of the gland.The superficial lobe was found to have significantly higher PSMA PETuptake than in the deep lobe. The superficial lobe of the parotid gland issituated laterally to the deep lobe and the two lobes are divided by thefacial nerve for the purposes of surgical procedures. The two lobes have nopreviously established anatomical differences [504, 505]. However, superficialparotid lobe-sparing Intensity Modulated Radiation Therapy (IMRT) hasbeen found to significantly reduce the incidence of xerostomia post-RT [506].While the method of delineating regions of high uptake in the parotidglands via thresholding is favourable for examining patient-specific uptaketrends, as it does not require imposing arbitrary divisions, it is challengingfor determining the spatial variation of uptake on a population level. Di-viding the parotid gland into regions of equal volume using planar divisions181lends itself well to cross modality comparisons, as these divisions are well-defined and reproducible without PET images. As PSMA PET is costly andnot routinely acquired for head-and-neck patients, it would be fortuitous ifpopulation trends found in PSMA PET uptake were also observable usingCT imaging. One such example where CT was used as a proxy for PSMAPET findings is in the auto-segmentation model for PSMA PET - definedtubarial glands [17] using only CT images in Chapter 7.Determining the best cutting plane for alternatively maximizing andminimizing the difference in SUVMean and SUVMax between halves opensthe door to future radiotherapy dose-response studies for validating a cor-relation or anti-correlation between intra-parotid PSMA PET uptake andfunctional capacity within the parotid glands. Differences in therapeuticdose between regions with large PSMA PET uptake differences should alsolead to differences in xerostomia incidence rates and salivary output mea-surements. On the contrary, dose differences between regions with minimaldifferences in PSMA PET uptake could potentially lead to similar patientoutcomes. Such a study could also validate the preferential use of SUVMeanor SUVMax for characterizing salivary glands.SUVMean and SUVMax were normalized by lean body mass (SUVlbm) asopposed to body weight (SUVbw) to reduce the mass-dependence of uptake[507, 508]. Results have been reported in terms of the mean and maximumuptake in regions of the gland, as both metrics tend to be considered inthe literature. While the Society of Nuclear medicine and Molecular Imag-ing (SNMMI) recommends SUVMax as the preferred tumour uptake metric[406], there is evidence that SUVMean has better reproducibility and is lessimpacted by reconstruction methods [509\u2013511]. Parotid glands should beexpected to have less inter-patient variability than tumour volumes, render-ing SUVMean to be a suitable metric for quantitative parotid gland imagingwith PSMA PET.The strong correlation of PSMA PET with GLRLML and strong anti-correlation of PSMA PET with GLRLMS implies that regions of high up-take are found to occur in regions of higher homogeneity within CT images(long run lengths). This finding requires further validation. The lack of182a correlation between PSMA PET and CT HU images is to be expected,as increased attenuation of x-rays should not be expected from regions ofhigh PSMA PET uptake. Instead, it is the spatial relationships betweenneighbouring voxels that relate to PSMA PET uptake. Our results sug-gest that while intra-parotid heterogeneity of PSMA PET and CT texturefeatures appear to be related, the absolute, whole-gland statistics are unre-lated. Intra-parotid correlations were approximately unchanged when usingabsolute statistics or statistics normalized to whole-gland values.The GLRLM was chosen due to its wide-spread use, simplicity, and in-terpretability. A short- and long-run emphasis were included since it wasunknown which run lengths would have relevance. The number of radiomictexture features tested was minimized to avoid false discovery rates. How-ever, other radiomic texture features, or combinations of features, may havean even better ability to capture PSMA PET uptake trends. A follow-upstudy focusing solely on correlations between PSMA PET and CT texturefeatures would help to better define these relationships.The strength of correlations between PSMA PET regional uptake andCT texture features within parotid glands was higher than anticipated. Webelieve this result is worth emphasizing, as it suggests the possibility ofusing CT texture features as a proxy for PSMA PET imaging of salivaryglands, which is ideal, as PSMA PET images are not expected to become astandard of care for head-and-neck cancer patients. It has been previouslydemonstrated that PSMA PET uptake patterns may also be linked withT2-weighted magnetic resonance imaging texture features [512].The relationship between PSMA PET and CT texture features requiresfurther investigation. In particular, it would be of interest to see how up-take patterns of PSMA PET throughout the body correlate with CT texturefeatures, in areas outside the parotid glands. The primary objective of thiswork was to investigate PSMA PET intra-parotid heterogeneity, and thecorrelation between PSMA PET and CT texture features should be investi-gated thoroughly, and throughout the body, in future studies. Furthermore,investigating how intra-parotid PSMA PET uptake relates to gland func-tionality would facilitate the creation of practical, clinical methods for using183CT texture features as a proxy for PSMA PET. We plan to investigate thisin a follow-up study.Computing radiomic features with different voxel sizes is expected tochange radiomic feature values. Since our values were averaged over ROIsand only used for computing correlations, we anticipate that the method isrobust to the choice of voxel size. It was previously shown that varying slicethickness by 3 mm has a small effect on CT radiomic feature values in livertumours [513]. However, the voxel size should be considered when compar-ing results in future works. It may be necessary to standardize voxel sizes forcross-institution radiomic comparisons and analyses. CT was used to delin-eate parotid glands for this study, and it is possible that some parotid glandtissue was not captured within contours. Variation in delineation strategiesbetween centres will add to variation in reproducibility. Furthermore, re-construction methods of PET systems and differences between institutionsshould be considered when reproducing results.PSMA PET images have increased levels of noise compared to CT, andcan be dependent on extrinsic factors, such as food intake [513], which makesthe limited cohort (n=30) a weakness of this study. These results will requireexternal validation. A retrospective study correlating the heterogeneity ofthe dose response and PSMA PET uptake in parotid glands would be auseful future study for translating these findings into a clinically-valuablefinding.8.5 ConclusionIn conclusion, PSMA PET uptake in parotid glands is heterogeneous, withregions of high uptake being generally situated towards the posterior and lat-eral portions of glands. We have identified specific and well-defined regionsof high and low uptake in the gland, as well as the optimal planes for dividingparotid glands in half to maximize and minimize differences in PSMA PETuptake. These results lend themselves well to future dose response studiesfor head-and-neck radiotherapy patients. Lastly, we demonstrated PSMAPET uptake in parotid glands to be strongly correlated with CT texture184feature maps, anticipating the potential utility of CT texture feature mapsas a proxy for using PSMA PET uptake patterns to tailor patient-specificradiotherapy dose constraints.185Chapter 9Evaluation of RegionalImportance Estimates in theParotid Glands Using PSMAPET9.1 IntroductionIntensity Modulated Radiotherapy (IMRT) allows for the creation of treat-ment plans with high dose conformity in cancerous regions while minimizingdose to healthy tissue [514]. However, high dose levels in cancerous tissueinevitably tail off into healthy tissue, so treatment planners and oncolo-gists must prioritize which healthy regions to spare. Treatment planningin the head-and-neck region is particularly challenging, as there are manyorgans in close proximity which often abut or overlap with tumour volumes[472]. Dose levels in the salivary glands are of particular concern, as xeros-tomia (subjective sensation of oral dryness) remains a common side effectfor head-and-neck cancer patients [515]. Dose to the largest salivary glands,the parotid glands, is the greatest risk factor for post-treatment xerostomia[474].The content of this chapter has been submitted for publication in a peer-reviewedjournal. The name of the article is, \u201cPSMA PET as a predictive tool for sub-regionalimportance estimates in the parotid gland,\u201d and the co-authors are Caleb Sample, ArmanRahmim, Carlos Uribe, Jonn Wu, and Haley Clark.186The current standard of care is to minimize the whole-mean dose toparotid glands [516], which were previously considered to have a uniformdose response [517]. However, there have been numerous attempts in recentyears to quantify the relative importance of various parotid gland subregionsfor predicting post-treatment complications [12, 14\u201316].A potential quantitative imaging method for assessing functionality withinsalivary glands is prostate-specific membrane antigen (PSMA) positron emis-sion tomography (PET). PSMA PET radioligands target the PSMA, a type2 integral membrane protein that is expressed in all forms of prostate tissue,including carcinoma [166]. PSMA PET is typically used to stage prostatecancer [399] due to the high relative abundance of PSMA, which increases inproportion to the stage and grade of tumours [171]. PSMA ligand radiotrac-ers developed for PSMA PET imaging have demonstrated high physiologicaluptake in the salivary glands, as well as the lacrimal glands, liver, spleen,kidneys, and colon [179, 400\u2013402]. PSMA PET was furthermore used byValstar et al. in 2021 [17] to discover previously undocumented bilateralsalivary glands in the posterior nasopharynx, the \u201ctubarial glands.\u201d It isunclear whether uptake in non-prostate tissue is mediated by the expressionof PSMA in these tissues, or if PSMA ligand uptake is a result of otherphysiological mechanisms [179].PSMA ligand uptake in salivary glands has been suggested [180] to cor-relate with functional capacity, and mounting evidence supports this re-lationship [180\u2013183]. It was also recently shown that PSMA PET in theparotid and submandibular glands decreased exponentially with radiothera-peutic dose received in the glands during radiotherapy [518]. The same studyshowed that decreases in PSMA PET uptake following treatment were corre-lated with post-treatment xerostomia. Furthermore, uptake within parotidglands has been found to be non-uniform, with high uptake regions tendingtowards lateral, posterior, and superior regions (Chapter 8). We hypothe-size that intra-parotid gland uptake variability of PSMA PET is predictiveof functional importance.The purpose of this study is two-fold. First, we use a data set of 30PSMA PET images to compare intra-parotid PSMA PET uptake trends187with several regional importance estimates from the literature [12, 14\u201316].Second, we develop a population-level model of Clark et al.