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Assessment of spatially inhomogeneous intra-organ radiation dose response in salivary glands Clark, Haley 2017

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Assessment of spatially inhomogeneous intra-organradiation dose response in salivary glandsbyHaley ClarkB.Sc. Hon. in Physics, The University of Alberta, 2010M.Sc. in Physics, The University of British Columbia, 2013a thesis submitted in partial fulfillmentof the requirements for the degree ofDoctor of Philosophyinthe faculty of graduate and postdoctoralstudies(Physics and Astronomy)The University of British Columbia(Vancouver)April 2017© Haley Clark, 2017AbstractCancers treated with radiotherapy must be adequately irradiated to suppressgrowth at the site of origin. To achieve doses high enough to attain ‘localcontrol’ and inhibit growth of metastases, surrounding normal tissues areselectively co-irradiated. Current clinical practice for head-and-neck cancersinvolves salivary gland irradiation. Threshold doses that minimize adverseinduced toxicities are currently based on whole-organ mean dose. Modernradiation delivery techniques are able to sculpt the dose profile to accom-modate sub-organ irradiation, but knowledge of the relative importance ofsub-organ structures remains unknown. As tissue-sparing techniques improve,assessment of the normal tissue toxicity risk becomes increasingly important.Loss of salivary function and xerostomia (subjective dry mouth) arecommon normal tissue toxicities in head-and-neck cancer patients. Radiother-apy-induced dysfunction and xerostomia can drastically reduce oral hygieneand health and may negatively impact the ability to eat, speak, sleep, orswallow. These pervasive toxicities detract from overall quality of life andcan be permanent, perpetuating the negative impact.The purpose of this work is to quantify the relative importance of spatialregions within the major salivary glands for late salivary function (i.e., ‘re-gional effects’). The ultimate aim is to improve knowledge of toxicity risk.Broad regional effects have been noted in rat parotid, and it has recently beenclaimed that a localized ‘critical region’ has been located in human parotidglands. Furthermore, a morphological dependence on the dose profile hasbeen noted for subjective xerostomia. Clinical trials involving lobe and regionsparing are underway, yet comprehensive quantification of the importance ofiisub-organ structures remains unknown.To this end, the association between radiation dose delivered to regionswithin the largest salivary glands and measurements of whole-mouth salivaryflow is quantified. Independent analysis procedures are developed that arecapable of quantifying the relative importance of sub-segments. Evidence isfound that sub-segments are inhomogeneously important for maintenance oflate salivary flow, with the caudal parotid aspects having greatest importance.An imaging protocol is developed which may help pinpoint specific tissues orfunctional units residing within these regions.iiiPrefaceThe identification and design of this research program was completed collab-oratively by Vitali Moiseenko, Steven Thomas, Jonn Wu, Allan Hovan, andmyself. In particular, the original idea was established, and the collection ofpatient data began, prior to Haley Clark’s involvement in the project.The collection of patient data has been ongoing for nearly a decade.Collection was performed by the department of oral oncology at the BritishColumbia Cancer Agency (BCCA) Vancouver, Fraser Valley, and Centre forthe North sites. Patient data was managed primarily by Haley Clark, butthe earliest efforts before his involvement were headed by Vitali Moiseenko.Clinical contour verification and quality assurance was performed by JonnWu.Unless otherwise indicated, all methodology and analysis presented hereinis original work designed and performed by Haley Clark under the supervisionand guidance of Steven Thomas, Stefan Reinsberg, Jonn Wu, and VitaliMoiseenko. Hal Clark, alone, was responsible for writing this document.This work is a continuation of, and expansion upon, earlier work by HaleyClark which was summarized in a MSc thesis submitted to the Universityof British Columbia (UBC) in October 2010 entitled ‘On the Regional DoseSusceptibility of Parotid Gland Function Loss and Recovery: An Effort TowardAmelioration of Radiotherapy-Induced Xerostomia’ [1]. Though the theme issimilar to the present thesis, there is no overlap in the work described. Allmethodology, analysis, and other developments described in the present thesiswere performed after acceptance of the MSc thesis (except where clearly andexplicitly described, such as for comparison purposes).ivEthics approval from the UBC BCCA REB was granted for the collectionand analysis of patient data under the title A review and comparison ofsalivary function toxicity from standard techniques in head-and-neck cancerat BCCA and calculation of a radiation dose-salivary function response curveand certificates H01-02073 and H07-02073.The introductory chapters in part I were written for the sole purpose ofinclusion in this document. The contents of chapters 4, 6 and 14 have notbeen submitted to academic journals or scientific conferences, but may bein whole or in part in the future. Some figures in chapter 2 were publishedin the author’s MSc thesis (see [1]) in the UBC cIRcle archives and areadaptations by the author from the work of Toldt and Dalla Rosa [2] (nowin the public domain, but originally published by the Rebman company, NewYork in 1919). Some figures in chapter 4 were published in the Journal ofPhysics: Conference Series (2014; vol. 489, pp. 012009) during the author’sMSc thesis under the title ‘Automated segmentation and dose-volume analysiswith DICOMautomaton.’ The list of authors was Haley Clark, Steven Thomas,Vitali Moiseenko, Richard Lee, Bradford Gill, Cheryl Duzenli, and JonnWu. Haley Clark was responsible for generation of the figures, writing themanuscript, developing the methods, writing all software, ans performing allanalysis.The contents of chapter 11 have been submitted for publication in anacademic journal under the title ‘Prefer Nested Segmentation to CompoundSegmentation.’ The list of authors was Haley Clark, Stefan Reinsberg, VitaliMoiseenko, Jonn Wu, and Steven Thomas. Haley Clark identified the researchproblem, developed the study and methodology, performed all analysis, andwrote all drafts.The contents of chapter 12 have been submitted for publication in anacademic journal under the title ‘Caudal Aspects of the Parotid Gland areMost Important for Radiation-Induced Salivary Dysfunction.’ The list ofauthors was Haley Clark, Steven Thomas, Jonn Wu, Allan Hovan, Carrie-Lynne Swift, and Stefan Reinsberg. Haley Clark identified the researchproblem, developed the study and methodology, performed all analysis, andwrote all drafts.vThe contents of chapter 13 have been submitted for publication in anacademic journal under the title ‘Fine segmentation shows anterior-caudalparotid is most important for salivary loss.’ The list of authors was HaleyClark, Steven Thomas, Stefan Reinsberg, Allan Hovan, Vitali Moiseenko, andJonn Wu. Haley Clark identified the research problem, developed the studyand methodology, performed all analysis, and wrote all drafts.The contents of chapter 15 are an updated version of an early manuscriptthat was later published under the title ‘Development of a method forfunctional aspect identification in parotid using dynamic contrast-enhancedmagnetic resonance imaging and concurrent stimulation’ in Acta Onco-logica (2015 Oct 21; vol. 54, no. 9, pp. 1686-90; Taylor & Francis Ltd.,http://www.tandfonline.com/loi/ionc20) by Haley Clark, Vitali Moi-seenko, Thomas Rackley, Steven Thomas, Jonn Wu, and Stefan Reinsberg [3].Haley Clark developed the study and methodology, orchestrated all imagingand data collection, designed experimental apparatus, performed all analysis,and wrote all drafts.Permission has been sought and granted to reproduce all submitted andpublished materials, both from publishers and co-authors, where applicable.viTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviiGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . .xxxiiDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xxxiii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Motivation and Overview . . . . . . . . . . . . . . . . . . . . 11.2 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . 3I Introductory Topics . . . . . . . . . . . . . . . . . . . . . 52 Anatomy and Physiology of Salivary Glands . . . . . . . . . 62.1 Parotid Glands . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2 Submandibular Glands . . . . . . . . . . . . . . . . . . . . . . 112.3 Sublingual Glands . . . . . . . . . . . . . . . . . . . . . . . . 12vii2.4 Minor Glands . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.5 Saliva . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 Salivary Gland Imaging and Contouring . . . . . . . . . . . 183.1 Survey of Imaging Techniques . . . . . . . . . . . . . . . . . . 183.2 Computed Tomography Imaging . . . . . . . . . . . . . . . . 223.2.1 Current Clinical Practices . . . . . . . . . . . . . . . . 233.3 Magnetic Resonance Imaging . . . . . . . . . . . . . . . . . . 273.3.1 Current Clinical Practices . . . . . . . . . . . . . . . . 293.4 Contouring Practices in the Clinic . . . . . . . . . . . . . . . 323.4.1 Clinical ROI Statistics . . . . . . . . . . . . . . . . . . 343.5 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . 394 Salivary Gland Morphology and Topology . . . . . . . . . . 404.1 Space-Filling Curves . . . . . . . . . . . . . . . . . . . . . . . 434.2 Barycentric Coordinates . . . . . . . . . . . . . . . . . . . . . 454.3 Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . 544.4 Deformable Registration . . . . . . . . . . . . . . . . . . . . . 564.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595 Why are Salivary Glands Irradiated? . . . . . . . . . . . . . 615.1 Primary Cancers Within Salivary Glands . . . . . . . . . . . . 615.2 Practical Head-and-Neck Anatomical Constraints . . . . . . . 625.3 Metastases and Second Primary Cancers . . . . . . . . . . . . 625.4 Lymph Nodes Must be Irradiated . . . . . . . . . . . . . . . . 635.5 Head and Neck Cancer Epidemiology . . . . . . . . . . . . . . 645.6 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . 656 Salivary Dysfunction and Xerostomia . . . . . . . . . . . . . 666.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 666.2 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 686.3 Complications . . . . . . . . . . . . . . . . . . . . . . . . . . . 696.4 The Association Between Xerostomia and Dysfunction . . . . 70viii6.4.1 Association in the BCCA Cohort . . . . . . . . . . . . 716.5 Grading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 746.6 Dysfunction and Recovery . . . . . . . . . . . . . . . . . . . . 766.7 Overview of Toxicity Facets for Analysis . . . . . . . . . . . . 816.7.1 Xerostomia or Dysfunction? . . . . . . . . . . . . . . . 816.7.2 Early or Late? . . . . . . . . . . . . . . . . . . . . . . 826.7.3 Loss or Recovery? . . . . . . . . . . . . . . . . . . . . 856.7.4 Stimulated Saliva or Resting Saliva? . . . . . . . . . . 886.7.5 Parotids, Submandibulars, or minor glands? . . . . . . 896.7.6 Relative or Absolute? . . . . . . . . . . . . . . . . . . 906.7.7 Summary and Conclusions . . . . . . . . . . . . . . . . 937 Toxicity Assessment: Instruments and Protocols . . . . . . 947.1 Clinical Xerostomia Assessment . . . . . . . . . . . . . . . . . 947.2 Clinical Salivary Function Assessment . . . . . . . . . . . . . 967.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 988 Other Relevant Topics From the Literature . . . . . . . . . 998.1 Are Parotids Serial or Parallel Organs? . . . . . . . . . . . . . 998.2 The Growing Importance of Stem Cells . . . . . . . . . . . . . 1028.3 Relevant Clinical Factors . . . . . . . . . . . . . . . . . . . . . 1038.4 Factors Affecting Availability of Data . . . . . . . . . . . . . . 1058.5 Clinical Recommendations . . . . . . . . . . . . . . . . . . . . 1119 Statement of Research Questions . . . . . . . . . . . . . . . 1129.1 Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1129.2 Outline of Approach . . . . . . . . . . . . . . . . . . . . . . . 113II Analytics . . . . . . . . . . . . . . . . . . . . . . . . . . 11510 The Basics of Segmentation . . . . . . . . . . . . . . . . . . . 11610.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11610.2 DICOMautomaton . . . . . . . . . . . . . . . . . . . . . . . . . . 11610.3 Solutions to Elementary Geometrical Problems . . . . . . . . 117ix10.4 Planar Segmentation . . . . . . . . . . . . . . . . . . . . . . . 11910.5 Projective Segmentation . . . . . . . . . . . . . . . . . . . . . 11910.6 Iterative Segmentation . . . . . . . . . . . . . . . . . . . . . . 12410.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12511 Segmentation Methodology . . . . . . . . . . . . . . . . . . . 12611.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12611.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . 12711.2.1 Segmentation . . . . . . . . . . . . . . . . . . . . . . . 12711.2.2 Compound Segmentation . . . . . . . . . . . . . . . . 12811.2.3 Nested Segmentation . . . . . . . . . . . . . . . . . . . 12911.2.4 ROI Segmentation Comparison . . . . . . . . . . . . . 12911.2.5 Statistics . . . . . . . . . . . . . . . . . . . . . . . . . 13111.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13111.3.1 Analytic Comparison . . . . . . . . . . . . . . . . . . . 13111.3.2 Segmentation into Thirds . . . . . . . . . . . . . . . . 13411.3.3 Segmentation into 18ths . . . . . . . . . . . . . . . . . 13511.3.4 Segmentation into 96ths . . . . . . . . . . . . . . . . . 13711.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14011.4.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . 14412 Parametric Approach to Regional Effect Assessment . . . . 14512.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14512.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . 14812.2.1 Cohort Selection, Quality Assurance, DosimetricExtraction . . . . . . . . . . . . . . . . . . . . . . . . . 14812.2.2 Models . . . . . . . . . . . . . . . . . . . . . . . . . . 14912.2.3 Statistics . . . . . . . . . . . . . . . . . . . . . . . . . 15012.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15112.3.1 Mean-scaling 2y Expectorate Measurements . . . . . . 15112.3.2 Distribution of Baseline-Normalized SalivaryMeasurements . . . . . . . . . . . . . . . . . . . . . . . 15212.3.3 Whole Parotid . . . . . . . . . . . . . . . . . . . . . . 154x12.3.4 Cranial-Caudal 1/2-Volume Sub-Segments . . . . . . . 15612.3.5 Cranial-Caudal 1/3-Volume Sub-Segments . . . . . . . 15912.3.6 Cranial-Caudal 1/4-Volume Sub-Segments . . . . . . . 16012.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16212.4.1 Model Fitting . . . . . . . . . . . . . . . . . . . . . . . 16312.4.2 Explained Variance Importance . . . . . . . . . . . . . 16512.4.3 Model Ranking Importance . . . . . . . . . . . . . . . 16612.4.4 Sensitivity Analysis Importance . . . . . . . . . . . . . 16712.4.5 Overall Assessment and Comparison with Earlier Studies16712.4.6 Implications and Limitations . . . . . . . . . . . . . . 16913 Non-Parametric Approach to Regional Effect Assessment . 17113.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17113.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . 17313.2.1 Cohort, Measurements, Treatment, Tooling . . . . . . 17313.2.2 Importance Techniques . . . . . . . . . . . . . . . . . 17313.2.3 Statistics . . . . . . . . . . . . . . . . . . . . . . . . . 17513.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17613.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18413.4.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . 18814 Other Regional Effects . . . . . . . . . . . . . . . . . . . . . . 18914.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18914.2 Parotids and Xerostomia . . . . . . . . . . . . . . . . . . . . . 18914.3 Submandibulars and Unstimulated Flow . . . . . . . . . . . . 19314.4 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . 20015 Development of a DCE-MRI Imaging Protocol . . . . . . . 20115.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20115.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20315.2.1 Ethics and Accrual of Volunteers . . . . . . . . . . . . 20315.2.2 Image Collection and Processing . . . . . . . . . . . . 20315.2.3 Statistics – Variance Analysis . . . . . . . . . . . . . . 20515.2.4 Image Maps . . . . . . . . . . . . . . . . . . . . . . . . 206xi15.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20715.3.1 Variance Analysis . . . . . . . . . . . . . . . . . . . . . 20715.3.2 Image Maps . . . . . . . . . . . . . . . . . . . . . . . . 21215.3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 21215.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21616 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21816.1 Summary of Contributions . . . . . . . . . . . . . . . . . . . . 21916.2 Avenues for Future Research . . . . . . . . . . . . . . . . . . . 220Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222A The Optimal Obliquity of Cleaving Planes . . . . . . . . . . 280xiiList of TablesTable 3.1 BCCA head-and-neck Region of Interest (ROI) clinicalcontouring: structures bordering major salivary glands andthe oral cavity. . . . . . . . . . . . . . . . . . . . . . . . . 33Table 3.2 BCCA head-and-neck ROI contouring practice statisticsfor salivary glands and the oral cavity (886 patientsexamined). ROI count refers to the number of thespecified ROI present in the cohort. Sample population20th, 50th (i.e., median), and 80th percentiles are shown.‘Slab volume’ refers to total planar area multiplied by theimage slice thickness. Lateral symmetry is strong. . . . . 36Table 3.3 BCCA head-and-neck ROI extreme linear dimensions (i.e.,‘caliper width’) along orthogonal anatomical directions(886 patients examined). ROI count refers to the numberof the specified ROI present in the cohort. Samplepopulation 20th, 50th (i.e., median), and 80th percentilesare shown. Lateral symmetry is strong. . . . . . . . . . . 37Table 6.1 Pearson’s correlation coefficients (r) betweenbaseline-normalized whole-mouth stimulated salivameasurements and normalized and inverted individualQuality-of-Life (QoL) responses. W representswhole-mouth saliva, N is the number of questionnairesavailable. QoL instrument questions are described insection 7.1. . . . . . . . . . . . . . . . . . . . . . . . . . . 72xiiiTable 6.2 Pearson’s correlation coefficients (r) betweenbaseline-normalized whole-mouth unstimulated salivameasurements and normalized and inverted individual QoLresponses. W represents whole-mouth saliva, N is thenumber of questionnaires available. QoL instrumentquestions are described in section 7.1. . . . . . . . . . . . 73Table 11.1 Ratios of the fair fractional area for compoundsegmentation sub-segments in terms of the apothem (h)and fractional area (f). All ratios are fractions of the fairlydistributed area (pir2/9) in which each sub-segment has anequivalent area. Centre sub-segments have four planaredges, centre-adjacent have three, and corner sub-segmentshave two. . . . . . . . . . . . . . . . . . . . . . . . . . . . 133Table 11.2 Comparison of median voxel counts, quartile coefficients ofdispersion (QCD), and runtime for compound and nestedsegmentation. Sig. K-S tests refers to the number ofstatistically significant Kolmogorov-Smirnov tests (out of4560; α = 0.05). Runtime is per (individual) sub-segmentand was measured on an Intel® Xeon® X5550 CPU. Theuse of oblique cleaving planes and fine supersamplingreduced sub-segment median voxel range relative to themedian. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138Table 12.1 Akaike’s Information Criterion (AIC)-ranked W1y/Wbregression models using 1/2-volume sub-segments. Modelsare ranked by AIC (lower is better). All quantities aredimensionless. AW denotes the Akaike weight. In all casespruns > 0.14. . . . . . . . . . . . . . . . . . . . . . . . . . 157xivTable 12.2 Parameters for the best 1/2-volume W1y/Wb whole-parotidregression models. All parameters except A have unitsGy-1; A is unitless. Superscripts denote (i)psi- and(c)ontralateral; subscripts denote (u)pper (cranial) and(l)ower (caudal) sub-segments. . . . . . . . . . . . . . . . 158Table 12.3 AIC-ranked W1y/Wb regression models using 1/3-volumesub-segments. All quantities are dimensionless. In all casespruns > 0.18. . . . . . . . . . . . . . . . . . . . . . . . . . 160Table 12.4 Parameters for the best 1/3-volume W1y/Wb whole-parotidregression models. All parameters except A have unitsGy-1; A is unitless. Superscripts denote (i)psi- and(c)ontralateral; subscripts denote (u)pper (cranial),(m)iddle, and (l)ower (caudal) sub-segments. . . . . . . . 161Table 12.5 AIC-ranked W1y/Wb regression models using 1/4-volumesub-segments. All quantities are dimensionless. In all casespruns > 0.16. . . . . . . . . . . . . . . . . . . . . . . . . . 163Table 12.6 Parameters for the best 1/4-volume W1y/Wb whole-parotidregression models. All parameters have units Gy-1; A isunitless. Superscripts denote (i)psi- and (c)ontralateral;subscripts denote (u)pper (cranial), (m)iddle-(u)pper,(m)iddle-(l)ower, and (l)ower (caudal) sub-segments. . . . 164Table 13.1 Summary of results and most importance sub-segments.All quantities are dimensionless. rpa denotes thecorrelation coefficient between actual and predictedmean-scaled W1y/Wb. Whole, halves, thirds, and quarterssegmentation used both ipsi- and contralateral parotids;18ths and 96ths used only contralateral parotids to reducecomputational burden. The most important sub-segment(SS) is specified; refer to fig. 13.3 for sub-segment locations.Importances given are relative to the expected result for ahomogeneous parotid. . . . . . . . . . . . . . . . . . . . . 177xvTable 14.1 Pearson’s correlation coefficients (r) between patientself-reported xerostomia questionnaire responses and theresponses predicted using only mean dose to 18equal-volume parotid gland sub-segments. Both early (i.e.,three month) and late (i.e., one year and mean-scaled twoyear) responses were used. The QoL instrument questionsare described in section 7.1. . . . . . . . . . . . . . . . . . 190xviList of FiguresFigure 2.1 Parotid, submandibular, and parotid accessory glands.The ear lobe has been folded so as to not obscure view ofthe parotid. The parotid accessory gland occurs as aseparate gland in 20-40% of the population [4, 5]. Imageadapted from Toldt and Dalla Rosa [2], the Rebmancompany, New York, 1919. . . . . . . . . . . . . . . . . . 9Figure 2.2 Left parotid gland as extracted from computedtomography patient contours demonstrating location, size,and transversely-inverted pyramid shape. . . . . . . . . . 10Figure 2.3 View of salivary glands medial to the mandible.Submandibular and sublingual glands can be seen, alongwith sublingual ducts (draining to the oral cavity) andWharton’s duct. Image adapted from Toldt andDalla Rosa [2], the Rebman company, New York, 1919. . 13xviiFigure 3.1 Two example BCCA routine axial CT images (at 120 kVpand 350 mA) showing parotid contours around 2cminferior to the ear canal. The left parotid is indicated ineach, and a view with and without ROI is shown todemonstrate tissue contrast differences. Other ROIinclude the pharynx, spinal cord and margin, clinical andplanning target volumes encompassing the tongue andright nodes, and a portion of the left oral cavity that hasbeen subtracted from the target volume for sparingpurposes. . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Figure 3.2 Example BCCA routine axial CT images (at 120 kVp and350 mA) at various levels demonstrating visibility ofsub-structures within the left parotid (variously indicated;all are most likely vasculature owing to the relatively lowpermeability of acinar cells to ioversol). . . . . . . . . . . 26Figure 3.3 Example anatomical (T1-weighted, with TE = 16ms andTR = 619ms) Magnetic Resonance (MR) axial images inthe vicinity of the ear canal. Tissue differentiation cangenerally improve upon the equivalent ComputedTomography (CT) scan by adjusting the contrastsensitivity (cf. fig. 3.1). No contrast enhancement agentswere administered. . . . . . . . . . . . . . . . . . . . . . 30Figure 3.4 Example anatomical (T1-weighted, with TE = 16ms andTR = 619ms) MR axial images at various levelsdemonstrating clear tissue borders. No contrastenhancement agents were administered. . . . . . . . . . . 31xviiiFigure 4.1 Examples of a non-conforming (left) and a conforming(right) coordinate system superimposed over a singleparotid contour. The contour can be traced in theconforming (i.e., adaptive) coordinate system locally bytranslation along individual coordinate directions. Theconforming system is a semi-conformal (i.e.,angle-preserving) mapping of R2 Euclidean space. . . . . 40Figure 4.2 Topology of a typical parotid gland as clinically contouredat the BCCA from several viewpoints aiming at the‘saddle point.’ Arrows trace sequential rotations of asingle parotid gland. Top row: superior view panning tomedial-anterior view; middle and bottom rows:medial-anterior view panning to lateral view. . . . . . . . 42Figure 4.3 Construction of a space-filling Hilbert curve (i.e., openapproximating polygons of increasing order). In thelimiting case, every point in the unit square is surjectivelymapped to a line segment. Locality is approximatelypreserved. . . . . . . . . . . . . . . . . . . . . . . . . . . 44Figure 4.4 A parotid demonstrating two kinds of curvature(Gaussian on left, mean on right) which were computedusing a discretization scheme described by Meyer et al. [6].Red and blue represent mean curvature extremes(maximum and minimum). Mean curvature highlights thesaddle surface more intuitively than Gaussian curvature,but neither consistently highlight the ridges. . . . . . . . 49Figure 4.5 Mean curvature for six parotid gland pairs. Features areeasy to visually identify, but difficult to robustly detectand locate computationally due to natural variations. . . 51xixFigure 4.6 Demonstrations of topological ambiguity due to clinicaltissue demarcation using ROIs. Top: ambiguousconnectivity between image slices – both are valid andcould be connected such that a 2-manifold homeomorphicto a sphere is produced. Bottom: ambiguous curvature forextrema contours – both satisfy the terminating boundarycondition imposed by the adjacent slice. . . . . . . . . . 53Figure 4.7 Tiling segmentations of a single contour of an axial ‘body’contour at the shoulder level. From left to right: first, aheuristic segmentation based on absolute radiation dose,clearly demonstrating sparing of the spinal cord in theencircled region (n.b. adapted without modification from[7]); second, a heuristic segmentation based onspatially-varying heuristic based on the local dosegradient; and third, a recursive, scale independentCartesian tiling. . . . . . . . . . . . . . . . . . . . . . . . 56Figure 4.8 Recursive mixed segmentation that progressively tiles anaxial body contour at nose level (left to right). The firstsegmentation is a medial-lateral projective segmentation(n.b. described in chapter 11) and the second is aper-sub-segment coronal planar segmentation. This figurewas adapted from [7] and modified to simplify presentation. 57xxFigure 4.9 More advanced recursive single-contour tilings. From leftto right: first, a semi-random, semi-periodic triangulationof an axial body contour at the level of the ear in whichall internal edges are constrained to one of fourrandomly-chosen directions (n.b. adapted withoutmodification from [7]); second, a challengingsemi-Cartesian tiling tiling on a star-shaped optic chiasmcontour; and third, a telescoping segmentation of a leftparotid contour with blocks of Cartesian grid arrangedinside larger ‘neighbourhood’ sub-segments. Theseexamples highlight that recursion can be used to generateadaptive, arbitrary tilings within n-polygons. . . . . . . . 57Figure 4.10 Volumetric segmentation of a whole left parotid ROI(top-left) into: (bottom-left) a core and peel, (middle)medial and lateral volumetric halves via projectivesegmentation (n.b. described in chapter 11), and (top totop-right and bottom-right) recursive or ‘nested’ planarsegmentation into equal-volume sub-segments. Theseexamples highlight that recursion can be used to generateadaptive, arbitrary tilings within oriented polyhedrawhich have been sliced to produce co-parallel planarcontours. Parts of this figure were adapted from [7] andrecoloured to simplify presentation. . . . . . . . . . . . . 58Figure 6.1 Violin plot of whole-mouth stimulated salivameasurements over time. The red dot represents themedian, the blue dot represents the mean, and the shaperepresents a kernel density that estimates themeasurement probability density. The optimal kerneldensity bandwidth was estimated by the method of [8].Note the similarity of one- and two-year distributionscompared with baseline and three-month distributions. . 83xxiFigure 6.2 Violin plot of whole-mouth resting saliva measurementsover time. The red dot represents the median, the bluedot represents the mean, and the shape represents akernel density that estimates the measurement probabilitydensity. The optimal kernel density bandwidth wasestimated by the method of [8]. One- and two-yeardistributions are differentiated than the stimulated case,but are still the most similar compared with baseline andthree-month distributions. . . . . . . . . . . . . . . . . . 84Figure 10.1 Demonstration of planar segmentation resulting in twosub-segments (collectively above and below the plane).Planar segmentation is always well-behaved whenpolygons are simple or weakly simple (i.e., holes withpartial seams). . . . . . . . . . . . . . . . . . . . . . . . . 120Figure 10.2 Demonstration of projective segmentation on awell-behaved simple polygon. The casting direction isindicated by gray arrows and the fractional width is 1/2.Figure 4.8 shows recursive applied projective segmentation. 122Figure 10.3 Unintuitive ‘jumps’ and the failure of projectivesegmentation on a simple polygon (indicated with anarrow). The top figure is projectively segmented into themiddle figure. Note the cleave line passes outside theoriginal polygon. The bottom figure represents a cleavethat is more intuitive, but not attainable using projectivesegmentation. . . . . . . . . . . . . . . . . . . . . . . . . 123Figure 11.1 Demonstration of compound segmentation with threeparallel pairs of mutually orthogonal planes (six planes intotal). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129Figure 11.2 Demonstration of nested segmentation on a circle withf = 1/3. All sub-segments have area pir2/9. . . . . . . . 130xxiiFigure 11.3 Partitioning of a circle into nine sub-segments usingcompounded segmentation (exploded view). Eachsub-segment is bounded by two parallel pairs of mutuallyorthogonal planes. . . . . . . . . . . . . . . . . . . . . . . 132Figure 11.4 Calculation of sub-segment areas in terms of the area of awedge, right triangle, and square defined by f = 1/3,h ≈ 0.264932r, and r. Three distinct types ofsub-segments are shown: (1) “corner,” (2) “centre,” and (3)“centre-adjacent.” . . . . . . . . . . . . . . . . . . . . . . 133Figure 11.5 Nested segmentation of a circle into nine sub-segmentseach with area pir2/9. The orientation of the first cleavecan be chosen two ways. Both are shown. The cleavingorder is important in nested segmentation, but not forcompound segmentation. . . . . . . . . . . . . . . . . . . 134Figure 11.6 Depiction of the way in which the parotid gland ROIvolume was segmented to achieve sub-segments withvolume 1/3 that of the whole parotid. Nested andcompound segmentation produce identical results in thiscase. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135Figure 11.7 Depiction of nested (left) and compound (right)segmentation of whole parotid (centre) into 18sub-segments. . . . . . . . . . . . . . . . . . . . . . . . . 136Figure 11.8 Depiction of nested (left) and compound (right)segmentation of whole parotid (centre) into 96sub-segments. . . . . . . . . . . . . . . . . . . . . . . . . 137Figure 12.1 Kernel density estimate of the difference between W1y/Wband mean-scaled W2y/Wb. The optimal bandwidth wasestimated by the method of [8]. . . . . . . . . . . . . . . 153Figure 12.2 Quantile plot showing clear deviation from normality, butconsistency with a gamma distribution. . . . . . . . . . . 154xxiiiFigure 12.3 Distribution classification plot as proposed by Cullen andFrey [9]. 5000 bootstraps were performed. The empiricaldistribution is approximately equal parts gamma andlog-normal. . . . . . . . . . . . . . . . . . . . . . . . . . . 155Figure 12.4 Scatterplot of whole ipsi- and contralateral parotid meandoses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156Figure 13.1 Relative c-tree conditional permutation importance ofsub-segments for 18ths segmentation. Importance is givenas the percentage of relative importance compared to ahomogeneous organ (which would be 100%). Refer tofig. 13.3 for sub-segment (‘SS’) spatial correspondence.Anatomical groupings display the per-group median (filledcircles). Importances span ∼0-3.85× that of equivalentsub-segments in a homogeneous parotid. . . . . . . . . . 179Figure 13.2 Relative c-tree conditional permutation importance ofsub-segments for 96ths segmentation. Importance is givenas the percentage of relative importance compared to ahomogeneous organ (which would be 100%). Refer tofig. 13.3 for sub-segment (‘SS’) spatial correspondence.Anatomical groupings display the per-group median (filledcircles). Importances span ∼0-4.04× that of equivalentsub-segments in a homogeneous parotid. . . . . . . . . . 180Figure 13.3 Relative c-tree conditional permutation importance ofsub-segments for 18ths (left) and 96ths (right)segmentation. Equal-volume sub-segments are representedby a single slice of axial plane encompassed by thesub-segment. In segmentation into 18ths (96ths),importances span ∼0-3.85× (∼0-4.04×, respectively) thatof equivalent sub-segments in a homogeneous parotid.The most important sub-segments are indicated. . . . . . 181xxivFigure 13.4 Sample population contralateral parotid dosimetriccharacteristics: mean dose (left) and the inner-most 50thpercentile of mean dose (right) for each sub-segment (SS).Mean doses span 15.4-50.2Gy (SS09 and SS01,respectively). Inner 50th percentiles span 16.1-33.9Gy.Caudal-medial aspects received the highest dose whilecranial-lateral aspects received the lowest dose, both withlow variation across the sample population. . . . . . . . . 183Figure 14.1 C-tree conditional permutation regional importance mapusing parotid gland sub-segment mean dose and patientself-reported late xerostomia questionnaire responses (#6on left, #7 on right). Questions are described insection 7.1. Like with stimulated saliva, caudal aspectsare most important (cf. fig. 13.3). . . . . . . . . . . . . . 192Figure 14.2 Quantified c-tree conditional permutation importance forindividual sub-segments corresponding to QoL question#6. Sub-segment (‘SS’) numbering is shown in fig. 14.1and is identical to fig. 13.3. Importance is presented asthe percentage of relative importance compared to ahomogeneous organ (which would be 100%). Anatomicalgroupings display the per-group median (filled circles).Caudal-posterior aspects are most important, withrelative importance up to ∼4.0× that of an equivalenthomogeneous organ sub-segment. . . . . . . . . . . . . . 193xxvFigure 14.3 Quantified c-tree conditional permutation importance forindividual sub-segments corresponding to QoL question#7. Sub-segment (‘SS’) numbering is shown in fig. 14.1and is identical to fig. 13.3. Importance is presented asthe percentage of relative importance compared to ahomogeneous organ (which would be 100%). Anatomicalgroupings display the per-group median (filled circles).Caudal-posterior aspects are most important, withrelative importance up to ∼3.5× that of an equivalenthomogeneous organ sub-segment. . . . . . . . . . . . . . 194Figure 14.4 C-tree permutation (non-conditional) regional importancemap using submandibular gland sub-segment mean doseand late resting saliva facets. Cranial aspects (closest tothe floor of the mouth) are most important. . . . . . . . 197Figure 14.5 C-tree conditional permutation regional importance mapusing submandibular gland sub-segment mean dose andresting saliva facets. Cranial aspects (closest to the floorof the mouth) are most important. Agreement with c-treenon-conditional importance (in fig. 14.4) is strong. . . . . 198Figure 14.6 Quantified c-tree conditional permutation importance forindividual sub-segments. Sub-segment (‘SS’) numbering isshown in figs. 14.4 and 14.5. Importance is presented asthe percentage of relative importance compared to ahomogeneous organ (which would be 100%). Anatomicalgroupings display the per-group median (filled circles).Cranial-posterior aspects (closest to the floor of themouth) are most important, with relative importance upto ∼3.5× that of an equivalent homogeneous organsub-segment. . . . . . . . . . . . . . . . . . . . . . . . . . 199xxviFigure 15.1 A typical spatially averaged voxel C(t) demonstratingtemporal stages of the protocol. From left: pre-contrastagent injection window (left-most grey box); rapid uptakeperiod, where high concentrations of contrast rapidlyperfuse into parotid tissues, peak, and begin to drain;stimulatory period running from 230-240s from scancommencement, and a stimulatory response manifest as amodest contrast agent concentration increase; andcontinued slow washout. An empirical fit omitting thestimulatory period and Bezier spline interpolation areshown as visual guides. Figure previously published in [3],reproduced with permission from Taylor & Francis Ltd.;http://www.tandfonline.com/loi/ionc20. . . . . . . . 208Figure 15.2 Examples of time courses similar to fig. 15.1, but showingvarying responses to the stimulation beginning at 230s.Positive, negative ‘blips’ and ongoing shifts are seen.Splines are used as a visual guide; note the strongdeviation 10-30s after stimulation. Figure previouslypublished in [3], reproduced with permission from Taylor& Francis Ltd.;http://www.tandfonline.com/loi/ionc20. . . . . . . . 209Figure 15.3 Variance analysis time courses in parotid (stimulated andunstimulated, with Gaussian kernel smoothed trend linesas a visual guide) showing a clear distinction in trendafter stimulation occurs (300s). Means before and afterstimulation are significantly different (p < 0.0001 ;two-tailed t-test), suggesting a differing contrast dynamicsresulting from stimulation. Figure previously published in[3], reproduced with permission from Taylor & FrancisLtd.; http://www.tandfonline.com/loi/ionc20. . . . . 210xxviiFigure 15.4 Comparison of parotid and masseter response tostimulation. Compared with nearby tissues, parotidresponse is more rapid and greater in amplitude. Figurepreviously published in [3], reproduced with permissionfrom Taylor & Francis Ltd.;http://www.tandfonline.com/loi/ionc20. . . . . . . . 211Figure 15.5 A single slice example of image maps for two volunteers(top and bottom). At centre: temporally-averagedT1-weighted images; at left: contrast agent; at right:difference of changes in slope maps in parotid. In thelatter, voxels which showed no response to stimulation(within the ROI) are midtone, those that responded witha positive change in slope are brighter, and those thatresponded negatively are darker. . . . . . . . . . . . . . . 213Figure 15.6 Enlarged example image map slice. At left: atemporally-averaged T1-weighted image with thedifference of changes in slope map overlaid on theparotids; at right: enlarged parotid maps. In the latter,voxels showing no stimulatory response are midtone.Those that responded positively (negatively) are brighter(darker). Figure previously published in [3], reproducedwith permission from Taylor & Francis Ltd.;http://www.tandfonline.com/loi/ionc20. . . . . . . . 214Figure A.1 Depiction of voxel spacing at the min-max angle whennearest-neighbours (origin and red; red lines) andnext-nearest-neighbours (origin, red, and blue; blue lines)are included. Figure A.2 depicts how these angles arelocated. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281xxviiiFigure A.2 Minimum spacing between distances of voxel centresabove line to line vs line angle for various box radii (i.e., abox of radius n centred at the origin contains (2n+ 1)2vertices). The next-nearest-neighbours example of fig. A.1corresponds to a box radius of 1. Grid spacing is∆x = ∆y = 1 (arb. units). The min-max angle is theangle that maximizes this function. For square regions theleft-most peak is maximal and shrinks as the box radiusgrows. For arbitrary geometry (e.g., ROIs) this is nolonger generally true. . . . . . . . . . . . . . . . . . . . . 282xxixGlossaryAIC Akaike’s Information CriterionARL AIC Relative LikelihoodCT Computed TomographyCTCAE Common Terminology Criteria for Adverse EffectsDCE-MRI Dynamic Contrast-Enhanced Magnetic Resonance ImagingDICOM Digital Imaging and Communication in MedicineDOF Degrees of FreedomDVH Dose-Volume HistogramEORTC European Organization for Research and Treatment ofCancerIMRT Intensity-Modulated Radiotherapy TreatmentKPS Karnofsky Performance StatusLENT-SOMA Late Effects Normal Tissue - Subjective, Objective,Management, Analytic late toxicity grading systemMAE Mean Absolute ErrorMSE Mean Squared ErrorMR Magnetic ResonancexxxMNAR Missing Not At RandomNTCP Normal Tissue Complication ProbabilityPCA Principal Component AnalysisPET Positron Emission TomographyOAR Organ-at-RiskQCD Quartile Coefficient of DispersionQoL Quality-of-LifeQUANTEC Quantitative Analysis of Normal Tissue Effects in theClinicREB Research Ethics BoardRMSE Root-Mean-Square ErrorRSE Residual Standard ErrorRSS Residual Sum of SquaresROI Region of InterestRTOG Radiation Therapy Oncology GroupSAR Specific Absorption RatioVMAT Volumetric Arc TherapyxxxiAcknowledgmentsThe author would like to expressgratitude for financial support from theBC Cancer Agency, the University ofBritish Columbia, and the Walter C.Sumner Memorial Foundation.The author would also like to express gratitude forsupport from Cheryl Duzenli, Kirpal Kohli, AllanHovan, Bradford Gill, the BCCA Machine Shop staff,and the UBC MRI staff. All kindly offered theirinsights or facilitated the author’s research efforts.The author was lucky to have an amicable, flexible, and tolerantcommittee. The author wishes to thank Steven Thomas, StefanReinsberg, Jonn Wu, and Vitali Moiseenko for their support.Each contributed in meaningful ways to the development ofthis work. Each went the extra mile, always.Finally, the author relied on love and support from family, especially Sarah.xxxiixxxiiiChapter 1Introduction1.1 Motivation and OverviewThis thesis concerns the most prevalent radiotherapy-induced toxicities inhead-and-neck cancer patients, salivary gland dysfunction and xerostomia[10]. Dysfunction manifests as (objective) reduction of salivary flow, andxerostomia is the (subjective) condition of persistent dry mouth. Theseconditions are ultimately distinct. However, in some sense, for example intypical clinical settings, they may be considered two sides of the same coin.Organs are composed of a heterogeneous mix of tissues. Some typesare more radiosensitive than others, and some types are more critical fororgan function than others. Currently, it is assumed (clinically) that thetissues that are both radiosensitive and critical for organ function (hereafterreferred to as ‘critical’ tissues) are distributed homogeneously throughoutthe major salivary glands. If a consistent, inhomogeneous distribution withspatial clustering were observed, it would be known as a ‘regional effect.’ Theconverse, ‘dose-volume effects,’ are evidence for the homogeneous distributionof critical tissues.Strong dose-volume effects have been known for many decades, so theclinical approximation of a homogeneous distribution has thus-far been con-structive. This was partially due to the clumsiness of traditional radiotherapydelivery. Modern technologies, however, have become both precise and accu-1rate. Advancements primarily in computational support technologies haveprecipitated advancements in machine delivery, improvements in planningcapabilities and accuracy, and enabled a plethora of substantial localizationimprovements through technologies such as on-board imaging [11, 12]. Thereis correspondingly more control over the delivered dose profile in modern times,and cracks in the homogeneous distribution approximation are beginning toshow.At the same time, overall increases in human longevity and the efficacyof cancer treatments, along with a rise in the number of cancer incidences,have caused the number of cancer survivors to explode [13]. Between 1970 to2007 Canadian cancer incidence more than tripled [14]. Accordingly, patienthardship has become increasingly important and research into methods forimproving patient outcomes has burgeoned. A culmination of circumstancesinvolving improvements in treatment technology and the steady erosion ofthe homogeneous distribution approximation, as well as the growing needto improve patient outcomes have resulted in a clinical need for this thesis –the broad aim of which is to quantify regional effects in the major salivaryglands.More specifically, the first aim of this thesis is to demonstrateregional effects in the parotid gland, primarily using parotid glanddysfunction. It is academically interesting to demonstrate such an effect.However, there is also a pressing clinical need to reduce xerostomia anddysfunction incidence and severity. Acknowledging the effect is merely thefirst step. If the effect can be quantified and incorporated into treatmentplanning, it may improve toxicity risk estimates and thereby improve patientoutcomes. The second aim of this thesis is therefore to quantify anyregional effects. Preferably in a consistent way rather than merely locatingcritical sub-structures.It is not clear how to accomplish the second aim, in particular, and a greatdeal of effort was therefore spent devising analytical (and physical) machineryto do so. Because the problem is both multi-factorial (i.e., many relevantstructures and candidate regions) and multi-faceted (i.e., many endpoints,including stimulated and unstimulated salivary flow, subjective xerostomia2reports), many approaches were considered and tested. A complete descriptionwould be inappropriately voluminous. Therefore, only the most promising orsuccessful approaches are reported herein.1.2 Thesis OrganizationThe introductory materials span part I. They begin with an overview offactors marginally related to radiotherapy that might still impact regionaleffects or the ability to detect them. Salivary gland anatomy and physiologyare reviewed in chapter 2. A review of imaging techniques and contouringpractices are given in chapter 3. A related discussion of salivary glandmorphology and topology, and how they are dealt with in later analysis,follows in chapter 4.The focus then broadens to incorporate radiotherapy-related factors. Adiscussion of the rationale for irradiating salivary glands is given in chapter 5,and a discussion of the ensuing post-irradiation dysfunction and xerostomiafollows in chapter 6. An overview of the instruments employed to assess thesetoxicities by measuring or estimating endpoint facets is given in chapter 7.Finally, a variety of short, independent topics of relevance derived fromthe literature over the last decade are presented in chapter 8. At this point,the reader should have essential understanding of the issues and will be readyto jump into the analysis. Before doing so, the research questions and ‘lineof attack’ are more precisely recapitulated in chapter 9.Analytical work is contained in part II. Chapters 10 and 11 are largelyindependent of radiotherapy, but cover topics instrumental for controllingbias in later analyses. Chapters 12 and 13 describe two related but ultimatelydissimilar approaches to assessing regional importance within the parotidgland, and largely accomplish the main goals of this thesis by quantify-ing and characterizing regional effects using parotid gland and dysfunctionfacets. Chapter 14 is a follow-up that applies the most successful methodsdeveloped in chapters 12 and 13 to similarly quantify regional effects us-ing submandibular gland and xerostomia facets. Chapter 15 is the mostanalytically-disconnected. It describes an Magnetic Resonance (MR) imaging3protocol that was developed to try probe parotid structures important forfunction within a volunteer cohort. As a volunteer pilot study, there isno possibility of incorporating radiological effects. However it may in thefuture present a pathway to radiotherapy treatments that are tailored to anindividual’s anatomy or physiology, perhaps most promisingly when guidedby, or used in conjunction with, the population-level regional importancefindings from earlier chapters.Finally, concluding remarks and avenues for future research are discussedin chapter 16.4Part IIntroductory Topics5Chapter 2Anatomy and Physiology ofSalivary GlandsHumans have several salivary glands. The major salivary glands compriseparotid, submandibular, and sublingual glands – those responsible for themajority of saliva production. The major glands are characterized by theirlarge size, significant contribution to whole-mouth saliva, remoteness fromthe oral mucosa, and encapsulation by connective tissue. Comparatively,the minor (and accessory) salivary glands are smaller, more numerous, anddistributed throughout the oral cavity [15]. Embryologically, the major glandsdevelop from the ectoderm, whereas minor glands develop from the mesoderm[16].Interestingly, human salivary gland anatomy and physiology is similarto that of many other terrestrial species [17]. Some species possess radicallymodified glandular structures which are, for example, capable of producingvenomous saliva in both invertebrates and vertebrates (including mammals)[18]. Owing to the difficulties inherent to studying human tissues, animalmodels are frequently studied. Rat parotid and sublingual glands are themost common surrogates, rabbit is not uncommon, while mice and drosophilaare seen less often [19] [17]. Morphologically, the feline submandibular glandsbear a closer resemblance to human submandibulars [20]; despite vitiation,rat studies dominate.6There is considerable variation in shape, size, and location amongst themajor salivary glands. It may be surprising, then, that the major glandsare somewhat similar in structure, composition, and function. All salivaryglands consist of functional parenchyma (i.e., the tissue which specializesin secretion of salivary fluids) and supporting stroma (i.e., the connectivetissue). Parenchyma are connected to the oral cavity through a networkof hollow ducts through which salivary fluid is passed. Duct or ‘lumen’formation is concurrent with embryogenic development of salivary glands.Branches of solid epithelial tissues that infiltrate the glands are hollowed viaapoptosis to form a series of interlinked ducts that permit free passage ofsaliva [21]. Apoptosis is mediated by members of a family of proteins knownas endogenous caspase inhibitors (the only known apoptosis inhibitors knownto occur naturally in mammals), including the aptly named survivin [22, 23].Mature ducts are functional shortly after birth. Secretory cells cluster at theterminus of the ducts in roughly spherical groups, which are referred to as‘endpieces’ [24].Endpieces are composed of acinar cells which are specialized to each glandand grouped into small clusters (similar to the gross structure of a raspberry)known as acini. In humans there are serous acinar cells, which secrete seroussaliva, and mucous acinar, which secrete mucous secretions. Serous saliva ismainly water in content [15]. It has digestive properties and is not otherwiseused for lubrication [25]. The salivary fluid produced by mucous acinar cellsis thicker and is primarily used for lubrication and protection of surfaces [26].The two types of saliva are created in various proportions in different glandsand are ultimately combined to form whole-mouth saliva. In the endpieces,serous cells tend to form spheroidal clusters while mucous cells form into atubular shape [24].The ducts have a distinct, regular branching hierarchy. Endpieces secretedirectly into intercalated ducts, which themselves drain into striated ducts,then excretory ducts, and finally into the main excretory duct which passesinto the oral cavity. Duct stroma have low water permeability – considerablyless than the parenchyma. Nonetheless, stroma modify the electrolyte com-position of fluid passing through the ducts, primarily via removal of sodium7chloride and addition of potassium and bicarbonate [16, 24, 27].Other tissues present in major salivary glands include: myoepithelialcells, which may help expel various substances from the duct system [16, 28];plasma cells within the interstitial regions separating glands, which secreteimmunoglobulins; blood vessels, which supply the salivary water; parasym-pathetic and sympathetic autonomic nerves; lymphatic tissues [4]; and atough, fibrous connective capsule which envelopes each gland. The capsuleinterposes various septa within the glands which partition the parenchymainto functional groups or ‘lobules.’ Collective ducts (i.e., intercalated andstriated ducts) span lobules and are mostly contained by the septa, whereasexcretory ducts pass within the septa, ultimately draining outside the capsule[24].It is estimated that the major salivary glands supply approximately 60-90% of total saliva secreted [24, 29] [30]. Naturally, as the minor glandssecrete less and are more geographically distributed than the major glands(and are thus generally easier to individually spare from incidental radiationdamage), they are thought to play a lesser role in radiotherapy-inducedxerostomia.2.1 Parotid GlandsThe parotid glands (figs. 2.1 and 2.2) are the largest of the salivary glands.Each parotid is located in the retromandibular fossa (behind the jaw, beloweither ear). Parotids are bound posteriorly by the sternocleidomastoid muscleand the mastoid process. They lie posterior to, and wrap around (see fig. 2.2),the posterior border of both the mandible angle and ramus [4].The parotid capsule is composed of a superficial layer of deep cervicalfascia. The stylomandibular ligament – the structure separating the inferiorportion of the parotid (the ‘tail’) from the submandibular gland – is formedby the capsule thickening anteriorly and inferiorly. The parotids tend toswell and enlarge under stress. It has been shown that even bulimia cansignificantly enlarge the parotid [31]. Sensations of pain as the parotidencroaches against the bounds of the capsule are common [32]. Parotids have8Figure 2.1: Parotid, submandibular, and parotid accessory glands. Theear lobe has been folded so as to not obscure view of the parotid.The parotid accessory gland occurs as a separate gland in 20-40% of the population [4, 5]. Image adapted from Toldt andDalla Rosa [2], the Rebman company, New York, 1919.9Figure 2.2: Left parotid gland as extracted from computed tomographypatient contours demonstrating location, size, and transversely-inverted pyramid shape.both a superficial lobe (external to the mandible) and a retromandibularlobe (deep to the mandible). The superficial lobe extends superiorly and issubstantially larger than the deep lobe. It therefore contains the majorityof the glandular tissues. The deep lobe passes within the stylomandibulartunnel (defined as the posterior border of the mandible’s ramus, the skullbase, and the stylomandibular ligament) [4].The parotids are supplied with arteries derived from the external carotid,which enters the posteromedial portion of the deep lobe, forks the posteriorauricular branch, and terminates into the maxillary and superficial temporal10arteries. The maxillary artery passes out of the parotid along the deep surface,while the superficial temporal artery passes out through the superior pole [33].Veins follow a similar course. The superficial temporal and maxillary veinsjoin within the parotid to form the posterior facial vein, which ultimatelyanastomoses with the external jugular vein [4].Lymphatics pass into and terminate within both superficial and deeplobes. Two to four lymphatic nodes are embedded within the parotid surface[33] while a variable number of nodes are scattered around the vicinity [4].Nodes drain to the cervical lymph and spinal accessory node groups. Bothsympathetic and parasympathetic nerves innervate the parotids. Sympathet-ics originate from the carotid plexus, whereas parasympathetics originatefrom the auriculotemporal nerve [4]. Discussion of the role that nerves playin the salivation process is deferred until section 2.5.Of the two acinar cell types, parotids are comprised almost exclusively ofserous type, which produce low-viscosity serous saliva. The parotids mainlysecrete under stimulated conditions, such as chewing, when they supplyapproximately 60% of whole-mouth saliva [15]. They secrete little otherwise[16].The main excretory salivary duct is 5-7cm long and is known as either theparotid duct or Stensen’s duct. It passes over the masseter muscle, pierces thebuccinator muscle and buccal fat, and drains into the oral cavity at the uppersecond molar tooth level [15]. Parotid ducts are not generally visible usingconventional Computed Tomography (CT), though they can be imaged usingMR, MR sialography, conventional sialography, scintigraphy, ultrasonography,and other less well-known techniques (discussed in chapter 3).2.2 Submandibular GlandsFollowing parotids, the largest salivary gland pair are the submandibularglands (figs. 2.1 and 2.3). They are located under the floor of the oralcavity, medial to the mandible [15]. Like parotids, they are characterized ashaving two major lobes. The larger superficial lobe separates the mandiblefrom the mylohyoid muscle and it itself separated from the parotid by the11aforementioned stylomandibular ligament [4]. The smaller deep lobe lies deepto the mylohyoid muscle and can be easily palpated in the floor of the mouth(see fig. 2.3). Superficial to the submandibular gland are: the platysmamuscle, deep cervical fascia, both facial vein and artery, and a portion of themandibular branch of the facial nerve. Posteriorly the submandibular glandborders the hyoglossus muscle. Both the lingual and hypoglossal nerves tracethis border [4].Both types of acinar cells are present in the submandibular, but theserous usually outnumber the mucous. They mainly secrete saliva underunstimulated conditions, during which they supply 70-90% of whole-mouthsaliva. During stimulation they produce approximately 20-40% of whole-mouth saliva [15]. The main excretory salivary duct is known either as thesubmandibular duct or Wharton’s duct. Like parotid ducts, submandibularducts are ∼5cm in length [34]. Exiting from the anterior aspect, submandibu-lar ducts pass anteriorly and superiorly between the hyoglossus and mylohyoidmuscles and drains near the lingual frenula, posterior to the lower incisors[15] (see fig. 2.3).Submandibular glands, like parotids, receive a rich sympathetic inner-vation from external carotid plexuses. Parasympathetic innervation comesfrom both facial and glossopharyngeal nerves [4]. The lingual nerve, whichsupplies sensory innervation to the tongue and carries some parasympatheticfibres, passes over submandibular ducts in two places but directly suppliesneither ducts nor submandibulars itself; rather, parasympathetic secretomo-tor innervation is received from postganglionic fibers that pass through thesubmandibular ganglion. Lymphatic fluid in the submandibular gland andsurrounding tissue drains into the submandibular lymph nodes, which areembedded on the surface of the glands. There are three to six such nodes;small nodes can occasionally be found within the glands.2.3 Sublingual GlandsThe sublingual glands (fig. 2.3) are the smallest and last of the major salivaryglands. They are located in the floor of the oral cavity, inhabiting the space12Figure 2.3: View of salivary glands medial to the mandible. Sub-mandibular and sublingual glands can be seen, along with sub-lingual ducts (draining to the oral cavity) and Wharton’s duct.Image adapted from Toldt and Dalla Rosa [2], the Rebmancompany, New York, 1919.directly inferior to the mucosa, superior to the submandibular glands [15],and between the mandible and genioglossus muscle. Like the parotids andsubmandibulars they are composed of both serous and mucous acinar cells;they differ in that the primary type are mucous. Sublingual glands thussecrete a viscous, mucosa-lubricating saliva.Compared with the submandibular, the sublingual contains few sympa-thetic nerves. This may be surprising as embryologically both submandibularand sublingual glands develop within the same capsule and descend fromthe same progenitor cell population [4] (i.e., submandibular and sublingualepithelia branch in the same mesenchyme capsule [35]). Parasympatheticnervous innervation is similar to the submandibular. Lymphatic fluid in thesublingual gland will drain into the submental nodes and, along with thesubmandibulars, into the submandibular nodes.The duct structure of the sublingual is also similar to the submandibular.Internal ducts drain into the duct of Rivinus, Bartholin’s duct, or directly13into the oral cavity through 8-20 small excretory ducts. These small ductsdrain under the tongue on the sublingual fold [34] [24].Upon stimulation the sublinguals produce an estimated 2-5% of whole-mouth saliva [15]. Despite the modest contribution, they, along with thesubmandibular glands, synthesize the majority of mucin present in saliva [36].2.4 Minor GlandsThe minor salivary glands comprise some 500-1000 small (∼ 1mm in diameter)glands that are distributed throughout the oral cavity and upper aerodigestivetract [24, 37]. They appear with varying probability in the oral mucosa of thehard palate, tongue, within the discontinuities of the mylohyoid muscle [38],the medial border of the cheeks and lips, and throughout the oropharynx[24]. Infrequently, minor gland tissues appear in intraparotid spaces along theneck, bordering the mandible, and within both the middle ear and externalear canal [39].Despite their multitudinousness, minor glands produce less than 10% ofthe total mucins present in whole-mouth saliva [15] and contribute less than5% of whole-mouth saliva. The structure and function of the minor glandsdiffers amongst themselves and from the major glands [24]. For example,minor glands may or may not have an exclusive excretory duct. Whileminor glands are surrounded by connective tissue, they are not necessarilyencapsulated by it as the major glands are. It is generally believed thatthey are of lesser consequence for total salivary function, though research hasshown that they are not completely insignificant [40].Other types of glands exist (e.g., Von Ebner’s glands) but are not discussedhere. While such glands are usually of minor importance, they are confusinglynot generally classified as minor glands. Accessory glands (e.g., the parotid’saccessory glands – see fig. 2.1) are distinct from the parotid in only 20% ofthe population [4]. For this reason, accessory glands are usually consideredto be lobes of major glands and not minor glands in and of themselves.142.5 SalivaSaliva is composed mainly of water (99.5% by volume) and small amounts ofproteins, peptides, and enzymes such as α-amylase, inorganic salts, mucins,bicarbonate, and other compounds (0.5% altogether) [41]. Total salivaryflow (stimulated and unstimulated) is estimated to be 1.0-1.5L per day [34] –roughly half comes from the parotids and half from the submandibulars overthe span of a day.Saliva is responsible for moistening and softening food, breaking downstarches and a small number of triglyceride lipids, protecting oral mucosaand teeth, and various antibacterial functions. Given the warm, moistenvironment the mouth presents for aerobic and anaerobic microorganisms,the antibacterial functions of saliva are eminently important for general health.Patients under heavy sedation (which often induces temporary reduction insalivary function) for two weeks or longer have demonstrated a shift in oralmicroflora from gram-negative to gram-positive species. The normal salivary‘flush’ of oral bacteria into the gut in patients with salivary dysfunction thuspermits opportunistic pathogens to invade and spread rapidly into the gutand respiratory tract [42, 43]. Salivary enzymes responsible for digestion areinactivated by gastric acidity, so saliva plays a limited role in digestion [24].However, many proteins thought to be synthesized in salivary endpieces havebeen detected throughout the body [44]. The function of many proteins andpeptides present in saliva are currently unclear [45]. Mucins act as mucosallubricants; their presence on the mucous membrane surfaces help to maintaina hydrated state [36].The composition of saliva will change in response to specific stimuli.Human parotid saliva produced in response to citric acid contains far lesssecretory immunoglobulin-A than that produced in response to mastication[46]. Likewise, stimulation with sweet-tasting solutions elicits a higher proteinconcentration compared to acidic solutions [47]. In rabbits α-amylase issecreted in higher concentration when fed carrots, but at a threefold-lowervolume, compared with pellets [48]. Psychosocial stress is known to stronglyaffect α-amylase concentrations in human secretions – so much so that it has15been suggested as a reliable, noninvasive indicator of psychosocial stress [49].The composition of saliva is also known to closely follow circadian rhythms.Similarly, the rate of unstimulated whole-mouth salivary output varies withthe time of day; low production occurs during sleep. Peak stimulated whole-mouth salivary output occurs daily around 17:00, is lowest at 05:00, andapproximately follows a sine wave with a period of one day [25]. Gustatoryand olfactory perceptions (i.e., the sensation of taste or smell) or stimulationof either mechanoreceptors (pressure) or nocireceptors (pain) via masticationwill greatly increase the rate of salivation – in some cases, up to ten timesthe baseline [16].In all salivary glands, production of saliva is stimulated by both parasym-pathetic and, to a lesser degree, sympathetic nervous systems. The secretionof proteins and salivary fluid is controlled by autonomic nerves [16]. Secretionof saliva occurs when cholinergic parasympathetic nerves emit acetylcholine.Acinar endpieces are evoked and secrete saliva when the acetylcholine bindsto the cell’s muscarinic receptors. Salivation is a rapid response to nervousstimulation. Cessation of parenchymal secretion occurs rapidly when theparasympathetic nerve stimulation is interrupted [16], but salivation maypersist after the stimulus subsides due to residual drainage in the ducts. Afew minor salivary glands will spontaneously secrete in absence of nervousstimuli, but maintenance of a continuous, normal secretory rate requires anautonomic nerve supply [50].162.6 ConclusionsParotid and submandibular glands contribute the most to whole-mouth saliva.They appear to have complimentary functions, with parotids responsible forthe majority of stimulated saliva and submandibulars responsible for themajority of resting/unstimulated saliva. Salivary gland dysfunction leadsto increased susceptibility to opportunistic pathogens, which, absent theprotective aspects of saliva, are able to pass from the aerodigestive tract intothe gut. Both parotids and submandibulars are known to have lymph nodeinvolvement, which, as will be discussed in chapter 5, has ramifications forhead-and-neck cancer patients treated with radiotherapy.17Chapter 3Salivary Gland Imaging andContouring3.1 Survey of Imaging TechniquesSalivary glands are highly accessible from an imaging perspective. The majorparotid gland duct (Stensen’s duct) papilla is visible at the upper second molartooth level and the major submandibular gland duct (Wharton’s duct) isvisible in the floor of the mouth; both are readily cannulated [15]. Historically,sialographic radiology exploited this accessibility to visualize ducts by flushinga contrast-enhancing agent via cannula [51]. The process is simple; a scoutis taken – normally at an oblique lateral-anterior angle, local anesthesia isapplied around the papilla of the duct or lidocaine is initially passed throughthe orifice, the duct is dialated using a lacrimal probe and saline, a contrastagent is flushed, and one or more radiographs are taken to observe agentperfusion [52, 53]. This technique was first recorded in vivo in 1925 and hasbeen employed for nearly a century [54, 55]. The earliest contrast agentscontained bismuth, were wholly mercury, or used early precursors to moderniodinated compounds, such as potassium iodide or lipiodol [52, 54, 56, 57].Intraoral radiography is sometimes employed [58]. However, conventionalradiography without cannulation or contrast enhancement, despite havingexcellent spatial resolution is generally insufficient to resolve salivary gland18ductal structures due to the complex head-and-neck anatomy [59].Despite long-time use of radiological sialography, several well-knowndetractors persist. Grievously for patients, it requires painful dilation andcannulation of the duct. It can also cause retention of contrast agent and isof limited use when perfusion is impossible [54, 57]. Other minimally-invasiveand non-invasive techniques are also amenable owing to the accessibility.Ultrasound sonography is non-invasive and causes no discomfort. In salivaryglands it is primarily used for resolving duct calcifications; older studies foundcalcification detection capabilities similar to sialography [60]. It can also beused to quantify morphological aspects of salivary glands [61]. The resolutionof ducts themselves is (or has historically been) generally poor without dilatingthe ducts (requiring the examination to be somewhat invasive). So it mostlyemployed to examine stroma and the protective capsule rather than ducts.Sonography appears to be underused considering it is one of the least invasivetechniques available; it is thought that sonography, in general, has somewhatbeen displaced by the wide availability and applicability of general radiology,CT, and MR [62]. Recent technological advancements in beamforming,ultrafast techniques, and low-cost construction methods may eventually leadto better ductal imaging and greater ubiquity [63, 64, 65, 66, 67].Scintigraphy is frequently used to image salivary action in parotid andsubmandibular glands by quantifying excretion of a radiotracer directly fromthe parenchyma [52, 68, 69]. Many tracers have been investigated, butthe most popular are 11C-methionine and 99mTc-pertechnetate. Becausescintigraphy can quantify function, it can therefore be applied to detectradiotherapy-induced dysfunction by comparison of pre- and post-treatmentimages. However, the highest-precision scintigraphic imagers – those for smallanimals – have a spatial resolution limit of around 2mm and are thereforenot able to resolve fine salivary gland internal structure [70]. Additionally,scintigraphy and other radioisotope-based methods are generally unsuitablefor continued observation due to limits on patient exposure, and may thereforelimit the total number of imaging applications possible [71].The current most popular imaging methods for applications in radiother-apy, sialadenitis, and sialolithiasis (i.e., obstruction via calcifications) appear19to be CT and the emerging technique of MR sialography [72]. CT is widelyavailable and offers millimetre or sub-millimetre spatial resolution in thehead-and-neck [52, 73]. It is widely applied to assess salivary obstruction anddysfunction, and is capable of quantifying radiotherapy-induced morphologi-cal changes [74, 75]. MR sialography is a non-invasive modality that uses insitu saliva secretions as an endogenous contrast medium [72]. No additionalcontrast agents are required. It has been shown to be effective for quantifyingradiotherapy-induced dysfunction and duct damage [76]. The flexibility incontrast derivation (i.e., endogenous or exogenous agents) and freedom inchoice of coil apparatus (i.e., microscopy coils) makes MR sialography aversatile and attractive imaging tool.Many other imaging methods have recently emerged or are currentlyunder intense development. Examples include: Sialoendoscopy, which in-volves insertion of a small endoscope into the parotid duct, but requiresessentially the same preparations as sialographic techniques and is of limiteduse for assessing whole-organ flow [77, 78]; MR spectroscopy, which allowsspatially-localized measurement of metabolite concentration in tissues [79];MR diffusion-weighted imaging [80], which can assess characteristics of glandfunction; Dynamic Contrast-Enhanced Magnetic Resonance Imaging, whichuses the flow of a contrast-enhancing agent through the vasculature (‘perfu-sion’) to derive information about blood flow from a volumetric image timeseries (which is employed later in this thesis) [81, 82, 83]; chemical exchangesaturation transfer (CEST), which exploits the chemical exchange betweenfree water and mobile exogenous or endogenous agents [84, 85]; multipara-metric methods that combine signals from multiple imaging techniques intonovel facets (e.g., cell density) [86]; Positron Emission Tomography (PET), invarious capacities [69, 86]; and various methods based on electrical impedance[87, 88, 89, 90]. A theme in modern imaging research appears to be de-velopment of multi-modality imaging techniques that can be combined toovercome limitations of individual techniques. Issues with such approachesvary, but often are more costly (both money and time), may require highercumulative patient doses, and often require image registration. Examplesinclude sialoendoscopy coupled with MR sialography [91], conventional MR20coupled with MR sialography [92], and scintigraphy coupled with CT [93].The most commonly-used modalities for diagnostic imaging are radiogra-phy, sonography, CT, and MR, with CT and MR use growing faster than theother modalities [94, 95, 96]. Presently, CT and MR imaging methods aremost common for assessing radiotherapy-induced toxicity in salivary gland.CTs are currently needed for tissue density estimation and radiotherapytreatment planning, so CT scanners are thus widely available. A recentdevelopment has been reliable estimation of electron density using only MRto improve MR clinical adoption and reduce reliance on CT [97, 98, 99, 100].Alternatively, there are efforts to combine fully-capable CT and MR imagingunits into a single clinical unit [101]. Contrast-enhanced CT and MR are bothminimally-invasive. CT is fast and cheap, MR is less common, less cheap, lessfast, and presents more contraindications, including any implanted or embed-ded ferromagnetic materials and implanted medical devices. However, MRis arguably more versatile, permitting more complicated imaging protocolsand a larger number of ways in which contrast can be derived. For example,continual scanning is permitted over long time spans, and the contrast mecha-nism can be switched on-the-fly. X-ray and CT imaging use ionizing radiationand patients therefore receive radiation dose. Doses received from routinehead-and-neck clinical scans are comparable to natural background levels andare therefore acceptable for diagnostic purposes, but they impose limits onthe duration and contrast possible [102]. MR scans use no ionizing radiation,sparing patients dose, but can breach Specific Absorption Ratio (SAR) limits.SAR limits present lower biological risk than x-ray dose at typical clinicallevels. Overall though, CT is cheaper and has an established presence in theclinic. It is therefore unlikely to abate in the near future. Since the aim ofthis research is not only to characterize regional effects within the parotid,but also to develop an assessment procedure which can incorporate toxicityrisk into treatment planning, and treatment planning is currently performedexclusively with CT images, the almost wholesale reliance on clinical CTfor analysis of regional effects has been deliberate. An overview of CT as itpertains to clinical practice at the British Columbia Cancer Agency (BCCA)is given below. Additional MR imaging support was also pursued, so it is21also briefly discussed below.3.2 Computed Tomography ImagingComputed Tomography emerged commercially in 1972 as a three-dimensionalcounterpart to two-dimensional radiographic imaging [103]. Many technicalaspects had been dealt with theoretically decades prior. For example, theRadon transform was devised in 1917 for the abstract purposes of functionreconstruction over non-Euclidean manifolds and higher-dimension spaces[104]. The primary advantage of CT was not merely that images were digital,but rather that cross-sectional ‘slices’ of tissue could be generated rather thanhaving to direct x-rays orthographically through a large perpendicular section.The mechanism, in brief, is simple but computationally demanding. An x-raytube emits photons that are directed through the target tissue. X-rays areselectively absorbed with different probabilities in different tissues (relatedto the photon scattering cross-section). A detector records x-ray intensity onthe opposing side of the target. This projection scheme is iterated in severalorientations, but the x-ray source and detector are usually rotated in lockstep.Image reconstruction is a field of ongoing research, but a crude, illustrativeimage can be generated simply. First, connect a line segment between eachindividual detector position and the source position at each iteration. If theline segments are given a weight (or grayscale value) related to the intensity,then the total accumulation of line segment weight at each location (i.e.,density) in the virtual target will be crudely related to the contrast andan image may be recognizable. However, even in the early days of CT thisapproach would be considered inappropriate [105]. Modern iterative methodsthat require less irradiation and thus lesser patient dose are now used [106].Historically, inter-centre routine CT clinical scan parameters varied andwere known to be subjectively influenced by perceived contrast and patientweight [107, 108]. Modern scanners automatically control exposure by ad-justing tube current using measured patient beam attenuation. This notonly improves image consistency, but can also decrease overall patient dose[109, 110, 111].22Radiocontrast agents can be used to improve CT contrast. At typicalclinical CT energies, the photoelectric effect dominates the x-ray absorptionspectrum. The enhancement mechanism relies on the photoelectric effectx-ray absorption coefficient, (µ), having a stronger dependence on atomicnumber (Z) than mass-density (ρ), photon energy (E), and atomic mass(mA) [112]. Specifically,µ ∝ ρZ4mAE3. (3.1)An incident x-ray with energy sufficient to displace an atom’s K-shell (i.e.,inner-most shell) electron will be absorbed. Since this energy – called the‘absorption edge’ – increases as Z increases, increasing Z while keeping grosstissue ρ constant will alter the x-ray absorption spectrum. Directed up-take of high-Z radiocontrast agents in soft tissues will therefore improveimage contrast. Since such agents alter effective electron densities, whichare derived from CT images, and then the densities are used for radiother-apy treatment planning, there is a small discrepancy introduced betweenplanned and delivered dose. The effects are within normal tolerances andwork-around techniques have been developed if the impact on dose is too great[113, 114, 115, 116]. Radiocontrast agents are employed for some routinediagnostic imaging at the BCCA; primarily ioversol (Optiray 300, Mallinck-rodt Pharmaceuticals), an iodide-based, nephrotropic, low osmolarity agent.Dosage is uniformly 120mL for patients ≥45kg. It is injected intravenouslyand followed by a saline flush.A generic CT imaging protocol consists of a ‘pilot’ scan to identify tissuetarget boundaries, a ‘localizer’ scan with coarse spatial resolution to alignthe imaging coordinate system and ensure tissue targets are within the fieldof view, and a final, single-pass axial scan.3.2.1 Current Clinical PracticesRoutine CT imaging parameters remained fixed for head-and-neck cancerpatients at the BCCA over 2005-2015. For a sampling of 886 head-and-neck23cancer patients (that were assigned a study identifier and considered for lateranalysis), tube characteristics were nominally 120 kVp (median: 120.0 kVp,mean: 120.7 kVp) and 350 mA (median: 350.0 mA, mean: 332.3 mA). Themedian total patient exposure was 93.0 mAs (20th percentile: 77.0 mAs; 80thpercentile: 93.0 mAs). Patients were almost always positioned head-first inthe supine position (99.9% of the time). Slice thickness was nominally 2.5mm(91%). CT simulators used to image patients in this cohort included GEMedical Systems LightSpeed RT16 (approximately 83% of scans) or OptimaCT580 (8%), a Picker International, Inc. (n.b. acquired by Philips Healthcare)PQ 5000 (7%), and a Philips Healthcare Brilliance Big Bore (2%).Example routine CT images with common imaging characteristics (at 120kVp and 350 mA) demonstrating Region of Interest (ROI) contours and tissuecontrast differences are shown in fig. 3.1. Images showing visible internalparotid sub-structure and demonstrating contrast enhancement (same patientand scan as fig. 3.1) are shown in fig. 3.2.24Figure 3.1: Two example BCCA routine axial CT images (at 120 kVp and 350 mA) showing parotid contoursaround 2cm inferior to the ear canal. The left parotid is indicated in each, and a view with and withoutROI is shown to demonstrate tissue contrast differences. Other ROI include the pharynx, spinal cordand margin, clinical and planning target volumes encompassing the tongue and right nodes, and aportion of the left oral cavity that has been subtracted from the target volume for sparing purposes.25Figure 3.2: Example BCCA routine axial CT images (at 120 kVp and 350 mA) at various levels demonstratingvisibility of sub-structures within the left parotid (variously indicated; all are most likely vasculatureowing to the relatively low permeability of acinar cells to ioversol).263.3 Magnetic Resonance ImagingClinical whole-body MR imaging emerged in the late 1970’s and early 1980’s[117]. The first published images were in 1973-74 with the proposed name‘magnetic resonance zeugmatography’ [118, 119]. The name is now disused,but the technique was quickly adopted by the community. The first clinicalscanners were available in the early 1980’s and were generally <1T, though1.5T scanners followed shortly [117].Contrast in MR imaging ultimately derives from the excitation and sub-sequent relaxation of particles that develop a magnetic dipole moment whenplaced in a magnetic field. The only requirement is that the particles possessspin, so elementary particles such as electrons and neutrinos, composite parti-cles such as neutrons and protons, and composite objects such as nuclei, atoms,and some molecules could in principle be used for MR imaging. However, thehydrogen atom proton is used exclusively for clinical imaging. In brief, thepotential energy of spins within a magnetic field become biased. Collectionsof particles that develop a magnetic dipole moment will thus become slightlypolarized when placed in a static field. Radiofrequency pulses can be usedto transition individual spins from state to state. The potential energy forinteraction with a static magnetic field ( ~B0) and a spin-12 particle with dipolemoment ~µ is V = −~µ· ~B0; the ground spinor state is |↓〉 with energy − |~µ|∣∣∣ ~B0∣∣∣and the excited state is |↑〉 with energy + |~µ|∣∣∣ ~B0∣∣∣, so the potential differencebetween spinor states is 2 |~µ|∣∣∣ ~B0∣∣∣. This means the radiofrequency pulsemust have a frequency of 2 |~µ|∣∣∣ ~B0∣∣∣ /(2pi~) where ~ is the reduced Planck’sconstant. This is the so-called ‘Larmor frequency.’ For protons the Larmorfrequency scales with field strength (in Tesla) like ∼42.578 | ~B0|1T MHz which is∼63.867MHz at 1.5T and ∼127.734MHz at 3T. After spins have transitionedto the higher energy state and the radiofrequency signal is discontinued,spins will gradually return to the equilibrium polarization through thermalrelaxation. Spins transitioning back to the ground state emit a characteristicradiofrequency pulse at the Larmor frequency, which can be detected.A magnetic resonance imager consists of three essential components: a27static magnetic field ( ~B0), an excitation radio, and a measurement radio withappropriate antennae. Additional components are needed to process the data,though rudimentary techniques may yield a reasonable image. Only modestfield strengths are needed, for example the Earth’s ‘ultra low’ magnetic fieldwill suffice for some magnetic resonance spectroscopic applications [120]. Atable-top scanner can be scavenged for as little as $200-300 [121]. Modernscanners vary in cost considerably, but in the United Kingdom in 2011 atypical 1.5T scanner cost $1.4MUSD to purchase and roughly the same inmaintenance costs for the lifetime of the scanner [122].Modern clinical scanners with active magnets generally have field strengths1.5-3.0T. Manufacturing high field-strength devices is much harder than lowfield-strength counterparts. The high | ~B0| means special considerations mustbe given to all components, internal or external. Homogeneity of the Bo fieldis important for minimizing image artifacts, and characteristic times dependstrongly on | ~B0| [123]. Superconducting magnets are often used, which requirespecial precautions such as persistent staffing or monitoring, ventilation incase the magnet ‘quenches,’ and shielding from outside noise sources andfringe magnetic fields. Scanners impose other constraints, including economicand special containment room construction. Older 1.5T scanners required50-90 tonnes of iron to shield fringe fields [124]. More recent 3.0T scannersthemselves weighed ∼10 tonnes (even with active shielding, which sheds somebulk). A 7.0T scanner weighs ∼30 tonnes and may require 100 tonnes ormore of shielding to contain fringe fields [125].283.3.1 Current Clinical PracticesMR imaging is not used for routine diagnostic imaging for head-and-neckcancer patients at the BCCA. However, as will be discussed in chapter 15,MR imaging of a volunteer cohort was performed. Example images of generaltissue differentiation in the head-and-neck are shown in fig. 3.3. Parotids inthe same patient at various levels are shown in fig. 3.4 to demonstrate theclear borders between tissues. Both fig. 3.3 and fig. 3.4 are T1-weighted spin-echo sequences that derive contrast from spin-lattice interaction relaxation(TE = 16ms, TR = 619ms).29Figure 3.3: Example anatomical (T1-weighted, with TE = 16ms and TR = 619ms) MR axial images in thevicinity of the ear canal. Tissue differentiation can generally improve upon the equivalent CT scan byadjusting the contrast sensitivity (cf. fig. 3.1). No contrast enhancement agents were administered.30Figure 3.4: Example anatomical (T1-weighted, with TE = 16ms and TR = 619ms) MR axial images atvarious levels demonstrating clear tissue borders. No contrast enhancement agents were administered.313.4 Contouring Practices in the ClinicOne of the key purposes of CT imaging for radiotherapy patients is to createtreatment plans. Creation of plans requires two necessary tasks. First,demarcating ROI contours for radiotherapy targets (i.e., diseased tissue) andOrgans-at-Risk (OARs), such as parotids, which in some sense can be thoughtof as ‘spectator’ tissues that should not be substantially irradiated. Thesecond task is to determine how to deliver the prescribed radiation dose tothe targets while minimizing dose to OARs. The second task is simulatingthe interaction between tissue and radiation and optimization of radiationdelivery to achieve several criteria simultaneously (e.g., 70Gy to the primarydisease site, dose limits for OARs, dose shape limits in some cases). Due touse of machine optimization it is not always intuitive how small changes to theinputs or optimization criteria will impact candidate plans, and optimizationis something of a ‘black-box.’ It is therefore important to be consistent incontouring practices. Clinical contouring guidelines at the BCCA are fixedfor key OARs to help reduce subjectivity.There are BCCA guidelines for contouring parotid and submandibularglands, the gross oral cavity, laryngopharynx, mandible, lips, brainstem, andoptic chiasm and nerves. Not all structures are contoured in every case.For example, some less critical OARs may be omitted for low-dosage plans.Clinical borders for key structures are described in table 3.1.Parotid contouring instructions are to begin superiorly, identify the parotidgland behind the ramus of mandible, contour every second slice until theinferior border, and then interpolate contours. Submandibular instructionsare to begin inferiorly around the level of the carotid bifurcation, identifythe submandibular gland lateral to the hyoid bone, contour every secondslice until the superior border, and then interpolate contours. The oralcavity is begun superiorly where the hard palate is seen covered with mucosa,every second slice is contoured until the inferior border, and contours areinterpolated. Lips are excluded from the oral cavity, and the oropharynx isgenerally not contoured so the communicating border is taken at the posteriorlevel of the epiglottis or Laryngopharynx.32Structure 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, LaryngopharynxMedial Hyoid bone, Tongue, OropharynxLateral Platysma muscle, MandibleOral Cavity Anterior Teeth, MandiblePosterior Laryngopharynx, (communicates with the Oropharynx)Superior Palate (hard, soft)Inferior Tongue, Mucosa, Geniohyloid and Mylohyloid musclesMedial Teeth, MandibleLateral Teeth, MandibleTable 3.1: BCCA head-and-neck ROI clinical contouring: structures bordering major salivary glands andthe oral cavity.333.4.1 Clinical ROI StatisticsVariations in contouring practices have been described across centres [126,127], inter-observer1 in the same centre [128, 129, 130, 131], and intra-observerduring repeatability tests [132, 133, 134, 135]. Both OAR and target con-touring are impacted.Recent research efforts into creating ‘oracles’ – algorithms or computer sys-tems that can establish ground truth for certain structures in a consistent way– have been successful [136, 137]. Most approaches are based on deformationand construction of one or more atlases that have been manually contouredby one or more experts [138]. The Simultaneous Truth and Performance LevelEstimation approach is common [139]. But salivary organ oracles specifically,while steadily improving in the literature, are not yet reliable enough toestablish ground truth without manual intervention [138, 140, 141, 142, 143].Therefore, it is worthwhile to report sample population (descriptive) statis-tics for later comparison to help assess similarity of contouring practices orhighlight specific differences that may translate into significant differences inanalysis.Simple statistics for all available BCCA ROI (886 patients that had beenassigned an anonymous identifier; pre-radiotherapy planning CTs) were esti-mated (see table 3.2). Strictly R2 volumetric and surface quantity estimatorswere employed to avoid topological ambiguities and surface reconstructionissues (discussed in section 4.2). Volume was estimated by the ‘slab volume,’which is total planar contour area multiplied by the image slice thickness.It may over- or under-estimate the true volume, especially when ROI arehighly curved and the (true) surface area is comparable to the total planararea. Slab volume will exactly estimate the true volume for shapes with faceseither parallel or perpendicular to the axial plane (i.e., not oblique), such asaxes-aligned rectangles and cylinders. Salivary organs are relatively cylindri-cal, being elongated along the superior-inferior direction, and are generallynot small enough for surface effects to dominate. Total contour polygon1An encompassing term that can refer to oncologists, medical physicists, surgeons,clinical therapists, and physician assistants, but rarely students or those with limitedclinical experience.34perimeter length is used to convey information about average circumferenceof individual contours. It can also be used to roughly approximate surfacearea when image slice thickness is uniform. In any case, the statistics intable 3.2 are meant for direct comparison with other cohorts, and should becompared to data computed using the same methods.Deviations from lateral symmetry were unremarkable. Parotids were foundto have approximately 3.8× the slab volume of submandibulars. Parotids hadapproximately 2.7× the total perimeter of submandibulars, but only 1.6×as many contours, suggesting submandibulars are more elongated along thesuperior-inferior direction. Parotids, in comparison, have a more round shapein the medial-lateral and/or anterior-posterior directions. For comparison, theoral cavity has approximately 2.7× the slab volume and 1.4× the perimeter.While larger, it is morphologically more compact compared to both parotidand submandibular glands.35ROI ROI Count ROI Count Slab Volume (mm3) Total Perimeter (mm)20th% median 80th% 20th% median 80th% 20th% median 80th%Left Parotid 641 20 24 27 21893 29042 39005 1723 2159 2632Right Parotid 632 20 24 27 21844 29898 38515 1736 2185 2629Both Parotids 1273 20 24 27 21872 29471 38717 1730 2168 2632Left Submand. 589 12 15 18 5612 7902 10170 627 799 968Right Submand. 588 12 15 18 5640 7679 10170 613 790 960Both Submand.’s 1177 12 15 18 5619 7855 10184 621 793 963Oral Cavity 507 16 19 22 55529 79774 109114 2376 2944 3719Table 3.2: BCCA head-and-neck ROI contouring practice statistics for salivary glands and the oral cavity(886 patients examined). ROI count refers to the number of the specified ROI present in the cohort.Sample population 20th, 50th (i.e., median), and 80th percentiles are shown. ‘Slab volume’ refers to totalplanar area multiplied by the image slice thickness. Lateral symmetry is strong.36ROI ROI Count Ant.-Post. (mm) Med.-Lat. (mm) Sup.-Inf. (mm)20th% median 80th% 20th% median 80th% 20th% median 80th%Left Parotid 641 35.4 39.7 45.3 39.7 47.4 58.7 52.5 60.0 67.5Right Parotid 632 35.3 40.1 46.0 39.7 47.7 60.1 52.0 60.0 67.5Both Parotids 1273 35.3 39.9 45.6 39.7 47.5 59.8 52.5 60.0 67.5Left Submand. 589 20.0 22.8 26.1 23.1 27.3 31.9 32.5 37.5 45.0Right Submand. 