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Myelin water imaging in health and disease - techniques, applications, and multimodal integration Baumeister, Tobias Robert 2019

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Myelin Water Imaging in Health and Disease–Techniques, Applications, and Multimodal Integration–byTobias Robert BaumeisterB.Sc., University of Applied Science Koblenz, RheinAhrCampus, 2009M.Sc., University of Applied Science Koblenz, RheinAhrCampus, 2013A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Biomedical Engineering)The University of British Columbia(Vancouver)December 2019© Tobias Robert Baumeister, 2019The following individuals certify that they have read, and recommend to theFaculty of Graduate and Postdoctoral Studies for acceptance, the dissertationentitled:Myelin Water Imaging in Health and Disease–Techniques, Applications, and Multimodal Integration–submitted by Tobias Robert Baumeister in partial fulfilment of the requirementsfor the degree of Doctor of Philosophy in Biomedical EngineeringExamining Committee:Co-supervisor: Martin J. McKeown, NeurologyCo-supervisor: Z. Jane Wang, Electrical & Computer EngineeringUniversity Examiner: Stefan Reinsberg, Physics & AstronomyUniversity Examiner: Purang Abolmaesumi, Electrical & Computer EngineeringExternal Examiner: Bruce Pike, Radiology & Clinical NeurosciencesAdditional Supervisory Committee Members:Supervisory Committee Member: Alex MacKay, Physics & Astronomy and Radiol-ogySupervisory Committee Member: Shannon Kolind, NeurologyiiAbstractNeuroimaging with magnetic resonance imaging (MRI) has made great contri-butions to our understanding of neurological diseases. Among the many differ-ent imaging techniques, myelin water imaging (MWI) appears to be particularlypromising for investigating white matter microstructure, particularly in terms ofits myelin content. MWI has shown great success in identifying and characterisingalterations of myelin content in neurological diseases but is still only available inresearch settings. In order to bring it closer to clinical practice, its utility, efficacy,and robustness need to be examined.In this work, we investigated the utility of MWI by applying it to Parkinsonsdisease (PD), a neurodegenerative disease with typically unremarkable changesin the white matter in a clinical setting. We show that MWI and data-drivenmultivariate analysis methods can predict distinct PD symptom domains.Furthermore, we have demonstrated a robust relation between myelin, cog-nitive performance and clinical characteristics in Multiple Sclerosis (MS) with adata fusion analysis that finds joint patterns of covariation among the differentmodalities.Additionally, we have devised new methods to analyse MWI images that notonly offer more information about the white matter microstructure, but also makeuse of complementary information of multimodal MRI experiments. We havedemonstrated a characteristic myelin pattern along major white matter fibre bun-dles that shows superior accuracy in classification of sex than traditional analysis.We have also shown that MWI can be linked to the topological organisation of func-tional brain networks, either on its own or in combination with other parametersiiicharacterising the white matter microstructure.Lastly, we have devised a novel method that makes use of spatiotemporalsimilarity of white matter voxels in order to denoise MWI data. This method leadsto spatially-smoother myelin maps and prove to be more robust in the presence ofnoise, ultimately leading to more accurate in vivo measurements of myelin in thebrain.In summary, we have shown the utility of MWI by applying it to neurodegen-erative diseases, developed methods to leverage joint information of multimodalwhite matter imaging techniques, and proposed a novel method to denoise T2relaxation data.ivLay SummaryMagnetic resonance imaging (MRI) can help doctors examine tissue changes in thebrain, aiding in the diagnosis of neurological diseases. In this dissertation we haveexamined one new MRI extension, Myelin Water Fraction (MWF), in order to bringit closer to clinical practice. We have shown how MWF is altered in both MultipleSclerosis and Parkinson’s diseases. We have developed methods that make MWFmore accurate and robust, so it can be more useful in assessing brain diseases ingeneral and even in monitoring natural ageing and development.vPrefaceAll of the work presented henceforth was conducted at the Pacific Parkinson’sResearch Centre at The University of British Columbia, Point Grey campus. Thisdissertations is primarily based on three published journal papers, one publishedconference paper, and two journal papers in preparation for publication. In allpublications I was responsible for concept formation, data analysis and evaluation,as well as manuscript composition. All other co-authors contributed to editing themanuscripts. Ethics approval for acquiring the patient data was issued by the UBCResearch Ethics Board (H09-02016, H12-01510).Chapter 2 is based on the publication:• Baumeister, T. R., Kim, J. L., Zhu, M., and McKeown, M. J. (2018). WhiteMatter Myelin Profiles Linked to Clinical Subtypes of Parkinsons Disease. Journalof Magnetic Resonance Imaging 50(1), 164-174.Kim J. L. and Zhu M. contributed with MRI data collection and psychologicalassessments of participants. Zhu M. helped with data analysis in SPSS. McKeownM. J. helped with data analysis suggestions and interpretation. All co-authorscontributed to editing the manuscript.Chapter 3 is based on the publication:• Baumeister, T. R., Lin, S. J. Vavasour, I., Kolind, S., Kosaka, B. Li, D. K. B.,Traboulsee, A., MacKay, A., McKeown, M. J. (2019). Data Fusion Detects Consis-tent Relations Between Non-Lesional White Matter Myelin, Executive Function, andviClinical Characteristics in Multiple Sclerosis. NeuroImage:Clinical 24, 101926.Lin S. J. contributed to data interpretation and helped with suggestions for dataanalysis. Vavasour I., Kolind S., Kosaka B., Li D. K. B., Traboulsee A., and MacKayA. provided clinical and myelin water imaging expertise. McKeown M. J. providedfeedback for improving the methodology and data interpretation. All co-authorscontributed to editing the manuscript.Chapter 4 is split into two parts,• part one is based on work currently in preparation for publication:Baumeister, T. R., Wang, J. Z., McKeown, M. J., Changes in Functional NetworkTopology can be Estimated by White Matter Integrity in Parkinson’s Disease.• part two is currently under preparation for publication:Baumeister, T. R., Wang, J. Z., McKeown, M. J., White Matter Integrity Similar-ity Networks, a Novel Method to Investigate White Matter Integrity in a NetworkContext.For both parts, Wang J. Z. and McKeown M. J. provided feedback for improvingthe methodology, helped interpret the findings as well as contributed to manuscriptediting.Chapter 5 is based on the publication:• Baumeister, T. R., Wang, J. Z., McKeown, M. J. (2019), A Multivariate Approachfor Denoising of T2 Relaxation Decay Curves in Myelin Water Fraction Imaging.Proceedings of 2019 IEEE Global Conference on Signal and InformationProcessing (in press)Wang J. Z. and McKeown M. J. provided feedback for improving the methodol-ogy and contributed to manuscript editing.Chapter 6 is based on the publication:vii• Baumeister, T. R., Kolind, S., MacKay A., McKeown, M. J. (2019). InherentSpatial Pattern of Myelin Water Fraction Maps. Magnetic Resonance Imaging(in press)Kolind S. and MacKay A. provided valuable feedback of data interpretation.McKeown M. J. contributed to refinement of data analysis and data interpretation.All co-authors contributed to manuscript editing.viiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xivList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviiiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxivDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxv1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Myelin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2.1 Central Nervous System . . . . . . . . . . . . . . . . . . . . . 31.2.2 Myelin Structure & Function . . . . . . . . . . . . . . . . . . 41.3 Myelin Water Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3.2 MWI in Health . . . . . . . . . . . . . . . . . . . . . . . . . . 12ix1.3.3 MWI in Disease . . . . . . . . . . . . . . . . . . . . . . . . . . 141.4 Combining Multimodal MRI Data . . . . . . . . . . . . . . . . . . . 191.5 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211.6 Thesis Organisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 Myelin Water Imaging in Parkinson’s Disease . . . . . . . . . . . . . . . 272.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.2 Materials & Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.2.1 Participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.2.2 Clinical Assessment . . . . . . . . . . . . . . . . . . . . . . . . 302.2.3 MRI Data Acquisition . . . . . . . . . . . . . . . . . . . . . . 302.2.4 Processing of Imaging Data . . . . . . . . . . . . . . . . . . . 312.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423 Multimodal Data Fusion in Multiple Sclerosis . . . . . . . . . . . . . . 483.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.2 Materials & Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 513.2.1 Statistical Analysis . . . . . . . . . . . . . . . . . . . . . . . . 543.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.3.1 Multiset Canonical Correlation Analysis . . . . . . . . . . . . 573.3.2 Effects of Lesions . . . . . . . . . . . . . . . . . . . . . . . . . 603.4 Post-Hoc Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664 Linking White Matter Integrity to Functional Connectivity . . . . . . . 754.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 764.2 Introduction to brain networks . . . . . . . . . . . . . . . . . . . . . 764.2.1 Functional networks . . . . . . . . . . . . . . . . . . . . . . . 774.2.2 Brain Network Analysis . . . . . . . . . . . . . . . . . . . . . 784.3 Functional Modularity Estimated by White Matter Integrity in Parkin-son’s Disease . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82x4.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 824.3.2 Materials & Methods . . . . . . . . . . . . . . . . . . . . . . . 834.3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 874.3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 894.3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 934.4 White Matter Integrity Similarity Networks Associated with Parkin-son’s Disease Symptoms . . . . . . . . . . . . . . . . . . . . . . . . . 944.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 944.4.2 Construction of White Matter Integrity Similarity Networks 964.4.3 Materials & Methods . . . . . . . . . . . . . . . . . . . . . . . 984.4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1014.4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1015 Spatiotemporal Filtering of T2 Decay Curves . . . . . . . . . . . . . . . 1095.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1105.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1115.2.1 Selection of Voxels with Similar Decay Curves . . . . . . . . 1125.2.2 Multivariate Empirical Mode Decomposition . . . . . . . . . 1125.2.3 Multiset Canonical Correlation Analysis . . . . . . . . . . . . 1145.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1145.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1186 Inherent Spatial Structure in Myelin Water Fraction Maps . . . . . . . 1206.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1216.2 Materials & Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 1246.2.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1246.2.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1256.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1286.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1367 Conclusion & Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . 1417.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141xi7.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1437.2.1 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1447.2.2 Multimodal Integration . . . . . . . . . . . . . . . . . . . . . 1457.2.3 Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182A Supporting information for Chapter 6 . . . . . . . . . . . . . . . . . 182xiiList of TablesTable 2.1 Demographics and Clinical Scores for the PD and Healthy Cohort. 31Table 2.2 Comparison of average MWF and FA across all 20 investigatedWM ROIs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Table 2.3 Average and standard deviations of clinical scores per cluster. . . 43Table 3.1 Demographics, clinical, and cognitive measures. Displayed areaverages and standard deviations. For clinical measures (EDSSand disease duration) the median and their respective ranges areshown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52Table 3.2 Listings of canonical loadings of the imaging features and associ-ated p-values in the MCCA model including and excluding lesiontissue. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62Table 3.3 Listings of canonical loadings of the cognitive features and associ-ated p-values in the MCCA model when including and excludinglesion tissue. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63Table 3.4 Listings of canonical loadings of the demographic and clinicalfeatures and associated p-values in the MCCA model when in-cluding and excluding lesion tissue. . . . . . . . . . . . . . . . . . 63Table 3.5 Comparison of clinical and demographical indices between clusters. 67Table 6.1 Classification results from a LDA. Shown are the sensitivity, speci-ficity, accuracy, and AUC for each LDA when using the tractprofiles or whole tract average as input. . . . . . . . . . . . . . . . 135xiiiList of FiguresFigure 1.1 Illustration of a brain and its microstructure with an illustrativeWM connection (fibre bundle) on the left. A neuron, as part ofthe WM fibre bundle, with its myelinated axon is shown on theright. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Figure 1.2 Diagram of the process of calculating MWF maps. . . . . . . . . 8Figure 1.3 Pictogram of thesis organisation illustrating to which categoryof Applications, Techniques, or Multimodal Integration eachchapter belongs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Figure 2.1 Comparison of MWF and FA between PD and healthy controls. 38Figure 2.2 Relation between imaging features and clinical scores for the firstPLS component linking UPDRS and MoCA scores to distinctWM regions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Figure 2.3 Relation between imaging features and clinical scores for thesecond PLS component linking UPDRS and tremor scores todistinct WM regions. . . . . . . . . . . . . . . . . . . . . . . . . . 40Figure 2.4 Relation between imaging features and clinical scores for thethird PLS component linking depression and apathy scores todistinct WM regions. . . . . . . . . . . . . . . . . . . . . . . . . . 41Figure 2.5 Results from cluster analysis on the PLS transformed imagingdata showing three clusters. . . . . . . . . . . . . . . . . . . . . . 42xivFigure 3.1 White Matter ROIs used to extract the average MWF and link tocognitive and demographic variables. . . . . . . . . . . . . . . . 53Figure 3.2 Correlation of canonical variates . . . . . . . . . . . . . . . . . . 58Figure 3.3 MCCA loadings of each feature per set on their respective canon-ical variate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59Figure 3.4 Color coded canonical profiles to visualise the opposing pullof some demographic and cognitive features on the canonicalvariates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60Figure 3.5 MCCA loadings of each feature per set on their respective canon-ical variate when excluding lesions from the analysis . . . . . . 61Figure 3.6 Comparison of MCCA loadings with and without lesions . . . . 64Figure 3.7 MCCA loading comparison in cognitive and demographic setswhen including and excluding lesions . . . . . . . . . . . . . . . 64Figure 3.8 Color coding of ROIs showing lesion presence across subjects. . 65Figure 3.9 k-means clustering results on canonical variates. . . . . . . . . . 66Figure 4.1 Process of generating a FC matrix . . . . . . . . . . . . . . . . . . 78Figure 4.2 Illustration of the graph theoretical measures in a toy network. . 79Figure 4.3 Differences in global network features over different densitylevels between PD and HC. Stars signify significant differencesbetween groups at significance level of 0.05. Shaded areas signifystandard errors of the mean. N (PD) = 29, N (HC) = 15. . . . . . 88Figure 4.4 True and estimated functional modularity by the LASSO regres-sion with MWF in WM as predictors. The model explains 74% ofthe variance with a p-value of 0.020 based on permutation tests.N = 29. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89Figure 4.5 Weights of the selected WM regions by LASSO. Errorbars repre-sent standard errors across all bootstrapping runs. . . . . . . . . 89Figure 4.6 PLS correlation between combined imaging and clinical features 90Figure 4.7 Process of generating WISN. . . . . . . . . . . . . . . . . . . . . . 97xvFigure 4.8 Fiedler Value and GT features of WISNs at different densitythresholds for healthy controls and PD. . . . . . . . . . . . . . . 102Figure 4.9 WISN network features at density threshold that maximallydifferentiates groups. Stars indicate significant differences atp< 0.05. Errorbars are standard errors of the mean. N (PD) = 29,N (HC) = 15. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103Figure 4.10 CCA results between WISN and clinical features . . . . . . . . . 104Figure 4.11 Explained covariance per LV and associated p-value from per-mutation tests from the PLS analysis. The horizontal grey linesignifies the 0.05 significance threshold. . . . . . . . . . . . . . . 104Figure 4.12 PLS results for associating WISN features to FC . . . . . . . . . 105Figure 4.13 Absolute bootstrap ratios of FC in the PLS analysis with WISNfeatures. Shown are the top 15 % of positive bootstrap ratios,including long range frontal to temporal connections as well asoccipital to parietal areas. . . . . . . . . . . . . . . . . . . . . . . 106Figure 5.1 Comparison of MWF maps with the three investigated methods:MEMD-MCCA-rNNLS, rNNLS, nlsrNNLS . . . . . . . . . . . . 116Figure 5.2 Comparison of average MWF in WM across all subjects in (a) andaverage CoV in WM in (b). Errorbars are standard deviationsacross subjects. N = 12. . . . . . . . . . . . . . . . . . . . . . . . . 116Figure 5.3 Comparison of structural consistency of computed maps . . . . 117Figure 5.4 Test-retest reliability comparison between the three methods . . 118Figure 6.1 Schematic Illustration explaining the subdivision of a fibre bun-dle and its corresponding tube. . . . . . . . . . . . . . . . . . . . 127Figure 6.2 Histogram of local CoV values comparing MWF with FA maps. 129Figure 6.3 Rendering of the extracted major fibre bundles. . . . . . . . . . . 129Figure 6.4 Coefficient of Variation (CoV) of whole tracts and tubes in a)MWF and b) FA. N = 41. . . . . . . . . . . . . . . . . . . . . . . . 130Figure 6.5 CoV gradient comparison between adjacent fibre tract segmentsto perpendicular directions. . . . . . . . . . . . . . . . . . . . . . 131xviFigure 6.6 MWF and FA tract profiles in the left hemisphere . . . . . . . . . 132Figure 6.7 Age estimation with fibre tract profiles and tract averages . . . . 133Figure 6.8 MWF (green) and FA (orange) tract profiles of tracts able to sig-nificantly estimate age based on MWF predictors. Stars indicatesignificant segments in the model along the MWF profile. N = 41. 134Figure 6.9 LDA accuracy and AIC when differentiating sex based on MWF 136Figure 6.10 LDA ROC curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137Figure A.1 MWF and FA CoV gradient comparison between adjacent fibretract segments to perpendicular directions in right hemisphere. 183Figure A.2 MWF and FA tract profiles in right hemisphere. . . . . . . . . . 184Figure A.3 MWF tract profiles in the two individual cohorts . . . . . . . . . 185Figure A.4 FA tract profiles in the two individual cohorts . . . . . . . . . . 186xviiAcronymsAAL automated anatomical labellingAD Alzheimer’s diseaseADHD attention-deficit / hyperactivity-disorderAFQ automatic fibre quantificationAIC Akaike information criterionANTs advanced normalization toolsASD autism spectrum disorderAUC area under the curveaD axial diffusivityBDI Beck depression indexBG basal gangliaBICAMS brief international cognitive assessment for multiple sclerosisbSSFP balanced steady state free precessionCCA canonical correlation analysisCNS central nervous systemxviiiCoV coefficient of variationCSF cerebrospinal fluidCV cross validationDAWM diffusely abnormal white matterDMD dynamic mode decompositionDMN default mode networkDSI diffusion spectrum imagingDTI diffusion tensor imagingDWI diffusion weighted imagingEDSS expanded disease severity scaleEMD empirical mode decompositionFA fractional anisotropyFAST FMRIB’s automated segmentation toolFC functional connectivityFLIRT FMRIB’s linear image registration toolfMRI functional magnetic resonance imagingFNIRT FMRIB’s non-linear image registration toolFSL FMRIB software libraryFSS fatigue severity scaleFWHM full width half maximumxixGM grey matterGRASE gradient and spin echoGT graph theoryHC healthy controlH & Y Hoehn & YahrICA independent component analysisIMF intrinsic mode functionJHU Johns Hopkins UniversityLARS Lille apathy rating scaleLASSO Least Absolute Shrinkage and Selection OperatorLDA linear discriminant analysisLEDD levodopa equivalent daily doseLV latent variableMACFIMS minimal neuropsychological assessment of multiple sclerosis patientsMANOVA multivariate analysis of varianceMCCA multiset canonical correlation analysismcDESPOT multicomponent driven equilibrium single pulse observation of T1and T2MCI mild cognitive impairmentMD mean diffusivityMEMD multivariate empirical mode decompositionxxMNI Montreal neurological instituteMoCA Montreal cognitive assessmentMR magnetic resonanceMRI magnetic resonance imagingMS multiple sclerosisMSA multiple systems atrophyMSE mean squared errorMSN morphometric similarity networkMT magnetisation transferMTR magnetisation transfer ratioMWF myelin water fractionMWI myelin water imagingNAART north american adult rating testNAWM normal appearing white matterNMO neuromyelitis opticaNNLS non-negative least squaresPCA principal component analysisPD Parkinson’s diseasePLS partial least squaresrD radial diffusivityxxiROC receiver operator characteristicROI region of interestRRMS relapsing remitting multiple sclerosisrs-fMRI resting-state functional magnetic resonance imagingSAS Starkstein apathy scaleSCN structural covariance networkSGPR rapid spoiled gradient recalledSN substantia nigraSNR signal to noise ratioSPSS statistical package for the social sciencesSSIM structural similarity indexSVD singular value decompositionSVM support vector machineSWI susceptibility weighted imagingTE echo timeTI inversion timeTR repetition timeUPDRS unified Parkinson’s disease rating scaleWAIS-IV Wechsler adult intelligence scale - IVWISN white matter integrity similarity networkxxiiWM white matterWMI white matter integrityxxiiiAcknowledgementsI would like to thank my supervisors Dr McKeown and Dr Wang for their valuablesuggestions and direction throughout my studies. I’d also like to express mygratitude towards the members of my supervisory committee Dr Alex MacKay andDr Shannon Kolind for their continued encouragement and thoughtful insights.I’d also like to thank my examination committee Dr Stefan Reinsberg and DrPurang Abolmaesumi and the external examiner Dr Bruce Pike for their valuablecriticism and insightful feedback.I want to thank the Pacific Parkinson’s Research Centre and my current andformer lab mates Saurabh, Maria Zhu, Soojin Lee, Nino Hernandez-Torres, VanessaWiggermann, Tom Brosch, and Sue-Jin Lin. You guys provided the right balance ofmeaningful, work-related discussions and ramblings about anything else. It was apleasure working with all of you.I want to express my gratitude towards all the participants of the MRI experi-ments, the MRI technicians for acquiring the data, and for the support from theParkinson’s Society of Canada, the MS Society of Canada, the UBC/PPRI Chairin Parkinson’s research, and the UBC Biomedical Engineering Graduate Programwith the Engineers in Scrubs program.I like to thank may family for the support throughout all these years and whohave encouraged and enabled me to go to Canada.Finally, I owe my gratitude to my girlfriend Sue whose love and support carriedme through this thesis. Your encouragement over the years means the world to me.xxivDedicationTo my grandmotherxxvChapter 1Introduction1.1 MotivationMyelin is critical for healthy brain function. It plays a fundamental role in de-termining the speed of action potentials; when myelin integrity is compromised,brain function is affected. Alternatively, when new brain functions are learned orcompensatory pathways are formed following neuronal damage, one expects tosee modulation of myelination in the involved nerve tracts. Therefore, an accuratein vivo measure of myelin content has important implications for understandingbrain plasticity and pathological aspects in neurological disorders.Magnetic resonance imaging (MRI) is a useful tool to study in vivo brain struc-tures, providing superb contrast between tissue types. With typical spatial reso-lutions that range from 0.6 - 3mm, MRI is able to provide great detail about thebrain’s morphology. In a clinical setting, MRI is predominantly used in a qual-itative manner, with diagnoses based on visual inspection by evaluating shapeand contrast of the brain structure or tissue in question. While this approach oftenleads to the desired outcome, e.g. a brain structure was found to be abnormallysmall based on the reviewers expertise, this approach may lack reproducibility,introduce inter-rater bias or result in misinterpretation. In order to alleviate theaforementioned drawbacks, quantitative MRI aims to characterise the shape or1Chapter 1. Introductiontissue of brain structures in a unbiased manner by utilizing various MRI param-eters that enhance contrast or measure tissue specific properties. In recent yearsmany MR techniques have been developed and implemented for imaging in vivomyelination. In this thesis we focus primarily on one of these techniques - myelin waterimaging (MWI) based on T2 relaxation curves.MWI has been introduced to study healthy as well as pathological processes inthe brain white matter (WM), ranging from myelination patterns during develop-ment in children to changes in myelin content during healthy ageing. In diseasepopulations such as neurological and neurodegenerative disorders, studies haveshown that myelin content can differentiate a diseased population from a healthyone (Dayan et al., 2016). Associating myelin with disease severity, or monitoringand characterising myelin to evaluate the effects of interventions has providedbetter understanding of disease states (Kolind et al., 2012).Despite the increased knowledge obtained by applying MWI to neurologicaldisorders, much work is needed to be done in order to establish MWI as a safe, ef-ficient, and reliable clinical tool to help diagnose or monitor neurological disorders.In particular, providing proof that MWI informs disease processes, even in thesetting of unremarkable conventional MRI scans (e.g., Parkinson’s disease (PD)),would open up a whole new research avenue of a previously mostly neglectedarea. In addition, given the complex nature and diverse clinical manifestations ofneurological diseases, it is unlikely that a single symptom can be associated with asingle MRI feature. There is rather a multitude of MRI features that can be linkedto either one or multiple symptoms, and one should take advantage of all availabledata in order to make inferences about diseases. Lastly, given that MWI is still in aresearch state and not commercially available for clinical use, tools for new anglesof data analysis are highly desirable as they can elevate our understanding andprovide potentially more accurate characterisation of myelin in the human brainsuitable for clinical use.As such, we have identified three domains in the field of MWI that can bringit closer to routine clinical applications. While each domain captures a specificaspect of MWI, overlap between them is both unavoidable and necessary, owing2Chapter 1. Introductionto the interdisciplinary expertise of engineers, physicians, and physicists requiredto advance the field of MWI. The three domains and their respective objectives inthis thesis are:1. Techniques – technical developments to robustly calculate the myelin proxy,myelin water fraction, as well as providing new analysis methods2. Applications – broaden the utility of MWI by applying it to new neurologicaldiseases3. Multimodal Integration – leverage complementary information among fea-tures of different modalities to reveal hidden links as well as to characteriserelationships between them1.2 Myelin1.2.1 Central Nervous SystemThe central nervous system (CNS) is comprised of the brain and spinal cord.Broadly, their tissue composition can be divided into WM and grey matter (GM).The nerve cells, or neurons, found in the CNS can be broken down into theirfunctional parts, the soma (cell body; the site of major metabolic activity), theaxon (elongated extensions, myelinated or unmyelinated, that transmit electricalimpulses), and the dendrites (axon terminals connecting to other neurons), seeFigure 1.1 for a schematic illustration of a neuron. An axon’s diameter is variablebetween 1 and 20µm and its length lies between a few millimeters more than onemeter. The GM consists predominantly of somas and thus is responsible for sensoryperception, muscle control, cognitive performance, and self awareness, and otherfunctions (Frackowiak, 2004). The WM is organised in bundles of axons, or fibrebundles, connecting and facilitating effective signal transport and communicationbetween different brain across the GM (Fields, 2008).3Chapter 1. IntroductionFigure 1.1: Illustration of a brain and its microstructure with an illustrativeWM connection (fibre bundle) on the left. A neuron, as part of the WMfibre bundle, with its myelinated axon is shown on the right.1.2.2 Myelin Structure & FunctionIn the CNS, myelin is produced by oligodendrocytes and envelopes axons withmany layers trapping water molecules between them. Myelin is a fatty substanceconsisting of lipids and proteins and accounts approximately for 50% of the WMdry weight, giving the WM its distinct color. Axons are typically not continuouslywrapped with layers of myelin, but rather with shorter myelin sheaths interspersedwith unmyelinated focal points (nodes of Ranvier), Figure 1.1. This organisationstrikes a balance between energy cost and efficient signal transmission (Heath et al.,2018).Myelin acts as an electrical insulator enabling conduction of action potentialsand is thus considered a key component of the CNS. Compared to unmyelinatedaxons, a myelinated axon can transport action potentials up to 10 to 100 timesfaster (Purves and Williams, 2001). This is achieved by having the action potentialsjump from one node of Ranvier to the next, while the intermediate myelin sheathsact as insulators with high resistance and low conductance (Laule et al., 2007).The resulting saltatory conduction is much faster than a continuous conductionalong unmyelinated axons (Laule et al., 2007). As speed and coherence of signaltransmission is considered to play an essential role in complex motor or cognitivefunctions, myelin is of crucial importance.4Chapter 1. IntroductionA compromised myelin structure inhibits neuronal signal transmission whichmanifests a wide range and with varying degrees of physical and cognitive dis-abilities. Additionally, myelin provides trophic support for the axons and thusa demyelination could lead to irreversible axonal loss. Therefore, the ability tomeasure myelin in vivo holds great promise to study neurological diseases as wellas healthy development and ageing. It can be used to track myelination dur-ing development, characterise demyelination in disease, and monitor potentialremyelination processes from clinical or pharmaceutical interventions.1.3 Myelin Water ImagingMWI is a quantitative MRI technique with the goal to provide an in vivo markerfor myelin content. While it is not possible to quantify the amount of myelindirectly, it is possible to quantify a surrogate marker for myelin: the water trappedwithin the myelin bilayers wrapped around the axons. MWI exploits the fact thatdifferent water environments behave slightly differently in an MR experimentand thus can be teased apart by careful analyses. MWI provides a proxy marker,the myelin water fraction (MWF), which relates the myelin water (water trappedbetween myelin layers) to the total water measured. This fraction has been shownto correlate well with histopathological measures of myelin content (Laule et al.,2008).The basic principle behind MWI is that the MR signal primarily stems fromhydrogen protons found in water molecules. Depending on the environment ofthe molecules, their corresponding T2 relaxation time varies, with free movingwater molecules having a slightly longer T2 than water molecules trapped withinmyelin bilayers. Differentiating these two water environments and putting themin relation to each other is foundation of MWI.1.3.1 TheoryIn a homogeneous environment, the transverse relaxation time, T2, follows a mono-exponential decay, whereas complex biological tissue exhibits a multiexponential5Chapter 1. Introductiondecay. This behaviour stems from the fact that physically distinct biological mi-crostructures possess different MR properties. The water in WM in humans canbroadly be divided into two discrete microstructures, the myelin water within themyelin bilayers, and water between intra- and extracellular membranes each withtheir respective T2 times. In a T2 relaxation experiment, one acquires a series ofimages at multiple echo times in an effort to characterise a T2 relaxation curve ateach individual voxel. Given the multiple water components in biological tissue,the measured T2 relaxation curve can be described as a superposition of M T2components with the following expressionyi =M∑j=1s je−tiT2 j , i= 1,2, . . . ,N, (1.1)where yi is the signal amplitude at measurement time point ti, s j is the amplitudeof the j-th T2 component, and N is the total number of measurements. The solutionto finding the unknown s j in Equation 1.1 is a numerically ill-posed problem andthus sensitive to noise (Graham et al., 1996; Istratov and Vyvenko, 1999). These decaycurves are most commonly analysed using a non-negative least squares (NNLS)fitting procedure, enabling the decomposition of the signal into a distribution of T2times.Whittal and MacKay (Whi‚all and MacKay, 1989) suggested a multi-exponentialanalysis framework for T2 relaxation studies based on the NNLS from (Lawsonand Hanson, 1995). This method inverts a multi-exponential decay curve into arelaxation time distribution and thus offers insight into tissue composition basedon the respective water compartments. A group of basis exponential functionscharacterizes the measured signal in yi:yi =M∑j=1s je−tiT2 j =M∑j=1ai js j, i= 1,2, . . . ,N, (1.2)with ti is the measurement time, M is the number of logarithmically spaced T2decay times, N is the total number of measurements, s j are the amplitudes of the T26Chapter 1. Introductiondistribution which we need to solve for, and A = [ai j]N×M. The NNLS is then usedto minimizeχ2min =mins≥0 N∑i=1∣∣∣∣∣ M∑j=1ai js j− yi∣∣∣∣∣2 . (1.3)The authors then suggested a constraint to be incorporated to provide more robustfits in the presence of noise in the form ofχ2reg =mins≥0 