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ROI-based brain functional connectivity using fMRI : regional signal representation, modelling and analysis Cai, Jiayue 2019

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ROI-based Brain FunctionalConnectivity Using fMRI: RegionalSignal Representation, Modelling andAnalysisbyJiayue CaiB.Sc., China Agricultural University, 2013M.Sc., China Agricultural University, 2015A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinThe Faculty of Graduate and Postdoctoral Studies(Electrical and Computer Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)December 2019c© Jiayue Cai, 2019The following individuals certify that they have read, and recommend to the Faculty of Grad-uate and Postdoctoral Studies for acceptance, the thesis entitled:ROI-based Brain Functional Connectivity Using fMRI: Regional Signal Represen-tation, Modelling and Analysissubmitted by Jiayue Cai in partial fulfillment of the requirements for the degree of Doctorof Philosophy in Electrical and Computer Engineering.Examining Committee:Z. Jane Wang, Electrical and Computer EngineeringCo-supervisorMartin J. McKeown, Faculty of MedicineCo-supervisorShannon Kolind, Faculty of MedicineSupervisory Committee MemberPurang Abolmaesumi, Electrical and Computer EngineeringUniversity ExaminerAlex MacKay, Department of Physics & AstronomyUniversity ExaminerAdditional Supervisory Committee Members:Rabab Ward, Electrical and Computer EngineeringSupervisory Committee MemberiiAbstractInferring brain functional connectivity from functional magnetic resonance imaging (fMRI) dataextends our understanding of systems-level functional organization of the brain. Functionalconnectivity can be assessed at the individual voxel or Region of Interest (ROI) level, with prosand cons of each approach. This thesis focuses on addressing fundamental problems associatedwith ROI-based brain functional connectivity inference, including regional signal representation,brain functional connectivity modelling and brain functional connectivity analysis.Functional connectivity involving brainstem ROIs has been rarely studied. We propose anovel framework for brainstem-cortical functional connectivity modelling where the regional sig-nal of brainstem nuclei is estimated by Partial Least Squares and connections between brainstemnuclei and other cortical/subcortical brain regions are reliably estimated by partial correlation.We then apply the proposed framework to assess functional connectivity of one particular brain-stem nucleus – the pedunculopontine nucleus (PPN), which is important for ambulation, andis affected in diseases putting people at risk for falls (e.g., Parkinson’s Disease).A key issue for ROI-based brain functional connectivity assessment is how to summarizethe information contained in the voxels of a given ROI. Currently, the signals from the sameROI voxels are simply averaged, neglecting any inhomogeneity in each ROI and assuming thatthe same voxels will interact with different ROIs in a similar manner. In this thesis, we developa novel method of representing ROI activity and estimating brain functional connectivity thattakes the regionally-specific nature of brain activity, the spatial location of concentrated activity,and activity in other ROIs into account.Finally, to facilitate the interpretation of the estimated brain functional connectivity net-works, we propose the use of dynamic graph theoretical measures (e.g., the newly introducedgraph spectral metric, Fiedler value) as potential MRI-related biomarkers.The proposed methods were applied to real fMRI datasets, with a primary focus on Parkin-son’s disease. The proposed methods demonstrated enhanced robustness of brain functionalconnection estimation, with potential use in disease assessment and treatment evaluation. Moreiiibroadly, this thesis suggests that brain functional connectivity offers a promising avenue fornon-invasive and quantitative assessment of neurological diseases.ivLay SummaryFunctional magnetic resonance imaging (fMRI) is a way to non-invasively assess the brain inaction. Instead of determining which areas of the brain activate, another way of assessing thebrain is to look at brain areas that appear to work together. We specifically looked at how wecould improve our ways of determining how brain Regions of Interest (ROIs) interact with oneanother. One improvement was to examine the case when an ROI was part of the brainstem –a small vital structure at the base of the brain. Another improvement was how to summarizethe activity within an ROI, even when a single ROI may encompass different clumps of activity.We also examined how connectivity between ROIs change over time. While our emphasis wason Parkinson’s Disease, our approaches can be used to assist in evaluation of a number of braindiseases, and in assessing normal brain functioning.vPrefaceThe work in this thesis is conducted by the candidate, under the supervision of Dr. Z. JaneWang and Dr. Martin J. McKeown. This thesis is based on a collection of manuscripts thathave been published in international journals and conferences or submitted for publications.Chapter 2 is based on the following manuscripts:• Jiayue Cai, Z. Jane Wang, Soojin Lee, and Martin J. McKeown, “Assessing FunctionalConnectivity of Brainstem Nuclei in fMRI Data”,2017 IEEE Global Conference on Signaland Information Processing (GlobalSIP), November 2017, Montreal, Canada.• Jiayue Cai, Soojin Lee, Fang Ba, Saurabh Garg, Laura J. Kim, Aiping Liu, Diana Kim, Z.Jane Wang, and Martin J. McKeown, “Galvanic Vestibular Stimulation (GVS) AugmentsDeficient Pedunculopontine Nucleus (PPN) Connectivity in Mild Parkinson’s Disease:fMRI Effects of Different Stimuli”, Frontiers in Neuroscience, 12(101): 1-9, 2018.The author was responsible for data analysis and writing the manuscript. The work was con-ducted with the guidance and editorial input from Dr. Z. Jane Wang and Dr. Martin J.McKeown. The experimental fMRI data was provided by Dr. Martin J. McKeown (UBCClinical Research Ethics Board: H09-02016). Dr. Soojin Lee, Laura J. Kim, and Diana Kimconducted the experiment and data acquisition, and Saurabh Garg performed the preprocessingof fMRI data. Dr. Fang Ba and Dr. Soojin Lee contributed to neurological interpretations ofthe results and editorial input on the manuscript. Dr. Aiping Liu provided valuable feedbackon the data analysis and editorial input on the manuscript.Chapter 3 is based on the following manuscript:• Jiayue Cai, Aiping Liu, Sun Nee Tan, Taylor Chomiak, Bin Hu, Z. Jane Wang, andMartin J. McKeown, Fang Ba, “Walking Exercise Induces Dose-dependent Modulation ofPedunculopontine Nucleus Functional Connectivity in Parkinson’s Disease”, submitted.viThe author was responsible for data analysis and writing the manuscript. The work was con-ducted with the guidance and editorial input from Dr. Z. Jane Wang and Dr. Martin J.McKeown. The experimental fMRI data was provided by Dr. Martin J. McKeown (UBC Clin-ical Research Ethics Board: H13-02074). Sun Nee Tan, Dr. Taylor Chomiak and Dr. BinHu contributed to the experiment design and data acquisition. Dr. Fang Ba contributed toneurological interpretations of the results and editorial input on the manuscript. Dr. AipingLiu provided valuable feedback on the data analysis and editorial input on the manuscript.Chapter 4 is based on the following manuscript:• Jiayue Cai, Aiping Liu, Yuheng Wang, Martin J. McKeown and Z. Jane Wang, “NovelRegional Activity Representation with Constrained Canonical Correlation Analysis forBrain Connectivity Network Estimation”, IEEE Transactions on Medical Imaging, underrevision.The author was responsible for the development of the proposed algorithm, performing simu-lations and real fMRI application, and writing the manuscript. The work was conducted withthe guidance and editorial input from Dr. Z. Jane Wang and Dr. Martin J. McKeown. YuhengWang contributed to data organization and part of the implementation of the experiment. Dr.Aiping Liu contributed to the formulation of the problem, evaluation of the methods, andproviding editorial input and valuable feedback.Chapter 5 is based on the following manuscript:• Jiayue Cai, Aiping Liu, Taomian Mi, Saurabh Garg, Wade Trappe, Martin J. McKeownand Z. Jane Wang, “Dynamic Graph Theoretical Analysis of Functional Connectivity inParkinson’s Disease: The Importance of Fiedler Value”, IEEE Journal of Biomedical andHealth Informatics, 23(4): 1720-1729, 2018.The author was responsible for literature review, implementing the proposed methods, analyzingthe results and writing the manuscript. The work was conducted with the guidance and editorialinput from Dr. Z. Jane Wang and Dr. Martin J. McKeown. The real fMRI data was providedby Taomian Mi (Institutional Review Board of Xuanwu Hospital of Capital Medical University:[2011] No.12). Taomian Mi contributed to data collection, and Saurabh Garg performed thepreprocessing of the data. Dr. Wade Trappe and Dr. Aiping Liu provided valuable feedbackand editorial input on the manuscript.viiOther publications related to my PhD work are:• Jiayue Cai, Z. Jane Wang, Silke Appel-Cresswell and Martin J. McKeown, “FeatureSelection to Simplify BDI for Efficient Depression Identification”, 2016 IEEE CanadianConference on Electrical and Computer Engineering (CCECE), May 2016, Vancouver,Canada.The author was responsible for data analysis and writing the manuscript. The work wasconducted with the guidance and editorial input from Dr. Z. Jane Wang and Dr. MartinJ. McKeown. Dr. Silke Appel-Cresswell contributed to the medical interpretations of theresults.• Yuheng Wang, Jiayue Cai, Daniel C. Louie, Harvey Lui, Tim K. Lee, Z. Jane Wang,“Classifying Melanoma and Seborrheic Keratosis Automatically with Polarization SpeckleImaging”, 2019 IEEE Global Conference on Signal and Information Processing (Global-SIP), November 2019, Ottawa, Canada.The author contributed to part of the data analysis and provided editorial input on themanuscript. Yuheng Wang was responsible for formulating the problem, implementingthe proposed method, analyzing the results and writing the manuscript. Daniel C. Louiecollected the experimental data and provided editorial input on the manuscript. Dr. Z.Jane Wang, Dr. Tim K. Lee and Dr. Harvey Lui provided valuable feedback and helpededit the manuscript.• Yuheng Wang, Jiayue Cai, Daniel C. Louie, Z. Jane Wang, Harvey Lui, Tim K. Lee, “Ap-plying Deep Learning and Traditional Machine Learning to Polarization Speckle Imagesfor Skin Cancer Detection”, submitted.The author contributed to part of the data analysis and provided editorial input on themanuscript. Yuheng Wang was responsible for formulating the problem, implementingthe proposed method, analyzing the results and writing the manuscript. Daniel C. Louiecollected the experimental data and provided editorial input on the manuscript. Dr. Z.Jane Wang, Dr. Harvey Lui and Dr. Tim K. Lee provided valuable feedback and helpededit the manuscript.• Aiping Liu, Soojin Lee, Jiayue Cai, Taomian Mi, Saurabh Garg, Laura Kim, Maria Zhu,Xun Chen, Z. Jane Wang and Martin J. McKeown, “Galvanic Vestibular StimulationviiiImproves Subnetwork Interactions in Parkinson’s Disease”, submitted.The author contributed to part of the data analysis. Dr. Aiping Liu was responsiblefor the problem formulation, data analysis and writing the manuscript. Dr. Soojin Lee,Taomian Mi, Laura Kim, Maria Zhu conducted the experiment and collected the data.Dr. Soojin Lee contributed to the medical interpretation and provided editorial input.Saurabh Garg performed the preprocessing of the data. Dr. Martin J. McKeown, Dr. Z.Jane Wang and Dr. Xun Chen provided valuable feedback and helped edit the manuscript.ixTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xivList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xx1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 An Overview on Functional Connectivity . . . . . . . . . . . . . . . . . . . . . . 21.2 Regional Signal Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.3 Brain Functional Connectivity Modelling . . . . . . . . . . . . . . . . . . . . . . 71.3.1 Brainstem Functional Connectivity Modelling . . . . . . . . . . . . . . . 101.3.2 Time-varying Functional Connectivity Modelling . . . . . . . . . . . . . . 121.4 Brain Functional Connectivity Analysis . . . . . . . . . . . . . . . . . . . . . . . 