588 20.6 23.2 26.5 23.3 27.2 31.1 32.5 37.5 45.0Both Submand.’s 1177 20.4 23.1 26.3 23.1 27.3 31.5 32.5 37.5 45.0Oral Cavity 507 47.0 54.7 63.3 59.6 66.0 74.3 38.0 47.5 55.0Table 3.3: BCCA head-and-neck ROI extreme linear dimensions (i.e., ‘caliper width’) along orthogonalanatomical directions (886 patients examined). ROI count refers to the number of the specified ROIpresent in the cohort. Sample population 20th, 50th (i.e., median), and 80th percentiles are shown.Lateral symmetry is strong.37Extreme linear dimensions (i.e., the distance a caliper would measure)along orthogonal anatomical directions are computed in table 3.3 to helpfurther describe organ morphology. Parotids are shortest in the anterior-posterior direction and largest along the superior-inferior direction; theirrespective volumetric aspect ratio is 1:1.2:1.5, on average. Submandibularsdisplay a similar aspect ratio (1:1.2:1.6), which confirms the slight elongationalong the superior-inferior direction. The oral cavity is largest along themedial-lateral direction and smallest along the superior-inferior direction.The parotid slab volumes of table 3.2 (i.e., median of 29.5 cm3) areconsistent with parotid volume estimates reported in the literature, whichare generally within 25-35 cm3, e.g., [74, 144, 145, 146, 147]. However,some reports differ, having either substantially higher (e.g., 43.1 cm3 [148])or substantially lower parotid volumes (e.g., 17.7 cm3 [75]). In all studiesdescribed here, the range or uncertainties reported encompass the slab volumemedian of 29.5 cm3. While this does not directly imply overall ROI consistencywith the literature, it suggests both the lack of gross differences and somecontouring practice congruence with other centres.Many ROIs are missing from tables 3.2 and 3.3 (n.b. ROI counts arenot equivalent). There are many reasons this can happen, including surgicalremoval (most common for neck dissections), poor tissue contrast, and treat-ment demarcation irrelevancy, such as when the primary tumour is withina salivary gland and sparing is impossible. Some patients are born missingone or more organs (‘congenital aplasia’ or ‘agenesis’) or with intact glandsin abnormal locations (‘aberrant’ or ‘ectopic’) that are not detected duringroutine imaging [149, 150, 151].383.5 Summary and ConclusionsBCCA head-and-neck cancer imaging and tissue demarcation practices appearto be typical. The parotid is indeed the largest salivary gland and is mostwidely contoured (∼72% of patients) followed by the submandibular (∼65%)and lastly the oral cavity which is not often contoured (∼29%). The routineCT imaging protocol has remained static for the decade from which thecohort considered in this work was derived.39Chapter 4Salivary Gland Morphologyand TopologyFigure 4.1: Examples of a non-conforming (left) and a conforming(right) coordinate system superimposed over a single parotid con-tour. The contour can be traced in the conforming (i.e., adaptive)coordinate system locally by translation along individual coordi-nate directions. The conforming system is a semi-conformal (i.e.,angle-preserving) mapping of R2 Euclidean space.A key requirement for performing inter-patient or inter-parotid analysisis defining a consistent spatial mapping between parotids. Parotids vary40considerably in size and shape. Not being able to consistently resolve parotidfine internal structure in CTs (i.e., ducts, vasculature, nerves, and lymphnodes) presents a major impediment for assessing regional effects. Devel-opment of a systematic mapping or correspondence is required not only forcomparing like-regions within the parotid, but also for later understanding theassociation between critically important regions and anatomical structures orparenchyma.Figure 4.1 shows grid lines for Euclidean space mapped into a singlecontour in two ways. While the non-conforming coordinate system (on theleft) provides a valid mapping, it is not sufficient for inter-parotid analysis.The issue is that there is no notion of similarity when it is applied to differentparotids. Intuitively, a suitable mapping would be consistent, bijective1,and respect topological features, meaning a point along the mandible in oneparotid should map to an equivalent point along the mandible in anotherparotid, and vice versa, for any two parotids. The conforming coordinatesystem on the right of fig. 4.1 meets these three criteria. However, thiscoordinate system is merely a sketch of what such a mapping might looklike; development of a specific mapping procedure remains to be addressed.Furthermore, this illustrative mapping is for a single contour but a volumetricmapping is needed.Parotids exhibit a distinct topology that is challenging for development ofa consistent mapping. Two-manifolds (i.e., watertight surfaces) can always betriangulated, so assuming ROI contours are not directed (i.e., the orientationof individual contours is ignored, and all contours are homeomorphic to adisc, so that there cannot be annuli or holes in individual contours), it willalways be possible to create a two-manifold regardless of ROI details [152].Figure 4.2 shows orthographic projections of a single parotid from severalviewpoints aiming at the characteristic ‘saddle surface’ which wraps aroundthe mandible. The inferior ‘tail’ (toward the bottom of the page) and lateral1Or, if not bijective, then at least surjective, meaning that the entire domain of theparotid must be covered, but there can portions of the domain of the map that do not mapto the parotid. In other words, there can be disused elements in the domain of the map,but there cannot be any ‘spares’ in the domain of the parotid. Bijectivity would present asuperior mapping as it would link the domains in a more meaningful way.41Figure 4.2: Topology of a typical parotid gland as clinically contouredat the BCCA from several viewpoints aiming at the ‘saddle point.’Arrows trace sequential rotations of a single parotid gland. Toprow: superior view panning to medial-anterior view; middle andbottom rows: medial-anterior view panning to lateral view.42and medial extrema (right and left of the page, respectively). Constructingtwo-manifolds from ROIs improves topological consistency, making it easierto identify characteristic features (n.b. compare fig. 4.2 with fig. 2.2). Butalso the triangulated two-manifold (i.e., homeomorphic to a hollow sphere)will bound a compact, oriented three-manifold (i.e., homeomorphic to a ball)which is homeomorphic to R3 Euclidean space [153, 154]. This implies thattriangulated two-manifolds are in principle capable of supporting consistent,bijective mappings that respect topological features – all that remains is toactually find such a mapping using tessellated parotid two- or three-manifolds.As will be demonstrated in the following sections, this problem is difficult inpractice.4.1 Space-Filling CurvesContinuous space-filling curves that surjectively map every point in a confinedregion in R2 (usually a unit square) to a position on a line segment are well-known [155, 156]. (They are however surjective and not bijective becausethey are continuous and self-intersect.) Space-filling curves are special casesof fractal constructions, and though they are continuous they are not smooth,and are thus everywhere nondifferentiable. Variations exist2 that fulfilldimensionality reduction, such as space-filling trees [157], rapidly-exploringrandom trees [158], and others [159]. More generally, they appear to be ableto map arbitrary topological spaces (i.e., two- or three-manifolds) to a linesegment (or at least be ‘stitched together’ to do so), though the literatureis sparse on this topic, particularly for polyhedra in dimensions greaterthan two [160, 161, 162]. In particular, most polygon-filling curves rely onparametrization, optimization (such as simulated annealing), or both, whichwould make curve construction non-deterministic and therefore potentially3unsuitable for intra-organ comparison [163].Space-filling curves can be constructed so that locality of position along2Note that space-filling polyhedra (and the related concept of ‘packing’) are entirelyunrelated from space-filling curves and trees.3Wasser et al. [163] describe a heuristics-based method that may result in a sufficiently-deterministic construction.43the line segment reflects locality in the topological space (i.e., ‘spatial clus-tering’) which would be beneficial for intra-organ comparison. Hilbert [156]introduced such a curve more than a century ago, and it is thought to providethe best clustering of any known space-filling curves [164]. Constructioniteratively becomes infinitesimally small, and iterations are known as (open)‘approximating polygons.’ The first few approximating polygons are shownin fig. 4.3.Figure 4.3: Construction of a space-filling Hilbert curve (i.e., openapproximating polygons of increasing order). In the limiting case,every point in the unit square is surjectively mapped to a linesegment. Locality is approximately preserved.Spacing-filling curves have a variety of surprising uses, including appli-cations in optimization [165], manufacturing [166], and scheduling [167]. Inthe present case, development of a locality-preserving curve that can mapparotid three-manifolds was investigated. Despite being capable in princi-ple of programmatically traversing parotid three-manifolds, they can notgenerally guarantee intra-parotid consistency, especially when parotid mor-phology differs substantially. It is not known if locality/spatial clustering44can be guaranteed when extended to polyhedra in dimensions greater thantwo. Furthermore, it is known that there are no continuous bijections fromR2 to a line segment [168], so either bijectivity or continuity must be sac-rificed – both of which would be convenient for inter-parotid assessmentof intra-parotid regional effects. An effort was made to develop criteria todefine suitable space-filling curves, but was ultimately abandoned in favour ofother approaches. Helpful starting points for pursuing this approach are theframework for recursively generating multi-dimensional space-filling curves ofJin and Mellor-Crummey [169], the two-manifold density-based Hilbert curveresampling parameterization method described by Quinn et al. [160], and theheuristically-guided polygon-filling approach described by Wasser et al. [163].4.2 Barycentric CoordinatesBarycentric coordinates can be used in simplicies to provide smooth mappingsthat conform when the hull is altered [170]. This feature, conceptually, makesthem attractive for intra-parotid comparison. They are commonly used tointerpolate within simplicies in which some quantity is known at the verticesbut not within the simplex. They can also be used as a generic coordinatesystem within a simplex which abstracts the underlying coordinate system(e.g., Euclidean). Using this abstraction, they provide a means independentof the coordinate system of computing distance and can simplify integration(e.g., of partial volume, or radiation dose) [170]. The theory of generalizedBarycentric coordinates which extend to n-sided polygons (i.e., in R2) iswell-known [171], but extensions to arbitrary n-polytopes (i.e., in R3 andhigher) appear to be limited only to convex polytopes [172, 173]. This meansthe method is only applicable in the present (R3) case to simplicies sincesalivary gland ROIs define, in general, non-convex shapes. Conceptuallysimilar methods, such as Wachspress basis functions [174], similarly appear tobe limited to convex polytopes [175]. So-called ‘mean value coordinates’ areable to interpolate (and even smoothly deform) arbitrary n-polytopes, but donot appear to be usable as a coordinate system due to lack of isomorphism[176, 177]. Even if they could be adapted to provide a coordinate system,45they do not appear to generalize easily when the intra-parotid correspondencebetween ROI vertices or 2-manifold facets are unknown (which is preciselythe problem that these methods are supposed to address). Compared toother interpolating approaches, Barycentric coordinates over simplicies aretherefore the most viable way to generate a vertex-based coordinate system.In R2 simplicies are triangles and in R3 simplicies are tetrahedrons; tetrahe-drons individually are woefully incapable of representing generic ROI-derivedthree-polytopes, which may comprise thousands of facets. On the other hand,if the equivalent three-manifold is tessellated with tetrahedrons, then pointswithin each individual tetrahedron can be smoothly mapped, and all that isneeded to achieve a consistent bijective intra-parotid mapping is to find acorrespondence between intra-parotid tetrahedrons4. This correspondenceproblem presents many difficulties: tessellation can be made to producedissimilar three-manifolds with differing numbers of tetrahedrons themselveswith distinctly different positions and orientations. Any correspondencewill need to be robust to all three differences, but still provide consistencyand bijectivity. Deriving a suitable mapping by finding a correspondencewithout additional information is unlikely due to the complexity. Auxiliaryinformation in the form of topological landmarks present a pathway outof the quagmire. If correspondence between tetrahedrons is eschewed forcorrespondence between landmarks, the problem is simplified considerably. Iflandmarks are suitably chosen, all that will be needed to establish correspon-dence are a list of volume-normalized geodesic distances5 from each landmark,4If this is confusing, consider that this technique shares many similarities with finiteelement methods (a.k.a. finite element analysis). The aim of finite element methods are tosolve for a field (usually by solving a differential equation) over a tessellated three-manifold.However, finite element analysts may be confronted with the present problem if they havesolved a demanding problem over one geometry and wanted to extend it to another similargeometry without having to re-solve the problem. In other domains the problem maybe referred to as a ‘correspondence’ problem or maximal similarity problem. It is alsoconceptually similar to ’deformable registration’ which is discussed shortly.5Be aware that these distances can not be represented as a vector because they do notform a linear space; for example, their sum is meaningless. Likewise, an arbitrary numberof landmarks can be specified which will result in a list with greater or fewer elements thanthe number of dimensions, leading to an under- or over-specified problem. If landmarksare carefully chosen (e.g., to avoid collinearity) then an exact location may be found. Ingeneral, though, an as-close-as-possible system should be employed to improve robustness,46e.g., x units from landmark A, y units from landmark B, and z units fromlandmark C. Then Barycentric coordinates can be employed to locate thecorresponding point somewhere within a tetrahedron. Note that landmarksin this system could be anywhere in either the ROI two- or three-manifold.As already noted parotids present several topological landmarks, suchas the saddle surface, tail, and other extrema (see fig. 4.2). However, notonly do parotids vary in volume and size, as described in section 3.4, butthe overall shapes can be inconsistent, even in the same individual. It istherefore not reasonable specifically to specify features, not only because theymay be absent in some parotids, but also because specification would naivelyrequire manual (and thus subjective) identification. This approach would notbe consistent. However, an objective measure that can be used to identifytopological features is curvature.There are multiple types of curvature for two-manifolds. ‘Mean curvature’intuitively describes the change in surface area relative to the change involume when a surface is deformed. It is defined as the mean of the principalcurvatures6 – the largest and smallest curvature of all possible R1 slices thatintersect a given point [178]. Another, Gaussian curvature, is the product ofprincipal curvatures. Discrete approximations of curvature can be computedon two-manifolds using the method described by Meyer et al. [6]. It isknown that saddle surfaces have negative Gaussian curvature [179], andthat the mean curvature of symmetric saddles should be zero (which maybe easier to algorithmically detect), but otherwise it is not a priori clearwhich curvature will best isolate the distinctive parotid features. As canbe seen in fig. 4.4, mean curvature more uniformly highlights the saddlesurface, ridges, and protruding lobes than Gaussian curvature. It is thereforeused for visualization purposes. Ultimately, the most general approach is tocreate several derivative curvature maps tailored to select specific features.which means that a true coordinate system and exact correspondence may not be possible.Global positioning systems face similar issues and provide good enough geolocation formost purposes. Likewise, for the present purposes a scheme employing geodesic distancesmay be good enough.6Principal curvatures are more precisely defined as the inverse of the radius of thelargest and smallest osculating circles at a given point on a two-manifold.47Indeed, measures other than curvature can also be used, such as the ‘shapediameter function’ which estimates the local diameter and can be used tolocate protruding lobes and the tail [180].48Figure 4.4: A parotid demonstrating two kinds of curvature (Gaussian on left, mean on right) which werecomputed using a discretization scheme described by Meyer et al. [6]. Red and blue represent meancurvature extremes (maximum and minimum). Mean curvature highlights the saddle surface moreintuitively than Gaussian curvature, but neither consistently highlight the ridges.49Landmarks must be consistently and precisely located. If they are not,the internal coordinate system will be tainted by the imprecision. In otherwords, the method is not robust to landmark specification errors. Therefore,detection of landmarks from derivative curvature maps (and other maps)needs to be robust. Clustering techniques can be used to locate curvature-connected groupings over the two-manifold using geodesic distances. Thenrepresentative points, such as a curvature-weight averaged vertex positionprojected back onto the two-manifold, or the point within the cluster withmaximal geodesic distance from the boundary, can then be taken as thelandmark (e.g., the saddle point at the centre of the saddle surface).Performing this procedure with the ‘Density-based spatial clustering ofapplications with noise’ (DBSCAN) clustering algorithm [181] and a varietyof curvature derivative maps lead to landmarks with inconsistent positions.Mean curvature for six pairs of parotid glands is shown in fig. 4.5; it is clearthat there is substantial variation in the position and extent of features. Inparticular, the saddle surface has a disperse spatial extent, which leads tolocalization errors when clustering, and ridges and protruding lobes do notpresent consistent curvature. In addition to normal intra-parotid variations,curvature (and all quantities derived from two-manifolds) were found tostrongly depend on: (1) contouring minutiae, (2) the method of triangulation,and (3) any post-processing performed on the triangulated mesh, such asrefinement/subdivision. (Figures 4.2, 4.4 and 4.5 were all triangulated usingDelaunay triangulation and two iterations of Loop’s subdivision method[182, 183].)50Figure 4.5: Mean curvature for six parotid gland pairs. Features are easy to visually identify, but difficult torobustly detect and locate computationally due to natural variations.51Furthermore, these problems can not easily be overcome; there is inher-ent ambiguity in two-manifold reconstruction using clinically-defined ROIcontours. Figure 4.6 demonstrates two ambiguities that can strongly affectsurface shape and curvature. To this end, the clinical Digital Imaging andCommunication in Medicine (DICOM) standard provides a supplementalstandard for storing two-manifolds directly, without conversion to planarcontours [184, 185]. However, uptake by vendors has been slow and it is notused in the BCCA.52Figure 4.6: Demonstrations of topological ambiguity due to clinical tissue demarcation using ROIs. Top:ambiguous connectivity between image slices – both are valid and could be connected such that a2-manifold homeomorphic to a sphere is produced. Bottom: ambiguous curvature for extrema contours– both satisfy the terminating boundary condition imposed by the adjacent slice.53The specific failings of two-manifold-based approaches are hard to ascribeto any single factor. It is likely that triangulation ambiguities can be overcomeby consistently triangulating all parotids in the same way. However, theapproach is inherently sensitive to the ROI surface rather than the volume.This means it is likely sensitive to factors that affect contouring, such asimage contrast, window and level settings, variations in individual contouringpractices and quirks, contouring subjectivity, and possibly even vertex densityor the total number of vertices used in individual contours. Use of non-curvature measures may decrease reliance on surface minutiae. However,seemingly more robust volumetric measures defined over two-manifolds, suchas the shape diameter function, may similarly be affected by contouringminutiae; as can be seen in fig. 4.5 the local diameter of protruding lobes isextremely variable and likely also subjectively contoured. Furthermore, alandmark-based approach is unable to handle parotids with missing landmarks.So a small number of landmarks, the ‘lowest common denominator,’ mustbe identified beforehand. This implies that the technique may fail to beapplicable to ROIs added at a later date, which severely limits generalizabilityof the approach. It also reduces the robustness of landmark specification.Work on two-manifold methods including Barycentric coordinates was thusdiscontinued in favour of methods involving three-manifolds or that do notrequire tessellation.4.3 SegmentationA more robust method of defining position and locality within the parotidis to (1) temporarily do away with the notion of a coordinate system, and(2) recursively sub-divide the volume into discrete sub-volumes. If infiniterecursion is permitted, then in principle a coordinate system based on infinites-imal bounding volumes could be reconstructed. However, infinite recursion,compared with finite recursion, would more strongly rely on contours be-cause larger sub-volumes are more broad and therefore resilient to errors intranslation. Recursively sub-dividing a small number of times will effectively54tile7 the parotid. If sub-volumes are taken as atomic entities of space, thenposition and locality are discretized, but are also more robust to contouringdiscrepancies. For example, if recursive volumetric sub-division is performedthen, ceteris paribus, as long as the volume remains the same, surface curva-ture has no bearing on sub-volumes that do not intersect the surface. Thedifference between volumetric and surface-based approaches is somewhat akinto the difference between the mean and median of a distribution – the meanis sensitive to every sample, but the median is only sensitive to rank.Segmentation generically refers to the act of demarcating an object intosmaller, more cohesive entitites. The term ‘contour segmentation’ was coinedby the author to refer to the volumetric recursive sub-division tiling approachwhen it is applied directly to ROI contours without performing two-manifoldtessellation8 [7]. More generally, contour segmentation can be applied repeat-edly – recursively or sequentially – to construct a tessellation of collectionsof solid shapes, including polygons embedded in R3. A tool for robust andcomposable segmentation of planar contours was constructed: DICOMauto-maton. An ROI contour approach is taken, rather than two- or three-manifoldapproaches, which eliminates issues stemming from tessellation. Operatingon planar contour polygons also enables ‘lossless’ reversible segmentation andis dramatically faster than surface reconstruction or bitmap/voxel-centric ap-proaches [7]. No prior work was found in the literature, and DICOMautomatoncontinues to be the only tool capable of direct contour (sub-)segmentation(that the author is aware of).Details on the specific segmentation methodology applicable to this thesisare provided in chapters 10 and 11, but a brief depiction of the variouscontour segmentation capabilities of DICOMautomaton are shown in figs. 4.7to 4.10. Figure 4.7 demonstrates simple, single-contour tilings using radiationdose heuristics (left and centre) and a scale independent Cartesian tiling(right) reminiscent of the left side of fig. 4.1. Figure 4.8 demonstratesrecursive segmentation, first using projective segmentation (n.b. uses ray-7Note that in the following, ‘tiling’ should be taken to mean both proper and impropertiling, since vertices are not always shared by all adjacent sub-segments.8Not to be confused with image segmentation or mesh segmentation.55casting – described in chapter 11) and then using per-sub-segment planarsegmentation, resulting in a somewhat conforming tiling reminiscent of thenearly-conformal mapping of fig. 4.1. Figure 4.9 demonstrates more advancedrecursive single-contour tilings, including (on the left) a semi-random, semi-periodic tessellation in which all internal edges are aligned in one of fourrandomly-chosen directions, (centre) a challenging optic chiasm tiling withinternal edges aligned with Cartesian-axes, and (on the right) a telescopingsegmentation of a left parotid contour with blocks of Cartesian grid arrangedinside larger ‘neighbourhood’ sub-segments. Finally, fig. 4.10 demonstratesvolumetric segmentation of whole left parotid ROI into: (bottom-left) acore and peel, (middle) medial and lateral volumetric halves via projectivesegmentation, and (top to top-right and bottom-right) planar segmentationinto equal-volume sub-segments. In all cases contour area is used as asurrogate for volume (i.e., slab-volume).Figure 4.7: Tiling segmentations of a single contour of an axial ‘body’contour at the shoulder level. From left to right: first, a heuristicsegmentation based on absolute radiation dose, clearly demon-strating sparing of the spinal cord in the encircled region (n.b.adapted without modification from [7]); second, a heuristic seg-mentation based on spatially-varying heuristic based on the localdose gradient; and third, a recursive, scale independent Cartesiantiling.4.4 Deformable RegistrationAn alternative to segmentation is deformable registration. Deformable regis-tration methods are well-known, and can provide a way to map CT images,56Figure 4.8: Recursive mixed segmentation that progressively tilesan axial body contour at nose level (left to right). The firstsegmentation is a medial-lateral projective segmentation (n.b.described in chapter 11) and the second is a per-sub-segmentcoronal planar segmentation. This figure was adapted from [7]and modified to simplify presentation.Figure 4.9: More advanced recursive single-contour tilings. Fromleft to right: first, a semi-random, semi-periodic triangulationof an axial body contour at the level of the ear in which allinternal edges are constrained to one of four randomly-chosendirections (n.b. adapted without modification from [7]); second,a challenging semi-Cartesian tiling tiling on a star-shaped opticchiasm contour; and third, a telescoping segmentation of a leftparotid contour with blocks of Cartesian grid arranged insidelarger ‘neighbourhood’ sub-segments. These examples highlightthat recursion can be used to generate adaptive, arbitrary tilingswithin n-polygons.57Figure 4.10: Volumetric segmentation of a whole left parotid ROI(top-left) into: (bottom-left) a core and peel, (middle) medialand lateral volumetric halves via projective segmentation (n.b.described in chapter 11), and (top to top-right and bottom-right)recursive or ‘nested’ planar segmentation into equal-volume sub-segments. These examples highlight that recursion can be usedto generate adaptive, arbitrary tilings within oriented polyhedrawhich have been sliced to produce co-parallel planar contours.Parts of this figure were adapted from [7] and recoloured tosimplify presentation.dosimetric volumetric images, and ROI. There are several reliable registrationalgorithms that develop bijective mappings (i.e., ‘diffeomorphic’ algorithms;note that not all algorithms are diffeomorphic – see [186, 187, 188, 189] fordiscussion and [190] for a widely-available and popular diffeomorphic algo-rithm). Cross-registration can be used to register each parotid to each otherparotid individually, but this will result in poor scaling with the number ofROI and will in general result in registration cycles that are not bijective(i.e., if a point in parotid A is mapped to parotid B, and then that point58is mapped to parotid C, and then that point is mapped back to parotidA, it will in general not coincide with the original point). These problemsare overcome by deforming all parotids to a single ‘prototypical’ parotidand then performing all mappings using the prototype as an intermediary.However, while this approach solves the cycle non-bijectivity problem, itcauses a specific dependency on the prototype. As seen in fig. 4.5, parotidsare highly variable and selection of a representative prototype – no matterhow appropriate – will inevitably present ramifications for the deformationquality of dissimilar parotids. Additionally, not all registration algorithmsare ‘symmetric.’ Symmetric algorithms produce the same mapping whetherimage A is registered to image B or vice versa, but non-symmetric algorithmsdo not necessarily. Non-symmetric algorithms clearly spoil cross-registrationregistration cycle bijectivity. Segmentation, in contrast, is prescriptive, mean-ing that bijectivity is tautologically maintained in all cycles and no prototypeis needed.4.5 ConclusionsSpace-filling curves, Barycentric coordinates, registration, and segmenta-tion are all potentially viable techniques for investigating regional effects.Each have specific trade-offs. Space-filling curves are in some ways theleast-constrained approach, but will require an unknown amount of work todevelop curves that are applicable to ROI and describe parotid morphologyand topology in a meaningful way. Barycentric coordinates suffer from sensi-tivity to contouring and ROI two-manifold tessellation ambiguities, and theapproach ultimately relies on subjective assessment of landmarks. Deformableregistration requires selection of a prototype to guarantee bijectivity whenintra-parotid analysis is required, but is otherwise a flexible and generalapproach. Segmentation generally requires use of non-standard spatial local-ization and locality (e.g., using the adjacency of sub-segments), but otherwisepresents a minimally-subjective, flexible paradigm that can be adapted toalmost any segmentation problem. Given these findings, and owing to theversatility, simplicity, recursive generalizability, and avoidance of prototypes,59segmentation was selected for assessment of regional effects.It is worth mentioning that a space-filling approach to segmentation –tree-based methods, in particular – would provide the most flexible approach.This route was not pursued because segmentation based on volumetric speci-fications was found to be sufficiently flexible on its own.60Chapter 5Why are Salivary GlandsIrradiated?5.1 Primary Cancers Within Salivary GlandsCancers of the salivary glands themselves are uncommon, accounting for ∼6%of head-and-neck cancer incidence and ∼0.3% of all cancer incidence [191].Benign tumours are also rare [192]. When cancers do occur, surgery followedby postoperative radiotherapy is common and leads to a reasonable amountof local tumour control [193].It is self-evident that patients undergoing radiotherapy for salivary glandcancers would receive substantial salivary gland irradiation. However, almostall head-and-neck cancer patients treated with therapy receive non-negligiblesalivary gland dose. There are two key reasons. First, head-and-neck anatomyis complex, and given the distribution of salivary glands, some irradiationis inevitable. Second, healthy tissues (both surrounding and distant to theprimary disease site) are often irradiated to reduce risk of additional primarycancers. These two topics and some related issues are the focus of theremainder of this chapter.615.2 Practical Head-and-Neck AnatomicalConstraintsAs discussed in chapter 2 minor salivary glands are distributed throughout theoral cavity and upper aerodigestive tract. Major salivary glands wrap around,behind, and below the mandible, shielding much of the nasopharynx andoropharynx from lateral radiation. The brainstem and spinal cord awkwardlyblock the same anatomy from posterior radiation, and radiosensitive visualstructures block superior-anterior radiation. Superior access for radiationdelivery is, in almost all head-and-neck cancers, blocked by the brain1 (whichis bulky and sensitive to radiation) or brainstem (a crucial structure that cancause severe complications when irradiated). Even if the presence of theseorgans is ignored, radiation delivered from a superior position along the lengthof the body would result in a deeply-penetrating dose profile. Additionally,recurrence in the primary tumour site is fairly common at ∼12% and oftenrequires aggressive treatment with additional spatial margins to eliminatemicroscopic spread of disease [194]. Therefore, salivary glands are irradiatedas a geometrical consequence of the complex head-and-neck anatomy in orderto spare more critical tissues and obtain local control over the primary diseasesite.5.3 Metastases and Second Primary CancersThe majority of head-and-neck cancers are squamous cell carcinomas [195].Initially, squamous cell carcinomas are confined from invading adjacenttissues by basement membranes or other fascial tissues (a.k.a. “squamouscell carcinomas in situ”) [196]. In some cases these encapsulations remainintact, but most often when the disease penetrates these encapsulations (i.e.,it becomes ‘invasive’) it is able to metastasize, spreading throughout the bodycreating ‘second primary cancers’ [197]. Metastatic tumourigenesis proceedsfrom progenitor cells originating within the primary tumour site [198]. Mostcells cannot withstand incompatible microenvironments in other anatomicalregions, but distant tissues may begin to support cells with compatible1Note: brain cancers are not classified within the head-and-neck cancer category.62phenotypic abnormalities [199]. Tumours are thus spread, but biologicalcharacteristics of the metastasizing cells are retained. However, they canbecome compatible by gradual diversification through tumour evolution orprogression, and thus tumours can adapt to their environment [198].Survivors of squamous cell carcinoma head-and-neck cancers face life-longrisk of new primary cancers in addition to frequent aerodigestive tract andcardiac illnesses [200]. The risk of developing additional primary tumoursis 3-5% per year, and all sites in the aerodigestive tract are likely [201, 202].Five-year survival varies substantially (20-90%) relative to those withoutearlier cancers depending on the origin site and progression [13], but overallfive-year survival is around 40-60% for combined head-and-neck cancers[195, 203, 204, 205].Many patients with squamous cell carcinoma head-and-neck cancersinitially present at a relatively advanced stage due to ongoing difficultieswith early detection [206, 207]. Given the grim survival prospects oncea tumour has metastasized, generally high recurrence rates, issues withdetection methods, advanced disease progression before diagnosis, and chronicdifficulties in treatment due to critical structure placement, preventativemeasures are often taken to reduce the risk of second primary cancers. theeasiest measure is to aggressively irradiate cancerous tissues, but this impingesupon salivary gland toxicities.5.4 Lymph Nodes Must be IrradiatedCancerous cells can spread to lymph nodes near the primary tumor (referredto as ‘nodal involvement’) which will distribute them throughout the body.Some will eventually metastasize; carcinomas most often metastasize via thislymphatic pathway [208].Lymph nodes are distributed throughout the head-and-neck (‘cervicallymphatics’) [209]. Some are proximally inferior to the parotid gland; othersare proximal to the submandibular gland. Submandibular glands are removedalong with lymph nodes during (standard) radical neck dissections due tofrequent lymph involvement [209]. Because lymph nodes need to be irradiated63to destroy cancerous cells, parotids often receive radiation dose regardless ofthe primary tumour site. Patients without metastases are treated anyways,unnecessarily, because of difficulties assessing metastatic state and high risksassociated with loss of local control [210].Cervical lymph nodes (throughout the neck) are typically wholly resectedduring neck dissections [210]. However, even in this case, or if proximityto major lymph nodes in the neck is ignored, there is frequent lymph nodeinvolvement in the parotid. In some cases node infiltration is a commoncondition in its own right (e.g., Sjörgens syndrome) and it is therefore sen-sible to irradiate the parotid to protect against lymphatic infiltration andmetastatic transport. Thus, the proximity of lymph nodes often necessitatessome salivary gland irradiation, even when the tumour site is distant.5.5 Head and Neck Cancer EpidemiologyLifetime risk of cancer for American citizens in any site is ∼40%, and mortalityrates due to cancers surpass heart disease in those younger than 85 years ofage [211, 212]. In 2005, globally the head and neck region was the sixth mostcommon site for cancers. Head-and-neck cancers alone represented ∼6% ofnew cancer burden (∼650k incidences) and caused ∼350k deaths [213, 214].There is considerable incidence variation around the world [13, 215].This is thought to be due mostly to systematic and habitual exposure tocarcinogens, especially smoking (or other tobacco products) and alcoholconsumption, but several cancers present geographical, genetic, diet, andviral predispositions [13, 216, 217, 218, 219, 220]. Tobacco and alcohol havea ‘knock-on’ multiplier effect, and are implicated in approximately 3/4 of allsquamous cell carcinomae [219, 221, 222].Global head-and-neck cancer incidences have fallen slightly in recent years[195], but have risen in many populations, including Canada [13]. Recently,oral cancers kill one person worldwide each hour [223]. This toll is greater thancancers of the liver, kidney, brain, and gonads. Complications surroundingtreatment of head-and-neck cancers, therefore, are frequently encounteredin the clinic and remain a significant issue for newly diagnosed patients and64long-time survivors alike.5.6 Summary and ConclusionsIn almost all head-and-neck cancers the major salivary glands are irradiatedto destroy primary cancer microscopic disease or to reduce risk of metastaticlymphatic transport. Modern technologies like Intensity-Modulated Radio-therapy Treatment (IMRT) and Volumetric Arc Therapy (VMAT), in whichthe radiation beam cross-section is ‘sculpted’ by moving jaws, or protontherapy are capable (or potentially capable) of delivering dose distributionsthat are tailored to selectively irradiate small sub-organ volumes. Therefore amore complete understanding of local resilience to radiation-induced salivarydysfunction will improve treatment planning risk assessment. Depending onthe distribution of critical regions, this knowledge may permit irradiationof lymphatic structures and the primary disease site in such a way that thetreatment efficacy is maintained but risk of toxicity is lowered.65Chapter 6Salivary Dysfunction andXerostomia6.1 IntroductionXerostomia is not itself a disease, but rather is a symptom of various medicalconditions which presents as subjective dry mouth. It often results fromdiseases or trauma that cause salivary dysfunction, such as radiotherapy;medication (including common chemotherapuetic agents); and autoimmunediseases such as sarcoidosis (an inflammatory disease in which granulomasdevelop throughout the body), Sjögren’s syndrome (a disease that suppressesfunction in mucous- and moisture-secreting organs), and rheumatoid arthritis[224, 225].The impact of salivary dysfunction in cancer patients is multifarious.Advanced cases are known to severely reduce a patient’s perceived Quality-of-Life (QoL) [226]. Even moderate, temporary dysfunction can impact apatient’s primary faculties, reducing eating, sleeping, and communication todifficult, tedious, and painful exercises [148, 227].As described in chapter 5, salivary glands are frequently irradiated out ofnecessity due to complex head-and-neck geometry and the confined presenceof multiple organs at risk (e.g., brain stem, spinal cord, larynx and pharynx,oral cavity, and parotids). High doses of radiation are capable of completely66and permanently ceasing salivary function [10, 228]. However, the intensityof glandular damage can be curbed by controlling exposure, such as limitingthe dose received and limiting the volume of irradiated tissues [40, 229, 230,231, 232].Radiotherapy dose profiles will sometimes irradiate a large volume andnumber of distinct tissues, including a variety of salivary glands distributedthroughout the oral cavity. It is not a prior clear whether damage to large,concentrated glands or small, distributed glands will produce better patientoutcomes. At a basic level, surgical removal of the submandibular has shownto increase risk of xerostomia [233]. Conversely, surgical transplantation ofsubmandibular glands away from the target volume prior to radiotherapy canreduce xerostomia risk [234, 235]. Furthermore, mean dose to the accessoryglands is a significant predictor of xerostomia, though not the most important[40]. This evidence suggests that xerostomia is not strictly an affliction of thelargest glands, and that both submandibular and accessory glands contribute.Nevertheless, the parotid gland is known to contribute the largest portionof stimulated whole-mouth saliva. The most heavily impacted primaryfaculties (i.e., swallowing, eating, speaking) are predominantly impacted bydysfunctional stimulated salivary flow1 [227]. Additionally, the parotid almostalways receives a significant dose in head-and-neck cancers while lesser glands,which by merit of their distribution, may be collectively spared. The parotidis therefore decidedly the most important gland and thus forms the basis forcurrent clinical guidelines involving salivary glands [236].In the remainder of this section, aspects of xerostomia and dysfunctionare elaborated upon with an eye toward reducing their many facets to alevel manageable for analysis of regional effects. Questions that remainopen (or disputed) in the literature are provided heuristic answers that willallow analyses to proceed under the assumptions made. In particular, thefollowing is addressed: the link between dysfunction and xerostomia, effectiveprioritization of dysfunction and xerostomia measurements (when both areavailable for analysis), whether short-term or long-term xerostomia is mostrelevant, and how to make headway when a surplus of dosimetric data is1This is shown to be true in the BCCA cohort in section 6.4.67available.6.2 HistoryXerostomia – before it was known as xerostomia – was first considered amedical condition in its own right by Bartlet in 1868 [237, 238]. It wasprecisely defined and named from the Greek ‘xeros’ (meaning dry) and‘stoma’ (mouth) in 1886 by Hutchinson [239]. He described severe xerostomia.The tongue is red, devoid of epithelium, cracked, and absolutelydry, its appearance being like raw beef. The inside of the cheeks,the hard and soft palates, are also dry; the mucous membranesmooth, shiny, and pale. The salivary glands appear normal, andno mechanical obstruction has been detected in their ducts. [. . . ]Articulation is difficult in consequence of the absence of moisture,and swallowing has to be assisted by constant sipping. [. . . ] Thedisease reaches its greatest intensity suddenly, and then remainswithout change for years.Of particular note is that he drew a distinction between xerostomia (andthe ramifications of having a dry mouth) and dysfunction. Indeed, salivaryglands may produce or be able to produce saliva, but the saliva is eitherchronically inhibited or of insufficient quality (e.g., lacking an mucin content)to accomplish the normal functions of lubrication and protection.Radiation-induced xerostomia is likely to be induced by different mech-anisms than xerostomia induced by medication or immune diseases. Theearliest recording of radiation-induced xerostomia was described in 1938by Martin [240]. It may have been known earlier, though, as the reportwas accompanied with descriptions of secondary complications and remedies.Remediation of these complications has proven difficult and many remainproblematic in modern times.686.3 ComplicationsXerostomia is a pathway for a diverse and numerous set of adverse effects. Be-sides the direct impact on primary eating, sleeping, swallowing, and speakingfaculties, xerostomia is known to have a commanding impact on emotionalwelfare [241]. Even overall QoL is tainted by chronic pain resulting fromxerostomia [226]. Dysfunction will often lead to increased opportunistic in-fection of the oral cavity which can itself cause severe complications. Specificcomplications that have been noted to result from xerostomia include: lossof taste, osteoradionecrosis, trismus (spasm of the jaw muscles causing thejaw to remain tightly shut), mucositis, and dental caries [242].Dental caries are particularly prevalent and aggressive after head-and-neckirradiation [243]. This was well-known nearly 80 years ago; Martin [240]described the situation.A complication occasionally associated with radiation xeros-tomia is a peculiar form of dental caries. [. . . ] Beginning abouttwo or three months after irradiation of the pharynx or of the oralcavity, metal fillings and inlays tend to loosen and fall out. In thecases of greater involvement the teeth may lose their natural glis-tening appearance and assume a dull, chalky hue. The substancebecomes rather brittle and may wear away at the occlusal surfaces.Numerous cavities develop, especially near the gingival margin, sothat the teeth tend to crumble or break off, leaving the root exposedat the gum level. Toothache is a prominent symptom. The directcause of these dental complications is somewhat obscure.The modern belief is that radiation caries are caused by hyposalivation,though it has been suggested that diffuse radiation on the bones of thejaws and a reduction of blood supply through apical arteries could be toblame [244, 245, 246]. It is also thought that radiotherapy may exacerbatedemineralization, which supports the loosening of fillings and bone deadeningobserved by Martin [240] [243]. Due to the potentially severe impact ongeneral health, early recommendations included complete extraction of teethprior to irradiation. This was generally to the detriment of the patient as69osteoradionecrosis and osteomyelitis of the mandible often followed extraction[247]. Nearly 80 years later, this practice remains in some parts of the worldand the criteria for preventative dental extraction are still somewhat contro-versial [248, 249, 250, 251, 252]. Part of the issue is that post-radiotherapydental extraction can directly lead to osteoradionecrosis, so there may be abenefit to pre-radiotherapy extraction in some cases [253].Overall, it is generally accepted that dental extraction is warranted inpatients with questionable prognosis or motivation [242, 254, 255]. If teethare not extracted, modern preventative measures require heightened oralhygiene and include frequent application of fluoride solutions, limitation ofcariogenic, sugar-rich or acidic foods, and application of artificial salivaryagents [256]. There are also changes in dental practice, such as use ofglass ionomer cements that have more favourable adhesive properties forradiation-stricken enamel and dentine [243]. Though a patient may be ableto avoid such complication through diligence, effectiveness is limited by thepatient’s tolerance and rigor [242]. It is well-known that the majority do notfollow pre-radiotherapy dental guidelines (see, e.g., [257]). Adhering to morestringent guidelines therefore seems unlikely for patients inflicted with themost severe or indefinite xerostomia, or who have been substantially andnegatively impacted by complications. It is therefore difficult to develop ageneral course of action because the prognosis is multi-faceted.6.4 The Association Between Xerostomia andDysfunctionPatient-reported xerostomia, by definition, is subjective. Conversely, salivaryflow can be measured quantitatively. It is clear that these two quantitiesare not exact surrogates. For example, xerostomia is a broad concept thatencapsulates overall perception of the adequacy of salivary flow in distinctsituations. It is also impacted by changes in salivary composition (e.g.,viscosity) and the state of a patient’s oral cavity mucosal lining (e.g., soreor infected) [225, 258, 259]. Conversely, salivary function can be impactedby factors that may not affect sensation of xerostomia, such as circadian70rhythms and hydration [25, 260, 261].It should be unsurprising, then, that correlation between radiation-induced xerostomia and dysfunction has generally been found to be weak[10, 15, 40, 226, 262, 263, 264, 265, 266]. Differences are likely to stem fromthe aforementioned factors, difficulties in reliably measuring flow rates, andgeneral perceptions of oral dryness [40, 263]. Conversely, some studies havefound significant or mixed correlations [26, 226, 229, 267, 268]. It is unclearwhat the nature of the discrepancy is, but it could stem from use of multiple,inconsistent assessment instruments and techniques (n.b. discussed in sec-tions 7.1 and 7.2). Unfortunately, despite weak-at-best evidence, salivary flowand xerostomia are frequently used interchangeably in the literature (e.g.,[269]). Confusion is perpetuated by the use of various grading systems thatintentionally conflate the two conditions for clinical purposes (see section 6.5).Besides surrogacy of the conditions, the implicit assumption of clinical gradingschemes is that both conditions are ‘switched on’ by radiation, when in fact itis possible for a patient to develop xerostomia without dysfunction and viceversa [263]. Confusion of radiotherapy-induced xerostomia and dysfunction isless grievous than the general case owing to a correlation (however weak), andsince salivary measurements likely are the most defensible objective surrogatefor a subjective condition. But the practice is still technically conflation of twounrelated conditions and care should be taken to appropriately