N∑i=1∣∣∣∣∣ M∑j=1ai js j− yi∣∣∣∣∣2+µK∑k= j∣∣∣∣∣ M∑j=1hk js j− fk∣∣∣∣∣2 (1.4)where H = [hk j]K×M representing K additional constraints and f is the correspond-ing vector of right hand side values. The regularization parameter µ is selectedsuch that χ2reg from Equation 1.4 is equal to 1.02χ2min of the unregularized minimummisfit found in Equation 1.2. The constant factor of 1.02 results in a 2% increasein the misfit which was empirically defined as a good fit (Whi‚all and MacKay,1989). The T2 distribution can be estimated from the s j from Equation 1.4 from theirrespective decay times T2 j. Matrix H is typically selected to the identity matrix andvector f is set to zero, resembling standard Tikhonov regularization, which worksas a L2 norm regularizer to produce smooth distributions. This analysis placesminimal assumptions on the underlying T2 distribution which is advantageous incases of alterations of T2 times due to pathological processes.The MWF is then defined as the signal less than 40 ms at 3 T relative to thetotal signal of the T2 distribution and has been shown to be proportional to themyelin content in histopathological studies (Laule et al., 2008, 2006, 2004) as well asa decrease in known degenerate areas (Laule et al., 2004). Figure 1.2 shows thisprocess pictorially.1.3.1.1 Improvements in MWIDue to its noise sensitivity and low signal to noise ratio (SNR), many efforts havebeen undertaken to improve the reconstruction of MWF maps. Methods relying7Chapter 1. IntroductionFigure 1.2: Illustration of the process of calculating the MWF with NNLS. Themeasured decay curve (left) is decomposed with a NNLS algorithm intoa T2 distribution where the amplitudes of respective T2 times reflect thecontribution to the measured signal (middle). Once the T2 distribution isobtained, the amplitudes in the myelin water, and intra-/extracellularwater range get integrated and the ratio of myelin water to total watercontent is computed to produce the MWF. Inset of myelin electonmi-croscopy image adapted from (Siegel et al., 1999).on the NNLS have incorporated temporal or spatial filters to produce more robustmaps under the influence of noise. One method used principal component analysis(PCA) to achieve spatial smoothing based on a low rank representation of imagepatches (Does et al., 2019). A different approach is to include spatial priors, includinglocal and non-local similarities between T2 distributions, to obtain MWF maps lessinfluenced by noise (Bouhrara et al., 2018; Kumar et al., 2018, 2012, 2016; Yoo andTam, 2013). Other methods include using Bayesian inference (Layton et al., 2013), acombination of Wald distributions (Akhondi-Asl et al., 2014), orthogonal matchingpursuit (Drenthen et al., 2018), or filtering (Jones et al., 2004). In addition, recent deeplearning methods have found some success in calculating MWF maps as well (Leeet al., 2019).1.3.1.2 Other Techniques to Infer Myelin ContentMultiecho T2 relaxation studies are not the only technique to study in vivo myelincontent. Although this thesis makes use of the T2 multiecho sequences, for com-pleteness sake, a brief overview of some alternative methods follows below.8Chapter 1. IntroductionDi€usion MRI One of the most widely used techniques to study white matterintegrity (WMI) is diffusion weighted imaging (DWI). The basic principle of DWIis to measure the diffusion of water molecules by applying a set of diffusionweighted gradients in a wide variety of directions. Water molecules that move dueto Brownian motion will cause a signal attenuation along the respective gradientdirection and is a measure of diffusion along that direction. The diffusion ofwater in the brain is guided by its underlying microstructure of the tissue thatcan be described by diffusion tensor imaging (DTI) (Basser et al., 1994). In DTI, thediffusion of water in a given voxel can be described by a tensor that is characterisedby its three eigenvalues λ1,λ2,λ3 and their associated eigenvectors µ1,µ2,µ3 wherethe eigenvalues and eigenvectors reflect the degree and direction of diffusion,respectively. In homogeneous tissue, the diffusion is isotropic and the tensoris approaching a sphere with λ1 = λ2 = λ3. In biological tissue, the diffusion isconstrained by its microstructure and the tensor will be elongated with in thedirection of main diffusion λ1 > λ2 ≥ λ3.DTI is widely used and its most common measures to characterise the WMmicrostructures areFractional Anisotropy(FA) =√32√(λ1−λ )2+(λ2−λ )2+(λ3−λ )2√λ 21 +λ22 +λ23, (1.5)Mean Diffusivity(MD) =λ1+λ2+λ33, (1.6)Axonal Diffusivity(aD) = λ‖ = λ1, (1.7)Radial Diffusivity(rD) = λ⊥ =λ2+λ32, (1.8)with λ = λ1+λ2+λ33 . fractional anisotropy (FA) is used as a measure of generaldiffusion anisotropy, mean diffusivity (MD) reflects the average diffusion in agiven voxel, axial diffusivity (aD) is a measure of diffusion along an axon andthought of reflecting axonal integrity, and radial diffusivity (rD) is a measure ofdiffusion perpendicular to axons and is believed to represent myelination. A study9Chapter 1. Introductionby (Song et al., 2002) was the first to suggest this relation of DTI parameters to theunderlying microstructure but has since been controversially discussed (Wheeler-Kingsho‚ and Cercignani, 2009). However, since then many studies have revealedthe ambiguity of the diffusion signal due to its inference of WM microstructurebased on water diffusion and thus is unable to identify the biological source ofdiffusion changes. The DTI parameters are influenced by axonal packing, axonaldispersion thus making them an unspecific marker for myelin. The correlationbetween DTI parameters and MWF was shown to be modest at best (Ma¨dler et al.,2008).mcDESPOT Another alternative to multiecho relaxation experiments is a techniquecalled multicomponent driven equilibrium single pulse observation of T1 and T2(mcDESPOT) (Deoni et al., 2008). It is based on rapid spoiled gradient recalled(SGPR) echo and balanced steady state free precession (bSSFP) sequences withvarying flip angles and thus benefits from high SNR efficiency (West et al., 2019).The data is fitted to a two-pool model comprising a fast relaxing (myelin water)and slow relaxing (intra- and extracellular water) portion with potential exchangebetween them. The model includes parameters for T1 f ,T2 f and T1s,T2s where f ands represent the fast and slow relaxing compartments, their relative sizes representedby their equilibrium magnetisation M0 f and M0s, and intercompartmental exchangerates k f s and ks f making it a complex model that may be poorly posed (Heath et al.,2018).The mcDESPOT approach provides MWF values in differing ranges comparedto T2 relaxation studies but has been able to demonstrate altered myelin content indisease groups. In general, the MWF derived from mcDESPOT are overestimatedthan the ones from a multiecho relaxation experiment (Alonso-Ortiz et al., 2015;Deoni et al., 2013; Zhang et al., 2015). Potential sources for this discrepancy may bean ill-conditioned model, or the neglect of magnetisation transfer in the model(Deoni and Kolind, 2015; Lankford and Does, 2013). Nevertheless, mcDESPOT has beenshown to reflect changes in myelination in a multiple sclerosis (MS) cohort (Kolindet al., 2015), produce maps with reasonable separation of WM and GM (Zhang et al.,10Chapter 1. Introduction2015), in addition to be able to model and predict developmental trajectories ofMWF (Dean et al., 2015; Deoni et al., 2013).Magnetisation Transfer Magnetisation transfer (MT) imaging explores the exchangeof energy between solid and free pools of water. Non-aqueous protons, such asprotons in hydrogen molecules bound to lipids and proteins, exhibit extremelyshort T2 times causing their signal to decay too fast to be measured by imagingmethods. MT imaging techniques aim to exploit the interactions between motion-unrestricted protons in water (solid pool) and restricted non-aqueous protons(water pool) (Wol€ and Balaban, 1989). It utilizes the exchange of magnetisationbetween these two environments by diffusion and chemical processes to obtainan indirect measure of the usually MR-invisible non-aqueous protons (Vavasouret al., 2011). This is achieved because the non-aqueous protons have a much widerrange of resonance frequencies compared to the protons in the water pool so thata radio frequency pulse applied off resonance to the water pool will excite onlythe protons in the solid pool. In order to return back to equilibrium, these newlyexcited protons exchange magnetisation with the protons in the water pool whichin turn results in a signal attenuation in the water signal. With the assumptionthat most non-aqueous protons are bound to myelin in the CNS, the magnetisationtransfer could be used as an indirect marker of myelin (Heath et al., 2018). Atypical MT experiment consists of two acquired images, one with an off resonancepulse to excite the sold pool and one without. Given these two acquisitions, themagnetisation transfer ratio (MTR) can be calculated as followsMTR =(1− MsM0)(1.9)with Ms and M0 as the measured magnetisation with and without the off resonancepulse, respectively.MTR offers sensitivity to altered WM microstructure showing a decrease innormal appearing WM (Catalaa et al., 2000; Vavasour et al., 1998) and lesions (Pikeet al., 2000) in MS subjects. Histological validation studies have shown that MTR11Chapter 1. Introductioncorrelates with myelin staining in post mortem MS brains (Schmierer et al., 2004),as well as in animal models (Dousset et al., 1995). Similarly, in a study by (Vavasouret al., 1998) the decreased MTR in MS subjects was reported to correlate with MWF.However, similar to DTI parameters, changes in MTR are not specific to myelin,so that although a change in myelin likely causes a change in MTR, the reversemay not necessarily be true. A change in MTR need not be caused by alteredmyelination alone, but can also be due to other factors such as inflammation(Brochet and Dousset, 1999; Gareau et al., 2000; Vavasour et al., 2011) or edema (Cooket al., 2004).1.3.2 MWI in HealthMyelin is a key component for normal brain development and proper brain func-tioning. Myelogenesis, i.e., the profileration of myelin sheaths around axons, beginsaround the fifth fetal month (Kinney, 2018) and lasts well into adulthood (Filley, 1998;Yakovlev and Lecours, 1967). Studies have utilized MWI to assess myelin in healthypopulations during different stages of development as well as in later periods oflife in order to gain an understanding how the myelination process is linked tocognitive and physical abilities. One crucial aspect during development is theestablishment and facilitation of rapid communication pathways throughout theWM, especially in light of a recently emerging hypothesis that abnormal myeli-nation in these formative years may lead to neurodevelopmental or psychiatricdisorders (Halperin et al., 2012; Xiao et al., 2014). On the other hand, WM undergoesbiophysical changes throughout adulthood, including a decline of myelin contentin old age. It is thus important to investigate age related changes of myelin inlater stages in life in order to establish fundamental references to disease relatedneurodegeneration.1.3.2.1 DevelopmentThe myelogenesis in the WM during the first years of life is essential for normalneurodevelopment by establishing and facilitating effective signal transmission12Chapter 1. Introductionthrough WM pathways. The myelination during the first five years is a complexprocess of rapid myelin production in concert with dynamic changes in the brain’sstructure to reflect the formation of cognitive and behavioural functions (Deoniet al., 2016). The cerebellum and pons are the first structures to myelinate, followedby the splenium of the corpus callosum. The occipital and parietal lobes are next,with anterior regions such as genu of corpus callosum and frontal lobes among thelast structures to be myelinated (MacKay and Laule, 2016). This observed pattern ofmyelination, moving caudocranially from the corticospinal tract to posterior andlastly to anterior regions of the brain, has been noted before in autopsied infants(Kinney et al., 1988). When this pattern of myelination is disturbed, neurodvelop-mental and psychiatric diseases such as autism spectrum disorder (ASD) (Xiaoet al., 2014) or attention-deficit / hyperactivity-disorder (ADHD) (Halperin et al.,2012) may manifest.MWI has been able to provide new insights into the development of myelin inbabies and children. In a study of children from three to 60 months, a significantassociation between MWF and in the corpus callosum and general cognitive abilitywas found (Dean et al., 2015; Deoni et al., 2016). The same study also noted a dynamicrelationship between cognitive abilities and distinct WM areas that varied withage. Another study reported sex differences during myelogenesis (Dean et al., 2015),while another study noted that initially slower developing myelin but a longergrowth phase lead to higher cognitive abilities (Deoni et al., 2016). Moreover, amodel of myelin trajectories was developed that could be used to identify aber-rant developmental patterns to potentially counteract the adverse effects early on(Dean et al., 2014). It should be noted that the majority of these studies used themcDESPOT protocol to obtain a marker for myelination.1.3.2.2 Healthy AgeingAs the brain ages, it undergoes many biophysical as well as biochemical processesthat lead to cortical thinning (Bajaj et al., 2017; Pacheco et al., 2015), reduction ofbrain volume (Scahill et al., 2003), or a decrease in WM integrity (Madden et al., 2012;Yang et al., 2016) among others. These changes occur in concordance with a decline13Chapter 1. Introductionin cognitive functioning such as processing speed (Ebaid et al., 2017) or memoryloss (Ebaid and Crewther, 2018), while these processes are part of the normal humanphysiology, they may mask changes in disease or even be falsely attributed to adisease.In order for MWI to become a reliable biomarker, studies should be undertakento assess the normal evolution and decline of myelin in order to establish a robustreference for comparison against disease populations. One study with a cohorts’age spanning multiple decades from their teens to the eighth decade of life found ageneral reduction of MWF with age (Faizy et al., 2018). They noted a negative linearrelation between MWF and age while reporting no differences between malesand females. Of note, they did not detect a significant decrease in MWF in thefirst four decades of life, reaffirming a prolonged myelination process well intoadulthood. Another study with a slightly younger cohort found only moderatepositive correlations between MWF and age (Billiet et al., 2015), while a study by(Arshad et al., 2016) observed a negative quadratic relation between MWF and agein addition to higher MWF in females. These differences may be due to differencesin calculation of MWF maps, chosen regions of interest (ROIs) or uneven subjectcohorts. A commonality between these studies is however, a noted monotonicrelation between MWF and age during the first four to five life decades. This issupported by other results, with a cohort reaching the fourth decade of life, thatreported a positive correlation between frontal MWF and age (Flynn et al., 2003), aswell as reading ability and years of education (Lang et al., 2014).1.3.3 MWI in DiseaseNeuroimaging, and MRI, has been proven very useful to detect changes in brainstructure and metabolism in almost all neurological diseases due to its excellentspatial resolution and ability to probe for specific tissue properties. Some have beenextensively studied to find biomarkers for MS (Filippi and Agosta, 2010), Alzheimer’sdisease (AD) (Dickerson et al., 2011), schizophrenia (Dazzan, 2014), and others. Somebiomarkers are accessible with standard clinical scans such as T1 weighted images14Chapter 1. Introductionto investigate differences in cortical thickness (ƒerbes et al., 2009), others makeuse of T2 weighted images to better detect and visualize lesions, focal points ofstructural tissue alterations (Mostert et al., 2010). On the other hand, advancedimaging techniques such as MWI, DTI, susceptibility weighted imaging (SWI),resting-state functional magnetic resonance imaging (rs-fMRI) have been utilizedto gain advanced knowledge of the pathophysiology of many neurological diseases(Cochrane and Ebmeier, 2013; Laule et al., 2007; Lee et al., 2013; Mi‚al et al., 2009).Given the ubiquitous presence of myelin and its imperative role for proper brainfunctioning, a reliable characterisation of in vivo myelin content is of great interest.The ability to robustly measure WM myelination has widespread applications tostudy neurological diseases by obtaining insights into disease processes as well astracking the efficacy of therapeutic interventions. In particular, MWI found its wayinto the broad spectrum of neurological diseases with MS being the most widelystudied disease. In fact, much of the early development and application of MWIwas applied to MS and has greatly contributed to furthering our understanding ofthe disease. Other neurological disorders with widely accepted changes in the WMIsuch as neuromyelitis optica (NMO) (Manogaran et al., 2016), schizophrenia (Flynnet al., 2003), AD (Bouhrara et al., 2018), primary lateral sclerosis and amyotrophiclateral sclerosis (Kolind et al., 2013) have been shown to demonstrate altered MWF.Additionally, some disease that typically are not considered to be WM diseasessuch as PD have recently gained renewed interest in examining the WMI withadvanced quantitative MR techniques.In this thesis, two neurological diseases will be investigated. We use MWI toinvestigate the WM of PD in order to learn more about the involvement of WMchanges during the course of the disease. Additionally, we will use advancedanalysis techniques and apply these to MS to extend the current knowledge aboutMWF and its relation to clinical characteristics.1.3.3.1 Parkinson’s DiseasePD is the second most common neurodegenerative disorder affecting 1 - 2% ofpeople over the age of 65 years (Scandalis et al., 2001), with its prevalence escalat-15Chapter 1. Introductioning to as high as 3% with increasing age (Kouli et al., 2018). Pathologically, thedisease is defined by the unexplained degeneration of dopaminergic neurons inthe substantia nigra (SN) pars compacta (SNc). These neurons project to the basalganglia (BG), which facilitate the initiation and execution of voluntary movement.Accordingly, the most common symptoms in people with PD are characterized bymotor disorders such as bradykinesia (slowness of movement), rigidity, restingtremor and postural instability (Jankovic, 2008), as well as increasingly recognizednon-motor symptoms such as cognitive impairment (Meireles and Massano, 2012),apathy (Pagonabarraga et al., 2015), and depression (Becker et al., 2011). PD is consid-ered a very complex and heterogeneous disease (Politis, 2014) and patients sufferingfrom PD typically experience a substantial presymptomatic period by the timesymptoms start to emerge (McKeown and Peavy, 2015). Given the multitude ofdifferent symptom domains, the existence of widespread implications on a varietyof brain areas and tissue types is likely.Traditional imaging techniques, especially ones investigating WM, haven’tbeen commonly applied to PD due to the fact that traditional scans were notsensitive enough to reveal any changes. Thus, advanced imaging techniquesand advanced analysis methods need to be developed and applied in order toexamine the neurodegeneration of the WM in PD. Indeed, advanced structuralimaging studies have found a wide range of alterations, such as widespreadmodulations of DTI parameters in the WM, iron accumulation in the basal ganglia,and reported differences between PD and controls and other Parkinsonian diseases(Pyatigorskaya et al., 2013).The results of WM appear particularly intriguing, as they suggest underlyingchanges in the WM microstructure, despite not being detectable with standard MRIscans. Over the last few years, there is an increased number of studies examiningthe WM with DTI in PD (Atkinson-Clement et al., 2017). Alterations of the WMmicrostructure have been frequently observed with DTI parameters. Studies reportdifferences in frontal WM between PD and healthy controls that additionally arerelated to cognitive function (Melzer et al., 2013; Theilmann et al., 2013; Zheng et al.,2014). Moreover, widespread changes across the WM have been associated with16Chapter 1. Introductioncognition with significantly stronger changes in frontal areas in a follow up visit,in addition to DTI parameters being able to infer worsening of motor features(Mine‚ et al., 2018). Other studies are reporting conflicting results on an associationbetween DTI parameters and depression (Gou et al., 2018; Huang et al., 2014; Laceyet al., 2019; Matsui et al., 2007). A study by (Zhang et al., 2018) found reductions inFA in apathetic PD compared to non-apathetic PD subjects in several WM tracts.Furthermore, they found a negative correlation between FA and a clinical apathyscore in the differing tracts. A recent mcDESPOT study revealed increases in MWFin widespread regions when comparing PD to healthy controls, which may bemediated my the patients’ use of medication (Dean et al., 2016).Despite the recent reports of altered WM microstructure, most studies indexingWMI are utilizing DTI parameters to do so. However, even though MR diffusionparameters are highly sensitive to abnormalities in WM microstructure, they arenot specific to any particular pathology and can only be used to make limitedinferences about biological underpinnings. This leads to a limited understandingof the involvement and effect of changes in the WMI on the clinical manifestationof PD.Recent reports of autoantibodies against myelin-associated glycoprotein andglia cells (Papuc´ et al., 2014; Papuc´ and Rejdak, 2017) suggest a re-appraisal of therole of myelin in PD is warranted. MWI can fill the gap of unspecific in vivoWMI markers by providing a myelin specific marker and allowing potential newinsights into changes of the WM microstructure and ultimately to characterise thepathophysiology of PD in a more complete manner.1.3.3.2 Multiple SclerosisMS is a neuroinflammatory diseases which is characterised by demyelination, ax-onal loss, inflammation, and edema in the CNS (Reich et al., 2018). Its pathologicalhallmark is demyelinating focal plaques (lesions) with variable degrees of inflam-mation and neurodegeneration (Popescu and Lucchine‚i, 2012). The location, size,or number of lesions varies greatly among patients (Popescu and Lucchine‚i, 2012)and no strong relation to behavioural outcomes have been reported (Barkhof, 2002;17Chapter 1. IntroductionUher et al., 2018) While lesions can develop across the CNS, there seems to be apredisposition of appearance in areas such as the optic nerves and periventricularWM (Lopes, 2009). It encompasses a wide variety of disabilities including motorand cognitive deficits, impaired vision, fatigue, and mood disturbances (Loma andHeyman, 2011).Due to the fact that demyelination of the WM is a fundamental aspect of MS, itis a prime example of applying MWI. In fact, much of the early development ofMWI was in the field of MS research. For instance, the MWF in lesions is typicallyreduced to variable degrees compared to normal appearing white matter (NAWM)(Faizy et al., 2016; Laule et al., 2004; Mackay et al., 1994). Other studies reported adecreased MWF in NAWM, WM which appears asymptomatic on conventionalMR scans, compared to healthy subjects (Faizy et al., 2016; Kolind et al., 2012; Lauleet al., 2004).Diffusely abnormal white matter (DAWM), WM areas with no clearboundaries that may appear hyperintense on T2 images, has also been reportedwith decreased MWF (Kitzler et al., 2012; Laule et al., 2011), albeit not as strong as inlesions but stronger decreases than NAWM (Laule et al., 2011, 2004). Longitudinalanalysis of lesions found decreased MWF (Vargas et al., 2015) as well as reducedMWF in NAWM over five years (Vavasour et al., 2018). Furthermore, MWF hasbeen used to classify MS from healthy control 83.8% using features learned withdeep learning (Yoo et al., 2018). Despite much research, there is still a limitedunderstanding of an association between MWF and behavioural outcomes in MS.One study observed a link between decreased MWF and overall disease severityas well as negative correlations between MWF and mental scores (Kolind et al.,2012). Another recent study found an association between MWF and change inTimed-Up-And-Go task after a training intervention (King et al., 2018).A combination of new analysis methods together with MWI may provide newinsights towards a reliable link between imaging markers and behavioural indicessuch as motor or cognitive performance. Once a robust link is established, it canextent the current use of MWI in MS beyond disease diagnosis and monitoringefficacy of intervention to being able to infer the specific impairments during thedisease progression.18Chapter 1. Introduction1.4 Combining Multimodal MRI DataAlmost all neurological diseases affect the brain at many different scales and inmultiple ways, thus a combination of multimodal imaging features is likely to yieldthe best results when trying to characterise neurological diseases. Given the highlycomplex and heterogeneous nature of neurological diseases, their implications onbrain structure and function are just as multifaceted. In any given neurologicaldisease, it is very unlikely that a single feature from a single MRI technique willbe sensitive and specific enough to differentiate not only the disease at hand fromhealthy controls, but also differentiate the disease from other diseases (McKeownand Peavy, 2015). The same can be said about a MRI feature to track and infer diseaseprogression. Instead, it is far more likely that a set of different imaging featureswill be able to achieve better sensitivity and specificity to discriminate differentdiseases than any single feature could. A careful analysis of extracting featuresfrom complementary imaging modalities and combining them in a meaningfulway will enhance our understanding of brain functioning in neurological diseases.There are two broad avenues for combining multimodal data. On the one handthere is the integrative approach where relevant features of individual modalitiesget extracted and then combined at the end with the assumption that the changescaptured in the individual modalities are related in some way (Calhoun and Sui,2016). Typically, this is achieved by some form of univariate analysis where a typicalexample of this would be to extract an array of features from an MRI techniqueand then seek a correlation with clinical observations. In fact, these are the mostcommon studies in neuroimaging. On the other hand, there is the data fusionapproach in which two or more modalities are analysed jointly in a way such thatcommon covariations among them are being extracted. This can be achieved byeither asymmetric data fusion, where one modality is used to constrain the other, orby symmetric fusion where each modality contributes equally to maximise the jointinformation (Calhoun and Sui, 2016). Capturing these joint variations is often doneutilising multivariate approaches which are able to identify potentially weak andlatent effects among the data. Typical analysis methods are canonical correlation19Chapter 1. Introductionanalysis (CCA), partial least squares (PLS), independent component analysis (ICA)and their variations such as sparse, group or multiset models for CCA and PLS,and techniques such as linked or joint ICA.Studies that utilise multiple imaging modalities, in a data fusion approach, haveuncovered unique features in each data set that would not have been visible in eachmodality alone (Calhoun et al., 2006). It should be noted, a data fusion approach isnot only limited to find joint patterns between imaging data sets, but can also beused to reveal commonalities between imaging and clinical characteristics (Smithet al., 2015). Others have reported increased differentiability between diseases andhealthy cohort when utilising features from multiple image modalities (Bowmanet al., 2016; Schouten et al., 2016; Yoo et al., 2018). Of particular interest is the inter-play between structural and functional MRI and how it relates to neurologicaldisorders. Whereas structural MRI provides information about shape or or tissuecomposition of brain structures, functional magnetic resonance imaging (fMRI)provides information about neuronal response due to external or internal stimuli.The current consensus in the neuroimaging community is that most cognitive andmotor functions are implemented in the brain via large scale networks comprisedof different brain areas. Functional networks, a selection of GM areas respondingjointly to a stimulus, have also been detected in rs-fMRI where there are no stimuliapplied (Smith et al., 2009).An important, but little understood, aspect of these networks is the interplayof structural and functional connections. On the one hand, MRI techniques suchas DTI, can be used to construct structural networks representing the underlyingarchitecture of WM fibre bundles linking sub-cortical and cortical brain areas. Onthe other hand, temporal patterns of neural activity obtained with fMRI can beused to construct functional networks representing temporal correlations betweenbrain regions (Becker et al., 2015). Studies have attempted to estimate the functionalnetwork based on the structural network based on DTI tractography and hadsome success (Abdelnour et al., 2014; Be‚inardi et al., 2017; Deco and Kringelbach, 2016),however a large part of the interplay of the functional and anatomical networkremains still unknown. Given the importance of myelin for efficient brain signal20Chapter 1. Introductiontransmission, there is a surprising lack of studies investigating a potential link ofWM myelination and functional brain organisation.1.5 ContributionsDuring the course of investigating MWF features in health and disease, we havemade the following main contributions:Application1. We were the first group to show an association between MWF and PDdisease symptoms. By using a data-driven multivariate statistical approach,we were able to detect a robust relation between WM integrity in the formof MWF and PD symptoms. The analysis yielded a robust link between PDsymptom domains and associated but distinct WM regions and provides newevidence of myelin involvement during the course of PD.Application & Multimodal Integration2. We have shown a novel and reliable link between imaging, cognitive, andclinical features in MS. By utilizing a multivariate data fusion approach, wewere able to link MWF with cognitive performance, as well as disease severityand demographics in MS. In addition, our results were largely independent oflesion burden of subjects. This work has produced a joint profile of imaging,cognitive, and demographical variables, that was leveraged to find clustersof mild and moderately affected subjects.Multimodal Integration & Techniques3. We have demonstrated unseen associations between MWF and measuresfrom rs-fMRI, as well as proposed a novel framework for treating the WMas a network in a group of PD subjects. With a sparse machine learning21Chapter 1. Introductiontechnique we were able to show robust estimations of altered functionalnetwork topologies with MWF across different WM ROIs. Furthermore, wehave devised a method that utilises complementary information of differentMRI modalities that makes use of common changes in WMI values. Bytreating these changes as a network of joint changes across different WMROIs we show significant differences in network characteristics which arealso related to clinical and rs-fMRI measures.Techniques4. We have developed a novel framework for improved reconstruction ofMWF maps. We combined multivariate empirical mode decomposition(EMD) with multiset canonical correlation analysis in order to find the mostrobust T2 decay curve among voxels taking advantage of non-local similar-ity. By taking advantage of multivariate approaches we have developed aspatiotemporal filtering process which yields spatially smoother and morerobust MWF maps.Techniques & Application5. We have identified a spatial pattern in noisy appearing MWF maps andprovided evidence of trajectorial variations along major WM fibre bun-dles which can be leveraged to describe the WM integrity more accurately.When combining DTI and MWI, we were able to characterise major WM fibrebundles and provided evidence of distinct MWF profiles along fibre bundles.We have shown the superiority of MWF profiles compared to fibre bundleaveraged MWF by demonstrating more accurate age estimation as well assex differentiation.1.6 Thesis OrganisationThe rest of the thesis is organised into six chapters as outlined below. Figure 1.3showcases a high level overview of the organisation and which chapter made con-22Chapter 1. Introductiontributions to the defined domains of MWI research from section 1.1 of Applications,Techniques, or Multimodal Integration.Chapter 2–White Ma‚er Myelin Profiles Linked to Clinical Subtypes of Parkinson’s DiseaseThis work aimed to broaden the utility of MWI by applying it to a neurologicaldisease with typically unremarkable WM alterations.Here we apply MWI, in order to provide a biologically specific measure of WMintegrity, and multivariate data-driven methods to identify clinical and behaviouralphenotypes that are related to WM imaging features in subjects with PD. Specifi-cally, using partial least squares, we found a significant three component modellinking myelin content in different WM tracts and clinical scores no such associa-tion was detected with FA measures. The three components appeared to followalong broad motor/non-motor subtypes of “akinetic-rigid”, “tremor-predominant”and “depression/apathy” subtypes respectively. Our results suggest a robustrelationship between motor and clinical subtypes and myelin content profilesmeasured non-invasively with MWI in PD.Chapter 3–Data Fusion Detects Consistent Relations Between Non-lesional White Ma‚erMyelin, Executive Function, and Clinical Characteristics in Multiple Sclerosis This workutilised multiple, clinically relevant data sets such as imaging and behaviouraldata, in a multimodal fusion approach to identify latent relations between them.A data-fusion method, multiset canonical correlation analysis (MCCA), wasused to investigate the multivariate, deterministic joint relations between MWF,executive function, and demographic and clinical characteristics. MCCA revealedone significant component which consisted of three linked profiles of MWF, cog-nitive, and demographic features. White matter ROIs representing long-rangeintra-hemispheric tracts and ROIs connecting the two hemispheres were positivelyrelated through their individual profiles to overall cognitive performance, educa-tion and female gender, while age, expanded disease severity scale (EDSS), anddisease duration were related negatively. These findings indicate that there is astrong association between a pattern of MWF values and cognitive performance in23Chapter 1. IntroductionMS, which is modulated by age, education, and disease severity.Chapter 4–Linking White Ma‚er Integrity to Functional Connectivity This work aimedto elucidate the interplay between WM and measurements assessing brain functionby combining multiple measurements from MWI, DTI, and rs-fMRI.In the first part of this chapter we investigated if MWF can estimate knownchanges in functional network topology that are known to be altered in PD. Asparse machine learning technique identified a robust pattern of WM regionsthat can predict the altered modular organisation of functional brain networks.Additionally, the combination of WM and functional network features provided