141.5 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151.6 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 PLS-based Regional Signal Representation for PPN Functional ConnectivityEstimation in PD: fMRI Effect of GVS . . . . . . . . . . . . . . . . . . . . . . . 202.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20x2.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.2.1 Subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.2.2 GVS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.2.3 MRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.2.4 Rs-fMRI Preprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.2.5 Proposed Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.2.6 Brainstem Regional Signal Representation and Brain Region Selection . 272.2.7 Functional Connectivity Analyses . . . . . . . . . . . . . . . . . . . . . . 302.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.3.1 Brain Region Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.3.2 Functional Connectivity Analyses . . . . . . . . . . . . . . . . . . . . . . 322.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393 PLS-based Regional Signal Representation for PPN Functional ConnectivityEstimation in PD: fMRI Effect of Walking Exercise . . . . . . . . . . . . . . 413.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.2.1 Subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.2.2 Ambulosono . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.2.3 fMRI Data Acquisition and Preprocessing . . . . . . . . . . . . . . . . . 443.2.4 Brainstem Regional Signal Representation and Brain Region Selection . 453.2.5 Functional Connectivity Analyses . . . . . . . . . . . . . . . . . . . . . . 453.2.6 Statistical Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.3.1 PPN Functional Connectivity Changes after Ambulosono Exercise . . . . 473.3.2 PPN Functional Connectivity Correlates with Clinical Scores . . . . . . . 473.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504 Constrained Canonical Correlation Analysis for Brain Functional Connec-tivity Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53xi4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.2.1 Density Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.2.2 Spatially Constrained CCA . . . . . . . . . . . . . . . . . . . . . . . . . . 584.2.3 Integration of Regional Activity Structure into Network Modelling . . . . 634.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644.3.1 Synthetic Data Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644.3.2 Real fMRI Data Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.4 Discussion and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 745 Graph Theory Method for Dynamic Brain Functional Connectivity Analysis 765.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 765.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 795.2.1 Subjects and Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . 795.2.2 Dynamic Functional Connectivity Estimation . . . . . . . . . . . . . . . 805.2.3 Graph Theoretical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 815.2.4 Statistical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 835.2.5 Disease Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 845.3 Experimental Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 855.3.1 Dynamic Graph Theoretical Analysis . . . . . . . . . . . . . . . . . . . . 855.3.2 Classification Performance . . . . . . . . . . . . . . . . . . . . . . . . . . 875.3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 905.3.4 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 945.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 956 Conclusion and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 966.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 966.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 986.2.1 Multi-task Brainstem-cortical Functional Connectivity Analysis . . . . . 986.2.2 Regional Signal Representation with Constrained Multiset Canonical Cor-relation Analysis for Brain Functional Connectivity Network Estimation 986.2.3 Deep Clustering for Automated Brain Parcellation . . . . . . . . . . . . 996.2.4 Application to Parkinson’s Disease Studies . . . . . . . . . . . . . . . . . 100xiiBibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102xiiiList of Tables2.1 Clinical information on PD patients. . . . . . . . . . . . . . . . . . . . . . . . . . 242.2 The 58 ROIs used in the analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.3 Statistics on significant left PPN functional connectivity changes induced by GVSstimuli . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342.4 Statistics on significant right PPN functional connectivity changes induced byGVS stimuli . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.1 Demographic and clinical information on PD patients . . . . . . . . . . . . . . . 433.2 The PLS-selected ROIs from the 80 ROIs used in this study . . . . . . . . . . . . 464.1 The ROIs used in this study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685.1 Participant demographic and clinical characteristics . . . . . . . . . . . . . . . . 795.2 The 76 ROIs used in this study . . . . . . . . . . . . . . . . . . . . . . . . . . . . 805.3 Description on graph measures used in this study . . . . . . . . . . . . . . . . . . 825.4 The classification performance of dynamic graph measures . . . . . . . . . . . . . 905.5 Comparison between the proposed work and the state-of-the-art in PD classifi-cation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91xivList of Figures1.1 A typical fMRI scan and the resulting fMRI signals. . . . . . . . . . . . . . . . . 31.2 An example of brain activation study. . . . . . . . . . . . . . . . . . . . . . . . . 41.3 An overview on the general pipeline of the ROI-based brain functional connec-tivity study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4 An illustration on anatomical structures of the brain. . . . . . . . . . . . . . . . . 101.5 An overview of the challenges and objectives of this thesis. . . . . . . . . . . . . . 192.1 The placement of the PPN ROI on the T1 sequence. . . . . . . . . . . . . . . . . 262.2 The proposed framework for brainstem-cortical functional connectivity estimation. 282.3 PLS-derived ROIs in the PD group. . . . . . . . . . . . . . . . . . . . . . . . . . 312.4 PLS-derived ROIs in the control group. . . . . . . . . . . . . . . . . . . . . . . . 322.5 The correlation relationship between the overall PPN functional connectivity andUPDRS scores. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332.6 The overall PPN functional connectivity differences between GVS on and off. . 342.7 The GVS impact on the connectivity between the left PPN and PLS-derivedregions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.8 The GVS impact on the connectivity between the right PPN and PLS-derivedregions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.1 Flowchart for the study protocol. . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.2 The functional connectivity of the left and right PPN. . . . . . . . . . . . . . . . 513.3 The PPN functional connectivity changes due to the walking exercise and relatedrelationships with the UPDRS score. . . . . . . . . . . . . . . . . . . . . . . . . . 524.1 A schematic overview of the proposed method. . . . . . . . . . . . . . . . . . . . 554.2 Simulation results for the first scenario. . . . . . . . . . . . . . . . . . . . . . . . 664.3 Simulation results for the second scenario. . . . . . . . . . . . . . . . . . . . . . . 67xv4.4 Example of decision graph and the process of automatically determining thenumber of clusters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694.5 Density clustering on the Putamen. . . . . . . . . . . . . . . . . . . . . . . . . . . 704.6 A fully connected brain network estimated by the proposed LA-cCCA methodfor one subject. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 714.7 Comparison of estimated brain functional connectivity matrices between twosessions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724.8 Comparison of the reproducibility for different methods. . . . . . . . . . . . . . . 734.9 Correlation between the variation in the weights and the size of ROI. . . . . . . . 755.1 The proposed framework for the classification of Parkinson’s disease. . . . . . . . 855.2 Example of functional connectivity network at one time point. . . . . . . . . . . 865.3 The comparison of standard deviations between HC and PD groups. . . . . . . . 875.4 The comparison of coefficients of determination in the AR model between HCand PD groups. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 885.5 The loadings on dynamic graph measures and clinical information in the CCAanalysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 895.6 The classification performance differences between including and excluding eachdynamic graph measure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 925.7 The comparison of classification performance using stationary graph measures,dynamic graph measures and a combination of stationary and dynamic graphmeasures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93xviGlossaryAD Alzheimer diseaseAR AutoregressiveBOLD Blood oxygen level dependentBSS Blind source separationCCA Canonical correlation analysisCSF Cerebrospinal fluidDAG Directed acyclic graphDBS Deep brain stimulationDCA Discriminant correlation analysisDCM Dynamic causal modelDEC Deep embedded clusteringDEPICT Deep embedded regularized clusteringDTI Diffusion Tensor ImagingEEG ElectroencephalogramFDR False discovery ratefMRI Functional magnetic resonance imagingFOG Freezing of gaitGLM General Linear ModelGPi Globus pallidus internusGVS Galvanic vestibular stimulationxviiHCP Human connectome projectHC Healthy controlICA Independent component analysisKKT Karush-Kuhn-TuckerLA-cCCA Local activity constrained canonical correlation analysisLASSO Least absolute shrinkage and selection operatorLDA Linear discriminant analysisMAR Multivariate autoregressiveMCCA Multiset canonical correlation analysisMCI Mild cognitive impairmentMEG MagnetoencephalogramMLC Mesencephalic locomotor centerPCA Principal component analysisPD Parkinson’s diseasePET Positron emission tomographyPI Postural instabilityPIGD Postural instability gait difficultyPLS Partial least squaresPPN Pedunculopontine nucleusRBF Radial base functionRMSE Root of mean square errorROI Region of interestSEM Structural equation modelSMA Supplemental motorSNc Substantia nigra pars compactaxviiiSNr Substantia nigra pars reticulataSNR Signal to noise ratioSTN Subthalamic nucleusSVM Support vector machineTD Tremor dominantUPDRS Unified Parkinson’s disease ratingxixAcknowledgementsMy doctoral study has been a challenging, memorable, and happy experience, with the generoussupport of many people. I would like to take this opportunity to thank all of them for beingwith me throughout this journey.First and foremost, I would like to express my sincerest gratitude to my supervisors, Dr.Z. Jane Wang and Dr. Martin J. McKeown, for all the support they gave me throughout myPhD journey. A very big thank you for their constant guidance, encouragement and patiencethat led me to grow as a research scientist. The advice they offered me both academically andpersonally have been invaluable in my life. I feel extremely fortunate for having them as mysupervisors and role models.I would also like to thank my committee members for their valuable time, efforts andcomments.I am thankful to all my labmates, Dr. Liang Zou, Dr. Jiannan Zheng, Dr. Pegah Kharazmi,Nandinee Haq, Yongwei Wang, Xinrui Cui, Jianzhe Lin, Tianze Yu, and Dan Wang, for creatingsupportive and fun environment. Many thanks go to Dr. Aiping Liu for her insightful adviceand great assistance in my academic journey. I would also like to thank Dr. Soojin Lee andSun Nee Tan for providing me with the data and valuable discussions on Parkinson’s diseasestudies.My heartfelt thanks to my parents for their endless love. I am deeply grateful for everythingthey have done to support me and the best education they gave me.Last but not least, a special thank goes to my husband, Yuheng Wang, for his love, supportand considerate care. I am always grateful for having you on my side through the hardshipsand joys.xxChapter 1IntroductionThe human brain, then, is the most complicated organization of matter that weknow. – Isaac AsimovOur brain is one of the most important and intricate parts of a human body, which controlsour actions, thoughts, feelings and memory. It has been a long-standing challenge for neu-roscientists to