differentiatethem.6.4.1 Association in the BCCA CohortThe correlation between post-radiotherapy objective flow measurements (Wb,W3m, W1y, and W2y – whole-saliva measurements at baseline and three-months, one-year, and two-years post-radiotherapy, respectively) and subjec-tive patient-reported QoL was assessed for the entire head-and-neck cancerpatient cohort amassed at the BCCA over the decade spanning 2006-2016,omitting patients lacking data needed for each computation. The collectioninstruments and protocols are described in chapter 7, but in brief saliva ispassively collected over a span of five minutes, and a nine-question question-71naire is administered (n.b. questions are described in section 7.1). Saliva wasbaseline-normalized by dividing baseline (i.e., pre-radiotherapy) saliva mea-surements so that patients receiving no radiation (and thus experiencing noinduced dysfunction) would score 1.0 and patients with total loss of functionwould score 0.0. Individual QoL responses are of interval type (i.e., ordinalvariables with equally-spaced divisions) and were transformed to the samerange and ‘orientation’ by subtracting and dividing the maximum value (10in all cases). Only saliva measurements and QoL data collected at the sameappointment were considered (i.e., ‘per-questionnaire’ analysis, except forbaseline normalization). Results for stimulated saliva are shown in table 6.1.Results for unstimulated saliva are shown in table 6.2. Patient attendance atfollow-up appointments declines over time, so the number of datum comparedare stated in each case.Question Number W3m/Wb W1y/Wb W2y/Wbr N r N r N2 0.232 524 0.063 296 0.198 1823 0.303 522 0.171 298 0.178 1834 0.310 525 0.150 306 0.210 1835 0.325 521 0.221 306 0.283 1836 0.205 528 0.155 307 0.267 1817 0.328 525 0.188 305 0.234 1838 0.320 529 0.149 306 0.225 1839 0.213 527 0.156 308 0.123 183Table 6.1: Pearson’s correlation coefficients (r) between baseline-normalized whole-mouth stimulated saliva measurements andnormalized and inverted individual QoL responses. W representswhole-mouth saliva, N is the number of questionnaires available.QoL instrument questions are described in section 7.1.Both table 6.1 and table 6.2 display overall weak correlation2 between2The r partitioning method recommended by Evans [270] is used, in which r ∈ [0.20, 0.40)is ‘weak’ correlation. This approach was taken in lieu of explicit significance testing toavoid testing difficulties when N is large and conflation of (domain-specific) relevance withsignificance. See Taylor [271] for discussion of the pitfalls of testing r.72Question Number W3m/Wb W1y/Wb W2y/Wbr N r N r N2 0.187 523 0.197 295 0.163 1853 0.276 523 0.248 297 0.038 1864 0.269 526 0.224 305 0.023 1865 0.279 522 0.232 305 0.128 1866 0.270 527 0.158 306 0.131 1847 0.293 526 0.289 304 0.144 1868 0.283 529 0.228 305 0.177 1869 0.210 526 0.120 307 0.131 186Table 6.2: Pearson’s correlation coefficients (r) between baseline-normalized whole-mouth unstimulated saliva measurements andnormalized and inverted individual QoL responses. W representswhole-mouth saliva, N is the number of questionnaires available.QoL instrument questions are described in section 7.1.subjective QoL and objective salivary measurements in the BCCA dataset.Stimulated saliva correlate most strongly; the average correlation for stim-ulated saliva is 0.217 vs. 0.196 for unstimulated saliva. Early correlationis greater than later correlation; the average correlation for W3m/Wb (i.e.,baseline-normalized whole-mouth saliva during the three-month follow-up)was 1.30-2.21× that of W1y/Wb or W2y/Wb (stimulated and unstimulated).Note that objective and subjective measurements have been normalized dif-ferently. Saliva measurements are rarely exactly 0g/5min for pre-radiotherapypatients, and there is no practical upper limit to the amount of saliva pro-duced. It therefore is sensible to divide the baseline to give a patient-specificnormalization that nominally ranges over [0, 1]. In contrast, subjective ques-tions present an interval scale which naturally has both lower and upper limitsthat all patients are uniformly subjected to. Furthermore, while baselineflow is almost always non-zero, the median baseline questionnaire responsesfor questions 2-9 was 0 (N = 1531). The 75th percentiles for each questionwere all ≤2 (out of 10) and the 90th percentiles were all ≤5. By and large,baseline questionnaire responses are low and most frequently exactly zero,73and therefore cannot be used for multiplicative normalization. Recreatingtables 6.1 and 6.2 by subtractive baseline normalization resulted in weakercorrelations across both stimulated and unstimulated saliva, on average (meanr = 0.206 with no QoL normalization vs. 0.192 with QoL normalization). The20th and 80th percentiles showed similar shifts. Comparison of the differencesof r for individual questions showed that they increased by an average of0.015±0.007 (mean ± std. dev. of the mean). Differences were symmetricallydistributed about the mean. Overall, subtractive normalization is thought tobe inferior to foregoing normalization altogether. The topic of normalizationand how it impacts analyses is further elaborated upon in section 6.7.Table 6.1 and table 6.2 also demonstrate that missing datum are almostalways due to patients increasingly foregoing follow-up appointments as theirtreatment grows more distant in time. Xerostomia/dysfunction assessment isperformed as part of a more general dental examination, and it is rare forpatients to attend a dental examination and decline xerostomia/dysfunctionassessment, even when they can not produce an appreciable amount of salivaover five minutes of stimulation. Rather, patients who forego follow-upappointments most often cite logistical reasons or being unable to attend dueto work or family commitments [272]. Therefore, it seems likely that thereare no major systematic biases linking severity of toxicity and assessmentinstrument obstruction or patient-censored data. Further exploration of thistopic is presented in section 8.3.6.5 GradingPrecisely what constitutes ‘severe’ dysfunction is patient-dependent. Forexample, a reduction in salivary flow by 5g/5min may be significant for onepatient but not another. In cases where it is rapidly induced by an exter-nal factor, baseline normalization is commonly performed as in section 6.4.Grading – the process of converting continuous salivary flow measurementsinto a small number of interval quantities (and ‘stages’ or ‘grades’) to aidclinical judgment – is commonly applied using the analytic component ofthe Late Effects Normal Tissue - Subjective, Objective, Management, Ana-74lytic (LENT-SOMA) scale.In the LENT-SOMA system, induced xerostomia and salivary dysfunctionare conflated. Severity is divided into four grades, the worst of which repre-sents reduction of ≥75% of the whole-mouth baseline salivary output. This isreferred to as “severe” or “grade IV” xerostomia. As it is of primary use in theclinic and for developing clinical guidelines, much of the research literaturedo not precisely employ this scale. Sometimes the discrepancy is subtle.For example, whole-mouth saliva is occasionally replaced by single-organ(or single-organ-pair) output [273]. In this case “grade IV xerostomia” doesnot fully correspond to LENT-SOMA scale grade IV xerostomia because thesubjective component is not single-organ-separable.Several alternative grading systems exist, many with different origins.Many are reasonably widely used. Some are periodically updated and somultiple versions with small deviations can be found within the literature.Examples include the Common Terminology Criteria for Adverse Effects(CTCAE) system (versions: 1.0 from 1983, known as simply the ‘CTC’ system;2.0 from 1998 [274]; 3.0 from 2003 [275]; and most recently 4.0 from 2009[276]) which began as a means of grading adverse effects of chemotherapy[277], a system employed by the Danish Head and Neck Cancer Group(DAHANCA) [266], Dische’s early system [278, 279], and the RadiationTherapy Oncology Group (RTOG) EORTC [280] late morbidity system.Studies using outdated versions can be found within the literature, whichcan muddy interpretation and direct comparison (e.g., a study from 2013using CTCAE version 2, from 1998, which was two versions behind3 [281]).Translation between systems is not always obvious or, in some cases, possible[282]. For example, the CTCAE scale represents grade 3 dry mouth in termsof absolute flow, rather than relative flow (see e.g., [283]) and may thereforebe more suited for naturally occurring or slowly-induced dysfunction. Jensenet al. [266] provides a good but slightly dated guide to many such systems.The LENT-SOMA scale should generally be preferred as reports indicate it is3Note that there are many reasonable ways in which this situation can arise. Themost obvious is intentionally using old versions to maintain consistency with earlier orlong-running studies.75at least as good as alternative systems for scoring late radiotherapy-inducedsalivary toxicities [279, 282, 284, 285]. Note that like the LENT-SOMAsystem, most alternatives conflate dysfunction and xerostomia by treatingthem as a common toxicity.Grading systems are not directly used in this work. However, they areimportant because they inform clinical recommendations and make interpre-tation by medical staff easier. Treatment planning guidelines are developedspecifically to avoid the most severe toxicity risk, and the patient cohortconsidered in the present work were all subject to recommendations usingsuch guidelines (i.e., [285]). It is therefore important to understand howpopulation-level parotid radiation doses are impacted. For example, thedistribution of mean parotid doses around clinical guideline thresholds willnot be Gaussian because doses near to clinical sparing recommendations aremore likely to be aggressively optimized to achieve the threshold. In analyticscenarios, grading systems can also be used to convert continuous salivaflow measurements to ordinal/interval or nominal variables, and subjectiveordinal/interval reportings to nominal. These ‘munged’ variables can be usedfor statistical classification, to provide estimates of uncertainty (e.g., binning),or simply to reduce noise. In the present work, however, a sufficiently largecohort was available so regression was performed directly on continuousobjective data.6.6 Dysfunction and RecoverySalivary function loss can be induced in many ways. Surgical resection ofsialolith (calcifications) occasionally results in inflamed ducts. Atrophy mayensue, leading rapidly to dysfunction [16]. Sudden onset of ductal atrophyappears common in salivary glands. Dietary changes are commonly reportedto induce some atrophy via necrosis of acinar cells – even over the span of asingle day in rats [32, 286, 287]. The mechanism is thought to be related tochanges in masticatory activity [287]. Similarly in humans, extended periodsof masticatory inactivity resulting from autonomic denervation, intubation,ductal ligation, or trauma-induced fistulae (i.e., internal or external expression76of the duct contrary to the normal papilla) are known to induce salivarygland atrophy [288]. Glandular regeneration occurs after intubation-, ligation-, and fistulae-induced atrophies, but generally not after denervation. Thissuggests that the presence and maintenance of innervation may play a crucialrole in the recovery of function. The precise mechanism(s) by which nervesregenerate and integrate with acinar cells in not known [16], and the impactof radiotherapy on this mechanism is less certain. Furthermore, it is not clearthat the same mechanism is responsible in radiotherapy-induced disease.Function alterations and xerostomia can be induced by medication, butthe condition is usually transient and subsides when medication ceases [289].The most common medications include anticholinergic, sympathomimetic,cytotoxic, and antimigraine drugs, muscle relaxants, opioids, retinoids, andcytokines [290]. Both dysfunction and hyperfunction are possible, and somedrugs alter saliva chemistry to the extent that it becomes discolored [291].Fractionated radiotherapy for head-and-neck cancers often results indysfunction, even if the patient is unaware. Besides reduction in volume andflow rate, composition is impacted and an increased bacterial presence canresult [258, 289]. In contrast to medication, radiation-induced xerostomiaand dysfunction onset may be immediate, complications can be more severedue to severity of dysfunction and confounding complications (e.g., damageto nerves, vasculature, osteoporosis, or osteoradionecrosis), and can lastindefinitely [26, 224]. Though the nature of the dysfunction is not preciselyunderstood, its occurrence is well-known. Reports of recovery are more mixedand sometimes sporadic. Mossman et al. [292] remarked on the matter.Results of studies of the time and extent of recovery of normaltaste and salivary function in man following radiotherapy are con-tradictory. Several investigators have observed complete recoveryof taste and salivary function in patients 1-3 months followingtreatment, whereas others have not. Although little or no improve-ment in salivary function has been observed in some patients atleast two years following curative courses of radiotherapy, partialrecovery 8 months after radiotherapy has also been reported.77Eneroth et al. [293] reported the case of a patient irradiated with 65Gy (adose that would normally cause complete dysfunction) whose parotid tissueremained functioning up to nine years following conventional radiotherapy.This remarkable but not altogether uncommon case suggests a recoverymechanism that is able to withstand intense radiation. It also highlights thatwe are not (yet) capable of predicting specific complications, but rather therisk of complications.The mechanism of radiation damage in the parotid (which appears to bethe most well-studied salivary organ in general) remains poorly understood.Studies have shown that the magnitude of salivary gland damage in mammalsand humans increases in proportion with dose and irradiated volume [40,229, 230, 231, 232]. Damage to the parenchyma must clearly impact normalfunction, but it is not clear what portion of loss is attributable to specificparenchymal tissues. What is known is what has reliably been observed: thatacinar atrophy and chronic inflammation of the salivary glands occur whendysfunction or xerostomia are induced via radiotherapy [294].It is thought that some dysfunction is attributable to loss of vasculaturesupport. Vascular changes within the parotid resulting from irradiation havebeen observed, beginning generally with periarteritis (severe inflammationof the outer arterial coat) and endarteritis (severe inflammation of the innerarterial lining – the tunica intima). Inflammation progresses into fibrosisof the tunica intima and eventual destruction of the vessel lumena [295].The slow progression of inflammation is generally thought to result fromgradual necrosis rather than direct (acute) apoptosis [294]. Nearby bone isnegatively impacted and can become brittle [295, 296]. While it is clear thatloss of vasculature support can cause dysfunction, it is not known whether thefibrosis mechanism could itself support any form of functional recovery. Thevasculature model, even if partially valid, therefore does not fully describe theinteraction between radiation and dysfunction or xerostomia. Furthermore,even if the issue of recovery is ignored, the evidence that inflammationcontributes substantially to dysfunction is weak [297].Radiation damage to saliva-secreting acinar cells are also thought tocontribute to dysfunction and xerostomia severity. Both acinar cell types78– serous and mucinous – atrophy to an extent that is obvious in routinehistopathological observation [298]. However, saliva in patients suffering fromthe most severe xerostomia is generally thick, discolored, and contains anabnormally high level of mucins [237]. It is thought that the early response ofacinar cells to lethal doses of radiation appears to be rapid atrophy withoutinflammation, which suggests direct radiation-induced apoptosis or selectivedamage to the plasma membrane may be the causative mechanism ratherthan necrosis [294, 299, 300, 301, 302, 303]. Radiation injuries are knownto manifest within mere hours, even at low doses [298]. Inflammation fromvasculature damage and acinar cell atrophy are therefore likely to be twodifferent mechanisms that both contribute to dysfunction and xerostomia.Considering only observations of the change in saliva viscosity, serous cellsappear to be less capable of surviving irradiation than mucinous cells. Parotidglands are comprised almost entirely of serous cells, and a majority of acinarcells in submandibulars are of the serous type. The loss of a significant fractionof serous cells due to radiological sensitivity in either glands would matchwith the dual observations of substantially reduced quantity of saliva withsimultaneous thickening. This likely scenario could explain both dysfunctionand xerostomia incidence. It could also explain the weak correlation betweenthe two conditions if there was a small number of mucinous acinar cells withinthe parotid that varied in proportion with the serous cells from patient topatient. In patients with few parotid mucinous acinar cells, even a modest dosecould destroy serous acinar cells, leaving the parotid essentially functionallyinert. At the same time, the continued support from the relatively hardymucinous acinar cells in the submandibular and accessory glands would resultin thick, mucousy saliva. In this scenario, it is not clear what proportion ofstimulated saliva would be attributable to parotid vs. submandibular glands,but presumably the organ with the greatest number of intact mucinous acinarcells would supply the greatest proportion.Salivary gland volume reductions over the course of radiotherapy havebeen reported by many [74, 148, 297, 304, 305]. Both gross gland volumeand submandibular acini size reduction can be induced via sympatheticdenervation [306], but the ducts do not appear to substantially change. It is79thus unclear whether radiation damage to the nerve tissues directly contributessignificantly. Rather, volume changes may merely be a symptom of acinar cellatrophy [297]. Volume reduction of parotid and submandibular glands canbe manually induced in the absence of radiation damage through atrophy viaductal ligation and occlusion [297, 302]. Conversely, de-ligation or clearance ofthe occlusion is known to initiate an acinar cell regeneration process in whichretained acinar cells not only proliferate, but also new formations of cellsand parasympathetic innervation appear [302, 307, 308, 309, 310, 311, 312].Salivary function is restored in this regenerative process [302, 307, 311]. Thisprocess also hints that broad recovery from radiotherapy-induced dysfunctionmay be possible. However, ligation and ductal occlusion likely involve verydifferent atrophic pathways compared to radiation-induced atrophic pathways,and it is not yet clear if the same recovery can be induced in radiation-damagedglands. It is a promising line of inquiry though, so recent research efforts aredescribed in section 8.2.The above theories have not conclusively been demonstrated, though theyare fairly basic first-order theories that do not stray far from observations.Many supplementary and alternative theories have been proposed to describethe mechanisms behind radiotherapy-induced dysfunction. It has been positedthat: the presence of nitric oxide following radiotherapy [313], loss of salivarygland progenitor cells [314], or sublethal DNA damage which becomes lethalwhen acinar progenitor cells are undergoing reproduction [315] are mechanismsof functional loss. Such theories are covered in-depth in various review articles,including those of Konings et al. [303] and Carpenter and Cotroneo [297].Given the evidence of multiple potential pathways to dysfunction (i.e.,medication, autoimmune disease, radiation damage potentially from atrophyof acinar cells and/or inflammation, amongst others), the multiple pathwaysthat could influence subjective xerostomia (i.e., the confounding effects ofwhole saliva and contributions from minor and accessory glands, saliva volume,flow rate, chemical composition, and mechanical properties), and observationsof functional recovery by regeneration and reinnervation of parenchyma, itseems most likely that xerostomia/dysfunction are multifactorial and that nosingle mechanism is responsible. Rather, a multifactorial approach is likely80needed to accurately quantify toxicity risk, but it seems unlikely that a modelcould be concocted to incorporate all potentially confounding factors. In thefollowing section, various factors and measurements (collectively ‘facets’) areselected to provide the greatest likelihood of detecting regional effects.6.7 Overview of Toxicity Facets for AnalysisSeveral facets are recorded at the BCCA: stimulated and unstimulated whole-mouth salivary flow measurements and QoL questionnaire responses, eachcollected at four time points (before radiotherapy and each of three months,one year, and two years after therapy concludes). It is not feasible to performa single analysis with so many response variables and predictors, even if non-parametric methods are employed. First, there is multicollinearity amongstpredictors which may confound analysis. Second, combining some facets maylead to spurious findings (e.g., mixing stimulated and unstimulated facets fromdifferent time points could lead to physically nonsensical conclusions). Finally,including higher-order effects may result in high sensitivity to measurementnoise that will thwart analysis. We therefore prioritize available facets foranalysis. The relative merit of each selection is discussed in the remainder ofthis section.6.7.1 Xerostomia or Dysfunction?Xerostomia is the single most common complication following radiotherapyfor head-and-neck cancers [10]. As a subjective condition, xerostomia ques-tionnaire responses provide more detailed information about patient impactthan objective flow measurements. Indeed, it is well known that xerostomiacan have a substantial negative impact on a patient’s social, psychological,and overall well-being [316]. In this sense, objective measurements do nothave any bearing on xerostomia; if a patient with substantial flow feels likethey have dry mouth, then many (psychological, social, and QoL) negativeramifications will manifest. Conversely, if a hardy patient with little flowdoes not notice a dry mouth sensation, then psychological, social, and QoLnegative ramifications will not manifest. On the other hand, oral hygiene will81still be impacted.Meirovitz et al. [317] advocates the use of patient-reported xerostomiaover direct measurement. Others advocate the converse (e.g., [318]). Bothfacets are important. But there are trade-offs to using either (and both).Xerostomia is more relevant for psychological well-being, as patients with milddysfunction may not even be aware of it. On the other hand, risk of dentalcaries and increased oral infection risk may increase regardless of patientawareness if dysfunction presents. Dysfunction is not subject to patient psy-chology and is likely more regular from centre to centre, especially if differentxerostomia instruments are used. Conversely, objective measurements (e.g.,flow rates, saliva composition or viscosity) are more specific. Dysfunction islikely more applicable to general clinical practice, and objective salivary flowmeasurements were therefore prioritized over subjective xerostomia scores.6.7.2 Early or Late?Figures 6.1 and 6.2 show saliva measurements before and each of three months,one year, and two years after conclusion of treatment. Summarized stimulatedmeasurements are shown in fig. 6.1 and resting (unstimulated) measurementsare shown in fig. 6.2. The measurement process is described in section 7.2; inbrief, patients salivate into a beaker over five minutes and the total volumeis weighed.The median (red dot) and mean (blue dot) are shown in both figs. 6.1and 6.2. On average, patient salivary function drops to around 30-50% oftheir pre-radiotherapy function. The magnitude of recovery is much less thanthe initial loss of function, on average. Additionally, the differences betweenone year and two year distributions are small compared to either baseline orthree month distributions. This suggests long-term function approximatelystabilizes between three months and one year after treatment concludes.Another striking feature of figs. 6.1 and 6.2 is that dysfunction can (andoften does) remain two years after treatment or longer. While the early lossof function (three months) is unfortunate, it appears to partially subside, oneaverage, within the following nine months. Late dysfunction, on the other82Figure 6.1: Violin plot of whole-mouth stimulated saliva measure-ments over time. The red dot represents the median, the blue dotrepresents the mean, and the shape represents a kernel densitythat estimates the measurement probability density. The optimalkernel density bandwidth was estimated by the method of [8].Note the similarity of one- and two-year distributions comparedwith baseline and three-month distributions.83Figure 6.2: Violin plot of whole-mouth resting saliva measurementsover time. The red dot represents the median, the blue dotrepresents the mean, and the shape represents a kernel densitythat estimates the measurement probability density. The opti-mal kernel density bandwidth was estimated by the method of[8]. One- and two-year distributions are differentiated than thestimulated case, but are still the most similar compared withbaseline and three-month distributions.84hand, can last for years or even indefinitely. Therefore late salivary functionpresents an overall greater burden on survivors and was prioritized over earlydysfunction.6.7.3 Loss or Recovery?The ‘early vs. late’ debate implicitly focused on absolute measurementsrather than normalized measurements. An alternative approach, one thatmay appear at first to be more specific, is to focus on the difference ofmeasurements. The difference between baseline and three months, beforesubstantial recovery has taken place, could be called ‘early loss.’ Likewise,‘recovery’ could be taken to be the difference of one or two year and threemonth measurements. This approach was taken during the author’s MScand resulted in numerous difficulties, which are described in the remainder ofthis section. Briefly, the core difficulty of this approach is magnification ofnoise and multiplicative baseline normalization emerges as the best simplenormalization approach.In a comprehensive study of the variability of salivary flow, Burlage et al.[319] noted that standard deviations ∼24% should be expected for measure-ment of whole-mouth stimulated flow. A large single study with 1427 healthyvolunteers of varying sociodemographic backgrounds found 44% [320]. Blancoet al. [26] performed a repeatability experiment using five healthy volunteers.The baseline-equivalent measurement exhibited a standard deviation of only27%, but suggested patient measurement variability may be higher due todisease, comorbid conditions, or confounding factors. There are many factorsthat could confound whole mouth salivary measurements, such as changes inbody chemistry, hydration levels, and circadian rhythms [25]. Even mobilephone use impacts saliva production [61]. One consistently different factorbetween patient and volunteer studies is participant age. Though it is knownthat stimulated saliva production is not strongly associated directly withage, unstimulated production generally decreases and factors that themselvescorrelate with age, such as regular medication use, do negatively impactproduction [321]. Therefore, measurement noise may be greater than gener-85ally reported in volunteer studies. Most incidental reports of measurementvariability indicate standard deviations around 30-40% of baseline which isconsistent with age- or disease-related increases.Stimulated salivary flow is reasonably stable over the span of two hours[25]. Pooling of repeat measurements to reduce variability quickly runs intoissues, however. Continual saliva production cannot continue indefinitely, andsince daily salivary output is estimated to be around 1.0-1.5L, dehydrationat a level significant enough to impact repeated (i.e., back-to-back) flowrates could result [34, 322]. Given this limitation and other limits of clinicalacceptability (e.g., clinical time), repeat measurements appear to have thecapacity to make a negligible effect in reduction of noise [319]. It appearsthe measurement variability problem for whole-mouth saliva is indefeasibleand therefore must be accounted for in the analysis design.Examining absolute measurements conceptually involves a single measure-ment uncertainty4. Computing the difference of two measurements requiresboth uncertainties to be accounted for. Depending on the underlying process,the combination procedure (for two measurements WA and WB combined asW = WA −WB) can beδW =√(δWA)2 + (δWB)2or, more generally, when the nature of the uncertainties is unknown,δW ≤ δWA + δWBwhere δW represents the uncertainty in W [323]. Thus, the ratio of uncer-tainty to signal isδW|W | =√(δWA)2 + (δWB)2|WA −WB|4Depending on the the normalization scheme employed. This is discussed shortly insection 6.7.6.86or more generallyδW|W | ≤δWA + δWB|WA −WB| (6.1)which, in both cases, grow large when the magnitude of WA and WB areboth small compared to sup(δWA, δWB), even if |WA −WB| is reasonablylarge. In all physically sensible cases it follows thatδW|W | ≤δWAWA.Thus, the net effect of measurement differencing is a magnification of uncer-tainty compared to the absolute approach. Many patients at three monthscan produce very little (or zero) saliva, so the magnitude of the uncertainty(δW3m) is large compared with the measurement (W3m). When a difference iscomputed, δW3m ‘taints’ |Wb −W3m| and produces relatively large uncertain-ties which reflect the low reliability of the difference. Using stimulated salivarymeasurements, population-derived medians, and assuming an intrinsic un-certainty of 35%, δW/|W | ∈ [0.73, 0.97] where W = Wb −W1y depending onwhether uncertainties were known to be independent and random. In contrast,δW1y/W1y is 0.35 and if W1y is baseline normalized (discussed below) thenδW/|W | ∈ [0.50, 0.70] – which is 39-47% smaller than the difference approach.The unstimulated case is worse because measurement magnitudes are allsmaller, and the problem persists when W3m, W1y, or W2y are used or whena small constant uncertainty factor is included (e.g., ±0.1g/5min to accountfor scale calibration errors). Recovery presents the worst uncertainty ratiosat δW/|W | ∈ [1.6, 2.2] so that the magnitude of uncertainties even exceedsthe signal magnitude.Disregarding the uncertainty magnification issue, and despite interestingrecent developments linking stem cells to recovery (mentioned earlier insection 6.6 and discussed in greater detail in section 8.2), it is not clear ifrecovery (currently) is more clinically relevant than loss. As noted in figs. 6.1and 6.2, the magnitude of recovery is much smaller than the magnitude ofloss. Earlier work on a portion of the BCCA data set showed the magnitude87of recovery had virtually zero dependence on the gross dose profile, witheach patient recovering around 20-30% of baseline function regardless of dose,sometimes (rarely) even beyond baseline levels [324]. The finding is difficultto interpret. It may be that use of current clinical guidelines (based on meandoses) limits recovery. It is also possible that clinical guidelines are incidental,and that recovery truly does not have dose-profile dependence. What is clear,however, is that the prospects are limited for investigation of recovery usingonly clinical treatment plans that are subject to uniform parotid gland sparingprocedures. Such investigations would be best done through radiobiologicalstudies or clinical trials. On the other hand, given that modern treatmenttechnologies are currently capable of delivering more specific dose-profileswith sub-organ features, and the current clinical magnitude of loss is greaterthan that of recovery, it therefore seems clinically prudent to investigatefunction loss rather than recovery.6.7.4 Stimulated Saliva or Resting Saliva?Resting saliva may play a greater role in regulating oral health than stim-ulated saliva, and submandibulars – which provide the majority of restingsaliva – are known to be important for predicting xerostomia [233, 325, 326].However, scenarios where salivary dysfunction have the greatest negative im-pact are predominantly those involving stimulation, such as eating, chewing,swallowing, and speaking. As seen in tables 6.1 and 6.2, baseline-normalizedwhole stimulated saliva measurements generally correlate more strongly withQoL questionnaires, or at least do not seem to correlate any worse than wholeresting saliva. (The average correlation for stimulated saliva was 0.217 vs.0.196 for resting saliva.) This finding is not unique to the BCCA cohort[227, 327]. Furthermore, stimulated saliva measurements are also greaterin magnitude than resting saliva in all cases, on average, as can be seen infigs. 6.1 and 6.2. Use of more voluminous measurements will improve analysisprecision since fewer of the worst affected patients will present sub-thresholdwhole saliva.Therefore, stimulated saliva will be prioritized. Note that parotids are in88all analyses paired with stimulated saliva whereas submandibulars are pairedwith resting saliva owing to the relative contribution by each gland.6.7.5 Parotids, Submandibulars, or minor glands?As discussed in section 6.1, parotid glands are known to contribute the largestproportion of stimulated whole-mouth saliva. Parotids also form the basis forcurrent clinical guidelines [236]. Parotids should therefore be the first-orderorgan considered for analyses investigating whole-mouth stimulated salivadysfunction.There are subtle differences in clinical contraints reported throughout theliterature that complicate assessing non-parotid salivary gland importance.Blanco et al. [26] attempted to spare neither oral cavity nor submandibularglands. Rather, patients for which glands could be spared were excludedfrom their study. It my be unsurprising then that they found only a smallassociation between xerostomia and non-parotid salivary gland dose. Similarly,Chao et al. [229] intentionally considered only high submandibular meandose patients (≥ 50Gy) which is likely to have impacted their (similar toBlanco et al. [26]) conclusions. Nishimura et al. [148] found no statisticallysignificant mean dose dependence, though submandibular sparing was notexplicitly described. Overall, submandibulars appear to be less studied inthe literature compared to parotids.As discussed in section 6.1, submandibular glands are known to contributethe greatest proportion of resting whole-mouth saliva. Their surgical removaland transplantation are known to impact xerostomia risk [233, 234, 235]. Onthe other hand, submandibular gland often sparing is somewhat controversialas they are known to frequently coincide with primary targets, and localcontrol can be compromised [233, 326]. The submandibulars are smaller andless geographically distributed than parotids, which means sparing one isharder, and the capacity to separate effects from each submandibular willthus be harder than for parotids. Submandibulars should therefore be thesecond-order organ considered.Regrettably, sublingual glands are not contoured at the BCCA and thus89cannot be directly included5. However, they are included in the broad oralcavity ROI. Previous studies are mixed: dose to the oral cavity, and thusto some accessory and minor salivary glands, has been found to be bothsignificant [40] and insignificant [26] for prediction of xerostomia. Because thelesser glands contribute less saliva than larger organs, they should thereforebe included in analyses only after parotids and submandibulars, and possiblyafter other accounting for other factors such as age, gender, dose-volumeeffects, and bath-and-shower effects (n.b. discussed in section 8.1).Ideally, all salivary organs should be considered in analysis of regional ef-fects. The reality is that contouring and other clinical support efforts are timeconsuming and must be prioritized. The parotid is most frequently contouredat the BCCA in order to adhere with clinical guidelines. Submandibulars arealso frequently contoured, but less often. The oral cavity is often contoured,but least of all structures containing salivary glands, and the definition canbe subjective. Also, patient positioning does not always include maintainingthe shape of the oral cavity. Sublingual glands are rarely contoured. Theavailability of contours reflects their (current) clinical utility, which makes itdifficult to investigate higher-order effects. Therefore, the parotid is primarilyconsidered in this thesis. Submandibulars are investigated briefly, but lesserglands and the oral cavity are not considered.6.7.6 Relative or Absolute?Patient anatomy and physiology dictates the magnitude of saliva response,and what is considered low flow or highly viscous for one patient may notdirectly translate to other patients. In other words, salivary measurementsare patient-specific. A brief discussion of salivary function measurement andxerostomia questionnaire response normalization was given in section 6.4.However, it did not address the issue of how to make the most of the datathrough normalization.As shown in section 6.7.3, the most natural normalization method –subtraction of baseline – magnifies measurement uncertainties. The next most5Note that studies involving sublingual glands are comparatively rare in the literatureand often seem to be lumped into the more generic oral cavity.90natural method, division of baseline, yields a reasonable compromise betweenmeasurement uncertainty amplification and per-patient normalization. Moreprecisely, with W = WA/Wb, propagation of uncertainties for baseline-normalization yieldsδW|W | ≤δWA|WA| +δWb|Wb| (6.2)generally, orδW|W | =√(δWA|WA|)2+(δWb|Wb|)2when errors are known to be independent and random [323]. As shown insection 6.7.3, there is an uncertainty penalty incurred by baseline normaliza-tion compared to direct use of raw measurements (i.e., 0.35 vs. [0.50, 0.70] inthe example of section 6.7.3), but it is substantially less than the differencingapproach (i.e., [0.73, 0.97] or [1.6, 2.2] depending on the signal of interest).It is natural to wonder if there is a better means of bolstering signalwithout also amplifying uncertainty. In terms of δW and W , this question istantamount to minimizing δW/|W | for some physically meaningful functionW involving at least two of Wb, W3m, W1y, or W2y. First, it is more generaland convenient to avoid assumptions about the nature of the measurementuncertainties especially since the scedasticity will change for arbitrary W .Uncertainties can be propagated in generality viaδW|W | ≤1|W |N∑i=1∣∣∣∣∂W∂xi∣∣∣∣ δxiwhere x ≡ {Wb,W3m,W1y,W2y} and N ∈ [2, 4] for some function for somefunction W (x) when |W | 6= 0 [323]. Any W involving only products ordivisions of any two xi trivially reduces to the RHS of eq. (6.2); any functionsinvolving more than two reduce to the RHS of eq. (6.2) with an additional(positive) factor, and are thus strongly amplify uncertainties. Similarly, anyW involving two or more additions or subtractions reduces to the RHS of91eq. (6.1), possibly with an additional positive factor, which makes δW/|W |trivially larger than the RHS of eq. (6.2). So there are no simple arithmeti-cal combinations of factors, including linear transformations, that improveupon multiplicative baseline-normalization in their ability to suppress mea-surement uncertainties. Clinical relevancy requires W to be monotonic inresponse to W3m, W1y, and W2y. Non-linear transformations will generallyskew uncertainties, and logarithm and power transformations are sometimes(controversially) employed to de-skew distributions to improve symmetry[328, 329]. Power transformations have already been shown to magnify un-certainties. However, logarithms may or may not magnify uncertainties. IfF ≡ logW then it can be shown thatδF|F | ≤1|W logW |N∑i=1∣∣∣∣∂W∂xi∣∣∣∣ δxiwhich may or may not be a stronger bound than that of δW|W | due to thefactor |1/ logW |. For example, the factor will cause uncertainty amplificationif W = W1y/Wb and population-average values are used. Perhaps moreimportantly, uncertainties will not uniformly by magnified, which couldconfound some analysis and may require delicate accounting of the natureof measurement uncertainties. If this is not possible linear transformationsshould be preferred, and the multiplicative baseline-normalization is thereforelikely the most consistently optimal method. For purposes of analysis ofregional effects, objective salivary measurements are multiplicatively baseline-normalized, yielding a value nominally within [0, 1].Xerostomia questionnaire responses may also require normalization, butare much more difficult to analyze. First, as discussed in section 6.4, thesample-population baseline score medians are all zero and therefore do notadmit a reasonable multiplicative per-patient normalization. On the otherhand, there is already a natural, common scale that each patient is subjectedto, which presents a natural normalization opportunity. Second, there aremany questions to consider, and some may be impacted by question order oradjacency, or possibly even recent (and distant) patient memories and mood.92Finally, though the questions are qualified, individual questions designed toprobe specific aspects of saliva (e.g., the mucin content) may inadvertentlyamalgamate unrelated circumstances that confuse the specificity (e.g., con-fusing speaking and sleeping). Combining responses may likewise destroyspecificity. Trying to select related questions results in even more subjectiv-ity, but examining responses individually will reduce overall specificity andwill necessarily impact the statistical approach to account for the multiplecomparison problem.Xerostomia question responses were therefore individually examined with-out additional normalization, but with appropriate multiple comparisoncorrections where appropriate.6.7.7 Summary and ConclusionsObjective dysfunction is less susceptible to clinical variation, patient psy-chology, and easier to normalize. Late toxicity has a greater total impact onpatients, while early toxicity is usually limited in duration and the potentialfor improvement is confounded by factors such as medication. Parotids and,to a lesser extent, submandibulars are the most relevant organs for analysesinvolving whole-mouth saliva. Relative normalization, when possible, providea way to compare different individuals in a consistent way.In this thesis, late, objective stimulated saliva was analyzed along withparotid dosimetric data. A follow-up analysis using late, objective restingsaliva and submandibulars is also provided. In particular, the oral cavity andearly measurements were not considered in any analysis, but all remainingavailable data was analyzed in some fashion.93Chapter 7Toxicity Assessment:Instruments and Protocols7.1 Clinical Xerostomia AssessmentAn instrument is needed for self-assessment of xerostomia. At the BCCA asingle-page hard-copy questionnaire is employed. It has been approved by thejoint BCCA-UBC Research Ethics Board (REB) and patients must consentto participate. Patients responses are collected four times over roughly 2.5y(prior to radiotherapy and three times after radiotherapy is concluded: threemonths, one year, and two years, nominally). Patients answer each of the nineEnglish language questions themselves. Verbal translation into Mandarin,Hindi, and Farsi is provided by bilingual nurses when available, but themajority of patients are able to read the questionnaire themselves.All responses are interval-type responses that can range from zero (nega-tive; meaning “not at all,” “no,” or “infrequently”) to ten (affirmative; meaning“strongly,” “yes,” or “frequently”). All questions are worded such that a re-sponse of ten will affirmatively convey symptoms of xerostomia. The questionsare (verbatim) as follows:1. Rate the discomfort of our dentures due to dryness (if you do not weardentures please check ).942. Rate the difficulty you experience in speaking due to dryness of yourmouth and tongue.3. Rate the difficulty you experience in chewing food due to dryness.4. Rate the difficulty you experience in swallowing food due to dryness.5. Rate the dryness your mouth feels when eating a meal.6. Rate the dryness in your mouth while not eating or chewing.7. Rate the frequency in sipping liquids to aid in swallowing food.8. Rate the frequency of fluid intake required for oral comfort when noteating.9. Rate the frequency of sleeping problems due to dryness.While all questions correlate with salivary measurements only weakly(see tables 6.1 and 6.2), questions 5 and 6 correlate consistently in the top-ranks, and in many cases are the top-ranked correlates. This may be due toquestions 5 and 6 explicitly and directly polling oral dryness. Questions 4 and7 may be specifically more sensitive to dysphagia (i.e., persistent difficultiesswallowing) than xerostomia, but are certain to be sensitive to xerostomiatoo. Conflation of symptoms is known to commonly occur, and may furtherconfuse the association between xerostomia and salivary dysfunction [330].The BCCA questionnaire derives from the eight-question xerostomia-specific QoL questionnaire of Eisbruch et al. [40], but some phrasing wasmodified and an additional question was added (#1) with the aim of assessingdental practices pertaining to dentures. Evaluation of the reproducibilityand validity of the original questionnaire was performed “. . . according tostandard methods of evaluating QoL instruments” [40]. There are a plethoraof self-reporting instruments that are xerostomia-specific or are QoL-focusedbut encompass aspects of xerostomia.Ojo et al. [331] give a systematic review of (>50) QoL instruments relat-ing to head-and-neck cancers. The aim was to assess the heterogeneity ofquestionnaire use in the literature. The most widely used xerostomia-related95instruments were the ‘Dysphagia Inventory’ of MD Anderson [332], the ques-tionnaire of Eisbruch et al. [40], and the ‘Oral Health Impact Profile’ (14-itemversion) [333]. A significant basis for the selection of an appropriate BCCAquestionnaire was minimal respondent and administrative burden, since itwould be administered several thousand times; the shortest xerostomia-specificquestionnaire was that of Eisbruch et al. [40]. While the unmodified originalquestionnaire of Eisbruch et al. [40] was found to be used in only 14 of the 710considered studies, it appears to be the most prevalent xerostomia-specificquestionnaire in use.It is worth reiterating that, whichever instrument is used, most stud-ies report a rapid decrease in patient QoL shortly after radiotherapy withgradual improvement over the following year. It is unclear precisely howthis observation relates to salivary dysfunction, or is impacted by patientperceptions of oral dryness, or the emotional burden of cancer and cancertreatment. Additionally, given the large number of assessment instrumentsand especially their variations, objective flow presents as a more universalmeasure.7.2 Clinical Salivary Function AssessmentA comprehensive and unusually thorough1 study by Navazesh et al. [334]found that unstimulated whole saliva and stimulation (chewing withouttasting) had the greatest test-re-test repeatability. This is the procedureemployed at the BCCA for objective saliva measurements. The procedure iswidely used and has been described numerous times in the literature (e.g.,[26, 229, 335]). While it appears to have been well known even prior to 1992,the specifics of the procedure were adapted from the report from Chao et al.