\u2019s [12] regionalimportance using radiomic features from PSMA PET and Computed To-mography (CT). We also demonstrate how such a model can be used topredict a patient\u2019s deviation from population-derived importance estimates,creating a single metric with population-derived, and patient-specific com-ponents.9.2 Methods9.2.1 DatasetThis study was approved by an institutional review board. The data setincluded de-identified [18F]DCFPyL PSMA PET\/CT images for 30 previ-ous prostate cancer patients (Mean Age 68, Age Range 45-81; mean weight:90 kg, weight range 52 - 128 kg). Scans were acquired two hours follow-ing intravenous injection, from the thighs to the top of the skull on a GEDiscovery MI (DMI) scanner.The mean and standard deviation of the in-jected dose was 310\u00b1 66 MBq (minimum: 182 MBq, maximum: 442 MBq).PET images were reconstructed using VPFXS (OSEM with time-of-flightand point spread function corrections) (pixel spacing: 2.73 - 3.16 mm, slicethickness: 2.8 - 3.02 mm). The scan duration was 180 s per bed position.Helical CT scans were acquired on the same scanner (kVP: 120, pixelspacing: 0.98 mm, slice thickness: 3.75 mm). Images were scaled to standarduptake values normalized by lean body mass (SUVlbm). Registered CTimages were used for delineating parotid and submandibular glands. LimbusAI [419] was used for preliminary auto-segmentation of the glands, whichwere then manually refined by a single senior radiation oncologist, Jonn Wu.9.2.2 Correction of Partial Volume EffectsOne weakness of PET as an imaging modality is its intrinsically low spatialresolution [403]. The burden of partial volume effects is less pronouncedwhen analyzing large geometric regions with homogeneous uptake, but can-188not be ignored when attempting to compare heterogeneous uptake in smallregions-of-interest (ROIs), such as subregions of the parotid glands. Chap-ter 5, a method has been developed for simultaneous deblurring and super-sampling of PSMA PET images using neural blind deconvolution, which weemploy in this work for preprocessing PSMA PET images. This model hasbeen shown to illuminate fine uptake trends within small regions of parotidglands. We performed all calculations with both \u201cenhanced\u201d images, andunmodified original images.9.2.3 Comparison of PSMA PET with Parotid GlandImportance ModelsPSMA PET uptake trends were compared with four models of intra-parotidgland importance found in the literature, detailed in the following sub-sections. Uptake metrics included the mean, median, and maximum, cal-culated in ROIs defined according to each specific model. As importancemodels were all population-level estimates, uptake metrics were averagedover the 60 parotid glands from the 30 patients.Clark et al.\u2019s model [12] estimates the relative importance of 18 equal-volume subregions of the contralateral parotid gland for predicting salivarydysfunction following radiotherapy. Stimulated saliva measurements werecollected for 332 patients before and at one year after radiotherapy. Therelative differences were predicted with conditional inference trees using ra-diotherapeutic dose levels in parotid gland subregions. Parotid glands weresub-segmented using nested planar segmentation (planes: 2 axial, 1 coronal,2 sagittal). Regions of high relative importance tended towards caudal-anterior regions, as shown in Fig 9.1. We sub-segmented parotid glandsaccording to the same regimen, and voxels within each of the 18 subre-gions were used to calculate uptake statistics. To test whether intra-parotidPSMA PET uptake is related to Clark et al.\u2019s importance estimates, Spear-man\u2019s rank correlation coefficient, rs, was computed between uptake in the18 subregions along with their corresponding importance estimates.189Figure 9.1: 3D rendering of voxels within a parotid gland corresponding toClark et al\u2019s relative importance subregions are shown from two angles.Han et al.\u2019s modelHan et al. [16] assess the relative importance of 9 parotid gland subregionsfor predicting injury (\u2265 grade 2 xerostomia at 6 months post-radiotherapy)and recovery (\u2265 grade 2 xerostomia at 6 months post-radiotherapy, followedby < grade 2 xerostomia at 18 months post-radiotherapy). Subregions weredefined by first applying a 3 mm margin to whole parotid glands, then divid-ing glands into three radial sectors (anterior, medial, posterior), then furtherdividing these sectors along the inferior-superior axis into 3 equal-length re-gions. Voxels within a parotid gland corresponding to these importanceregions are shown in Fig 9.2. Han et al. [16] determined the relative im-portance of 9 dose-volume statistics in 10% volume increments from D10(Minimum dose to 10% volume) to D90 (Minimum dose to 90% volume) ineach subregion. For our purposes, the mean importance computed over all190Figure 9.2: 3D rendering of voxels within a parotid gland corresponding toHan et al.\u2019s relative importance subregions are shown from two angles.dose statistics was used as a single relative importance estimate for each sub-region. Spearman\u2019s rank correlation coefficient, rs, was calculated betweenuptake and relative importance for predicting injury, and recovery.Van Luijk et al.\u2019s ModelVan Luijk et al. [15] used stimulated saliva measurements and radiother-apeutic dose levels to locate \u201ccritical\u201d regions within parotid glands whichare most predictive of salivary outcome at one year post radiotherapy. Thestudy did not specify a well-defined location of this critical region over thepopulation, however, it is stated to be in close proximity of the Stensen\u2019sduct, adjacent to the dorsal side of the mandible. For our purposes, we ap-proximated the critical region by applying a 9 mm margin to the mandible,which was intersected with the top half of the parotid gland (Fig 9.3). The 9mm margin was found to consistently intersect a region of the parotid gland191approximately corresponding Van Luiijk et al.\u2019s [15] critical regions. UptakeFigure 9.3: The approximate location of Van Luijk et al.\u2019s critical region ofthe parotid gland used for computing uptake statistics is shown.statistics were compared within expanded critical and non-critical regionsusing a paired t-test.Buettner et al.\u2019s ModelBuettner et al. [14] evaluated the predictive ability of various dose \u201cmo-ments\u201d in a regression model for post-treatment xerostomia in 63 head-and-neck cancer patients, treated with either IMRT or conventional radiotherapy.Important variables included mean dose to the superficial lobe, skewness ofdose in the cranial-caudal direction within the deep and superficial lobe,and relative concentration of dose in the caudal-medial region of the deeplobe. While the parotid glands were only segmented into superficial and deep192lobes, dose moments calculated within these regions evaluated the spatialvariance of the dose response.9.2.4 Development of a predictive Model for parotid glandrelative importance using PSMA PET and CTTo demonstrate the predictive ability of PSMA PET radiomic features forparotid gland regional functionality, we develop a model for predicting Clarket al.\u2019s [12] relative importance estimates using radiomic features extractedfrom both PSMA PET and CT images. We then demonstrate how such amodel can be used for predicting patient-specific perturbations away frompopulation-level importance estimates.To explicitly demonstrate the benefit of model-building using radiomicfeatures versus using only standard uptake statistics (mean, median, max-imum), we also develop another model using the same methods to be de-scribed but using only the mean, median, and maximum uptake as inputfeatures.Feature ExtractionThe standardized pyradiomics library [424] was used for computing radiomicfeatures of PSMA PET and CT within all 18 of Clark\u2019s subregions. The fullset of Gray Level Co-occurrence Matrix (GLCM), Gray Level Run LengthMatrix (GLRLM), Gray Level Size Zone Matrix (GLSZM), Gray Level De-pendence Matrix (GLDM), and first order features, computed with originalsquared, square root, and wavelet image types, were computed for a totalof 1060 features. For gray level discretization, a fixed bin width was chosenover a fixed bin count, as a fixed bin width has been shown to have betterreproducibility [519], especially when chosen to yield a bin count between16-128 [520]. We therefore set the bin width to 0.2 for original, 0.1 for squareroot, and 1 for square. For the wavelet features, a fixed bin count of 100was used, due to uncertainty in the expected range.Radiomic features were calculated for individual patients, and averagedover each parotid gland for all 18 subregions. This yielded a population-level193design matrix of shape (36, 1060) prior to feature selection. Features werecalculated for both enhanced and original PSMA PET images.Double Cross ValidationThe small size of our data set made it inappropriate to define a single testset for final performance evaluation, and we therefore used double cross val-idation, or sometimes called nested cross validation, where our test set wasrotated through 9 outside folds, each having its own inner cross validationloop for tuning the feature selection algorithm, model, and hyper-parameters(Fig 9.4).194Figure 9.4: For model testing and validation, a double cross validationscheme was employed, where the outside test set is rotated through a 9-foldcross validation loop, each including its own 8-fold inner cross validationloop for parameter tuning.195Feature Selection and ModelsTo avoid overfitting, the large number of features extracted must be prunedusing feature selection methods prior to model training. For this purpose,we include 3 feature selection algorithms within the cross validation loops,including a linear combination filter, a pairwise correlation filter, and princi-ple component analysis as used by Delzell et al. [521] to predict lung cancerusing radiomic features. The linear combination (lincom) filter uses QR de-composition to iteratively remove features which are linear combinations ofothers. The pairwise correlation filter tests the correlation between featuresand removes those who are correlated above a specified cutoff. Principalcomponent analysis changes the basis of the feature space to capture a largeportion of the variance using a smaller number of feature vectors. For moreinformation, refer to the work by Delzell et al. [521]Five different regression model types were included within cross valida-tion. This included a linear regression, support vector machine, randomforest, conditional inference tree, and kernel ridge model. Model perfor-mance is highly dependent on a variety of hyper-parameters which can betuned for the different models and feature selection algorithms. A set ofdifferent hyper-parameters for each model were iterated over within crossvalidation. All models, feature selection algorithms, and their correspondinghyper-parameters tested are listed in Table 9.1 Models were scored accordingto the mean absolute error (MAE).Error AnalysisFor estimating the uncertainty of model predictions, we employ the method-ology described by Cawley et al. [522] for kernel ridge models. This involvescomputing the leave-one-out absolute error for each sample in the data set,and then training a second kernel ridge model for predicting the absoluteerror of predictions based on the same input features and using this as anestimate of prediction variance.196Table 9.1: Models and feature selection (F.S) algorithms, along with theircorresponding hyper-parameters tested in cross-validation, are shown.Model Hyper-parametersSupport Vector Machine \u03f5 = [0.01, 0.05, 0.1]Kernel = [Linear, radial basis function, sigmoid, poly]Degree = [2,3]\u03b3 = [scale, auto]coef0 = [\u22120.3,\u22120.2,\u22120.1, 0]Random Forest number estimators = [3, 5, 7, 10]max depth = [3, 5, 8, None]Criterion = [Absolute Error, Squared Error]Conditional Inference Trees Max Depth = [5, 10, 15, 20, 25, None]Criterion = [Absolute Error, Squared Error]Kernel Ridge \u03b1 = [0.1, 0.5, 1, 5, 10]Kernel = [Linear, Radial Basis Function, Sigmoid]Linear Regression N\/AF.S. Algorithm Hyper-parametersPairwise Correlation Filter feature count = [1,2,3,4,5,6], cutoff = [0.85, 0.88, 0.9, 0.92]PCA feature count = [1,2,3,4,5,6,8,10,15,20,30]Linear Combination Filter correlation cutoff = [0.05, 0.1, 0.2, 0.3]Demonstrating a method for predicting patient-specificimportance perturbationsFinally, we demonstrate how patient-specific deviations from population-level importance estimates can be obtained, to create a single, combinedimportance estimate including both population-level and patient-specificcomponents. This is obtained by first computing and processing a patient\u2019sradiomic features according to the feature selection algorithm employed bythe final model. As the model has been trained to understand the relation-ship between specific features and relative importance estimates, inputtingpatient specific features into the model for all 18 parotid gland subregionsprovides an estimate of relative importance for said patient. A single com-bined importance estimate is created by taking the population level sub-region importance estimates, IPj , j \u2208 Z, 1 \u2264 j \u2264 18 and the differencein patient specific and population estimates, \u2206j , j \u2208 Z, 1 \u2264 j \u2264 18 and197computingI =\uf8f1\uf8f2\uf8f3IPj \u2206j<02IPj1+e\u22122\u2206j\u2206j > 0(9.1)This defines a minimum importance estimate using the population-levelestimates, and increases estimates in regions of high patient-specific im-portance, levelling off as the patient-specific estimate approaches about3x the maximum population-level importance estimate. Using this ap-proach, patient-specific predictions can be used to supplement or perturbpopulation-level estimates in regions predicted to be of high radiotherapeu-tic importance. Combined importance estimates for subregions are neverlower than population-level estimates, to avoid potential negative impactsassociated with under-estimating importance.9.3 Results9.3.1 Comparison of PSMA PET with Importance ModelsOverall, uptake of PSMA PET was found to be inversely proportional withsubregional importance estimates from the literature. These trends ap-peared stronger when enhanced images were used for uptake calculations.Clark et al.