abetter association with clinical symptoms of PD than each modality alone.In the second part of this chapter, we proposed a novel method to investi-gate the WMI, by combining the complementary information offered by differentimaging modalities. We constructed networks of WMI based on the commoncovariations of different indices of WMI among different WM ROIs. We demon-strated widespread differences in network characteristics between PD and healthycontrols and found relationships of these network features between clinical indicesas well as measurements from rs-fMRI.Chapter 5–A Multivariate Approach for Denoising of T2 Relaxation Decay Curves in MyelinWater Fraction Imaging This work aimed to provide a new analysis framework fora more robust reconstruction of MWF maps by incorporating spatial as well astemporal information from non-local voxels.In a multiecho T2 experiment, low signal- to-noise ratios in later echoes, sub-optimal flip angles, and the fact that robust decomposition into multiple expo-nential curves is notoriously difficult, all conspire to reduce the accuracy of MWFestimates. The resulting maps are typically spatially noisy – despite the fact thatadjacent WM voxels are usually assumed to have similar myelin measures in vivo.We propose a spatiotemporal filtering process prior to the standard fitting based ona combination of multivariate empirical mode decomposition (MEMD) and MCCAto decompose and find the most robust temporal decay pattern among voxels24Chapter 1. Introductionthat have similar overall decay curves and across the WM. Based on enhancedspatial smoothness measures, increased test-retest reliability within subjects, anddecreased Coefficient of Variation of MWF scores, we suggest that the proposedapproach provides enhanced accuracy of the ultimately-computed MWF maps.Chapter 6–Inherent Spatial Structure in Myelin Water Fraction Maps The goal of thiswork is to widen the applicability of MWI by establishing a spatial pattern of MWFmaps and providing a more detailed description of major WM structures. A novelanalysis framework is provided to showcase the efficacy of this newly gainedinformation.We investigated the existence of an inherent spatial structure in MWF maps andexplored the benefits of examining MWF values along DTI-derived WM structures.The MWF coefficient of variation (CoV) was compared between WM structures andtheir immediate surroundings. In addition, a sub-sampling of each WM structurerevealed a characteristic profile of MWF values. The spatial pattern of MWF mapswas confirmed as WM structures demonstrated lower CoVs within and along theirtrajectories compared to outside regions. The MWF profiles were found to yielda superior estimation of subjects’ age as well as a better differentiation betweensex compared to traditional analysis. The results are suggestive of a spatial MWFdistribution that follows along its underlying WM microstructure that can beleveraged to provide more sensitive and results when investigating neurologicaldiseases.Chapter 7–Conclusion This chapter summarizes the findings from this thesis andput them into the context of the current literature highlighting the advancementsin each study. I will finish with an outlook of future work based on the resultspresented here.25Chapter 1. IntroductionFigure 1.3: Pictogram of thesis organisation illustrating to which categoryof Applications, Techniques, or Multimodal Integration each chapterbelongs.26Chapter 2White Ma‚er Myelin Profiles LinkedtoClinical Subtypes of Parkinson’sDis-easeIn this chapter we investigated whether or not the myelin content of the WM isassociated with PD-related clinical symptoms. Several recent studies reportedalterations of the WMI to varying degrees during the course of PD. However, themajority of these studies could not establish a biological source of these changes inthe WM microstructure due to employing non-specific markers that are sensitiveto a multitude underlying changes in the microstructure. We utilize MWI tospecifically probe the WM for its myelin content and relate that to typical PDsymptom domains. By applying MWI as well as a data-driven multivariate analysiswe are able to resolve specific PD symptoms and their associated WM regions andthus provide unique evidence of myelin involvement in PD.Our results broaden the utility of MWI to a neurodegenerative disease previ-ously not associated with myelin, and opens up new research opportunities tofurther characterise the pathophysiology of PD.27Chapter 2. Myelin Water Imaging in Parkinson’s Disease2.1 IntroductionPD is the second most common neurodegenerative disease after AD and is clinicallycharacterised by a progressive loss of dopaminergic neurons in the substantia nigra.The death of these dopaminergic neurons and resultant accumulation of Lewybodies is considered to be the primary cause of the clinical pathophysiology of PD(Davie, 2008). Lewy bodies are mainly comprised of α-synuclein proteins, whichmay exacerbate neural cell death and lead to a loss of other proteins in neurons(Al-Radaideh and Rababah, 2016).PD is primarily classified as a movement disorder with cardinal motor deficitsof tremor, rigidity, bradykinesia, and postural instability arising from nigrostriataldopaminergic depletion. However, the symptomatology of PD includes a largehost of non-motor related symptoms, including those that involve the limbicand olfactory domains (Pfei€er, 2016). Among others, the most common non-motor symptoms are behavioural and mood changes, apathy, depression, cognitiveimpairments, sensory abnormalities, and sleep abnormalities (Pfei€er, 2016). Studiesexamining non-motor symptoms reported that nearly all PD patients sufferedfrom at least one non-motor symptom, and with higher prevalence and severitycompared to age-matched healthy subjects (Khoo et al., 2013; Krishnan et al., 2011).The complexity of the disorder is highlighted by the clinical heterogeneity exhibitedby different PD phenotypes and the varying degree of disease progression acrosssubjects (Lewis et al., 2005).Consistent with widespread symptomatology and clinical heterogeneity, PDresults in a myriad of systems-level brain changes. PD can affect grey matter withchanges in cortical thickness (Zarei et al., 2013) and shape changes in the thalamus(McKeown et al., 2008). Changes in functional connectivity are also widespread (Gaoand Wu, 2016) as well as oscillatory changes (Brown, 2003).White matter changes can also be seen in PD, although less reliably than otherneurodegenerative diseases, such as AD (Nasrabady et al., 2018) and Huntingtonsdisease (Novak et al., 2014). Alterations of the WM microstructure can differentiatePD subjects from healthy controls as well as other PD subtypes, and correlate with28Chapter 2. Myelin Water Imaging in Parkinson’s Diseasesome PD symptoms (Melzer et al., 2013; Zhang et al., 2018). Although there are alsoreports of concomitant WM hyperintensities in qualitative studies, their origin islikely due to concomitant small-vessel disease unrelated to PD pathology (Picciniet al., 1995).Assessing WM microstructure non-invasively in neurodegenerative disease isusually done via DTI. Based on the diffusion of water molecules, DTI providesand indirect marker of predominantly axonal fiber orientation as well as myelinintegrity (Melzer et al., 2013; Zhang et al., 2018). However, the commonly-usedparameters from DTI, such as FA, are also sensitive to axon density, axon calibre,cell swelling, fibre architecture and myelin thickness (Ma¨dler et al., 2008). Yetthere is increasing evidence that myelin can be directly involved in PD, e.g., viaautoantibodies against oligodendrocyte proteins (Papuc´ et al., 2014; Papuc´ and Rejdak,2017). Specific imaging markers targeting myelin would be desirable.Here we make use of the MWF gained from MWI (Whi‚all et al., 1997) that isan in vivo surrogate marker of myelin content. It has been extensively studiedin multiple sclerosis (Laule et al., 2006) and has been validated with histologicalstaining of myelin post-mortem (Laule et al., 2006). We sought to determine ifmyelination in PD subjects is altered and whether or not this measure of WMmicrostructural integrity can be linked to disease related symptoms.2.2 Materials & Methods2.2.1 ParticipantsThis work was approved by the University of British Columbia Ethics ReviewBoard, and all subjects provided written, informed consent according to the Dec-laration of Helsinki prior to undergoing the MRI scan and neuropsychologicalexamination. A total of 33 idiopathic PD subjects and 15 age-matched HC partici-pated in this study. Patients with secondary or atypical Parkinsonism, dementiaor cognitive degeneration causing impairment of ability to give informed consent,changes to antiparkinsonian medications within the past 6 months, or contraindi-29Chapter 2. Myelin Water Imaging in Parkinson’s Diseasecations to safe participation in MRI were excluded from the study.2.2.2 Clinical AssessmentAll participants received the following clinical questionnaires: Montreal cognitiveassessment (MoCA), Beck depression index (BDI), Starkstein apathy scale (SAS),Lille apathy rating scale (LARS), fatigue severity scale (FSS). All PD patients wereassessed in the ON state, using part III of unified Parkinson’s disease rating scale(UPDRS) for symptom severity and Hoehn & Yahr (H & Y) scale for disease staging.Motor assessments were administered by one of two experienced research person-nel who were certified by the International Parkinson and Movement DisorderSociety. The MoCA and LARS questionnaires were administered by one of threeresearch personnel using a common script, to limit interviewer bias. The remainderof the assessments were self-reported by participants. For PD patients, the dosagesof antiparkinsonian medications were converted to levodopa equivalent daily dose(LEDD). A summary of the clinical and demographical characteristics is availablein Table 2.1.2.2.3 MRI Data AcquisitionThe subjects were scanned with a 3.0 Tesla MR scanner (Philips Achieva 3.0 Tesla;Philips Medical Systems, Netherlands) with an eight-channel head coil. We ac-quired a full brain 3DT1-weighted scan for structural references with an inver-sion recovery MPRAGE sequence inversion time (TI)= 808ms, repetition time(TR)= 1800ms and an isotropic voxel size of 1mm3. T2 relaxation data were col-lected using a modified gradient and spin echo (GRASE) sequence with 32 echoeswith 10ms echo spacing and TR= 1000ms. Twenty slices were acquired at 5mmslice thickness and reconstructed to 40 slices at 2.5mm. The in-plane voxel size was1×1mm. DTI data sets were collected with echo time (TE)= 69ms, TR = 6179ms,with 32 gradient orientations, a b-value of 700s/mm2 and one b0 volume. Thein-plane resolution was acquired at 2.2×2.2mm and reconstructed to 0.8×0.8mmwith a slice thickness of 2.2mm. All subjects were scanned on the same day as30Chapter 2. Myelin Water Imaging in Parkinson’s DiseaseTable 2.1: Demographics and Clinical Scores for the PD and Healthy Cohort.PD cohort Control cohort p-valueAge (years) 68.00±5.98 69.40±4.76 0.44Sex (f/m) 9/20 5/10 —UPDRS-III 27.52±9.62 — —H & Y 2.10±0.67 — —DD (years) 9.38±5.35 — —MoCA 25.97±2.54 26.93±1.94 0.20SAS 11.90±5.27 8.07±5.51 0.030LARS −24.48±6.19 −28.80±0.018 0.018FSS 3.92±1.55 2.36±1.32 0.002BDI 8.70±6.61 3.07±3.90 0.004LEDD (mg/d) 1214.9±547.15 — —administration of clinical questionnaires. PD subjects were typically scanned 30minutes after a dose of antiparkinsonian medication (or as determined throughdiscussion with the participant) to capture their ON medication state throughoutthe duration of the scan.2.2.4 Processing of Imaging Data2.2.4.1 T2 Relaxation DataThe multi-echo GRASE sequence was analysed using in-house written MATLABcode that uses a NNLS fitting method to approximate the multi-exponential decaycurve with a number of exponential basis functions. The algorithm includescorrection for stimulated echoes as well as a regulariser to make the fit more robustagainst noise in the time domain (Prasloski et al., 2012b), resulting in one whole31Chapter 2. Myelin Water Imaging in Parkinson’s Diseasecerebrum MWF map per subject. Briefly, the algorithm works as follows. Per voxel,the multi-exponential relaxation signal yi can be expressed asyi =M∑j=1sie− tiT2 j , i= 1,2, ...,n, (2.1)with ti being the measured time points, M are 40 logarithmically spaced T2times within a range of 15ms to 2 seconds, n is the total number of data samples(32 in this case), and s j is the relative amplitude for each T2 time. The NNLS thenminimizes both a χ2 and an energy constraint which regularises the T2 distributions j(T2 j), providing more robust fits in the presence of noise. The expression beingminimized is as follows,χ2+µM∑j=1s2j , µ ≥ 0 (2.2)Where µ regulates the smoothness of the T2 distribution at the cost of misfit.The target misfit was set to χ2 = 1.02. The MWF was then defined as the signal of T2relaxation times of 40ms and below relative to the total signal in the T2 distribution.We used 20 WM ROIs covering the majority of the WM and delineating majorWM tracts to get the most reasonable coverage for biological interpretations. TheROIs are in the MNI standard space and part of the FMRIB software library (FSL)package and contributed by the Johns Hopkins University (JHU). In order toextract the average MWF per ROI, the ROIs were non-linearly registered to eachsubjects’ native space using the first echo of the multi-echo T2 relaxation data. Theregistrations were done with FLIRT and FNIRT, part of FSL, (Jenkinson et al., 2012).In order to account for potential misalignments due to the registration processof the ROIs, they were masked with a WM mask (obtained with FAST, part ofacfsl (Jenkinson et al., 2012), on the high resolution T1 images and registered to eachsubjects T2 relaxation data) once the ROIs were in each subjects native space.2.2.4.2 DTI DataDTI data were corrected for geometric distortions and subject motions prior to32Chapter 2. Myelin Water Imaging in Parkinson’s Diseasefitting the tensors and computing a FA map per subject using DTIFIT from FSL(Jenkinson et al., 2012). The same 20 WM ROIs as for the T2 relaxation data wereused, but this time the registrations were based on the subjects FA map and anFA template in MNI space. All registrations were again performed with FLIRTfor initial linear transformations and FNIRT for the subsequent non-linear trans-formations. The ROIs were then masked with the WM after registering them tothe subjects DTI data mask to ensure that only WM voxels were considered in theanalysis.Of the initial 33 PD subjects, four of them were excluded due to not havingwell-registered WM ROIs or being considered an outlier in either the imaging orclinical data. Outliers were defined as subjects with a feature score (MWF per ROIor clinical test score) that was greater or smaller than three standard deviationsaway from the median across all subjects. None of the healthy control subjectswere excluded using the same exclusion criteria. In summary, the imaging datawas stored in a matrix Xn×20 with n as number of subjects (either 29 or 15 for PDor healthy cohort respectively) and 20 WM ROIs with either averaged MWF orFA values per ROI. The clinical scores were summarised in a matrix Yn×7 with nsubjects and seven clinical scores (UPDRS-III, MoCA, BDI, SAS, LARS, FSS, tremor)for PD subjects. The tremor scores were obtained by simply summing the scoresfor lower and upper extremities and rest-, kinetic-, and postural-tremor. Tremorsscores for left (L) and right (R) were computed separately. The clinical scores forthe healthy control cohort were MoCA, BDI, SAS, LARS, and FSS summarised inthe matrix Yn×5.2.2.4.3 Statistical AnalysisWe compared the two WMI measures, MWF and FA, between the PD subjects andhealthy controls with a univariate two-sample t-test in each of the 20 ROIs. In orderto explore the relation between WM microstructural integrity and clinical features,we employed PLS.33Chapter 2. Myelin Water Imaging in Parkinson’s DiseasePartial Least Squares PLS is a multivariate method to identify latent associationsbetween a set of predictor variables and a set of response variables, particularly incases where the number of predictors is greater than the number of observations aswell as in cases of multi-collinear predictor variables (Abdi, 2010). The goal of PLS isto extract low dimensional commonalities between high dimensional predictor andresponse variables. A PLS regression is related to PCA regression, but where PCAregression reduces the dimensionality of the predictors to explain as much varianceas possible, PLS does not. As there is no guarantee that the explained variance ofthe predictors is related to the response variables, PLS instead finds componentsfrom the predictors that maximally covary with the response variables.PLS finds latent variables comprised in a matrix T that model X and simultane-ously estimate Y. Formally, this can be expressed asX = TPT +Fx (2.3)Yˆ = TBCT +Fy, (2.4)with P and C as loadings, B as a diagonal matrix, and the matrices Fx and Fy asresiduals. The latent variables are sorted according to their explained variancein Yˆ, such that the first PLS components provide the optimal low dimensionalrepresentation of the covariance between predictors and responses. Each latentvariable of X describes a unique aspect of the variance of X that best estimatesthe features in Y. Vice versa, the latent variables of Y describe unique aspectsof features best estimated by X. Typically, the latent variables are computed byiteratively applying singular value decomposition (SVD) to produce orthogonallatent variables for X and Y. Consider the mean centered matrices X0 and Y0, thenthe covariance between them can be computed withR1 = XT0Y0. (2.5)34Chapter 2. Myelin Water Imaging in Parkinson’s DiseaseSubsequently, SVD is performed on R1 in order to obtain the singular vectors W1and C1, as well as the corresponding singular values in Σ1:R1 =W1Σ1C1, (2.6)where the first pair of singular vectors are w1 and c1 representing the first columnsof W1 and C1. The first latent variable of X is then defined as t1 = X0w1, with theconstraint tT1 t = 1.One can then obtain the loadings of X0 onto t1 withp1 = XT0 t1, (2.7)and the least squares estimate of X is given byXˆ1 = tT1 p1. (2.8)The first latent variable of Y is obtained byu1 = Y0c1. (2.9)Once the first pair of latent variables are found, Y can be reconstructed withYˆ1 = u1cT1 = t1b1c1, (2.10)with b1 = tT1 u1. In order to find the next pair of latent variables, a deflation processis performed withX1 = X0− Xˆ1 (2.11)andY1 = Y0− Yˆ1 (2.12)such that the matrices X1 and Y1 serve as the new input for the processes above.This process, the extraction of latent variables, is repeated L times with L= rank(X).To determine statistical significance, we used a non-parametric permutation35Chapter 2. Myelin Water Imaging in Parkinson’s Diseasetest where we randomly permuted (N = 5000 permutations) the order of X, thusdestroying the inter-dependency between X and Y and repeated the PLS analysis,creating a null distribution of explained variance in Y explained by X. Significancewas then assessed by the ratio of how many times the explained variance wasgreater using the permuted data than the original data to the number of permuta-tions. The robustness of individual features of the imaging set was examined usingbootstrapping with replacement (N = 5000 iterations). Subjects were sampled withreplacement in both X and Y and repeating the PLS analysis, generating a set ofweights used to estimate the error for each imaging feature. This error was usedto generate 95% confidence intervals in order to assess the importance of eachimaging feature. A feature was deemed important if the confidence interval didnot include zero. The statistical significance level for all tests was set to p= 0.05.The effects of age and gender were regressed out of all imaging and clinicalfeatures and the results were normalised to z-scores prior the PLS analysis.Post-Hoc Analysis We further tested whether WM abnormalities reflected in thePLS components tended to cluster in patient sub-groups. To this end, we applieda hierarchical clustering, an unsupervised method to discover groups of patientswith similar patterns of WMI. We calculated a dissimilarity matrix based on theEuclidean distance between every pair of subjects and then used Wards minimumvariance method to iteratively link subjects in closest proximity to form largerclusters in a hierarchical tree.2.3 ResultsUsing simple t-tests, there were no significant differences in overall MWF or FA ineach ROI between the PD and control groups (Fig. 2.1 and Table 2.2). We thereforefocused on MWF profiles in PD subjects.In these subjects, since we obtained three general clinical domains with motor,cognitive, and mood (apathy/depression) scores, we used a PLS model withthree components that explained 36% of the variance (p = 0.034, assessed with36Chapter 2. Myelin Water Imaging in Parkinson’s DiseaseTable 2.2: Comparison of average MWF and FA across all 20 investigated WMROIs.MWF FAPDmean ± sdHCmean ± sd p-valuePDmean ± sdHCmean ± sd p-valueThalamic RadiationL 0.10±0.01 0.10±0.02 0.752 0.35±0.04 0.35±0.03 0.837Thalamic RadiationR 0.09±0.01 0.10±0.02 0.306 0.35±0.04 0.35±0.04 0.63Corticospinal tract L 0.20±0.02 0.20±0.02 0.206 0.52±0.02 0.52±0.02 0.748Cortiospinal tract R 0.20±0.02 0.19±0.02 0.148 0.51±0.03 0.52±0.02 0.299Cingulum L 0.07±0.01 0.07±0.02 0.405 0.50±0.03 0.47±0.05 0.074Cingulum R 0.06±0.01 0.06±0.02 0.180 0.45±0.06 0.44±0.06 0.789Cingulumhippocampus L 0.08±0.03 0.08±0.03 0.779 0.39±0.08 0.39±0.05 0.747Cingulumhippocampus R 0.07±0.02 0.07±0.02 0.914 0.35±0.03 0.34±0.03 0.494Splenium 0.15±0.02 0.15±0.02 0.804 0.51±0.04 0.52±0.03 0.202Genu 0.07±0.01 0.07±0.02 0.929 0.34±0.03 0.34±0.03 0.966IFOF L 0.09±0.01 0.09±0.02 0.620 0.39±0.03 0.39±0.03 0.887IFOF R 0.10±0.01 0.10±0.02 0.725 0.38±0.03 0.38±0.02 0.609ILF L 0.09±0.02 0.09±0.02 0.891 0.40±0.03 0.40±0.03 0.719ILF R 0.11±0.02 0.11±0.03 0.947 0.42±0.03 0.41±0.03 0.707SLF L 0.12±0.02 0.12±0.02 0.519 0.33±0.02 0.34±0.03 0.226SLF R 0.13±0.01 0.13±0.02 0.747 0.34±0.03 0.35±0.05 0.291Uncinate L 0.05±0.01 0.05±0.01 0.699 0.35±0.04 0.36±0.04 0.756Uncinate R 0.05±0.01 0.06±0.01 0.814 0.38±0.05 0.39±0.03 0.564Arcuate L 0.08±0.03 0.08±0.02 0.941 0.38±0.05 0.41±0.06 0.083Arcuate R 0.10±0.02 0.09±0.02 0.506 0.46±0.08 0.48±0.06 0.34437Chapter 2. Myelin Water Imaging in Parkinson’s DiseaseFigure 2.1: Average MWF in each ROI. Shown are boxplots of all 29 Parkin-sons disease subjects and 15 healthy controls for each ROI. No signifi-cant differences between the two groups were found with a significancelevel of p= 0.05 (uncorrected for multiple comparisons). N (PD) = 29, N(HC) = 15.permutation test). The first PLS component showed a strong correlation withUPDRS-III (r = −0.43, p = 0.0196) and MoCA (r = 0.44, p = 0.0171) scores (Fig.2.2A). The PLS weights with confidence intervals for each WM ROI reveal ROIsconnecting the two hemispheres (genu, splenium) as well as ROIs reflecting longrange association fibres (such as left/right cingulum cingulate fibres, left/rightinferior fronto-occipital fibres) showing the highest weights in this component (Fig.2.2B). A 3D rendering of their spatial location can be seen in Figure 2.2C.The second component showed significant correlations with UPDRS-III (r =−0.58, p= 0.0009) and tremor scores (r =−0.48, p= 0.0091) (Fig. 2.3A). The corre-sponding weights identified projection fibres such as left/right thalamic radiation,left/right corticospinal tract, left/right cingulum hippocampus as the regions withthe most substantial impact on this component (Fig. 2.3B). Figure 2.3C displays a3D rendering of the ROIs and their location in the brain.The third PLS component is associated with BDI (r =−0.60, p= 0.0006), LARS(r = −0.66, p = 0.0001), and SAS (r = −49, p = 0.0072) (Fig. 2.4A). The WM ROIs38Chapter 2. Myelin Water Imaging in Parkinson’s DiseaseFigure 2.2: Relation between imaging features and clinical scores for the firstPLS component. The first PLS component linked a) UPDRS-III andMoCA to b) WM regions, predominantly association and interhemi-spheric fibre bundles. c) shows a 3D rendering of ROIs with mostprominent weightings. Colour coding: orange: genu and splenium,green: inferior fronto-occipital fasciculus, yellow: uncinate, red: superiorlongitudinal fasciculus, blue: cingulum, purple: inferior longitudinalfasciculus, turquoise: cingulum hippocampus. N = 29.most associated with this component were a mixture of association and projectionfibres such as the thalamic radiation, cingulum cingulate, cingulum hippocampus,and uncinate (Fig. 2.4B). The spatial location of the most prominent ROIs in thebrain can be observed in Figure 2.4C.No significance in the goodness of fit (explained variance) with a three-component39Chapter 2. Myelin Water Imaging in Parkinson’s DiseaseFigure 2.3: Relation between imaging features and clinical scores for the sec-ond PLS component. The second PLS component linked a) UPDRS-IIIand tremor scores to b) WM regions, which mostly involve projectionfibres. c) shows a 3D rendering of ROIs with most prominent weightings.Colour coding: blue: anterior thalamic radiation, yellow: uncinate, red:corticospinal tract, turquoise: cingulum hippocampus. N = 29.PLS model could be found when using FA values as a measure of structural in-tegrity of the WM with p = 0.4476. In the healthy control group, no significantrelation between imaging and clinical data could be established with either mea-sure of WMI (p = 0.4522 for MWF and p = 0.4472 for FA). Because the controlgroup did not have a UPDRS assessment, and hence was missing a “motor do-main” variable we repeated the PLS analysis with two components, reflecting thecognitive as well as the depression and apathy domain. The two component PLS40Chapter 2. Myelin Water Imaging in Parkinson’s DiseaseFigure 2.4: Relation between imaging features and clinical scores for the thirdPLS component. The third PLS component linked a) depression and ap-athy scores to b) a mixture of association and projection fibre bundles. c)shows a 3D rendering of ROIs with most prominent weightings. Colourcoding: blue: anterior thalamic radiation, yellow: uncinate: turquoise:cingulum hippocampus. N = 29.model also yielded no significance with either measure of WMI (not shown).Post-hoc Results The clustering analysis revealed three patient clusters that weremaximally dissimilar from each other (Fig. 2.5).Cluster one was comprised of seven subjects, cluster two of 13 subjects, andcluster three of nine subjects. We compared the clusters according to their clinicalscores and found that the group of patients in cluster three had the least impair-41Chapter 2. Myelin Water Imaging in Parkinson’s Disease0.40.2PLS 20-0.2-0.40.50PLS 10.60.40.20-0.2-0.4-0.5PLS 3Cluster 1Cluster 2Cluster 3Figure 2.5: Clusters obtained from hierarchical clustering on the PLS trans-formed imaging data. Three clusters were found with seven subjectsbelonging to cluster one, 13 subjects comprised cluster two, and ninesubjects were part of cluster three.ments, while cluster one constituted the most severely impaired patients. Thedetails of their clinical variables can be seen in Table 2.3. A one-way multivariateanalysis of variance (MANOVA) with clinical variables as dependent variablesand clusters as independent variables confirmed that the three clusters showedsignificant differences among their clinical variables (F14,40= 2.457, p= 0.011, Wilkslambda = 0.289). The MANOVA was performed in SPSS version 25.2.4 DiscussionThis study presents a link between several PD symptom domains and WMI. Themultivariate, data-driven nature of our analysis revealed distinct patterns of myelinprofiles associated with specific PD symptom domains.Myelin changes have been reported in multiple systems atrophy (MSA), aParkinsonian syndrome with α-synuclein inclusions found in oligodendrocytes(Ahmed et al., 2013), but typically not in PD. All patients in the current study werein the “clinically definite PD” category, each with robust response to dopaminergicmedication, so we do not believe the changes we observed were due to a mischarac-terization of MSA subjects as PD. We do note that autoantibodies against proteins42Chapter 2. Myelin Water Imaging in Parkinson’s DiseaseTable 2.3: Average and standard deviations of clinical scores per cluster.Cluster 1 Cluster 2 Cluster 3UPDRS-III 38.29±6.47 26.08±7.11 21.22±8.18MoCA 23.86±2.49 26.62±2.47 26.67±1.94BDI 10.29±7.67 11.31±6.17 3.67±3.12SAS 13.14±3.98 14.00±5.03 7.89±4.54LARS −22.71±6.90 −22.00±5.82 −29.33±2.92FSS 4.50±1.36 4.18±1.63 3.09±1.37Tremor 5.14±2.68 3.54±1.56 3.22±1.56of oligodendrocytes can be detected in PD, and that there is increasing evidence ofglia cells playing a larger role than previously thought during the course of the dis-ease (Papuc´ et al., 2014; Papuc´ and Rejdak, 2017). How this affects the MWF is unclear,but it does suggest a plausible mechanism, given that oligodendrocytes providethe basis of myelination, much akin to how normal-appearing white matter can beassociated with pathological processes such as microglial activation in multiplesclerosis (Allen et al., 2001). Furthermore, axoglial disruptions have previously beendescribed in the pathology in PD (Howell et al., 2010), although similarly, the impactthese may have on MWI patterns are also unclear. Prior studies (Melzer et al., 2013;Mine‚ et al., 2018; Theilmann et al., 2013) linking FA and other DTI measures toclinical symptoms likely have produced variable results because FA is less specificin probing myelin content.We did not find differences in WMI measures between the PD cohort andhealthy controls using univariate tests. This may be due to only slight changesseen across multiple ROIs. However, when viewed collectively, as was done here,subtle, but robust patterns can be discerned. This is reflected in the PLS resultswhere WMI, specifically MWF and not FA, could be linked to clinical variables ofPD subjects but not in the healthy control group. The fact that MWF and not FA43Chapter 2. Myelin Water Imaging in Parkinson’s Diseasecould be associated with several PD symptoms may indicate that MWF is a moresensitive and biologically more meaningful measure of WM microstructure in theearly stages of the disease. Further, the fact that a combination of WM areas couldbe linked to distinct PD symptom domains reinforces a network concept to PDpathophysiology.We believe that the PLS components we observed, which reflect profiles ofWMI specifically in regard to myelin content, correspond well to motor and non-motor subtypes in PD. Importantly, by utilizing a data driven approach, thesesubtypes emerged naturally from the analysis: the joint multivariate approachemployed here attempts to tease out independent WM profiles that are correlatedto the entire range of clinical presentations across a broad spectrum of PD subjects.The first two components correspond nicely to the traditional designations of“akinetic-rigid” and “tremor-dominant” Parkinsons motor subtypes (Jankovic et al.,1990) respectively. Both components correlated negatively with UPDRS-III scores,but the first component correlated positively with MoCA scores (consistent withthe observation that the akinetic rigid subtype is associated with greater riskof cognitive dysfunction (Vingerhoets et al., 2003)), and the second componentcorrelated negatively with tremor. It has been suggested that the two motorsubtypes may be related to differential basal ganglia/cerebellar involvement (Lewiset al., 2011), but unfortunately, due to technical considerations, we were unable toinclude the cerebellum and its immediate connections in the MWF measurements.The third PLS component corresponds to a depression/apathy non-motor subtype,which may involve cholinergic as well as dopaminergic dysfunction (Pagonabarragaet al., 2015).Contrasting the loadings on the fascicles in the “akinetic-rigid” and “tremor-dominant” components is informative. Some loadings are remarkably similar,likely related to the fact that both components correlate with UPDRS-III scores (e.g.L and R cingulum and cingulum hippocampus, and uncinate), but there are alsodistinct differences. For the first (akinetic-rigid) PLS component, there were promi-nent loadings in regions important for cognition, including the IFOF, the ILF andSLF, as well as the right arcuate fasciculus. The IFOF connects occipital, temporal44Chapter 2. Myelin Water Imaging in Parkinson’s Diseaseand superior parietal regions to the frontal lobe, and may be involved in reading,attention, and visual processing (Catani and Thiebaut de Scho‚en, 2008). The SLFhas traditionally been segmented into three distinct parts. The first part connectsthe superior parietal lobule and premotor cortices, and the second part connectsthe caudal-inferior parietal cortex and dorsolateral prefrontal cortex and may beimportant for spatial memory and working memory. The first two parts weremerged in our SLF ROI. The third part of the SLF, which is considered the arcuatefasciculus ROI in our study, links the supramarginal gyrus and ventral premotorand prefrontal cortices. Interestingly the right arcuate fasciculus, loading signif-icantly in the first PLS (akinetic-rigid) component, has recently been implicatedin inferring affective states in human faces (Nakajima et al., 2018), a well-knowndeficit in PD (Palmeri et al., 2017). The other fascicle implicated in the akinetic rigidcomponent, the inferior longitudinal fasciculus, connects the temporal lobe andoccipital lobe, and is part of the ventral visual pathway, associated with objectidentification. In contrast, only the second (tremor-predominant) PLS componenthad significant loadings in thalamic radiation and corticospinal tracts.Our results are partly consistent with prior studies looking at white matterchanges in PD. A recent study reported a widespread decrease in FA and increasein radial diffusivity in WM areas such as the left/right cingulum, corpus callosum,left/right IFOF, right ILF, left/right SLF, in PD subjects relative to healthy con-trols, FA changes correlate with verbal working memory in mid-anterior corpuscallosum, the anterior cingulate, and left external capsule (Theilmann et al., 2013).Parkinsons disease patients with dementia have FA differences in the SLF, ILF,IFOF, uncinate, and cingulum fascicles (Ha‚ori et al., 2012) compared PD withoutdementia. Alterations in mean diffusivity in a cohort of PD patients with mildcognitive impairments compared to cognitively normal PD patients and a deterio-ration of WM could be used to infer longitudinal changes in cognitive outcomeswas recently reported (Mine‚ et al., 2018). Their results and ours reinforce the notionof different PD phenotypes having distinct patterns of WM degeneration.Previous studies have attempted to delineate different WM changes in PDmotor subtypes. Changes in mean diffusivity and axial diffusivity in the cerebral45Chapter 2. Myelin Water Imaging in Parkinson’s Diseasepeduncles, thalamus, internal capsule, superior corona radiata (Luo et al., 2017),and increases in FA in the left anterior thalamic radiation, left IFOF, left/right SLF,left/right ILF, and right corticospinal tract (Wen et al., 2018), were specifically seenin tremor-dominant PD subjects.The third PLS component we found displayed a robust relationship betweenmyelination in a mixture of association and projection fibres and clinical depressionand apathy scores. The loadings on this component, specifically the thalamicradiation, and cingulum bundles, have previously been implicated in apathy anddepression in PD (Zhang et al., 2018). In addition to reduced FA in the genu and bodyof corpus callosum, left cingulum, and bilateral anterior and left superior coronaradiata seen in PD subjects with apathy (Zhang et al., 2018). Studies investigatingdepression in PD noted a reduction of FA in WM tracts of left anterior thalamicradiation, uncinate, and left