understand the underlying mechanism of the brain. A tremendous number ofinteracting neural elements consist of a complicated brain network. The mapping of brain net-works by conducting a connectivity analysis has thus been a rapidly moving field, advancingthe understanding of the organization of the brain.Brain connectivity can be delineated as structural or functional. Structural connectivitydenotes anatomical links (e.g., synapses or fiber pathways) of neuronal elements (neurons orbrain regions). It measures the physical presence of axonal projection in the brain, which canbe detected by diffusion tensor imaging. Such anatomical architecture supports the emergenceof physiological activity, giving rises to the concept of functional connectivity. Functionalconnectivity models the statistical dependence between spatially distributed neuronal elements,which is considered to provide the basis for information processing and mental representation.While structural connectivity provides the anatomical basis for functional connectivity, theexistence of functional connectivity is not only limited to direct structural connections, but alsocan be derived from indirect anatomical connections via mediating brain regions. In this thesis,we focus on functional connectivity to elucidate the functionally interregional coordination ofthe brain.Brain functional connectivity provides insights into the organizations of the brain in bothhealthy and diseased states. Neurological diseases, such as Alzheimer disease (AD), Parkin-son’s disease (PD), schizophrenia, affect a large population worldwide. Their relatively highprevalence and serious consequences have a significant impact on global health. Of particularimportance, neurological disorders can be characterized as dysconnection syndromes [163]. The1abnormal brain functional connectivity patterns could serve as potential biomarkers for neuro-logical diseases, assisting in the clinical diagnosis of the diseases. In addition, brain functionalconnectivity offers a promising way for the evaluation of therapeutic intervention. Therefore,the aim of this thesis is to develop novel methods to assess brain functional connectivity andexplore appropriate ways to quantitatively interpret/analyze the estimated brain functional con-nectivity networks, which ultimately leads to a better understanding of functional connectivitychanges induced by neurological diseases and/or clinical interventions.In this chapter, we provide a comprehensive introduction on brain functional connectivityand outline the objectives of this thesis. We first start with an overview on functional con-nectivity using fMRI data in Section 1.1, followed by Section 1.2, 1.3 and 1.4 where we reviewcurrent popular methods across the general pipeline of brain functional connectivity study, thatis, regional signal representation, brain functional connectivity modelling and brain functionalconnectivity analysis respectively. In Section 1.5, we then present the research objectives ofthis thesis. Finally, we describe the thesis outline in Section 1.6.1.1 An Overview on Functional ConnectivityThere are diverse modalities for studying brain functions, including Electroencephalogram(EEG), Magnetoencephalogram (MEG), Positron Emission Tomography (PET) and fMRI. EEGmeasures neural activity by recording electrical signals through electrodes placed on the scalp,and MEG measures brain activity by monitoring magnetic fields generated by electrical ac-tivity through sensitive magnetometers. These two neuroimaging techniques have advantagesin studying the temporal dynamics of neural activity because of the high temporal resolutionat the level of milliseconds. Nevertheless, they have a low spatial resolution with the level ofcentimeters and exhibit difficulties in localizing the underlying brain activity. PET is an imag-ing technique that measures brain metabolism and radioactivity by using a radioactive drug(tracer) to reflect the neural activity. It has a particular advantage in studying brain neuro-physiology and neurochemistry, such as monitoring the activity at dopamine receptors which isvery useful in the study of PD. Nevertheless, the temporal resolution of PET is very low fromtens of seconds to minutes, and the injection of radioactive tracer is required in a PET scan,which becomes limitations of this imaging technique.Among various neuroimaging techniques, fMRI has become prevalent and widely adopted,2in large part due to a relatively high spatial resolution and the non-invasiveness. It measures therelative changes in the blood oxygen level-dependent (BOLD) signal induced by neural activity.The BOLD signal indirectly measures brain activity via the effects on blood oxygenation andblood flow, affecting magnetic properties and MRI contrast in turn. Figure 1.1 shows anexample of fMRI scan and the resulting fMRI signals.(a) (b)Figure 1.1: (a) A typical fMRI scan and (b) the resulting fMRI signals. Image courtesy of [173].Conventional fMRI analysis has focused on determining brain areas activated during theconduction of certain tasks or under specific stimuli. In order to detect the effects of interest,it is necessary to use contrasts and repetitions in the fMRI experiment. This is usually doneby utilizing a block design, where subjects are asked to alternate between the task of interestand some control task such as at rest and repeat the tasks as often as possible. Figure 1.2(a)shows an example of a block design involving alternations between finger-tapping and rest.To locate brain activation in response to a certain task, statistical analysis is typicallyperformed using the univariate approach, i.e., by constructing a separate model at each voxel.The most commonly used method is the General Linear Model (GLM) [67], which considers thefMRI signals as a linear combination of model functions and noise. The GLM is formulated asY = Xβ +  (1.1)where Y is a vector representing the fMRI time courses from a single voxel, X is the design ma-trix reflecting the experimental design factors included in the model, β is a vector correspondingto the model parameters and  is the error term.After GLM is separately fitted at each voxel, a statistical test is performed on the estimatedmodel parameters to examine if each voxel is activated significantly in response to the task.3Figure 1.2: An example of brain activation study. (a) Block design in a fMRI experiment.Subjects perform the experiment of alternating blocks of finger-tapping and rest. (b) Statisticalparameter map for one subject. The colored regions indicate significant brain activation inresponse to a certain task (e.g., a finger-tapping task). Image adaption from [185].This results in a statistical parameter map across all voxels, where voxels with task-relatedsignificant activation are colored according to their significance levels (see Figure 1.2(b) for anexample).Rather than determining the isolated brain areas activated under experimental conditionsas mentioned above, recent fMRI studies have witnessed a change of focus from functional spe-cialization to functional integration. The study of functional integration aims to examine howdifferent brain regions connect, interact and communicate with each other, giving rise to the con-cept of “brain functional connectivity”. Brain functional connectivity provides a macroscopicview of functional coordination of the interacting brain regions. Since many neurological dis-eases can be delineated as dysconnectivity syndromes, brain functional connectivity study offerspromising ways for developing MRI-related biomarkers and understanding abnormal functionalintegration of diseased brains.With the emergence of brain functional connectivity, a particular type of paradigm, theso-called “resting-state” becomes prevalent in fMRI study. Unlike task-related brain activationstudies, resting-state fMRI, wherein the individuals are free of any task and required to relaxwithout thinking of anything, is well-suited to brain functional connectivity analyses, as the4intrinsic co-activation patterns of the brain are reflected. The studies of resting-state brainfunctional connectivity revealed that the brain is not idle during rest, but rather exhibitssubstantial spontaneous neuronal activity.Inferring brain functional connectivity from fMRI data can take place at voxel or Region ofInterest (ROI) level. In voxel-based models, there are usually a large amount of voxels involvedin the analysis, making such models less attractive in practice particularly since some models(e.g. Bayes network models) become impractical with very high-dimensional data. Second,statistical power is dramatically reduced due to the need to correct for multiple comparisons.Another critical issue is dealing with the fact that people’s brains are of different size and shape.To perform a group study using a voxel-based analysis, all brain images must be spatiallytransformed to a common template, possibly inducing registration errors, with unknown effectson downstream analyses. In contrast, with an ROI-based analysis, the ROIs can be defined ineach subject’s native space, without the need for a common registration process. Therefore,ROI-based models have been frequently adopted for analyses in fMRI studies. Figure 1.3 showsthe general pipeline for the ROI-based brain functional connectivity study.Figure 1.3: An overview on the general pipeline of the ROI-based brain functional connectivitystudy.51.2 Regional Signal RepresentationA key issue for assessing the ROI-based brain functional connectivity is how to represent theinformation in a given ROI. A common practice is to simply take the average signal from same-ROI voxels for regional signal representation. The simpleness and straightforwardness of theaverage signal method make it very popular and widely adopted by functional connectivitystudies. One drawback of this method lies in the possible functional inhomogeneity of the ROI.Since one ROI may actually encompass several functional sub-regions [88, 115], the use of theaverage signal ignores the intrinsic data structure and is prone to introduce biases, thus lessoptimally reflecting the on-going activity in the ROI [150, 206].Another way to represent ROI activity is to select a “representative” voxel for the ROIsignal representation. This representative voxel can be chosen based on a pre-defined seedvoxel [175, 186], or fMRI activation [176]. For the activation-based selection, the peak activatedvoxel can be selected as the representative voxel and its time signal can be used as the ROIrepresentative signal. Considering the fact that a single voxel may not be fully representative,an extensive way is to select a cluster of voxels around the peak voxel and take the averagetime signal of selected voxels as the ROI representative signal. Several strategies can be usedto choose the surrounding voxels, such as clusters that contain the peak voxel, a sphere or afew top contiguous voxels around the peak voxel.Alternatively, Principal Component Analysis (PCA) can be performed on time series ofall voxels in a ROI and the first principal component can be used as the ROI representationsignal. In [205], the combination of PCA and regression model was developed to assess brainfunctional connectivity from fMRI data. Another study used PCA in conjunction with Grangercausality to examine causal influences between distinct brain regions [206, 207]. This providesan alternative method for ROI signal representation in addition to the average signal method.However, the PCA method may also tend to be sensitive to functional inhomogeneity andexhibit poor reliability [181].To date, there have been limited studies investigating related approaches on regional sig-nal representation, compared to the relatively large number of studies developing novel brainfunctional connectivity modelling methods (on top of the estimated ROI signals). However,this is a general research problem worthy of careful investigation, since different ROI signalrepresentation strategies may significantly impact the subsequent results inferred from fMRI6data [176]. Extensive work will be necessary to develop appropriate regional signal representa-tion approaches that take into account intrinsic data structure of the ROIs for a reliable fMRIanalysis.1.3 Brain Functional Connectivity ModellingHuman brain can be considered as a complicated network consisted of a large number of differentbrain regions that interact with each other. Brain connectivity, particularly in this thesis, func-tional