\u2019s [12] importance predictions in the 18 equal volume regionswere significantly anti-correlated with mean and median uptake (Table 9.2).A scatter plot of importance vs mean uptake in Clark et al.\u2019s subregions isshown in Fig 9.5.198Figure 9.5: Clark\u2019s relative importance versus mean PSMA PET uptake in18 equal-volume parotid gland subregions, averaged over 30 patients. Rela-tive importance was found to have a significant (p = 0.015) anti-correlationwith regional PSMA PET uptake. Calculations were performed with de-blurred PSMA PET images. A best fit line is shown in red.Table 9.2: Spearman\u2019s rank correlation coefficients for PSMA PET uptakewith Clark\u2019s relative importance estimates. Correlations are calculated formean, median, and maximum uptake, normalized by lean body mass. Re-sults are calculated using enhanced (deblurred and supersampled) and orig-inal PSMA PET images.Mean Median MaximumEnhanced rs = \u22120.56, p = 0.015 rs = \u22120.55, p = 0.016 rs = \u22120.25, p = 0.31Original rs = \u22120.50, p = 0.03 rs = \u22120.51, p = 0.03 rs = \u22120.30, p = 0.22199Han et al\u2019s [16] model predictions for relative importance in 9 regionsof unequal volume were not significantly correlated with uptake metrics.There did however exist weak trends of anti-correlation of uptake with im-portance for predicting injury, and direct correlation for predicting recovery(Table 9.3). A scatter plot of importance vs mean uptake in Han et al.\u2019ssubregions is shown in Fig 9.6.Figure 9.6: Han\u2019s relative importance versus mean PSMA PET uptake innine parotid gland subregions, averaged over 30 patients. Relative im-portance was found to have a statistically insignificant (p = 0.015) anti-correlation with regional PSMA PET uptake. Calculations were performedwith deblurred PSMA PET images. A best fit line is shown in green.Uptake levels were found to be approximately two times higher in Van-Luijk et al.\u2019s [15] non-critical region than in the critical region (p < 0.01)(Table 9.4). A boxplot of mean uptake in critical and non-critical regions isshown in Figure 9.7200Figure 9.7: Box plot of the mean PSMA PET uptake in critical and non-critical regions of parotid glands, as defined by Van Luijk et al. [15]. Resultsare calculated using a dataset of 30 patients. Mean uptake in critical regionswas found to be significantly (p < 0.01) lower than in non-critical regions.Calculations were performed with deblurred PSMA PET images.Table 9.3: Spearman\u2019s rank correlation coefficients for PSMA PET uptakewith Han\u2019s relative importance estimates for predicting both injury, and re-covery. Correlations are calculated for mean, median, and maximum uptake,normalized by lean body mass, using enhanced (deblurred and supersam-pled) and original PSMA PET images.hline rs, p (Mean & Imp) rs, p (Median & Imp) rs, p (Maximum & Imp)Injury Recovery Injury Recovery Injury RecoveryEnhanced -0.27, 0.49 0.39, 0.29 -0.07, 0.86 0.12, 0.76 -0.56, 0.11 0.49, 0.18Original -0.41, 0.26 0.42, 0.26 -0.19, 0.61 0.18, 0.64 -0.56, 0.11 0.49, 0.18201Table 9.4: Comparisons for mean, median, and maximum uptake, normal-ized by lean body mass, in Van Luijk et al.\u2019s [15] critical and non-criticalparotid gland subregions. Calculations are shown using enhanced (deblurredand supersampled) and original PSMA PET images.Mean Median MaximumCritical Non-Critical Critical Non-Critical Critical Non-CriticalEnhanced 3.1\u00b1 2.1 7.2\u00b1 2.1 2.7\u00b1 2.1 7.2\u00b1 2.2 9.4\u00b1 5.1 20.0\u00b1 6.0Original 3.2\u00b1 2.0 6.3\u00b1 1.7 2.9\u00b1 2.1 6.2\u00b1 1.8 7.6\u00b1 4.0 15.6\u00b1 4.5Uptake statistics in parotid gland subregions corresponding to Buettneret al.\u2019s important regions [14] are shown in Table 9.5. As shown in Chap-ter 8, uptake in parotid glands appears skewed towards lateral, posterior,and superior regions. Buettner et al. found the superficial and the deep lobeto be important, with importance concentrating slightly towards caudal re-gions. The caudal-medial subregion of the deep lobe, which was predictedto be of high importance, was found to have significantly lower (p < 0.01)uptake than in the caudal-lateral subregion. Caudal regions, in general, tendto have lower uptake than superior regions of the glands.202Table 9.5: Buettner et al. [14] found that dose to the superficial lobe, relative concentration of dose in thecaudal\/cranial region of both superficial and deep lobes, and relative concentration in the caudal-medial regionof the deep lobe, were predictive of post-treatment xerostomia for head-and-neck radiotherapy patients. It isunclear whether xerostomia is directly or inversely proportional to these metrics, so we simply report differencesin PSMA uptake within corresponding regions. Correlations are calculated for mean, median, and maximumuptake, normalized by lean body mass, using enhanced (deblurred and supersampled) and original PSMA PETimages. Corresponding subregion pairs are shown side-by-side using the same shading.Sup Deep Sup Cranial Sup Caudal Deep Cranial Deep Caudal Deep Caudal-Medial Deep Caudal-LateralEnhanced Mean 7.4\u00b1 2.2 5.7\u00b1 2.0 8.4\u00b1 2.7 7.2\u00b1 2.1 6.2\u00b1 2.0 5.1\u00b1 2.2 4.2\u00b1 2.3 5.9\u00b1 2.6Medial 7.6\u00b1 2.4 5.3\u00b1 2.3 8.8\u00b1 2.8 7.0\u00b1 2.2 5.8\u00b1 2.3 4.6\u00b1 2.6 5.7\u00b1 2.6 5.7\u00b1 3.0Maximum 19.8\u00b1 6.0 16.3\u00b1 4.7 18.8\u00b1 5.6 18.3\u00b1 5.8 15.7\u00b1 4.6 13.8\u00b1 4.6 14.8\u00b1 4.7 15.2\u00b1 4.2Original Mean 6.5\u00b1 1.9 5.2\u00b1 1.7 8.0\u00b1 2.5 6.3\u00b1 1.8 5.6\u00b1 1.9 4.5\u00b1 1.9 3.5\u00b1 1.9 5.4\u00b1 2.3six Median 6.5\u00b1 1.9 5.1\u00b1 1.9 8.4\u00b1 2.7 6.3\u00b1 1.9 5.6\u00b1 2.1 4.2\u00b1 2.1 3.1\u00b1 2.0 5.4\u00b1 2.7Maximum 10.9\u00b1 5.6 8.9\u00b1 4.5 14.8\u00b1 4.0 14.1\u00b1 4.0 11.9\u00b1 3.2 10.5\u00b1 3.5 8.1\u00b1 3.6 10.2\u00b1 3.62039.3.2 Model Performance for Predicting Parotid GlandRelative ImportanceFor each of the nine test-sets of the outer cross validation loop, the MAE,along with best model and feature selection algorithm, as determined viainner cross validation, are shown in Table 9.6 The average MAE for theradiomics model was 0.08 using enhanced images, and 0.15 with originalimages. This out-performed the model created using only the mean, medianand maximum, which had an MAE of 0.18 and 0.22 for enhanced and orig-inal images, respectively. Overall, the best performing model and featureselection algorithm was kernel ridge regression with principal componentanalysis using 20 features. A performance comparison between all modelsand feature selection algorithms is shown in Fig 9.8. The most importantfeatures for principal component analysis (determined by projecting princi-pal components scaled by their singular values onto original feature axes),are shown in Table 9.7. The overall-best hyper-parameters were found tobe a polynomial kernel of degree 2, with \u03b1 = 0.1, and coef0= 1. \u03b1 is theregularization strength, and coef0 is the variable-independent coefficient inthe kernel function.All model predictions for importance in the 9 test sets are collected andplotted against Clark\u2019s estimates in Fig 9.9. Prediction error was estimatedby a separate kernel ridge model which was trained to predict model esti-mation error, as previously described.9.3.3 Estimating Deviations of Patient-Specific Importancefrom population EstimatesThe best performing model, feature selection algorithm, and hyper-parametersas determined via cross validation, were then used to train a final population-level model using the entire population-level data set. Importance estimatesfor parotid gland subregions of individual patients could then be obtainedby inputting a given patient\u2019s radiomic features into the model. Exam-ples of how individual predictions deviate from population-level estimates,along with prediction errors estimated with the kernel ridge error model, are204Table 9.6: Mean absolute error for each test set of the outer cross validationis shown, along with the best performing model and feature selection algo-rithm determined during the inner cross validation. Results are shown forthe radiomics model and the model created using only the mean, median,and maximum uptake staitstics. Results are shown for models created withboth enhanced and original PSMA PET images.Radiomics ModelEnhanced Images Original ImagesFold M.A.E Model F.S Algorithm M.A.E Model F.S Algorithm1 0.08 K.R P.C.A 0.31 C.I.T P.C.A2 0.10 K.R P.C.A 0.29 R.F P.W.C3 0.06 K.R P.C.A 0.08 K.R P.C.A4 0.04 K.R P.C.A 0.11 K.R P.C.A5 0.06 C.I.T P.C.A 0.24 R.F P.C.A6 0.09 K.R P.C.A 0.03 C.I.T P.C.A7 0.07 K.R P.C.A 0.02 C.I.T P.C.A8 0.13 C.I.T P.C.A 0.04 K.R P.C.A9 0.08 K.R P.C.A 0.20 C.I.T P.C.AAverage 0.08 0.15Mean, Median, Maximum ModelEnhanced Images Original ImagesFold M.A.E Model F.S Algorithm M.A.E Model F.S Algorithm1 0.08 Lin Reg N\/A 00.27 Lin Reg N\/A2 0.28 SVM N\/A 0.27 Lin Reg N\/A3 0.16 SVM N\/A 0.17 Lin Reg N\/A4 0.03 SVM N\/A 0.09 K.R N\/A5 0.22 SVM N\/A 0.20 Lin Reg N\/A6 0.20 SVM N\/A 0.31 K.R N\/A7 0.12 SVM N\/A 0.16 Lin Reg N\/A8 0.28 SVM N\/A 0.21 Lin Reg N\/A9 0.23 SVM N\/A 0.25 Lin Reg N\/AAverage 0.18 0.22demonstrated for six different patients in Fig 9.10205Table 9.7: Relative importance of radiomic PSMA PET \/ CT features de-termined via principal components analysis for modelling of parotid glandsubregion importance.Feature Name Modality Relative Importance1. Original GLCM - Inverse Difference PSMA PET 1.02. Square Root GLCM - Run Variance PSMA PET 0.983. Original GLCM - Inverse Difference Moment PSMA PET 0.974. Square Root GLCM Inverse Difference PSMA PET 0.975. Original GLCM Inverse Variance PSMA PET 0.966. Square Root GLCM Inverse Difference Moment PSMA PET 0.957. Square Root First Order RMS CT 0.958. Square GLSZM GLNUN PSMA PET 0.949. Original GLRLM Long Run Emphasis PSMA PET 0.9410. Original GLDM Large Dependence PSMA PET 0.9311. Original GLRLM Run Variance PSMA PET 0.9112. Wavelet HHH GLCM Joint Average CT 0.9113. Wavelet GLCM Sum Average CT 0.9114. Wavelet HHH GLSZM High Gray Level Zone Emphasis CT 0.9115. Square Root GLCM Inverse Variance CT 0.9016. Wavelet HHH GLDM High Gray Level Emphasis CT 0.9017. Wavelet HHH GLRLM High Gray Level Run Emphasis CT 0.9018. Wavelet LLL GLCM Dependence Entropy CT 0.9019. Wavelet HHH GLCM Autocorrelation CT 0.8920. Square Root First Order Entropy CT 0.88206Figure 9.8: To compare performance across models and feature selectionalgorithms, the mean absolute error (MAE) of the top-performing model andfeature selection algorithm from each test fold was computed and averagedover all folds. Overall, kernel ridge regression and principal componentanalysis using 20 features demonstrated the best performance. Error barscorrespond to the standard deviation of prediction accuracy over varioushyper-parameters.207Figure 9.9: Model-predicted relative importance estimates for all subregionsare plotted along with Clark et al.