anterior corona radiata among others (Wu et al., 2018).The differentiation of clinical symptoms was also observed in a study usingPLS in order to relate brain atrophy with a range of clinical measures (Zeighamiet al., 2017). Interestingly, they found three distinct patterns of clinical presentationsof PD, each related to a distinct atrophy pattern of grey matter. Their analysiswas able to separate a pattern of clinical features such as high UPDRS-III, lowcognitive performance, lower striatal dopamine innervation in component 1, andmore severe depression from a pattern showing higher tremor scores and bettercognitive performance in component 2, and lastly from a pattern of more severepostural and gait disabilities together with more prominent mood and behaviouralsymptoms in component 3. Our distinction of clinical symptoms follows closelythe one from (Zeighami et al., 2017) despite the different imaging modalities beingused. In fact, while they report mostly atrophy patterns in the basal gangliarelated to component 1, they also note atrophy in frontal lobes, the cingulatecortex, and insular cortex which are cortical regions that some of our WM ROIsconnect to. Furthermore, the atrophy pattern related to component 2 includesareas in the motor cortex and temporal gyrus, both areas are connected by WMregions we identified in the second PLS component, either the corticospinal tract oruncinate fasciculus. In addition, their component describing patterns of mood and46Chapter 2. Myelin Water Imaging in Parkinson’s Diseasebehavioural measures is related to a mix of frontal, temporal and occipital atrophypatterns, roughly in line with WM regions we find. Taken together, PLS proved tobe a powerful analysis technique which can reliably differentiate clinical sub-typesof PD across multiple imaging modalities.The post-hoc cluster analysis found that different clusters were distinguishablewith UPDRS-III, MoCA, depression, and apathy scores but not tremor scores. Thislikely suggests that tremor scores cannot be easily be predicted from localizedwhite matter changes, in keeping with prior suggestions that widespread, jointbasal ganglia/cerebellar dysfunction is required for tremor to emerge (Helmichet al., 2011).There are a number of limitations to our study. We had a cohort with heteroge-neous symptom presentations, and presumably different PD subtypes may havevarying changes of WMI dependant on the sub-type of disease. This cohort waschosen, not to represent a specific PD phenotype, but rather to encapsulate a widerange of motor deficits and apathy scores. An increase in the sample size andsubdivision of subjects into particular subtypes may refine our results further.To conclude, we found widespread regions of the WMI associated with distinctsymptom patterns in PD. By taking advantage of a data-driven multivariateapproach, we were able to investigate WMI in terms of myelin content and itsrelation to various clinical phenotypes of the disease in an unbiased manner. Theanalysis revealed three specific symptom patterns, each with a set of associatedwhite matter regions. The results are in line with other studies investigatingindividual clinical symptoms in relation to WMI but provide a more comprehensiveframework in that several symptoms are investigated simultaneously. Further, ourmeasure of MWF provides a more biologically meaningful interpretation of theunderlying white matter microstructure than DTI studies. The clustering based onMWF revealed a reasonable sub-division of patient groups into clinically relevantdisease sub-groups.47Chapter 3Data FusionDetectsConsistentRelationsBetweenNon-lesionalWhiteMa‚erMyelin,Executive Function, and Clinical Char-acteristics in Multiple SclerosisIn this chapter we combine MWI with features of cognitive performance as well asclinical and demographic indices in an effort reveal a joint pattern of covarianceamong them. A link between myelin and cognition has long been implied, howeverevidence of this relation in MS is scarce. Furthermore, cognitive performance inMS is likely to be modulated by a number of factors such as WMI or severityof disease manifestation. This work aimed to account for the multiple cognitioninfluencing aspects by utilising a multimodal feature fusion approach. Our resultssuggest a joint correlation of MWF in a broadly distributed pattern of WM regions,with cognitive performance and clinical indices. Furthermore, this result is largelyindependent of demyelination in lesions, indicating a robust relation between allthree data sets even in earlier stages of MS.This work illustrates the utility in employing novel analysis methods thatleverage latent relations between different modalities, as well as showcasing novelevidence of MWF being related to cognition in MS.48Chapter 3. Multimodal Data Fusion in Multiple Sclerosis3.1 IntroductionMS is an autoimmune disease of the central nervous system with a wide spectrumof motor and non-motor impairments such as fatigue, vision impairments, balanceissues, and cognitive impairments that greatly affect quality of life. A hallmarkof MS is the deterioration of the WMI, due to inflammation, edema, axonal loss,and demyelination. Lesions, or focal plaques, typically seen as hyperintensities onproton density or T2 weighted magnetic resonance images, are often characterisedby a high degree of demyelination. In addition to focal loss of myelin in lesions, ageneral decrease in overall myelin can be observed in non-lesional tissue, both inDAWM and NAWM (MacKay and Laule, 2016).MS disease manifestations are highly variable in both symptom presentationand radiological MRI markers (Chard and Trip, 2017). Lesions appearing similarto each other on conventional MRI may not correspond to consistent patternsof clinical symptoms. Besides lesion location, the extent of lesioned tissue alsoprovides limited information about behavioural consequences. This mismatchbetween radiological markers and disease manifestation has been termed theclinical-radiological paradox and has hampered the ability to robustly infer diseasestatus and course based on MRI lesion characteristics alone (Chard and Trip, 2017).Despite much research, there is still limited understanding of the relationsbetween cognitive impairments and WM lesions in MS, likely because higher cog-nitive functioning requires a distributed network of multiple brain regions actingin concert (McIntosh, 2000; McIntosh and Korostil, 2008), as opposed to independentactivity in discrete loci. A crucial aspect of effective communication between dis-tinct brain regions is the myelination of axons in the WM, as speed and coherenceof signal transmission is a critical factor in complex motor and cognitive function.In previous in vivo research inferring relations between MRI WMI measures andcognition, most relied on measures only partially associated with myelin contentsuch as the DTI measures of FA and radial diffusivity (Kerchner et al., 2012; Rizioand Diaz, 2016; Roberts et al., 2013). Other studies have also utilized the MTR asa measure of WMI in disease (Faiss et al., 2014) and healthy ageing (Seiler et al.,49Chapter 3. Multimodal Data Fusion in Multiple Sclerosis2014). While there is some degree of correspondence between these measures andmyelination of underlying tissue, they do not directly quantify myelin content norare they specific to it (Ma¨dler et al., 2008; Vavasour et al., 2011). External factors suchas direct axonal damage, or underlying architecture of WM fibre bundles can affectDTI measures (Bouhrara et al., 2018). Similarly, a change in myelination may not bequantitatively reflected in these measures, rendering them non-specific to myelin.In contrast, the MWF gained from in vivo T2 relaxation studies has a very goodcorrespondence to stained myelin content examined histopathologically, the goldstandard of assessing myelination (Laule et al., 2008, 2006). While MWF has beenextensively utilized in MS research, a direct link to cognitive performance is stilllacking.Previous studies exploring the association between WM microstructure andcognitive performance have also largely attempted to relate performance on aparticular cognitive test to a measure in a specific WM region; however, it is farmore likely that several brain regions jointly engage in a given task. Moreover,since it is difficult to design cognitive tests that selectively probe one particularaspect of cognition in isolation, changes in myelin markers will probably havewidespread downstream effects across multiple cognitive tests and domains. Thus,methods that accommodate multivariate clinical and imaging data, to assess thejoint relations between two or more sets of variables may be more advantageous.In this study we have tried to address the aforementioned limitations by 1) us-ing a myelin specific measure of MWI 2) using a data-driven multivariate approachsuitable for fusion of cognitive performance, demographic and clinical data in acohort of MS subjects. We use the multivariate, data-driven method of MCCA toexamine the associations between overall myelin content and cognitive profiles,and clinical variables such as age, gender, years of education, and disease severity.We hypothesized that a significant association would exist between overall cog-nitive performance across multiple tests, overall MWF values, and demographicvariables.50Chapter 3. Multimodal Data Fusion in Multiple Sclerosis3.2 Materials & MethodsThis study received ethical approval from the University of British ColumbiaClinical Research Ethics Board, and all subjects provided written, informed consent.We enrolled a total of 46 subjects (35F / 11M) diagnosed with relapsing remittingmultiple sclerosis (RRMS) based on the McDonald 2005 criteria (Polman et al., 2011),with an average (± standard deviation) age of 42.9± 10.9 years (Table 3.1). Allimaging data were acquired on a Philips (Netherlands) Achieva 3 T MRI scannerwith an 8 channel head coil. We acquired a full brain 3DT1-weighted scan forstructural references with an inversion recovery MPRAGE sequence TI= 808ms,TR= 1800ms and an isotropic voxel size of 1mm3. T2 relaxation data were collectedusing a modified GRASE sequence with 32 echoes with 10ms echo spacing andTR= 1000ms. Twenty slices were acquired at 5mm slice thickness and reconstructedto 40 slices at 2.5mm. The in-plane voxel size was 1×1mm. A dual echo PDw/T2wscan with TE1= 8.4ms, TE2= 80ms, TR= 2800ms and voxel size of 0.97× 0.97×5mm2 was used for lesion identification.The multi-echo GRASE sequence was analysed using in-house MATLAB codewhich uses an NNLS fitting methods to approximate the multi-exponential decaycurve with a number of basis functions, resulting in one whole cerebrum MWFmap per subject. The algorithm includes correction for stimulated echoes as well asa regulariser to make the fit more robust against noise in the time domain (Prasloskiet al., 2012a). The calculation of MWF was performed as described in (Prasloski et al.,2012b).WM lesions were delineated semi-automatically utilizing the PDw/T2w images.A radiologist with extensive experience in MS lesion identification digitally markedall lesions with seed points using a custom-built software interface. T2 lesionswere then segmented using a previously validated method (McAusland et al., 2010)that automatically computes the extent of each marked lesion using a customizedParzen window classifier to estimate the intensity distribution of the lesions.We used 20 WM ROIs, part of the FSL package, which cover the majority ofthe WM and delineate major WM tracts (Figure 3.1). A full list of ROI names can51Chapter 3. Multimodal Data Fusion in Multiple SclerosisTable 3.1: Demographics, clinical, and cognitive measures. Displayed areaverages and standard deviations. For clinical measures (EDSS anddisease duration) the median and their respective ranges are shown.Demographics & clinical measures mean ± sdAge (years) 42.9±10.8Sex (f/m) 36 F, 10 MEducation (years) 14.8±2.4median, [range]EDSS 2, [0, 6]DD (years) 10, [0.3, 36]Neuropsychological scores mean ± sdWorking Memory Index (WMIX) 93.73±12.42Processing Speed Index (PSI) 101.88±16.01Verbal Letter Fluency Test (FAS) 41.03±10.74Trail Making Test A (TMT A) 30.73±12.25Trail Making Test B (TMT B) 74.18±61.03be found in Figure 3.3top. In order to extract the average MWF per ROI, the ROIswere non-linearly registered to each subjects’ native space using the registrationparameters obtained from registering the MNI template to the first echo of themulti-echo T2 data, and the FNIRT program of FSL (Jenkinson et al., 2012). Allregistrations were visually checked for accuracy and if necessary, registrationswere re-performed with adjusted parameters to ensure an appropriate alignmentbetween images. Once the ROIs were registered, a white matter mask (obtainedfrom the 3DT1 image with FAST (Jenkinson et al., 2012) and registered to the multi-echo data with FLIRT (Jenkinson et al., 2012)), was applied to ensure only WM voxelswere being considered for analysis. The MWF averages of all WM ROIs comprisedthe imaging set Xn×k with n= 46 subjects and k = 20 WM ROIs (features).All subjects were assessed with a cognitive battery evaluating performance in52Chapter 3. Multimodal Data Fusion in Multiple SclerosisFigure 3.1: Visualisation of the WM ROIs used in this study. The ROIs weretaken from the JHU atlas provided in FSL. A full list of ROI names canbe found in Figure 3.3top.processing speed, working memory, executive function and attention domain. Weadministered the subtests of the Wechsler adult intelligence scale - IV (WAIS-IV)(Wechsler, 1939) that included digit span, arithmetic, letter number sequencing,symbol search, and coding. Composite index scores from the WAIS-IV wereobtained for use in the analysis including WMIX, which utilized scores fromdigit span, arithmetic, and letter number sequencing subtests. The WAIS-IV PSIwas based on the symbol search and coding subtests. In addition to WAIS-IV, wefurther assessed FAS (Lezak, 2012), and Trail-Making Test, (TMT A and B) (Arne‚ andLabovitz, 1995) to evaluate executive function and attention. Detailed explanationsof the evaluated abilities of each test can be found in our previous study (Linet al., 2017). In the end, WMIX, PSI, FAS, and the TMT A/B raw scores formed thecognitive set Yn×l with n= 46 subjects and l = 5 cognitive features.The subjects age, gender, years of education, Kurtzke EDSS, and DD in yearswere collated to form the demographic set Zn×o with n = 46 subjects and o = 5demographic and disease severity features.53Chapter 3. Multimodal Data Fusion in Multiple Sclerosis3.2.1 Statistical Analysis3.2.1.1 Multivariate Correlation AnalysisOne method to relate two sets of multivariate data is CCA (Hotelling, 1936), withthe goal of finding linear combinations of the original variables that are maximallycorrelated. In other words, CCA finds linear transformations (canonical vectors)for each set, such that the correlation between the projections of the original data(canonical variates) onto these canonical vectors are maximised, where the first pairof canonical variates exhibits the largest correlation with a decrease in correlationfor subsequent pairs. Formally, this can be expressed as follows.Consider two data sets Xm×n and Ym×k, with m as the number of observations, andn, k as the number of features in each set. The maximum number of canonicalvariate pairs is rank min(n,k). As described in (Nielsen, 2002), CCA then searchesfor linear combinations of X and Y such thatU =n∑i=1aiXi = aTX,V{U}= aTΣ11a (3.1)andV =n∑i=1biY i = bTY,V{V}= bTΣ22b, (3.2)where V{·} denotes variance, have maximum correlation withρ = Corr{U,V}= Cov{U,V}√V{U}V{V} =aTΣ12b√aTΣ11abTΣ22b. (3.3)Let R= Cov{U,V} denote the covariance between U and V , then in order tomaximise ρ we set ∂ρ/∂a= ∂ρ/∂b= 0 and obtainaTΣ11aΣ12b= RΣ11a (3.4)bTΣ22bΣ21a= RΣ22b. (3.5)Without loss of generality, we constrain [a,b] to aTΣ11a = bTΣ22b = 1 which54Chapter 3. Multimodal Data Fusion in Multiple Sclerosisleads toρ2 =aTΣ12Σ−122 Σ21aaTΣ11a=bTΣ21Σ−111 Σ12bbTΣ22b. (3.6)In other words, we find the projections for X by considering the eigenvectorsa1, ...,an corresponding to the eigenvalues ρ21 ≤ ...≤ ρ2n of Σ12Σ−122 Σ21 with respectto Σ11, and similarly for b.MCCA is an extension to CCA in cases of more than two datasets (Ke‚enring,1971). Consider the case of l data sets, then MCCA searches for linear combinationsUT = [U1,U2, ...,Ul] of XT =[XT1 ,XT2 , ...,XTl]asU1 = aT1X1,V{U1}= aT1 Σ11a1 (3.7)U2 = aT2X2,V{U2}= aT2 Σ22a2 (3.8)...Ul = aTl Xl,V{Ul}= aTl Σllal (3.9)with its covariance matrixΣU =aT1 Σ11a1 aT1 Σ12a2 . . . aT1 Σ1lalaT2 Σ21a1 aT2 Σ22a2 . . . aT2 Σ2lal...... . . ....aTl Σl1a1 aTl Σlla2 . . . aTl Σllalor ΣU ={aTi Σi ja j}= {ρi j} for short.As in the case of two sets, the correlation of Corr{aT1X1,aT2X2}gets maximised,in MCCA, all correlations get maximised simultaneously. In this thesis we aim tomaximise the sum of squares of all correlations with W = Σli=1Σlj=1(aTi Σi ja j)2.In this application, the projections are called canonical variates (Pi), withi = X,Y,Z for each respective set, and can be viewed as condensed representa-tions, or profiles of each set, while sharing commonalities across sets. Furtherprofiles/canonical variates can be extracted with new sets of canonical vectors such55Chapter 3. Multimodal Data Fusion in Multiple Sclerosisthat they have maximum correlation among them but are uncorrelated to the priorcanonical variates. Canonical loadings are often used to assess the contributionof the original variables to the canonical variates in a set, and are defined as thecorrelation between each variable and the canonical variate.3.2.1.2 Methodological ConsiderationsAll three sets, X (MWF), Y (cognitive scores), and Z (demographics) served as theinput to the MCCA model. To avoid overfitting, we utilized PCA to reduce thedimensions of each data set to a common dimensionality of five components priorto the MCCA step. The significance of MCCA components was assessed with anonparametric permutation test in which the order of subjects was permuted andMCCA was performed again. This procedure was done 1000 times to generate anull distribution of pairwise correlation values and the original correlations wereassessed against this distribution to define significance. To estimate the robustnessof the loadings, we performed a leave-one-out cross validation.3.2.1.3 E€ects of LesionsIn order to investigate the effects of lesion tissue in this methodology, we computedtwo measures of lesion contribution per ROI. The first measure, lesion percentageis the ratio of lesional voxels to total number of voxels for a given ROI. The secondmeasure, subject lesions is the count of subjects that had at least one lesion ina particular ROI. We performed multiple linear regression with the two lesioncontribution measures as predictors and MCCA loadings on ROIs as outcomevariables. As a second test, MCCA was performed twice. Once as described above,and repeated, but specifically excluding voxels that were contained within thelesions, by subtracting the lesion mask from the ROI mask prior to calculating theaverage MWF per ROI. We then compared the results from the MCCA when lesiontissue was included and when it was excluded.56Chapter 3. Multimodal Data Fusion in Multiple Sclerosis3.2.1.4 Post-Hoc TestsIn order to determine the biological significance of the significant canonical variate,we performed different post-hoc analyses. First, we employed k-means clusteringon the weighted values from the X,Y,Z (i.e. MWF, cognition and demographic)data sets constituting the significant canonical variate. As per design, these combi-nations were ones that resulted in the largest correlation between data sets. In theclustering we were looking for a differentiation between mildly and moderatelyaffected subjects, thus we limited the number of clusters to two. We used thenon-parametric Kruskal-Wallis test to compare the two groups with regards totheir disease state.For further validation of the clusters, and to demonstrate that the canonicalvariate had biological meaning, we used an independent measure, the averagewhole brain cortical thickness based on the high resolution 3DT1 sequence andobtained from Freesurfer (Fischl, 2012), to test for differences between the twoclusters.3.3 Results3.3.1 Multiset Canonical Correlation AnalysisWe found one significant MCCA component relating imaging, cognitive, anddemographic variables (permutation test p = 0.009). The pairwise correlationsbetween the profiles were rxy = 0.37, rxz = 0.31, andryz = 0.64, with ri j and i, j beingthe imaging, cognitive, or demographic profile (Figure 3.2). Figure 3.3 shows thecanonical loadings, which are Pearsons correlations between the profiles and theoriginal features in their respective set and reflect the shared variance between theoriginal features and its profile. Error bars are 95% confidence intervals, determinedwith a leave-one-out cross validation.All features across all three sets contributed significantly to their respectiveprofiles, as suggested by the confidence intervals not spanning zero. At the sametime, there was considerable variability amongst the loadings, indicating a distinct57Chapter 3. Multimodal Data Fusion in Multiple SclerosisFigure 3.2: Correlations of the canonical variates or profiles. Top: A 3D rep-resentation of the correlation between canonical variates. Bottom: Thepairwise correlations between canonical variates P are: 0.38 between setX (MWF) and Y (cognitive), 0.31 between set X and set Z (demographicsand disease severity), and 0.64 between set Y and set Z. The overall sig-nificance of the component was p= 0.009, assessed with a permutationtest. N = 46.hierarchy of contributions between features towards each profile. Three WMROIs display a negative loading, while the remaining 17 ROIs showed a positiveloading on the WM profile. In the cognitive profile, WMIX, PSI, and FAS showedpositive loadings whereas TMT A and B exhibited a negative loading. This oppositecontribution of cognitive tests to the cognitive profile was expected since higherscores of the WMIX, PSI, and FAS indicate better performance, while the oppositeis true for the TMT A/B tests as higher scores signify worse performance. Thevariables of the demographic set demonstrated a mix of positive and negativeloadings, with gender and education showing positive contributions to this profile.58Chapter 3. Multimodal Data Fusion in Multiple SclerosisFigure 3.3: Loadings of individual features per set when lesions were includedin the analysis. Top: displays loadings of the imaging set, lower left:shows the loadings of cognitive set, lower right: shows the loadings ofdemographic set. Ant. Thal. radiation = anterior thalamic radiation, cin-gulum hipp. = cingulum hippocampus, IFOF = inferior fronto-occipitalfasciculus, ILF = inferior longitudinal fasciculus, SLF = superior longitu-dinal fasciculus; DD = disease duration. N = 46.59Chapter 3. Multimodal Data Fusion in Multiple Sclerosis-4-2PX0EDSS color coded220PY-21-3-2-102PZEDSS0246-4-2PX0PSI color coded220PY-21-3-2-102PZPSI80100120-4-2PX0TMT A color coded220PY-21-3-2-102PZTMT A20406080Figure 3.4: Scatter plots of canonical variates with color coding of differentvariables from set Y and set Z. Left: shows subjects with higher EDSSare clustered along the negative axes. Middle: color coding accordingto PSI scores where strongly performing subjects are clustered along thepositive axes displaying an inverse pattern than plot on the left. Right:performance in TMT A scores color coded where poorly performingsubjects cluster along the negative axes, showing a similar pattern tothat of left figure which means that subjects with higher EDSS performworse on TMT A. Size of markers reflects the distance from the pointfurthest back in Px−Py plane. N = 46.In contrast, age, EDSS, and disease duration loaded negatively onto this profile.Figure 3.4 illustrates the opposing contributions to their respective profiles fromsome of the variables showing some of the highest loadings from the cognitiveand demographic sets. The figure displays the profiles with subjects color-codedaccording to their EDSS score (Figure 3.4 left), their PSI score (Figure 3.4 middle),and their TMT A score (Figure 3.4 right).3.3.2 E€ects of LesionsA multiple regression model estimating the profile loadings of WM ROIs, as thedependent variable, with lesion percentage and subject lesions, as the independentvariables, was not significant (F(17,20) = 2.47, p= 0.114).The repeat MCCA analysis with lesion tissue removed resulted in a very similarcorrelation pattern among the three profiles with one significant component (p=0.005) and pairwise correlations of rxy= 0.37, rxz= 0.31, and ryz= 0.64. The loadings60Chapter 3. Multimodal Data Fusion in Multiple SclerosisFigure 3.5: Loadings of individual features per set when lesions were excludedin the analysis. Top: displays loadings of the imaging set, lower left:shows the loadings of cognitive set, lower right: shows the loadings ofdemographic set. ant. Thal. radiation=anterior thalamic radiation, cin-gulum hipp. = cingulum hippocampus, IFOF=inferior fronto-occipitalfasciculus, ILF=inferior longitudinal fasciculus, SLF=superior longitudi-nal fasciculus; DD=disease duration. N = 46.of FAS in the cognitive set and the loading of education in the demographic setnow reached significance, suggesting that these two indices may be influencedby heavily demyelinating regions more than others. The MCCA loadings whenexcluding lesions can be seen in Figure 3.5. A qualitative comparison betweenloadings are listed in Tables 3.2-3.4.61Chapter 3. Multimodal Data Fusion in Multiple SclerosisTable 3.2: Listings of canonical loadings of the imaging features and associatedp-values in the MCCA model including and excluding lesion tissue.Including lesions Excluding lesionsROI correlation r p-value correlation r p-valueThalamicRadiation L0.103 0.4975 0.102 0.4993ThalamicRadiation R0.278 0.0615 0.253 0.0900Corticospinaltract L0.715 < 0.0001 0.708 < 0.0001Cortiospinaltract R0.562 < 0.0001 0.545 < 0.0001Cingulum L 0.092 0.5428 0.104 0.4910Cingulum R −0.219 0.1429 −0.201 0.1809Cingulumhippocampus L0.185 0.2184 0.183 0.2243Cingulumhippocampus R−0.438 < 0.0001 0.586 0.0035Splenium 0.566 < 0.0001 0.586 < 0.0001Genu 0.301 0.0388 0.219 0.0307IFOF L 0.627 < 0.0001 0.637 < 0.0001IFOF R 0.372 0.0110 0.637 0.0078ILF L 0.463 0.0012 0.472 0.0009ILF R 0.557 0.0001 0.574 < 0.0001SLF L 0.545 0.0001 0.553 0.0001SLF R 0.389 0.0075 0.412 0.0044Uncinate L 0.069 0.6459 0.075 0.6188Uncinate R −0.275 0.0642 −0.264 0.0761Arcuate L 0.445 0.0019 0.448 0.0018Arcuate R 0.257 0.0852 0.279 0.060162Chapter 3. Multimodal Data Fusion in Multiple SclerosisTable 3.3: Listings of canonical loadings of the cognitive features and associ-ated p-values in the MCCA model when including and excluding lesiontissue.Including lesions Excluding lesionsCognitive test correlation r p-value correlation r p-valueWMIX 0.661 < 0.0001 0.680 < 0.0001PSI 0.706 < 0.0001 0.712 < 0.0001FAS 0.287 0.0533 0.301 0.0425TMT A −0.903 < 0.0001 −0.894 < 0.0001TMT B −0.638 < 0.0001 −0.628 < 0.0001Table 3.4: Listings of canonical loadings of the demographic and clinical fea-tures and associated p-values in the MCCA model when including andexcluding lesion tissue.Including lesions Excluding lesionsDemographic &Clinical feature correlation r p-value correlation r p-valueAge −0.411 0.0046 −0.401 0.0057Gender 0.424 0.0034 0.415 0.0042Education 0.282 0.0577 0.294 0.0472EDSS −728 < 0.0001 −0.736 < 0.0001DD −0.735 < 0.0001 −0.727 < 0.000163Chapter 3. Multimodal Data Fusion in Multiple SclerosisFigure 3.6: Comparison of MCCA loadings with and without lesions. Ant.Thal. radiation = anterior thalamic radiation, cingulum hipp. = cingulumhippocampus, IFOF = inferior fronto-occipital fasciculus, ILF = inferiorlongitudinal fasciculus, SLF = superior longitudinal fasciculus; DD =disease duration. N = 46.Figures 3.6-3.7 display a direct comparison of loadings when performing theanalysis with and without lesions for each set.Figure 3.7: MCCA loading comparison in cognitive (left) and demographic(right) sets when including and excluding lesions. N = 46.Figure 3.8 shows the WM ROIs with a substantial lesion contribution (in thiscase measured by how many subjects presented a lesion in an ROI), that also had a64Chapter 3. Multimodal Data Fusion in Multiple SclerosisFigure 3.8: Color coded ROIs that showed lesions in at least 50% of subjects(red) and 33% of subjects (orange) with some of the largest loadings ontothe WM profile. The bilateral thalamic radiation in blue showed lesionsin at least 50% of subjects but did not show large loadings. Even thoughthere was a substantial lesion contribution in those ROIs, it had minimaleffects on the loadings.significant loading on the WM profile.3.4 Post-Hoc ResultsAfter a k-means clustering looking for two clusters, cluster one was comprisedof 36 subjects and cluster two included 10 subjects (Figure 3.9). The clusteringseparated subjects into a mildly affected (average EDSS = 2.09, average DD = 9.32years) and a moderately affected (average EDSS = 3.80, average DD = 19.10 years)group with p = 0.0065 for EDSS and p = 0.0093 for DD (Table 3.5). As expected,cluster 2, with greater EDSS and higher DD, exhibited greater cortical thinning(2.61mm vs 2.51mm p= 0.0143, for cluster 1 and cluster 2, respectively).65Chapter 3. Multimodal Data Fusion in Multiple SclerosisFigure 3.9: Using k-means on canonical variates of significant component look-ing for two clusters (one mildly (average EDSS = 2.09, average DD = 9.32years) and one moderately (average EDSS = 3.80, average DD = 19.10years) affected subgroup). The number of subjects per cluster are 36, and10, respectively.3.5 DiscussionWe utilized a multivariate, data-driven approach, in order to reveal a joint patternof covarying features consisting of profiles of WM myelin integrity, cognitiveperformance, and demographic and disease factors in a cohort of RRMS subjects.The data fusion performed here is completely data-driven and uses simple linearweights in order to decompose the data sets into latent, maximally cross-correlatedprofiles. The data-driven nature of the analysis minimises a priori assumptionsabout potential interactions within and across data domains, while its multivariatenature allows the modeling of shared features across data sets. This is in contrast tounivariate approaches where only local or distinct features can be examined. Thepower of the MCCA analysis approach lies in its ability to naturally reveal cross-modality relationships and it suggests some interesting conclusions: 1) factorssuch as disease duration, gender and age predict cognitive performance in early66Chapter 3. Multimodal Data Fusion in Multiple SclerosisTable 3.5: Comparison of clinical and demographical indices between clusters.Cluster 1mean ± sdCluster 2mean ± sd Kruskal-Wallisp-valueAge (years) 41.5±10.97 47.9±9.36 0.1126Sex (f/m) 30 F / 6 M 5 F / 5 M —Education (years) 14.94±2.45 14.30±2.58 0.2419DD (years) 9.32±6.80 19.10±10.90 0.0093EDSS 2.09±1.62 3.80±1.60 0.0065WMIX 94.11±13.46 83.50±8.51 0.0230PSI 102.31±13.39 85.30±14.91 0.0044FAS 40.78±11.40 37.10±12.35 0.5938TMT A 28.41±7.29 54.00±11.46 < 0.0001TMT B 67.41±38.09 144.40±83.84 < 0.0001Cortical thickness (mm) 2.61±0.10 2.51±0.09 0.0143MS more than myelin features (correlation between profiles of cognition anddemographics r = 0.64, MWF vs cognition r = 0.37, and MWF vs demographicsr = 0.31), 2) relative independent of lesion presence and exact lesion location, thereis a robust association between myelin content in long-range intrahemisphericconnections and the corpus callosum and cognitive performance.Many cognitive domains can be profoundly affected by altered microstructuralintegrity as seen in MS. Processing speed and tasks requiring the ability to focusattention, scan quickly, discriminate and order information in order to process it,and working memory, are all commonly impaired in MS (Chiaravalloti and DeLuca,2008; Guimara˜es and Sa´, 2012; Pujol et al., 2001). Complex attention involving alertness,selective/focused/divided attention, and vigilance rather than “simple” attention(e.g. repeating a series of digits) is also impaired (Chiaravalloti and DeLuca, 2008;Guimara˜es and Sa´, 2012). Impairments in executive function, a set of abilities which67Chapter 3. Multimodal Data Fusion in Multiple Sclerosisfacilitate goal-oriented behaviour as well as adaption to environmental changessuch as planning, shifting, and fluency, appears to impact the quality-of-life themost amongst the cognitive deficits seen in MS (Foong et al., 1997; Holland et al.,2014; Preston et al., 2013). Early research proposed that memory deficits in MS werecaused by an inability to sustain or support effective information retrieval (Bea‚y,1993), however difficulty in acquiring new knowledge (i.e. memory encoding)might be a greater problem than information retrieval (i.e. memory retrieval)(Chiaravalloti and DeLuca, 2008).Several studies have attempted to establish the links between white matterchanges and cognitive decline in MS. Demyelination, inferred by lesions in con-ventional MRI images in the medial frontal region, is associated with slow re-sponses in an attention task (Pujol et al., 2001). Studies utilizing DTI have suggestedthat processing speed deficits were related to reduced FA in the corpus callosumand superior longitudinal fasciculus, two major tracts connecting the two hemi-spheres and frontal, temporal, and parietal lobes (Genova et al., 2013). Comparedto cognitively-preserved MS patients, cognitively-impaired patients evaluated inspatial and verbal memory, information processing speed, working memory, andverbal fluency spheres exhibited reduced FA in the corpus callosum, superior andinferior longitudinal fasciculus, corticospinal tracts, forceps major, cingulum, andfornices (Hulst et al., 2013).While here we have shown a significant relation between cognition and MWFmeasures in RRMS, relations between MWF imaging and cognition have alsobeen explored in the non-MS literature. In children (n = 108 children ages: 2.5months - 5.5 years), a significant positive association between myelination andcognitive and motor abilities can be shown (Dean et al., 2015; Deoni et al., 2016).Further, a relation was found between highly myelinated axons in the corpuscallosum and the Wechsler Intelligence Scale for Children in five male childrenaged between 8 and 12 (Whitaker et al., 2008). A myelin water imaging study foundpositive relations between frontal lobe myelination and both age and years ofeducation in controls (n = 27) but not in subjects with schizophrenia (n=30) (Flynnet al., 2003). A more recent study of young adults with ages ranging from 15 to 3868Chapter 3. Multimodal Data Fusion in Multiple Sclerosisyears found a positive relation between frontal lobe myelination and age, northamerican adult rating test (NAART) IQ, and years of education (Lang et al., 2014).In older patients with mild cognitive impairment (MCI), substantial decreasedmyelin integrity has been observed; however, associations between decreasedmyelination and poor cognitive performance were not documented (Bouhrara et al.,2018). Finally, a study of myelination in 61 healthy volunteers aged 18 to 84 yearsfound a quadratic relation between MWF and age (Arshad et al., 2016) emphasizingthat age affects myelin differently across lifespan. Overall, these studies highlightthe importance of often widely spatially distributed myelin profile integrity tocognitive function. However, the link between myelin integrity and cognitiveabilities in MS is lacking. This study potentially overcomes the research gap ofmyelin-cognition relations in MS as we discovered multivariate relations betweenmyelin and cognitive performance. Perhaps, the multivariate approach used inthis study is a key factor to study human brain and behaviour.As executive function profoundly affects the quality-of-life of people