connectivity, studies such interaction relationship by examining the statistical associationbetween distinct brain regions. Brain functional connectivity modelling is often proceeded byspecifying a set of “functional nodes” and then analyzing functional connectivity between thesenodes. In ROI-based models, the nodes usually correspond to spatial ROIs identified based onanatomical brain atlas. Alternatively, the spatially independent components (accompanying bytheir associated time courses) obtained from independent component analysis (ICA) can alsobe used to define the nodes [4, 146, 195]. A variety of approaches have been developed forestimating brain functional connectivity between the ROIs, ranging from pairwise measures toglobal network models, from linear to non-linear measures, and from directional to bidirectionalmodels.The most straightforward one is correlation coefficient. The more correlated the time coursesare between two brain regions, the more possible it is that there is a functional connectionbetween them. Therefore, we can evaluate the brain functional connectivity by computing thecorrelation coefficients between any pair of brain regions and by setting up a threshold, withthose pairs of brain regions whose correlation coefficients are larger than the threshold beingconsidered associated with each other. However, correlation does not give necessary informationregarding whether or not the functional connectivity between a pair of brain regions is direct. Inthis case, another simple yet effective method, partial correlation [53, 107], is a more appropriateway to infer the direct brain functional connectivity, since it works by estimating the correlationbetween two time courses with the effect from other variables being removed. In addition tothe correlation method, mutual information [36, 204] is another widely used estimation methodwhich quantifies the shared information between two time courses and reflects linear as well as7nonlinear dependence relationships (Equation 1.2).I(X,Y ) =∑x∈X∑y∈Yp(x, y)logp(x, y)p(x)p(y)(1.2)where X and Y are two random variables, p(x, y) is the joint probability of X and Y , and p(x),p(y) are two marginal probabilities of X and Y respectively.Correlation, partial correlation and mutual information are popular estimation approaches,however, they cannot solve the problem of the direction of the functional connection. For theestimation of the direction, one of the common approaches is Granger causality [40, 140] whichis a lag-based measurement. It defines causality based on the statistical interpretation whereone variable X is considered to cause another variable Y if X can at least partially contributeto the prediction of Y . Another available method is Patel’s conditional dependence measure[129, 154] which estimates the causality by looking at the imbalance of conditional probabilitybetween two variables.Different from the aforementioned pairwise brain functional connectivity estimation meth-ods, some multivariate regression models, such as structural equation model (SEM) [21, 153],multivariate autoregressive (MAR) model [77, 144] and dynamic causal model (DCM) [66, 171],have also been widely used for brain functional connectivity studies. While SEM aims to es-timate the instantaneous interaction between brain regions, MAR characterizes inter-regionalrelationships utilizing lag-based models which incorporates temporal effects one brain regionhas on another. The MAR method models one sample of an N-dimensional time courses as alinear combination of its previous ones, as formulated in Equation 1.3. Different from SEM andMAR, DCM deals with the nonlinear and dynamic activities between brain regions, and theneuronal activities are modeled as hidden variables.xt =P∑p=1Apxt−p + p (1.3)where xt is an N-dimensional vector representing the fMRI signal of N ROIs at the tth timepoint, p is the order of the model with the maximum value of P , Ap is an N × N matrix ofcoefficients (weights) at the time lag of p, and p is the error term.The multivariate regression models are statistically rigorous and relatively flexible methodswith many available algorithms being developed. However, one disadvantage of these models8concerns their computational feasibility. When considering the computational cost, regularizedinverse covariance is an effective way to assess the brain functional connectivity. The inversecovariance matrix (precision matrix) has been used to infer brain functional connectivity, encod-ing conditional independence relationships between brain regions. Under the assumed sparsenature of brain functional connectivity networks, a regularization strategy, such as the LASSOmethod 1 can be applied to impose a sparsity constraint on the inverse covariance matrix,leading to a sparsity structure on the coefficients [31, 64]. A sparse estimate of the inversecovariance matrix can be obtained by minimizing the penalized negative log likelihoodΘˆ = arg min {tr(SΘ)− log |Θ|+ λ ‖Θ‖1} (1.4)where Θ is the inverse covariance matrix, S is the sample covariance matrix, ‖Θ‖1 is theelement-wise L1-norm of Θ, and λ is the penalty parameter controlling the sparsity of thenetwork.Graphical models have been employed to estimate brain functional connectivity and at-tracted increasing attention in the field of brain functional connectivity network modelling.Bayesian network [119, 188] is a typical graphical model which is based on conditional indepen-dence relationships among the variables. For example, PC algorithm (“Peter and Clark”;[114])is one of the popular Bayesian network modelling methods. It searches for causal graphs underthe constraint of directed acyclic graph (DAG), first constructing the structure of the graphbased on conditional independence and then determining directions with a specific set of rules.An extension of PC algorithm was also proposed by incorporating a false discovery rate (FDR)control [97].Overall, brain functional connectivity modelling is a rapidly moving research area, attractinga large number of researchers to make diverse contributions. Based on different assumptions, avariety of novel approaches have been proposed to address certain aspects of brain functionalconnectivity modelling, all having their own advantages and limitations. In real applications,different methods have been employed according to the specific demands in certain scenarios,resulting in a collection of significant findings that provide insights into disease mechanism interms of brain functional connectivity. Recent fMRI studies have witnessed a huge growth inthe area of brain functional connectivity; over the coming years, brain functional connectivity1LASSO: Least Absolute Shrinkage and Selection Operator, a regularization method for linear regressionwhich minimizes the objective function with a bound on the sum of the absolute values of the coefficients.9will remain a vital tool and receive further growth regarding both technical and modellingchallenges, and its applications.1.3.1 Brainstem Functional Connectivity ModellingBrainstem is extremely important in the neural system, which is located at the posterior partof the brain, as shown in Figure 1.4. Many neurological diseases can involve in functionaldisruptions of the brainstem, such as PD, AD and multiple sclerosis. Even small lesions in thebrainstem can have profound effects and result in serious neurological deficits. There are variousnuclei in the brainstem, which are important components of almost every functional neuralsystem, controlling for many body functions such as motor, sensory, circulation, respiration andmood. It has been suggested by some experts that a complete dysfunction of the brainstem isequal to the death of the brain.Figure 1.4: An illustration on anatomical structures of the brain. Image adaption from [190].Exploring functional connectivity of the brainstem not only facilitates a comprehensiveunderstanding of brain functions, but also contributes to unravelling the pathogenesis of manybrain disorders and the development of potential treatment strategies. In clinics, brainstemremains a major target for many neurological disorders. For example, in PD, gait impairmentis associated with increased fall risk, which remains a major source of morbidity in patients.The pedunculopontine nucleus (PPN) is one of the brainstem nuclei, which importantly involvesin the control of gait due to its close interconnections with cortical motor areas. Inspired by itsvital function, a novel treatment, deep brain stimulation (DBS), has been developed targetingat the PPN for ameliorating gait freezing in PD.10Despite the indisputable importance of the brainstem, it is frequently neglected by neu-roimaging communities in the studies of brain functions and dysfunctions. To date, the vastmajority of fMRI studies have been focused on the functional connectivity between corticaland subcortical brain regions, however, the functional connectivity of the brainstem is poorlyunderstood. Several reasons that hindered the study of brainstem functional connectivity in-clude: (1) Compared to other cortical/subcortical brain regions, brainstem nuclei are alwaysvery small with an average diameter level of only a few millimeters, which makes it difficult tolocalize their anatomical structures. (2) Due to its peculiar anatomical locations, fMRI signalsfrom the brainstem suffer from strong physiological noise including respiration and pulsation.(3) Different brainstem nuclei with distinct functions can be located very close to each other,leading to difficulties in distinguishing these structures.Although brainstem is a tough structure which exerts difficulties on related research, therecent few years have witnessed some significant advances in brainstem fMRI studies. Some pi-oneering studies have successfully examined the activity of single brainstem nuclei [52, 57, 174].Consecutively, Baissner et al. investigated for the first time the inter-nuclear and nucleo-corticalconnectivity, wherein they identified intrinsic brainstem networks and inferred the brainstem-cortical functional connectivity using fMRI data [16]. More recently, Ba¨r et al. investigatedtopological characteristics of brainstem nuclei using graph theory. These studies advanced thefundamental understanding of human brainstem functions [12]. In addition, other studies inves-tigated the mechanism of functional brainstem disruptions in neurological diseases, suggestingaltered brainstem functional connectivity patterns in patients [58, 156]. Such studies demon-strated contributions of brainstem degeneration to the pathophysiology of brain diseases andprovided insights into potential biomarkers and treatment strategies of neurological disorders.With regard to the methods, technically speaking, all general brain functional connectivitymodelling methods can be used to estimate the brainstem functional connectivity. For example,in voxel-level analysis, seed-based analysis was utilized to estimate functional connectivity ofseveral brainstem nuclei in [156]; another study applied ICA to detect functional brainstemnetworks from the whole brainstem BOLD signals [16]. Other popular approaches, such as(partial) correlation and SEM were also utilized to assess brainstem functional connectivity[12, 83, 167].It should be noted that because of the anatomical peculiarity one needs to be particu-larly careful when inferring brainstem functional connectivity. Due to the structural differ-11ences between cortical/subcortical regions and brainstem, many procedures operated on cor-tical/subcortical regions may be sub-optimal for brainstem structures. For example, sincebrainstem nuclei are always quite small, the error can be larger than the average size of thestudied structures during the whole brain registration, leading to less precise results. Therefore,it would be desirable to use appropriate procedures specially tailored for brainstem structures.In [12], a separate fMRI preprocessing steps were carried out on the brainstem to avoid potentialproblems. In addition, special care needs to be taken to reduce physiological noise in brainstemstructures. This can be done by recording physiological signals during fMRI scans and then per-forming temporal noise regression [26]. Alternatively, Baissner et al. developed a novel maskedICA method to suppress physiological noise of the brainstem [16]. This method restricted ICAanalysis to an anatomical brainstem mask based on the observation that the major physiologi-cal noise came from the vicinity instead of