\u2019s (in this case, ground truth) importanceestimates. Predictions are shown with their associated model predicted er-rors. Predictions were made using the best performing model and featureselection algorithm found with nested cross validation - a kernel ridge re-gressor model and principal component analysis feature selection using 20features.208Figure 9.10: Importance estimates obtained for six individual patients using the population-level model, are shown.Population level estimates for the 18 subregions are shown as purple squares, with the patient specific estimatesas gold circles. The population-level model captures the relationship between important radiomic features andimportance estimates, and can be used for estimating approximate shifts in importance estimates for an individualpatient\u2019s parotid gland subregions. Error estimates were obtained with the kernel ridge error model.209Fig 9.11 illustrates an example of how an individual patient\u2019s parotidgland radiomic features can be used to supplement the population impor-tance estimate, using the equation described in the methods.210Figure 9.11: Patient-specific parotid subregional importance estimates (left)can be used to supplement population-level importance estimates (middle)using the formula described in the methods, such that final estimates arenever lower than population-level estimates, but further increased in re-gions where patient-specific estimates are high. Only positive perturbationsto regional importance were made, to avoid negatively impacting patientsin the case where importance estimates are to be used for designing doseconstraints.2119.4 DiscussionThe results of this work indicate that intra-parotid gland PSMA PET up-take may be inversely related to subregional relative functional importance.Anticorrelative relationships were found to exist between PSMA PET up-take and four independent models of subregional parotid gland importancefrom the literature [12, 14\u201316]. These findings are interesting in relation torecent findings that suggest a direct relationship between inter-parotid glandPSMA PET uptake and whole-gland functionality [181\u2013183, 518]. While itappears from previous studies that whole-parotid gland functionality is di-rectly proportional to the magnitude of PSMA PET uptake, these resultssuggest that subregions of high relative functional importance within glandstend to have lower uptake. It is unclear which physiological mechanismsthese findings correspond to.Based on the present findings, PSMA PET may be a useful quantitativeimaging modality for assessing intra-parotid gland functionality. As xeros-tomia remains a common burden for head and neck radiotherapy patients[515], deeper understanding of intra-parotid gland functionality is importantfor enabling modernized parotid gland dose constraints to be designed.Clark et al.\u2019s [12] and Han et al.\u2019s [16] relative importance estimateswere practically advantageous in that they define numerous, well-defined,and non-overlapping subregions of parotid glands where correlations be-tween relative importance and PSMA PET uptake could be assessed. Bothmodels predict higher importance towards medial and caudal-middle regionsof the gland, while Clark et al.\u2019s predicts much higher importance in the an-terior half of the gland. Clark et al.\u2019s model was significantly (p < 0.02)anti-correlated with PSMA PET uptake, while Han et al.\u2019s model was alsoanti-correlated, but not significantly. It should be noted, however, that re-gions of high importance predicted by both models correspond to regionsof lower than average uptake (Chapter 8). Han et al.\u2019s sub-segmentationmethod yields subregions of unequal volume, which also creates problemswhen comparing uptake statistics. Due to the shape of the parotid glands,subregions within central regions will be larger than those at the superior212and especially the inferior portion when segmention yields subregions ofequal superior-inferior length. Both Clark et al.\u2019s and Han et al.\u2019s modelswere developed using stimulated salivary measurements.We were able to approximate the location of Van Luijk et al.\u2019s [15] criticalregions and compute PSMA PET uptake statistics within and outside saidregions. Uptake statistics within critical regions were significantly lowerthan non-critical regions, corroborating the anticorrelative trend betweenimportance and PSMA PET uptake observed with Clark et al. and Han etal.\u2019s subregions. Sparing dose in Van Luijk\u2019 et al.\u2019s [15] critical regions ofparotid glands for radiotherapy patients was recently shown to insignificantlyimpact patient outcomes [523]. However, dose to critical regions was morepredictive of salivary dysfunction than whole-gland dose. Comparing uptakewith importance in regions defined by Buettner et al.\u2019s [14] analysis alsopointed towards an anticorrelative relation of importance with PSMA PETuptake.Simultaneous deblurring and supersampling of PSMA PET images [461]prior to uptake calculations led to stronger correlations between uptake andimportance estimates, and better model performance for predicting regionalimportance. Better performance using enhanced images was expected, aspartial volume effects cause fine detail wash-out in small regions of PETimages.The relationship between PSMA PET and relative importance appearsnon-linear (Fig 9.5) and proved to be better predicted using radiomic fea-tures and non-linear modelling (Fig 9.9. Model development for predictingrelative importance with PSMA PET and CT radiomic features was success-ful, yielding a relatively low MAE (0.08) for test predictions, considering thesmall size of the data set. Kernel ridge regression with a quadratic kernelout-performed all other models tested. This suggests that the relationshipbetween PSMA PET uptake and regional importance is not simply linear.This is further supported by the most important features determined byprincipal component analysis (Table 9.7). A relatively high number of fea-tures (20) was found to perform best on tests sets of cross validation. Thisnumber was a hyperparameter of training, and many smaller values were213compared (as well as one larger value) as indicated in Table 9.1.Using radiomic features of PSMA \/ PET and CT images was advanta-geous over using only the mean, median, and maximum uptake statisticsfor model-building to predict regional importance. Radiomic features ofsquared PSMA PET uptake were found to be particularly predictive of sub-regional parotid gland importance. The top six most important featureswere all forms of the GLCM of PSMA PET images. Based on this finding,we recommend including radiomics of squared uptake in future predictivemodels of functional importance for salivary glands.A method of using PSMA PET and CT radiomic features to predictpatient deviations from population-level estimates of parotid gland regionalimportance was demonstrated. The purpose was to present a hypotheticalmethod of extracting patient-specific parotid gland importance estimatesfor tailoring patient dose constraints for radiotherapy [2]. PSMA PET isnot acquired as a standard-of-care image for head-and-neck cancer patients,and it is likely cost-prohibitive to add PSMA PET to the standard-of-care.Therefore PSMA PET images would not be practically available in mostclinical situations. However, we believe further PSMA PET studies couldbe critical in shedding light on importance trends and variability within theparotid glands.The incidence of head and neck cancers in patients under the age of 45has increased sharply in the last two decades due to a rise in oropharyn-geal cancers caused by the human papillomavirus (HPV) [185, 196], andxerostomia remains a common side effect for head-and-neck cancer patients[515]. Xerostomia leads to significant reductions in self-assessed quality-of-life scores [7\u201310], and is largely a result of radiation received in salivaryglands during radiotherapy. Dose to the the parotid glands is the greatestrisk factor for post-treatment xerostomia [474]. The current standard of careis to minimize the whole-mean dose to parotid glands [516], despite evidenceof intra-gland functional variability [12, 14\u201316]. Advancements in the under-standing of intra-parotid gland functional heterogeneity and the ability topredict relative subregional importance using PSMA PET has the potentialapplication of creating and testing new salivary gland dose constraints for214radiotherapy treatment planning.The results of this study support the potential utility of using PSMAPET\/CT for designing relative-importance based dose constraints that canbe validated in clinical studies. Radiomic features appear to be particularlyuseful for predicting importance, and will likely play a central role in fu-ture studies which aim to develop population-level or patient-specific doseconstraints whose efficacy can be validated in a clinical study.Our data set was small, comprised of only 60 parotid glands from 30patients. This necessitated the double cross validation methodology usedfor model development, where the test set was rotated through, along withinner validation sets for each, to determine model parameters. Outer testsets had no influence on model development and were used to independentlytest the models predictive accuracy of all subregions. The majority of Clarket al.\u2019s [12] subregions have low relative importance, with only a few re-gions having high relative importance. As a result of this behaviour, doublecross-validation was warranted to help mitigate biased error estimates whenvalidating with high importance values that were not adequately representedin the training set. As all PSMA PET\/CT images in this dataset were ac-quired on a single scanner, top performing parameters found in this studyshould not necessarily be expected to match those found in future model-building studies using external datasets.9.5 ConclusionThe results of this work, which compared four models of parotid gland sub-regional importance from the literature with regional PSMA PET uptake,demonstrate an inverse proportionality between relative importance andsubregional PSMA PET uptake. We demonstrated the utility of PSMAPET radiomic features for predicting regional importance by building a pre-dictive model for Clark et al.\u2019s regional importance estimates (MAE = 0.08).Lastly, we demonstrated a methodology for supplementing population-levelimportance estimates using patient-specific radiomic features. PSMA PETappears to be a promising quantitative imaging modality for analyzing sali-215vary gland functionality.216Chapter 10Intra-Parotid Gland DoseConstraints In RadiotherapyTreatment Planning UsingArtifical Base Plans10.1 IntroductionThe development and clinical implementation of modulated therapies suchas VMAT has proven to be one of the most important advancements inoncology in recent years [524], allowing for a significantly higher precisionof target volume dose conformality to be achieved in radiotherapy [525].However, parotid-sparing VMAT or IMRT alone is inadequate for completesparing of salivary function, [526] and it remains common for head-and-neckradiotherapy patients to be burdened by a severe loss in saliva productionfollowing treatment [473]. Head and neck target volumes commonly existadjacent to or over-lapping with the parotid and submandibular glands [472],which along with sharp dose gradients and setup error, results in burden-some dose to salivary glands being probable during head-and-neck radiationThe content of Chapter 10 has been peer-reviewed and accepted for publication in theJournal of Applied Clinical Medical Physics [2]. The name of the article is, \u201cIncorporatingparotid gland inhomogeneity into head-and-neck treatment optimization through the useof artificial base plans,\u201d and the co-authors are Caleb Sample, Jonn Wu, Steven Thomas,and Haley Clark.217treatment [527]. Xerostomia and hyposalivation significantly impact one\u2019squality of life by crippling common abilities such as speech, chewing, swal-lowing, or tasting [7], while also causing oral infections, dental caries, andother oral sequela [8\u201310]. Radiation to the parotid gland is the greatest riskfactor for post-treatment xerostomia [474].The risk of xerostomia following VMAT or IMRT is dependent on thequality of parotid gland dose constraints used during optimization. As dis-cussed in Chapter 4, constraints on the whole-mean dose is effective forpreserving function of OARs that exhibits a pure parallel functional architec-ture, given that the spatial variance of dose within the OAR is unimportant.The parotid gland was once believed to exhibit a pure parallel architectureand hence to have a spatially homogenous dose response [517], and to thisday, the current standard of care for minimizing the risk of post-RT xeros-tomia incidence for head-and-neck patients is to constrain the whole-glandmean dose [364]. However, recent preclinical studies have demonstratedheterogeneous radiosensitivity within parotid glands [12, 14\u201316, 384, 528].In a recent study by Jiang et al., a model including voxel dose data aswell as patient demographic and clinical pathology features [528] found thesuperior\u2013anterior portion of the parotid gland to be the most influential inpredicting xerostomia recovery. Furthermore, it was found that patients whodeveloped xerostomia had a much higher mean dose to the caudal aspect ofthe parotid gland. Another study by Van Luijk et al. [15] used a tenfold crossvalidation methodology to show that dose to the region of the parotid glandcontaining stem\/progenitor cells, around the first branching of the Stensen\u2019sduct, was more predictive of xerostomia at 1 year post radiotherapy thandose to any other subregion of the gland. The same study also showedthat the spatial distribution of dose in rat parotid glands affected salivaryoutput recovery after treatment. Dose to the cranial 50 percent of the glandresulted in more than a 50 percent loss in salivary output, as well as tissuedegeneration throughout the entire gland [15]. Regional importance in theparotid gland was also investigated by Han et al. [16] and Buettner et al.