with MS,the original study design was to investigate the relations between imaging fea-tures, clinical variables, and primarily executive performance in MS. Therefore, thetest battery for this study was based on widely-used tasks in assessing executivefunctioning and processing speed rather than commonly-used cognition screeningtests such as the brief international cognitive assessment for multiple sclerosis(BICAMS) (Langdon et al., 2012). Another neuropsychological battery that targetsspecific domains affected in MS is the minimal neuropsychological assessmentof multiple sclerosis patients (MACFIMS) (Benedict et al., 2002), which providescomprehensive evaluation of cognitive function in MS. In fact, our test batteryevaluates some domains that are also examined in MACFIMS such as workingmemory, processing speed, and executive function. Due to the fact that executivefunction and processing speed were our primary and secondary targets to eval-uate, we specifically chose tests tailored to assess these domains, rather than thestandardized test used in MS. Therefore, we decided to use sub-tests of WAIS-IVto evaluate working memory and processing speed and executive function wasalso examined with TMT A/B and FAS. We note that the loadings across specific69Chapter 3. Multimodal Data Fusion in Multiple Sclerosiscognitive tests in the significant MCCA component were relatively uniform (notethat for TMT A/B, longer times represent worsening performance, so the loadingsin Figure 3.3, lower left are reasonable since higher scores on TMT A/B are an-ticorrelated to the remaining cognitive tests where higher scores indicate betterperformance). We therefore do not believe that differing cognitive tests would alterour overall conclusions substantially.We used MCCA to create profiles of WM myelin integrity, cognitive perfor-mance, and demographic and disease factors which were closely related to oneanother. Since WMIX, PSI, and FAS together with gender and education all loadedpositively on their respective profiles, it is implied that subjects with higher edu-cation and being female (females were coded 1, males were coded 0 in analysis)performed better in these cognitive tests. Most WM ROIs loaded positively on itsprofile, and the aforementioned cognitive tests loaded positively on their profile.This implies a positive relation between MWF and cognitive performance, edu-cation, and female gender. In contrast, the negative loadings of age, EDSS, anddisease duration on the demographics profile, and the positive loadings of WMIX,PSI, and FAS on the cognitive profile, suggest that age and disease progressionhave adverse effects on cognitive performance. Similarly, age, EDSS, and diseaseduration showed opposite loadings to that of WM ROIs on their respective profiles,indicating an inverse relation between MWF and age, and disease duration.The cognitive tests TMT A/B loaded negatively on the cognitive profile, whilein the demographics profile, age, EDSS (disease severity), and disease duration hadnegative loadings, and years of education had a positive loading. This indicatesthat age and a more severe disease state were associated with higher TMT A/Bscores (i.e., slower times to complete the task, reflecting a worse performance), butyears of education was not. Similarly, the mostly positive loadings of most WMROIs in the myelin profile, suggest a worse performance in TMT A/B with lowMWF, an imaging feature associated with more severe disease involvement.Our results further support the notion that higher-order functions require mul-tiple brain regions to coordinate together, especially the longitudinal fasciculuswhich connect frontal/parietal/occipital areas (i.e. long-range intrahemispheric70Chapter 3. Multimodal Data Fusion in Multiple Sclerosisconnections) and the corpus callosum which links the two hemispheres (i.e. inter-hemispheric connections) (Schulte and Mu¨ller-Oehring, 2010). In the present study,white matter ROIs associated most with the imaging profile included the bilateralcorticospinal tract, forceps major, forceps minor, bilateral inferior fronto-occipitalfasciculus, bilateral inferior longitudinal fasciculus, bilateral superior longitudinalfasciculus, and left arcuate. These WM tracts connect geographically remote brainregions, as well as cortical and subcortical areas connecting regions for processingspeed ability, higher-order cognitive functions, and motor function (Roberts et al.,2013). The forceps minor, forceps major, superior and inferior longitudinal fasci-culus, and inferior fronto-occipital fasciculus have been reported to be involvedin processing speed function, and influencing TMT performance in both olderadults and MS subjects (Genova et al., 2013; Kerchner et al., 2012). The inferior andsuperior longitudinal fasciculi have been shown to play a role in higher-ordercognitive function as they connect association cortices key regions for higher-orderfunctions (Jung et al., 2016). Indeed, the cognitive tests that are positively expressedin the cognitive profile are WMIX, PSI, and FAS, tests that assess working memory,processing speed, and verbal fluency and are all impaired in MS (Chiaravalloti andDeLuca, 2008; Guimara˜es and Sa´, 2012; Pujol et al., 2001). On the other hand, the timedTMT A/B tests, where higher scores signify worse performance, are negativelyassociated with the cognitive profile, indicating an inverse relation between theimaging features and these particular tests.The fact that the corticospinal tract WM ROI was also loading positively on theimaging profile is perhaps surprising. A DTI study suggested that the corticospinaltract has been related to motor performance but not higher-order cognitive func-tions (Lo¨vde´n et al., 2014), as would be expected. While the quantitative measure ofmyelin and joint multivariate data analysis utilized here may be more sensitive,there may be other explanations. For example, the corticospinal tract is required toexecute the processed information required in different cognitive tasks. One modelparcellates executive function into three components input (require long-rangeconnections), core process (in the prefrontal cortex), and output (require coordi-nation of motor and subcortical connections for taking actions) (Miller and Cohen,71Chapter 3. Multimodal Data Fusion in Multiple Sclerosis2001). This model implies that the corticospinal tract might be involved in theoutput component to execute actions based on processed information. Therefore,as a resource to execute the information, it is reasonable that WMI in the corti-cospinal tract is involved in executive function. Further, there may be a correlativeas opposed to a causal relation between corticospinal tract integrity and cognitivefunction: presumably people with worsening disease, and reduced WMI would bemore likely to also have impairments in their motor system.Some of our results describing factors preserving executive function in MS areperhaps unsurprising. We found positive loadings of WMIX, PSI, FAS, as well as apositive loading of education onto their respective profiles, suggesting a positiverelation between these features. In the theory of cognitive reserve (Stern, 2002;Sumowski and Leavi‚, 2013; Tucker-Drob et al., 2011), higher levels of education mayalter synaptic organization and/or neuronal networks so individuals can still sus-tain damage and maintain adequate cognitive function (Stern, 2002). Also, we foundthat age, EDSS and disease duration loaded negatively on the demographic profileindicating a negative association with cognitive tests that loaded positively on thecognitive profile. Of note, EDSS and disease duration had the highest loadingsin the demographics profile, indicating a central role of these measures influenceon both imaging and cognition sets. We also observed that better cognitive per-formance was associated with female gender. Although we speculate that such apattern may support the purported neuroprotective effects of estrogen (Jacobs andD’Esposito, 2011; Miller and Cronin-Golomb, 2010), more evidence is needed to drawsuch conclusion.The cluster analysis produced a reasonable separation of mildly- and moderately-affected sub-groups across all three sets, further supporting a strong relation be-tween MWF, cognitive abilities, and demographics. The additional comparison ofan unrelated measure, namely cortical thickness, reinforces the utility of MCCA aswell as strengthens our results of finding an association between MWF, cognitiveperformance, demographics and clinical variables. The groupings based on theMCCA results show a similar pattern of cortical thinning with the moderatelyaffected sub-group having a decreased overall cortical thickness and are in line72Chapter 3. Multimodal Data Fusion in Multiple Sclerosiswith previous research (Steenwijk et al., 2016).Importantly, our results were largely independent of exact lesion location. Amultiple linear regression model was unable to detect a relation between lesioncontribution per ROI and the MWF loadings we found suggesting that MWFloadings are independent of lesion contribution. Furthermore, when the MCCAanalysis was performed with and without lesion tissue included in WM ROIs theresults were largely unchanged. There has been a long-standing debate on localvs distributed representation of brain function (Kaas, 1987). In MS there can bea very close association between lesion location and clinical effects, with opticneuritis being a prime example. However, with higher cognitive functions, suchclinicopathological correlation between lesion location and behavioural effect isless clear, as distributed brain regions must be recruited to facilitate complextasks. While we have shown a relationship between NAWM and some cognitivefunctions, we cannot discern, with the current analysis, whether or not this relatedto primary dysfunction in the NAWM, or secondary changes from focal lesions.There are a number of limitations to our study. Since none of the MS subjectsdemonstrated overt cognitive impairment at the time of examination based on ourprevious report which investigated the same cohort (Lin et al., 2017), the resultsof this study reflect brain-behaviour associations at early stages of the disease.Further, the analyzed cohort was comprised solely from early stages of the RRMSsubtype which was owed to the study design, extrapolations to different subtypesof MS should be taken with care. Due to the fact the analysis was based on a setof WM ROIs from a template, not all of the WM is necessarily covered, althoughwe note that most major WM fibre bundles were included. This may have led toindividual lesions not being accounted for in this analysis in case they did notoverlap with any of the standard ROIs. In addition, the investigated cohort wasin the relatively early stages of MS with low to moderate lesion burden such thatthe impact of focal demyelination of lesions within the ROIs was limited. Thus,the minor change in results of the MCCA when including and excluding lesionsmay be partly due to the fact that not all lesion had been considered. Finally, acomplicating factor is that myelin as a function of age may follow a quadratic73Chapter 3. Multimodal Data Fusion in Multiple Sclerosisfunction (Arshad et al., 2016), so extrapolating to broader age ranges may pose a risk– our results may therefore only be interpretable for the age range of our cohort.To conclude, with quantitative WM myelin measures and a joint multivariateanalysis, we found individual profiles of myelin integrity, cognition, and demo-graphical features in MS that where highly similar. Higher myelin integrity sup-ported better cognitive function and was positively related to education as well asfemale gender; while disease severity and ageing were associated with worseningcognitive performance. In the future, a multimodal approach including functionalmeasures gained from fMRI may be used to study the interplay between structureand function and use their complementary information to further prognosticatecognitive deficits in MS.74Chapter 4LinkingWhiteMa‚er Integrity to Func-tional ConnectivityIn this chapter we investigated whether or not indices of WMI can be linkedto indices parametrising functional MRI. Despite much research, the exact linkbetween structural and functional MRI is still largely unknown and we investigatedthis elusive relation in two parts. In the first part, we examine if the often-reportedchanges in functional brain network organisation in PD can be estimated by theWMI, and if a combined set of features can be linked to clinical and behaviouralindices. We show that a particular set of WM ROIs can estimate the communityorganisation of functional networks in PD that can also be linked to disease severity.In the second part, we propose a novel method to investigate changes in theWMI that makes use of multiple, complementary parameters probing differentaspects of the WMI. The underlying assumption of our proposed method is that achange in WMI in one ROI may have consequences for the WMI of other areas andthat changes appear in concert throughout the WM and rarely only in focal points.With this new approach, we are able to demonstrate widespread differences inWMI that are correlated not only with clinical characteristics but also with indicesfrom functional MRI.Our results demonstrate that changes in functional brain organisation can beestimated by MWF and that this multimodal integration can be used to find clinical75Chapter 4. Linking White Ma‚er Integrity to Functional Connectivitycorrelates. In addition, our proposed framework of combining different indices ofWMI provides a novel way of leveraging complementary information and offersnew ways of characterising joint changes across the WM.4.1 IntroductionStructural and functional MRI have greatly contributed to gain insight into neu-rological diseases. Over the last few years, the concept of “brain networks” hasemerged and continues to receive great interest in the research community. In thischapter, we aim to link structural and functional MRI in the framework of networkscience. We provide results from two overarching methods, 1) a hypothesis-drivenanalysis in which we investigate if commonly-reported changes in functional net-work organisation can be estimated by MWF in the WM and 2) a data-drivenanalysis in which we propose a novel method to construct networks based onsimilarities of WMI across different regions.First a brief introduction to brain networks and the generation of functionalnetworks is presented. We then report the results from the hypothesis-drivenanalysis before we show the results from our new proposed method.4.2 Introduction to brain networksPathological alterations of the brain are rarely confined to a single location. Instead,oftentimes they spread via axonal pathways to influence other regions not directlyinvolved in the pathological perturbation. The patterns of such disease propagationare constrained by the complex, yet highly organized, topology of the underlyingneural architecture; the so-called connectome (Sporns et al., 2005). Thus, networkorganization fundamentally influences brain disease, and a connectomic approachgrounded in network science is integral to understanding neuropathology (Fornitoet al., 2015).Modern network science has introduced new opportunities for understandingthe brain as a complex system of interacting units. The discovery of small-worldnetworks and scale-free networks has given rise to a rapidly growing interdisci-76Chapter 4. Linking White Ma‚er Integrity to Functional Connectivityplinary science of complex networks (Stam, 2014). There is a growing consensusthat normal brain networks are organized as cost-efficient small-world networks,which combine dense local connectivity with efficient long-distance connections tooptimally integrate and segregate information flow (Bullmore and Sporns, 2012). Inbrain networks some regions are highly connected, called hub areas. Hubs play acentral role in the overall network organisation (van den Heuvel and Sporns, 2011)and these brain areas facilitate effective communication within a network (Poweret al., 2013). Further, brain networks exhibit a hierarchical modularity, where eachmodule corresponds to a major functional system such as motor, visual, and associ-ation networks (Meunier et al., 2010). Recent studies are challenging the idea thatbrain diseases involve either “local” or “global” pathology. In particular, in severaltypically global brain disorders, such as AD, network studies have shown thatthe pathology is in fact not equally distributed over the brain, but preferentiallyaffects the hub areas (Tijms et al., 2013; van den Heuvel and Sporns, 2013). Conversely,network studies have revealed that local brain pathologies, such as brain tumoursor vascular lesions, have a far more global impact than has been recognized before,and this can explain some of the executive cognitive deficits in these disorders(Fornito et al., 2015).4.2.1 Functional networksFunctional networks are obtained with fMRI where the subject is placed in theMRI scanner and its neuronal activity is monitored by a proxy measure over aperiod of time. The level of coactivation among cortical brain regions is reflected intheir correlation of timeseries and is defined as functional connectivity (FC). TheFC is typically organised in a matrix termed FC matrix where each entry displaysthe correlation between the respective brain areas. Typically, the FC matrices arebinarised by applying a threshold on the FC matrices, either an absolute thresholdor a proportional threshold before subsequent topological analysis. Althoughrecent trends are also investigating the weighted connectivity matrices. Figure 4.1illustrates the generation of an FC matrix.77Chapter 4. Linking White Ma‚er Integrity to Functional ConnectivityFigure 4.1: Illustration of generating an FC matrix. The cortical area is par-cellated into different ROIs of which the average timeseries (among allvoxels per ROI) is extracted. The degree of connectivity is quantified by apairwise correlation between all ROIs which is organised in a symmetricmatrix where each entry indicates the FC between two ROIs.4.2.2 Brain Network AnalysisGraph theory provides a conceptual framework for analysing and characterisingnetworks. This framework allows the examination of global and local architecturesof networks. Consider a graph G= (V,E) with V being a set of vertices or nodesreflecting brain regions, and E as links or edges reflecting the degree of interactionbetween brain regions. Figure 4.2 illustrates the graph theoretical measures usedin the following analysis.Common graph theory measures that were used in this dissertation are listedbelow:Basic concepts and notation for binary and undirected networks (Rubinov and Sporns, 2010):N is the set of all nodes in the network, and n is the number of nodes. L is the set ofall links in the network, and l is the number of links. (i, j) is a link between nodesi and j, (i, j ∈ N). ai j is the connection status between i and j: ai j = 1 when a link(i, j) exists; ai j = 0 otherwise (aii = 0 for all i).78Chapter 4. Linking White Ma‚er Integrity to Functional ConnectivityFigure 4.2: Illustration of the graph theoretical measures in a toy network. De-scriptive network measures are shown in boldface, while specific graphtheory measures are listed below their respective category. Adaptedfrom (Rubinov and Sporns, 2010)• characteristic pathlengthThe characteristic path length of node i provides information about how closenode i is connected to all other nodes in the network and is given by thedistance di, j between node i and all other nodes j in the network. In otherwords, it is the average shortest path length between all pairs of nodes, andis defined as,L=1n ∑i∈N(4.1)Li =1n ∑i∈N∑ j∈N, j 6=i di jn−1 , (4.2)where Li is the average distance between node i and all other nodes and di jas the shortest path length between nodes i and j defined as di j = ∑auv∈gi↔ j ,where gi↔ j is the shortest path between node i and j.• global efficiencyGlobal efficiency is the average inverse shortest path length. Global efficiencyis suitable to examine disconnected graphs as it can assess paths between79Chapter 4. Linking White Ma‚er Integrity to Functional Connectivitydisconnected nodes as they have infinite length and thus zero efficiency. Itfollows that characteristic pathlength is primarily influenced by long paths,while global efficiency is primarily affected by short paths and, depending onthe investigated network, provide complementary information. It is given by,E =1n ∑i∈N(4.3)Ei =1n ∑i∈N∑ j∈N, j 6=i d−1i jn−1 , (4.4)where Ei is the efficiency of node i.• clustering coefficientThe clustering coefficient Ci of node i provides information about the localconnectedness of that node in the graph. It is defined by the ratio of thenumber of connections between the direct neighbours of node i and themaximum number of possible connections between the neighbours of node i.Formally it is given by,C =1n ∑i∈N(4.5)Ci =1n ∑i∈N2tiki(ki−1) , (4.6)where C is the clustering coefficient of node i, ti is the number of trianglesaround node i with ti = 12∑ j,h∈N ai jaiha jh, and ki as the degree of node i thatrepresents the number of links connected to a node with ki = ∑ j∈N ai j.• modularityThe modularity of a graph describes the possible formation of communitiesin the network, indicating how strong groups of nodes form relative isolated80Chapter 4. Linking White Ma‚er Integrity to Functional Connectivitysub-networks within the full network and is given by,Q=1l ∑i, j∈N(ai j− kik jl)σmi,m j , (4.7)where mi is the module containing node i, and σmi,m j = 1 if m j = m j, and 0otherwise.• betweenness centralityCentrality as a concept revolves around the idea that central nodes participatein many short paths, connecting many nodes and hence act as important relaynodes that control the flow of information. The betweenness centrality isdefined as the fraction of all shortest path in the network which pass througha given node. Formally it is given by,bi =1(n−1)(n−2) ∑h, j∈N,h 6= j,h6=i, j 6=iρh j(i)ρh j, (4.8)where ρh j is the number of shortest paths lengths between h and j, and ρh j(i)is the number of shortest paths between h and j that pass through i.In addition to the graph theoretical measure mentioned above, we also includedthe Fiedler Value as a measure of global robustness of the network in our analysis.The Fiedler Value is a measure from spectral graph theory and is defined as thesecond smallest eigenvalue of the Laplacian matrix of a graph G. We used thesymmetric normalised Laplacian that factors out differences in degree and is thusonly reflecting relative connectivity with,Lsym =D−12LD12 , (4.9)where L is the regular Laplacian as L = D−A with D as a diagonal matrix withthe degree of each node on its diagonal and A as the FC matrix. The Fiedler Valuecan then obtained by calculating the eigenvalues of Lsym and extracting the second81Chapter 4. Linking White Ma‚er Integrity to Functional Connectivitysmallest (first non-zero) eigenvalue from the eigenvalue spectrum. The FiedlerValue describes the algebraic connectivity among the elements of the networkwhere a Fiedler Value of 0 indicates a disconnected network. A study suggestedthe Fiedler Value to be an important characteristic of brain networks in PD (Caiet al., 2018).4.3 Hypothesis Driven Approach: Changes inModularity of Functional Networks can beEstimated by White Ma‚er Integrity inParkinson’s Disease4.3.1 IntroductionPD is a neurodegenerative disorder of the CNS characterised by cardinal motorsymptoms with accompanied by a wide variety of non-motor symptoms resultingfrom a progressive degeneration of dopaminergic neurons in the substantia nigra(Chaudhuri et al., 2006). Typical motor features of PD are tremor, bradykinesia, rigid-ity, and later, postural instability. Besides these debilitating motor impairments,non-motor features such as cognitive impairments, apathy, depression, sleep dis-turbances, and visuospatial impairments are increasingly recognised as a majorcontributor to a decline of quality of life in PD subjects.PD has a highly heterogeneous presentation and progression, and some ofthis variability may arise from alterations in activity in brain neural networks(de Schipper et al., 2018). In recent years, resting-state fMRI has been employed tostudy functional brain network(s), demonstrating altered functional connectivity inPD compared to controls (Fiorenzato et al., 2019; Li et al., 2019; Zhan et al., 2018). Withgraph theory (GT), a mathematical framework to characterise network propertieson global and local scales, research has shown altered properties of topologicalbrain characteristics (Baggio et al., 2015; Cai et al., 2018). In particular, a commonoccurrence in PD is increased modularity, i.e., the network gets reorganised into82Chapter 4. Linking White Ma‚er Integrity to Functional Connectivitysmaller, more highly specialized functional units, but with a decreased globalintegration of information (Baggio et al., 2014; Lin et al., 2018). While these changesin functional connectivity and functional brain organisation have been implicitlyattributed to altered dopaminergic levels (Bell et al., 2015; Kelly et al., 2009), otherfactors, including changes in the WM microstructure, may also play a role.Recent studies utilising advanced quantitative MRI have shown alterations ofthe WM microstructure in PD. DTI has found widespread differences between PDand healthy subjects, and differentiate those with PD and mild cognitive impair-ments and those with dementia (Gorges et al., 2019). Other studies have relatedstructural changes to non-motor symptoms such as cognitive performance (Melzeret al., 2013; Theilmann et al., 2013) and apathy (Lucas-Jime´nez et al., 2018; Zhang et al.,2018). More recently, structural brain networks, on the basis of DTI, have beenused to describe changes in the structural connectome in PD (Koirala et al., 2019).However, how documented changes in the WM microstructure relate to functionalconnectivity changes in PD remains largely unknown.Most studies investigating WM have utilized DTI, which may be be a relativelyunspecific marker of white matter changes ref. Recently, we have shown that anin vivo marker for myelin content, the MWF in the WM can be associated withdistinct PD symptom domains (Baumeister et al., 2018).Here we investigated if WMI, specifically, myelin content measured with theMWF, can estimate changes in functional segregation. Further, we investigated iffeatures of functional topology and WMI can be jointly related to PD symptoms.4.3.2 Materials & Methods4.3.2.1 Subjects and Data AcquisitionThis analysis used the same cohort as in chapter 2. The MWI data were analysedin the same way as before. Furthermore, we used the JHU label atlas with atotal of 36 WM ROIs and registered the each label file to the native MWI spaceusing advanced normalization tools (ANTs) (Avants et al., 2008). In addition to83Chapter 4. Linking White Ma‚er Integrity to Functional Connectivitythe MRI data from before, rs-fMRI were collected with an echo planar imagingsequence with TE = 30ms, TR= 2000ms, 90◦ flip angle with a spatial resolution of3×3×4mm and 240 time points.4.3.2.2 fMRI Processingrs-fMRI data were processed including standard preprocessing steps such as slicetime correction, isotropic resampling to 3mm3, motion correction using rigid bodyalignment. Nuisance time courses were regressed out voxel-wise in order toremove influences from head motion, their temporal derivatives, the average WMsignal as well as the average cerebrospinal fluid (CSF) signal. Lastly, the imagesspatially smoothed with a 6×6×6mm full width half maximum (FWHM) Gaussiankernel and bandpass filtered at 0.01−0.08Hz. We used the automated anatomicallabelling (AAL) atlas (Tzourio-Mazoyer et al., 2002) to extract time courses of 90 ROIsby first registering the AAL template to each subjects native fMRI space and thenaveraging the voxel-wise time courses within each ROI.4.3.2.3 Graph Theoretical AnalysisIn order to construct a functional connectivity matrix, we used the Pearson correla-tion coefficient to correlate each ROIs time course with each of the remaining ROIs,thus we obtain a 90×90 (symmetric) FC matrix per subject where each entry repre-sents the correlation between two ROIs. Common graph theoretical measures werecalculated with the Brain Connectivity Toolbox (h‚ps://sites.google.com/site/bctnet/).We calculated the characteristic pathlength, which is the average number of edgesin the shortest paths between every pair of nodes in the network (van Wijk et al.,2010). We calculated the global efficiency, which is the average inverse shortestpath length in the network, and is a measure of global integration. Additionally,we extracted the modularity, which represents the optimal community structureto divide the network into non-overlapping subnetworks (i.e., groups of nodes)in a way that maximizes the number of within-group edges, and minimizes thenumber of between-group edges. The modularity quantifies the degree to which84Chapter 4. Linking White Ma‚er Integrity to Functional Connectivitythe network may be subdivided into such clearly delineated groups and is a mea-sure of segregation. Lastly, we calculated local measures of clustering coefficientand betweenness centrality, as measures of nodal importance and averaged themacross all nodes.In addition to graph theoretical measures, we calculated the Fiedler Value as ameasure of global robustness of the network. The Fiedler Value is computed as thesecond smallest eigenvalue of the Laplacian matrix of a Graph G and is defined asfollows,L(G) = D(G)−A(G), (4.10)where G is a graph with n nodes, D(G) is the degree matrix, an n× n diagonalmatrix with entries on its main diagonal according to the degree of each node, andA(G) is the adjacency, or connectivity matrix. In this study we used the normalisedFiedler Value, which obtained from the normalised Laplacian.4.3.2.4 Statistical AnalysisWe computed GT measures mentioned in paragraph 4.2.2 and the Fiedler Value ofthresholded and binarised the FC matrices. Due to the fact that GT measures areinfluenced by the number of links in a graph, we applied a proportional thresholdsuch that only a percentage of links with the highest correlation were retained.We used a range of density based thresholds were we retained 1 - 35% in 1%increments of the total amount of links. Typically, the optimal density threshold isunknown and for this reason we compared the GT measures and Fiedler Value ateach density threshold with two-sample t-tests between the healthy and PD group.We set the significance threshold to p< 0.05 and applied a false discovery rate forcorrection for multiple comparisons in each feature separately. The density basedthreshold was chosen so that the comparison between groups would be based onthe same number of links in a given network.85Chapter 4. Linking White Ma‚er Integrity to Functional Connectivity4.3.2.5 Disease ClassificationWe then tested the discriminative power of the investigated functional features. Weperformed a linear discriminant analysis (LDA) with all five features as the inputat each sparsity level and selected the sparsity level at which the differentiation ofPD and HC had maximum accuracy. All further analysis is based on the functionalfeatures at this level of sparsity. We used a 10-fold cross validation (CV) schemewhere we divided our cohorts into stratified groups such that each fold has roughlythe same proportion of PD and HC subjects. We then trained our model on 9/10 ofour data and applied the trained classifier to the test set. We repeated the 10-foldCV 20 times and assessed the overall classification performance on the averagedaccuracy, specificity, and sensitivity.4.3.2.6 Estimating Modularity with WM IntegritySince changes in functional modularity are commonly reported in PD (Baggio et al.,2014, 2015; Ma et al., 2017), we focused on estimating this parameter with features ofWMI. To this end, we used the Least Absolute Shrinkage and Selection Operator(LASSO) with WM features as predictors and modularity as the outcome variable.We employed a 10-fold CV to find the most robust selection of features as well as apermutation (N = 500) test to assess the significance of the LASSO model. For this,we permuted the rows of our predictor matrix X such that the original relation tothe outcome variable in Y is no longer present and repeated the LASSO analysis.Significance was then assessed by the ratio of how many times the explainedvariance was greater using the permuted data than the original data to the numberof permutations. Further, we used a bootstrapping with replacement approach(N = 500) to examine the robustness of the selected features by calculating thestandard errors of the mean for each feature across all bootstrapping runs.We further tested the robustness of selected WM features by employing anelastic net regression, again with permutation and bootstrapping tests, and foundonly minor changes in the selection of features over a range of elastic net thresholds.86Chapter 4. Linking White Ma‚er Integrity to Functional Connectivity4.3.2.7 Associating Imaging Features to Clinical IndicesWe used a multivariate correlation approach to associate the selected WM andfunctional features with clinical indices of PD. PLS correlation was used to relatethe combined WM feature, obtained from LASSO, and the six functional features toclinical scores. The PLS significance was assessed with a permutation test (N = 500)and the robustness of its weights was based on bootstrapping with replacement(N = 500).4.3.3 ResultsWe found widespread alterations in the investigated functional network features,that persisted over large density levels, see Figure 4.3. PD subjects demonstrated,for the most part, a lower Fiedler Value although this was not statistically signifi-cant. Higher GT measures were observed in the PD cohort, except for global effi-ciency, indicating a more modular topological network organisation that possessesmore individual links in small communities, hence higher values in clusteringcoefficient and betweenness centrality.The LDA revealed a reasonable separation of PD from HC with only fivefunctional features with an average accuracy of 72.7±4.4%, specificity of 69.3±6.3%, and sensitivity of 75.4±3.9%. The sparsity level at maximum discriminationis shown in Figure 4.3 as a vertical grey line. We note that similar levels of accuracy,specificity, and sensitivity were obtained with a support vector machine (SVM)classification.The LASSO regression yielded a significant model explaining 74% of the vari-ance p-value of 0.020 and a mean squared error (MSE) of 0.002, see Figure 4.4. Theselected WM regions and their corresponding bootstrap standard errors can beseen in Figure 4.5.We obtained one significant PLS component as shown in Figure 4.6. The cor-relation between the latent variables of imaging and clinical features can be seenin Figure 4.6 left. The latent variables explain 64% of the variance with a p-valueof 0.0299. The correlation between the imaging and clinical scores is r = 0.58 with87Chapter 4. Linking White Ma‚er Integrity to Functional ConnectivityFigure 4.3: Differences in global network features over different density lev-els between PD and HC. Stars signify significant differences betweengroups at significance level of 0.05. Shaded areas signify standard errorsof the mean. N (PD) = 29, N (HC) = 15.p= 0.00048. The weights of the imaging and clinical features can be seen in Fig-ure 4.6 middle and right, respectively. A PLS analysis with either only WM orfunctional GT features revealed a shared covariance of 62% with p= 0.0343 and anon-significant model, respectively.88Chapter 4. Linking White Ma‚er Integrity to Functional ConnectivityFigure 4.4: True and estimated functional modularity by the LASSO regressionwith MWF in WM as predictors. The model explains 