the inside of the brainstem. Another issue concernsthe BOLD signal representation of brainstem nuclei. Despite the small size of brainstem nuclei,they tend to have a relatively large functional heterogeneity. Hence, the commonly used aver-age time courses may not optimally represent brainstem ROI signals. Appropriate ROI signalrepresentation methods would be in demand for brainstem fMRI studies.1.3.2 Time-varying Functional Connectivity ModellingIt is of great interest in assessing the brain functional connectivity, advancing our understandingof functional brain organizations. However, most brain functional connectivity studies havebeen conducted with the assumption that the interactions between distinct brain regions areinvariant, and thus providing static descriptions of functional connectivity. Until recently, ithas been proposed that investigating temporal variations in functional connectivity may offergreater insights into fundamental brain network properties [82]. This encourages the emergenceof the modelling of dynamic brain functional connectivity.Sliding window analysis is a common method for examining the dynamics in brain functionalconnectivity. This approach works by identifying a time window of fixed length and shiftingthis time window by a certain number of data points. In principle, any functional connectivitymetric that can be applied to the static-assuming investigations, such as correlation, can be usedto assess the time dependent functional connectivity at each time window in the sliding windowanalysis. Recently, regularized precision matrix [189] and multiplication of temporal derivatives[157] have been introduced for the within-window functional connectivity estimation. However,12one issue concerning the sliding window approach is choosing the window size. If the windowsize is too small, it will not allow for the robust estimation of functional connectivity; otherwise,if the window size is too large, it will not detect the potential interesting transients. Also, thecommon choice of window shape, rectangular window which assigns the same weights to thetime points inside the window, may increase the sensitivity to the noise. Alternatively, taperedwindow has been employed in some recent studies [13, 43].To circumvent the issue associated with the window choice, one may consider using time-frequency analysis [37, 198] which can be implemented with the wavelet transform coherence.With this approach, there is no need to apply a fixed window size. Instead, the effective windowis adapted according to the intrinsic time-scale of the frequencies in original signals. Time-frequency analysis allows the temporal exploration of functional connectivity across a range offrequencies, resulting in a rich time-frequency map for each pair of ROIs. One drawback of thismethod concerns the large number of information resulted from the analysis, which inducesadditional steps to handle the growth of outputs.Another approach that avoids the arbitrary choice of window is to use a data-driven methodto determine time change points in brain functional connectivity, which is called dynamic con-nectivity regression (DCR) [49]. This method performed a recursively temporal partition using abinary search tree structure and estimated interaction relationships between ROIs using graph-ical Lasso. It enables both the detection of change points and the estimation of functionalconnectivity within each temporal interval. However, the computational cost of DCR methodcan be extremely high with a large number of ROIs. To deal with high-dimensional data, anadjusted version, called dynamic connectivity detection (DCD) [197], can be employed to inferthe time-varying functional connectivity.Efforts towards the explicit temporal modelling, i.e., including the influence of time onbrain functional connectivity in the computational model, have also been dedicated for studyingdynamic functional connectivity. One example is the modelling of temporal smoothness, thatis, temporally adjoining brain functional connectivity networks have similar network structuresand connection strengths. Such studies include fused multiple graphical lasso (FMGL) [189],sticky weighted time-varying model (SWTV) [99] and time-varying graphical lasso (TVGL)[29]. In these studies, the temporal smoothness was achieved by imposing a fused penaltywhich encouraged the adjoining brain functional connectivity networks to have similar patterns.Another attempt is to apply hidden Markov model (HMM) to model dynamic brain functional13connectivity [56, 169], wherein the brain is assumed to stay at one particular state correspondingto every time point.Since the initial findings on dynamic behavior of functional connectivity, increasing atten-tion has been paid to investigate time-varying functional connectivity. Capturing temporalchanges on functional connectivity enables the exploration on the full extent of brain activityand expands our understanding of the dynamic evolution of functional networks. Althoughmany methodological variants have been proposed, studies on examining the utility of braindynamics for assessing brain disease states are still in its infancy. Further work on the in-terpretation of dynamic brain functional connectivity networks and its underlying relationshipwith neurological disorders will be in demand, providing new potential biomarkers on MRIassessment of brain diseases.1.4 Brain Functional Connectivity AnalysisIn the last section, we focused on the examination of brain functional connections betweendistinct brain regions. By extension, another problem of interest is how to extract usefulinformation from the inferred brain functional connectivity network. Such process will helpanswer many exciting questions such as what the underlying organizations of brain functionalconnections are, how well our brain can process the information and which brain regions mayact as specialized roles in this information processing system.One popular way to extract meaningful information from functional connectivity networksis to utilize graph theoretical analysis, which characterizes the architecture and information flowof brain networks. One of the popular graph theoretical studies using fMRI data is related tosmall-worldness of brain networks, which displays both short path lengths and high clusteringlevels [28]. There have been studies showing the small-worldness in human brain networks[15], indicating that our brain is an efficient information processing system. Also, topologicalproperties of brain networks can be quantitatively described by many other graph measuressuch as clustering coefficient, modularity, global efficiency, characteristic path length, centralityand node degree[28]. These topological properties help provide a comprehensive understandingof brain network organization, and assist in the assessment of disease states. In literature,altered graph theoretical properties have been found in different neurological diseases, such asAD, PD and schizophrenia [10, 14, 170] , suggesting the abnormal functional organization of14diseased brain networks.With the prevalence of dynamic brain functional connectivity studies, dynamic graph the-oretical analysis has been explored as well, examining the temporal changes in topologicalproperties of brain networks. By applying dynamic graph theoretical analysis, graph measuresare computed on each temporal brain network, yielding a series of graph measures over time.It should be mentioned that temporal models (e.g., the smoothness between subsequent timepoints) can also be used in the level of graph measures [118]. Recent studies have shown thatvarious graph measures exhibited temporal fluctuations, suggesting functional reorganizationof brain networks over time [203].In particular, further analysis can be required for dynamic brain functional connectivitynetworks to get potentially useful insights from the rich temporal and spatial information. Forexample, clustering methods can be applied to the correlation matrices calculated from slidingwindow analysis to extract reproducible, transient functional connectivity patterns, which canbe termed as “connectivity states”. K-means clustering [4] and hierarchical clustering [201] havebeen employed in such a manner to extract connectivity states. Alternatively, modularity [202],temporal ICA [199], PCA [96], HMM[125] approaches have also been introduced to describedynamic functional connectivity states.Extracting useful information from the inferred brain networks prompts the meaningful in-terpretation of functional connectivity. Such analysis advances our understanding of underlyingworking mechanism of both the healthy and diseased brains. Further work will be of interestto discover effective network features for the assessment of diverse neurological diseases.1.5 Research ObjectivesThe study of brain functional connectivity provides deep insights into the large-scale brain func-tional coordination. It not only helps with the understanding of the fundamental mechanism ofbrain functioning at the normal state, but also reveals the disrupted brain interaction patterns atthe diseased state. While inferring brain functional connectivity can take place at voxel or ROIlevel, this thesis focuses on the latter and aims to develop novel methods to address fundamentalproblems associated with ROI-based brain functional connectivity study, including regional sig-nal representation, brain functional connectivity modelling, and brain functional connectivityanalysis. Additionally, brain ROIs can be broadly categorized into cortical/subcortical ROIs15and brainstem structures, we aim to study both of them in this thesis.Motivated by the particular applications in our study, we are interested in addressing the fol-lowing concerns and challenges. First, the brainstem is an extremely important part of the braininvolving in almost every function of human bodies. Inferring brainstem functional connectivitycan make a profound contribution to understanding the pathophysiology of brain diseases anddeveloping treatment strategies. However, relatively few studies have been conducted to modelfunctional connectivity of the brainstem, in large part due to its anatomical peculiarity. It isa challenging problem to get reliable fMRI signals from the complicated brainstem structuresand represent their regional signals in a reasonable manner.Second, representing the signal in a given ROI is an important issue for assessing the ROI-based brain functional connectivity. With most current approaches, the signals from same-ROIvoxels are simply averaged, neglecting any inhomogeneity in each ROI and thus less optimallyreflecting ongoing activity in the ROI. Therefore, improved brain functional connectivity mod-elling methods that incorporate intrinsic data structure for regional signal representation arerequired to guide the fMRI analysis.Finally, interpretation of the inferred brain functional connectivity networks is also chal-lenging because of the spatial complexity. After the estimation of brain functional connectivitynetworks, extracting the useful information from the complex network, particularly in the dy-namic setting which contains rich spatiotemporal information, is anything but easy. Seekingappropriate summary measures is required to facilitate the interpretation and assist in theassessment of brain disease states.The objective of this thesis is to address the aforementioned challenges present in the gen-eral pipeline of ROI-based brain functional connectivity study, including regional signal repre-sentation, brain functional connectivity modelling, and brain functional connectivity analysis.Specifically, the main contributions of the thesis are summarized as follows:• Propose a brainstem-cortical functional connectivity modelling framework which incor-porates a novel brainstem regional signal representation method and special care in thepreprocessing. The proposed framework was applied to assess functional connectivityof one particular brainstem nucleus – pedunculopontine nucleus, and perform treatmentevaluations of two kinds of therapeutic interventions in PD.• Develop a novel method of representing ROI activity and estimating brain functional16connectivity that takes the regionally-specific nature of brain activity, the spatial locationof concentrated activity, and activity in other ROIs into account.