[229] and are described here.Assessment immediately followed administration of the xerostomia ques-tionnaire from section 7.1, namely prior to radiotherapy and three timesafter treatment concluded: three months, one year, and two years, nominally.1Practice saliva collection was performed and the chew rate was controlled via synchro-nization with a metronome.96Patients were asked to avoid consuming food one hour prior to assessment.They were asked to fill out the questionnaire while resting. Excess salivawas cleared from the mouth, and the patient was asked to lean forward andexpectorate whole-mouth (unstimulated) saliva into a pre-weighed collectioncup. After five minutes, the cup was weighed. Stimulated whole-mouth salivafollowed using the same procedure, but a small block of flavourless paraffinwax was provided to chew on. Both procedures were supervised by qualifiedpersonnel to ensure adherence.Collection of time-integrated saliva volumes allows estimation not only oftotal volume but also sustained flow rate. Instantaneous (a.k.a. ‘on demand’)or nearly-instantaneous flow may be the most perceptible aspect of stimulatedsaliva. For example, chronically being unable to swallow the first few bitesof a meal, or failing to develop a full mouth salivary response when a tartsubstance is tasted are likely to invoke strong negative emotional responses.However, as previously discussed, saliva measurements are notoriously noisyand estimation of the instantaneous flow rate may involve only <10mg ofsaliva per second. Estimation by whole-mouth collection is therefore notfeasible.Whole-mouth saliva is contributed from both major and minor salivaryglands. Organs with left-right symmetry separately contribute. Normalanatomy, disease, damage (e.g., trauma, radiation, medicinal), or other fac-tors may lead to an unbalanced contribution from individual organs, and thuswhole-mouth saliva measurements convolute the signal from each. There arewell-known suction apparatuses that can measure contributions individualglands, including Carlson-Crittenden collectors, which were first describedover a century ago [336]; the Lashley cup modifications and variations thereof[337, 338]; and Schneyer’s devices [339, 340]. Compared with whole-mouthsaliva measurements, dose response discrepancies have been noted for in-dividual parotid saliva measurements [40, 229]. It is not known to whatextent such discrepancies result from differences in collection technique [341].It remains unclear if individual parotid flow measurement is more or lessrelevant than whole-mouth saliva. Regardless, minimization of clinical impactwas the primary motivation for collection of the decidedly low-technology97whole-mouth saliva rather than use of specialized devices. Other whole-mouthcollection methods have been devised, such as the Wolff method, based on theweight loss of a hard candy over a fixed duration, and manual oral swabbing.Both have been shown to be less repeatable than the method employed atthe BCCA [334, 342].Due to clinical constraints, it was not possible to ensure repeat mea-surements occurred at a consistent time of day. Collection predominantlyoccurred between 9:00 and 15:00.7.3 ConclusionsBCCA xerostomia and dysfunction assessment protocols are based on themost reliable saliva collection techniques and the most widely-used xerostomia-specific QoL instruments.98Chapter 8Other Relevant Topics Fromthe Literature8.1 Are Parotids Serial or Parallel Organs?Parotids have been treated as parallel organs since the inception of radiother-apy, and current practice makes use of mean dose to the parotids. This ispartly because the distribution of functional burden appears to be homoge-neous to first order, and partly out of convenience to work around limitationsof early treatment devices [343, 344, 345]. Dose-volume histograms are alsoused for treatment planning purposes; their validity is predicated on theassumption that organs are parallel and that functional burden distributionis homogeneous. Modern radiation delivery techniques have shed new lighton the question of whether parotids are parallel or serial – or, rather, whetherthere are potential clinical gains to had by accounting for deviations fromthe purely parallel approximation. In the remainder of this section a briefoverview of recent developments is given.In 2005, Blanco et al. [26] considered six distinct whole mouth salivamodels motivated by physical arguments. All involved exponential suppressionof function with increased radiation dose. The best-performing model was aparallel-exponential model that treated the parotid as if it were composedof independent functional subunits. Belief in the applicability of the model99appears to have been limited, though, because simple models were ultimatelyadvocated [26]. Many others have concluded the same (e.g., [346, 347]). Onthe other hand, the conclusions of this ‘early modern’ re-examination appearto have reinforced the belief that the parotid is parallel, which more or lesscontinues even now.Many explicit dose-volume effects have been reported for parotid glands.For example, Konings et al. [348] (and later Konings et al. [349]) reportedlate dose-volume effects pertaining to salivary dysfunction in the parotidglands of rats. The greater the partial volume of parotid that was irradiated,the greater the magnitude of dysfunction that resulted.In 2010 Houweling et al. [347] pooled data from multiple centres for alarge study involving 384 patients. Their aim was to select the best NormalTissue Complication Probability (NTCP) model amongst the Lyman-Kutcher-Burman, mean dose, relative seriality, critical [sub-]volume, parallel functionalsubunit, and dose-threshold models. No model could be rejected, but themean dose model was recommended. The same year Deasy et al. [236]reviewed the literature on late parotid xerostomia dose-volume effects anddevised clinical guidelines based on mean whole-parotid doses that wouldnominally avoid severe late xerostomia. The mean dose paradigm, whichforms the basis for current clinical guidelines, is not purely dose-volume.Rather, because the statistical mean is sensitive to every datum, mean dose issensitive to dose in all regions within a ROI. Nonetheless mean doses do notaccount for specific spatial information and are rooted deeply in the parallelorgan paradigm.By 2010 dose-volume effects had been decried for nearly 30 years. Theconvenient assumption that functional burden is homogeneously distributedthroughout the salivary organs was, and remains, widely criticized by radiobi-ologists [350, 351, 352]. Dose-volume models are based on the assumption ofhomogeneity. Early reports used the Lyman-Kutcher-Burman model, whichuses a power law with an exponent that controls the strength of the volumeeffect and is only applicable for single-organ contributions [346]. In 2000,Hopewell and Trott [353] wrote (about the homogeneous distribution theoryin general) that100There is little or no [dose-]volume effect for structural radiationdamage, however, some very pronounced [dose-]volume effects havebeen reported for functional damage. Volume, as such, is not therelevant criterion, since critical, radiosensitive structures are nothomogeneously distributed within organs. [. . . ] Volume effectsin patients and experimental animals are more related to organanatomy and organ physiology than to cellular radiobiology.It therefore seems that volume, from a radiobiological perspective, is merely asurrogate for discretely distributed parenchyma (or some other critical tissues)that are only approximately homogeneously distributed at the whole-organscale. Over a decade ago, when Konings et al. [348] reported dose-volumeeffects in rat, they also found that the character of the dose-volume effectdiffered in cranial and caudal aspects. This is an example of a weak regionaleffect. However, this aspect of the finding appears to have been somewhatdisregarded until recently.In the latter part of the decade spanning 2000-2010, the introduction ofIMRT led to improvements in treatment outcomes and QoL. For example,Mortensen et al. [283] showed that incidences of both xerostomia and dys-phagia were reduced following the introduction of IMRT. Others have foundthe magnitude of QoL impairment lessened, and recovery was both morerapid and more complete compared to conventional radiotherapy [226, 241].However, the improvements in treatment capabilities highlighted shortcom-ings of various dose response models, which became highly scrutinized. Thefailure of NTCP models in animals was investigated by van Luijk et al. [354].Dijkema et al. [355], using ten years of patient data, reported failure of meandose based models to fully describe the effects of radiotherapy on parotidglands.Other deviations from a purely parallel organ were reported prior todevelopment of the modern clinical guidelines. The most striking was reportednearly almost concurrently with the guidelines of Deasy et al. [236] in 2009,namely the bath-and-shower effect reported by van Luijk et al. [356] in ratparotid. Again, the cranial and caudal aspects were irradiated. It was found101that the sub-effect threshold dose of one aspect depends on irradiation of theother aspect. A confirmation of the effect was noted in human parotids usingxerostomia as the response variable in 2012 [233].Recently, more direct evidence of regional effects has emerged. In 2015van Luijk et al. [357] reported isolation of a ‘critical’ region; irradiation ofthe critical region is supposed to strongly influence patient outcomes. Thedegree of influence and specific sensitivity is not known, but histopathologicalwork indicates the region is dense with stem/progenitor cells. van Luijket al. [357] reports that a clinical trial is underway to assess the impact ofsparing the confined critical region. If the trial is successful in showing theregion is critical, it still may not be able to quantify the relative importanceof other (potentially critical) regions. Likewise, reports of lobe sparing arelimited in their ability to impact clinical treatment planning because theypresent information only relating to the (binary) decision to spare only asingle region [358]. The findings are still noteworthy and could potentiallyimpact treatment planning however. Even if sparing is found to be ineffectualfor reducing toxicity risk, these findings still represent potentially clinically-relevant cracks in the parallel organ theory. It is hoped that the regionaleffects demonstrated by the present work will also deliver a significant blowto the atomic-organ clinical practice.8.2 The Growing Importance of Stem CellsRecently, advances have been made in understanding the role of stem cells inrecovery of both parotid and submandibular gland function after radiotherapydamage. A seminal work on the subject is provided by Coppes and Stokman[302] that builds on nearly a decade of investigatory work.As described in section 6.6, stem cells appear to play a central role in therestructuring of glands that have had temporary ductal ligation. In short, stemcells can (almost) fully restore functional capabilities by proliferating survivingacinar cells along with recruitment of new cells and fresh innervation. Newly-generated ducts express proteins usually observed only during embryogenesis[359]102These findings have sparked efforts to selectively protect regions containingthe ducts so that greater stem cell recruitment from protected, stem cell-denseregions can more rapidly and consistently replenish damaged regions (i.e.,[356]; cf. section 8.1).Recently, researchers have attempted to transplant stem cells into dys-functional parotid glands following radiotherapy [214, 360, 361]. Additionalrecovery has been observed. These findings have sparked a flurry of researchinto the mechanisms and clinical applicability of cell transplantation, as wellas efforts to locate suitable sources of cells. Stem cells have been observed inthe ducts of mice [362]. Candidate stem/progenitor cells have been found inuninjured salivary glands [363], pancreas [364], and minor salivary glands ofthe lips [365]. There is thus some possibility that transplantation could enterclinical practice rather than just remain an academic curiosity.However, stem cell therapy to correct radiotherapy-induced dysfunctionis not currently clinically feasible. Reports of functional restoration in axenotransplantation model of human salivary glands have recently beenreported that suggest it may be reasonably possible in the future [366,367]. Efforts are currently underway to construct replacement salivary gland‘neotissues’ for permanent implantation [368].As described in section 6.7.3, the focus of this thesis is on reduction ofdysfunction rather than improving recovery, and stem cells appear to bemost relevant for recovery. So the relevance of stem cells are confined topossible regional effects resulting from inhomogeneous cell distribution, butthere is no analytical way to derive cell populations from the BCCA cohort.Stem/progenitor cells are thus largely incidental for the purposes of this work.8.3 Relevant Clinical FactorsThe utility of many clinically-relevant factors has been investigated in salivaryoutput prediction models. The use of multivariate logistic regression andother model parameter selection techniques are widely reported. In thissection a sampling of these findings are provided. In brief, dosimetric factorsare universally found to be most relevant for risk of developing xerostomia103and salivary dysfunction following head-and-neck cancer radiotherapy.Using multivariate analysis, Chao et al. [229] investigated correlationbetween salivary function and radiation dose to the parotid glands. Theyfound that the rate reduction of stimulated salivary flow at six monthspost-radiotherapy was not significantly influenced by a patient’s gender, age,tumour stage, radiation technique (IMRT vs. conventional radiotherapy), oradjuvant chemotherapy. A parotid dose derivative was found to be the solesignificant factor for xerostomia.A similar, more comprehensive analysis by Blanco et al. [26] involvedpatient age, gender, ethnicity, date of treatment start, treatment technique(IMRT alone vs. otherwise), treatment aim (definitive vs. postoperative radio-therapy), Karnofsky Performance Status (KPS), whether adjuvant chemother-apy was delivered, tumour stage, treatment duration, histopathologic features(squamous vs. other), tumour subsite, and a derivative of mean parotid dose.The mean dose-exponential model was the most independently significantfactor, followed by the considerably less significant gender and KPS factors[26].A meta-analysis of xerostomia incidence in the elderly found that non-institutionalized elders had only a small additional xerostomia risk comparedto the general public (17-40% vs. 6-39%) [369]. This suggests only a weakdependence of xerostomia with age. Wider socio-economic factors are knownto moderately impact overall oral function. However, the strongest impactresults from the most extreme and least common conditions involving psy-chiatric disorders, heavy smoking habits, and low socio-economic status.Furthermore, the impact appears to be greatest on xerostomia rather thandysfunction [370, 371, 372, 373].In a multivariate study, El Naqa et al. [346] demonstrated a consistentpreference of variables when constrained to five factors (only): mean parotiddose, gender, KPS (the three most significant), and technique and treatmentaim (the two of considerably lower significance than the previous three).El Naqa et al. [346] recommend using a simplified model with few factors.Teshima et al. [305] found a correlation between decreased parotid glandvolume and decreased saliva production following radiotherapy. They noted104that no such correlation existed between total volume and total salivaryoutput following radiotherapy. Many others have reported similar findings(e.g., [74, 148, 374]).Recently Buettner et al. [233] employed Bayesian multivariate logisticregression, considering the parotid volume, submandibular gland mean dose,surgical removal of the ipsilateral submandibular, gender, tumour site (hy-popharynx or oropharynx), age, utilization of neo-adjuvant chemotherapy,and hypertension assessment reports. Dosimetric factors were most signifi-cant, though surgical submandibular gland removal was found to significantlyincrease xerostomia risk.Another recent study by Lee et al. [375] making use of the robust bootstrap-based least absolute shrinkage and selection operator (LASSO) statisticalmethod found that mean dose to the either parotid gland were the mostsignificant predictors for moderate-to-severe xerostomia. Patient age, financialstatus, tumour stage, and education were variously found to important, butnot consistently. Other factors considered included patient gender, (current)marriage status, smoking status, history of alcohol abuse, and family historyof xerostomia, amongst others.Consistently, dosimetric factors have been shown to be most relevant forprediction of xerostomia and dysfunction. It therefore seems acceptable toforgo clinical and socio-economic factors and control for surgical, medicinal,and historical factors.8.4 Factors Affecting Availability of DataStudies have shown that logistical factors impact treatment prescriptions,availability of treatment options, treatment quality, and patient complianceto, and participation in, post-treatment procedures [376, 377]. Olson et al.[378] found that breast cancer patients from rural BC communities presentedwith more advanced disease than their urban counterparts. Conversely, medi-cal travel1 is well-known in the literature (e.g., [379, 380]) and is pronounced1n.b. patients seeking more timely treatment or expertise not locally available – not tobe confused with ‘medical tourism’, which specifically refers to patients seeking lower-cost,typically cosmetic treatments105in Canada [381]. One oncologist in California estimated that in 2006 approx-imately 40% of his patients were from outside the United States and 30%were from outside California [382]. Travel is known to disrupt continuity ofcare and follow-ups [383]. In BC and other places with centralized medi-cal agencies, medical travel for cancers are thought to be most pronouncedwith advanced and specialized cancers for which specialized expertise can besought, or waiting times are perceived to be too long, but a lack of academicliterature or even empirical evidence limits understanding of the practice[377, 384].All of these factors can be broadly classified as socio-economic. Directinclusion of socio-economic factors does not appear to improve outcomesprediction (see section 8.3). However, they may significantly impact the dataavailable for analysis, which can lead to a statistical situation referred toas Missing Not At Random (MNAR). Failure to account for confoundingfactors or use of MNAR data can lead to incorrect conclusions [385]. Socioe-conomic factors were not recorded in the BCCA head-and-neck cohort, andretrospective assessment was not feasible. Generalizability of results fromthe literature is not easy to estimate, given the varying degrees of livingstandards and access to treatment options around the world. Therefore, anoverview of findings from the literature with varying applicability is providedto help estimate the impact of the confounding missing data phenomena.Since the aim of this study is to characterize patient outcomes, patientsurvival does not need to be accounted for. In toxicities that are directlylife-threatening, failure to account for mortality may occlude the most severetoxicities. Salivary dysfunction and xerostomia can become strongly detri-mental to overall QoL, but cannot directly (and do not often indirectly) causemortality. There are even treatment options for patients dealing with chronicinfections stemming from dysfunction, such as artificial saliva, medicationsthat induce hyperfunction, and even transplantation or relocation of salivaryglands. However, there is still potential for systematic bias if patients withthe worst (or least) severe toxicities are systematically not reported. Treat-ment efficacy and local control are therefore de-coupled from development oftoxicities, at least in the first-order.106Hypothetical BiasesCancer treatment can be a significant economic burden. Even in Canada,where healthcare is publicly funded, radiotherapy treatment fractionation,frequent trips for follow-ups and monitoring, and concurrent modalities (i.e.,imaging, administration of chemotherapy) cause significant strain on patients[386, 387]. Even seemingly mundane psychological and economic factorssuch as availability of (or payment for) parking are known to negativelyimpact patient involvement [377, 388, 389]. It therefore seems reasonablethat socio-economic factors that mutually correlate with wealth, education,or social status, along with factors that impact aspects of disease, such asprimary tumour site or proliferation of disease, could impact data availability.Smoking history is potentially one such factor. While smoking sta-tus/history is known to substantially influence risk of head-and-neck cancers,predictions of toxicity risk/severity and treatment efficacy are only moder-ately improved when smoking status/history are included [201, 390, 391, 392,393, 394]. The impact of smoking on data availability, however, is presentlyunknown. Consider a hypothetical pathway in which data availability couldbe negatively impacted; a rural-dwelling ‘chain smoker’ who spends much oftheir income on cigarettes. Because they live in a rural community, they donot have regular access to medical services, or the services they do have accessto do not have substantial experience identifying cancers, and they presentwith an advanced stage cancer of the upper aerodigestive tract. (Many pa-tients with head-and-neck cancers present at a relatively advanced stage [206],so disease in this hypothetical case may be extremely advanced or late stage.)Such a person would be predisposed to excessive head-and-neck cancer risk[391, 395] and may either find it difficult to travel for post-therapy follow-upsfor logistic or economic reasons [386], or may be otherwise disinterested [272](e.g., existing poor dental hygiene due to lack of regular checkups and lack ofinterest in attending concurrent dental examinations). Radiotherapy treat-ment would likely need be aggressive to obtain local control, and extensivelymph node irradiation would ensue. The parotid would thus be heavilyirradiated. Socio-economic forces in this hypothetical case would result in107(1) increased cancer risk, (2) advancement in tumour stage and reducedprognosis, and (3) self-censorship of study involvement.Whether this specific hypothetical case is far-fetched is unknown. Fur-thermore, it is merely one of many such pathways to developing a systematicbias in the available data. Other hypothetical self-censorship differencesstemming from socio-economic factors might include greater allotment ofsick leave for white-collar workers, greater accumulated savings and thereforeless sensitivity to economic hardship and/or reduced reliance on friends andfamily for the wealthy, and greater treatment options for those in populatedurban areas [389].Literature on the interplay between socio-economic factors and data avail-ability is sparse, so reliable estimation of their impact is not currently possiblein generality. However, specific factors have received focused attention. Rele-vancy to the BCCA are discussed for each.RuralityOne comparatively well-studied factor is distance to treatment centres. Itis known that distance to a clinic negatively impacts patient involvement,such as attendance at follow-up appointments [388, 389]. It is also knownthat logistic factors impact utilization of radiotherapy [272]. It is not clear,however, whether there is any link between toxicity risk or severity anddistance to the nearest treatment centre within BC. The BCCA is province-wide and implements similar practices throughout the province, includingclinical OAR sparing. Currently mean doses are used, which are not sensitiveto specifics of the dose profile, and thus no intra-parotid sparing is performedat any site. The same planning software is used to generate plans, andthere are provincial tumour groups set up to collectively review specific cases,meaning there is open communication between sites, experience sharing,and continuing education amongst staff. Recent unpublished work by Olsondemonstrated that treatment outcomes were indistinct for head-and-neckcancer patients treated at different BCCA centres [396]. Rurality thereforedoes not seem likely to have had a significant impact on data availability.108Additionally, the BCCA head-and-neck cohort was selected predominantlyfrom large urban centres (Vancouver and Fraser Valley) rather than fromall five provincial centres, which helps to further minimize impact clinicalvariations.Ethnic FactorsPatients of Asian ethnicity are more susceptible to Nasopharyngeal Carcinoma(NPC) than those of other ethnicities [13, 397]. The Hong Kong NPC StudyGroup proposed the now common ‘maxillary swing’ surgical method andare world-renouned for specializing in NPC [398, 399]. Because a significantnumber of patients in the BC lower mainland, and therefore in the patientcohort, are of Asian ethnicity, it is possible that some will engage in medicaltravel and seek specialized treatment elsewhere. However, NPC is consideredrare with a world-wide incidence of <1 per 100k per year [400]. Ethnic factorsare therefore believed to have a low impact on data availability. Furthermore,in the specific case of NPC, medical travel may potentially help regress theBC incidence rate toward global averages.Competing ModalitiesPotentially confounding factors that could bias data availability are not lim-ited to socio-economic factors. For example, alternative treatment options.Chemotherapy is most often administered concurrently with radiotherapy[202], but not always. Studies involving novel or specialized chemotherapyagents appear to most often select patients based on genetic predisposition,or viral status rather than disease stage or proximity to OARs (except inexceptional cases where radiotherapy treatment complication risk is excep-tional, such as immediate proximity to the spinal cord, or if patient survivalrisk is low using existing treatment options). However, many chemotherapyagents, even those routinely used, are known to induce transient xerostomia[225, 401, 402]. Addition of chemotherapy afforded an overall reduction oftoxicity compared with conventional radiation-only therapy [202, 403]. Tomitigate potential bias, in all analyses we have therefore excluded patients109receiving non-standard chemotherapy agents. In addition, use of late salivaryfunction rather than early function will further avoid conflation of chronicsequelae with transient chemotherapy-induced xerostomia or dysfunction.Other transient effects such as temporary changes in diet, depression, sleepinghabits, and other early factors that may directly or indirectly affect hydrationand salivation are also minimized this way [322, 404, 405].Surgery (both relating to the cancer or previous surgical intervention) isanother treatment option that impacts salivary function and xerostomia. In allanalyses we have excluded patients with prior interfering surgeries. Otherwise,assessment of surgically-induced dysfunction, potentially confounding effects,and estimation of the impact on data availability due to patient enrollmentin surgical treatments is well beyond the scope of this thesis. Howeverradiotherapy with concomitant chemotherapy has displaced surgery as theprimary treatment modality and is widely used in the clinic [202, 403, 406,407].ConclusionsNo comprehensive studies of the impact of missing data on radiotherapyanalysis was found in the literature. Surprisingly, only a few specific remarkswere found. It is therefore difficult to assess how missing data may impactanalysis.On the other hand, whatever the impact of socio-economic or otherfactors on data availability, the BC cohort is likely one of the most reliableand cohesive large head-and-neck cancer data sets available. The Canadianpopulation is one of the most ethnically diverse ‘western’ countries [408]and a provincial mandate means that all radiotherapy services are deliveredthrough the BCCA. Medical services are not privatized in Canada meaningthat all patients are able to afford (at least out-of-pocket) treatment expense,and collaboration between individual centres is high. Furthermore, nearlya decade of head-and-neck cancer outcomes (all using the same assessmentprocedures) are available. The results of this study are therefore likely to beat least as valid as the majority of studies reported in the literature, especially110if multi-agency data sharing was employed.8.5 Clinical RecommendationsIn 1999, Eisbruch et al. [409] recommended a mean dose ≤26Gy in 30-35fractions to permit substantial sparing of the parotid. In 2003 Amosson et al.[267], based on patient-reported QoL questionnaires, found that patients feltthey had ‘too little’ saliva when the contralateral parotid received a meandose ≥22.5Gy. Six years after Eisbruch et al. [409], in 2005, Blanco et al. [26]recommended a mean dose ≤25.8Gy. Variation in recommendations havesince appeared to be minimal, though many have been given [273].In 2010 a joint effort by many researchers, authors, reviewers, and supportpersonnel provided comprehensive summaries of the available dose-volumeand outcomes data and accompanying clinical recommendations referred to asthe Quantitative Analysis of Normal Tissue Effects in the Clinic (QUANTEC)guidelines. For parotids, <20Gy mean dose to the contralateral gland or<25Gy mean dose to both is advised. It is currently recommended to followthe QUANTEC guidelines [236, 273, 410]. The BCCA adheres to theseguidelines.111Chapter 9Statement of ResearchQuestions9.1 StatementChapters 2 to 8 have presented relevant introductory topics that frame andmotivate the research topic, but also permit the specific aims to be moreclearly stated. The goals of this thesis are to address the following questions.1. Are all regions of the parotid gland homogeneously responsible forradiotherapy-induced dysfunction? Will delivering dose of equal magni-tude to different regions of the parotid lead to an appreciable differencein risk of dysfunction?2. If the regional importance is not homogeneously distributed, are thereaspects that are more important? Are they clustered (i.e., are there‘critical’ regions)?3. Can the relative importance of parotid aspects for dysfunction bequantified? Can the entire gland be quantified?4. If a strong effect is found for parotid dysfunction, does it manifest inthe same way for xerostomia?1125. If a strong effect is found for parotid dysfunction, can similar effects bedemonstrated for submandibulars?Elucidation of regional effects in parotid may lead to improvements intreatment planning and either reduced risk or reduced severity of radiotherapy-induced toxicities for head-and-neck cancer patients. Demonstration of re-gional effects will be sufficient to warrant further research, but isolationof critical regions and quantifying their importance relative to less criticalaspects within the parotid will have greater (immediate) clinical relevance.Quantification of the relative importance of the whole parotid will have thegreatest clinical relevance since then toxicity risk could be more completelyintegrated into the treatment planning process. Finally, if other regionaleffects can be found (i.e., involving xerostomia, resting saliva, or submandibu-lar facets) then a viable alternative to the current clinical practice of treatingsalivary organs as atomic (i.e., irreducible) parallel organs may be realized.9.2 Outline of ApproachThe following chapters describe and implement an analysis that is capable ofachieving the research goals.A glut of information is available to analyze. In order to provide the mostclinically-relevant and widely applicable assessment, the analysis should (atfirst)• employ segmentation to deal with morphological deviations,• consider dysfunction rather than xerostomia,• prioritize parotids over other salivary organs,• make use of stimulated saliva rather than resting saliva,• make use of late rather than early patient outcomes data, and• make use of patient-specific baseline-normalization.Several questions remain. First, discussion of the specifics of segmen-tation have been deferred to chapters 10 and 11; chapter 10 describes the113segmentation approach in generality, whereas chapter 11 presents a specificapproach that navigates around a major analytical pitfall and is particularlysuited to assessment of regional effects.With the segmentation procedure outlined, analysis of the link betweenparotid sub-segment mean dose and whole-mouth stimulated saliva mea-surements proceeds. Chapters 12 and 13 describe two different analyticalapproaches; chapter 12 describes a model-based (i.e., parametric) approach,and chapter 13 describes a model-free (i.e., ‘non-parametric’) approach. Theparametric approach is limited in that it cannot reasonably scale to accom-modate many sub-segments, but it provides a crucial, well-grounded linkbetween importance and clinical relevance that is needed for finer analysis.Using this link, the non-parametric method described in chapter 13 is ableto perform analysis on fine sub-segments – all the way down to 1/96th of aparotid, each with a volume of ∼0.3cm3 on average.Chapters 12 and 13 successfully demonstrate regional effects in parotid, sotwo addenda are provided. First, a limited follow-up analysis is performed onsubmandibulars and using xerostomia rather than dysfunction in chapter 14.Second, an MR imaging protocol is developed in chapter 15 that may beable to detect salivary gland parenchyma. Detection of parenchyma beforeradiotherapy could potentially provide patient-specific estimates of toxicityrisk rather than reliance on population-averaged importance.Overall conclusions and a summary of contributions is provided in chap-ter 16.114Part IIAnalytics115Chapter 10The Basics of Segmentation10.1 IntroductionSegmentation is open-ended. It can be applied in any number of ways whichstrongly depend on the representation of the underlying geometry. In thischapter the basics of segmentation as it is applied to ROI are described.Enough information to re-create the specific segmentation approach frombasic principles.Examples of ROI contour segmentation were shown section 4.3 – thischapter provides a more generic look at the approach rather than specificexamples. It also provides sufficient preparation for chapter 11, which com-pares the merits of two distinct approaches to handling R2 planar contoursembedded in R3 when volumetric aspects of ROIs are desired.10.2 DICOMautomatonDICOMautomaton is a computational framework developed by the author thatpresents a comprehensive system for manipulation and segmentation ofcontours and ROIs. Capabilities of have been described elsewhere (i.e.,[7, 411, 412]), however the mathematical approach has not been describedand is therefore presented here. DICOMautomaton is capable of rapid and losslesssegmentation by operating directly on ROIs (i.e., a ‘vector’ approach) rather116than rasterizing (a ‘bitmap’ approach; referred to as ‘generating masks’) orvolume reconstruction. DICOMautomaton operates on simple geometric primi-tives, including points, lines, line segments, and planes. Segmentation consistsof the composition of elementary geometrical problems, and can be imple-mented using any computational geometry kernel, such as Boost.Geometry[413] or the Computational Geometry Algorithms Library (CGAL) [414, 415].The vector approach is presented in the remainder of this chapter.10.3 Solutions to Elementary GeometricalProblemsFast and reliable computational algorithms for elementary R2 geometryproblems have been described elsewhere and are not repeated here. However,a list of the primitive operations necessary for a vector segmentation approachare provided along with references to efficient algorithms. The list is shortbecause the geometric primitives (points, lines, line segments, and planes)can be represented using a compact set of basic, atomic entities: points andvectors.To perform vector segmentation, the following routines need to be imple-mented.• Compute the distance between a line and a point [416].• Compute the distance between a plane and point. The signed distance,which inherits a negative when the point is on the negative side of theplane, is useful. It is often ambiguous which side of the plane shouldbe positive (especially since the coordinate system is not common toall patients), so an orientation must be consistently enforced.• Find the intersection of a plane or line segment with another linesegment [417]. If only the finite field is considered, there is a degeneratecase where the plane and line segment coincide over the entire linesegment which must be handled correctly.• Compute the area and ‘slab volume’ for simple planar polygons [418].‘Slab volume’ was defined in section 3.4.1; in brief, it is the volume of117a planar polygon extruded perpendicular to the plane of coincidence.Signed area, which takes a polygonal orientation to arbitrarily bepositive, is useful to describe polygons with holes, but is not strictlynecessary for segmentation. As with signed planar distance, the issueof ambiguous orientation must be dealt with because the polygons (R2)are embedded in R3.• Find the ‘centroid’ of a polygon, which is equivalent to the centre-of-mass when polygons are simple (or weakly simple) and the interior isassumed to be filled with a uniform density material [419].• Find the optimal planar orientation when the plane intersects a (single,known) point (e.g., the centroid). This optional routine allows contoursto be de-coupled from images, which describe the planes each contourscoincide with. It is especially helpful when image planes are oblique. Aleast-squares solution has a closed form that is trivial to solve for.• Projection of non-planar points onto a plane. This routine permitsR3-embedded contours to be projected into R2, which can simplifyimplementation of other routines, such as computation of area andlocation of centroids.• Determining if a point is interior or exterior to a planar polygon1 [420].This routine is crucial for differentiating entities within ROIs fromthose exterior. Planar projection is needed here unless perpendicularextrusion is employed, but extrusion is more costly due to the greaterdimensionality.The composition of these primitive operations into segmentation aredescribed in sections 10.4 to 10.6.1This problem has many names and is known as the “is point in poly” problem in somecomputational literature.11810.4 Planar SegmentationPlanar segmentation involves cleaving ROIs using infinite planes. For thepurposes of planar segmentation, individual contours are treated as thoughthey are two-dimensional planar closed contours embedded in R3 (i.e., theyhave zero volume and zero thickness).Planar segmentation is accomplished, in a nutshell, by specifying a cleav-ing plane, walking each contour to locate the intersecting line segments,determining the precise intersection point and creating a new internal vertex,connecting internal vertices in a manner congruent with the contour orienta-tion, and sorting resultant sub-segments by the side of the plane on whichthey rest. See fig. 10.1 for a graphical depiction.Note that this procedure is indifferent to ROI ‘thickness.’ However,any procedure that makes use of planar segmentation and is sensitive tovolume needs to account for plane-contour obliquity when specifying thecleaving plane. Slab volume may over or under-estimate the true volume,however accounting for volumes explicitly makes the problem considerablymore difficult, including requiring primitives with volumetric extent ratherthan embedded planar contours with only an implicit thickness. If a two-manifold surface is reconstructed from an ROI then Gauss’s theorem can beadapted to discretely compute enclosed volume [418]. However, using slabvolume leads to no worse sub-segment volume estimates than estimates of theoriginal ROI volumes, avoids ROI tessellation and the inherent topologicalambiguities, and imposes substantially lower computational burden comparedto two- or three-manifold methods [7], so the difference can often simply beignored. Mitigation techniques include aligning planes and contours (so thereis no obliquity) and iterative estimation of volume using slab-volume or bysampling vertices of a regular grid.10.5 Projective SegmentationPlanar segmentation is confined to produce sub-segments that have convex(planar) faces. While this improves efficiency when recursive segmentationis performed, reducing the number of vertices that need to be processed119Figure 10.1: Demonstration of planar segmentation resulting in twosub-segments (collectively above and below the plane). Planarsegmentation is always well-behaved when polygons are simpleor weakly simple (i.e., holes with partial seams).120(to a single vertex per face for sub-segments not containing original ROIsurface in as few as six segmentations), it limits the shapes representable bysub-segments.An alternative technique is called projective or ray-casting segmentation,in which contours are segmented by specifying a casting direction and frac-tional width, sending rays through the contour at each vertex, backtrackinguntil the fractional width is located, and creating a new internal vertex.Internal vertices are strung together in a manner congruent with the contourorientation and resultant sub-segments are sorted by orientation along theinternal edge. See fig. 10.2.Projective segmentation, which in some sense can more closely approxi-mate what is implied by ‘splitting a volume in two’ by incorporating surfacedetails, is more strongly affected by contour minutiae. Similar to differencebetween the mean and median discussed in section 4.3, projective segmenta-tion is more sensitive to contour shape than planar segmentation and canproduce sharp ‘jumps’ along the seam, particularly at the seam extrema (seefig. 10.3). Additionally, while cleave vertices are confined wholly within theoriginal contour, the cleave edges are not (also shown in fig. 10.3) which canresult in sub-segments with greater or lesser combined area/volume thanthe whole. On other words, area/volume is not strictly conserved. Thesefailures are not pathological, and can occur whenever positive curvature issurrounded by negative curvature and dis-aligned with the casting direction.Alternative approaches involving ray casting, such as spacing out raysevenly (or more finely such as recursively at vertex midpoints) over thepolygon diameter only partially mitigate failures. In some cases they canmake the problems worse. Additionally, projective segmentation can onlybe applied to individual contours. Combining adjacent sub-segments canlead to inconsistent seams and jumps (see fig. 4.10). Therefore, though itis sometimes more intuitive than planar segmentation, recursive projectivesegmentation is not reliable enough for assessing regional effects.121Figure 10.2: Demonstration of projective segmentation on a well-behaved simple polygon. The casting direction is indicatedby gray arrows and the fractional width is 1/2. Figure 4.8shows recursive applied projective segmentation.122Figure 10.3: Unintuitive ‘jumps’ and the failure of projective segmen-tation on a simple polygon (indicated with an arrow). The topfigure is projectively segmented into the middle figure. Notethe cleave line passes outside the original polygon. The bot-tom figure represents a cleave that is more intuitive, but notattainable using projective segmentation.12310.6 Iterative SegmentationIf one knows the location and orientation of a desired cleaving plane before-hand (e.g., centroid and an axes-aligned plane intersecting the ROI centroid),then planar segmentation can be used directly. However, often the goal isto sub-segment based on volumetric criteria so that a specific fraction ofresultant sub-segment volume is above (or below) a given plane. Projectivesegmentation is able to incorporate this criteria as the fractional width pa-rameter and tautologically find sub-segments of a given fractional volume(up to the area/volume conservation discrepancy), but planar segmentationcannot. In this case the offset of the plane is unknown (but the orientation isassumed to be known).Determination of the planar offset can, in principle, be solved analytically,however the solution must account for all ROI vertices and their connectivity,and is therefore cumbersome to specify in closed form. An alternativeapproach is to create an objective function based on the volumetric criteriaand optimize the planar offset. In practice, iterative bisection convergesquickly, reliably, is guaranteed to make forward progress at each iteration,and can directly use a volume estimate objective function.The algorithm proceeds by specifying the plane orientation (via a unitvector perpendicular to the final plane), a desired volume constraint (e.g.,the sub-segment on the positive side of the final plane should contain 23.46%of the whole ROI(s) volume), and a suitable tolerance (e.g., 0.05%). First,two planes with the given orientation that bound the whole ROI(s) arefound by scanning for extremal vertices. (An additional margin can beadded to improve convergence in some cases.) The volume of the (whole)ROI(s) is computed. Then, a loop is entered. First, the plane intersectingthe midpoint between the bounding planes is computed. The ROI(s) issegmented along it (planar segmentation). The volume of one sub-segment iscomputed and compared to the desired constraint. If it is within tolerance,segmentation is considered sufficient and iteration stops. Otherwise, oneof the bounding planes is replaced with the midpoint plane depending onwhether the segmented volume is above or below the criteria. The loop is124iterated until the stopping criteria is met.Bi-section is useful because it can be applied to any planar segmentationscenario; it does not need to be adapted in any way except to find useful initialbounds which is a minor, straightforward problem. Bi-section as applied inthis context can be thought of as a branch-and-bound algorithm [421]; thenumber of candidate planes are fixed spatially by the mid-point and harmonicsof the original bounding planes and form an infinite tree of potential solutions.The replacement of a bound by the midpoint at each step guarantees forwardprogress and also prunes the tree of unsuitable candidates which are thennever visited. These well-known characteristics have caused branch-and-bound methods to be widely applied for challenging computational problemsfor which no polynomial-time algorithms are known [422, 423, 424]. No priorrecord of application to the problem of ROI segmentation was found in theliterature.10.7 ConclusionsDICOMautomaton implements a novel ‘vector’ approach to ROI segmentation.Iterated bi-section of planar segmentation provides an efficient and robustway of partitioning ROI into sub-segments with specific volumetric criteria;only a cleaving plane orientation and tolerances must be specified.125Chapter 11Segmentation Methodology111.1 IntroductionHeterogeneous functional dose response for OARs is becoming increasinglyrelevant for clinical radiotherapy planning. In 2005, Konings et al. [348] foundevidence of region-dependent volume effects in rat parotid. Years later in 2010,as part of the encompassing Quantitative Analysis of Normal Tissue Effects inthe Clinic (QUANTEC) organ-focused reviews for clinical guidelines, Deasyet al. [236] concluded that better predictive models were needed to modelxerostomia risk. One factor recommended for investigation was whetherregions within the parotid could be located that exhibited variable dosesensitivity, increased or decreased functional burden, or otherwise controlledfunction preservation to a higher degree than surrounding tissues. Otherarticles in the same report provided similar recommendations for other organs[425, 426, 427]. In response, organ ROIs are increasingly being segmented orhandled heterogeneously to model dose response to various aspects withinthe organ. Reports of trials underway are emerging [357, 358, 428].Methods for complex contour segmentation, including planar segmen-tation, have been demonstrated in the literature [7] and were described in1The contents of this chapter and appendix A were submitted to Physics in Medicineand Biology under the title ‘Prefer Nested Segmentation to Compound Segmentation’ onthe 27th of October, 2016. The list of authors was Haley Clark, Stefan Reinsberg, VitaliMoiseenko, Jonn Wu, and Steven Thomas.126chapter 10. A recent paper by van Luijk et al. [357] made use of a planarsegmentation method in which fractional volumes were used to implement acompounded Boolean sub-segment selection mechanism. Here we show that,perhaps unintuitively, such a scheme will result in sub-segments of differingvolume depending on the shape of the ROI and selection location within it.Inconsistent segmentation volumes can be problematic for investigation ofsub-organ effects because sub-segments will represent inconsistent portions ofthe whole ROI. Performing sensitivity analysis, model fitting, or tests of asso-ciativity (e.g., correlation) will result in bolstered or undermined sub-segmentimportance, model parameters, or associativity, which must be corrected.We propose an improvement, which we call nested segmentation, that is“fair” in the sense that it will produce equal-volume sub-segments uniformlythroughout the ROI when the cleaving method is free of bias. Furthermore, itis robust – if the cleaving method is biased, as-fair-as-possible sub-segmentsare produced. It is also faster than compound segmentation, requiringequivalent or less geometrical processing. An implementation based onsegmentation of planar contours is tested using clinical data from 510 head-and-neck cancer patients.We also present two methods that can be used in conjunction with seg-mentation that help ensure an equal number of grid voxels (e.g., radiotherapydose matrix voxels) are contained within the boundaries of each sub-segment:oblique cleaving planes and grid supersampling. We show that both methodsameliorate issues arising from collinearity of dose grid and ROI boundaries.11.2 Materials and Methods11.2.1 SegmentationSegmentation2 refers to the process in which part of a volume delineated byclosed contour lines (i.e., a ROI) is partitioned into connected pieces (“sub-segments”) and one or more are retained (“selected”). We refer specifically to2Alternatively contour sub-segmentation or just sub-segmentation, to differentiate itfrom image segmentation.127segmentation, but the process is equivalent to volume truncation for polyhedraand generic division or partitioning of areas, volumes, and hypervolumes (e.g.,geometric primitives, such as triangles, spheres, and cubes). Sub-segmentselection can be accomplished in a variety of ways, but in this work wefocus on the method described by van Luijk et al. [357], which we refer toas compound segmentation. Our improved method, nested segmentation, isbelieved to be more robust toward the ‘fair distribution’ problems of ensuringthat selected sub-segments have equivalent volume and contain an equivalentnumber of entities (e.g., dosimetric grid voxels) regardless of the ROI shapeand selection location (e.g., periphery vs. centre). Salient differences aredescribed in the following subsections.11.2.2 Compound SegmentationCompound segmentation is a planar segmentation technique that makes useof (infinite) cleaving planes. The cleaved sub-segment faces are flat, andthus when the ROI is convex all cleaved surfaces remain convex. Compoundsegmentation proceeds by specification of cleaving plane orientations andvolume percentiles (i.e., fractional volumes). Each fractional volume (f ∈[0, 1]) unambiguously specifies a cleaving plane which contains f on one sideof the plane and 1− f on the other3. Each plane requires a single unit vectoror two free parameters to orient the plane. In [357] six planes are locatedand used to select a sub-segment interior to the boundary of a parotid ROI.There are three sets of parallel planes; each set is orthogonal to the others(see figure 11.1). Use of one less plane would permit selection of an arbitrarysub-segment with a single portion of the ROI surface4, use of two less planeswould permit either one or two disjoint ROI surface portions, etc..In compound segmentation, all cleaving planes are derived using per-centiles or fractional volumes that refer to the whole ROI. Only after allplanes are located is segmentation performed by application of cleaving planesto the ROI volume, and only the interior is selected.3Both f = 0 and f = 1 are ambiguous because they are not unique. The ambiguity isnot relevant for segmentation.4In the case of convex ROIs.128Figure 11.1: Demonstration of compound segmentation with threeparallel pairs of mutually orthogonal planes (six planes in total).11.2.3 Nested SegmentationWe propose an improved method in which sub-segments are selected as theinterior region between two parallel planes, as with compound segmentation,however cleaves are performed eagerly, before the next pair of planes can belocated. The location of cleaving planes are thus derived from the volumeof remaining sub-segments, not the original ROI (see fig. 11.2). As eachindividual stage of segmentation achieves a fair divvy of the remaining volume,sub-segments are expected to always contain an equivalent portion of theROI volume when the partitioning method is fair.11.2.4 ROI Segmentation ComparisonWe compare segmentation methods on a data set of 510 parotid glandROIs from 510 head-and-neck cancer patients (one per patient, to avoid anypotential bias from shape correlation between left and right parotid). Weperform segmentation to generate 3, 18, and 96 sub-segments from each ROI,chosen so that sub-segments are not excessively elongated along any onelinear dimension but the discrete axial nature is accommodated. 