74% of the variancewith a p-value of 0.020 based on permutation tests. N = 29.Figure 4.5: Weights of the selected WM regions by LASSO. Errorbars representstandard errors across all bootstrapping runs.4.3.4 DiscussionOur results suggest that previously reported changes in functional topologicalproperties in PD are at least in part, driven by the WM microstructure and that acombination of these features is associated with clinical indices.89Chapter 4. Linking White Ma‚er Integrity to Functional ConnectivityFigure 4.6: PLS correlation between LASSO selected WM regions and func-tional modularity with clinical indices. The latent component explains58% of the covariance between imaging and clinical features which issignificance with a permutation p-value of 0.0299. Top left: The correla-tion between the imaging and clinical scores is r= 0.58 with p= 0.00048.PLS weights with boostrapped standard errors of the imaging featuresin bottom and clinical features in top right. N = 29.4.3.4.1 Altered Functional Topology in PDWe have shown robust alterations in global functional network features often ob-served in PD. Specifically, altered modularity of the whole brain network has beenconsistently reported in PD (Ghahremani et al., 2018; Go¨‚lich et al., 2013). A modular90Chapter 4. Linking White Ma‚er Integrity to Functional Connectivityorganisation of brain areas into specialised communities with comparably fewconnections between them, has been shown to be the preferred network model inthe brain that strikes a balance between efficiency and energy demand (Basse‚ andSporns, 2017; Bullmore and Sporns, 2012). This is particularly important given the hy-pothesis that higher order cognitive functions arise due to information integrationfrom distributed networks or communities (McIntosh, 2000). In healthy subjects,variability in modularity is linked to individual working memory capacity (Stevenset al., 2012). Following this, an abnormal modularity may thus have aberrant effectson ones cognitive performance. This is supported by studies investigating func-tional modularity in PD that report not only alterations in modularity in PD butalso that the changed modularity is linked to cognitive decline. Specifically, theydemonstrated a link between cognitive performance such as memory and visu-ospatial functions (Baggio et al., 2014), as well as attention and executive functions(Lin et al., 2018), two common cognitive impairments in PD.4.3.4.2 WM Integrity Can Estimate Functional Modularity in PDWe have also demonstrated that white matter microstructure is linked to the alter-ations of functional topology in PD brain networks. A recent study suggested thatchanges in WM can precede or potentially drive changes in the grey matter (Rektoret al., 2018). Our results suggest the WM regions driving the changes in functionalmodularity are mostly long range connections, which have been previously impli-cated to be involved in functional segregation (Baggio et al., 2014). The cingulumand cingulum hippocampus, both WM areas with large weights in the LASSOregression, connect to the posterior cingulate and precuneus. These regions havebeen considered to be structural hubs and are highly connected to other regions,forming a part of the structural core for functional connectivity (Bullmore and Sporns,2009). This suggests a direct link between WM regions connecting structural greymatter hubs, being highly impactful in estimating functional segregation. Thisis reinforced by the fact that the cingulum ROIs are also highly involved in themultivariate correlation with clinical indices and cognition, which have been linkedto altered functional modularity (Baggio et al., 2014; Lin et al., 2018).91Chapter 4. Linking White Ma‚er Integrity to Functional ConnectivityOther WM regions driving the modularity are regions connecting or runningthrough structures in the basal ganglia, namely the anterior and posterior limb ofthe internal capsule, posterior and superior corona radiata, as well as the posteriorthalamic radiation. Previous studies have reported an atrophy pattern in basalganglia structures which is related to PD disease severity as well as to the striatumbinding ratio (a measure of dopamine density) (Zeighami et al., 2015). Therefore, weconclude that the WM regions connecting these regions are implicated in changesin functional modularity, possibly suggesting a direct relation between structuraland functional networks.The regions of the superior longitudinal fasciculus and uncinate fasciculuswere also selected by the LASSO regression, and are regions previously associatedwith depression in PD (Wu et al., 2018). It has been demonstrated that the superiorlongitudinal fasciculus exhibits modulated WM microstructre in PD (Ga‚ellaroet al., 2009).Lastly, the genu and body of corpus callosum, which have been shown asregions important for estimating functional modularity in this study, are keyregions for facilitating interhemispheric connections. Furthermore, microstructuraldamage in these areas has been reported to correlate with disease severity in PD(Galantucci et al., 2014). Callosal atrophy has also been shown to correlate withcognitive performance in PD and suggested to contribute to the development todementia in PD (Goldman et al., 2017).4.3.4.3 A Combination of WM and Functional Modularity is Linked to ClinicalFeatures of PDThe association of imaging features with clinical indices revealed that the WMregions with largest weights are again areas that connect the two hemispheres andlong range connections connecting anterior and posterior parts of the brain. Func-tional modularity was also amongst the features that showed a large weighting,suggesting that both structural and functional features weight heavily on the latentvariable (LV) that links the imaging data to clinical indices. Several studies haveimplicated the cingulum bundle to have altered WMI in PD when compared to HC92Chapter 4. Linking White Ma‚er Integrity to Functional Connectivityand that these alterations get more severe with as the disease progresses (Guimara˜eset al., 2018; Kamagata et al., 2012). With UPDRS and MoCA showing the largestweights in the clinical set, we conclude that overall disease severity, as capturedby UPDRS, and cognitive performance were the main clinical features that wererelated to the combination of functional and structural MRI features. This is in linewith current literature that overall disease severity and cognitive performance aremost often reported to be associated with MRI biomarkers. However, it should benoted that this may also be due to the lack of studies examining the non-motoraspects of depression and apathy in PD.This investigation is not without its limitations. For one, it does not considerthe temporal dynamics in the rs-fMRI timeseries, that has been gained increasedrecognition recently. Studies have shown alterations in GT features measured atdifferent time intervals in PD and have shown that a combination of static anddynamic features yields the best classification results (Cai et al., 2018). Additionally,including a PD cohort with a wider range and more severe degree of non-motorsymptoms should may be able to differentiate which imaging features are predom-inantly related to certain PD symptoms. Finally, a sparse PLS may be useful tonarrow down the most impactful imaging features.4.3.5 ConclusionHere we investigated if WMI, and specifically myelin content, can predict changesin functional segregation, as assessed with modularity. Further, we investigatedif altered functional topology and white matter integrity can jointly predict PDdisease progression.Our results suggest an intimate relation between WMI and functional networktopology and further, our results indicate that previously reported changes infunctional topological properties in PD are at least partly driven by changes inmyelin microstructure. Moreover, a combination of functional and structuralfeatures can achieve a better relation to PD related symptoms than either modalityalone.93Chapter 4. Linking White Ma‚er Integrity to Functional Connectivity4.4 Data Driven Approach: Novel White Ma‚erIntegrity Similarity Networks can be Associatedwith Parkinson’s Disease Symptoms andFunctional Connectivity4.4.1 IntroductionInvestigations into anatomical networks are based around the fact that anatomicalconnections between cortical and sub-cortical GM areas are shaping their functionalcoactivation. Indeed, it has been shown that underlying anatomical connectionsconstrain the functional organisation of the brain to a large degree (Abdelnour et al.,2014; Deco et al., 2013; Misˇic´ et al., 2016; Shen et al., 2015). Studies have reported amuch more robust FC between remote cortical areas that also shared an anatomicalconnection, whereas the FC between areas without a direct physical connectionwas much more fluid and less reliable (Damoiseaux and Greicius, 2009; Messe´ et al.,2014). Currently a standard approach to construct anatomical networks is withdiffusion imaging and some variation of fibre tracking. In this way, the anatomicalconnections between distant GM areas are defined by some metric of the diffusionor tracking process such as number of streamlines counted between two areas,average FA of the fibre tract, or average length of tracts.While this method has led to some success in the past and has demonstrated theexistence of a WM scaffold connecting various GM areas (Irimia and Van Horn, 2014),it implicitly assumes that the underlying WM is only the facilitator connectingcortical and sub-cortical areas. In fact, a reduction of the anatomical connectionsbetween brain areas down to a single number, such as number of streamlinesor average FA, may be an oversimplification of the complex underlying WMI.This is supported by studies reporting changes in many aspects of the WMI, suchas changes in FA, MD, aD, rD, MWF, among others during disease processes(Baumeister et al., 2018; Heath et al., 2018; Tae et al., 2018). In addition, it is widelyacknowledged that the fibre tracking produces many false positive connections94Chapter 4. Linking White Ma‚er Integrity to Functional Connectivity(Maier-Hein et al., 2017), and underestimates long range connections which mightadversely contribute to conclusions about the network topology. Moreover, over-coming issues of crossing and touching fibres for more accurate reconstruction offibre tracts continues to be an active area of research (Chowdhury et al., 2014). Lastly,applying tractography in diseases with severe WM damage such as MS oftentimesleads to very sparse anatomical connections due to failure of tracking through focallesions (Horbruegger et al., 2019; Shu et al., 2016), although methods to mitigate theseeffects have been developed (Horbruegger et al., 2019; Stamile et al., 2016).An alternative approach, morphometric similarity network (MSN) has recentlybeen proposed for examining joint variations in GM (Seidlitz et al., 2018) as analternative to the typical fibre tract networks or structural covariance network(SCN). The underlying idea of MSN is to utilise several micro- and macrostructuralindices to assess inter regional variations of GM areas. MSN could replicate knowncortical cytoarchitectonic modules as well as demonstrated an association withcognitive variations (Seidlitz et al., 2018). It should be noted that while MSNs showpromising results for examining cortical networks, it ignores the often reportedchanges in WMI in diseases as they only assess GM characteristics.Given the manifold changes in the WMI integrity in many neurological dis-eases, we propose a novel method that puts the focus on the WMI itself ratherthan using it as a vehicle to construct a network of connected WMI regions. Thismethod takes advantage of the complementary information of multiple imagingmodalities assessing the WMI as well as utilises the network concept by examin-ing joint variations of WMI across different regions and we call it white matterintegrity similarity network (WISN). We demonstrate the usefulness of WISNs bycomparing topological features between a healthy cohort and subjects with PD.Additionally, we relate WISN features to PD related clinical indices as report a linkof WISN features with FC.95Chapter 4. Linking White Ma‚er Integrity to Functional Connectivity4.4.2 Construction of White Ma‚er Integrity SimilarityNetworksThe underlying assumption of WISN is that a pathological process causes widespreadalterations across the WM. Even in cases of focal damage, widespread implicationsto other, distant WM areas are very likely. This is supported by the concept thatthe brain is organised as a complex network where disease related alterationspropagate through local and global networks (Fornito et al., 2015). With WISN wemake use of the different but complementary information about WMI offered byvarious MRI modalities. In this way, the goal is to capture many different aspectsof the WMI in an effort to obtain more information than a single modality couldoffer.An advantage of WISN over SCN is that here we obtain individual WISN persubject, whereas in SCN one typically obtains one network per group, which doesnot allow linking individual features such as clinical characteristics to features ofthe SCN. Moreover, the construction of SCNs usually depends on a large cohortand only considers a single MRI feature such as cortical thickness. Althoughmethods to obtain individual SCN exist (Kong et al., 2015; Tijms et al., 2012), theneurobiological interpretation of SCNs remains problematic (Seidlitz et al., 2018).Figure 4.7 illustrates the generation of an individual WISN. First, we use a totalof 36 WM ROIs from the JHU label atlas (originally containing 48 ROIs but dueto limited coverage in MWI, we reduced the number to ROIs that were found inboth MWI and DTI coverage) and co-register them to each subjects MWI and DTIdata. We then extract the spatial heterogeneity in each ROI by means of extractinghigher order moments that are invariant to spatial orientation and organise themin a WMI feature matrix. Each WMI feature vector per ROIs is then normalisedto sample mean and standard deviation. The Pearson correlation coefficient isthen computed for each pair of ROIs quantifying the similarity of WMI betweenareas and organised in a similarity matrix, not unlike a FC matrix. This matrix isgenerated for every subject.96Chapter 4. Linking White Ma‚er Integrity to Functional ConnectivityFigure 4.7: Process of generating WISN.97Chapter 4. Linking White Ma‚er Integrity to Functional Connectivity4.4.3 Materials & Methods4.4.3.1 MaterialsThis analysis used the same cohort as in chapter 2. The MWI and DTI data wereanalysed the same as well with the exception that in this instance, the DTI param-eter maps for MD, aD, and rD were also computed. Furthermore, we used theJHU label atlas with a total of 36 WM ROIs and registered the each label file to thenative MWI and DTI space using ANTs (Avants et al., 2008). As measures of WMIwe employed invariant 3D moment descriptors (Ng et al., 2009), and specificallywe used the spatial variance as a descriptor of WMI heterogeneity in each ROI.Subject individual WISNs were then computed according to subsections 4.4.2.4.4.3.2 WISN AnalysisWe computed GT measures mentioned in paragraph 4.2.2 and the Fiedler Value ofthresholded and binarised WISNs. Due to the fact that GT measures are influencedby the number of links in a graph, we applied a proportional threshold such thatonly the links with the highest correlation were retained. We used a range ofdensity based thresholds were we retained 1 - 35% in 1% increments of the totalamount of links. Typically, the optimal density threshold is unknown and for thisreason we compared the GT measures and Fiedler Value at each density thresholdwith two-sample t-tests between the healthy and PD group.4.4.3.3 Classification Based on WISN FeaturesIn order to find the optimal density threshold for further analysis we used thefive GT features and the Fiedler Value as inputs for a classification experiment.We utilised LDA and SVM in a 10-fold cross validation scheme, at each densitythreshold. The cross validation was repeated 50 times per threshold and theaverage accuracy, specificity, and sensitivity were calculated. In any subsequentanalysis we used the GT features at the density threshold where the classificationyielded maximum accuracy.98Chapter 4. Linking White Ma‚er Integrity to Functional Connectivity4.4.3.4 Linking WISN Features to Clinical CharacteristicsTo assess if GT features of WISNs have biological meaning, we used a multivariatecorrelation analysis to examine a potential link between WISN features and clinicalcharacteristics of PD. For this, we used CCA with feature set Xi× j comprisedof the GT features and Fiedler Value at the density threshold that maximallydifferentiated between groups with i as the number of PD subjects and j as thenumber of GT features and Fiedler Value. Feature set Y i×k consists of PD relatedclinical indices with k as the number of clinical indices such as UPDRS, MoCA,H & Y, BDI, LARS, and age. We used a permutation test (N = 1000) to assess theoverall significance of the CCA and a bootstrapping with replacement (N = 1000)to obtain 95% confidence intervals for the feature loadings.4.4.3.5 Linking WISN Features to Functional ConnectivityTo further validate the utility of WISNs, we investigated if their GT features can belinked to FC, essentially linking network characteristics from a purely WM networkto functionally linked GM regions. FC was extracted from the AAL atlas with 90cortical and sub-cortical regions. The lower triangle of the symmetric FC matrixwas vectorised per subject to a 1× l with l = (n ·n−n)/2 with n = 90, FC featurevector. The total feature matrix Xm×l with m as the total number of subjects. Thematrix containing the WISN features Ym× j with j as the number of WISN features.Together they were used in a PLS correlation analysis to find a multivariate relationbetween these two feature sets. In this analysis we seek to find weighted linearcombination of of the features in X and Y that maximally covary with each other.The respective linear combinations can be viewed as FC patterns that are associatedwith WISN features.Partial Least Squares Correlation The underlying methodology of PLS correlationanalysis is SVD. Let X and Y be two matrices of z-scored multivariate feature99Chapter 4. Linking White Ma‚er Integrity to Functional Connectivityvectors, the PLS employs SVD on the covariance matrix such that:X′Y =U∆V ′ (4.11)with U′U = V ′V = 1. The matrices U and V are matrices of left and right singularvectors and ∆ is a diagonal matrix with singular values. The decompositionproduces orthogonal LVs consisting of pairs of singular values and left and rightsingular vectors. The maximum number of LVs to be extracted is equal to theminimum rank of the covariance matrix. The singular vectors can be interpretedas weights on the original features in their respective matrix, which indicate therelative contribution of each feature to the linear combination. The associatedsingular value is proportional to the covariance captured by the LVs.Subject specific contributions, called scores, to the LVs were calculated byprojecting the weight patterns in U and V onto the original feature space with:FC score = XU (4.12)WISN score = YV (4.13)We used a permutation test (N = 1000) to assess the significance of the PLScorrelation and performed bootstrapping (N = 1000) to assess the stability of featureweights. In both, the permutation and bootstrapping performance, we utilisedthe Procrustes transformation to correct for axis rotations (Gower and Dijksterhuis,2004) due to the newly ordered or resampled data. The stability of features wasexamined with bootstrapping ratios which are defined as the ratio of the singularvector weight from the original and unpermuted data to its bootstrap estimatedstandard error. A large bootstrap ratio thus indicates a feature that has a largecontribution to its latent variable and is stable across participants (indicated by alow standard error).100Chapter 4. Linking White Ma‚er Integrity to Functional Connectivity4.4.4 ResultsThe Fiedler Value and GT features for all investigated density thresholds are shownin Figure 4.8. The PD group demonstrates a generally lower Fiedler Value andglobal efficiency while other GT features are generally higher. The nodal measuresof clustering coefficient and betweenness centrality are shown as averages over allnodes.The LDA revealed a maximum average accuracy of 73.6±6%, a specificity of73.1±9%, and a sensitivity of 73.9±5% at a density threshold of 28%. Figure 4.9displays the investigated WISN features at this threshold.The CCA revealed one significant component that linked GT features and theFiedler Value of WISNs to PD relevant clinical characteristics. The correlationbetween the canonical variates was r = 0.84 with p = 0.0345 and a permutationp-value of 0.0422. The Fiedler Value and the clustering coefficient demonstrateda positive loading, while all other GT had a negative loading onto the canonicalvariate. For the clinical features, BDI displayed a positive loading, while UPDRS,LARS, and age had a negative loading. Figure 4.10 displays the canonical variatestogether with their respective loadings from the CCA analysis.The PLS revealed one significant component which explains 76% of the covari-ance between FC and WISN features with p= 0.020, see Figure 4.11.The results from linking FC to GT features of WISN are displayed in Figure 4.12.The correlation of the LVs is shown on the left with a correlation of r = 0.56, p=00003. The plot in the middle and right show the bootstrap ratios of the FC andWISN features, respectively. Figure 4.13 display the top absolute bootstrap ratioson FC connections in a 3D brain.4.4.5 DiscussionWe demonstrated a novel method to investigate joint changes across different WMROIs based on multiple aspects of their individual WMI. The proposed methodof WISN makes use of the complementary nature of different imaging modalitiesto interrogate and relate patterns of common changes of remote brain areas. The101Chapter 4. Linking White Ma‚er Integrity to Functional ConnectivityFigure 4.8: Fiedler Value and GT features plotted over different density thresh-olds of WISNs. Shown are averages with their respective standard errorsfor each group. Stars indicate significant differences with p < 0.05. N(PD) = 29, N (HC) = 15.technique assumes, based on the concepts of brain networks (Basse‚ and Bullmore,2009; van den Heuvel and Hulsho€ Pol, 2010) and pathological processes spreadingthrough connected regions (Fornito et al., 2015), that changes in the WMI do notappear isolated but have large scale effects on multiple areas. We have shown that102Chapter 4. Linking White Ma‚er Integrity to Functional ConnectivityFigure 4.9: WISN network features at density threshold that maximally dif-ferentiates groups. Stars indicate significant differences at p < 0.05.Errorbars are standard errors of the mean. N (PD) = 29, N (HC) = 15.the different aspects of WMI can also be characterised as a network and normaland abnormal topological organisations can be quantified with GT. We verify theusefulness of WISNs by linking them to PD typical clinical symptoms as well aslinking them to the FC of GM regions drawing a basic link between structure andfunction in the human brain.103Chapter 4. Linking White Ma‚er Integrity to Functional ConnectivityFigure 4.10: Results from CCA between WISN features and clinical indices.left shows the correlation of the canonical variates, middle showsthe canonical loadings of the imaging features, and right displays theloadings of the clinical characteristics onto the canonical variate. N = 29.Figure 4.11: Explained covariance per LV and associated p-value from permu-tation tests from the PLS analysis. The horizontal grey line signifies the0.05 significance threshold.The analysis of global and local GT features revealed widespread differencesbetween PD and healthy controls over many network densities. The PD subjectsgenerally displayed a lower Fiedler Value, indicating a less robust network that ismore easily disturbed. Further, the PD group displayed higher values in examinedGT features, including higher characteristic pathlength, higher modularity, higherclustering coefficient, and higher betweenness centrality. The global efficiencywas decreased in the PD cohort. The measures of characteristic pathlength, globalefficiency, and modularity indicate a global reorganisation of the WISN where104Chapter 4. Linking White Ma‚er Integrity to Functional ConnectivityFigure 4.12: PLS correlation analysis results. left shows the correlation ofthe first component explaining 76 % of the covariance with p< 0.001.middle shows the bootstrap ratios of each FC, and right shows thebootstrap ratios of the WISN features. N (PD) = 29, N (HC) = 15.individual WM regions are more densely connected forming smaller communitiesin PD as compared to healthy controls. The nodal measures of clustering coefficientand betweenness centrality indicate that some ROIs are more prominent in the PDnetwork than in the healthy cohort, suggesting that the heterogeneity of WMI ofsome regions has a widespread impact on other regions.The classification of PD based on WISN GT features revealed a moderate accu-racy with only six features at a density threshold where each individual featureshows a significant difference. Similar levels of accuracy, specificity, and sensitivitywere obtained when utilising SVM with linear or radial kernels. Other studiesattempting to classify PD and healthy subjects based on WMI integrity are scarce.There are reports on good accuracy with area under the curve (AUC) of 0.75-0.85based on DTI anatomical connectivity analysis (Galantucci et al., 2017). This paucitymay be due to the fact that mixed results of increased and decreased values ofWMI have been reported in the past (Ha‚ori et al., 2012; Li et al., 2018). Classificationstudies using DTI in GM and sub-cortical areas demonstrated accuracies of 83.3%(Lei et al., 2017) and 77.2% (Salamanca et al., 2015), respectively.The CCA revealed one significant component associating the six WISN featuresto a set of clinical characteristics. The loadings indicate an opposing contribution of105Chapter 4. Linking White Ma‚er Integrity to Functional ConnectivityFigure 4.13: Absolute bootstrap ratios of FC in the PLS analysis with WISNfeatures. Shown are the top 15 % of positive bootstrap ratios, includ-ing long range frontal to temporal connections as well as occipital toparietal areas.the Fiedler Value and measures of disease severity as displayed by the contrastingsigns of the respective loadings, suggesting a less robust network as the diseaseprogresses. On the other hand, the majority of GT measures exhibit positive load-ings, as do the clinical measures of disease progression, indicating higher levels ofGT features with a more severe disease. Among the features with highest loadingswere the characteristic pathlength, and clustering coefficient in the imaging setand total UPDRS, MoCA, and H & Y in the clinical set hinting at a close relationbetween these global and local WISN features and clinical characteristics.The PLS analysis integrated both functional and structural features in whichthe FC of sub-cortical and cortical regions was linked to topological features of106Chapter 4. Linking White Ma‚er Integrity to Functional ConnectivityWISNs. The result yielded one significant component explaining the majorityof shared variance between the two sets. The bootstrap ratios indicated that theFiedler Value, as a measure of robustness of the WISN, is mostly associated withlong range functional connections including frontal to temporal regions. Thesefunctional connections have previously been implicated to be altered in PD and alsorelated to cognitive performance (Dı´ez-Cirarda et al., 2017). Another study reportedimpaired long range connections from frontal to parietal and temporal areas insubjects PD with mild cognitive impairment (Baggio et al., 2014). Furthermore,decreased FC in medial temporal and inferior parietal lobes, as part of the defaultmode network (DMN), were found in cognitively unimpaired PD subjects (Tessitoreet al., 2012).Additionally, there is considerable overlap between the FC of GM regionshighlighted in the PLS analysis and brain areas of the DMN, including frontalareas such as the anterior cingulum, temporal areas such as middle and superiortemporal gyrus, as well as parahippocampal gyri and the cuneus. The DMN is anetwork typically more active when the brain is in a wakeful state of rest and itsactivity is reduced when the brain performing tasks or subject to external stimuli(Raichle, 2015). The DMN and changes therein have been implicated in PD in priorstudies (van Eimeren et al., 2009) that are accentuated in PD subjects suffering fromcognitive impairment Hou et al. (2016). Most notably, a reduced FC in the DMNwas found to be correlated with reduced WMI indexed by FA in a cohort of PDsubjects (Lucas-Jime´nez et al., 2016). Our results are somewhat in line with thecurrent literature as we implicitly find altered FC pertaining to the DMN beinglinked to modulated WMI in PD.An advantage of this methodology lies in its focus on the covariation of distinctWM ROIs directly and treating the WM as a network. Techniques utilising DTItractography to construct a network of WM connections rely on the performanceof the fibre tracking, which in cases of severe WM damage breaks down, leadingto very sparse networks and ultimately to limited power in the network analysis ifonly a fraction of connections are being examined. The WISN on the other handcan be constructed based on any segmentation of WM ROIs covering the whole107Chapter 4. Linking White Ma‚er Integrity to Functional ConnectivityWM. In addition, the effect of lesions on WISNs can be assessed by comparing theGT features with and without lesion tissue.A limitation in this study is that only static FC was considered, despite therebeing evidence of the brain being a complex dynamical system in which thetemporal variability of FC may provide additional insights of functional brainnetworks. Studies investigating the temporal dynamics of FC have shown newand complementary information to the static analysis, and that a combination ofboth can characterise PD to a greater extend than either of them (Cai et al., 2018).Furthermore, we acknowledge that a the assessment of similarity between WMROIs based on correlations with five individual features may lack robustness tosome degree. However, the study employing MSNs found good reliability whenutilising ten or five features to construct the network (Seidlitz et al., 2018). Anotherstudy utilised seven features for the construction of MSNs (Morgan et al., 2019). Thisgives us some confidence of robustness of the generated WISNs.In summary, we have demonstrated a novel method to investigate the WMIfrom a network perspective which takes advantage of multiple imaging modalities.By investigating joint changes of different measures of the WMI among WM ROIsone is able to use the complementary information, which individually may not besensitive enough to characterise robust changes. In addition, treating the WM as anetwork in which changes may propagate not only to regions in close proximitybut also to distal areas, and characterising the topological features of the WISNallows the study of the WM beyond simple analysis of individual ROIs. Morework is required to validate the utility of WISNs including a larger subject cohortand more measures of WMI such as MTR or SWI based measures.108Chapter 5AMultivariateApproach forDenoisingof T2RelaxationDecayCurves inMyelinWater Fraction ImagingIn this chapter we propose a novel method to denoise T2 decay curves in an effortto improve the calculation of MWF maps. Due to the noise sensitivity of the NNLSto produce MWF maps, some form of regularisation is necessary to produce robustand meaningful maps. Previous methods have focused on either temporal orspatial regularisation and here we propose a spatiotemporal filtering process. Wemake use of the similarity of decay curves of local and non-local voxels, decomposethem to find common noise patterns, and then utilise these patterns to find themost robust common decay curve among these voxels. We show that our methodis comparable with state-of-the-art spatial smoothing operations, while resultingin a more complete MWF map in regions of high noise. It should be noted that theproposed method can be seen as a preprocessing step which enables the applicationof some of the spatial regularisation techniques on top to potentially produce evenmore robust MWF maps.This work provides a novel technique for denoising T2 relaxation decay curvesthat, when applied to MWI has beneficial effects in calculating more robust MWFvalues. The proposed method is magnetic resonance (MR) vendor independent109Chapter 5. Spatiotemporal Filtering of T2 Decay Curveswhich makes it applicable to a wide variety of T2 relaxation studies.5.1 IntroductionThe fatty myelin bilayers surrounding the majority of axons in the central nervoussystem are indispensable for efficient signal transmission as they enable saltatoryconduction that greatly increases the propagation velocity of action potentialsalong nerve fibres. Because speed of signal transmission and synchronous activitybetween spatially distinct loci are critical for complex motor and cognitive func-tions, myelin pathology can have a significant impact on brain function (Fields,2008). While prior emphasis on myelin imaging has been on predominately whitematter diseases such as MS, white matter pathology can also be associated with awide range of neurodegenerative diseases (Laule et al., 2007). Thus, obtaining anaccurate and robust measure of the myelin content is important for studying andcharacterising the brain in disease states.Myelin water imaging is a quantitative MRI technique that can be used tocalculate the MWF, a surrogate measure validated by myelin content assessed atautopsy (Laule et al., 2006). MWF exploits the fact that the measured signal in a multi-echo T2 relaxation study is a composite signal from various water compartments. Inthe WM, there are two main water compartments, one within the myelin bilayers,and one with intra- and extracellular water. The MWF is then defined as the ratio ofmyelin water to the total amount of water. A prominent method to extract the MWFis by producing a T2 distribution used to fit the measured T2 decay curve with aNNLS algorithm (Prasloski et al., 2012b). However, such an approach is ill-posed andlacks robustness in the presence of noise (Graham et al., 1996), a frequent occurrencein T2 relaxation data, making some form of regularisation necessary (MacKay et al.,2006). This leads to instability of the NNLS algorithm causing spatially noisy mapsand ultimately leads to limited reproducibility.A number of methods to improve the MWF calculations have been proposed,such as implicit temporal filtering by applying spatial filters at each time point(Hwang et al., 2011; Jones et al., 2003), averaging the decay curves of adjacent voxels110Chapter 5. Spatiotemporal Filtering of T2 Decay Curves(Meyers et al., 2009), or spatial smoothing operators (Hwang et al., 2011; Kumar et al.,2015; Yoo and Tam, 2013). While these methods have shown an improvement incalculating robust MWF to varying degrees, the temporal filtering approaches onlyconsider a small neighbourhood and assign the same weight to each neighbouringvoxel. Spatial filtering methods do consider multiple voxels for their operation,but some of them still require calculations from the original (possibly inaccurate)NNLS method as the starting point for their subsequent calculation.In the proposed approach, we utilize joint temporal information from multiplevoxels in order to obtain a denoised T2 relaxation curve for each voxel, which thenserves