• Propose the use of dynamic graph theoretical measures to extract useful information frombrain functional connectivity networks as potential MRI-related disease biomarkers. Inparticular, a novel graph spectral metric, Fiedler value, is introduced for studying thedynamics of brain functional connectivity.Figure 1.6 illustrates challenges and objectives of the thesis.1.6 Thesis OutlineThe rest of the thesis is outlined as follows:In Chapter 2 and Chapter 3, we propose a novel framework for brainstem-cortical func-tional connectivity modelling where the regional signal of brainstem nuclei is represented byusing partial least squares approach and the connections between brainstem nuclei and othercortical/subcortical brain regions are estimated by partial correlation. Additionally, consid-ering the anatomical peculiarity of the brainstem, in our proposed framework, special care istaken in the preprocessing wherein a separate brainstem motion correction is performed. Weapply the proposed framework to assess functional connectivity of one particular brainstem nu-cleus – pedunculopontine nucleus. Specifically, we investigate the effect of Galvanic VestibularStimulation (GVS) and walking exercise on the PPN functional connectivity in PD respectively.In Chapter 4, we propose a novel method for simultaneous regional signal representationand brain functional connectivity estimation. The proposed method detects regional-specificnature of brain activity via density clustering and incorporates such intrinsic structure intoROI signal representation and brain functional connectivity estimation via constrained canon-ical correlation analysis. We evaluate the proposed method on both simulated and real fMRIdata, resulting in higher accuracy of brain functional connectivity estimation and/or a morereproducible connectivity pattern.In Chapter 5, to facilitate the interpretation of the estimated brain functional connectivitynetworks, we leverage graph measures to extract useful information from dynamic brain func-tional connectivity networks. Dynamic graph measures and the potentials of such dynamics1Ambulosono: A home-based music walking program.2CCA: Canonical Correlation Analysis.17as MRI-related biomarkers of PD are investigated. In particular, we propose a novel graphspectral measure to characterize global integration of brain functional connectivity networks inPD and evaluate its important role in the disease assessment.Finally, Chapter 6 presents a summary of the thesis contributions and discusses future work.18Figure 1.5: An overview of the challenges and objectives of this thesis1,2.19Chapter 2PLS-based Regional SignalRepresentation for PPN FunctionalConnectivity Estimation in PD:fMRI Effect of GVSAnatomically, the brain can be broadly divided into two categories: cortical/subcortical re-gions and brainstem structures. While functional connectivity between cortical/subcorticalregions is commonly studied, functional connectivity between brainstem structures and corti-cal/subcortical regions is rarely investigated. In this chapter, we propose a novel framework toassess brainstem-cortical functional connectivity, wherein a separate brainstem motion correc-tion is performed to cope with the anatomical peculiarity of the brainstem, and the partial leastsquares method is introduced for brainstem regional signal representation (see Figure 1.5). Theproposed framework is applied to investigate functional connectivity of one particular brainstemnucleus – the PPN. Specifically, we investigate the effect of GVS on PPN functional connectivityin PD.2.1 IntroductionFalls in older adult populations are a significant cause of morbidity and mortality [32] withnon-fatal injuries initiating a vicious cycle leading to a fear of falling, social isolation, loss ofindependence, deconditioning, and a significantly greater use of health care services [165, 193].In Parkinson’s Disease, gait disturbances such as decreased stride length and gait variabilityare associated with increased risk of falls. Balance and gait deficits in PD are frequentlyrefractory to therapy [9, 133] and may be actually worsened by pharmacological and surgical20interventions [18], making falls a significant source of morbidity in PD [152]. Freezing of gait(FOG) is a syndrome normally seen in advanced PD and can occur when subjects are eitheron or off medication. FOG may be partly due to a failure to adequately scale amplitudes forthe intended movement [39] and/or defective motor programming setting by the SupplementalMotor Area (SMA) and its maintenance by the basal ganglia, leading to a mismatch betweenintention and automation [39].Cognitive and motor function must be carefully integrated to execute gait. Dysfunctionof the basal ganglia in PD results in impaired motor control of skilled voluntary movements[104] and movements become excessively slow and underscaled in size [17]. Biochemically,imbalance in multiple neurotransmitters (including but not limited to dopamine, acetylcholine,and GABA) is seen not only in basal ganglia and motor structures, but also limbic circuitries[124, 132]. Balance disturbance and falls in PD may be more related to disruption in cholinergicrather than dopaminergic neurotransmission [20].A key part of the subcortical cholinergic system is the pedunculopontine nucleus, whichappears critically involved in gait disturbances in PD [1, 5, 111], as PPN neuronal loss isevident in PD [138] (Note that although we refer to the PPN throughout this thesis, at theresolution of the imaging used here, it would perhaps be more accurate to refer to this regionas the mesencephalic locomotor region as it likely includes the cuneiform nucleushowever, weuse PPN as this terminology is consistent with much prior literature (e.g., [1, 5, 111]).Connectivity to/from the PPN appears critical for FOG in PD [61]. Structural deficits inconnectivity are evident between basal ganglia-PPN and other tracts in FOG [61, 182]. Diffusiontensor imaging (DTI) tractography obtained with 3T MR imaging in PD patients with FOG hasdemonstrated asymmetrically decreased connectivity between the PPN and the SMA, comparedto PD subjects without FOG [61]. FOG is also associated with diffuse white matter damageinvolving major cortico-cortical, corticofugal motor, and several striatofrontal tracts with DTI[182]. In addition to structural/anatomical connectivity, advanced neuroimaging techniqueshave enabled the studies of functional connectivity, which refers to the statistical temporaldependences between anatomically separated brain regions, to reveal the functional communi-cation in the brain. Functional imaging studies (e.g., fMRI) have reported increased activityor altered connectivity during gait visualization in the midbrain locomotion centers betweenFOG episodes [75], possibly reflecting compensatory mechanisms which might be overwhelmedwith stress by turning or multitasking [158]. Moreover, resting-state functional magnetic reso-21nance imaging (rs-fMRI) has allowed the inference of functional connectivity by measuring thelevel of spontaneous co-activation between fMRI time courses of brain regions recorded duringrest. In vivo functional connectivity studies with rs-fMRI suggest that FOG patients may havesignificantly altered connectivity between PPN-SMA [61], which might reflect a maladaptivecompensatory mechanism.While the PPN has most often been investigated in PD in the context of FOG, it is unclearif altered PPN activity is present in non-FOG PD patients. Surgical targeting of the PPN isusually reserved for people with FOG resulting in significant impairment. Yet, even in earlystages of the disease, there are a number of ways in which Parkinsonian gait is different fromcontrols. While mildly affected PD patients can usually perform simple straight-line walk taskswithout difficulty, they experience difficulties with turning, and when performing simultaneousmotor or cognitive tasks (dual tasks), and/or crossing obstacles [22, 33]. They may have anabnormal gait pattern characterized by a shortened stride length, increased stride variability,and reduced walking speed [27, 116].Ways to modulate PPN activity and connectivity have proven elusive. Acetylcholinesteraseinhibitors may affect the PPN but such effects are likely to be modest. PPN DBS has beenshown to (inconsistently) improve gait difficulties in PD [1, 74, 111, 130, 177, 191]. However, thePPN tends to be spatially diffuse and is difficult to visualize on standard T1-weighted images,making electrode placement for DBS therapy difficult. Another potential way to modulatePPN is through the vestibular system, as PPN neurons tend to be highly vestibular-responsive[6]. GVS is a non-invasive technique that activates vestibular afferents to the thalamus andalso the basal ganglia [166] which in turn are directed to the PPN [184], possibly explainingwhy GVS may positively impact posture/standing balance in PD [85]. A few studies havedemonstrated that noisy GVS improved postural and balance responses [127, 149] as well asmotor deficits in PD [93, 94, 128, 200]. These studies have speculated that noisy vestibularinput may have improved information flow through the basal ganglia via stochastic facilitation(SF). SF is a phenomenon observed in a non-linear system where stochastic biological noiseparadoxically increases sensitivity of a system to detect a weak stimulus possibly resulting infunctional benefits [113]. In addition to noisy stimuli, sinusoidal stimuli have been suggestedas a means to activate steady-state, as opposed to transient balance responses that would beinduced with pulsed stimuli [91]. Sinusoidally oscillating stimuli may also activate irregularvestibular afferents [69] relying on voltage dependent K-channels [55]. While a couple of fMRI22studies have shown sinusoidal GVS modulated activations in various brain regions [54], GVS’sinfluence on the PPN has not yet been investigated. A recent study in healthy older adults(n = 20) found that noisy GVS resulted in sustained reduction in Centre of Pressure (COP)parameters, such as velocity, and Root Mean Square (RMS) [68]. The mechanisms of thisreduction was speculated to be on the basis of induced synaptic plasticity in the vestibularnuclei and the flocculus of the cerebellum, but effects on the PPN were not considered [68].Given the non-invasive, and potentially portable nature of GVS, we wished to determineif PPN functional connectivity could be modulated in mildly-affected PD subjects who maydemonstrate reduced stride length for example, and thus may be at increased risk for falls, butdid not exhibit FOG. Thus, in this chapter, we proposed a novel framework for brainstem–cortical (e.g., PPN–cortical) functional connectivity estimation. We then applied the proposedframework to investigate whether or not functional connectivity between the PPN and othercortical/subcortical regions could be reliably assessed, whether or not these connections weresignificantly modulated by GVS, and if the connectivity was modulated in a stimulus-specificmanner. Since a priori knowledge about functional connectivity to/from the PPN at the spatialand temporal resolution afforded by fMRI is unknown, this was essentially an exploratoryapproach. Careful care was taken to detect robust activation from PPN structures by analyzingthe data in native space (without registration to a template) and utilizing subject-specificweightings of voxels within the PPN region. We demonstrated that PPN functional connectivityis sensitive to vestibular stimulation in PD in a stimulus-dependent manner.2.2 Methods2.2.1 SubjectsTwenty-three PD patients (see Table 2.1 for the clinical information) and 12 age-matchedhealthy controls [5 females; age: 63.3± 10.4 (mean ± standard deviation)] participated in thestudy. The PD patients had mild to moderate PD (Hoehn and Yahr stage IIII) (see Table2.1) and were scanned at the on-medication state. All participants were recruited from thePacific Parkinson’s Research Centre (PPRC) at the University of British Columbia (UBC) andprovided written, informed consent prior to participation. All studies were approved by theUBC Ethics Review Board. The data were collected in two experiments: in the first groupGVS was assessed both ON and OFF L-dopa medication and has been partially reported in a23separate short report [93], and the second group were only assessed in the ON medication state.Only the ON medication studies from the first group are reported here. In the first group,UPDRS scores were assessed in the OFF medication state, while in the second group UPDRSscores were assessed in the ON medication state. A regression model was used to control forthese differences (described below).Table 2.1: Clinical information on PD patients.CharacteristicsStatistics(mean ± standard deviation)Age 66.4 ± 7.0Sex 17 males, 6 femalesUPDRS motor score 22.3 ± 12.4UPDRS assessed during on/off 13 on-medication, 10 off-medicationHoehn and Yahr stage 1.9 ± 1.0LEDD 988.8 ± 798.9UPDRS = Unified Parkinson’s Disease Rating Scale; LEDD = L-dopaEquivalent Daily Dose.2.2.2 GVSDigital signals of the GVS stimuli were first generated on a PC with MATLAB (MathWorks,MA, USA) and were converted to analog signals via a NI USB-6221 BNC digital acquisitionmodule (National Instruments, TX, USA). The analog command voltage signals were thensubsequently passed to a bipolar, constant current stimulator (DS5 model, Digitimer Ltd.,U.K.). The DS5 constant current stimulator was isolated in the console room with the outputcable leading into the scanning room through a waveguide. Along the twisted coaxial outputcable, four inductance capacity filters spaced 20 cm apart and tuned for the Larmor frequency(128 MHz) were custom-built. Near the subject, high-resistance radiotranslucent carbon-fiberleads (Biopac Inc., Montreal, Canada) were connected to pre-gelled Ag/AgCl electrodes thatwere MR-compatible (Biopac Inc., Montreal, Canada). For bilateral stimulation, an electrodewas placed over the mastoid process behind each ear. Since the GVS stimuli are alternatingcurrent (AC), the anode and cathode are not fixed on one side (as for DC) but they arealternating. The order of GVS condition was kept consistent to be rest, noisy GVS, andsinusoidal GVS across all the participants. The potential caveat of keeping the sequence the24same is the case where there are any post-stimulation effects. To avoid such confounding effects,we allowed a 2-min break between the two GVS conditions. To the best of our knowledge, after-effects of GVS on cortical activation have not yet been investigated. However, we think that thebreak time was sufficient to avoid after effects based on literature on after-effects of transcranialalternating current stimulation [168].Since individuals have an inherently subjective perception of GVS, prior to scanning, wedetermined the individual sensory threshold level (cutaneous sensation at the electrode site)utilizing systematic procedures used in prior GVS studies [81, 178, 192]. We delivered twodifferent types of stimuli at 90% of the individual threshold level: noisy and sinusoidal. Thenoisy stimulus was zero-mean with 1/f-type power spectrum between 0.1 and 10 Hz and thesinusoidal stimulus was a 1 Hz sine wave.2.2.3 MRIResting-state data were collected on a 3 Tesla scanner (Philips Achieva 3.0T R3.2; PhilipsMedical Systems, Netherlands) equipped with a 8–channel head coil. During the scanning,all the subjects were instructed to be awake with eyes closed. High-resolution T1 weightedanatomical images were acquired using the following parameters: a repetition time of 1970 ms,echo time of 3.9 ms, inversion time of 1100 ms and flip angle of 15◦. BOLD contrast echo-planar(EPI) T2*-weighted images were taken with the following specifications with a repetition timeof 1,985 ms, echo time of 37 ms, flip angle of 90◦, field of view of 240.00 mm, matrix size of128× 128, and with pixel size of 1.9× 1.9 mm. The duration of each functional run was 8 minfor rest condition and 5 min for GVS condition with noisy and sinusoidal stimulus, respectively.As stated above, the order of functional runs was rest, noisy GVS and sinusoidal GVS, andit was kept consistent across all subjects. We allowed 2 min gaps after the noisy stimulus toaccount for possible post-stimulation effects.An ROI presumed to include the PPN and cuneiform nucleus was drawn manually on theT1 sequence at the level of the superior cerebellar decussation between medial lemniscus andsuperior cerebellar peduncle [7, 210] (Figure 2.1). T1 and the fMRI data were registered viaFLIRT (with Boundary-Based Registration option) in FSL [161]. The PPN voxels drawn onthe T1 were then registered to the fMRI data by applying the inverse transformation calculatedby registering the fMRI to the T1 weighted image. After registration, we included neighboringvoxels around PPN voxels in our analysis to account for possible partial volume effects.25Figure 2.1: The placement of the PPN ROI on the T1 sequence. The red area represents wherethe PPN ROI is placed.2.2.4 Rs-fMRI PreprocessingThe acquired fMRI data were preprocessed using both AFNI and SPM8 software packages. Onthe whole brain, several preprocessing steps from the AFNI software package were performed.These included despiking, slice timing correction, and 3D isotropic correction (3 mm in eachdimension). While the subjects were asked to keep the head still during the scanning session,some head movements occurred during the acquisition process. Motion correction using rigidbody alignment was performed to correct for any major head motion during the scan. Besidesthe fMRI scans, we also collected a T1-weighted structural scan of each of the participants.FreeSurfer was performed on the T1-weighted scans to get the different ROI masks in the T1space. Each of the subjects’ structural scans was then registered to the fMRI scan using rigidregistration. This registration step provided us with the FreeSurfer segmented ROI mask inthe fMRI space. All analysis was done in the individual fMRI space rather than transformingall fMRI data to a common template. This was done to prevent introducing any unwanteddistortions in the fMRI data by registering it to a common template. In the next step, sev-26eral sources of variance such as head-motion parameters, their temporal derivatives and theirsquares, white-matter signal, cerebrospinal fluid (CSF) signal were removed using nuisance re-gression. The fMRI signal was then detrended, and any linear or quadratic trends in the fMRIsignal were removed. The signal was then iteratively smoothed until it reached 6 FWHM ofsmoothness. Finally, bandpass filtering was performed to retain the signal between the recom-mended frequencies of interest (0.01-0.08 Hz).Since the brainstem can move independently from the rest of the brain, motion correctionon the whole brain motion estimates may not be ideal. Therefore, a separate motion correctionof the brainstem was performed. First, the brainstem mask was generated using FreeSurferon the T1-weighted image of the same subject. The mask was then transferred over to thefMRI using registration as mentioned before. The registered mask was then dilated using aspherical structuring element of radius 3 to incorporate for any errors in the segmentation andregistration process. The motion within the brainstem was then corrected independently usingthe SPM toolbox.2.2.5 Proposed FrameworkThe proposed framework for brainstem-cortical functional connectivity estimation is graphicallyshown in Figure 2.2. Given the fMRI data, we first perform the preprocessing wherein a separatebrainstem motion correction is conducted in consideration of the anatomical peculiarities of thebrainstem. Next, we design a two-step brainstem-cortical functional connectivity estimationmethod: the first step is to represent the brainstem regional signal and select a candidate set ofcortical and subcortical regions by utilizing Partial Least Squares (PLS), and the second stepis to perform a functional connectivity analysis between the brainstem structure and the PLS-selected brain ROIs by utilizing partial correlation. The final output of the proposed frameworkis then the functional connectivity between the brainstem nucleus and other cortical/subcorticalbrain regions. Here the studied brainstem nucleus is specifically PPN.2.2.6 Brainstem Regional Signal Representation and Brain RegionSelectionWe included 58 ROIs automatically segmented by FreeSurfer as shown in Table 2.2. Two PPNROIs were manually drawn on the T1-weighted images to include the PPN on each side, namelyleft PPN and right PPN, respectively. When assessing the functional connectivity between PPN27Figure 2.2: The proposed framework for brainstem-cortical functional connectivity estimation.and other cortical/subcortical brain regions, we first utilized PLS to initially select candidatecortical/subcortical brain regions that significantly covaried with PPN voxels.PLS is a statistical method that explores the predictive models between predictor variablesand response variables [194]. It constructs a linear regression model by projecting the predictorvariables and response variables to a new set of latent variables the covariance of which ismaximized. PLS is particularly useful when the predictor variables are highly collinear, orwhen the number of predictor variables is larger than that of observations, while classicalmultiple linear regression models will fail in these cases. PLS has been widely used in variousfields of chemometrics, social science, bioinformatics, and neuroscience [44, 208].When applying PLS, we used the 58-ROI dataset as predictor variables, X, and the PPNvoxels as response variables, Y, and then tried to predict PPN activity from those 58-ROI timecourses.28Table 2.2: The 58 ROIs (in addition to the 2 PPN ROIs) used in theanalysisNo. Name No. Name1 Left-Cerebellum-Cortex 30 Right-Cerebellum-Cortex2 Left-Thalamus-Proper 31 Right-Thalamus-Proper3 Left-Caudate 32 Right-Caudate4 Left-Putamen 33 Right-Putamen5 Left-Pallidum 34 Right-Pallidum6 Left-Hippocampus 35 Right-Hippocampus7 Left-Amygdala 36 Right-Amygdala8 Left-Accumbens-area 37 Right-Accumbens-area9 ctx-lh-caudalanteriorcingulate38 ctx-rh-caudalanteriorcingulate10 ctx-lh-caudalmiddlefrontal 39 ctx-rh-caudalmiddlefrontal11 ctx-lh-cuneus 40 ctx-rh-cuneus12 ctx-lh-entorhinal 41 ctx-rh-entorhinal13 ctx-lh-inferiorparietal 42 ctx-rh-inferiorparietal14 ctx-lh-inferiortemporal 43 ctx-rh-inferiortemporal15 ctx-lh-lateralorbitofrontal 44 ctx-rh-lateralorbitofrontal16 ctx-lh-medialorbitofrontal 45 ctx-rh-medialorbitofrontal17 ctx-lh-middletemporal 46 ctx-rh-middletemporal18 ctx-lh-parahippocampal 47 ctx-rh-parahippocampal19 ctx-lh-paracentral 48 ctx-rh-paracentral20 ctx-lh-postcentral 49 ctx-rh-postcentral21 ctx-lh-posteriorcingulate 50 ctx-rh-posteriorcingulate22 ctx-lh-precentral 51 ctx-rh-precentral23 ctx-lh-precuneus 52 ctx-rh-precuneus24 ctx-lh-rostralanteriorcingulate53 ctx-rh-rostralanteriorcingulate25 ctx-lh-rostralmiddlefrontal 54 ctx-rh-rostralmiddlefrontal26 ctx-lh-superiorfrontal 55 ctx-rh-superiorfrontal27 ctx-lh-superiorparietal 56 ctx-rh-superiorparietal28 ctx-lh-superiortemporal 57 ctx-rh-superiortemporal29 ctx-lh-insula 58 ctx-rh-insulaThe general model for PLS isX = TP T + EY = UQT + F(2.1)where X is a t-by-m matrix of ROI data (predictor variables), with t corresponding to the29number of time points, and m (= 58) representing the number of subject-independent (non-PPN) ROIs; Y is a t-by-n matrix of PPN voxel time courses (response variables), where n isthe number of PPN voxels (which was subject-dependent); T and U are, respectively, t-by-ccomponent matrices decomposed from X and Y (T and U are also called X Score and Y Score,respectively), where c is the number of components; P is an m-by-c loading matrix of ROIdataset, and Q is an n-by-c loading matrix of PPN voxels; and E, F are the t-by-m and t-by-nmatrices, respectively, representing error terms. Essentially, PLS performs the decompositionsof X and Y to maximize the covariance between T and U.We then interrogated the loadings of the X components (i.e., the columns of P) to determineif they were significantly different from zero across subjects. The same procedure was conductedfor both left PPN and right PPN, respectively, and then the union set of the selected regionsfrom left PPN and right PPN was used as the final candidate set of brain regions. In addition,we used the first component of Y (i.e., the first column of Y Score) to represent the PPNregional signal in the subsequent functional connectivity analyses.2.2.7 Functional Connectivity AnalysesWe further performed functional connectivity analyses between the PPN and PLS-derived re-gions. Functional connectivity measures were obtained by computing the partial correlationcoefficients between the represented PPN signal, which was obtained by the PLS analysis, andthe averaged time courses of each PLS-derived region. We conducted the functional connec-tivity analyses on a subject-by-subject and task-by-task basis. Specifically, for each subject,functional connectivity was assessed for each of the three conditions, i.e., rest, noisy and sinu-soidal GVS conditions, by taking the time courses