18ths and96ths segmentation used 6 cleaving planes (i.e., three mutually orthogonalsets of parallel planes) for each sub-segment whereas segmentation into thirdsused a single pair of planes parallel to the ROI contours. Because ROIsare defined in terms of equidistant, parallel, planar contours with no gaps,contour area is used as a surrogate for volume.129Figure 11.2: Demonstration of nested segmentation on a circle withf = 1/3. All sub-segments have area pir2/9.Each parotid in this data set includes a radiotherapy treatment planningdosimetric grid which is used to derive dose-volume statistics of interest. Wecompute the number of voxels lying within each sub-segment and comparedistributions for each sub-segment. Cardinal axes-aligned cleaving planesare often desired for ease of specification or bounding of anatomical regions(e.g., posterior region, lateral-caudal region, etc.). However, raster grids arecommonly aligned with the cardinal directions, and are in this data set, whichmakes perfectly fair partitioning of voxels impossible (i.e., due to collinearity;a row locally aligned with the contour boundary is either within or outsideof the sub-segment, but the row may contain many voxels). We employ twotechniques which can help to more fairly partition sub-segments: raster gridsupersampling and oblique cleaving planes. Supersampling used fine (15×)cubic interpolation so that each voxel was effectively interpolated into 225voxels. A cyclic rotation of 22.5◦ between cardinal axes was used to orientoblique planes.Contours are operated on directly rather than rasterizing them onto avolumetric grid. Bisection is used to locate planes corresponding to therequisite f . The bisection method used for R3 ROI segmentation had a130stopping tolerance set to 1% for all clinical data segmentation, but contourslying in planes parallel to the cleaving plane were treated atomically andwere thus indivisible. Parotids with few contours therefore could not achieve1% tolerance. Voxels for each dose matrix were of fixed volume, so summarystatistics about the distribution of sub-segment voxel counts estimate sub-segment volume.Segmentation into thirds employed only two planes parallel to contours.Nested and compound segmentation should produce identical results inthis case because only a single pair of cleaves are performed. However, itis challenging because contours are not divided in this case. We includethe comparison to demonstrate that bisection is produces sufficiently fairsub-segments. All ROI and dose manipulations were performed using DICOM-automaton [7, 411].11.2.5 StatisticsDistributions of volumes and voxels counts for sub-segments were comparedusing a non-parametric Kolmogorov-Smirnov test. The null hypothesis isthat one of the distributions is drawn from the same parent distributionas the other, so that the distributions are statistically identical. Individualsub-segment volumes are compared with other sub-segments in the sameROI using voxel counts to determine the spread due to the cumulativeeffects of the segmentation method and raster grid voxel alignment. TheQuartile Coefficient of Dispersion (QCD) provides a normalized measure ofthe dispersion of sub-segment areas for each patient [429]. Median QCD andmedian-normalized ranges are reported to characterize the population. Astandard statistical significance threshold (α) of 0.05 was used.11.3 Results11.3.1 Analytic ComparisonThe R2 analog to ROI segmentation is individual planar contour segmentation.We segment a circle of radius r into nine sub-segments using compound131Figure 11.3: Partitioning of a circle into nine sub-segments using com-pounded segmentation (exploded view). Each sub-segment isbounded by two parallel pairs of mutually orthogonal planes.segmentation (see fig. 11.3). The fractional area on the small side of eachcleaving plane is 1/3. Cleaving plane orientations are fixed, but the offsetsfrom the origin are unknown and are derived analytically or located through,e.g., bisection. Using elementary methods, it can be shown that the fractionalarea enclosed by a plane offset from the origin (n.b. a secant line) and aparallel plane intersecting the origin, in terms of their separation (h ∈ [0, r];i.e., the apothem; cf. [430]) isf =2pi(arcsinhr+h2r2cot arcsinhr). (11.1)Inversion is used to determine h. When f = 1/3, h ≈ 0.264932r. Derivation ofthe nine sub-segment areas is then straightforward (see fig. 11.4). Results aresummarized in table 11.1. The smallest, as a ratio of the ‘fairly distributed’area (pir2/9) is the centre sub-segment at ≈ 0.8043; the centre-adjacentsub-segments are the largest at ≈ 1.0978.Nested segmentation, on the other hand, generated sub-segments with132Figure 11.4: Calculation of sub-segment areas in terms of the areaof a wedge, right triangle, and square defined by f = 1/3,h ≈ 0.264932r, and r. Three distinct types of sub-segments areshown: (1) “corner,” (2) “centre,” and (3) “centre-adjacent.”Ratio of FairSub-segment (general f) (f = 1/3)centre 36pi(hr)20.804306×centre-adjacent 92f − 18pi(hr)21.097847×corner 94 (1− 2f) + 9pi(hr)20.951077×Table 11.1: Ratios of the fair fractional area for compound segmenta-tion sub-segments in terms of the apothem (h) and fractionalarea (f). All ratios are fractions of the fairly distributed area(pir2/9) in which each sub-segment has an equivalent area. Cen-tre sub-segments have four planar edges, centre-adjacent havethree, and corner sub-segments have two.equal area (see fig. 11.5). If all partitions can be made fairly, so that a cleavingplane that achieves the desired fractional areas is located exactly, then eachsub-segment area is tautologically known as the product of requested fractionalareas. For example, each final sub-segment in figure 11.2 has an area 1/3of 1/3 of the total. The first cleave is identical to compound segmentation133and so the apothem is given by eq. (11.1). Because nested segmentation is agreedy algorithm and the first cleave does not take into account later cleaves,sub-segments are in general asymmetric. The two asymmetries possible forsegmentation into nine sub-segments (n.b. with fixed cleave plane orientations)are shown in fig. 11.5.Figure 11.5: Nested segmentation of a circle into nine sub-segmentseach with area pir2/9. The orientation of the first cleave canbe chosen two ways. Both are shown. The cleaving orderis important in nested segmentation, but not for compoundsegmentation.Moving to R3, compound segmentation applied to a sphere partitionedinto 3×3×3 = 27 sub-segments yielded a centre sub-segment volume ≈ 0.596that of the fair volume. Centre-adjacent-adjacent sub-segments had areas≈ 1.105 that of the fair volume. Nested segmentation again produced fairvolumes that were tautologically, in this case, 1/27th of the whole. A sphereconstructed of discrete stacks of contours sharing a planar orientation, whichis common for medical image ROIs, approached both compound and nestedsegmentation results asymptotically as the contour thickness shrunk.11.3.2 Segmentation into ThirdsUsing compound segmentation, whole ROI were segmented into three sub-segments (faxial spanned[0, 13],[13 ,23], and[23 , 1]). Bisection was employedand cleaving planes were held parallel to contours. The median number ofvoxels in each sub-segment spanned 587.5− 605.0. The distribution of voxel134Figure 11.6: Depiction of the way in which the parotid gland ROIvolume was segmented to achieve sub-segments with volume 1/3that of the whole parotid. Nested and compound segmentationproduce identical results in this case.counts in cranial, middle, and caudal sub-segments were compared with aKolmogorov-Smirnov test. Each unique comparison in {left, right} parotid ⊗{cranial, middle, caudal} sub-segments was performed, yielding ten tests. Inall cases the two-sided p > 0.20. These tests indicate the bisection approachresults in appropriately partitioned sub-segments that contain 1/3 of theoriginal parotid volume without systematic bias detectable at the α = 0.05level. Results were identical for nested segmentation.11.3.3 Segmentation into 18thsFigure 11.7 shows nested and compound segmentation of whole parotid into 18sub-segments. Sub-segments are composed of axially-adjacent slices coloureduniformly5. Both faxial and fsagittal spanned[0, 13],[13 ,23], and[23 , 1]; fcoronalspanned[0, 12]and[12 , 1]. The cleaving order was axial→ coronal→ sagittal.As can be seen in figure 11.7, nested and compound method sub-segment5Colours were chosen for maximum contrast using a modification of the palette describedin [431].135Figure 11.7: Depiction of nested (left) and compound (right) segmen-tation of whole parotid (centre) into 18 sub-segments.locations differ only slightly. However, it is apparent that sub-segments inthe compound method do not all have equivalent volume.Using compound segmentation without supersampling or oblique cleavingplanes, sub-segment voxel counts had a mean of 100.0 voxels within eachsub-segment (std. dev. = 64.0; std. dev. of the mean = 0.7; median = 92.0).The median number of voxels in each sub-segment spanned 38− 152. Only57.6% of sub-segment voxel counts had an absolute percent difference of lessthan 50% of the mean. Direct comparison of the voxel count distributionswithin sub-segments was performed using Kolmogorov-Smirnov tests. Uniquecomparison of all 18 sub-segments required 153 tests – in 124 cases (81%) thenull hypothesis failed to be rejected and distributions were found to differsignificantly (i.e., p < 0.05 in 124 cases). Skewness of the combined voxelcount distribution was 0.991 using the ratio of moments technique, whichindicates a strong positive skew. However, the mean voxel count in eachtype of sub-segment were more symmetrically distributed with a skewnessof 0.075 and a std. dev. = 28.0. No significant correlation was detectedbetween the average sub-segment mean voxel count and position relativeto the parotid centre (e.g., with relativity denoted by −1, 0, or +1 in thecardinal directions).Using nested segmentation without supersampling or oblique cleavingplanes, sub-segment voxel counts again had a mean of 100.0 voxels within136each sub-segment (std. dev. = 49.8; std. dev. of the mean = 0.6; median= 97.0). However the median number of voxels in each sub-segment spanned92.5 − 101. 70.2% of sub-segment voxel counts had an absolute percentdifference of less than 50% of the mean. Direct comparison of the voxel countdistributions within sub-segments using Kolmogorov-Smirnov tests showedthat the null hypothesis failed to be rejected in only 2 of 153 (1.3%) cases(i.e., p < 0.05 in 2 cases).11.3.4 Segmentation into 96thsFigure 11.8: Depiction of nested (left) and compound (right) segmen-tation of whole parotid (centre) into 96 sub-segments.For segmentation into 96ths, both faxial and fcoronal spanned[0, 14],[14 ,12],[12 ,34], and[34 , 1]whereas fsagittal spanned[0, 16],[16 ,13],[13 ,12],[12 ,23],[23 ,56],and[56 , 1]. The cleaving order was axial → coronal → sagittal. As can beseen in figure 11.8, nested and compound segmentation again produce similar-shaped sub-segments in roughly similar locations. However, compoundsegmentation produces sub-segments with substantially different volumes,such as those with vanishingly small volume (in the centre-bottom of fig. 11.8;right side). The comparable nested segmentation sub-segments, on the otherhand, are larger and have the same apparent volume as all other sub-segments(left side of fig. 11.8). Nested method sub-segment median QCD were lessdisperse than the compound method (0.097 vs. 0.37). Oblique planes reduceddispersion nearly 25× for nested method sub-segments (0.097 → 0.0041).Conversely, they increased compound method dispersion (0.37→ 0.46).137Compound NestedOblique + Supersampling Unmodified Oblique Supersampling Oblique + SupersamplingMedian range 91.5− 13829 20− 30 18− 20 4027.5− 4200 4212− 4287Median 5558 24 19 4103 4246Range/Median 2.47 0.417 0.105 0.042 0.018Sig. K-S tests 2435 (53.3%) 258 (5.7%) 1 (0.02%) 0 (0%) 0 (0%)QCD 0.46 0.097 0.0041 0.097 0.0041Runtime 143ms 36ms 29ms 135ms 131msTable 11.2: Comparison of median voxel counts, quartile coefficients of dispersion (QCD), and runtime forcompound and nested segmentation. Sig. K-S tests refers to the number of statistically significantKolmogorov-Smirnov tests (out of 4560; α = 0.05). Runtime is per (individual) sub-segment and wasmeasured on an Intel® Xeon® X5550 CPU. The use of oblique cleaving planes and fine supersamplingreduced sub-segment median voxel range relative to the median.138A comparison of voxel counts and runtime for compound and nestedsegmentation is summarized in table 11.2. Using compound segmentationwithout supersampling or oblique cleaving planes led to unusable data; foreach sub-segment, at least one patient had a vanishingly small sub-segmentencompassing zero voxels. Using fine supersampling and oblique planes, sub-segment voxel counts had a mean of 6244.5 voxels within each sub-segment(std. dev. = 4417.6.0; std. dev. of the mean = 96.1; median = 5558.0).The median number of voxels in each sub-segment spanned 91.5 − 13829,encompassing two orders of magnitude. Direct comparison of the voxel countdistributions within sub-segments via Kolmogorov-Smirnov tests showed thenull hypothesis failed to be rejected and distributions were found to differsignificantly in 2435 of 4560 (53.3%) unique test cases (i.e., p < 0.05 in 2435cases).Nested segmentation was markedly different. Using nested segmentationwithout supersampling or oblique planes, sub-segment voxel counts had amean of 27.2 voxels within each sub-segment (std. dev. = 12.3; std. dev.of the mean = 0.15; median = 24.0). The median number of voxels ineach sub-segment spanned 20 − 30. Direct comparison of the voxel countdistributions within sub-segments via Kolmogorov-Smirnov tests showed thenull hypothesis failed to be rejected and distributions were found to differsignificantly in 258 of 4560 (5.7%) unique test cases (i.e., p < 0.05 in 258cases). Applying the oblique planes method yielded a mean sub-segmentvoxel count of 19.4 voxels within each sub-segment (std. dev. = 9.0; std.dev. of the mean = 0.04; median = 19.0). The median number of voxels ineach sub-segment spanned 18 − 20. Direct comparison of the voxel countdistributions within sub-segments yielded significance in a single case outof 4560 (0.02%; i.e., p < 0.05 for the Kolmogorov-Smirnov test in one case).Applying supersampling with axis-aligned planes yielded a mean sub-segmentvoxel count of 4199.3 voxels within each sub-segment (std. dev. = 2139.3; std.dev. of the mean = 9.7; median = 4103.0). The median number of voxelsin each sub-segment spanned 4027.5 − 4200. No voxel count distributionswere significantly distinct according to the Kolmogorov-Smirnov test (i.e.,p < 0.05 in zero of 4560 tests).139Using both oblique planes and supersampling improved fairness of nestedsegmentation even more, though either oblique planes or supersampling alonewere sufficient for most purposes. The mean sub-segment voxel count was4270.2 voxels within each sub-segment (std. dev. = 2004.8; std. dev. ofthe mean = 9.1; median = 4246.0). The median number of voxels in eachsub-segment spanned 4212 − 4287. Direct comparison of the voxel countdistributions again found no significantly distinct distributions (i.e., p < 0.05in zero of 4560 tests).11.4 DiscussionPlanar segmentation can be accomplished using a variety of existing tools, e.g.,via Boolean structure combination [432, 433], conversion of ROIs to polygonsurface meshes and computing the intersection [414, 415] or via tessellation[434], or directly on ROI contours via bisection [7]. Whatever the method,sub-segments are effectively specified by the fractional volume between mu-tually orthogonal pairs of cleaving planes. It may then seem intuitive thatsub-segments with the same fractional volume between bounding planes,but at different positions in the ROI, would have the same volume. Thisintuition is valid for nested segmentation, but not for compound segmentation.Compound segmentation only generates fair sub-segments when the ROI isrectangular and faces are aligned with the cleaving planes, and thus may leadto erroneous conclusions if used for sub-segment comparison. A number ofarticles investigating the link between patient outcomes and radiotherapydose to parotid sub-volumes have recently emerged [324, 358, 428] and useof compound segmentation has been reported in the literature [357]. Theaim of this study was to demonstrate that nested segmentation is fairerthan compound segmentation, and should be preferred for analyses involvingsub-segment comparison.By analytically solving R2 and R3 analogues, we showed that compoundmethod sub-segments have intrinsically non-uniform area/volume. In R2,compound method centre sub-segment area differed from that of adjacentsub-segments by nearly a third of the fair area. The problem grew worse140in R3 with the difference assuming more than half the fair volume. Nestedmethod sub-segments were fair in both cases.The successful segmentation of clinical ROIs into thirds indicates bisectionis appropriate for locating cleaving planes despite being unable to fairly parti-tion due to discrete nature of contours along the axial direction. Compoundsegmentation into 18ths was not fair. Distribution skewness and distinctnesstests imply that the parotid was not fairly partitioned into sub-segmentsof equivalent volume. At the same time, the lack of correlation betweensub-segment mean voxel count and relative position indicates the bisectionapproach is not systematically biasing results and that sub-segment volumesappear to be comparable on average. Nested segmentation, in comparison,was fair. Distribution distinctness test results were substantially improvedcompared with compound segmentation (2 vs. 124 of 153 tests found distinctdistributions). The low number of distinct distributions (1.3%) was compara-ble with the bisection tolerance (1%) and therefore represents an acceptabledeviation. Performance on the Kolmogorov-Smirnov test is notable becausethe transverse cleave generally can not achieve fair cleaving. The transversecleave was performed first, and it is apparent that subsequent cleaves arefairer than those of compound segmentation.The distinction between compound and nested segmentation was em-biggened by segmentation into 96ths. Some peripheral compound methodsub-segments with vanishingly small volumes – even when oblique planes andintensive supersampling were employed. Nested method sub-segments werenot quite fair when oblique planes and supersampling were abstained from(5.7% of Kolmogorov-Smirnov tests were significant), but this was correctedwhen oblique planes, supersampling, or both were employed (0.02% or less inall cases). The normalized range of voxels contained within a sub-segmentdropped when using oblique planes or supersampling, indicating sub-segmentvolumes became fairer when either were employed. Compared to compoundsegmentation, nested segmentation produced normalized ranges that weretwo orders of magnitude smaller. Additionally, QCD differed by 1-2 orders ofmagnitude depending whether oblique planes were used, suggesting nestedmethod sub-segments were substantially less disperse, and thus more uniform,141than compound method sub-segments. These observation support the claimthat nested segmentation is resilient to partitioning errors. When a faircleave could not be located, i.e., due to discrete nature of contours alongthe axial direction, child sub-segments were made as fairly as possible (i.e.,sub-segments equally shared the remaining volume with sibling sub-segments).The increase of dispersion noted in compound method sub-segments whenoblique planes were used supports the claim that compound segmentationintrinsically can not fairly partition ROIs.Nested segmentation was not only fairer than compound segmentation,but it was also faster. Sub-segments have planar edges/faces that can bedescribed with few vertices. In nested segmentation, recursive segmentationneed only process a simplified geometry for each planar edge/face. The fullROI is processed once; afterwards, each additional segmentation is continuallyreduced by the increasing number of planar edges. Compound segmentation,however, must continually re-process the full ROI. The exact speed-updepends on ROI geometry, contour sampling density, and nesting depth.One downside of nested segmentation is that the shape of sub-segmentsdepends on the order of cleaves, resulting in shape asymmetries. For example,when partitioning a circle into 1/6 using three orthogonal sets of parallelcleaving planes, both compounded and nested segmentation perform the samefirst cleave (f = 1/3), which results in a plane with distance h ≈ 0.264932rfrom the centre of the circle. The compound method finds the second cleavein the orthogonal direction to have the same distance from the centre, whichresults in lower-than-fair sub-segment area, whereas the nested segmentationmethod finds h ≈ 0.329392r, which makes the sub-segment area fair (= pir2/9)but is asymmetric. A perfectly symmetrical method may be possible andwould find h = r√pi/36 ≈ 0.295408972r in both directions, but wouldrequire advance knowledge of all intended fractional volumes and cleavingplanes and would most likely require an iterated relaxation step. A perfectlysymmetrical segmentation method may be possible, but would most likelyrequire iteration or back-tracking and re-processing whole ROIs for eachsub-segment. In contrast, nested segmentation requires neither back-trackingnor re-processing geometry. Nested segmentation is directly applicable to142organs where anatomical structure is ignorable or a priori unknown. It canalso be employed within larger anatomical groupings, such as within lobes orcavities (e.g., liver, lung), and can make use of oriented cleaving planes orshuffled cleaving orders that align with local anatomy (e.g., muscle tissues,vessels, ducts). The use of planar segmentation combined with (iterated)bisection is a flexible paradigm that enables the use of individual R2 contours,raster grids, disconnected collections of contours, contours with holes, andvolumetric surface manifolds, and would therefore be suitable addition tosoftware packages that can potentially operate on any such primitives (e.g.,[7, 433]).It is worthwhile to compare an alternative routine that would use relax-ation to adjust sub-segment locations based on a penalty function, heuristic,or clustering. The method of nested segmentation is fast and requires nobacktracking or recomputation. A technique based on clustering or optimiza-tion would likely require iterated relaxation. An improved method would beaware of the entities within the sub-segments (e.g., voxel count) but as shownit may be impossible to make perfectly fair partitions even if there is specificknowledge of each entity. Nested segmentation is therefore not substantiallyworse than a more advanced algorithm, but is extremely easy to implementand verify.Oblique cleaving planes addressed the issue of ROI segment and voxelgrid collinearity, but can result in awkward plane orientations in some cases.There is an optimal cleave plane orientation that can be determined exactlywhen sub-segment extents are known. The optimal angle is found for somespecial cases in R2 in a appendix A. This orientation maximizes the minimumspacing between voxel distances to the plane, ensuring small changes inthe plane position results in the smallest possible number of voxels crossingthe plane at one time (e.g., minimizing spatial resonances). Unfortunately,even estimation is difficult and costly [435, 436] so throughout this work acyclic rotation of 22.5◦ between cardinal axes defined by the Cartesian dosegrid was assumed. Supersampling is also useful for improving sub-segmentfairness, though it can not itself help the collinearity issue if planes areaxes-aligned. However, when oblique planes and supersampling are combined,143supersampling will reduce the amount of obliquity needed, which can assistin adapting to underlying anatomy. It will also result in sufficiently fairsub-segments if supersampling can be performed to an arbitrary level, thoughit is computationally difficult and questionable to supersample too finely.Oblique planes were more computationally efficient than supersampling, butapplication of either method independently for nested segmentation into 96thsresulted in small median voxel ranges and acceptably indistinct distributions(i.e., > 99.9% with p > 0.05).11.4.1 ConclusionsNested segmentation was found to be superior to compound segmentationwhen sub-segment volume consistency is needed.144Chapter 12Parametric Approach toRegional Effect Assessment112.1 IntroductionCurrent clinical guidelines recommend treating the parotid gland as a parallelorgan and advocate use of whole parotid mean dose thresholds for sparing[236]. However, mounting evidence suggests there may be dosimetricallycritical sub-structures within the parotid that strongly influence productionof saliva after radiotherapy [324, 357, 358].Volume effects in parotid have a storied history, and many attemptshave been made to locate critical regions and elucidate the mechanism(s) ofdysfunction. In 2005, prompted by the spread of IMRT and the correspondingneed for assessment of independent functional unit distribution within theparotid, Konings et al. reported observing region-dependent late volumeeffects in rat parotid [348]. Dose delivered to cranial and caudal parotid halvesresulted in different outcomes; salivary dysfunction was more pronouncedafter irradiation of the cranial aspect. Additionally, cranial aspect irradiation1The contents of this chapter have been submitted to Acta Oncologica under the title‘Caudal Aspects of the Parotid Gland are Most Important for Radiation-Induced SalivaryDysfunction’ on the 15th of November, 2016. The list of authors was Haley Clark, StevenThomas, Jonn Wu, Allan Hovan, Carrie-Lynne Swift, and Stefan Reinsberg.145caused secondary damage to appear in the non-irradiated caudal aspect.Konings et al. surmised that the effect was caused by injury to majorexcretory ducts, blood supply, and innervation in the region between ventraland dorsal lobes. Dijkema et al. reported in 2008 that mean dose modelsanomalously failed to describe human parotid function loss when comparingconventional radiotherapy to IMRT [355]. In particular, dose-response ‘left-shifted’ compared to conventional radiotherapy, meaning lower doses wererequired to achieve the same loss of function. They also hypothesized thatthe pervasive low dose spread by IMRT throughout the parotid might directlycause dysfunction via acinar cell plasma membrane damage. In 2009, vanLuijk et al. noticed that earlier studies, including that of Dijkema et al.and Konings et al., could be consolidated using a so-called bath-and-showereffect. This effect, which is more well known to occur in spinal cord, causesthe impact of radiation damage to a contained aspect of the parotid to beexacerbated by a lower dose to surrounding tissues [356]. van Luijk et al.demonstrated the effect in rat parotid and hypothesized that, analogouslyto spinal cord, enhanced radiation damage might be caused by depletion ofstem/progenitor cell populations within excretory ducts. They also surmisedthat hampered cell replenishment would stymie recovery. Transplantation ofstem cells have since been found to aid functional recovery [214, 360, 361].Meanwhile, the primary aim of concurrent observational studies was tolocate critical regions so as to alter the dose profile and naturally facilitaterecovery and prevent, rather than correct, functional loss. Buettner et al.in 2012 reported that the use of dose distribution descriptors (moments)improved prediction of xerostomia over whole parotid mean dose [233]. Usingmoments, they demonstrated that a concentration of dose in the medial-caudal aspect is preferable to homogeneous delivery across the whole parotidwith the same mean dose, demonstrating, observationally, a region-dependentbath-and-shower effect in human parotid. More recently, in 2015, Clark etal. employed sub-segmentation to partition ROI, including ‘cleaving’ segmen-tation with coronal and sagittal planes to generate volumetric halves [324].As a whole, evidence of regional variations was negative, but, owing to thedirect approach taken, function loss profiles were distinctly and significantly146related to the mean dose of individual parotid aspects. Shortly thereafter vanLuijk et al. also applied planar segmentation, but instead used axial planes[357]. A confined critical region was identified near the middle-dorsal edge ofthe mandible. Focused dosimetric and histopathological work with animalparotids were used to support their finding, and an in vitro human samplewas found to contain stem/progenitor cells in the vicinity of the critical area.Most recently, Miah et al. showed that bilateral sparing of the superficiallobe – not the edge adjacent to the dorsal edge of the mandible – will reducesevere xerostomia compared to the more conventional approach of sparingthe whole contralateral parotid [358].Recent findings have generated excitement (e.g., a recent article entitled“Radiation-induced salivary hypofunction may become a thing of the past”[437]). However, several issues remain. First, there is not yet consensuson the location of the most critical region(s). Second, varied or relativelysmall cohorts (N < 100) have been used to produce these findings. Third,disproportionate representation of parotid aspects or multiple comparisonmay have inadvertently been applied when comparing candidate regions.Finally, no interventional trials have thus far been reported; only data fromanimal and observational studies have been used. The latter shortcomingis especially significant because clinical best practices impose strong dosecontraints on contralateral parotid. Coupled with the small spatial extent ofparotid, dose profiles are therefore likely to exhibit strong inter- and intra-parotid correlation. Regressor correlation will confound relative importanceanalysis [438].In this work, the theory that there are dosimetrically critical sub-structureswithin the parotid that strongly influence production of saliva after radiotherapyis tested. A single, large (N=332), prospectively-collected clinical cohortis analyzed. Instead of relying on direct comparison of correlate measuresor model goodness-of-fit metric, relative importance of organ sub-segmentsare assessed using sensitivity analysis, explained variance methods, andimportance drawn from ranking of candidate models that exclusively andproportionally represent individual sub-segments. Regressor correlation isanticipated and managed. Entire parotid volumes are segmented into sub-147segments with equal volumes instead of relying on any ‘central’ points orregions of varying extent. Sub-segment proportionality is ensured. Sub-segment extent does not depend on arbitrary parameters other than choiceof segmentation, and segmentation is varied to minimize impact on ourfindings. No individual statistical metric is relied upon; multiple comparisonsare avoided by applying importance methods in orthogonal domains, notrepeating individual statistical tests, and with ranking, rather than absolutecomparison. Finally, our analysis procedure was developed with a clinicalfocus so that the location of critical region(s) can be identified using onlytreatment planning ROIs, instead of requiring detailed knowledge of structure(e.g., lobes, fine anatomy, or functional information).12.2 Materials and Methods12.2.1 Cohort Selection, Quality Assurance, DosimetricExtractionThis provisional study passed institutional ethical review. All patients gaveinformed consent. Stimulated saliva was measured prior to radiotherapy(‘baseline’; Wb) and both 1y (W1y) and 2y (W2y) following treatment by mea-suring accumulated whole-mouth spittle stimulated by chewing unflavouredparaffin wax over 5 minutes. Patients were excluded if: W1y/Wb > 5 (i.e.,accounting for naturally low baseline and standard measurement variability);salivary glands were surgically removed; parotids had tumour involvement;or they received atypical chemotherapy agents, electron therapy, or previousinterfering radiotherapy. Radiotherapy planning ROI contours were scruti-nized by a single senior head and neck oncologist (JW). The entire cohortwas collected within the BC Cancer agency.Ipsilateral (i.e., ‘hot’) and contralateral (i.e., ‘cold’ or ‘spared’) parotid aredifferentiated by clinical guidelines. This distinction was carried forward intoour analysis. Sub-segments with equal volume were generated using nestedsegmentation (n.b. discussed in chapter 11). Dosimetric data extraction andROI manipulation were accomplished with DICOMautomaton [411].14812.2.2 ModelsModels were fitted to saliva measurements via sub-segment mean dose regres-sors. Earlier work with non-parametric methods by Clark et al. demonstratedthe dose-response shape for various sub-segments is primarily linear [324]. Inthis work, four prototypical linear models were considered. We demonstratetheir form for 1/2-volume cranial-caudal segmentation. The first prototype(“lin-split”) combines regressors without co-linkage except a shared intercept.The form isW1yWb= A− biuM iu − bcuM cu − bilM il − bclM cl . (12.1)A is the intercept, M iu refers to the mean dose delivered to the (u)pper (i.e.,cranial) sub-segment of the (i)psilateral parotid, and bcl is the (c)ontralateral(l)ower (i.e., caudal) sub-segment slope. Ipsi- and contralateral sub-segmentsslopes are independent, permitting individual assessment. The second proto-type (“lin-locked”) unites regressors (left-right) providing combined ipsi- andcontralateral parameters. The form isW1yWb= A+ bu(M iu +Mcu)+ bl(M il +Mcl). (12.2)The third prototype provides sub-segment-exclusive variations of the “lin-split”type (e.g., cranial only: “lin-split-cranial“). The fourth provides sub-segment-exclusive variations of the “lin-locked” type. Sub-segment-exclusive modelranking provides relative importance derived from foundational informationtheory [439].Exponential models are recommended for whole parotid in the literature(e.g., [26]). No specific recommendation for or against exponential models wasfound for sub-segments, so analogous exponential prototypes were included.The first prototype (“exp-split”) isW1yWb=A4(e−αiuMiu + e−αcuMcu + e−αilMil + e−αclMcl). (12.3)Every regressor has a pseudo-slope. The factor A consumes the ‘scaling’149degree of freedom consumed by the linear A. Exponential prototype #2(“exp-locked”) has the formW1yWb=A4(e−αuMiu + e−αuMcu + e−αlMil + e−αlMcl). (12.4)As with linear prototypes, the third and fourth exponential prototypes aresub-segment-exclusive. Exponential models are scaled such that A is unityunder the null hypothesis.12.2.3 StatisticsA standard statistical significance threshold (α) of 0.05 was used. Modelsare compared primarily on the basis of Akaike’s Information Criterion (AIC)[440], but Mean Absolute Error (MAE) is also considered. AIC ranks modelson the basis of an information-theoretic argument by accounting for bothgoodness-of-fit and model complexity. Akaike Weights (AW) are used toestimate the relative importance of groups of models (e.g., caudal vs. cranial,linear vs. exponential) [439]. Throughout, AW are used to report family-wisepercentage-normalized Relative Importances (ARI) that describe the like-lihood of the stated factor being most important. MAE and other relatedmetrics, e.g., Root-Mean-Square Error (RMSE), eschew model complexityand characterize predictive power. There is debate over the appropriatenessof MAE and RMSE for model comparison [441]. Both are common. MAEweights residuals equally, whereas RMSE gives higher weight to larger residu-als, bolstering importance. Because whole-mouth salivary measurements arenoisy, MAE was chosen. Model ranking performs dual function; identificationof the best model(s) and factor importance assessment. Therefore, both AICand MAE are considered when rejecting models.To ensure an apples-to-apples comparison, linear and exponential modelswere fitted identically. A good model fit will have residuals that are notdependent on the regressors and distributed randomly (i.e., not systematically)about zero [442] when noise is normally distributed. However, baseline-normalized salivary measurements will not be normally distributed (norhomoscedastic) so residual normality was not tested. Instead, the non-150parametric ‘runs’ test was used to test for residual sign autocorrelation (i.e.,detecting conspicuously consecutive runs of positive or negative residuals)[442].Besides importance derived from AIC model ranks, fitted parameters arereported for representative models and compared (sensitivity analysis). Athird class of methods that estimate ‘dispersion’ importance via ascribingfractions of the explained variance to individual regressors are also used[438]. Permutation methods (a.k.a. averaging over orderings methods) arerepresented by the ‘LMG’ measure of Lindeman, Merenda, and Gold [443].Permutation methods are robust to multicollinearity, but are computationallydemanding [438]. Another, simpler, less robust measure (referred to as‘LI’) is employed as foil to LMG. It uses the increase in the coefficient ofdetermination when including each regressor after all others are included.Since parotids have limited spatial extent, multicollinearity is anticipated.Spearman’s rank correlation coefficients (ρ) are reported for adjacent andpairwise (left-right) sub-segment mean doses.12.3 Results12.3.1 Mean-scaling 2y Expectorate MeasurementsThis work focused on late dysfunction. It is not a priori clear what follow-uptime is sufficient to capture late dysfunction, but based on section 6.7.2salivary measurements appear to stabilize prior to the one year follow-up andremain approximately static, on average, until the two year follow-up. Manypatients were unable to attend, or declined to attend either one year or twoyear follow-ups. We believe random factors contributed most significantly topatients missing follow-ups (e.g., patient commute being too far or challenging,recurrence leading to a second, interfering radiotherapy treatment), and socompared W1y and W2y distributions for equality. The hypothesis was thatone year and two year follow-ups yield whole stimulated saliva measurementsthat can be considered drawn from the same base distribution. In other words,that patient-specific W1y is identical to W2y and can be used as surrogates for151one another. A Kolgomorov-Smirnov test showed that the distributions arenot significantly distinct (two-sided p = 0.12), but the means (W1y = 4.02g/5min and W2y = 4.64 g/5min) differed by 13% of W2y. Scaling W2yby W1y/W2y also led to two significantly indistinct distributions (two-sidedp = 0.63), but the means were identical. For reference, a comparison of Wband W3m yield a significant distinction (two-sided p < 0.0001), with means(7.00 g/5min and 3.02 g/5min, respectively) which differed by 132% of W3m.Subtraction of W1y/Wb and W2y/Wb (for patients with both measurementsonly) resulted in a distribution that was not normal according to Shapiro-Wilk (p < 0.001), Anderson-Darling (p < 0.001), or Pearson’s χ2 (p = 0.012)normality tests. Subtraction of W1y/Wb and mean-scaled W2y/Wb achievednormality according to the Pearson’s χ2 normality test (p = 0.077) butnot Shapiro-Wilk or Anderson-Darling tests. However, the distribution wascentered near zero and evenly distributed with 57% of differences lying tothe left of zero (see figure 12.1) so we believe the distribution is ‘normalenough’ for purposes of this work. The average W1y/Wb was 0.584 if twoyear measurements were not used (N = 303), 0.580 (N = 332) if W2ywere substituted for missing W1y, and 0.577 (N = 332) if mean-scaled W2ywere substituted. Based on these findings, mean-scaled W2y were used assubstitutes for missing W1y as-needed in 29 cases. The total number ofpatients available for analysis was 332.12.3.2 Distribution of Baseline-Normalized SalivaryMeasurementsSalivary measurements are not normally distributed. First, they cannot benegative. Second, they ‘lean’ toward zero. Normalization using the baselinemeasurement (e.g., W1y/Wb) is a simple way to account for per-patientvariability. It also, unfortunately, results in a heteroscedastic dependentvariable.The distribution of baseline-normalized salivary measurements is not apriori known. Using quantile-quantile plots [444] and the graphical methodproposed by Cullen and Frey [9, 445], we have empirically determined thatthe distribution is approximately equal parts gamma and log-normal (i.e.,152Figure 12.1: Kernel density estimate of the difference betweenW1y/Wband mean-scaled W2y/Wb. The optimal bandwidth was esti-mated by the method of [8].Weibull [446]; see fig. 12.2 and fig. 12.3.) Both distributions are amenableto maximum likelihood estimation via least-squares [447, 448]. While fittedparameter uncertainty estimates may be skewed or unreliable on account ofnon-normality of fitted model residuals, no importance is derived from thesequantities and they are inconsequential to our analysis.153Figure 12.2: Quantile plot showing clear deviation from normality, butconsistency with a gamma distribution.12.3.3 Whole ParotidWhole parotid sample mean doses for ipsi- and contralateral parotid were30.50± 0.69 Gy and 16.67± 0.44 Gy respectively (± std. dev.). Mean dosesin this cohort were relatively ergodic. Figure 12.4 shows a scatterplot ofthe whole ipsi- and contralateral parotid mean doses. The region aroundthe QUANTEC clinical limits can be seen to be more densely sampled thansurrounding areas. Spearman’s rank correlation coefficient between ipsi- andcontralateral dose was 0.484.Whole parotid mean dose was modeled to establish baseline AIC. The154Figure 12.3: Distribution classification plot as proposed by Cullenand Frey [9]. 