[14], as discussed in Section 4.4As discussed in Section 4.4, Clark et al. [12] partitioned contralateral218parotid glands for a single cohort of 332 patients into 2, 3, 4, 18, and 96 equalvolume subregions and derived the relative importance of each from meandose regressors using random forests and conditional inference trees. Theparotid gland with the lowest mean dose in each patient was defined as thecontralateral parotid gland. Parotid gland structure sets and dose profileswere used to calculate the mean dose to various subregions, and outcomeswere described using stimulated saliva output at one-year post-radiotherapyand self-assessed xerostomia questionnaires. Using the 18 subregion split,the most important subregion (caudal\u2013anterior) had a relative importanceof 3.85\u00d7 the expected result for a homogenous parotid gland. The leastimportant subregion exhibited virtually no importance [12].If the spatial inhomogeneity of the dose response within the parotidgland is properly accounted for in external beam radiotherapy treatmentplanning, the risk of xerostomia could be reduced for head-and-neck can-cer patients. Studies have previously concluded that incorporation of non-homogeneous dose effects into treatment planning can lead to improved out-comes [493, 494]. The purpose of this work is to demonstrate the feasibility ofa simple technique for including subregional parotid gland importance datainto radiotherapy treatment plan optimization using artificial base plans(BPs). To demonstrate the technique, we used Clark et al.\u2019s [12] intra-parotid gland importance estimates.10.2 MethodsThe RapidArcTM optimizer in Varian Eclipse is equipped with the abilityto incorporate previously received radiotherapy dose distributions into op-timization. Pre-existing dose distributions can be loaded directly as BPsduring optimization, and the standard optimization workflow proceeds oth-erwise unaltered. We made use of this feature to apply a spatially varyingdose constraint to contralateral parotid glands to preferentially spare regionsof high relative importance from excessive dose during radiotherapy.The radiotherapy structure set object of the DICOM standard files (DI-COM RTSTRUCT) for 15 retrospective head-and-neck VMAT patients was219exported from the ARIA Oncology Information database (primary tumorsite: 5 tonsil, 4 tongue, 3 base of tongue, 1 nasopharynx, 1 thyroid, 1 leftneck; prescription dose: 14 with 70 Gy in 35 fractions, 1 with 60 Gy in25 fractions). Each patient received a single fractionation scheme using asimultaneous integrated boost. Sex and age statistics for the cohort wereunknown as this information had been removed during previous anonymiza-tion. The median volume of primary planning target volumes (PTV) was181.5 cc (maximum: 295.1 cc, minimum: 30.18 cc). Contralateral parotidglands were defined as the parotid gland having the lowest mean dose in theoriginal treatment plan for each patient and were split into 18 equal volumeregions using DICOMautomaton [475]. The average minimum distance be-tween the primary PTV and the contralateral parotid gland was 3.3 cm. Therelative importance of all 18 subregions was estimated using Clark et al.\u2019spopulation-level importance model [12]. subregions were labeled in order ofdecreasing relative importance as S1 to S18, where S1 is the subregion ofhighest relative importance. Parotid gland subregions are shown numberedin Figure 10.1.220Figure 10.1: subregions of contralateral parotid glands defined by Clark et al. [12] have varying relative importancefor predicting post-RT xerostomia. Here, the spatial distribution of importance is illustrated from (a) the anterior,and (b) the posterior. subregions are labeled according to their importance in (c).221DICOMautomaton was used to create artificial dose distributions (BPs)for each patient which adhered to the following formula:1. Dose to all voxels outside the contralateral parotid gland is zero.2. Dose to regions of overlap between the contralateral parotid gland andtarget volumes is zero. This ensures that the tumour coverage will notbe impacted by directly competing constraints.3. Within each subregion of the contralateral parotid gland, dose is uni-form.4. Dose to the region of highest relative importance (caudal-anterior,Figure 10.1) was D0, and the dose to other subregions was D0I, whereI is a scaling factor proportional to the relative importance of theregion compared to the most important subregion.Five different types of BPs were created for each patient. In the firstthree, D0 was set to 10 Gy, 20 Gy, and 30 Gy to create dose distributionsthat scaled linearly with importance, I, and these BPs were named BP10,BP20, and BP30, respectively. The values of D0 were chosen as they spanthe range of typical mean contralateral parotid gland doses in head and neckradiotherapy plans. Testing multiple values allows empirical determinationof the most effective base plan. In addition to the three BPs mentioned, afourth was made, identical to BP20 for subregions S1 \u2192 S5, while dose toall other subregions (S6 \u2192 S18) was zero. Lastly, a fifth BP was assigned50 Gy to subregions S1 \u2192 S5, and 0 Gy to all other subregions. These twoplans were named BP20,5 and BPTop 5.In Varian Eclipse, each patient had five placeholder plans created forthe five artificially constructed BPs that were imported for use in ExternalBeam Planning. As a control, VMAT plans were retroactively optimizedwhile adhering to standard clinical head-and-neck protocols (both parotidswhole mean < 25 Gy or one parotid whole mean < 20 Gy). For each patient,two arcs with opposing 360\u25e6 gantry rotations and a difference of 60\u25e6 incollimator rotation (30\u25e6 and 330\u25e6) were used. Plans were then re-optimized222using each artificial BP. Loading the BPs into the optimizer does not byitself implement a spatially varying dose constraint throughout the parotidgland, as the standard parotid dose constraint only computes the whole-mean dose. Therefore, an additional upper bound dose constraint must beplaced on the contralateral parotid gland. This constraint, combined withthe BP dose, provides a spatially varying dose constraint which preferentiallyrestricts dose to subregions of high relative importance. The ideal constraintdepends on the specific anatomy of the patient and was chosen to be between0 and 15 Gy over the maximum dose in whichever BP was currently loaded.In this manner, the constraint imposed on a given region of the contralateralparotid gland has varying strength, depending on the region\u2019s BP relativeimportance.Plans were optimized until all clinical dose constraints were satisfied.Plans were named P10, P20, P30, P20,5, and PTop 5,corresponding to the useof BP10, BP20, BP30, BP20,5, and BPTop 5. The plan optimized without aBP as a control is referred to as P0.When comparing the ability of different plan types to steer dose fromimportant subregions of contralateral parotid glands, it was paramount tominimize inter-plan bias and dose variability within structures other thanthe contralateral parotid gland. For this reason, plans were optimized tothe same objective of only marginally satisfying the V98 (percent volumereceiving at least 98 percent of the prescription dose) constraint for the PTVclosest to the contralateral parotid gland. P0 was optimized first, to bestsatisfy all OAR dose objectives while meeting all dose constraints for PTVsand critical OARs. Dose to all OARs not overlapping PTVs were made tosatisfy all clinical objectives. After optimizing P0, other plans using BPswere optimized in a random order. The priority of the PTV optimizationpriority was then adjusted minimally to attain marginal satisfaction of theconstraint. Dose constraints set for other OARs were only adjusted if theirdose objective had become violated.Each plan for a given patient started with the same constraint on thewhole-mean dose of the contralateral parotid gland (after adjusting for themean dose of the base plan), and plans using BPs all had the same difference223between the Dmax constraint and D0. For example, if P10 had the constraintDmax < 20 Gy, then P20 had the constraint Dmax < 30 Gy. These constraintsremained constant throughout optimization.A C# plug-in script was developed and run using the Eclipse ScriptingAPI (ESAPI) for calculating mean doses in subregions and exporting results.A MATLAB script was then created to analyse parotid gland subregion dosesin all 18 subregions of the 15\u00d7 6 = 90 plans (1,620 subregions).Mean subregion dose reductions between plans optimized with BPs werequantified and compared to determine which BP led to the most effectiveresults, and if mean dose to regions of high importance was significantlyreduced. Dose to all patient structures in each plan type were evaluated toensure satisfaction of all clinical dose constraints, and to determine if theuse of BPs significantly altered mean or maximum doses in other OARs.Significance was assessed at p < 0.05 with a paired t test. Mean doses in allsubregions of each plan were passed as parameters into a predictive modelfor stimulated salivary output at one year after radiotherapy, relative tobaseline (adapted from Clark et al. [12]).To reduce the effects of inherent model noise on estimates of outcomegains, Clark et al.\u2019s dose response model was used to generate a dose re-sponse curve (Hill Model [529]) for each individual subregion. Curves werefit using the method of least squares to salivary output vs. dose distributionsobtained by incrementing model dose inputs in each subregion from 0 to 40Gy in 2 Gy increments, while keeping all other subregion doses constant. Afinal predictive model of the formS(D1, D2, ..., D17, D18) = 1\u221218\u2211i=1\u2206i\uf8ee\uf8f01\u2212 11 +(DiD50,i)ni\uf8f9\uf8fb = 1\u2212\u03a318i=1\u2206i 11 +(DiD50,i)ni(10.1)was created, where Di is the dose to subregion Si,\u2206i is the maximum lossin salivary output predicted by infinite dose to Si independently, and D50,iand ni are parameters fit to the data, representing the dose that predicts aloss in salivary output of \u2206i2 , and the steepness of the curve. The predictedresponse when only dose to S1 is considered (Equation 10.1 with only i = 1)224is shown in Figure 10.2.225Figure 10.2: The dose response curve of stimulated saliva output at one year post-radiotherapy, relative to baseline,is shown for subregion S1. Dose curves were derived using Clark et al.\u2019s [12] model predictions.22610.3 ResultsThe mean dose in all contralateral parotid gland subregions is shown foreach plan type in Table 10.1 with statistically significant dose differencesindicated. PTop 5 resulted in the greatest reduction in the mean dose of S1(M = 8.6 Gy, SD = 3.9 Gy, p <0.001), followed closely by P30 (M = 8.1Gy, SD = 3.7 Gy, p < 0.001). All plans reduced the whole mean dose of thecontralateral parotid gland significantly, with the greatest reduction seenusing P30 (M = 2.1 Gy, SD = 1.2 Gy, p < 0.001), followed by P20 (M = 2.0Gy, SD = 1.0 Gy, p < 0.001). In general, dose to highly important parotidgland subregions, which tend towards caudal aspects of glands, was reducedwhen planning with BPs as seen in Figure 10.3. Planning with P20, P30, andPTop 5 significantly reduced dose to the top five most important subregionsof the contralateral parotid gland, while reductions in dose to S2 using P10and P20,5 were insignificant. The patient-average of the mean dose in eachcontralateral parotid gland subregion in each plan type is listed in Table1. PTop 5 significantly increased dose to several subregions of low relativeimportance (S13, S14, S16, S17, S18).All plans optimized with BPs demonstrated statistically significant im-provements in stimulated saliva predictions at 1-year post-radiotherapy. Op-timizing with BPs resulted in up to a 23 % improvement in predicted salivaoutput (mean = 18 %) as compared to optimizing without BPs, as shownin Table 10.2. BP30 and BPTop 5 demonstrated the greatest improvementsin salivary output, while BP10 resulted in the smallest improvement (13 %).One patient\u2019s isodose distribution in the middle of the contralateral parotidgland is shown for each type of plan in Figure 10.4.The mean overlap percentage of contralateral parotid glands with targetvolumes was 13.7% (median 13%, maximum 33%), and subregions along thecaudal\u2013medial portion of glands were most prone to overlap. The frequencyof overlapping for various subregions is summarized in Table10.3.Optimizing with BPs did not prevent clinical dose constraints for OARsor target volumes from being adhered to. Primary and secondary PTVshad no apparent trend toward decreasing or increasing dose coverage when227Table 10.1: The mean dose in each subregion of the contralateral parotidgland for each plan type is shown. A superscript \u201cS.R.