as the basis for a subsequent regularised NNLS approach. The derivedMWF maps can then be subjected to a spatial regularisation approach, if desired.We propose to first select voxels based on similar decay curves and then use MEMDto find common intrinsic oscillations among voxels. These intrinsic modes are theninput into MCCA to determine the most robust T2 decay curves.The contributions of this work can be summarized as follows: 1), we haveintroduced a data driven framework that exploits the temporal characteristicsof similarly decaying voxels with MEMD, and 2), using the resulting temporaldecompositions in order to find the most common decay curve among the selectedlocal and non-local voxels utilizing MCCA. In this way we were able to generatenew, spatiotemporally smoothed decay curves which can then be subjected to anNNLS algorithm in order to produce MWF maps.5.2 MethodsWe investigated 12 healthy subjects scanned on a Philips Achieva 3 T scanner withan 8-channel head coil. The multi-echo T2 relaxation sequence had the followingparameters: TE = 10ms, 32 total echoes, TR = 1200ms with a reconstructed voxelsize of 1 × 1 × 2.5mm.Our approach to denoise the T2 decay curves consists of three main steps, 1)finding voxels with similar decay curves, 2) decompose each voxel with MEMD,and 3) use MCCA to robustly find the most common temporal pattern among the111Chapter 5. Spatiotemporal Filtering of T2 Decay CurvesMEMD decompositions of all similar voxels.5.2.1 Selection of Voxels with Similar Decay CurvesDue to anisotropic voxel size, we performed our analysis on a slice-by-slice basisto limit possible partial volume effects across slices. For an image I, we extractthe decay curve s = {s(i) | i ∈ I} from an index voxel at location i and furtherextract the decay curves sk = {s(k) |k ∈ I} of all other voxels of the current slice.Next, the similarity between the index voxel and all other voxels is determined bycalculating the relative Manhattan distance with∑l=1:32 |(s(i)−s( j))| for j= 1,2, ..., I.A probabilistic WM mask was used to ensure that only voxels with a probability ofbeing a WM voxel≥ 0.5 were being selected. In order to select only the most similardecaying voxels, we used a heuristic adaptive process in which we selected voxelswith a Manhattan distance of ≤ 5% , starting at 0% and increasing in 0.5% stepsor so that at least 20 voxels are being chosen, whichever criterion is first fulfilled.These parameters were chosen as a reasonable balance between computational costand accuracy. It should be noted that this selection process can include local aswell as non-local voxels, purely based on the similarity of their decay behaviour tothe index voxel.5.2.2 Multivariate Empirical Mode DecompositionEMD is a fully data driven method which decomposes a nonlinear and non-stationary signal into a finite set of spectrally independent oscillatory componentstermed intrinsic mode functions (IMFs) and a residual (Huang et al., 1998). EachIMF represents a specific oscillatory mode such that for a given signal x we getx(k) =N∑i=1ci(k)+ r(k) , (5.1)where N is the number of IMFs, ci are the IMF time series, r is the residual and k isnumber of time points. The IMFs satisfy the following conditions 1) the numberof extrema and zero crossings differs at most by one, and 2) have symmetric112Chapter 5. Spatiotemporal Filtering of T2 Decay Curvesupper and lower envelopes. The extraction of the IMF take place with an iterativealgorithm called the sifting process Huang et al. (1998), which is described inAlgorithm 1. Upon finding the first IMF, the sifting process is repeated on theAlgorithm 1 EMD sifting process1: find extrema in x(k)2: interpolate between all minima (and maxima) to get lower emin(k) (and upperemax(k)) envelopes3: compute local means m(k) =(emin+ emax)/24: subtract the mean from the signal to obtain ’oscillatory mode’ s(k) = x(k)−m(k)5: if s(k) is within stopping criteria define IMF as d(k) = s(k), otherwise set x(k) =s(k) and repeatresidual r(k) = x(k)−d(k) in order to obtain the remaining IMFs.Applying EMD to multivariate data usually yields suboptimal results due tomode mixing and mode misalignments (Looney and Mandic, 2009). To overcomethese shortcomings, MEMD has been proposed (Rehman and Mandic, 2010). Theinput multivariate signals are mapped into multiple real-valued projected signalsalong directions in m-dimensional spaces and the corresponding multivariate IMFsare found similarly as in Algorithm 1.In order to utilize MEMD we calculate a weighted average decay savg fromthe currently selected index voxel i and the selected similar voxels as describedabove. The weights are corresponding to the inverse distance of each voxel. Wethen subtract all currently selected decay curves from the weighted average togenerate a set of residuals. These residuals are then decomposed with MEMD inorder to separate high and low frequency modes within them leading to a set ofIMFs per voxel. The set of IMFs per voxel is then added back to savg in order tocreate different decay curves, each with its own specific fast or slow oscillatingnoise contribution. These decay curves are then assessed with MCCA in order tofind the most robust decaying pattern among these voxels.113Chapter 5. Spatiotemporal Filtering of T2 Decay Curves5.2.3 Multiset Canonical Correlation AnalysisCCA is a statistical method that finds a linear transformation between two randomvectors so that they are maximally correlated (Hotelling, 1936). Given two randomvectors x1 and x2, CCA seeks two transformation vectors, a and b, such that thecorrelation between variables y1 = aT x1 and y2 = bT x2 is maximized (Hotelling, 1936).The variables yi with i = 1,2 are called canonical variates and represent the firstpair of correlated data between x1 and x2. Further pairs of canonical variates can beextracted with new sets of transformation vectors such that they have maximumcorrelation among them but are uncorrelated to the previous canonical variates.A maximum of min rank(x1,x2) pairs can be extracted. It is shown in (Anderson,1984) that all the transformation vectors of CCA can be obtained by solving aneigenvalue decomposition problem.MCCA extends the theory of CCA to include more than two data sets in orderto identify a correlation structure among canonical variates of multiple data sets bya series of linear transformations (Ke‚enring, 1971). Unlike CCA where correlationbetween two canonical variates is maximized, MCCA aims to optimise an objectivefunction of the correlation matrix of the canonical variates from multiple randomvectors such that the canonical variates achieve maximum overall correlation(Ke‚enring, 1971).Here, MCCA is used to find the most common decay pattern across all similarvoxels IMFs’, thus creating a new denoised decay curve summarising commontemporal patterns amongst spatially local and non-local voxels. Applying thisprocedure to every voxel will generate a new 4-dimensional image comprised ofdenoised decay signals which is ultimately subjected to a regularised NNLS inorder to produce a MWF map.5.3 ResultsHere we list the results of comparing the proposed method (MEMD-MCCA-rNNLS), the standard regularised NNLS (rNNLS) (Prasloski et al., 2012b), and aspatially regularised NNLS (nlsrNNLS) based on (Yoo and Tam, 2013). We compare114Chapter 5. Spatiotemporal Filtering of T2 Decay Curvesthe average MWF in the white matter, the CoV, and test-retest reliability betweenthe three methods, as well as measures of local smoothness (indexed by localentropy in a 7×7 voxel sliding window) and the structural similarity index (SSIM)to compare the MEMD-MCCA-rNNLS and nlsrNNLS to the rNNLS. Further wereport the number of “holes” in each method. The number of holes is defined asthe number of voxels pertaining to the WM with zero valued MWF. In this casethe probabilistic WM mask was thresholded at 0.9 to only include very highlyprobable WM voxels. This measure indicates how the calculation of MWF hasbeen particularly affected by noise such that the MWF is virtually negligible eventhough the voxel in question is part of the WM. All comparisons of numericalparameters were done with non-parametric rank sum tests.Figure 5.1 displays one slice of the three methods and it can be seen that theMEMD-MCCA-rNNLS (left) and nlsrNNLS (right) reduce spatial noise comparedto the rNNLS (mid) method, while the nlsrNNLS more strongly delineates thewhite matter / grey matter boundary. On the other hand, the MEMD-MCCA-rNNLS shows very little contributions in areas of clear noise, such as the ventriclesor areas of vasculature as well as exhibiting a similar spatial smoothness in theWM when compared to the nlsrNNLS.In order to assess if the MWF values were comparable between rNNLS andnlsrNNLS, and the spatiotemporal filtering did not introduce a systematic bias, wecompared the average MWF of the WM across the different methods (Fig. 5.2a).We further assessed the CoV in all subjects for each method (Fig. 5.2b). There wereno significant differences in the average MWF within all three methods indicatingthat neither the MEMD-MCCA-rNNLS nor the nlsrNNLS have a systematic biastowards over- or underestimating the MWF. The were significant differences inCoV between MEMD-MCCA-rNNLS and rNNLS (p< 0.005) as well as betweenthe nlsrNNLS and rNNLS (p< 0.001), with both smoothing methods presenting alower CoV when compared to the standard rNNLS.The percentage of MWF “holes” in WM voxels was significantly different be-tween MEMD-MCCA-rNNLS and rNNLS (p < 0.001), between nlsrNNLS andrNNLS (p < 0.001), as well as between MEMD-MCCA-rNNLS and nlsrNNLS115Chapter 5. Spatiotemporal Filtering of T2 Decay CurvesMEMD-MCCA-rNNLS rNNLS nlsrNNLS00.050.10.150.2Figure 5.1: MWF maps produced by the three methods for one representativesubject. left the proposed method demonstrating reduced spatial noisecompared to the rNNLS in middle. The nlsrNNLS in right shows re-duced spatial noise compared to rNNLS and comparable smoothness toMEMD-MCCA-rNNLS but shows clearer separation of white and greymatter.(a) Average MWF (b) Average CoVFigure 5.2: Comparison of average MWF in WM across all subjects in (a) andaverage CoV in WM in (b). Errorbars are standard deviations acrosssubjects. N = 12.(p < 0.045), (Fig. 5.3a). With the MEMD-MCCA-rNNLS method having theleast amount, suggesting a more complete MWF map of the WM voxels thanwith other methods. There were no significant differences in local entropy (Fig.5.3b), although a comparison between MEMD-MCCA-rNNLS and nlsrNNLS was116Chapter 5. Spatiotemporal Filtering of T2 Decay Curvestrending towards significance with lower values for the MEMD-MCCA-rNNLSwith p = 0.0514. No significant differences in the SSIM (Fig. 5.3c) could be de-tected between the MEMD-MCCA-rNNLS and nlsrNNLS. The MEMD-MCCA-rNNLS displayed a the lowest local standard deviations (although not significantlylower than the nlsrNNLS (p = 0.4119), but it had significantly less than rNNLS(p < 0.0001). The nlsrNNLS also had lower local standard deviations than therNNLS (p< 0.0001) (Fig. 5.3d).(a) Percentage of “holes” (b) Local entropy(c) SSIM (d) Local standard deviationFigure 5.3: Structural consistency of computed maps. a) Percentage of “holes”in WM voxels. Holes are defined as voxels with 0 MWF inside WM.b) Local entropy in a 7×7 voxel neighbourhood. c) SSIM of MEMD-MCCA-rNNLS and nlsrNNLS to the standard rNNLS. d) Local standarddeviation in a 7×7 voxel neighbourhood. N = 12.117Chapter 5. Spatiotemporal Filtering of T2 Decay CurvesFigure 5.4a depicts the average MWF in the test-retest reliability of three sepa-rate scans of one subject. There is no difference in average MWF over the separatescans between any of the maps. The MEMD-MCCA-rNNLS and nlsrNNLS mapsshow a lower CoV compared to the rNNLS maps in the test-retest reliability as-sessment (Fig. 5.4b), indicating a more robust MWF calculation. Due to the smallsample size here, no statistical tests were performed for the test-retest reliability.(a) Average MWF (b) CoVFigure 5.4: Test-retest reliability of the three methods. One subject wasscanned three times and the average WM MWF across the three scansis shown in (a). The CoV of MWF in the WM was assessed in all threescans and shown for all methods in (b). N = 1.5.4 ConclusionWe have presented a data-driven spatiotemporal filtering framework to producedenoised T2 relaxation decay curves to reliably estimate myelin content in vivo. Theproposed method leverages information from local and non-local WM voxels inorder to extract the most common T2 decay curve. By utilizing the decay of multipleWM voxels at once, we minimise the influence of noise corruption which is acommon concern in this analysis. Our approach performs favourably to a standardrNNLS in visual quality as well as indices of spatial smoothness (CoV, numberof holes, local entropy, SSIM, and local standard deviation) while performing as118Chapter 5. Spatiotemporal Filtering of T2 Decay Curveswell as a nlsrNNLS approach. Despite the local smoothness, there is no evidenceof a significantly decreased average MWF with our method compared to eitherrNNLS or nlsrNNLS. Of note, our approach produces the least number of holesin the WM, suggesting a more complete and more robust calculation of MWFmaps. Additionally, metrics of local entropy and standard deviation displayeda trend towards lower values in our approach, indicating a more homogeneousdistribution of MWF values in local neighbourhoods, which would reinforce theassumption of locally, slowly varying myelin across the brain. Our method iscomparable to the nlsrNNLS approach in a test-retest reliability test and performsbetter than the rNNLS.We note that, since the proposed method mainly operates in the temporaldomain and is essentially a preprocessing step, it can be combined with methodsrelying on spatial normalisation of rNNLS maps to further improve the calculationof in vivo myelin content. In addition, the proposed method is independent ofvendor and acquisition parameters and thus can potentially applied to a widevariety of T2 relaxation studies, including, for example, fusion with other imagingmodalities (Baumeister et al., 2019). Further work may include different approachesof selecting similarly-decaying voxels.119Chapter 6Inherent Spatial Structure inMyelinWa-ter Fraction MapsThis work aimed to establish the existence of a spatial pattern in noisy-appearingMWF maps. Due to the ill-conditioned calculation of MWF maps and its sensitivityto noise, MWF maps appear spatially noisy. Common analyses in MWI involvesaveraging the MWF over large areas, sometimes to deal with the spatial noisinessof the maps, and sometimes due to employing standard ROIs with fixed sizes,which may hinder the detection of subtle changes in myelin content. Here wecombined MWI with DTI in order to determine if the distribution of MWF acrossthe brain follows the underlying microstructure of the WM. This tractography-informed analysis provided evidence of a spatial pattern in MWF maps, andfurther illustrates a characteristic pattern of MWF values along major WM tracts.Moreover, we demonstrate the benefits of using these tract-specific MWF profilesby providing a framework for superior estimation of a subjects age as well asimproved differentiation between sex. This chapter outlines results that providea more detailed description of MWF maps and its analysis framework could beuseful to pinpoint subtle MWF changes in relation to disease progression.This work combines the Applications and Techniques domains of the thesis asthe proof of a spatial pattern can be used to broaden the utility of MWI by applyingit to diseases with suspected subtle changes of MWF and further provides analysis120Chapter 6. Inherent Spatial Structure in Myelin Water Fraction Mapstechniques that leverage the new details of MWF maps.6.1 IntroductionThe ability to assess myelin integrity with MRI in vivo holds great promise forcharacterising normal brain function as well as for identifying changes associatedwith disease or injury. The fatty myelin bilayers that make up myelin surroundingthe majority of axons in the central nervous system are indispensable for efficientsignal transmission, as they enable saltatory conduction that greatly increasesthe propagation velocity of action potentials along nerve fibres. A compromisedmyelin structure leads to detrimental brain function including impaired motorperformance, worsening cognitive abilities, and loss of vision (Fields, 2008). Theimportance of myelin is highlighted by the multitude of neurological and neu-rodegenerative diseases it has been implicated in such as MS (Laule et al., 2004;Vargas et al., 2014), schizophrenia (Lang et al., 2014), and even diseases previouslynot thought to involve myelin, such as PD (Baumeister et al., 2018). Although muchresearch has focused on assessing myelin at specific loci, such as lesions seenin multiple sclerosis (Vargas et al., 2014; Vavasour et al., 2007), often more diffusechanges in normal-appearing or diffusely affected tissue are of interest. In suchcases, myelin features are commonly assessed in large volumes of interest, suchas WM across the entire brain or whole fibre bundles (Laule et al., 2004). However,myelin changes during development (Deoni et al., 2012) ageing (Arshad et al., 2016;Billiet et al., 2015; Faizy et al., 2018), neurodegeneration (Laule et al., 2007), diseaseprocesses (Laule et al., 2007), and even sex differences (Liu et al., 2010) lead to spa-tial variability in myelin content, that may obscure findings if myelin content isintegrated over too large a volume.Myelin water imaging is a quantitative MRI technique that can be used tocalculate the MWF, a measure that has been validated as being directly correlatedwith myelin content (Laule et al., 2008, 2006). This technique uses a multi-echo T2relaxation sequence to sample a large range of echo times, enabling the decom-position of the measured decay curve into constituent T2 times. Myelin water is121Chapter 6. Inherent Spatial Structure in Myelin Water Fraction Mapsrepresented by short T2 times between 15 - 40ms. The MWF is then defined as thefraction of myelin water-related T2 amplitudes compared to the total water. AnNNLS algorithm is typically used to fit the multi-echo T2 decay curve with a set ofexponential basis functions (Prasloski et al., 2012b). However, such an approach ispotentially ill-posed due to the non-orthogonality of the different exponential basisfunctions and may lack robustness in the presence of noise (Graham et al., 1996).Thus, both biological and numerical processing factors may lead to visually noisyspatial maps with little apparent spatial structure apart from discerning whitematter from grey matter.DTI studies provide complementary information about WMI. DTI metricssuch as FA display consistent patterns along specific WM fibre bundles (Yeatmanet al., 2012) that are sensitive to pathology (Yeatman et al., 2011, 2014) and age (Daviset al., 2009). While DTI studies are somewhat quantitative and provide insight intogeneral WM microstructure, they do not easily correspond to known biologicalquantities such as myelin (Bracht et al., 2016; Jones et al., 2013) or iron content(Pfe€erbaum et al., 2010) that can be measured during pathological examination. Incontrast, MWF shows a strong correlation with myelin in histopathological studies(Laule et al., 2008).DTI measures and MWF have been shown to correlate to some degree (Ma¨dleret al., 2008), with both measures being confounded to varying degrees by otherWM microstructural factors such as crossing fibres (Tournier et al., 2011) and axonalpacking (Feldman et al., 2010) for DTI, and high SNR sensitivity (Graham et al., 1996)and potential exchange effects (MacKay and Laule, 2016) for MWF. However, almostall MWF reconstruction algorithms lead to maps that appear spatially “noisier”compared to DTI (e.g. FA) maps.Changes in myelin along tracts would be consistent with a large body of animalliterature. Studies in mice have shown a complex pattern of myelin ensheathmentthat varies in length and thickness along axons relative to its location in the brain(Tomassy et al., 2014, 2016). These differences in myelination along individual axonsmay be related to another critical role of overall myelination – the maintenance ofsynchronous firing of connected neurons. Maintaining synchronicity in timings122Chapter 6. Inherent Spatial Structure in Myelin Water Fraction Mapsof signals arriving at a given brain area but originating from different areas withdiffering lengths of axons could be another important aspect of brain signallingin order to elicit a neural response at the target brain area (McDougall et al., 2018;Pelletier and Pare´, 2002; Salami et al., 2003). This phenomenon has been observedin neural input originating from different thalamic regions and ending in thesomatosensory cortex and is believed to be due to the differing myelination ofthese axonal populations (Kimura and Itami, 2009; Salami et al., 2003). While thesestudies report findings on individual axons utilizing mouse models and electronmicroscopy, the effect of differently myelinated axons would conceivably be seen ona larger macroscale with MWI. Thus, investigating a spatial pattern of myelinationalong major fibre bundles could provide further evidence of distinct myelinationalong trajectories supporting synchronicity in the brain on the macroscale.A number of studies have started to examine imaging changes within WM tracts.De Santis et al. (De Santis et al., 2014) created a MRI atlas of white matter microstruc-ture in healthy subjects by comparing means and standard deviations in differentROIs of several measures calculated using DTI and mcDESPOT. mcDESPOT canbe used to calculate MWF, although the acquisition and analysis procedures differfrom the multi-echo T2 relaxation approach used here, and MWF values differbetween these two approaches. They investigated seven WM tracts and subsam-pled each measure along each tract where they found a left/right hemisphereasymmetry pattern with varying degree of asymmetry between measures. Com-pared to typical DTI measures, MWF calculated based on mcDESPOT generallyshowed more asymmetry. Furthermore, when taking the average of each tract,in five out of the seven WM tracts investigated, the mcDESPOT MWF requireda larger sample size than FA to reach significant results. While their work wasaimed at disentangling the interrelations between different measures of WMI inseveral ROIs, they only examined variations in measures along fibre tracts fortheir asymmetry analysis between hemispheres. Another study investigated MWFand rD along a selection of fibre tracts in both MS and healthy subjects and couldpinpoint differences along tract profiles that coincided with lesion locations (Dayanet al., 2016).123Chapter 6. Inherent Spatial Structure in Myelin Water Fraction MapsIn this work, we aimed to characterise the basic spatial structure of MWFmaps with respect to white matter structural organisation and relate the spatialstructure of MWF maps to that of FA maps. To this end, we examined whether theMWF variance within major WM fibre bundles is less than in regions immediatelysurrounding the fibre bundle. Additionally, we explored if MWF maps follow atight spatial pattern that follows the underlying fibre organisation, and thereforethe MWF variance gradient along fibre bundles should be smaller compared toan orthogonal direction. Furthermore, we investigated if different major whitematter tracts have a characteristic pattern of MWF values along their trajectoriesallowing for the identification of local changes that may be of diagnostic value andrelated this to structure and patterns in FA maps. Finally, to determine if therewas biological significance to the characteristic pattern along the fibre bundles weinvestigated the capabilities of tract MWF profiles versus tract MWF averages toestimate subjects age and differentiate between sex.6.2 Materials & Methods6.2.1 MaterialsAll subjects provided written, informed consent. We acquired data from a total of 41healthy subjects (18 M and 23 F), with median age of 28 years with a total age rangeof 32 years from 20 to 52 years. All subjects had no known history of neurologicaldisease. All data were acquired on a Philips (Netherlands) Achieva 3 T MRIscanner with an 8 channel head coil. We acquired a full brain 3DT1-weighted scanfor structural references with an MPRAGE sequence TI = 808ms, TR = 1800ms andan isotropic voxel size of 1mm3. T2 relaxation data were collected using a modifiedGRASE sequence with 32 echoes with 10ms echo spacing and TR = 1000ms. Twentyslices were acquired at 5mm slice thickness and reconstructed to 40 slices at 2.5mm(Prasloski et al., 2012a). The in-plane voxel size was 1× 1mm. Twenty subjects (meanage 26.8 ± 5.4 years, 9 females) had DTI data sets with TE = 69ms, TR = 6179ms,with 32 gradient orientations, a b value of 700 s/mm2 and one b0 volume. The124Chapter 6. Inherent Spatial Structure in Myelin Water Fraction Mapsremaining 21 subjects (mean age 35.6 ± 9.9 years, 14 females) had diffusion tensorimaging data sets acquired with TE = 75ms, TR = 7465ms, 16 directions, with ab value of 900 s/mm2 and one b0 volume. Both DTI sequences were acquiredat a 2.2× 2.2mm in-plane resolution and reconstructed to 0.8× 0.8mm in-planeresolution with a 2.2mm slice thickness.6.2.2 MethodsThe multi-echo GRASE sequence was analysed using in-house written MATLAB(Natick, MA, USA) code which uses an NNLS fitting method to approximatethe multi-exponential decay curve with a number of basis functions, includingcorrections for stimulated echoes as well as a regularizer to make the fit morerobust against noise in the time domain (Prasloski et al., 2012a), resulting in oneMWF map per subject.DTI data were corrected for geometric distortions and subject motions usingFSLs DTIFIT (Jenkinson et al., 2012) prior to fitting the tensors and performingwhole brain deterministic tractography using mrDiffusion, part of vistasoft (h‚p://white.stanford.edu/soware/). Sixteen major white matter tracts were segmented inboth hemispheres with the automatic fibre quantification (AFQ) toolbox (Yeatmanet al., 2012). Briefly, AFQ uses whole brain fibres and segments major fibre bundlesbased on predefined waypoint ROIs, after which it compares the selected fibrebundles to a probabilistic atlas to remove potential outliers. Once the fibre tractshave been segmented, they are clipped to contain the fibres in between two definingwaypoints per tract, as the intersubject variability beyond those endpoints wastoo large to robustly segment the tracts, precluding any quantitative attempt forcharacterization.In order to apply the fibre bundle masks to the MWF maps, for each subjectthe first echo of the GRASE data was registered to the non-diffusion weightedscan from the DTI acquisition (b= 0 s/mm2 or b0) and the resulting transformationmatrix was then applied to each MWF map. Registrations were done with FLIRT(Jenkinson et al., 2012). A white matter mask was generated using FAST (Jenkinson125Chapter 6. Inherent Spatial Structure in Myelin Water Fraction Mapset al., 2012) on the high resolution and skull-stripped 3DT1-weighted images andregistered to the b0 image using a transformation matrix generated by registeringthe 3DT1-weighted image to the b0 image. All registrations were visually checkedfor accuracy and, if needed, performed again with tweaked parameters in order toobtain well aligned images.In order to compare the spatial smoothness of MWF and FA maps, we firstcomputed the local CoVs in a 9× 9 voxel neighbourhood, on axial slices, acrossall white matter. The coefficient of variation was selected for a fair comparison tocompensate the different plausible numerical ranges between the MWF and FAmaps that will be accounted for in the CoV. Note that this comparison was doneon a MWF map that went through a coregistration process to DTI space, so thatthe spatial resolutions are the same, and thus some degree of smoothing occursduring this procedure. Nevertheless, this should only impact the result slightly,and if anything, increase the spatial smoothness of MWF maps.Following this, we compared the variances of MWF and FA values in WM fibrebundles to their respective “tubes” i.e. one-voxel layer of WM voxels surroundingeach tract. To account for possible partial volume effects, imperfect fibre tracking,and registration misalignments between the b0 and myelin data, we introduced agap of one voxel between the fibre bundles and their enclosing tubes (see Figure6.1 for a schematic illustration). To further limit the influence of potential partialvolume effects, we masked the generated tubes with the individuals WM mask toensure that only WM voxels were being considered. The WM masks were basedon the probabilistic output from FAST and only voxels with a probability of 95%or greater were retained. Note that this may lead to incompletely closed tubes insome fibre bundles that were close to the grey/white matter interface but allowsfor a fairer comparison between tracts and their enclosing tubes since only WMvoxels are being examined.We further tested if the gradients of MWF and FA CoVs along adjacent segmentsof fibre bundles differed compared to perpendicular directions. More specifically,we calculated the differences of CoV between two adjacent segments along eachtract and compared this gradient to the differences between a fibre segment and its126Chapter 6. Inherent Spatial Structure in Myelin Water Fraction MapsFigure 6.1: Schematic illustration explaining the subdivision of a fibre bundle(blue) into segments as well as the “tubes” (red), i.e. voxels enclosingthe fibre bundle with a one voxel gap (grey) in between.immediate tube-segment neighbour (voxels enclosing the fibre bundle voxels, inperpendicular direction to the main fibre bundle direction). We divided each fibrebundle into 15 equidistant sub-regions and extracted the averages and CoVs ofMWF and FA values in each segment. We used fibre bundles to create a weightedmask to subsequently interrogate MWF and FA values.Finally, we determined the biological significance of sampling MWF valuesalong fibre bundles in two ways: 1) we examined if the age of a subject could bebetter estimated by average MWF in segments along a fibre bundle compared tothe average MWF of the whole bundle and 2) we investigated if a classification bysex was more accurate with tract profiles than with tract averages.6.2.2.1 Statistical TestsAll statistical tests were performed using MATLAB v2015a (Natick, MA, USA).Results were deemed statistically significant at p< 0.05 without correction for mul-tiple comparisons, on a per fibre bundle basis, in this exploratory analysis. A twosample t-test was used to compare the local, slice-by-slice computed CoVs betweenone representative MWF and FA map. Differences in variance of the WM tracts,and tubes were assessed with signed ranksum tests. A multiple linear regressionmodel was used to examine the relation between age and the 15 segments per tractwhere all segments per tract served as predictors. In the case of the average MWF127Chapter 6. Inherent Spatial Structure in Myelin Water Fraction Mapsper fibre bundle, a simple linear regression was performed with the average MWFper tract as predictor and age as the outcome variable. A LDA was performed withthe goal to differentiate males and females based on their MWF. Two LDAs pertract, with either its segments or whole average as features, and with subjects asobservations were performed. LDA maximises the ratio of between-class varianceto within-class variance, thus finding the most discriminative projections of datafeatures so that the projected data is well distinguished between classes. We com-pared the accuracy of sex classification between tract profiles and tract averages aswell as computing the Akaike information criterion (AIC) for both, the regressionand LDA in order to test whether the models utilizing tract profiles were moreappropriate. Statistical significance is marked with black stars in all figures.6.3 ResultsDespite the differences in DTI acquisition parameters in the two cohorts, theextracted fibre bundles were visually comparable across subjects. An individualanalysis of MWF variances in fibre bundles and tubes in both cohorts demonstratedsimilar behaviour, so that the results shown here are from the combined cohort.Individual plots of the main findings can be seen in the appendix 7.2.3.Figure 6.2 shows the histograms of accumulated local CoVs for both maps,normalized to probabilities, in WM voxels only. It is apparent that MWF mapshave higher CoV than FA maps, consistent with the empirical observation that themaps appear less spatially smooth.All extracted major white matter fibre bundles from one representative subjectcan be seen in Figure 6.3.Comparing the CoV of MWF values between fibre bundles and their respec-tive tubes revealed that the CoV of tubes was higher in all WM tracts except thecallosum forceps minor, but only the left/right thalamic radiation, left/right corti-cospinal tract, callsoum forceps major, right ILF, left/right SLF, as well as left/rightarcuate showed significance (p< 0.05), see Figure 6.4a. A comparison of FA CoVbetween fibre bundles and their respective tubes revealed that all tubes show128Chapter 6. Inherent Spatial Structure in Myelin Water Fraction MapsFigure 6.2: Histogram of local CoV in a 9× 9 voxel rectangle comparing MWFand FA maps. Significantly lower variances can be observed in FA maps,indicating an overall smoother spatial appearance. N = 41.Figure 6.3: Rendering of the extracted major fibre bundles. a) blue: callosumforceps minor/major, red: thalamic radiation, green: cingulum cingu-late, orange: superior longitudinal fasciculus (SLF). b) blue: inferiorfronto-occipital fasciculus (IFOF), red: corticospinal tract, green: inferiorlongitudinal fasciculus (ILF), orange: arcuatehigher CoV than major WM tracts (p< 0.001 for all comparisons), Figure 6.4b.Comparing the CoV gradient along WM fibre bundles to the perpendiculardirection revealed a consistently lower variance gradient between adjacent fibresegments than between fibre segments and tubes (Figure 6.5). While this was truefor both MWF and FA, the MWF maps displayed slightly larger CoV gradients inmost WM tracts. CoV gradients in MWF maps were significantly lower along fibre129Chapter 6. Inherent Spatial Structure in Myelin Water Fraction MapsFigure 6.4: Coefficient of Variation (CoV) of whole tracts and tubes in a) MWFand b) FA. N = 41.bundles than in perpendicular directions in all examined WM tracts except in thecingulum cingulate and callosum forceps minor where some pairs of segment-to-segment and segment-to-tube gradients did not display significant differences. TheCoV gradients in FA maps exhibited a very similar behaviour in all tracts wherethe CoV gradient was lower between segments than between segments and tubes.The across-subject averages of MWF and FA along major fibre bundles aredisplayed in Figure 6.6. Note a characteristic pattern along the major fibre bundles.Further, some fibre bundles show a similar behaviour for both MWF and FA suchas the callosum forceps major or the ILF. Others, such as the thalamic radiation orIFOF, show only some commonalities between MWF and FA patterns. In the caseof the thalamic radiation, both show an increase of MWF and FA until roughly tothe middle of tract where the FA pattern shows a monotone decrease while theMWF pattern shows more complex decreases and increases.Note all Figures displaying either the CoV gradients or the averages of segmentsalong each fibre bundle are showing results from the left hemisphere WM tracts.Please refer to Figures A.1, A.2 for results of right hemisphere tracts.To determine if there was biological significance to the characteristic patternalong the fibre bundles, we performed a multiple linear regression in an effort toestimate the subjects age, as this is known to robustly influence myelin (Arshad et al.,2016; Billiet et al., 2015; Faizy et al., 2018) and compared the performance betweenincluding the individual averages of all segments per tract or the average of all130Chapter 6. Inherent Spatial Structure in Myelin Water Fraction Maps(a) MWF CoV gradients(b) FA CoV gradientsFigure 6.5: CoV gradients between adjacent fibre segments (blue) and betweenfibre and tube segments perpendicular to fibre tract orientation (red) in lefthemishperic tracts. MWF shown in a) and FA shown in b). Stars indicate sig-nificant differences. Errorbars depict standard errors across subjects. N = 41.131Chapter 6. Inherent Spatial Structure in Myelin Water Fraction Maps(a) MWF tract profiles(b) FA tract profilesFigure 6.6: Tract profiles of MWF and FA measures. a) average MWF and b)average FA in segments along each tract. Segments are shown along thex-axis indicating relative directions in the brain (A=anterior, P=posterior,L=left, R=right, I=inferior, S=superior). Errorbars show standard errorsacross subjects. Shown are tract profiles of left hemisphere tracts. N = 41.132Chapter 6. Inherent Spatial Structure in Myelin Water Fraction Mapssegments per tract as predictors. We found that using fibre segment averages wasmore predictive of age than a single average per tract. We found that the callosumforceps major (R2ad j = 0.41, p = 0.012), left IFOF (R2ad j = 0.36, p = 0.035), and leftarcuate (R2ad j = 0.54, p = 0.003) could significantly estimate age (Figure 6.7). Thespatial location of the aforementioned fibre tracts are plotted underneath eachscatterplot, with significant segments in the regression highlighted where darkercolors represent lower p-values.Figure 6.7: Top row: age estimations based on multiple linear regression usingtract profiles as predictors (blue) versus using only the tract average as apredictor (red). Shown are the significant estimation based on segments.The AICs for each model are listed below and showing lower valuesfor the tract profile models, indicating favourable models. Bottom row:the respective fibre bundles in a 3D brain with. Blue segments indicatesegments that were significant in the linear regression. N = 41.To ensure that the improved estimations were not only due to the increased133Chapter 6. Inherent Spatial Structure in Myelin Water Fraction Mapsnumber of predictors, we compared the AIC between the two models and foundthat the model including the segments outperformed the model using only theaverage (Figure 6.7).Additionally, we compared the tracts in which MWF values could estimate agewith the corresponding FA tract profiles in order to identify regional differences.Figure 6.8 illustrates the MWF profiles (green) and FA profiles (orange) in the threetracts. Stars indicate significant segments in the multiple linear regression esti-mating age using MWF values. The MWF profiles demonstrated mostly adjacentsegments that were significant predictors, except in the left IFOF. Furthermore,significant segments can be observed where the MWF and FA profiles differ intheir general trend.Figure 6.8: MWF (green) and FA (orange) tract profiles of tracts able to signifi-cantly estimate age based on MWF predictors. Stars indicate significantsegments in the model along the MWF profile. N = 41.The results from the LDA are shown in Figure 6.9a, where the accuracy ofdifferentiating males from females was higher for tract profiles in each tract. Thelower AIC as seen in Figure 6.9b indicates a superior model for the tract profiles aswell. Figure 6.10 displays the receiver operator characteristic (ROC) for each LDAperformed using either the tract profiles (blue) or whole tract (red). LDA modelsperformed on the tract profiles consistently outperformed the models utilizing onlythe tract averages. The average AUC for tract profiles was 0.87 while the averageAUC for the whole tracts was 0.69 (p< 0.0001). Individual sensitivity, specificity,accuracy, and AUC values can be found in Table 6.1.134Chapter 6. Inherent Spatial Structure in Myelin Water Fraction MapsTable 6.1: Classification results from a LDA. Shown are the sensitivity, speci-ficity, accuracy, and AUC for each LDA when using the tract profiles orwhole tract average as input.Sensitivity Specificity Accuracy AUCFibre tract profile tract profile tract profile tract profile tractThalamicRadiation L0.78 0.78 0.61 0.44 0.70 0.63 0.76 0.61ThalamicRadiation R0.91 0.95 0.77 0 0.85 0.53 0.89 0.64Corticospinaltract L0.69 1.0 0.61 0 0.65 0.56 0.79 0.63Cortiospinaltract R0.82 1.0 0.77 0 0.80 0.56 0.84 0.49Cingulum L 0.85 0.91 0.46 0.33 0.70 0.65 0.79 0.66Cingulum R 0.83 1.0 0.73 0 0.78 0.56 0.87 0.47CallosumForceps Minor0.90 0.82 0.72 0.33 0.82 0.60 0.87 0.63CallosumForceps Major0.82 0.73 0.72 0.27 0.78 0.53 0.85 0.59IFOF L 0.90 1.0 0.75 0 0.83 0.56 0.88 0.55IFOF R 0.91 0.91 0.83 0.16 0.87 0.58 0.91 0.61ILF L 0.86 1.0 0.70 0 0.80 0.56 0.87 0.56ILF R 0.69 0.65 0.55 0.38 0.63 0.53 0.76 0.63SLF L 0.86 0.69 0.83 0.72 0.85 0.70 0.93 0.77SLF R 0.86 0.86 0.83 0.38 0.85 0.65 0.87 0.69Arcuate L 0.86 1.0 1.0 0 0.91 0.56 0.99 0.38Arcuate R 0.85 0.69 0.72 0.27 0.79 0.51 0.92 0.59135Chapter 6. Inherent Spatial Structure in Myelin Water Fraction MapsFigure 6.9: LDA results for differentiating sex based on MWF. a) shows theaccuracy of LDA when using the MWF tract profile (blue) or MWF tractaverage (red). Higher accuracy can be seen for all tract profiles. b) AICper tract model, the model utilizing the tract profiles show a smallerAIC and are thus preferred. N = 41.6.4 DiscussionWe have shown that MWF maps, despite their spatially unsmooth appearance,possess a spatial structure that substantially follows tracts derived from DTI. Thisdraws into question how informative simply averaging MWF values over broadvolumes really is. We have demonstrated MWF values are more consistent along afibre bundle compared to “tube” surrounding the fibre bundles, although MWFvalues are still more variable than FA values. Furthermore, we report that thevariances of MWF as well as FA values exhibit a spatial gradient in major WMfibre bundles that is lower along fibre tracts compared to perpendicular directions.This lower gradient along axonal pathways indicates a central role of MRI-derivedmajor white matter tracts in the overall microstructural organisation of the cerebralWM and that indices of WMI should be evaluated with care to the underlyingmicrostructure.While MWF CoVs were typically less in fibre bundles than their surroundingtubes, only 10 out of the total 16 fibre bundles exhibited significant differences. Incontrast, FA CoVs displayed significant differences in all fibre bundles, making136Chapter 6. Inherent Spatial Structure in Myelin Water Fraction MapsFigure 6.10: ROC plots for each LDA. Light blue and light red show the ROCsfor each LDA per tract, thicker lines show the average. Mean AUC fortract profiles: 0.87, mean AUC for whole tracts: 0.69. N = 41.them appear to be a more stable measure of characterising WM microstructuralintegrity, albeit less biologically specific. However, it should be noted that theextraction of fibre bundles is directly biased towards FA values in terms of selectingvoxels to fibre tracking as well as indirectly when tracing each fibre. Additionally,the left/right IFOF are one of the longest bundles and tend to be more difficult totrack from occipital to frontal areas. In conjunction with the generally observedpattern of higher MWF values in posterior regions compared to anterior regions,these fibre bundles cover a wide range of MWF values.The lower CoV gradients along fibre tracts suggest evidence of MWF valuesfollowing a pattern of microstructural WM organisation, highlighting the impor-tance of WM fibre bundles. Both MWF and FA followed the same trend, in that theCoV gradient was lower between fibre bundle segments than in perpendicular di-rections with the difference being usually more pronounced in FA maps indicativeof a steeper change of FA values from within fibres to its surroundings.We have demonstrated that each major fibre bundle has its own specific patternof myelination, which is relatively consistent across subjects, with a general obser-vation of higher to lower MWF values when one moves from posterior to anterior.137Chapter 6. Inherent Spatial Structure in Myelin Water Fraction MapsSome structures such as the callosum forceps major/minor have quite intricatespatial patterns, which are completely lost when simply averaging over the entiretract. Thus, studies investigating age effects on myelination or inferring diseaseprogression based on tract informed analysis may potentially more sensitive tosubtle local changes in MWF. While it might be apparent that including moreinformation about MWF values would increase predictability of a clinical indexsuch as age, the key point is that the enhanced predictability implies consistencyacross subjects of MWF segments within a fibre bundle. It should be noted thatMWF tract profiles has been computed before, with the focus there on four fibrebundles of the right hemisphere that were relevant to their specific MS cohort athand (Dayan et al., 2016). In this work, we focused on characterising 16 major fibrebundles in a healthy cohort in order to outline the majority of healthy WM. Wenote that the overlapping investigated fibre bundles show qualitative similarities.The MWF tract profiles were able to significantly estimate age in three fibretracts, the callosum forceps major, left IFOF and left arcuate. The most importantsegments in the left arcuate were segments exhibiting a steady decline in MWFprofiles but showed a large variability in FA profiles. Similarly, the importantsegment in the left IFOF marked the point of a steep increase in the FA profilewhile in the MWF profile it was the start of a plateau. In case of the callosum forcepsmajor, both profiles showed a similar behaviour, however the steep increase anddecrease around the midline in the MWF profile seems to have profound effects inage estimation.Further, the MWF tract profiles could consistently better separate male andfemale sex when compared to using the tract average MWF and could present amethod to gain more detailed insight into WM microstructural differences basedon sex. While sex differences in MWF of the corpus callosum have been previouslyreported (Liu et al., 2010), other human adult studies of sex differences in MWFare scarce, potentially due to the limitation of commonplace ROI/tract averagemeasures used in statistical analysis. Additionally, since LDA estimates a projectionwhich maximises within to between class variance, it may be able to detect subtlesex differences more robustly than more traditional methods such as simple t-tests138Chapter 6. Inherent Spatial Structure in Myelin Water Fraction Mapsor logistic regression.We recognize that the true biological origin of the tract profiles cannot be fullydetermined in this study. The tract profiles could stem from differing myelinationpatterns along the axons that in sum produce a characteristic pattern of MWFvalues along each tract, in line with the synchronicity theory. Another explanationfor the tract profiles we observed could be due to different fibre bundles crossingand merging into each other creating a heterogeneous microstructure which maynot be resolved with the current MWF maps. The MWF profile of the callosumforceps minor/major, fibre bundles with little crossing or merging fibres, howeverdo suggest a distinct myelination pattern. Further studies with higher spatialresolution in both MWI and DTI as well as more DTI gradient directions are neededto obtain a more detailed description of the trajectories myelination patterns ofWM fibre bundles.We note that there are a number of limitations to this study. We had a rathernarrow age range that may have limited the capacity of the regression analysisto predict age in some WM tracts. The use of two different DTI data sets withdifferent acquisition parameters may introduce some confounding factors, namelyin the accuracy of fibre tracking. However, examining these two sub-data setsseparately did not reveal striking differences (see Figures A.3, A.4) except possiblythe thalamic radiation. A possible explanation could be imperfect fibre trackingin the thalamus, which is known to be a mixture of white- and grey matter tissueand thus finding a principal diffusion direction is always challenging and directlyrelates to the number of diffusion gradient used during data acquisition (16 vs32 directions in our cohorts). Since our main focus was to establish a biologicalsignificance of the tract profiles, this difference does not appear to affect ourconclusions. Future studies may use diffusion spectrum imaging (DSI) in order tomitigate the effects of crossing fibres and thus getting more accurate fibre trackingand consequently more robust measures. This could then be used to look furtherinto the differences between the MWF and FA profiles as an area with crossingfibres should influence FA more than MWF and thus provide information whetheror not crossing fibres are a dominant factor in the discrepancies between MWF139Chapter 6. Inherent Spatial Structure in Myelin Water Fraction Mapsand FA tract profiles. It should be noted that due to the healthy cohort, age andsex were the only available demographic variables to test usefulness of the tractprofiles. This can easily be extended to a patient population with various clinicaland behavioural data in order to pinpoint specific segments most associated withaberrant behaviour. Regarding the contribution of individual segments of the leftIFOF in the estimation of age, the only segment significantly contributing may beinfluenced by partial volume effects as this part of the tract is running throughthe external capsule, a very thin WM structure that may not be purely WM with a5mm slice thickness.In summary, our results suggest that there is a deterministic spatial patternin MWF despite the apparent unsmooth appearance of MWF maps. Our resultsindicate that when performing an ROI based analysis, one should be aware to theunderlying white matter microstructure when investigating large ROIs containingmultiple fibre tracts. When investigating whole fibre tracts, it may be inadvisableto integrate the MWF over the entire tract length rather than looking at smallersegments within each tract. The number of sections to divide each fibre bundlethat we chose is somewhat arbitrary; further work will be required to determinethe optimal number of segments.140Chapter 7Conclusion & Future Work7.1 ConclusionIn this thesis, we have worked on bringing MWI closer to clinical practice byaddressing three key areas, “Applications”, “Techniques”, and “Multimodal Inte-gration”, as outlined in chapter 1, section 1.1. We have demonstrated its usefulnessby applying it to a neurodegenerative disease previously not investigated withMWI, leveraged complementary information between MWI and other imagingmodalities as well as clinical and behavioural features to find robust relationships,and lastly devised a new method to denoise T2 relaxation data in order to calculatemore robust MWF maps. The specific contributions were as follows:For the Application domain, in the work of chapter 2 we presented evidenceof myelin involvement in a new and unique environment, where we report setsof WM regions myelin content related to distinct symptoms of PD. This resultcomplements and extends the current literature in a way that it offers a directinterpretation of biological changes in the WM microstructure as opposed to mostother current studies relying of inferences from indirect and unspecific measures.Furthermore, the multivariate nature enabled us to model joint interactions be-tween symptoms and myelin features that naturally separated commonly knownPD phenotypes.141Chapter 7. Conclusion & Future WorkThe work in chapter 3 combines the Applications and Multimodal Integra-tion aspect by demonstrating a robust joint multivariate relation between myelin,cognitive performance, and clinical features in MS. We extend the current MSliterature where we report a common profile of myelin, cognitive domains, as wellas demographic and clinical indices. These profiles are able to separate mild andmoderately affected MS subjects and are largely independent of lesion burden,offering evidence of the importance of normal appearing white matter in MS.Chapter 4 combines the Multimodal Integration and Techniques domains byproviding evidence of WM myelination being able to estimate topological featuresof functional networks. Additionally, it offers a novel framework that links fea-tures of WMI to functional connectivity. The results further demonstrate WMIinvolvement in PD, and emphasises the importance of WMI and its effects onthe organisation of functional brain networks. Moreover, we extend the currentview on brain networks to the WM which allows the investigation of joint changesamong different modalities probing the WMI and reveal an altered topology in PD.The work in chapter 5 addresses the Techniques aspect by providing a novelmethod for denoiseing T2 relaxation curves. Our technique of adopting MEMD+MCCA to extract robust T2 decay curves offers a way to provide denoised T2 decaycurves as a preprocessing step in order to obtain more robust MWF maps. Weextend the current literature to implement a data-driven denoising scheme as apreprocessing step, while most literature either focuses on a spatial regularisa-tion after or during the MWF reconstruction or perform a single voxel temporaldenoising prior MWF reconstruction, our approach offers combines spatial andtemporal denoising steps. Post-hoc spatial denoising schemes may still be appliedif necessary to further improve MWF maps.Lastly, chapter 6 combines the aspects of Applications and Techniques by show-ing evidence of a spatial pattern of MWF maps and providing a novel frameworkfor leveraging the information gained by a WM tract informed MWF analysis.We have reported an inherent spatial structure in MWF maps despite their noisyappearance. Additionally, major WM fibre tracts exhibit a characteristic patternof myelination along their trajectories. These patterns are superior in estimating142Chapter 7. Conclusion & Future Worka subjects age as well as perform better when one wishes to differentiate sex, ascompared to tract averaged values. Given the (in some cases) intricate pattern ofmyelination along tracts, the current practise of simply averaging over entire tractsor large WM regions may come at a cost of missing subtle, focal changes in theWM microstructure.In summary, this thesis explored and expanded on current trends in myelinwater imaging by providing new evidence of myelin involvement in a disease notpreviously associated with WM alterations and provided evidence of FC changesbeing linked to/modulated by changes in myelin. Fusing imaging, cognitive,and clinical features provided a latent and robust link between all three data sets.Developing a spatiotemporal smoothing approach for the reconstruction of MWFmaps. Demonstrating unique myelin profiles along major WM tracts suggesting achange from traditional averaging over large areas.7.2 Future WorkDespite our contribution to different aspects of MWI, more work is required toprime MWI for clinical application. In this research, several machine learningmethods have been applied such as CCA, MCCA, PLS, LASSO. However, due tolimited sample size in the thesis research, these methods may not fully demonstratetheir power. In the future, although always a critical point in neuroimaging studies,a larger cohort of people with both PD and MS should be considered. Althoughthere is no gold standard for how many subjects should be included in machinelearning approaches, recent studies demonstrate promising results in diseasedpopulations with the sample size of around 100 and above (Tam et al., 2019; Vieiraet al., 2017).Below are some possible avenues for future work, in the context of our contri-butions in each of the three domains.143Chapter 7. Conclusion & Future Work7.2.1 ApplicationsOur results from chapter 2 provide new evidence of myelin involvement in PDwhere research only recently began to investigate WMI with advanced quantita-tive MRI. The wide breadth of these techniques, and particularly MWI may beunderutilised and should be applied to neurological disorders that may not, atfirst sight, display apparent changes in the WMI. Finding evidence of modulatedMWF in these disorders, with seemingly intact WM, would lend MWI even greaterutility in a clinical setting and ultimately help physicians to better characteriseneurological diseases.The MWF profiles along major WM fibre bundles from chapter 6 should beverified with higher quality DTI data with increased b-values and more diffusion-sensitive gradient directions. This permits a more accurate estimation of thediffusion process and the reconstruction of WM fibres can be fed into more ad-vanced fibre tracking methods. With such methods, it is possible to limit the effectof crossing or touching fibres and potentially shed light on some local changes inMWF along each fibre bundle. It is possible that a change in MWF is not an inher-ent property of a given tract but may result from different fibre bundles mergingor diverging, in such cases, being able to resolve the fibre tracking with advancedmethods will prove useful. Additionally, it will be interesting to see when theMWF profiles are utilised in a diseased cohort where the profiles could be used topinpoint focal changes in relation to disease characteristics. Moreover, it wouldbe interesting to see if there are differences between left and right hemisphericMWF profiles due to handedness or language lateralisation. A study investigatedmyelin asymmetry during development and reported an association between asym-metry and language ability but only during the first four years of development(O’Muircheartaigh et al., 2013). MWF profiles could help potential asymmetries byproviding specific profiles of WM fibre bundles connected to language areas.Lastly, using MWF in structural connectome studies could serve as anotherway to expand the usage of MWI. In order to incorporate the connectomics aspect,one could use diffusion spectrum imaging or some higher order sequence that144Chapter 7. Conclusion & Future Workallows to resolve crossing fibres as well as provides additional measures of axonalintegrity. Once this is obtained, it would be very interesting to ascertain if MWFor the MWF profiles can be incorporated into structural connectomes. It wouldappear that simply averaging the MWF over a tract may not be the best choice inorder to implement some sort of conduction velocity that applies to a given tract ona fixed basis. Rather, one may have to consider other connected regions acting inconcert and apply a variable conduction velocity based on, for example, a weightedaverage over all segments, in order for appropriate communication between brainregions. Proceeding forward, one could also consider a piecewise conduction as afunction of location along the tract to even further refine the model.7.2.2 Multimodal IntegrationIn chapter 3 where we discuss data fusion analysis in MS, we only use MWF as animaging feature to establish an association with cognitive and clinical characteris-tics. A natural next step would be to include features from fMRI as well, as a wayto identify which common covariations in structural and functional MRI are mostrelated to behavioural and clinical indices. Features from fMRI can be based on theraw FC values or features characterising the functional network.By including more modalities and/or features, one might be able to find sub-tle patterns among the imaging features that correspond to specific subsets ofbehavioural or clinical symptom manifestation, that may not be obtainable withonly a limited amount of input data or with “weak” individual features (McKeownand Peavy, 2015). In order to establish a complementary model that could betterpredict disease progression, more modalities can considered to be included. Forexample, not only MRI measures (such as functional connectivity and structuralintegrity) and clinical scores, but metabolic imaging and blood/CSF markers couldbe considered as well. In this case, the model contains information of neuronalflow, brain structure, behaviour, metabolism. This model shall be even more robustand informative to predict disease progression so that precaution treatments can bedesigned before the symptoms manifest. In fact, it has been shown that a judicious145Chapter 7. Conclusion & Future Workcombination of multimodal neuroimaging features together with behavioural datacan predict disease progression as well as the effect of treatments (Iturria-Medinaet al., 2018, 2017). Such an approach implies a wide range of possibilities such asthe establishment of effective individualised treatment options as well as stratify-ing participants of clinical trials (Iturria-Medina et al., 2018). Given the increasedinterest in models that capitalise on the joint information of multiple imaging andnon-imaging features, the inclusion of MWI as a measure of WMI has the potentialto contribute considerably to the accuracy and robustness of these models.Both parts of the work in chapter 4 could be extended to include dynamic FCfeatures instead of only static FC. As the brain has been shown to be a dynamicalsystem, future work should include the dynamical aspect of FC to form a morecomplete characterisation of the functional brain network. Studies have reporteddistinct “states” of FC patterns that are altered in PD with cognitively impaired PDpatients having a reduced dwell time in hypoconnected states (Dı´ez-Cirarda et al.,2018). It would be interesting to investigate if the MWF can also be associated tothese dynamical states, further bringing structural and functional MRI together.Moreover, one could conjecture that a MWF weighted structural connectomecould provide additional information when trying to estimate the FC pattern ofsubjects. Research has shown that anatomical connections (obtained with diffusionimaging) can shape the functional dynamics (Deco et al., 2012) and that time delaysof information transmission in anatomical connections is a crucial part of themodeling process (Petkoski and Jirsa, 2019). Here, MWF could provide a delayparameter founded in biology rather than an experimental parameter that is used(Petkoski and Jirsa, 2019), which could lead to more accurate models.Finally, the inclusion of more features indexing the WMI could prove beneficialfor the generation of WISNs by potentially assisting in calculation of more robustpairwise correlations. Moreover, examining the eigenmodes of the WISN Laplacianmatrices could lend more insight into disease specific variations. These eigenmodeswould be comprised of sets of WM regions that are fast or slow varying andcould be used in spectral clustering to identify clusters of WM ROIs specific toneurological disorders.146Chapter 7. Conclusion & Future Work7.2.3 TechniquesAlthough our results in chapter 5 are promising, the results could still be improved.A different criteria for selection of similar voxels, as well as a careful expansionto 3D could lead to a more accurate common decay curve amongst voxels. Forexample, a hierarchical clustering scheme or k-means clustering could be employedto identify voxels with similar decay curves such that the clusters of voxels areoptimally grouped. Additionally, a weighting scheme which emphasises similarityin the first few echoes, i. e. echoes mostly pertaining to myelin decay, could proveuseful in the identification of similarly-decaying voxels. An expansion to 3D couldprovide a selection of voxels with potentially smaller error than voxels from thesame slice as there is no guarantee that voxels in the same slice have the samemyelin content. However, one has to define the selection criteria with care asthicker slices also pose a risk of including partial volume effects from unwantedareas.An accurate and robust decomposition of the multiexponential T2 decay curvesremains challenging in case of intrinsic perturbations in the T2 distribution dueto pathological effects. A purely data-driven method that does not rely on priorassumptions might offer new insights. One such method could be dynamic modedecomposition (DMD) (Schmid, 2010) and similarly to PCA and ICA, DMD is adimensionality reduction technique that decomposes the data into sets of spatialand temporal modes. 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Human Brain Mapping, 35:1325–1333. → page 16181AppendixA Supporting information for Chapter 6.The CoV gradients from the right hemisphere are shown below, the MWF CoVgradient is shown in Figure A.1a and the FA CoV gradient is shown in Figure A.1b.The MWF and FA tract profiles for the right hemispheres can be seen in FigureA.2a and Figure A.2b respectively.Figures A.3 and A.4 display the MWF and FA tract profiles, respectively for theindividual cohorts 1 and 2 (across rows) and for each hemisphere (across columns).182Appendix0 ← P A → 15MWF CoV gradient00.10.20.30.4ThalamicRadiation0 ← I S → 1500.10.20.30.4Corticospinal0 ← P A → 1500.10.20.3Cingulum Cingulate0 ← L R → 15MWF CoV gradient00.10.20.30.4Callosum Forceps Major0 ← L R → 1500.10.20.3Callosum Forceps Minor0 ← P A → 1500.10.20.30.4IFOFSeg/SegSeg/TubeSegment0 ← P A → 15MWF CoV gradient00.10.20.3ILFSegment0 ← P A → 1500.050.10.150.2SLFSegment0 ← A P → 1500.050.10.150.2Arcuate(a) MWF CoV gradient0 ← P A → 15FA CoV gradient00.10.20.30.4ThalamicRadiation0 ← I S → 1500.10.20.3Corticospinal0 ← P A → 1500.10.20.30.4Cingulum Cingulate0 ← L R → 15FA CoV gradient00.10.20.3Callosum Forceps Major0 ← L R → 1500.10.20.30.4Callosum Forceps Minor0 ← P A → 1500.10.20.3IFOFSeg/SegSeg/TubeSegment0 ← P A → 15FA CoV gradient00.10.20.3ILFSegment0 ← P A → 1500.050.10.15SLFSegment0 ← A P → 1500.050.10.150.2Arcuate(b) FA CoV gradientFigure A.1: CoV gradients between adjacent fibre segments (blue) and be-tween fibre segments and tube segments perpendicular to fibre tractorientation (red). MWF CoV shown in a) and FA CoV shown in b). Inboth cases the majority of segment-to-segment and segment-to-tubepairs show significant differences. Errorbars depict standard errorsacross subjects. Shown are tracts from the right hemisphere. 183Appendix1 ← P A → 15MWF0.060.080.10.120.140.16Thalamic Radiation1 ← I S → 150.150.20.25Corticospinal1 ← P A → 150.060.070.080.09Cingulum Cingulate1 ← L R → 15MWF0.120.140.16Callosum Forceps Major1 ← L R → 150.060.080.10.12Callosum Forceps Minor1 ← P A → 150.040.060.080.10.12IFOFSegment1 ← P A → 15MWF0.020.040.060.080.1ILFSegment1 ← P A → 150.10.110.120.130.14SLFSegment1 ← A P → 150.080.090.10.110.12Arcuate0.020.040.060.080.10.120.140.160.18(a) MWF tract profiles1 ← P A → 15FA0.30.40.5Thalamic Radiation1 ← I S → 150.40.50.6Corticospinal1 ← P A → 150.350.40.450.50.55Cingulum Cingulate1 ← L R → 15FA0.40.50.60.7Callosum Forceps Major1 ← L R → 150.40.50.60.7Callosum Forceps Minor1 ← P A → 150.40.450.50.55IFOFSegment1 ← P A → 15FA0.30.350.40.450.5ILFSegment1 ← P A → 150.40.420.440.46SLFSegment1 ← A P → 150.440.460.480.50.52Arcuate0.30.350.40.450.50.550.60.650.7(b) FA tract profilesFigure A.2: Tract profiles of MWF and FA measures. a) average MWF and b)average FA in segments along each tract. Segments are shown along thex-axis indicating relative directions in the brain (A=anterior, P=posterior,L=left, R=right, I=inferior, S=superior). Errorbars show standard errorsacross subjects. Shown are tract profiles of right hemisphere tracts. 184Appendix1 ← P A → 15MWF0.060.080.10.120.140.16Thalamic Radiation1 ← I S → 150.150.20.25Corticospinal1 ← P A → 150.050.060.070.08Cingulum Cingulate1 ← L R → 15MWF0.120.140.16Callosum Forceps Major1 ← L R → 150.040.060.080.10.12Callosum Forceps Minor1 ← P A → 150.050.10.15IFOFSegment1 ← P A → 15MWF0.020.040.060.080.1ILFSegment1 ← P A → 150.090.10.110.12SLFSegment1 ← A P → 150.080.10.120.14Arcuate0.020.040.060.080.10.120.140.160.18(a) MWF profile of cohort 1 (left hemish-pere)1 ← P A → 15MWF0.060.080.10.120.140.16Thalamic Radiation1 ← I S → 150.150.20.25Corticospinal1 ← P A → 150.060.070.08Cingulum Cingulate1 ← L R → 15MWF0.120.140.16Callosum Forceps Major1 ← L R → 150.040.060.080.10.12Callosum Forceps Minor1 ← P A → 150.020.060.10.14IFOFSegment1 ← P A → 15MWF0.020.040.060.080.1ILFSegment1 ← P A → 150.10.110.120.130.14SLFSegment1 ← A P → 150.080.090.10.110.12Arcuate0.020.040.060.080.10.120.140.160.18(b) MWF profile of cohort 1 (right hemish-pere)1 ← P A → 15MWF0.080.10.120.140.160.18Thalamic Radiation1 ← I S → 150.140.160.180.20.22Corticospinal1 ← P A → 150.060.070.08Cingulum Cingulate1 ← L R → 15MWF0.140.160.18Callosum Forceps Major1 ← L R → 150.060.080.10.12Callosum Forceps Minor1 ← P A → 150.040.060.080.10.12IFOFSegment1 ← P A → 15MWF0.040.060.080.1ILFSegment1 ← P A → 150.110.120.130.14SLFSegment1 ← A P → 150.080.10.120.14Arcuate0.020.040.060.080.10.120.140.160.18(c) MWF profile of cohort 2 (left hemish-pere)1 ← P A → 15MWF0.060.10.140.18Thalamic Radiation1 ← I S → 150.140.160.180.20.22Corticospinal1 ← P A → 150.060.070.080.09Cingulum Cingulate1 ← L R → 15MWF0.140.160.18Callosum Forceps Major1 ← L R → 150.060.080.10.12Callosum Forceps Minor1 ← P A → 150.040.060.080.10.12IFOFSegment1 ← P A → 15MWF0.040.060.080.1ILFSegment1 ← P A → 150.110.120.130.14SLFSegment1 ← A P → 150.080.090.10.110.12Arcuate0.020.040.060.080.10.120.140.160.18(d) MWF profile of cohort 2 (right hemish-pere)Figure A.3: To illustrate that DTI acquisition parameters were not drivingthe results, MWF tract profiles from cohort 1 (top row) and cohort2 (bottom row). Left column shows left hemisphere tracts, right col-umn displays right hemisphere tracts. (A=anterior, P=posterior, L=left,R=right, I=inferior, S=superior). Errorbars show standard errors acrosssubjects.185Appendix1 ← P A → 15FA0.350.40.450.50.55Thalamic Radiation1 ← I S → 150.40.50.6Corticospinal1 ← P A → 150.350.40.450.50.55Cingulum Cingulate1 ← L R → 15FA0.40.50.60.7Callosum Forceps Major1 ← L R → 150.40.50.60.7Callosum Forceps Minor1 ← P A → 150.40.450.5IFOFSegment1 ← P A → 15FA0.30.350.40.450.5ILFSegment1 ← P A → 150.420.440.460.480.5SLFSegment1 ← A P → 150.40.450.5Arcuate0.30.350.40.450.50.550.60.650.7(a) FA profile of cohort 1 (left hemishpere)1 ← P A → 15FA0.30.40.5Thalamic Radiation1 ← I S → 150.40.50.6Corticospinal1 ← P A → 150.30.40.5Cingulum Cingulate1 ← L R → 15FA0.40.50.60.7Callosum Forceps Major1 ← L R → 150.40.50.60.7Callosum Forceps Minor1 ← P A → 150.40.50.6IFOFSegment1 ← P A → 15FA0.30.40.5ILFSegment1 ← P A → 150.420.440.460.48SLFSegment1 ← A P → 150.460.480.50.520.54Arcuate0.30.350.40.450.50.550.60.650.7(b) FA profile of cohort 1 (right hemish-pere)1 ← P A → 15FA0.30.350.40.450.5Thalamic Radiation1 ← I S → 150.40.450.50.550.6Corticospinal1 ← P A → 150.30.350.4Cingulum Cingulate1 ← L R → 15FA0.40.50.60.70.8Callosum Forceps Major1 ← L R → 150.40.50.60.7Callosum Forceps Minor1 ← P A → 150.350.40.45IFOFSegment1 ← P A → 15FA0.30.350.40.45ILFSegment1 ← P A → 150.40.420.44SLFSegment1 ← A P → 150.40.450.5Arcuate0.30.350.40.450.50.550.60.650.7(c) FA profile of cohort 2 (left hemishpere)1 ← P A → 15FA0.30.350.40.450.5Thalamic Radiation1 ← I S → 150.450.50.550.60.65Corticospinal1 ← P A → 150.350.40.450.5Cingulum Cingulate1 ← L R → 15FA0.40.50.60.70.8Callosum Forceps Major1 ← L R → 150.40.50.60.7Callosum Forceps Minor1 ← P A → 150.350.40.450.5IFOFSegment1 ← P A → 15FA0.30.40.5ILFSegment1 ← P A → 150.380.40.42SLFSegment1 ← A P → 150.420.440.460.480.50.52Arcuate0.30.350.40.450.50.550.60.650.7(d) FA profile of cohort 2 (right hemish-pere)Figure A.4: To illustrate that DTI acquisition parameters were not driving theresults, FA tract profiles from cohort 1 (top row) and cohort 2 (bottomrow). Left column shows left hemisphere tracts, right column dis-plays right hemisphere tracts. (A=anterior, P=posterior, L=left, R=right,I=inferior, S=superior). Errorbars show standard errors across subjects.186

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