5000 bootstraps were performed. The empiricaldistribution is approximately equal parts gamma and log-normal.linear model performed best, with AIC 469.60, compared to the exponentialmodel (AIC +5.20; AW 0.07). Contralateral parotid dose-response slopesdominated ipsilateral in both linear (0.014± 0.003 Gy-1 vs. 0.0003± 0.0020Gy-1) and exponential models (0.044± 0.027 Gy-1 vs. 0.0061± 0.0066 Gy-1).Intercepts spanned 0.84-0.86 and MAE was 0.30 in both cases. The proportionof variance explained by the linear model was 7.7%. Both LMG and LImeasures showed the contralateral parotid to be substantially more important(both >7.0×).155Figure 12.4: Scatterplot of whole ipsi- and contralateral parotid meandoses.12.3.4 Cranial-Caudal 1/2-Volume Sub-SegmentsParotids were segmented into cranial and caudal halves. Sub-segment meandoses were significantly correlated when comparing adjacent sub-segments(i.e., cranial vs. caudal) in the ipsilateral parotid (Spearman’s ρ = 0.732)and contralateral parotid (0.640) and also when comparing pairwise cranial(0.551) and caudal (0.469) sub-segments (two-sided p < 0.0001 in all cases).The average cranial sub-segment mean dose was 17.19 Gy (min 0.02 Gy,max 72.10 Gy) whereas it was 29.98 Gy (min 0.03 Gy, max 72.68 Gy) forcaudal sub-segments; both had absolute percent differences of 25% with whole156parotid mean dose. In every patient at least one caudal sub-segment (i.e., leftor right) received a higher mean dose than the adjacent cranial sub-segment.Linear models fitted with the generic nonlinear regression framework wereidentical to those of ordinary least-squares. Table 12.1 shows model qualityparameters. Fits converged without issue. Runs tests were not obviouslycorrelated with either AIC nor MAE, but were highest for cranial-only andlocked variant models. The overall best performing model in terms of AICand MAE was lin-split (table 12.2). The ‘-split’ variants outperformed ‘-locked’ variants (AIC and MAE; ARI: 89.2% vs. 10.8%). Linear modelsoutperformed exponential models (ARI: 70.7% vs. 29.3%). Caudal-onlymodels performed better than their cranial-only counterparts in all cases andalso family-wise (ARI: 82.1% vs. 17.9%); caudal-only model AIC was reducedby at least two compared with their cranial-only counterpart. Additionally,some of the lowest AIC models (n.b. those performing best) were caudal-only.Conversely, the three models with the highest AIC (n.b. those performingworst) exclusively featured the cranial sub-segment. MAE were similar forall models.Model DOF MAE AIC AWlin-split 327 0.30 472.99 0.308lin-split-caudal 329 0.30 473.12 0.288exp-split 327 0.30 475.15 0.104exp-split-caudal 329 0.30 475.18 0.103lin-split-cranial 329 0.30 475.79 0.076exp-locked 329 0.30 477.28 0.036exp-locked-caudal 330 0.30 477.51 0.032lin-locked-caudal 330 0.31 478.56 0.019lin-locked 329 0.31 479.27 0.013exp-split-cranial 329 0.31 479.29 0.013exp-locked-cranial 330 0.31 481.42 0.005lin-locked-cranial 330 0.31 482.32 0.003Table 12.1: AIC-ranked W1y/Wb regression models using 1/2-volumesub-segments. Models are ranked by AIC (lower is better). Allquantities are dimensionless. AW denotes the Akaike weight. Inall cases pruns > 0.14.157Fitted parameters for the best whole-parotid models are shown in ta-ble 12.2. In all three models caudal sub-segments play a more dominant rolethan cranial sub-segments. Lin-split and exp-locked models provide the mostcompact slope estimates. In these models the caudal sub-segment slope was1.5-3.6× larger than the cranial slope.Model Param. Estimate Std. Err.lin-split A 0.819 0.070biu 0.0026 0.0034bcu 0.0056 0.0057bil −0.0020 0.0031bcl 0.0085 0.0037exp-split A 1.07 0.14αiu 0.004 0.010αcu 0.034 0.063αil 0.41 0.88αcl 0.033 0.054exp-locked A 0.925 0.098αu 0.0102 0.0093αl 0.036 0.022Table 12.2: Parameters for the best 1/2-volume W1y/Wb whole-parotidregression models. All parameters except A have units Gy-1;A is unitless. Superscripts denote (i)psi- and (c)ontralateral;subscripts denote (u)pper (cranial) and (l)ower (caudal) sub-segments.The proportion of variance explained by the top model, lin-split, was 7.9%.If patients missing W1y were excluded or mean scaling of W2y was not used,the fitted model was slightly worse, explaining only 7.7% or 7.8% respectively.The relative importance of the four sub-segment mean dose regressors wereestimated with explained variance measures. Contralateral parotid was moreimportant than ipsilateral (combined: 5.8× by LMG, 6.3× by LI), and caudalsub-segments were more important than cranial (combined: 1.3× by LMG,3.8× by LI). The single most important sub-segment was caudal (both LMGand LI).15812.3.5 Cranial-Caudal 1/3-Volume Sub-SegmentsParotid were segmented into cranial, middle, and caudal thirds. Combinedleft-right sub-segment average mean dose for cranial was 15.48 Gy, for middlewas 23.1 Gy, and for caudal was 32.7 Gy. In all cases extrema were <0.03Gy and >72.11 Gy. Caudal and cranial sub-segment average mean doses hadabsolute percent differences spanning 31-49% with whole parotid. Middle sub-segments had percent differences of −0.2% and 0.1% (ipsi- and contralateralparotids, respectively), implying middle sub-segments are most representativeof whole parotid mean dose. Adjacent sub-segment (i.e., cranial vs. middle)mean doses significantly correlated in ipsi- (Spearman’s ρ = 0.776-0.828) andcontralateral parotid (0.771-0.776); so did cranial (0.592), middle (0.472),and caudal (0.484) sub-segments (left-right parotid; p < 0.0001 in all cases).Introduction of a third sub-segment slightly improved model quality(AIC) but not predictive power (MAE; see table 12.3). No runs tests weresignificant. Predictive power (MAE) across all models differed by <0.015.The best model was lin-split-caudal and again the best whole-parotid modelwas lin-split. Linear models were preferred over exponential models (ARI:71.8% vs. 28.2%). Sub-segment models dispersed over the AIC spectrum; butfamily-wise caudal-only models had the best ARI (54.3%) followed by middle-only (40.0%) and cranial-only models (5.6%). Besides family-wise trends,individual sub-segment-exclusive models with the highest AIC (n.b. thoseperforming worst) predominantly were cranial-only. The best performingmodels were caudal-only and to a lesser extent middle-only.Fitted parameters for the best whole-parotid models are shown in ta-ble 12.4. Contralateral (pseudo-)slopes had the largest magnitudes in allbut one case, and were more physically sensible than their ipsilateral coun-terparts. In lin-split and exp-locked models the caudal sub-segments playmore dominant roles than cranial and middle sub-segments in the contra-lateral parotid (bcl / sup(bcu, bcm) > 2.0 and αl/ sup(αu, αm) > 2.6). Again,the exp-split ipsilateral caudal pseudo-slope was dominant, but it was alsoanomalously large in magnitude. Contralateral pseudo-slopes, in contrast,were all of comparable magnitude.159Model DOF MAE AIC AWlin-split-caudal 329 0.30 473.12 0.273lin-split-middle 329 0.30 473.47 0.229lin-split 325 0.30 474.24 0.156exp-split-caudal 329 0.30 474.80 0.118exp-split-middle 329 0.30 476.15 0.060exp-locked 328 0.30 477.55 0.030lin-split-cranial 329 0.31 477.63 0.029exp-split 325 0.30 477.63 0.029exp-locked-caudal 330 0.31 478.49 0.019exp-locked-middle 330 0.30 479.00 0.014lin-locked-caudal 330 0.31 479.52 0.011lin-locked 328 0.31 479.53 0.011exp-split-cranial 329 0.31 479.98 0.009lin-locked-middle 330 0.31 480.62 0.006exp-locked-cranial 330 0.31 481.57 0.004lin-locked-cranial 330 0.31 482.70 0.002Table 12.3: AIC-ranked W1y/Wb regression models using 1/3-volumesub-segments. All quantities are dimensionless. In all casespruns > 0.18.Variance explained by the lin-split model was 8.62%. Despite an anoma-lous ipsilateral caudal slope, the contra-lateral caudal sub-segment was themost important individual regressor according to either metric. Importanceratios were >1.4 (LMG) and >6.8 (LI) compared to other sub-segments.Contralateral sub-segments were >3.1× more important than their ipsilateralcounterparts in all cases (LMG). Combined LMG importances (percentage-normalized) were: 41.7% (caudal), 30.2% (middle), and 28.1% (cranial). LIimportances were 83.3%, 0.7%, and 16.0%, respectively.12.3.6 Cranial-Caudal 1/4-Volume Sub-SegmentsParotid were segmented into cranial, middle-cranial, middle-caudal, andcaudal quarters. Combined left-right sub-segment average mean dose was14.33 Gy for cranial, 20.00 Gy for middle-cranial, 25.99 Gy for middle-caudal,160Model Param. Estimate Std. Err.lin-split A 0.812 0.072biu 0.0042 0.0047bcu 0.0043 0.0076bim −0.0011 0.0058bcm 0.0010 0.0076bil −0.0022 0.0035bcl 0.0085 0.0037exp-locked A 0.96 0.12αu 0.032 0.043αm 0.002 0.012αl 0.080 0.090exp-split A 1.00 0.16αiu 0.023 0.080αcu 0.04 0.16αim −0.005 0.013αcm 0.04 0.18αil 0.4 1.4αcl 0.04 0.16Table 12.4: Parameters for the best 1/3-volume W1y/Wb whole-parotidregression models. All parameters except A have units Gy-1; Ais unitless. Superscripts denote (i)psi- and (c)ontralateral; sub-scripts denote (u)pper (cranial), (m)iddle, and (l)ower (caudal)sub-segments.and 34.11 Gy for caudal. In all cases extrema were <0.04 Gy and >72.16 Gy.Middle-caudal mean dose differed least from whole parotid (absolute percentdifference 11% and 15%); middle-cranial spanned 11-16% and cranial/caudalspanned 35-57%. Adjacent sub-segment (i.e., cranial vs. middle-cranial)mean doses significantly correlated in ipsi- (Spearman’s ρ = 0.863-0.881)and contralateral parotid (0.831-0.846); so did cranial (0.633), middle-cranial(0.499), middle-caudal (0.456), and caudal (0.490) sub-segments (left-rightparotid; p < 0.0001 in all cases).Introduction of a fourth sub-segment slightly improved model quality(AIC) but not predictive power (MAE; see table 12.6). The three best161performing models were all lin-split type. Linear models performed betteroverall compared with exponential models (ARI: 76.4% vs. 23.6%), thoughthey were undifferentiated when ranked by MAE. Caudal sub-segments weremore important than cranial sub-segments (ARI: 78.1% vs. 21.9%), but themiddle-caudal sub-segment was itself most important (ARI: 46.7%), followedby caudal (31.4%), middle-cranial (19.7%), and cranial sub-segments (2.1%).Besides poor AIC, cranial and middle-cranial models also had the worst MAE.Residuals in all models had insignificant runs test (all p > 0.16).Fitted parameters for the two best whole-parotid models are shown intable 12.6 (the third, exp-split, performed poorly). While the AIC of thethird-best whole-parotid model (lin-locked) differed from the top model(lin-split) by 8.64, the difference was explainable mostly by lost degrees offreedom (+8). MAE of lin-locked models were worst. The exp-split modelhad a reasonable MAE but had a poor AIC. Ipsilateral parameters weregreater in magnitude in all but one case. In the exp-locked model caudalsub-segments were dominant; in the lin-split model the middle-caudal ipsi-lateral sub-segment was the most dominant sub-segment, followed by themiddle-cranial ipsilateral sub-segment.The amount of variance explained by the lin-split model was 10.3%. Com-bined caudal sub-segments were most important using LI (38.4%), followed bymiddle-caudal (27.7%), middle-cranial (24.4%), and cranial (9.4%). Similarly,using LMG caudal sub-segments were most important (30.7%), followedby middle-caudal (27.5%), middle-cranial (23.6%), and cranial (18.1%; allpercentage-normalized). The LMG metric also showed that each contralateralsub-segment was more important that their ipsilateral counterparts. Themost important individual sub-segment was either caudal or middle-caudal(both LMG and LI).12.4 DiscussionThis work sought to locate sub-structures in the parotid gland that aredosimetrically critical for late loss of salivary function. Three differentparametric methods were used to derive relative importance: explained162Model DOF MAE AIC AWlin-split 323 0.30 471.94 0.414lin-split-middle-caudal 329 0.30 474.02 0.146lin-split-middle-cranial 329 0.30 475.00 0.090exp-split-caudal 329 0.30 475.12 0.084lin-split-caudal 329 0.30 475.21 0.081exp-split-middle-caudal 329 0.30 475.36 0.075exp-locked-middle-caudal 330 0.30 477.16 0.030exp-split-middle-cranial 329 0.30 478.21 0.018lin-locked-middle-caudal 330 0.31 478.67 0.014exp-locked 327 0.30 479.24 0.011exp-locked-caudal 330 0.31 479.67 0.009lin-split-cranial 329 0.31 480.12 0.007lin-locked 327 0.31 480.58 0.006lin-locked-caudal 330 0.31 480.77 0.005exp-split-cranial 329 0.31 481.79 0.003exp-locked-middle-cranial 330 0.31 481.79 0.003lin-locked-middle-cranial 330 0.31 483.00 0.002exp-locked-cranial 330 0.32 483.25 0.001exp-split 323 0.30 484.03 0.001lin-locked-cranial 330 0.32 484.33 0.001Table 12.5: AIC-ranked W1y/Wb regression models using 1/4-volumesub-segments. All quantities are dimensionless. In all casespruns > 0.16.variance, model ranking, and sensitivity analysis.12.4.1 Model FittingBaseline-normalized whole-mouth stimulated saliva measurements were fittedwith a variety of models via least-squares. The saliva measurement distri-bution can not be Gaussian because saliva measurements are non-negative,likewise baseline-normalized measurements are not Gaussian and are nec-essarily heteroscedastic. As our methods were parametric and based onmaximum-likelihood estimates, verification of the assumptions required byleast-squares was paramount. Inspection of the distribution of W1y/Wb163Model Param. Estimate Std. Err.lin-split A 0.792 0.072biu 0.0087 0.0052bcu −0.0013 0.0088bimu −0.0176 0.0074bcmu 0.0128 0.0098biml 0.0198 0.0073bcml −0.0085 0.0086bil −0.0097 0.0040bcl 0.0100 0.0042exp-locked A 0.99 0.13αu 0.038 0.064αmu −0.004 0.011αml 0.031 0.041αl 0.12 0.18Table 12.6: Parameters for the best 1/4-volume W1y/Wb whole-parotidregression models. All parameters have units Gy-1; A is unitless.Superscripts denote (i)psi- and (c)ontralateral; subscripts denote(u)pper (cranial), (m)iddle-(u)pper, (m)iddle-(l)ower, and (l)ower(caudal) sub-segments.showed an approximately log-normal or gamma distribution (section 12.3.2).For distributions in the exponential family (e.g., gamma), least-squares es-timates are equivalent to maximum-likelihood estimates [447]. Likewise forheteroscedastic log-normal distributed data [448]. Despite the equivalency,both heteroscedasticity and multicollinearity can render least-square standarderrors unsuitable for relative importance [438]. Robust regression methodscan be used to correct for heteroscedasticity, but multicollinearity remains anissue and statistical efficiency is sacrificed. The three importance methodswe have employed do not make use of least-square standard errors, and souse of least-squares is justified. Fitted model residuals are often tested fornormality to assess goodness-of-fit. However, such tests are futile in thiscase since W1y/Wb follow a strongly skewed distribution. A non-parametrictest (‘runs’) was performed instead. No model rejected the null hypothesis164(p > 0.14), and least-squares convergence was consistent and uneventful, sowe believe maximum-likelihood estimates were achieved.AIC cannot be compared when different data sets have been used. How-ever, proportional segmentation is equivalent to model reconfiguration overthe same data set (i.e., mean dose to whole parotid is equivalent to averagemean dose of all sub-segments), thus enabling inter-segmentation comparison.Mean dose to whole parotid remained the best predictor of salivary flow interms of AIC (469.60 vs. next-best 1/4-volume linear-split model with AIC+2.34), and was no worse in average prediction error (MAE 0.30). However,(1) the ∆AIC was too small to outright reject use of segmentation; (2) ig-noring extra model parameter degrees of freedom shows the log-likelihood issubstantially reduced via segmentation; and (3) refined segmentation resultedin greater explained variance (7.7% → 10.3%). Therefore, we cannot saydefinitely that use of segmentation improves salivary dysfunction prediction,but we can say it remains valid to use segmentation, and furthermore segmen-tation may indeed capture more detailed dose-response facets. Regardless ofthe predictive capacity, use of segmentation for deriving relative importanceof spatial portions within the parotid appears justified.12.4.2 Explained Variance ImportanceMulticollinearity was prevalent; all adjacent and left-right pairs of sub-segments were correlated (ρ > 0.456, all p < 0.0001). The robust LMGmethod discovered by Lindeman, Merenda, and Gold in 1980 [443] is ro-bust to multicollinearity and was therefore employed in our study. A majorlimitation of the method is that it is only applicable to the lin-split model.Conveniently, this was the best-performing whole-parotid model in every case.Therefore we believe LMG provides the strongest estimates of relative impor-tance compared with the other two importance methods we have employed.Contralateral parotid was at least 3.1× more important than ipsilateralparotid. The caudal-most aspects of the parotid (i.e., the caudal-most 1/3-1/2of the total volume) were found to be uniformly more important than cranialaspects for prediction of baseline-normalized salivary function. Caudal-most165aspects had at least 1.3× the importance of cranial-most aspects in everycomparison. Caudal sub-segments in both ipsi- and contralateral parotidwere more important than all other more cranial sub-segments in the sameparotid, indicating a gradient of importance highest in the caudal aspect. In1/4-volume segmentation, caudal and middle-caudal aspects were nearly ofthe same importance, with normalized importances differing by only 3.2%.The LI method is not robust to multicollinearity [438]. However, thedifferences between LI and LMG measures were unremarkable. There wasstrong agreement that caudal aspects and contralateral parotid were mostimportant.12.4.3 Model Ranking ImportanceLikelihood functions (opposed to maximum-likelihood model estimates) arenot strongly affected by multicollinearity. Relative importance derivedfrom AIC by family-wise factor comparisons originates from foundationalinformation-theory and is thought to be reliable [439]. Sub-segment com-parisons were performed on sub-segment-exclusive models. Sub-segmentproportionality was ensured by balancing the number of regressors in eachcomparison. Differences in sub-segment-exclusive model AIC do not stemfrom differing model free parameter counts because all models have thesame total number of free parameters. Therefore family-wise median AICdifferences are the result of model performance and goodness-of-fit alone.Significance testing of AW (e.g., via α-thresholding) is recommendedagainst [439], so percentage-normalized probabilities of the relative importanceof family-wise models are considered as-is. Joint comparison of all modelsshowed linear models were favoured over exponential models (ARI: 80.2% vs.19.8%). Sub-segment-exclusive models performed well compared to whole-parotid models, especially considering they had access to only 1/2, 1/3, or 1/4the information available to whole-parotid models. In two cases, 1/3-volumelin-split-caudal and lin-split-middle, they outperformed whole-parotid models(AIC and MAE). Caudal aspects of the parotid were both individually andfamily-wise more important than cranial aspects (family-wise ARI: 82.9%166vs. 17.1%). The next most important sub-segment was almost always theimmediately cranially-adjacent sub-segment, resulting in a caudal-cranialimportance gradient. In a single case – 1/4-volume segmentation – the middle-caudal aspect was most important.12.4.4 Sensitivity Analysis ImportanceSensitivity analysis is sufficient to determine relative dispersion importancein the absence of multicollinearity [438]. When present, results are skewedbecause correlated regressors become degenerate and it is difficult to separatethe effects of each. Multicollinearity was prevalent in our analysis butthe parotid’s small spatial extent caused it to be fairly consistent (ρ ∈[0.456, 0.633] inter-parotid, [0.640, 0.881] intra-parotid). We therefore believesensitivity analysis to be useful as a complementary technique.Caudal sub-segments were most important. For 1/2- and 1/3-volumesegmentation, caudal sub-segments had 1.5× or greater the importance ofcranial sub-segments. A caudal-cranial importance gradient was again noted.In 1/4-volume segmentation, caudal-most sub-segments were more importantthan middle sub-segments in all but one model. In that exception, themiddle-caudal sub-segment was most important.12.4.5 Overall Assessment and Comparison with EarlierStudiesCombining results from the three methods, it is clear that caudal aspectsof the parotid are most important for describing salivary performance oneyear after radiotherapy. In every case an importance gradient was noted withcaudal aspects most important and cranial least important. In 1/4-volumesegmentation, all three methods found that the middle-caudal sub-segmenthad comparable or greater importance compared with the caudal sub-segment.This finding is spatially consistent with 1/2- and 1/3-volume segmentationif the region encompassing 15-20% of the parotid volume, offset from thecaudal-most aspect by ∼20% of the volume, contains the most importantaspects. We find no reason to exclude this possibility.167Consensus about the existence and location of dosimetrically criticalregions within the parotid gland has not yet been established in the literature.Konings et al. reported that salivary dysfunction in rat parotid was morepronounced after irradiation of the cranial aspect and that the cranial aspectseemed to impact the (unirradiated) caudal aspect [348]. The bath-and-showereffect reported by van Luijk et al. made use of a 30 Gy ‘shower’ dose to thecaudal aspect with varying 0-10 Gy ‘bath’ doses to the cranial [356]. Theyfound that addition of a dose bath resulted in increased dysfunction. However,guided by the stem/progenitor cell hypothesis, follow-up work by the samegroup identified a confined critical region within the cranial aspect [357] (n.b.74 patients are shared between our analyses). Collectively, our findings donot appear consistent. While the discrepancy with rat parotid findings mightarise from greater control over the rat parotid dose profile or differences in ratand human anatomy. Additional analytical factors may also play a role. Forexample the selection of critical region(s) by van Luijk et al. was accomplishedwith a spatially-variable bounding method. Our analysis used sub-segmentswith fixed volume and position, and importance of all sub-segments wasquantified simultaneously. Our analysis differentiated ipsi- and contra-lateralparotids. Omitting this potentially confounding factor would have confinedour analysis to the ‘-locked’ model variants, which underperformed comparedto ‘-split’ variants. It could also reduce precision and give rise to a Yule-Simpson effect [385]. Despite differences, our conclusions on human parotidmay broadly agree with those of van Luijk et al. since the middle-dorsal andBuettner et al. found that dose distribution descriptors improved predic-tion over whole parotid mean dose, and noticed that dose concentrated inthe medial-caudal aspect was preferable to homogeneous delivery across thewhole parotid with equivalent mean dose [233]. In light of our findings, itmay be that the observed effect is not an example of a homogeneous bath-and-shower effect but rather that they have singled out the most importantaspect specifically (medial-caudal). Miah et al. showed that bilateral sparingof the superficial lobe reduces severe xerostomia incidence compared withconventional whole contralateral parotid sparing [358]. Laterality was notconsidered in our analysis, but our collective findings appear congruent if168the caudal aspects of superficial lobe are indeed the origin of the clinicalresponse. Congruence in this case seems likely since, based on our findings,the caudal aspects of the superficial lobe may be most important. Finally,it is interesting that our earlier work was not able to detect significantlydifferent dose-response in medial-lateral aspects. Given that the importancegradients observed in the present work are caudal-cranial, it seems likely thatcaudal-cranial tissue differentiation is more important than medial-lateral oranterior-posterior differentiation.Segmentation refinements, such as incorporating additional coronal orsagittal planes, may improve localization of the critical region(s). We didnot consider refinements for four reasons. First, radiotherapy is known toshrink parotid volumes by medial movement of the lateral aspects [305]. Thepresent method is robust to this shrinkage. Second, a parametric approachquickly becomes untenable as regressors are added, which limits segmentationrefinement. Third, refinement amplifies relative noise for individual sub-segments. Finally, refinement increases the difficulty of ensuring sub-segmentvolume proportionality.12.4.6 Implications and LimitationsZero parotid dose should result in no changes in function, so A=1 shouldhold in all considered models. Though linear models performed best, expo-nential model pseudo-intercepts (A) were closer to unity. They therefore mayrepresent the data in a more physically sensible way. Pinning exponentialA=1 did not alter model ranks; linear still performed best. Furthermorelinear models always comprised the top 2-3 models – even whole parotidfavoured linear models. It is possible that measurement noise, even withN=332, obscures fine details needed to distinguish models. Therefore linearmodels are recommended for cohorts approximately ≤500. This is contraryto the general consensus for whole parotid (i.e., typically exponential) butnot uncommon. To our knowledge this work is the first to compare modelsfor parotid sub-volumes in this way.Middle sub-segment mean doses were most representative of whole parotid169mean doses. If parotids are truly homogeneous organs, and whole parotidmean dose is the best predictor, then middle sub-segments may have inflatedimportance. Middle sub-segments were important, but caudal sub-segmentswere generally more so. Since caudal sub-segments were least representativeof whole parotid, their importance over middle sub-segments is noteworthy.Conversely, given that the amount of variance explained was 10.3% or less,and studies have shown the intensity of salivary gland damage and dysfunctionincreases in proportion to the irradiated volume [232], it seems likely thatno single, small critical region exists that substantially controls whole-glandfunction. Broad caudal sub-segments might contain bulky critical regions.Refined segmentation methods are needed to test this hypothesis.Finally, we emphasize this was an observational study. Treatments fol-lowed clinical guidelines and salivary dysfunction was aggressively minimized,which resulted in a relatively homogeneous (i.e., non-ergodic) cohort. Sub-segment importances may merely reflect the clinical dose profile, though wehave endeavoured to overcome this tautological conclusion. It is thereforedifficult to generalize our findings or ascribe radiobiologic significance. Inter-ventional studies are needed to establish generalizability. On the other hand,our findings should be applicable when current clinical guidelines are followed[236], in which case the caudal aspects of the parotid should be spared asmuch as possible to ameliorate radiation induced dysfunction.170Chapter 13Non-Parametric Approach toRegional Effect Assessment113.1 IntroductionWhole parotid mean radiation dose is currently used to predict risk of lateradiotherapy-induced salivary dysfunction [236]. The underlying assumptionis that functional burden is distributed homogeneously throughout the parotidgland [285]. Recent studies have found behaviour counter to homogeneousdistribution, including regions with elevated relevance for salivary flow [324,357], non-equivalence of dose-volume descriptors for dysfunction prediction[449, 450], and bath-and-shower effects [233, 356]. Others have noted thatincorporation of non-homogeneous effects into a radiotherapy treatment planleads or potentially could lead to improved patient outcomes [358, 428].Evidence of a bath-and-shower effect in parotid, in which high dose to aconfined sub-volume (the ‘shower’) is impacted by a low dose to an extendedvolume (the ‘bath’), was first reported by van Luijk et al. in 2009 in thecontext of objective salivary flow dysfunction [356]. A similar effect was found1The contents of this chapter have been submitted to Radiation Oncology under thetitle ‘Fine segmentation shows anterior-caudal parotid is most important for salivary loss’on the 31st of December, 2016. The list of authors was Haley Clark, Steven Thomas, StefanReinsberg, Allan Hovan, Vitali Moiseenko, and Jonn Wu.171using a separate cohort and subjective measurements in 2012 [233]. Likewise,several studies have confirmed that dose-volume measures are not equivalentin parotid, implying deviation from homogeneity. For example, Ortholan etal. found that salivary flow prediction improved compared to whole meandose models when the volume of the contralateral gland receiving ≥ 40Gywas incorporated [449]. Wang et al. found similar conclusions in 2011 [450].However, neither dose-volume effect deviations nor bath-and-shower effectsincorporate specific sub-volumes; incorporation of sub-volume extent andlocation has lead to less conclusive findings. There is continued debate overthe existence of critical regions (i.e., defined by specific anatomical, functional,or geographical criteria) that more strongly impact salivary dysfunction thancomparable regions in the parotid. Different studies have variously shown thatthe most important regions are (or contain, or are contained broadly within)cranial and medial-dorsal aspects adjacent to mandible [348, 357], caudalaspects2, caudal-medial aspects [233], the superficial lobe (i.e., approximatelylateral-caudal) [358], and the lateral portion [324]. Other work has focusedon the clinical feasibility of split delineation along the deep-superficial lobeboundary (i.e., anterolateral and posteromedial) [428, 451].In this prospective study a cohort comprised of 332 head-and-neck cancerpatients (collected within a single agency) is used to assess regional effectswithin parotid gland. Parotids are divided into 2, 3, 4, 18, and 96 equal-volume sub-segments. Sub-segment relative importance for prediction of latesalivary flow is assessed using non-parametric methods robust to overfittingand multicollinearity. Owing to the linear dose-response observed in sub-segments in chapter 12 and in some capacity within the literature (e.g.,[374]), and sub-segment volumetric equality, importances are interpretable asregional criticality for late salivary dysfunction.2See chapter 12.17213.2 Materials and Methods13.2.1 Cohort, Measurements, Treatment, ToolingThis prospective study passed institutional ethical review. Patients underwentradiotherapy for head-and-neck cancers and gave informed consent to partici-pate. Planning dose profiles and delineated organ-at-risk parotid contourswere employed for dosimetric assessment and segmentation. A single seniorhead and neck oncologist (JW) scrutinized contours for quality assurance.Stimulated late salivary measurements of whole-mouth saliva at baseline (pre-radiotherapy; Wb) and one year post-radiotherapy (“late”; W1y) were used.Measurements represent whole mouth expectorate collected over five minutesof chewing flavourless wax. Mean-scaling imputation was employed for (29)patients without W1y but with W2y late measurements. Exclusion criteria arethe same as in section 12.2.1. A total of 332 patients were eligible (medianage 58.6y, age range 19.0-90.6y; gender: 73% male, 27% female; prescriptiondose: 70Gy/35 fractions 55%, 60Gy/25 fractions 11%, 60Gy/35 fractions8%, other 27%; treatment type: 279 intensity- or volumetric-modulated, 53conventional; primary tumour site: 88 nasopharynx, 132 oropharynx, 61tongue, 61 tonsil, 31 oral cavity and gums, 20 unknown, 18 hypopharynx, 14larynx, 7 thyroid, 4 palate, and 22 other).Dosimetric accumulation and contour manipulation (nested segmentation)was accomplished via DICOMautomaton [7, 411] in accordance with the methodof chapter 11. To ensure sub-segment proportionality, cubic dose matrixsupersampling (15×) was employed. Counts of supersampled voxels withinsub-segments were compared to ensure mutual pairwise proportionality usingKolmogorov-Smirnov tests. Significance was ascribed at α=0.05. No correc-tion was made for multiple comparisons (i.e., to account for the so-calledbirthday paradox), which made for a more stringent test.13.2.2 Importance TechniquesThe Random Forest technique (RF) is a non-parametric ensemble learningmethod in which tree nodes are recursively constructed by randomly sampling173regressors at, and splitting, each node. An ensemble of trees is grown; regres-sion predictions are generated by averaging predictions from the ensemble.Importance was estimated using two measures: (1) ensemble-averaged totaldecrease in node impurities resulting from splitting on the regressor andmeasuring the Residual Sum of Squares (RSS) (“node impurity”), and (2)a more robust permutation-based measure in which the difference betweenun-permuted and each regressor permutation of the out-of-bag (i.e., excludeddata) Mean Squared Error (MSE) is ensemble-averaged and normalized bythe standard deviation of the differences (referred to as simply “MSE” here)[452, 453, 454]. Major weaknesses of RF arise when regressors have varyingscales, are mutually correlated (‘multicollinearity’), or when the ‘scale’ (i.e.,number of categories) of categorical variables differ [455]. In the present caseall regressors (i.e., sub-segment mean doses) have the same scale and arecontinuous. Multicollinearity is anticipated, but is believed to be sufficientlypervasive and constant so as to reduce impact on conclusions by uniformlysuppressing absolute importances and leaving relative importances intact.RF trees may nonetheless become biased. To overcome this, conditionalinference tree ensembles (“c-trees”) were employed [456]. Like RF, c-treescan be used for non-parametric regression [457]. C-tree methods differ fromRF by using conditional inference trees as base learners. The unbiased c-tree RF construction proposed by [455] is used, which is meant to addressregressor selection bias in individual classification trees. Regressor importanceis estimated using both (1) permutation and (2) conditional permutationmeasures. The former is a reliable measure of regressor importance foruncorrelated regressors when subsampling without replacement and unbiasedtrees are used to build the forest [455]. The latter, conditional permutation, isthought to be more suitable in the presence of multicollinearity and addressesregressor selection bias in individual classification trees [458].Both RF and c-trees are thought to be robust to overfitting due to useof bagging, the assemblage of many bootstrapped trees and use of predictionaveraging, which improves generalizability [452, 457]. Based on expectedmulticollinearity, the reliability of importance estimates were ranked as: c-treeconditional permutation (most reliable), c-tree permutation, RF MSE, and RF174node impurity (least reliable). The number of trees and splitting parameterwere grown until impact on importances diminished and the random seedhad no impact on conclusions (nominally 20k for both RF and c-trees).13.2.3 StatisticsAIC is typically used to compare (parametric) models [459]. Besides anasymptotic relationship between cross-validation and AIC [460], the authorsare not aware of any direct way to compute AIC for RF or c-trees. Instead,a metric that characterizes predictive power is used. Both MAE and RMSE[441, 461]. Both are reported. Fitted whole parotid mean dose models (lin-ear and exponential; standard in the literature) provide baseline MAE andRMSE. The distribution of baseline-normalized salivary measurements willbe heteroscedastic, so residual normality was not tested. Instead correla-tion coefficients (rpa) between predicted and actual W1y/Wb, are reported.Comparison is accomplished via a two-tailed Fischer z-transformation [462].17513.3 ResultsA summary of all models and methods is shown in table 13.1. Contralateralparotid was unanimously more important than ipsilateral parotid for segmenta-tion into halves, thirds, and quarters. Therefore, to reduce computational bur-den, segmentation into 18ths and 96ths used only contralateral parotids. MAE,RMSE, rpa, and summarized importances are shown where applicable. C-treemethods performed significantly better than whole parotid mean dose modelsand RF (linear and exponential; both p < 0.0001) at all segmentation levels.RF methods did not significantly improve prediction when segmentation wasintroduced (p ≥ 0.258) but c-trees improvement significantly strengthened(p < 0.039), improving from a correlation that was already nearly doublethe next-best method (0.531; linear model). Refinement-induced reductionsin both MAE and RMSE were similar for RF and c-tree methods (∆MAE:−0.013 vs. −0.016; ∆RMSE: −0.22 vs. −0.20). At all levels of segmentationa Kolmogorov-Smirnov test showed no statistically significant differencesbetween the number of supersampled dose matrix voxels contained withineach sub-segment (p > 0.05 in all (96·95+18·17+4·3+3·2+2·1)/2 = 4723comparisons).176Segmentation Method MAE RMSE rpa Type Most Important Sub-segment ImportanceWhole exp 0.301 0.491 0.252 – – –linear 0.295 0.487 0.277 – – –RF 0.315 0.506 0.222 – – –c-trees 0.259 0.437 0.531 – – –Halves RF 0.294 0.488 0.272 Impurity caudal (contralateral) 1.15×MSE caudal (contralateral) 1.45×c-trees 0.246 0.425 0.591 Permutation caudal (contralateral) 2.78×Conditional caudal (contralateral) 2.66×Thirds RF 0.308 0.494 0.246 Impurity caudal (contralateral) 1.31×MSE caudal (contralateral) 1.72×c-trees 0.249 0.422 0.611 Permutation caudal (contralateral) 3.49×Conditional caudal (contralateral) 3.05×Quarters RF 0.306 0.498 0.228 Impurity middle-caudal (contralateral) 1.29×MSE caudal (contralateral) 1.55×c-trees 0.247 0.421 0.614 Permutation caudal (contralateral) 3.25×Conditional caudal (contralateral) 2.70×18ths RF 0.306 0.489 0.276 Impurity SS04: caudal-anterior 1.47×MSE SS14: middle-posterior 1.42×c-trees 0.248 0.420 0.620 Permutation SS04: caudal-anterior 2.74×Conditional SS04: caudal-anterior 3.85×96ths RF 0.302 0.484 0.304 Impurity SS04: caudal-anterior 2.47×MSE SS26: middle-caudal-anterior 1.78×c-trees 0.243 0.417 0.637 Permutation SS21: caudal-posterior 3.75×Conditional SS04: caudal-anterior 4.04×Table 13.1: Summary of results and most importance sub-segments. All quantities are dimensionless. rpadenotes the correlation coefficient between actual and predicted mean-scaled W1y/Wb. Whole, halves,thirds, and quarters segmentation used both ipsi- and contralateral parotids; 18ths and 96ths usedonly contralateral parotids to reduce computational burden. The most important sub-segment (SS) isspecified; refer to fig. 13.3 for sub-segment locations. Importances given are relative to the expectedresult for a homogeneous parotid.177In almost every importance assessment method, a caudal-most sub-segment was most important. In the two exceptions, the most importantsub-segment (middle; between caudal-most and cranial-most sub-segments)was either fully or partially within the caudal 50%-volume. In one of theseexceptions, the 18ths segmentation RF-MSE case, the next most importantnon-middle sub-segment was caudal.The most important sub-segments, on average over all segmentationmethods, had importances 2.4× that of an equivalent sub-segment in atheoretical homogeneous parotid (see table 13.1). This figure increasedwhen segmentation and methodology was refined: 2.7× when only 18ths and96ths segmentation was considered, 3.0× when only 96ths segmentation wasconsidered, and 4.0× when only c-tree conditional permutation (the mostreliable method) was considered at the finest (96ths) segmentation.Other than the most important sub-segment, the least important sub-segment, median importances of family-wise groupings based on anatomy(e.g., caudal vs. middle vs. cranial, or anterior vs. posterior), and family-wise percentiles (e.g., 20% and 80%) conveyed similarly the importance ofcaudal aspects. Tables showing sub-segment importance of the most reliabletechnique, c-tree conditional permutation importance, are shown in figs. 13.1and 13.2. The same information is displayed in the form of heat maps for18ths and 96ths segmentation in fig. 13.3.178Figure 13.1: Relative c-tree conditional permutation importance of sub-segments for 18ths segmentation. Importance is given as thepercentage of relative importance compared to a homogeneousorgan (which would be 100%). Refer to fig. 13.3 for sub-segment(‘SS’) spatial correspondence. Anatomical groupings display theper-group median (filled circles). Importances span ∼0-3.85×that of equivalent sub-segments in a homogeneous parotid.179Figure 13.2: Relative c-tree conditional permutation importance of sub-segments for 96ths segmentation. Importance is given as thepercentage of relative importance compared to a homogeneousorgan (which would be 100%). Refer to fig. 13.3 for sub-segment(‘SS’) spatial correspondence. Anatomical groupings display theper-group median (filled circles). Importances span ∼0-4.04×that of equivalent sub-segments in a homogeneous parotid.180Figure 13.3: Relative c-tree conditional permutation importance of sub-segments for 18ths (left) and 96ths(right) segmentation. Equal-volume sub-segments are represented by a single slice of axial planeencompassed by the sub-segment. In segmentation into 18ths (96ths), importances span ∼0-3.85× (∼0-4.04×, respectively) that of equivalent sub-segments in a homogeneous parotid. The most importantsub-segments are indicated.181Figure 13.4 shows contralateral parotid dosimetric characteristics forthe cohort. Dose was highest in the caudal-medial aspects and lowest inthe cranial-lateral aspects, on average. Importances did not merely followsub-segment mean dose or dosimetric variability throughout the samplepopulation (cf. figs. 13.3 and 13.4).182Figure 13.4: Sample population contralateral parotid dosimetric characteristics: mean dose (left) and theinner-most 50th percentile of mean dose (right) for each sub-segment (SS). Mean doses span 15.4-50.2Gy (SS09 and SS01, respectively). Inner 50th percentiles span 16.1-33.9Gy. Caudal-medial aspectsreceived the highest dose while cranial-lateral aspects received the lowest dose, both with low variationacross the sample population.18313.4 DiscussionEffects that deviate from strict parotid functional-spatial homogeneity havebeen reported, but there is not yet consensus about the criticality of specificsub-volumes in relation to radiotherapy-induced salivary dysfunction. In thiswork, a regional effect is characterized via a segmentation refinement method.We improve upon existing studies primarily by being systematic in coverageof the parotid: no aspects were a priori omitted and importance of the wholeparotid is simultaneously developed.Four non-parametric methods were used in this work. Though theyvaried in susceptibility to multicollinearity and other biases, all confirmedthe importance of caudal aspects for predicting radiotherapy-induced latesalivary function. Contralateral parotids were found to be most important,which is consistent with much of the literature (e.g., [449]). Sub-segmentheat maps overlapped across segmentations and importance methods, whichsuggests conclusions do not substantially depend on the spatial resolution orother convergence factors (e.g., number of trees). A gradient of importanceemerged indicating both caudal-anterior aspects are most important and thatimportance gradually fades posteriorly and superiorly. Starting at the mostimportant sub-segment, movement to superiorly-adjacent regions affected thegreatest reduction in importance. Posterior movement less so, and medialand lateral movement affected importance only weakly and approximatelyequally. Lack of medial-lateral preference may result from parotid medialshrinkage during radiotherapy [74]; lateral aspects may have traveled mediallyand ‘smeared’ importance. It remains to be seen if this effect is a treatmentartifact.C-tree methods outperformed RF significantly, and while they bothgenerally improved MAE and RMSE as segmentation proceeded, only thec-tree rpa significantly improved. It is not possible to ascribe this to anyspecific factor, but it is likely that either (1) RF is intrinsically not capableof ferreting out the information that an equivalent c-tree ensemble can, or(2) RF was strongly impacted by multicollinearity or measurement noise andtree construction was biased. In either case, while RF did not significantly184perform better than whole parotid models, it was also not significantly worse,and we therefore believe it remains a valid tool for inspecting sub-segmentimportance.Though there is general consensus among researchers that the parotid isnot homogeneous, there is little consensus about the specifics of the inhomo-geneities. The existence of critical regions, mechanisms supporting them, andcomparative clinical relevance of various aspects and lobes are debated. Theregion we have found to be most important overlaps, at least somewhat, withcritical regions reported in previous studies. Buettner et al. in 2012 comparedthe relative importance of 50 clinical and physical factors (both categori-cal and continuous) for subjective xerostomia in 63 head-and-neck cancerpatients [233]. Four of the seven most important regressors (mean dose toeither parotid, contralateral parotid caudal-medial aspect dose concentration,and contralateral parotid superficial lobe cranio-caudal dose distribution)displayed agreement with our findings. Regressor importance changed whensub-cohorts were evaluated, but caudal aspects remained important. Theyconcluded, however, that minimizing dose to the lateral and cranial aspectswould reduce xerostomia incidence. Our relative importance assessmentsare in broad agreement, but our conclusions about clinical relevancy differ.Owing to the complexity of head-and-neck anatomy, minimizing dose tolateral and cranial aspects generally requires increasing caudal aspect dose.As we collectively have found caudal aspects to be important for clinicaloutcomes, the recommendation is surprising and implies our interpretation ofprediction importances and outcomes importances differ. In recent work byClark et al., a model-based approach incorporating sensitivity analysis wasused to assess relative importance (using the present cohort; see chapter 12).Linear models performed best and the collective caudal aspect slopes wereboth most important and largest in magnitude, implying that shifting dose tothe caudal aspects would overall negatively impact salivary function. Similarfindings have been reported by others [374]. We therefore believe that re-gressor importance (in this case) translates to clinical relevance. Differencesin study designs, outcomes, assessment, cohort size and demographics, andfactors considered (especially their response shape) may have contributed to185the discrepancy. However, our clinical recommendations are in agreementwhen the caudal aspects are dose-saturated and cranial or posterior aspectscan be spared by shifting dose to the (already saturated) caudal aspects,which may reduce dysfunction. This common clinical situation demonstratesthat characterization of regional effects throughout the entire parotid canimprove outcomes risk analysis compared to simple recommendations to sparespecific regions or lobes.Ortholan et al. found in 2009 that the contralateral parotid volumereceiving ≥40Gy (V40) was the best dose-volume factor for predicting recoveryof salivary function [449]. This finding suggests the non-equivalency of wholemean dose and V40 – both of which are dose-volume measures. Deviationsfrom expected dose-volume effects, which follow directly from inhomogeneousradiosensitive structure distribution, have been known for several decades[353, 463]. While the findings of Ortholan et al. do not specifically describea regional effect, the regions selected by our two approaches may overlap.Since standard clinical practice involves preventative irradiation of lymphnodes in the head-and-neck, proximate caudal parotid aspects often receivethe highest dose. Therefore, V40 may simply be selecting the aspects, whichwould represent a dose-volume manifestation of a regional effect. We believethe reverse (caudal aspect importance reflecting V40) is not true becausecontralateral parotid (lower dose) was found to be more important thanipsilateral parotid (higher dose), and axially the regions of highest dose followa medial-anterior to lateral-posterior ridge. Both, along with the mean doseheat maps of fig. 13.4, demonstrate that importance does not merely reflectthe dose profile. On the other hand, it is consistent that low-dose cranial-lateral sub-segments are the least clinically relevant and that sub-segmentswith greater relevancy are typically more heavily irradiated.A more recent report by van Luijk et al. showed the presence of a confinedcritical region in the medial-dorsal aspects adjacent to mandible [357]. Whileour findings are not quite consistent in the superior-inferior direction, theyappear to coincide in the anterior-posterior and medial-lateral directions. Bothmay coincide with major ducts, vasculature, or interfere with innervation;previous real-time imaging of stimulated parotids showed increased perfusion186variability focused in the vicinity of both regions [3]. The hypothesis thatdamage to stem/progenitor cells is the underlying cause of dysfunction, iftrue, would support ducts rather than vasculature or nerve impairment. Theconclusion of a well-confined critical zone, however, was not confirmed in thiswork. We found that even very small regions are not necessarily ‘critical.’ Atbest, the most important sub-segments appear to have 4× the importancethat a homogeneous parotid sub-segment would. It is possible that populationaveraging has ‘smeared’ importance. On the other hand, importance of themost caudal-anterior aspects were, in some cases, two orders of magnitude orgreater than cranial and posterior sub-segments and naturally formed smoothimportance gradients, which suggests an effectively critical (but somewhatbroad and smeared) clinically relevant region. A smeared critical regionwould be more consistent with Lyman normal tissue complication probabilitymodels with parallel volume dependence parameters than confined criticalregions, and may more accurately reflect stem/progenitor cell distribution[374]. Additional work is needed to characterize this effect.Both Buettner et al. and van Luijk et al. report observing a bath-and-shower effect, which may confound importance assessment, especially forintensity-modulated radiotherapies. Knock-on effects (indeed, also higher-order interactions) are accounted for in RF and c-trees by permutation-based importances [458]. Explicitly including all first-order interaction termsfor verification was not feasible even for segmentation into 18ths owing tothe increased complexity and decreased statistical power (i.e., a total of171 regressors would need to be considered; n.b. N=332). Heterogeneoussegmentation could in principle alleviate such issues, but it then becomesunclear how to robustly map regressor importance to clinical relevance.Finally, the uncertainty in our findings were hard to directly quantify.The most reliable technique, c-trees, are memory-bound and computationallydemanding. The bootstrap method is the most widely recommended methodof quantifying uncertainty. Performing just 500 bootstraps via cloud com-puting would cost an additional $30-40k USD. Uncertainty quantificationthrough bootstrapping is therefore not currently feasible. Instead, consistencyof the derived importance maps, RF and c-trees methods, and importance187techniques were used to gauge uncertainty. All methods were in agreementthat the caudal aspect is most important for salivary dysfunction. Further-more, the relatively smooth importance gradients observed emerged naturallysince neither RF nor c-tree methods had access to sub-segment localities.While it is not yet possible to directly quantify uncertainty in the importancemaps generated by this work, reliability is thought to be high owing to theconsistencies.13.4.1 ConclusionsCaudal-anterior aspects of the parotid were found to be most importantfor prediction of radiation-induced late baseline-normalized salivary flow.Conditional inference trees, combined with fine segmentation, were found tosignificantly outperform whole parotid mean dose for prediction of salivarydysfunction.188Chapter 14Other Regional Effects14.1 IntroductionThe non-parametric methods developed in chapter 13 are general-purposemethods that can be applied with little modification in other domains. In thischapter, the most robust and best-performing method (c-trees) is applied intwo limited follow-up analyses. In section 14.2 regional effects are investigatedin parotid using xerostomia questionnaire responses as response variables,and in section 14.3 regional effects are investigated in submandibular glandsusing resting saliva as the response variable. These two facets, xerostomiaand submandibular glands, were chosen both to investigate congruence withthe results of chapters 12 and 13 and because they are potentially clinicallyrelevant in their own right.14.2 Parotids and XerostomiaBecause each questionnaire response can be considered separately from allthe others, analysis of xerostomia can produce a plethora of independentanalyses and require careful control to mitigate the multiple comparisonproblem. Segmentation into 18ths was chosen to reduce the computationalload in this limited follow-up analysis of xerostomia-based regional effects.Using only patients with complete xerostomia QoL questionnaires at189baseline, three months, and either one or two years, the most successfulaspects of the non-parametric analysis of chapter 13 were applied using mean-scaled subjective responses. The same exclusion criteria (section 12.2.1) andmean-scaling technique (section 12.3.1) of chapter 12 were used. A total of218 patients were found to be suitable for analysis.QoL instrument questions are described in section 7.1. Each of questions 2-9 were assessed individually. The c-trees method was able to accurately predictquestionnaire responses for each question; Pearson’s correlation coefficientsbetween actual vs. predicted responses for early and late xerostomia are shownin table 14.1. They varied from 0.618 to 0.674 which signifies uniformly ‘strong’correlation (i.e., r ∈ [0.60, 0.80), a threshold recommended by Evans [270]).Question Number r (Early) r (Late)2 0.645 0.6473 0.664 0.6244 0.655 0.6405 0.674 0.6486 0.642 0.6367 0.645 0.6548 0.633 0.6549 0.618 0.674Table 14.1: Pearson’s correlation coefficients (r) between patient self-reported xerostomia questionnaire responses and the responsespredicted using only mean dose to 18 equal-volume parotid glandsub-segments. Both early (i.e., three month) and late (i.e., oneyear and mean-scaled two year) responses were used. The QoLinstrument questions are described in section 7.1.As with parotids in chapter 13, heat maps were generated to visuallydisplay relative sub-segment c-tree conditional permutation importance (cf.fig. 13.3). Heat maps and relative importance ratios were overall similarwith the caudal aspects being most important. Heat maps for questions1 61Question #6 was “rate the dryness in your mouth while not eating or chewing” andquestion #7 was “rate the frequency in sipping liquids to aid in swallowing food.” Thesetwo questions were selected randomly.190and 7 are shown in fig. 14.1. Quantitative relative importances are shown infigs. 14.2 and 14.3.Figures 14.2 and 14.3 show importances that are negative, which demon-strate the increased uncertainty in this analysis compared to the parotidvs. stimulated saliva case, possibly due to fewer datum being available, orxerostomia responses being more variable and/or bimodal. Regardless, thesame strong preference for caudal aspects of the parotid seen to be importantfor dysfunction are also found to be important for xerostomia. However,unlike the case of dysfunction posterior aspects appear to be more relevantthan anterior aspects for xerostomia. To first order, both toxicities are inagreement that the caudal aspects are most important. Whether this is for-tuitous or merely a consequence of the relationship between xerostomia andsalivary dysfunction is not entirely clear. However, it suggests that sparingradiation dose to the caudal aspect may reduce both salivary dysfunction andxerostomia.191Figure 14.1: C-tree conditional permutation regional importance map using parotid gland sub-segment meandose and patient self-reported late xerostomia questionnaire responses (#6 on left, #7 on right).Questions are described in section 7.1. Like with stimulated saliva, caudal aspects are most important(cf. fig. 13.3).192Figure 14.2: Quantified c-tree conditional permutation importance forindividual sub-segments corresponding to QoL question #6.Sub-segment (‘SS’) numbering is shown in fig. 14.1 and is iden-tical to fig. 13.3. Importance is presented as the percentage ofrelative importance compared to a homogeneous organ (whichwould be 100%). Anatomical groupings display the per-groupmedian (filled circles). Caudal-posterior aspects are most impor-tant, with relative importance up to ∼4.0× that of an equivalenthomogeneous organ sub-segment.14.3 Submandibulars and Unstimulated FlowSubmandibulars are more oblique to the axial plane than parotids. Whileparotids have a characteristic inverted pyramid shape along the superior-193Figure 14.3: Quantified c-tree conditional permutation importance forindividual sub-segments corresponding to QoL question #7.Sub-segment (‘SS’) numbering is shown in fig. 14.1 and is iden-tical to fig. 13.3. Importance is presented as the percentage ofrelative importance compared to a homogeneous organ (whichwould be 100%). Anatomical groupings display the per-groupmedian (filled circles). Caudal-posterior aspects are most impor-tant, with relative importance up to ∼3.5× that of an equivalenthomogeneous organ sub-segment.194inferior axes, submandibulars are aligned more so along the anterior-posteriorand superior-inferior axes. Segmentation is therefore slightly problematic.As submandibulars are demarcated on axial slices, there is a significantblurring of directionality. For example, if volumetric segmentation were usedto divide a submandibular into two halves using an axial plane, the resultingsuperior-most sub-segment may include substantial inferior portions due tothe obliquity.There are several ways to overcome this problem. The simplest way wouldbe to find the longest line-segment that can be fully enclosed within the ROI.This method suffers from topological sensitivity, but will locate the longestdimension of the submandibular to first order. A more robust method wouldemploy Principal Component Analysis (PCA), which is conceptually similarin purpose to the simple method, but can be used to generate a completeorthogonal set of directions along which planar segmentation could be aligned.PCA is also more robust to topology as it can be made to take into accountvolume (or density).However, the issue of whether it is worthwhile to correct this problem isnot clear. While it would give a planar segmentation that is independentof patient positioning (though not necessarily incorporating deformationdue to positioning), it would also present an additional barrier to clinicalapplicability. In particular, if segmentation is performed along axes respectingthe existing (axial) orientation, then it will be considerably easier clinically todetermine sub-segment mean doses. Furthermore, it is not clear a priori thatsubmandibular morphology, like parotid morphology, holds any importancefor regional effects. The distribution of functional sub-units may not respecttopology or morphology anyways. For these reasons, PCA was not employed.This analysis procedure used the same mean-scaling approach and exclu-sion criteria as described in chapter 13, except that surgeries that interferedwith submandibulars rather than parotids led to patient exclusion. As seenin table 3.2, fewer submandibulars are contoured compared to parotids dueto their increased clinical relevance. In total, 314 patients were found to besuitable for analysis.Segmentation into 8ths was performed to ease analysis but still provide195minimal anatomical groupings along the three cardinal axes. A heatmap forc-tree permutation importance is shown in fig. 14.4 and a heat map for c-treeconditional importance is shown in fig. 14.5. A quantitative importance chartthat shows differentiation between cranial and caudal aspects is shown infig. 14.6.Similar to parotid, the submandibular demonstrates a clear regional effect.The most important sub-segment (SS04) is the cranial-posterior sub-segmentnearest to the floor of the mouth. Relative importance is ∼3.5× that of anequivalent homogeneous organ sub-segment. However, like section 14.2, thelink between relative importance and clinical relevance was not investigatedand is only assumed to be linear in the sense of a first-order approximation.It is curious that the regional effect seen in submandibulars is transverselyinverted compared to parotids. It is not possible to identify if this result ismerely coincidental or the product of some underlying phenomena. However,speculatively, it is possible the apparent inversion has an anatomical basis, ora knock-on effect between parotid and submandibular glands exist such thathigh dose to both simultaneously produces a greater effect than would be hadby merely superimposing the effect of each individually, or that dosimetriccoupling between both glands creates a ‘pocket’ of undersampled data (i.e.,high parotid gland dose with low submandibular dose, and vice-versa). Whilethe parotid gland-only analysis did not suffer this ambiguity (since the ipsi-and contralateral glands are usually well differentiated), a more sophisticatedanalysis combining multiple facets is needed to provide a basis for inter-organimportance comparisons.196Figure 14.4: C-tree permutation (non-conditional) regional importance map using submandibular glandsub-segment mean dose and late resting saliva facets. Cranial aspects (closest to the floor of themouth) are most important.197Figure 14.5: C-tree conditional permutation regional importance map using submandibular gland sub-segmentmean dose and resting saliva facets. Cranial aspects (closest to the floor of the mouth) are mostimportant. Agreement with c-tree non-conditional importance (in fig. 14.4) is strong.198Figure 14.6: Quantified c-tree conditional permutation importancefor individual sub-segments. Sub-segment (‘SS’) numbering isshown in figs. 14.4 and 14.5. Importance is presented as thepercentage of relative importance compared to a homogeneousorgan (which would be 100%). Anatomical groupings displaythe per-group median (filled circles). Cranial-posterior aspects(closest to the floor of the mouth) are most important, with rela-tive importance up to ∼3.5× that of an equivalent homogeneousorgan sub-segment.19914.4 Summary and ConclusionsIn this limited follow-up analysis, the most consistent methods of chapter 13were applied to analyze resting saliva, submandibulars, and xerostomia.Regional effects were found. The caudal aspect of the parotid, like thestimulated saliva case, were most important for xerostomia. However, anteriorand posterior aspects were less differentiated. The submandibular showeddifferent regional importance, with the cranial aspect being most important.The meaning of importance in chapters 12 and 13 was derived froma combination of model selection, sensitivity analysis, and permutationtechniques. Linear models, which were the best candidate models in everycase considered, established a link between importance derived from analysisand clinical relevance. However, this association is not fully understood forsubmandibulars or xerostomia. In both cases, a more careful inspection isrequired to assess the relationship. The purpose of this chapter was notto fully demonstrate regional importance, but rather to motivate furtherresearch on the topic.200Chapter 15Development of a DCE-MRIImaging Protocol115.1 IntroductionSaliva supports ongoing tooth and gum solidity in various ways: by acting asa buffer against acids and bases; maintaining a healthy oral flora by flushingbacteria and mastication debris from the oral cavity; delivering digestiveenzymes to the oral cavity; and easing oral transport by lubricating oralsurfaces. These basic functions enable a variety of everyday facilities, suchas speech, efficient mastication and deglutition, and the perception of taste.Consequently, the loss of salivary function has a strong impact on one’s qualityof life [464]. Salivary function loss resulting from radiotherapy treatment ofhead-and-neck cancers is common [236].There are many critical tissues in the head-and-neck (e.g., spinal cord,brainstem, ocular nerves) for which delivering even moderate radiotherapydoses results in catastrophic repercussions for patients. On the other hand,1The contents of this chapter are an updated version of an early manuscript that waslater published under the title ‘Development of a method for functional aspect identificationin parotid using dynamic contrast-enhanced magnetic resonance imaging and concurrentstimulation’ in Acta Oncologica (2015 Oct 21; vol. 54, no. 9, pp. 1686-90; Taylor & Fran-cis Ltd., http://www.tandfonline.com/loi/ionc20) by Haley Clark, Vitali Moiseenko,Thomas Rackley, Steven Thomas, Jonn Wu, and Stefan Reinsberg [3].201delivering the prescribed dose to a suspected tumour volume is crucial formaintaining local control. Spectator tissues, which are not critically radiosen-sitive nor part of the tumour volume, are used as conduits for deliveringradiotherapy dose to inaccessible tumour volumes. Highly radiosensitivetissues are spared by shifting dose to spectator tissues like parotid glandsand other salivary organs [465]. Though such irradiation is unavoidable,treatment planners using modern treatment techniques like volumetric mod-ulated arc therapy or intensity modulated proton therapy have freedom toadjust intra-parotid radiation quantities and locations. Detailed knowledgeof tissue response and outcome risk is therefore needed for effectual planning[466, 467].Presently used consensus guidelines for parotid gland sparing assume ahomogeneous distribution of functional burden [236], are difficult to attainin practice, and do not ensure specific outcomes [410]. In recent years,evidence has mounted to suggest a heterogeneous distribution of functionalburden within the parotid [466]. Recent reports have found delivering doseto one region of rat parotid results in a different incidence of objectivexerostomia (dry mouth) than delivering that same dose elsewhere [356].Regional susceptibility of subjective (i.e., patient-reported) xerostomia hasbeen noted in human parotid [233]. In light of an earlier investigation by ourgroup, it is presently unclear to what extent these findings relate to objectivefunction alteration in humans, or whether such regions align with parotidparenchyma [324]. Pursuit of this avenue of research is enticing owing to thepotential ramifications on treatment planning and possible improvement ofoutcomes for head-and-neck patients.In a recent survey of salivary gland radiation reduction techniques, Vissinket al.. [465] advocate tissue sparing as the most effective method. There isgrowing evidence that functional imaging can be clinically relevant for moreclearly defining target volumes and assessing adverse normal tissue effects[466]. We report the development of a novel technique making use of DynamicContrast-Enhanced Magnetic Resonance Imaging and concurrent salivarystimulation which can potentially identify parotid parenchyma in healthyvolunteers. Inter- and intra-parotid tissue differentiation are possible, and202application of the protocol could potentially improve tissue sparing. Resultsfrom a small, healthy volunteer trial are provided.15.2 Methods15.2.1 Ethics and Accrual of VolunteersThe study protocol was approved by the BCCA University of British Columbia(UBC) REB, and is in accordance with agency ethical standards and theHelsinki Declaration. Between December 2014 and May 2015, four healthyindividuals (one female and three males, between 25 and 35 years of age)volunteered for this study, giving informed consent. Individuals were excludedif they presented any standard MR contraindications (e.g., incompatibleimplants, prosthetics, or clips; foreign metallic bodies, including shrapnel ordebris in their eyes; pregnancy), contraindications to intravenous gadoliniuminjection (e.g., history of adverse reactions, history of or family history ofrenal disease), or had metal retainers or amalgam fillings which could causesusceptibility artifacts. For the purposes of this study symmetrically pairedorgans (parotids, masseters) are effectively treated as individual organs,resulting in a total pool of eight unique organs.15.2.2 Image Collection and ProcessingPerfusion imaging was chosen as the primary imaging method due to its powerto non-invasively characterize functioning glandular tissues with high tempo-ral resolution. Reports have demonstrated the ability of Dynamic Contrast-Enhanced Magnetic Resonance Imaging (DCE-MRI) to quantitatively mea-sure radiotherapy-induced parotid gland perfusion alterations. These al-terations are thought to result from increased extracellular-extravascularspace and decreased vascular permeability stemming from radiation damage[468]. Likewise, function alteration can also be quantified via blood perfu-sion to parenchyma [469]. Perfusion changes measured via DCE-MRI reflectphysiological changes.Magnetic resonance images were collected using a dedicated research 3T203Philips Achieva MR scanner at the University of British Columbia. The imag-ing protocol is as follows. Volunteer hydration prior to imaging was controlledby asking them to abstain from food or drink the night prior and leadingup to the imaging session. DCE images used intravenously administeredgadolinium contrast agent (Bayer Magnevist gadopentetate dimeglumine) atthe manufacturer’s recommended total dose of 0.2mL/kg with an injectionrate of 4mL/s followed by a 20mL saline flush. DCE imaging comprised aT1-weighted spoiled gradient echo sequence with 2.960ms repetition time,1.351ms echo time, and a flip angle of 12◦. Images were reconstructed axi-ally with 1.46× 1.46× 4.00mm spatial resolution, 3.9s temporal resolution,375mm field of view in both phase-encode and frequency-encode directions,and 4mm slice thickness. Images were continuously collected for 450-600s.Contrast agent was administered 45-60s after DCE sequence commencement.Salivation was manually induced 170-240s after contrast agent injection bypassing a small amount (8mL) of a weak citric acid solution (2% by weight)into the oral cavity using a syringe via polyethylene tubing.Additional short gradient echo scans with a 3◦ flip angle were collectedprior to contrast injection. These were compared to the aforementionedlonger-running 12◦ flip angle images to generate per-voxel contrast agent timecourses C(t). To expedite total scan time by forgoing collection of imageswith additional flip angles, the signal difference method discussed by Ashton[470] was used to compute C(t). Specifically, pre-contrast signal was averagedand subtracted from post-contrast signal. Spatial averaging was used toreduce the impact of noise.For three of the four volunteers, two DCE sequences were performedback-to-back. In the first, 1/3 of the total contrast agent was injected, nostimulation was performed, and 450s of data was continuously collected. Inthe second, the remaining 2/3 was injected, salivation was stimulated, andimaging continued for 600s. Injection splitting was done to produce a baselinecontrast agent response curve from which we could more clearly access thestimulatory response. Scans without stimulation were shortened to reducetotal imaging duration. Splitting 1/3 – 2/3 produced a baseline curve withoutsubstantially reducing the second scan signal-to-noise ratio with lingering204contrast agent.ROIs (parotid, masseter, and pharyngeal tissues) were manually contouredfrom anatomical and DCE MR images using the DICOMautomaton softwaresuite [7]. Parotid ROIs were also partitioned into anterior/posterior halves.15.2.3 Statistics – Variance AnalysisNon-parametric techniques were employed. The primary technique developedfor inter-parotid analysis (and cross-organ analysis, e.g., parotid vs. masseter)is a topological analysis and involves characterizing the variance of C(t) on acluster-of-voxels basis. We refer to it hereafter simply as ‘variance analysis.’Variance was selected because the observed time courses proved difficultto model but were uniformly more variable after salivation was induced.The procedure is straightforward2. First, for each voxel in a given ROI,at a specific temporal point, the contrast agent present was computed byaveraging neighbouring in-plane voxels. For the entirety of this report, voxelswere included if they were less than two voxel-widths (2 × 1.46mm) awayfrom the centre of a given voxel. The specific number of neighbours useddid not appreciably affect findings. Second, time courses (spatially-averagedcontrast over time) were constructed for each voxel. Third, variance wasestimated using an unbiased estimator over a temporal sliding window. Forthe entirety of this report, the window extended ±20s from a given datum.While conclusions were not substantially affected by the width of the window,spikes in the resulting time courses broaden as this width is increased. Fourth,variance time courses were combined over the ROI by summation. Finally,because summed variance time courses depend on ROI volume, the totalamount of contrast injected, and other factors, they were normalized to oneanother in the window of time after the initial contrast agent uptake peakbut before stimulation occurred.Variance analysis admits a natural way to compare pairs of time courses:compute the difference between the curves, compute the mean of the differenceover all time points before and after stimulation, and examine whether the2Not only is it straightforward computationally, requiring only basic descriptive statistics,but it also has no underlying model which can be violated.205means are significantly different. The same procedure is applicable withoutsubtracting curves; instead of comparing the mean of the differences, themean absolute variances can be compared. Since the null hypothesis is thatthere is no response to stimulation, and variance should remain approximatelyconstant during the washout period, the mean will not change unless there isa stimulatory response.Means are compared using the standard two-sample unpooled t-test forunequal variances (Welch’s t-test). Approximate normality of differenceswas explicitly inspected in all cases. The paired Wilcoxon signed-rank testis used to assess whether population mean ranks differ between two pairedsamples. Both tests are invariant to uniform ordinate scaling, so for simplicityarbitrary units are used throughout.15.2.4 Image MapsA qualitative, non-parametric, topological method was developed to character-ize intra-parotid tissue variation before and after stimulation. The techniqueis as follows. First, spatially averaged contrast agent time courses are con-structed (as above) for each voxel in both stimulated and unstimulated DCEseries. Second, each series is broken into pieces and two parts are retained: (1)post-contrast agent injection and pre-stimulation, and (2) post-stimulation.For unstimulated series, the stimulation break point was taken to be identicalto the stimulated series break point. Third, a straight line was individuallyfit to each part (before and after stimulation). Fourth, the difference of slopesin the unstimulated case were subtracted from the difference of slopes in thestimulated case. As the shape (in contrast to the scale) of C(t) is not stronglyaffected by the specific quantity of agent, and is monotonically decreasing inthe washout phase, any residual quantity indicates a response (i.e., variationsin washout) to stimulation. Finally, a map is generated from the residualquantity. This technique is later referred to as the “difference of changes inslope” technique.20615.3 ResultsThe mean parotid volume was 19.9± 4.4cm3 (mean ±σ of the mean, median:18.2cm3). Left and right volumes correlate strongly (mean for left: 19.6cm3vs.right: 20.2cm3).A typical, spatially averaged per-voxel C(t) from parotid is shown infig. 15.1. Key features of the protocol are visible. From left to right: (1) thepre-contrast agent injection window (left-most grey box); (2) the rapid uptakeperiod, where high concentrations of contrast rapidly perfuse into the parotidtissues, peak, and then begin to slowly wash out; (3) the period of stimulation– in this case, beginning at 230s and continuing until approximately 240s fromthe scan start – and a response to stimulation manifest as a modest increasein contrast agent concentration; and (4) the continued slow contrast washout.Not all C(t) look as clear as fig. 15.1; the volunteer in fig. 15.1 received asingle injection of the full contrast agent to maximize the signal-to-noise ratio.Examples of other C(t) are shown in fig. 15.2. In particular, some voxelsdecrease, rather than increase, and many do not show any obvious responsewhatsoever. Response, if any, is generally delayed 10-30s after stimulationcommencement. The response shape varies from a fast positive or negative‘blip’ to an ongoing shift or bias.15.3.1 Variance AnalysisFor 3 of 4 volunteers (6 of 8 parotids), variance analysis demonstrated aclear distinction in apparent parotid stimulatory response (see fig. 15.3). Thefourth volunteer’s variance was uniformly high and consequently no responsewas detected. The mean of the difference before and after stimulation infig. 15.3 were significantly different (two-tailed t-test: 0.0 ± 1.1E − 4 pre-vs. 1.9 ± 0.1E − 3 (arb. units) post-stimulation mean ±σ of the mean;p < 0.0001). It is visually apparent that the paired Wilcoxon sign-rank testwas also significant as the curves are almost entirely separated by a large gappost-stimulation (p < 0.0001).In 4 of 6 parotids (2 of 3 volunteers) where both stimulated and unstimu-lated time courses were collected, the Wilcoxon test indicated a significant207 0  100  200  300  400  500  600C(t) [arb. units]Time [s]Contrast agent C(t)Bezier spline approx.Fitted double exponentialFigure 15.1: A typical spatially averaged voxel C(t) demonstratingtemporal stages of the protocol. From left: pre-contrast agent in-jection window (left-most grey box); rapid uptake period, wherehigh concentrations of contrast rapidly perfuse into parotidtissues, peak, and begin to drain; stimulatory period runningfrom 230-240s from scan commencement, and a stimulatoryresponse manifest as a modest contrast agent concentrationincrease; and continued slow washout. An empirical fit omit-ting the stimulatory period and Bezier spline interpolationare shown as visual guides. Figure previously published in[3], reproduced with permission from Taylor & Francis Ltd.;http://www.tandfonline.com/loi/ionc20.208Figure 15.2: Examples of time courses similar to fig. 15.1, but showingvarying responses to the stimulation beginning at 230s. Positive,negative ‘blips’ and ongoing shifts are seen. Splines are used as avisual guide; note the strong deviation 10-30s after stimulation.Figure previously published in [3], reproduced with permissionfrom Taylor & Francis Ltd.; http://www.tandfonline.com/loi/ionc20.difference in pre- and post-stimulation variances (p < 0.05). The other twoparotids were near significance (p = 0.05 and p = 0.08). Two-tailed t-testscould be applied to examine mean shift (i.e., mean variance pre- vs. post-stimulation) in all cases; examination of the stimulated time course showedthat 6 of 8 parotids had p < 0.02 (1.88± 0.17E − 2 pre- vs. 1.68± 0.33E − 2post-stimulation or greater separation). For unstimulated time courses, themean shift for 3 of 6 parotids had p < 0.05.For each individual volunteer, parotid (left and right) was significantly209 100  150  200  250  300  350  400  450Variance time course [arb. units]Time [s]Unstimulated courseStimulated courseFigure 15.3: Variance analysis time courses in parotid (stimulated andunstimulated, with Gaussian kernel smoothed trend lines as a vi-sual guide) showing a clear distinction in trend after stimulationoccurs (300s). Means before and after stimulation are signifi-cantly different (p < 0.0001 ; two-tailed t-test), suggesting a dif-fering contrast dynamics resulting from stimulation. Figure pre-viously published in [3], reproduced with permission from Taylor& Francis Ltd.; http://www.tandfonline.com/loi/ionc20.distinct from masseter (left and right) after stimulation in 13 of 16 cases: usinga paired Wilcoxon sign-rank test, p < 0.0001 for 12 of the 13 and p = 0.04in the remaining case. In 12 of 16 cases the mean of the differences weresignificantly different before and after stimulation using a two-tailed t-test(p < 0.02). Comparison of left and right masseter for each patient showedthat in 3 of 4 cases, masseters did not respond differently to stimulation (two-tailed t-test p > 0.07; similar Wilcoxon p-values). Comparison of masseterto a variety of nearby, non-specific pharyngeal tissues in a single volunteer210indicated they were, on average, not significantly different (Wilcoxon p = 0.07;two-tailed t-test p = 0.72). However, comparison of left and right parotidshow that they respond differently to stimulation: p < 0.0001 for all Wilcoxontests, p < 0.005 (0.9±4.2E−4 left vs. 4.2±0.6E3 right or greater separation)for all t-tests. 100  150  200  250  300  350  400  450Variance time course [arb. units]Time [s]ParotidMasseterFigure 15.4: Comparison of parotid and masseter response to stimu-lation. Compared with nearby tissues, parotid response is morerapid and greater in amplitude. Figure previously publishedin [3], reproduced with permission from Taylor & Francis Ltd.;http://www.tandfonline.com/loi/ionc20.The variance analysis technique found post-stimulation parotid to besignificantly distinct from masseter, pharyngeal tissues, and other parotids.An example comparison is shown in fig. 15.4. A variance analysis was alsorun on posterior and anterior parotid portions of equal volume. Similar towhole parotids, two-tailed t-tests quantified mean shifts. For anterior parotid,211stimulated time courses in 6 of 8 parotids had p < 0.05 (1.0± 0.3E − 2 pre-vs. 9.7± 0.7E − 2 post-stimulation), whereas for unstimulated only 2/6 hadp < 0.05. For posterior parotid, stimulated time courses in 4 of 8 parotids hadp < 0.05; 4 of 6 had p < 0.05 for unstimulated courses. Comparison of theanterior and posterior portions directly showed a significant discrepancy instimulatory response in right parotid (Wilcoxon p 0.001) in 3 of 4 cases. Thesame discrepancy was seen in the left parotid in all 4 cases. These findingsindicate that anterior and posterior aspects of the parotid show independentlydistinct responses to stimulation.15.3.2 Image MapsTo further assess intra-parotid variations, image maps were generated usingthe difference of changes in slope technique. In these maps, a voxel thathas no response to stimulation will be midtone. Voxels that respond with apositive change in slope are brighter, while those that respond negatively aredarker. Example slices from two volunteers are shown in fig. 15.5 which clearlyshows intra-parotid variation. An enlarged example is shown in fig. 15.6.15.3.3 DiscussionThe aim of this pilot study was to develop a DCE-MRI imaging protocolcapable of identifying parotid gland parenchyma in healthy volunteers. Noexisting literature on concurrent DCE-MRI and salivary stimulation wasfound. DCE-MRI was chosen for its temporal resolution and ability to assessfunctional alterations via blood perfusion to parenchyma [469]. Scintigraphyis a well known and historically well used technique for quantifying parotidfunction but produces 2D images and requires the use of costly radioisotopes(see [464] and references therein). A novel technique making use of dynamic11C-methionine PET analogous to DCE-MRI has been described by Buus et al.[69, 471] which improves on earlier single photon emission CT methods inspatial resolution. PET produces high quality volumetric images but requiresinjection of a positron-emitting tracer and may require an additional imagingmodality for (co-)registration [472]. Both potentially increase patient dose.212Figure 15.5: A single slice example of image maps for two volunteers(top and bottom). At centre: temporally-averaged T1-weightedimages; at left: contrast agent; at right: difference of changesin slope maps in parotid. In the latter, voxels which showed noresponse to stimulation (within the ROI) are midtone, thosethat responded with a positive change in slope are brighter, andthose that responded negatively are darker.Perfusion computed tomography is generally considered a low-cost, viablealternative to DCE-MRI [81, 473], but DCE-MRI generally has superiorspatial and temporal resolution, and requires no ionizing radiation [474].Perfusive changes were observed following stimulation, but response varied.Figure 15.1 shows a typical spatially averaged C(t) from a parotid voxel.Examples of other C(t) are shown in fig. 15.2. Response, if any, was generallydelayed 10-30s after stimulation commencement.For 3 of 4 volunteers (6 of 8 parotids), variance analysis demonstrated a213Figure 15.6: Enlarged example image map slice. At left: a temporally-averaged T1-weighted image with the difference of changesin slope map overlaid on the parotids; at right: enlargedparotid maps. In the latter, voxels showing no stimulatoryresponse are midtone. Those that responded positively (neg-atively) are brighter (darker). Figure previously published in[3], reproduced with permission from Taylor & Francis Ltd.;http://www.tandfonline.com/loi/ionc20.clear distinction in parotid stimulatory response. This result, combined withobserved differences before/after stimulation and differences in pre-/post-stimulation variances, suggests variation in parotid response depending onthe presence of a salivary stimulus.Image maps figs. 15.5 and 15.6 were generated using the difference ofchanges in slope technique to assess intra-parotid variations. Such variationwas observed. The portion of parotid nearest to the posterior edge of themandible (as indicated) was most dissimilar from surrounding parotid tissues.This region was recently found by van Luijk et al. to house stem/progenitorcells in rat parotid, and was reported as being strongly correlated withpost-radiotherapy salivary output in humans (personal communication3,2014). The alignment of regions found using different techniques suggests the3Note: was ultimately published as [357].214proposed techniques may be suitable for locating critical regions. Maps wereslowly varying and qualitatively regular across patients, suggesting a possibleheterogeneous functional burden distribution.Similar to the technique described by Buus et al. [69, 471], our varianceanalysis and difference of changes in slope techniques could be used to assessradiotherapy induced functional alterations. Unlike Buus et al.’s technique,through the use of MR, our technique could be used to directly observeregional salivary compensation in nearly real-time throughout the entire 3DROI.For each individual volunteer, parotid (left and right) was generallysignificantly distinct from masseter (left and right) after stimulation. Masseterwas not distinct from nearby non-specific pharyngeal tissues. Left and rightmasseters did not respond differently to stimulation, but left and right parotiddid. This indicates parotids are more strongly responding to stimulation thanmasseter. Distinction in parotid response was apparent. Variance analysisshowed that after stimulation, parotid was significantly distinct from masseter,pharyngeal tissues, and other parotids. Compared with parotids, the responseof nearby tissue to stimulation occurred later and with reduced amplitude.An example is shown in fig. 15.4. This finding is logical: salivation involvesthe transport of water which is rapidly replenished from the blood plasmaduring continued flow [25].A variance analysis performed on posterior and anterior portions of theparotid showed that, on average, there was a significant discrepancy in leftand right parotid stimulatory response, indicating that anterior and posteriorparotid aspects show distinctly different responses to stimulation.There are a number of limitations that remain to be addressed. It is notclear whether the proposed techniques can handle the so-called bath andshower effect observed in rat parotid [356], which complicates tissue sparing.An explanation for this effect proposed in [356] and observed by Konings et al.[348, 349] – that portions of the parotid can be regenerated by progenitor cellsin distant portions – would require a more sophisticated analysis if correct.However, parenchyma localization and sparing would likely remain valuablefor reducing early functional loss.215One limitation of the signal difference method is that it ignores non-linearity in the conversion from signal intensity to concentration that arisefrom simultaneous alteration of tissue T1 by the contrast agent [475]. Com-parison between C(t) reconstructed using a traditional method via three flipangles and the signal difference technique showed the latter to be more stable.Flip angle variability was not explicitly measured and remains unknown.The signal difference technique is thought to be more reliable in this regime.A limitation of the difference of changes in slope technique is that slopechanges represent a complicated admixture of pharmacokinetic parameterswhich cannot be easily interpreted as a specific change in tissues. Giventhat function alteration can be quantified via blood perfusion [469], perfusivechanges are likely to play a strong role. Further investigation is needed.Functional tissue localization could potentially be improved using moreadvanced, faster imaging techniques or supplementary imaging. Candidatesinclude relaxometry [476], blood oxygenation level dependent MR [477], andintravoxel incoherent echo-planar motion imaging [80, 478]. De Langen et al.[472] suggests that dynamic PET and DCE-MRI are largely complementarytechniques for assessing tumour blood flow – we believe simultaneous use ofBuus et al.’s [69, 471] PET technique is also amenable to our method andmay enable functional structures to be located with greater reliability sinceour method has no model assumptions that can be violated. These additionaltechniques were not investigated as a protocol relying only on DCE-MRI wasdesired.15.4 ConclusionsA non-parametric variance analysis technique has been developed whichappears suitable for spatially localizing parenchyma using stimulation inducedconcurrent with imaging. Using this technique, differences in response werenoted across parotid, masseter, and pharyngeal tissues. Both intra- and inter-parotid differences were observed, and a mapping procedure was developedto quantify intra-organ differences. It is hoped that this imaging protocol(or a variation upon it) may ultimately be useful in non-invasively locating216parenchyma in head-and-neck cancer patients prior to radiotherapy so thatthey can be spared. It is believed this would significantly reduce toxicity risk.217Chapter 16ConclusionsThe broad aim of this thesis was to improve knowledge of late salivary glandtoxicity risks for head-and-neck cancer patients treated with radiotherapy.More specifically, this work sought to: demonstrate the existence of regionaleffects involving late salivary dysfunction and regional radiation dose withinthe parotid gland, characterize the clustering nature which might lead tocritical regions, and finally quantify the relative importance of whole parotid.Demonstration of similar effects in other salivary organs or using other facetswas a secondary goal.Regional effects were demonstrated. Using a careful comparative approachbased on equal-volume segmentation, parametric methods that establishedthe existence of regional effects and also provided a link between relativeimportance and clinical relevance, and non-parametric methods that scaled toaccommodate fine segmentation, regional effects were also quantified. Limitingradiation dose to the caudal aspects of the parotid is most important forcurbing dysfunction. They may also be most important for xerostomia.Some clustering was noted, though it is somewhat broad and mostly spreadalong the anterior-posterior direction. Submandibulars may demonstratean inverted (in the superior-inferior direction) importance profile, but morecareful investigation is needed.21816.1 Summary of Contributions1. Systematically demonstrated the existence of a regional effect in parotidusing stimulated whole-mouth saliva and sub-segment radiation doses.2. Elucidated the clustering nature of parotid dysfunction regional ef-fects. Demonstrated that tightly-confined clusters do not appear atthe population-level1. Rather, regions with elevated importance aresomewhat broad and concentrated in the caudal aspect.3. Quantified parotid dysfunction regional effects throughout whole parotids,demonstrating that some regions have >4× the importance than theywould if the parotid were a pure parallel organ.4. Developed a non-invasive imaging protocol that appears able to locatesalivary gland parenchyma and may be suitable for patient-specifictoxicity risk assessment.5. Demonstrated a regional effect in submandibulars (for dysfunction)and again in parotids (for xerostomia) that broadly coincides withparotid-dysfunction regional effects.6. Devised both intra- and inter-analysis uncertainty estimation tech-niques based on congruence of unrelated importance methods and theemergence of smooth spatial gradients from spatially-unaware analyses.These methods are statistically underpowered, but remain viable whenmore sophisticated methods fail.7. Developed a spatially unbiased segmentation procedure.8. Extended a computational system (DICOMautomaton) to perform robust,iterated vector contour segmentation using a branch-and-bound tech-nique to achieve segmentation with arbitrary volumetric constraints.1It is possible that one or more confined critical regions are present within individualglands, however the somewhat anatomically-adaptive segmentation employed in this worksuggests that such regions, if present, are patient-specific or irregularly scattered.21916.2 Avenues for Future ResearchThough the findings described in this work are internally consistent, evenacross analysis methods and different toxicity facets, they are only in moderateagreement with the existing literature. The most promising and conclusivemeans of extending this research would be development of a clinical trial (orpilot study) in which the relative importance of parotid glands is accountedfor during treatment planning. There are, however, a few loose ends thatshould first be addressed.First, all importances derived in this work are population-level. It remainsto be seen how applicable they are at the individual patient-level. A promisingtechnique based on DCE-MRI was described in chapter 15, but it was devel-oped wholly on volunteers. The relevance to patients receiving radiotherapyremains unknown, and the link between parenchyma and relative importancealso remains unknown. A number of promising imaging techniques are emerg-ing or have emerged in recent years (see section 3.1) – any may be suitable toelucidate the link between parenchyma and importance. Whichever method issuccessful, if any are, could provide a pathway to patient-specific dysfunctionor xerostomia risk assessment if it can be introduced into regular clinicalpractice. Justification in the form of salivary organ sub-structure sparingmay provide an impetus to get around the chicken-and-egg problem.Second, the methods developed in this work are general and could inprinciple be applied to any OAR. As described in section 13.4, even compli-cations like the bath-and-shower effect are thought to be handled throughuse of permutation importances. While some limited follow-up analysis wasdescribed in chapter 14, a more thorough analysis in other OAR is alsopossible.Third, this thesis focused on the loss of salivary function. Given ex-citing developments linking functional recovery and stem/progenitor cells,it would be worthwhile to adapt the developed methods to try isolate re-gions most important for recovery. If the association between local density ofstem/progenitor cells and recovery was quantified, then treatment plans couldmake use of dose profiles that were sculpted to promote recovery of function220in addition to loss of function. It might also suggest the most effective regionsto deposit transplanted cells, as discussed in section 8.2.Finally, simultaneous analysis of multiple facets is not currently possibleusing the methods developed in this thesis. Extension to accommodatemultiple facets would lead to a more thorough analysis, such as derivationof inter-organ relative importance by simultaneously incorporating parotids,submandibulars, and oral cavity contributions to whole-mouth saliva wouldbe possible with little additional work. Conversely, the simultaneous handlingof multiple response variables in a single, comprehensive analysis, such asdysfunction and xerostomia, is an attractive end-goal with clear clinicalrelevance but a much clear analytical pathway. At the moment it is possibleto simply combine relative importance maps from separate analysis, but therobustness of this approach is suspect.Given that these four loose ends are all tractable, there is no practicalbarrier to translation of this work into a clinical pilot study. In particular,because the caudal aspect of the parotid appears to control the majority oftoxicity risk, importance maps may not even need to be directly introducedinto the treatment planning workflow. Rather, splitting parotid sparingpractices so that some dose from the caudal-most 40-50%-volume is shiftedcranially (which maintaining nodal doses on the inferior surface) may sufficeto demonstrate clinically-meaningful reduction in late toxicities. Takingthis ‘slow introduction’ approach, it may even be possible (and prudent, forcomparison purposes) to maintain existing clinical mean dose thresholds.221Bibliography[1] Haley Clark. 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