\u201d represents a sig-nificant (P < 0.05) reduction in dose, while superscript \u201cS.I.\u201d represents asignificant increase in dose.subregion Mean Dose (Gy)P0 P10 P20 P30 P20,5 PTop 5S1 27.8 22.5S.R. 20.9S.R. 19.8S.R. 20.7S.R. 19.2S.R.S2 11.1 10.8 9.9S.R. 10.0S.R. 10.9S.R. 10.0S.R.S3 29.6 24.6S.R. 23.8S.R. 23.3S.R. 23.4S.R. 21.5S.R.S4 40.2 36.2S.R. 35.5S.R. 34.7S.R. 35.2S.R. 33.2S.R.S5 18.3 15.7S.R. 14.6S.R. 14.2S.R. 14.8S.R. 13.5S.R.S6 22.3 21.5S.R. 20.8S.R. 20.9S.R. 22.6 22.8S7 8.3 8.3 8.2 8.3 9.0 9.4S8 40.7 37.2S.R. 36.8S.R. 36.3S.R. 36.9S.R. 35.5S.R.S9 10.2 10.0 9.5 9.7 10.4 10.1S10 20.9 17.7S.R. 17.2S.R. 17.1S.R. 17.4S.R. 15.6S.R.S11 6.5 6.5 6.4 6.6 7.0 7.1S12 5.9 6.0 5.8 6.0 6.4 6.6S13 7.8 7.7 7.8 7.9 8.5 9.0S.I.S14 12.7 12.3 12.8 12.7 13.5 14.5S.I.S15 12.4 12.1 11.7 11.8 12.6 13.3S16 15.7 15.0S.R. 14.7S.R. 14.9S.R. 15.8S.R. 17.2S.I.S17 6.8 6.8 6.9 6.8 7.4 7.9S.I.S18 25.3 24.5S.R. 25.0 25.1 26.0 27.8S.I.Whole Gland 18.3 16.7S.R. 16.3S.R. 16.2S.R. 16.8S.R. 16.6S.R.Table 10.2: Stimulated saliva output predictions at one year post-radiotherapy, determined using patient-averaged subregion doses in Clarket al.\u2019s [12] population-based model, are shown for each plan type. Thestatistical significance of improvements in saliva output were assessed usinga paired t-test.Plan Type Saliva Output Improvement from P0 Statistical Significance(Relative to Baseline) (%)P0 0.47 N\/A N\/AP10 0.54 13 t(14)=3.1, p < 0.01P20 0.57 19 t(14) = 5.3, p < 0.001P30 0.59 23 t(14) = 4.7, p \u00a1 0.001P20,5 0.55 15 t(14) = 2.8, p \u00a1 0.02PTop 5 0.59 23 t(14)=4.0, p \u00a1 0.002228Figure 10.3: Statistically significant reductions in dose to the top five mostimportant subregions of the contralateral parotid gland (S1 \u2192S5) were ob-tained using BP20, BP30, and BPTop 5 during optimization. (a) and (b):mean subregion doses for plans optimized without BPs (anterior and poste-rior view); (c) and (d): mean subregion doses for plans optimized with BP30(anterior and posterior view); (e) and (f): mean difference in dose betweenplans optimized with and without BP30 (anterior and posterior).229Figure 10.4: The dose distribution in a sagittal slice through the contralat-eral parotid gland is shown for each different plan type created for a singlepatient. (a): P0; (b): P10; (c): P20; (d): P30; (e): PTop 5; (f): P20,5. Themost important subregion derived with Clark et al.\u2019s [12] model is locatedin the caudal\u2013anterior (bottom right) portion of the gland, where isodoselines can be clearly seen to shift away from when using artificial base plans,and particularly with BP30 (D).230planning with artificial base plans. The cumulative DVH for one patient\u2019sPTV is shown for all different plan types in Figure 10.5. Submandibularglands had extensive overlap with target volumes in all 15 patients, makingit impossible for them to be spared from high dose without subsequentreductions in dose to target volumes. Contralateral submandibular glandmean doses significantly increased when optimizing with BPs, and PTop 5resulted in the largest difference (1.7 \u00b1 1.5 Gy, p < 0.01). Three patients\u2019contralateral submandibular glands had not been contoured thus were notincluded in this statistic. Mean dose to the oral cavity also increased withstatistical significance when using BPs, with the largest difference foundwith P20 (1.4\u00b1 1.7 Gy).Table 10.3: The number of patients with contralateral parotid gland sub-regions overlapping with planning target volumes is shown. A total of 15patients were included in the study.subregion Number OverlappingS1 11S2 1S3 11S4 13S5 2S6 11S7 4S8 13S9 0S10 4S11 0S12 0S13 0S14 0S15 0S16 8S17 0S18 11Whole Gland 13231Figure 10.5: The cumulative dose volume histogram for the primary PTV(a) and gross tumor volume (GTV, b) revealed no apparent trend towarddecreased or increased coverage when base plans were used during optimiza-tion, as demonstrated with a single representative patient.23210.4 DiscussionThe base plan approach for incorporating various intra-parotid gland doseconstraints into head-and-neck radiotherapy planning using artificially con-structed base plans demonstrated that the optimizer can effectively steerdose away from highly important regions of parotid glands. This methoddoes not require additional contouring or manipulation of extra dose con-straints for numerous subregions. Instead, the optimization workflow pro-ceeds normally after loading the base plan and setting the one additionalconstraint on the contralateral. It is important to avoid optimizing withunique dose constraints on all parotid gland subregions not only to avoiddifficulty, but also as this would likely have a noticeable impact on optimiza-tion time.We used population-level relative importance information of 18 equalvolume parotid gland subregions derived from a large dataset (n=332 [12])to decide upon various sub-parotid dose constraints to impose during opti-mization. Incorporating dose constraints that spatially vary with regionalimportance resulted in favourable saliva output predictions, as per Clark etal.\u2019s predictive model [12]. The predicted risk of xerostomia was loweredwith minimal additional effort during treatment planning. This methodimproves upon the current handling of parotid glands during radiotherapytreatment planning which simply minimizes the whole-mean dose. Numer-ous models of regional importance have been suggested [12\u201316], and it isimportant for these results to be validated then translated into clinical doseconstraints.The fact that parotid gland subregions of high relative importance showedsignificant reductions in dose, while less important subregions had moremodest improvements or even increases in dose, is not unexpected. Highlyimportant subregions had proportionally strict dose constraints in order toredirect dose away from important regions without compromising PTV cov-erage. Regions of high relative importance tend towards caudal aspects ofparotid glands, where the largest reductions dose were seen. The extent ofPTV overlap with parotid glands is correlated with patient outcomes [530\u2013233532] and the base plan approach proved less impactful for patients havingextensive overlap. Contralateral parotid glands were frequently found tooverlap with PTVs in this study, with 13\/15 parotid glands having some de-gree of overlap. Despite this difficulty, the whole-mean dose and mean doseto important subregions frequently found to overlap with target volumes(S1, S3, S4, S6) showed significant reductions in dose with P30.Five different types of base plans were used to reoptimize treatmentplans in this study. The two most effective plans for sparing importantsubregions and improving predicted patient outcomes were P30 and PTop 5,which resulted in identical predictions for stimulated saliva output at oneyear post-radiotherapy. The fact that these were the most effective plansis unsurprising as they offer the largest variance of constraints within thecontralateral parotid, allowing dose to be increasingly steered from regionsof high importance to regions of low importance. PTop 5 marginally out-performed P30 in terms of reducing dose to the top five most importantsubregions; however, this came at the expense of statistically significantincreases in dose to other parotid subregions of lower relative importance.While this is presumably a favourable trade-off, P30 is a more moderate planwhich also achieved the greatest reduction to the whole mean dose of thecontralateral parotid gland. Therefore, P30 was the plan adhering best tothe ALARA (As Low As Reasonably Achievable) principle [533].P30 is also favourable over PTop 5 as it is easier to manage while opti-mizing in Varian Eclipse. The base plan approach presents challenges whenimposing large dose penalties, as the maximum dose contained in the baseplan will contribute to the maximum body dose during optimization. Thissometimes impedes the planner\u2019s ability to determine if a dose constraint forthe body is violated during optimization. Another subtlety which must beconsidered during optimization is a shift in the mean dose constraint thatoccurs when using BPs. The contralateral parotid gland\u2019s mean dose in theBP is absorbed into the mean dose calculated during optimization, so theplanner must shift the mean dose constraint of the gland up by an amountequal to the mean dose within the BP. Both of these calculation issues canbe mitigated after optimization by copying the optimized fields to a new234plan without BPs.A significant reduction in dose to the top five important subregions aswell as the whole mean as seen with P30 demonstrates efficacy of the pro-posed technique. Dose to other OARs and target volumes continued tomeet clinical constraints when planning with BPs. Increases in dose to con-tralateral submandibular glands were not clinically significant, albeit didhave statistical significance (p < 0.05). The dose to these glands was eitherweakly constrained or not at all, and as a result, small increases in theiralready high doses had no effect on patient outcomes. Oral cavity meandoses were kept below the clinical mean dose objective, so the statisticallysignificant increase in mean dose in the oral cavity is unlikely to be clinicallyinsignificant.Clark et al.\u2019s [12] model for the relative functional importance of parotidgland subregions [12] has yet to be clinically validated since it was derived.Clark et al.\u2019s model was used in our methods as it was the most favourablefor designing constraints. However, the base plan method for imposing doseconstraints can be applied using data from other models of regional im-portance for any OAR. The emphasis of this study is on this new methodof incorporating subregional dose constraints using artificially-constructedbase plans.Clark et al.\u2019s model was chosen over other models for designing spatiallyvarying dose constraints for multiple reasons. For one, it is the only availablemodel that maps relative importance over equal-volume subregions through-out the entire parotid gland. It is important for subregions to have equalvolumes for accurate translation of derived importance values to clinical out-come predictions. Another reason why Clark et al.\u2019s model was chosen overother models for designing dose constraints is that it derives importance datausing the largest dataset of patient outcomes. Another useful characteristicof Clark et al.\u2019s model is that it derives importance within the original refer-ence frame of the parotid gland without transforming to alternate referenceframe, which is advantageous for practical purposes. Furthermore, segmen-tation into 18 equal volume subregions creates a desirable size for varyingconstraints, as it is large enough for dose to be effectively steered, while small235enough to account for the varying importance within the gland. Lastly, thesignificant anticorrelation found (Chapter 9) between Clark et al.\u2019s subre-gional importance estimates and PSMA PET uptake suggest that Clark etal.\u2019s importance estimates are linked with some physiological characteris-tic. The only other model dividing parotid glands into several adequatelysized subregions for dose constraint application was Han et al.\u2019s [16], buttheir importance estimates were insignificantly correlated with PSMA PETuptake.It was necessary to fit individual dose response curves for each parotidgland subregion to reduce the impact of noise on xerostomia estimates. Ingeneral, plans optimized in this study had lower mean subregional dosesthan the majority of clinical plans used to construct Clark et al.\u2019s model,causing xerostomia estimates to be prone to extrapolation error. Ideally, themulti-parameter nature of the predictive model would be maintained, whereall subregional doses are considered simultaneously to predict stimulatedsaliva. However, large fluctuations in predictions with small changes in doselevels occurred, leading to adoption of the present approach.It was a challenge to establish a valid inter-plan comparison for thisstudy, as the varying initial dose conditions of each base plan ensured thatoptimized dose profiles for plans are non-identical both inside and outsidethe contralateral parotid glands. To minimize systematic errors, dose con-straints to all PTVs and all OARs other than the contralateral parotidgland were set to the same value in all plans, and the same V98 goal forbordering\/overlapping PTVs was set in each case. Under real clinical cir-cumstances, these plans would be further optimized individually to achievethe best possible target coverage and combined OAR sparing. Plans werecreated in a random order by a single planner for all patients. However,variability in the optimization process for each plan was impossible to elim-inate entirely and could have impacted this study. We were unaware of afavourable method of comparing a new planning technique with traditionalmethods.An advantage of employing this base plan approach to optimization overscripting, is that dose constraints to individual subregions do not require236individual monitoring. A scripting approach would require that optimizationis done either automatically through the scripting back-end, which doesn\u2019tafford the planner the freedom to modify dose constraints according to thecurrent state of optimization, or that a script is first run for subsegmentationand constraint application before optimization is done manually. Of course,the manual planning case requires constraints on the 18 subregions to beassessed and updated individually. This would obviously be a cumbersometask, and it is therefore likely that a scripting approach would be limited toconstraining dose to a subset of highly important subregions.One benefit of a scripting approach is that base plans don\u2019t need tobe created before proceeding with treatment planning. For this reason, anopen source ESAPI program for automatic subsegmentation and planningin Varian Eclipse was also created. The program is called \u201cPlan n Check,\u201dand details on its use can be found in the Appendix.10.5 ConclusionIt is known that parotid glands exhibit an heterogeneous dose response,and there is promise that post-treatment xerostomia outcomes can be sig-nificantly improved by incorporating this information into clinical planningworkflows. A universal method for incorporating sub-OAR dose constraintsinto VMAT treatment planning has been featured as an effective means ofsteering dose away from important subregions of the parotid gland. Thismethod may also be applied to other OARs for which spatial importancedata exists.237Chapter 11Conclusion11.1 Summary of Scholarly FindingsThe underlying problem which gave rise to this research endeavour wasthat head and neck cancer patients commonly finish radiotherapy with aseverely diminished quality of life, due to a loss in salivary output. Thediverse range of research contributions in this thesis were made with theobjective of directly or indirectly addressing this problem. Specific scholarlycontributions include the following.1. Partial volume correction and supersampling of PSMA PET imageswith neural blind deconvolution led to fine detail recovery and higherimage quality in terms of blind image quality metrics. This methodol-ogy also improved outcome modelling and resulted in stronger correla-tions between PSMA PET uptake and functional importance estimatesin parotid glands.2. Neural blind deconvolution for deblurring and denoising diffusion MRIimages improves image quality in terms of blind image quality metricsand leads to better predictability of IVIM parameter changes followingradiotherapy. This methodology significantly suppressed noise andimproved monotonicity of the signal decay curve.3. Modelling the signal vs. b-value decay curve of IVIM MRI using themodel-independent Area Under the Curve (AUC) parameter led toimprovements over traditional, model-based parameters in terms ofpredictability of parameter changes following radiotherapy. AUC pa-rameters captured a higher proportion of dataset variance than tra-238ditional exponential model parameters, as determined via principalcomponent analysis.4. PSMA PET - defined tubarial glands can be effectively autosegmentedusing only computed tomography (CT), for which an open sourcemodel was developed. This method allows tubarial glands to be con-sidered during radiotherapy without additional imaging procedures.5. The uptake of PSMA ligands inside parotid glands, which mountingevidence suggests is correlated with gland functionality, is consistentlybiased towards lateroposterior aspects. It was previously reported tobe homogeneous. Intra-parotid gland PSMA PET uptake was signifi-cantly correlated with CT texture features, namely the GLRLM witha long and short run emphasis.6. Analysing the relationship between intra-parotid gland PSMA PETuptake and four models of subregional importance from the literaturerevealed a significant anticorrelation between uptake and importance.The ability of PSMA PET \/ CT to accurately predict regional impor-tance was demonstrated through the development of a cross-validatedmodel using PSMA PET \/ CT radiomic features to predict impor-tance.7. Stimulated saliva output predictions for patients are significantly im-proved by considering Clark et al.\u2019s [12] subregional parotid gland im-portance estimates during radiotherapy plan optimization. A simplemethod for implementing importance-derived subregional dose con-straints into the optimization engine was demonstrated.11.2 Further ExplorationsWhile all mentioned scholarly findings are important for advancing knowl-edge of the salivary glands and techniques that can lead to improved radio-therapy planning, the work required to attain clinical adoption of modern-239ized dose constraints is not over. This work is but a days walk of a multi-daytrek.Notably, the deblurring and denoising methods used on diffusion MRI,as well as the newly introduced parametrization technique for IVIM MRI,led to improvements in image and parameter quality which will translateto an improved ability to analyse saliva gland behaviour using IVIM MRI.Diffusion MR images acquired for the clinical study at BC Cancer wereset to encompass the parotid glands, as their analysis is the ultimate goalof the study. This analysis is currently underway but is excluded in theresearch contributions of this thesis due to time constraints. Results will besubsequently published in the literature upon completion.This deblurring methodology, using neural blind deconvolution, showsgreat promise as a tool for improving medical image quality after recon-struction. However, there is ample room for network and training methodoptimization. These methods require further development. For example,experimentation with the architecture of Gx, Gk and Gk, optimization lossfunctions, partial supervision, weight initialization, could lead to model im-provement. As training of deep learning models is a highly non-convexoptimization problem, it is likely that final models in this work converged tosome local minimum. Models have been made available as open-source pro-grams with the hope of them being continually iterated upon, so that neuralblind deconvolution gains traction as a viable deblurring methodology formedical images in the literature.The autosegmentation model for the tubarial glands has been madeopen-source with the intention of having other institutions improve modelperformance by continuing training with further PSMA PET data. However,the current model performs sufficiently as-is for reasonable approximation ofthe tubarial glands using CT only. A clinical study that assesses the abilityof tubarial gland dose constraints to improve outcomes is a logical next-stepfor advancing patient care, as a retrospective analysis has already proved itsefficacy.A clinical trial that assesses the benefit of constraining dose to impor-tant regions of parotid glands, as defined by Clark et al. [12] is called-for240in order to bridge the gap between these knowledge-based estimates andcurrent clinical treatment planning protocols. The retrospective analysisin Chapter 10 showed the how including this information during treatmentplanning leads to improved outcome predictions. It would also be useful toinclude the effects of chemotherapy on saliva output in the analysis of im-portance. However, the overall toxicity effects of chemotherapy are difficultto assess due to the use of various agents, doses, and body sizes. Whenplentiful data is available, machine learning models will likely be beneficialfor understanding these effects.The results of this thesis have advanced the current status of salivarygland subregional importance knowledge\/confidence by linking it with PSMAPET uptake. PSMA PET in parotid glands was found to be significantlyanticorrelated with regional importance. This knowledge, along with consis-tently biased uptake toward lateroposterior aspects of glands, suggest thatsparing dose to anteromedial aspects of glands could improve patient out-comes. This relationship must be validated with a larger, external dataset.PSMA PET has shown high promise for designing modernized dose con-straints for salivary glands, and more work is needed to bridge these findingstowards clinically-relevant solutions to patient care. Validating heteroge-neous intra-parotid gland uptake with a larger dataset, then conducting aclinical trial for assessing how sparing dose to regions of low uptake improvessaliva output following radiotherapy, is a logical next-step for confirming therelationship between PSMA PET uptake and functional importance.The relationship between PSMA PET and CT texture features requiresfurther exploration, as the strong correlation found suggests the potentialuse of CT texture features as a proxy for estimating importance in parotidglands. 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Journal of Applied ClinicalMedical Physics, 20(10):201\u2013207, 2019.315Appendix ADevelopment of anAutomatic TreatmentPlanning Tool For Use withVarian EclipseA.1 IntroductionAs previously discussed in Chapter 10 and 3.2.8, treatment planning forhead and neck radiotherapy is a complex task often involving multiple tu-mour sites with differing dose prescriptions in close proximity to many OARs(organs-at-risk). Modern planning requires dosimetrists to assign optimiza-tion objectives to all relevant ROIs (regions-of-interest) which consists of adose-volume constraint as well as a priority (integer value) indicating theweight of the optimization objective in the cost function of the Eclipse op-timization engine [534]. Furthermore, the planner must choose appropriatebeam parameters including jaw settings, collimator rotations and arc anglesin order to adequately concentrate dose to target volumes while minimiz-ing exposure to healthy tissue. After creation of a treatment plan, all doseconstraints must be evaluated for quality assurance.Varian Eclipse features the Eclipse Scripting Application ProgrammingInterface (ESAPI) which was first introduced in 2012 [322]. This interfaceallows C# .NET scripts and DLLs to be run within the planning window,reading and writing Eclipse data. ESAPI was originally released along withversion 11 of Eclipse as a read-only API, and a major upgrade in functional-316ity was introduced with the Eclipse Automation feature set, which includeswriteable scripting and script approval.A binary script for use in Eclipse called Plan n Check [535] was created forautomating planning and verification of head-and-neck Volume ModulatedArc Therapy (VMAT) plans. Upon loading a patient in Eclipse (includinga DICOM CT series and DICOM RT Structure Set), Plan n Check fullyautomates the planning process, producing a DICOM RT Plan file, and aPDF containing a plan check and optimization log. Furthermore, Plan nCheck can be used for applying segmented dose constraints to ROIs, and isconfigured to optionally apply importance-based dose constraints to parotidgland subregions (based on Clark et al.\u2019s model [12]).It is possible during manual planning in Varian Eclipse to modify con-straint parameters during VMAT optimization; however, this is not an ac-cessible feature using ESAPI scripts. To circumvent this, optimization canproceed with \u201cpreliminary optimization iterations\u201d which consist of a singleVMAT optimization cycle followed by a dose calculation and an evaluationof dose constraints which is then used to manipulate optimization objectivepriorities. After a number of optimization iterations, a 4-cycle multiresolu-tion VMAT optimization is performed and the final dose is calculated. As allpatients have anatomical differences and various target volume distributions,a variable number of preliminary optimization iterations will be required foran acceptable plan to be created patient-to-patient. It is important to de-termine the optimal default number of preliminary optimization iterationsto be performed by Plan n Check, as it is time consuming to perform a full4-cycle VMAT optimization between optimization objective modifications.The purpose of this work is to demonstrate the ability of Plan n Checkto create clinically acceptable head-and-neck VMAT plans and to determinethe number of preliminary optimization cycles required to produce a planconforming to all dose constraints. The results were used to determinethe default number of preliminary optimization cycles for Plan n Check toperform, as well as the initial optimization priorities to set for head-and-neckplanning. The subsegmentation abilities of Plan n Check are not includedin this analysis.317A.2 MethodsPlan n Check\u2019s head-and-neck plan applies standard dose constraints shownin Table 1 to corresponding structures in the patient\u2019s structure set. Thedefault target volumes that Plan n Check searches for are PTV 70, PTV 63and PTV 56, corresponding to prescription doses of 70 Gy, 63 Gy and 56Gy to the primary tumour site, intermediate risk sites, and low risk nodalsites, respectively. PTVs in the structure set with different prescriptiondoses encoded in their ID will also be assigned the V95 % > 98 % dose-volume constraint, as well as an upper bound dose constraint of 110 % ofthe maximum prescription dose.Plan n Check was used to create retroactive VMAT plans for a cohort of17 head-and-neck cancer patients (primary tumor site: 5 tonsil, 4 tongue,5 base of tongue, 1 nasopharynx, 1 thyroid, 1 left neck; prescription dose:16 with 70 Gy in 35 fractions, 1 with 60 Gy in 25 fractions). Patients re-ceived one fractionation scheme using a simultaneous integrated boost ona Varian TrueBeam LINAC. Sex and age statistics for the cohort are un-available as this information was previously excluded from DICOM files dur-ing anonymization. VMAT optimization was computed using the PhotonOptimizer (PO) Multi-Leaf Collimator (MLC) algorithm [536]. Dose calcu-lations were performed with the Analytical Anisotropic Algorithm (AAA)[301]. All structures were successfully matched to corresponding ROIs ofPlan n Check\u2019s head-and-neck plan for all patients in the cohort and did notrequire modification.Plan n Check creates dual arc beams centred on the target volume witha 60\u25e6 collimator angle difference between the two beams (30\u25e6 and 330\u25e6 col-limator angles). Dual arcs are used instead of single arcs to improve targetcoverage and conformality [? ]. Collimator jaws are automatically adjustedto adequately encompass target volumes. For compatibility with BC CancerVancouver\u2019s radiotherapy system, Varian TrueBeam fields are created. Stan-dard institutional head-and-neck dose constraints are automatically appliedto patient structures using a robust string-matching algorithm to identifyRegions of Interest (ROIs) within the structure set. Dose constraints for any318structure can then be added, removed or modified within the panel shown inFigure A.1 if necessary. Optimization structures for ROIs overlapping withtarget volumes are automatically created, excluding critical ROIs (nervoussystem: brain stem, spinal cord, etc).Figure A.1: A window of Plan n Check\u2019s graphical user interface is shown.Different features can be accessed simply, including the ability to view andmodify plan constraints.If an ROI overlapped with target volumes, a new planning structure wascreated by boolean-subtracting the PTV from the original ROI structure.the optimization structure volume was used to apply optimization objectivesand evaluate dose constraints. Satisfaction of all constraints in Table A.1was required for a plan to be approved by Plan n Check. Notably, a plan319could be approved only if both parotid glands mean dose was below 25 Gy orone parotid gland had a mean dose below 20 Gy. At least one submandibulargland for all patients within the cohort had partial or full overlap with PTVsand were inevitably subject to high dose.Optimization objective priorities are increased in proportion to the per-cent by which a dose constraint is failed after a preliminary optimizationiteration. However, a change in priority was limited to increasing by a max-imum value of 10 units per preliminary optimization iteration. If a constraintwas satisfied, then the priority was maintained. However, the priority wasdecreased if an OAR satisfied the constraint by at least 10 Gy. Constraintswhich failed by more than 20 Gy were removed from optimization as theywere unlikely to be feasibly achieved (such as in a submandibular glandimmersed in nodal tissue, etc).For each patient, a plan was first created with N = 0 preliminary op-timization cycles. Afterwards, the PDF created by Plan n Check for planverification was used to determine whether the plan conformed to all con-straints. If not, another plan was created with Plan n Check using N = 1preliminary optimization cycles. On the other hand, if all constraints weresatisfied then the created plan became the final treatment plan for the pa-tient. This process was then repeated, each time modifying N \u2192 N + 1 ifall constraints were not satisfied after plan creation.Afterwards, the mode for the number of preliminary optimization cy-cles, Nmode, required to produce an acceptable plan within the cohort wasdetermined. Nmode was used to determine the default number of preliminaryoptimization iterations to be implemented for head-and-neck plans createdby Plan n Check. Final priorities for structures were recorded for each pa-tient to determine the final mean priorities for each structure, which werethen used to modify the initial starting priorities used by Plan n Check.A.3 ResultsThe number of preliminary optimization iterations required for all dose con-straints to be satisfied for plans is shown in Table A.2. All patients had plans320created which satisfied all dose constraints after a maximum of two prelimi-nary optimization iterations. Nmode was found to be one, with 47 percent ofplans requiring a single preliminary optimization iteration in order for doseconstraints to be satisfied. 71 percent of plans met all dose constraints afterzero or one preliminary optimization iterations. Final mean optimizationobjective priorities for ROIs after VMAT optimization with Plan n Checkare shown in Table A.3.A.4 DiscussionPlan n Check made treatment plans satisfyied all dose constraints using twoor less preliminary optimization iterations for all but one of head-and-neckpatients in the study cohort. Plan n Check performed well overall in creatingplans which can be reviewed and modified as seen fit afterwards. A dosedistribution along with the dual arc beam profile is shown for a patient inFigure A.2. The use of automation for VMAT treatment planning savestime and helps identify regions which may require consideration for dosetrade-offs or compromises in objectives by radiation oncologists (ROs).321Table A.1: Head-and-neck plan dose constraints and initial optimizationobjective priority applied with Plan n Check.Region of Interest Constraint Initial PriorityBody Dmax < 110% 100Brain V60Gy < 0.1 cm3 100Brain Stem Dmax < 54Gy 100V50Gy < 0.1 cm3 100Brain Stem PRV V60Gy < 0.1 cm3 100Chiasm Dmax < 45Gy 20Chiasm PRV Dmax < 50Gy 20Globe (right\/left) Dmax < 45Gy 20Larynx\/Laryngopharynx Dmean < 45Gy 40Lens (right\/left) Dmax < 10Gy 20Lips Dmean < 25Gy 10Mandible Dmax < 70Gy 10Optic Nerve (right\/left) Dmax < 45Gy 20Oral Cavity Dmax < 50Gy 20Parotid (right\/left) Dmean < 20Gy(1) 50OrDmean < 25Gy (both)PTV 70 V95% < 98% 110Dmax < 110% 100PTV 63 V95% < 98% 110PTV 56 V95% < 98% 120Spinal Cord Dmax < 48Gy 100V45Gy < 0.1 cm3 100Spinal Cord PRV V52Gy < 0.1 cm3 100Submandibular (right\/left) Dmean < 20Gy (1) 30OrDmean < 25Gy (both)322Table A.2: The number of plans passing all dose constraints after N prelim-inary optimization iterations, as well as the mode of N required for a planto pass all dose constraints.N # plans passed0 41 82 4>2 1Nmode = 1Table A.3: Final mean optimization objective priority applied to each doseconstraint with Plan n Check. For structures which occurred five or lesstimes in the study cohort, initial priority is left blank due to an inadequatesample size for determination. Optimization objectives which finished witha priority of zero were not included in averages.Region of Interest Constraint Final Mean PriorityBody Dmax < 110% 105Brain Stem Dmax < 54Gy 88.75V50Gy < 0.1 cm3 100Brain Stem PRV V60Gy < 0.1 cm3 100Larynx\/Laryngopharynx Dmean < 45Gy 39Oral Cavity Dmax < 50Gy 37Parotid (right\/left) Dmean < 20Gy (1) 54OrDmean < 25Gy (both)PTV 70 V95% < 98% 109Dmax < 110% 105PTV 63 V95% < 98% 109PTV 56 V95% < 98% 120Spinal Cord Dmax < 48Gy 100V45Gy < 0.1 cm3 99Spinal Cord PRV V52Gy < 0.1 cm3 100323Figure A.2: A dose distribution for a head-and-neck VMAT plan created with Plan n Check is shown along withthe dual arc beam profiles324As 71 percent of plans required no more than one preliminary optimiza-tion cycle, Nmode = 1, Plann Check\u2019s default number of preliminary opti-mization iterations has been accordingly set to one, which can be modifiedif desired. Based on the results of this study, setting N = 1 will be sufficientfor the majority of head-and-neck plans created with Plan n Check to satisfyall dose constraints, and setting N = 2 would extend the required planningtime to meet all constraints, for the majority of patients. The mean finaloptimization objective priorities were used to edit initial priority values usedby Plan n Check. Priorities that ended up at zero after optimization werenot used in the calculation of final priorities. Cases that cannot meet theobjective will have priorities decreased to 0 automatically when a reasonableinitial priority is used.Plan n Check successfully matched all structures within the patient\u2019sstructure set to their respective head-and-neck ROIs in this study; however,the string-matching algorithm used for this was modified empirically whiletesting its performance on part of the cohort and therefore should not beexpected to have a 100 percent success rate with patients outside the cohort.Imperfections in matching may be submitted as issues on GitHub and willbe used to increase the robustness of the matching algorithm. Plan n Checkis freely available for download as an open source project on GitHub [535].Along with automation of head-and-neck VMAT planning, Plan n Checkmay easily be extended to automate planning for other types of treatmentby creating child classes of the abstract plan class, and modifying the beam-making function to create beams conventionally used for the given treatmenttype.Plan n Check optionally produces a detailed plan checking PDF file uponcreation of a treatment plan. This includes the overall status of the plan,patient\/plan details, jaw verification, constraint statuses for each ROI, anda log containing the optimization objective updating details from plan cre-ation. If desired, DVH plots can be easily added into the report with cus-tomized axes for any ROI by selecting these options in the special featuresmenu. DVHs can also be viewed directly within Plan n Check after plancreation (Figure A.3). Although plans created by Plan n Check still require325a thorough review by a treatment planner. The use of this program savesthe planner time by creating beams, setting optimization objectives, andcreating an initial plan that can then be further fine-tuned.Figure A.3: The scalable DVH viewing panel within Plan n Check is shown.DVHs with customizable axis boundaries are able to be saved into plan checkPDFs produced with Plan n Check.326","@language":"en"}],"Genre":[{"@value":"Thesis\/Dissertation","@language":"en"}],"GraduationDate":[{"@value":"2024-05","@language":"en"}],"IsShownAt":[{"@value":"10.14288\/1.0440991","@language":"en"}],"Language":[{"@value":"eng","@language":"en"}],"Program":[{"@value":"Physics","@language":"en"}],"Provider":[{"@value":"Vancouver : University of British Columbia Library","@language":"en"}],"Publisher":[{"@value":"University of British Columbia","@language":"en"}],"Rights":[{"@value":"Attribution-NonCommercial-NoDerivatives 4.0 International","@language":"*"}],"RightsURI":[{"@value":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/","@language":"*"}],"ScholarlyLevel":[{"@value":"Graduate","@language":"en"}],"Supervisor":[{"@value":"Clark, Haley","@language":"en"},{"@value":"Reinsberg, Stefan","@language":"en"}],"Title":[{"@value":"Towards improving radiotherapeutic treatment of the parotid glands : a cross-modality investigation","@language":"en"}],"Type":[{"@value":"Text","@language":"en"}],"URI":[{"@value":"http:\/\/hdl.handle.net\/2429\/87682","@language":"en"}],"SortDate":[{"@value":"2024-12-31 AD","@language":"en"}],"@id":"doi:10.14288\/1.0440991"}