for each condition time segment of interestfrom the PPN and PLS-derived regions and computing the partial correlation coefficients be-tween them. For simplicity, we summed the absolute values of the significant connectivitycoefficients from both left and right PPN to get an overall PPN functional connectivity.To investigate whether or not functional connectivity between the PPN nuclei and PLS-derived regions was significantly affected by GVS, we calculated overall PPN functional con-nectivity differences between GVS on (i.e., noisy/sinusoidal GVS condition) and GVS off (i.e.,rest condition). An independent one-sample t-test was then performed on the calculated con-nection coefficient differences across subjects, with the null hypothesis that the difference waszero, to determine if significant connectivity changes were induced by GVS.302.3 Results2.3.1 Brain Region SelectionThe PLS analysis results found 10 ROIs in the PD group and 5 ROIs in the control group thatsignificantly covaried with PPN voxels (p < 0.05). In the PD group, the ROIs included thecerebellum cortex, hippocampus, amygdala, inferior parietal, middle temporal, and precuneusregions on the left, and the pallidum, hippocampus, amygdala, and middle temporal on theright (Figure 2.3). In the control group, the caudate on the left, and the caudate, entorhinalcortex, inferior temporal, and parahippocampal regions on the right were associated with PPNactivity (Figure 2.4).Figure 2.3: PLS-derived ROIs in the PD group that are significantly covaried with PPN voxels.The detected 10 regions, including cerebellum cortex, hippocampus, amygdala, inferior parietal,middle temporal, and precuneus regions on the left, and the pallidum, hippocampus, amygdala,and middle temporal on the right, are marked with different colors.31Figure 2.4: PLS-derived ROIs in the control group that are significantly covaried with PPNvoxels. The detected five regions, including the caudate on the left, and the caudate, entorhinalcortex, inferior temporal, and parahippocampal regions on the right, are marked with differentcolors.2.3.2 Functional Connectivity AnalysesTo determine the effect of the LEDD on connectivity and to correct for the fact that somesubjects had their UPDRS assessed off medication, we performed a regression analysis whereconnection strengths across subjects was the dependent variable, and LEDD, UPDRS score,whether or not the UPDRS was done on or off medication were independent variables. We thenevaluated the regression coefficients for the LEDD to determine if it had a significant effect onoverall PPN functional connectivity, which it did not (p > 0.05).The functional analysis results demonstrated that GVS differently affected overall PPNfunctional connectivity in PD and control groups. In the control group, no significant differencesin overall PPN functional connectivity were found between GVS on (i.e., noisy/sinusoidal GVScondition) and GVS off (i.e., rest condition). In the PD group, the overall magnitude ofPPN functional connectivity correlated negatively with UPDRS scores (r = −0.39, p = 0.035,32Figure 2.5). Both noisy and sinusoidal GVS increased the magnitude of overall PPN functionalconnectivity (p = 6 × 10−5 and 3 × 10−4, respectively, Figure 2.6). Furthermore, in order todetermine if overall connectivity of the PPN was particularly related to postural instability,we also compared the connectivity to the retropulsion test score from the UPDRS (Figure 2.5,inset). Since our emphasis was on early patients, we could not perform a statistical analysis, asthere was only 1 subject with a score of 2 and 1 subject with a score of 4. However, as shownin Figure 2.5, and consistent with overall UPDRS scores, there was a trend toward decreasedconnectivity with higher retropulsion test scores.Figure 2.5: The correlation relationship between the overall PPN functional connectivity andUPDRS scores in the PD group. The inset shows the relationship between the overall PPNfunctional connectivity and the retropulsion test scores from the UPDRS.Although both types of stimuli augmented overall PPN functional connectivity (both pos-itive and negative connectivity as shown in Figure 2.6), in order to determine if there aredifferences between the types of stimuli, we performed a post-hoc analysis to determine whichPPN connections were most influential in determining changes in overall connectivity. Specifi-cally, we performed t-tests on each connection to determine if the different types of GVS stimuli33increased or decreased connectivity between the PPN and other brain regions.Figure 2.6: The overall PPN functional connectivity differences between GVS on (i.e., noisyand sinusoidal GVS condition) and GVS off (i.e., rest condition) in the PD group.For the left PPN, noisy GVS decreased connectivity with the right pallidum and sinusoidalGVS increased connectivity with the left inferior parietal region (Table 2.3 and Figure 2.7).For the right PPN, noisy GVS decreased connectivity with the left cerebellar cortex, increasedconnectivity with the right amygdala and increased connectivity with the left inferior parietalregion; sinusoidal GVS decreased connectivity with the left amygdala (Table 2.4 and Figure2.8). Note that only the connection between left PPN and left inferior parietal region wouldsurvive multiple comparisons.Table 2.3: Statistics on significant left PPN functional connectivitychanges induced by GVS stimuli in the PD groupConnectivity Type of Stimuli t-value p-valueRight pallidum Noisy GVS -2.32 0.015Left inferior parietal Sinusoidal GVS 2.81 0.00534Figure 2.7: The GVS impact on the connectivity between the left PPN and PLS-derivedregions in the PD group. The red areas represent the regions significantly affected by noisyGVS. The green areas represent the regions significantly affected by sinusoidal GVS. The blueareas represent the regions with no significant changes. The corresponding ROI names andsignificance values are labeled in the figure.Table 2.4: Statistics on significant right PPN functional connectivitychanges induced by GVS stimuli in the PD groupConnectivity Type of Stimuli t-value p-valueLeft cerebellum cortex Noisy GVS -1.89 0.036Right amygdala Noisy GVS 1.90 0.035Left inferior parietal Noisy GVS 2.05 0.026Left amygdala Sinusoidal GVS -2.09 0.0242.4 DiscussionBalance impairment remains a vexing problem in PD and is associated with considerable mor-bidity. Pharmacological (particularly dopaminergic) and surgical interventions have had vary-ing degrees of success. Development of novel therapies has also been challenging because the35Figure 2.8: The GVS impact on the connectivity between the right PPN and PLS-derivedregions in the PD group. The red areas (with three different color levels indicating the differentlevels of significance values) represent the regions significantly affected by noisy GVS. The greenareas represent the regions significantly affected by sinusoidal GVS. The blue areas representthe regions with no significant changes. The corresponding ROI names and significance valuesare labeled in the figure.pathophysiology and neuropathological substrates underlying gait disturbances are incompletelyknown.To the best of our knowledge, we have shown for the first time that is possible withGVS to non-invasively modulate the functional connectivity in PD subjects between corti-cal/subcortical ROIs and the PPN – a structure critical for normal supraspinal control oflocomotion. This demonstrated alteration in functional connectivity complements previouswork examining anatomic connectivity patterns. Anatomically, the PPN has been shown tohave connections with various areas such as the vestibular nuclei [6], deep cerebellar nuclei[78], premotor, SMA and primary motor cortices [7], frontal eye fields [109], thalamic nucleiand basal ganglia nuclei [38]. Widespread projections involving the PPN include direct glu-tamatergic inputs from the motor cortex, and GABAergic inputs from substantia nigra pars36reticulata (SNr), globus pallidus internus (GPi), subthalamic nucleus (STN), and deep nuclei ofcerebellum. Ascending efferent projections target GPi, substantia nigra pars compacta (SNc),and thalamus. Descending efferent projections connect to pontine, medullary reticular forma-tion, and the spinal cord vital for control of muscle tone and locomotion. Additionally, thePPN appears to be important in the initiation, acceleration, deceleration, and termination oflocomotion through connections to the basal ganglia and higher cortical regions [92].Our results indicate significant differences in the PPN functional connectivity between PDsubjects and controls. This is particularly relevant when noting that none of our PD subjectshad FOG, given their relatively mild disease. However, even mild disease is associated withaltered gait and our results suggest that PPN functional connectivity patterns change even inthe early stages of disease course.We have shown that both GVS stimuli patterns (noisy and sinusoidal) augment overalldeficient PPN functional connectivity in PD. Our results are consistent with previous studiesdemonstrating GVS activation of vestibular afferents to basal ganglia [166, 184], which are alsodirected to the midbrain locomotion network [130]. PET studies in humans have also shownactivation in the putamen in response to vestibular stimulation [24].We found differences in PPN network connectivity depending upon the type of stimulusused. Noisy GVS significantly decreased the functional connectivity between the left PPN andright-pallidum in PD. The PPN receives strong inhibitory, GABAergic inputs from the BGnuclei (GPi, STN, and SNr), which have disrupted connectivity in PD [126]. In particular,previous studies suggest that the PPN may be the principal target of pallidal outflow, sincemore than 80% GPi neurons were found to send axonal branches to both the PPN and thalamusin monkeys [76]. In PD, the inhibitory GABAergic synaptic activities from the GPi to thePPN is abnormally overactive, which may underlie the akinesia and the gait problems seen inthe PD [126]. Taken together, these studies demonstrate the important role of the PPN andpallidal connectivity in motor and gait dysfunctions of PD. We demonstrated that noisy GVSsignificantly decreased connectivity between the left PPN and right-pallidum in PD (but notnormal controls), which suggests that potential benefits of GVS on balance in PD may be partlymediated through attenuation of overactive pallidal inputs to the PPN.Noisy GVS also decreased connectivity between the right PPN and the left cerebellar cor-tex. A diffusion-weighted imaging study found the connectivity of the PPN region with thecerebellum, thalamus, pallidum, and STN [120]. The cerebellum functions that help control of37movement, coordination, and posture [143] are speculated to be associated with the existenceof the pathway with the PPN [120]. The fact that prior studies have suggested a beneficialeffect of noisy GVS [68] may indicate that hyperactive PPN-cerebellar connections are partlynormalized with GVS.We also found that GVS increased the functional connectivity between the left inferiorparietal cortex and the right PPN (with noisy stimuli) and left PPN (with sinusoidal stimuli).Previous studies in non-human primates examining cortical inputs to the pontine nuclei havesupported the anatomical and functional relationships between the PPN and the inferior parietalcortex [108, 110]. Like the PPN, the left inferior parietal cortex is involved in gait as well asvisuospatial information processing, motor planning, and preparation [35]. Imagining normalgait activates the left inferior parietal lobule, in addition to the precuneus and bilateral dorsalpremotor cortex, the left dorsolateral prefrontal cortex, and the right posterior cingulate cortex[105]. The left inferior parietal cortex appears to be especially related to FOG. Gray mattervolume in the left inferior parietal region is significantly reduced in PD subjects with FOGpatients compared to both PD subjects without FOG and healthy controls [90]. Thus, ourresult that noisy GVS increased the connectivity between the PPN and the left inferior parietalcortex might suggest GVS could improve gait difficulties in PD by augmenting the connectivity.In the current study, one of the advantages is that we performed analyses keeping eachsubject’s data in their original space without warping the data to a common template. We arefrankly skeptical of fMRI studies suggesting robust activation from brainstem structures (e.g.,PPN) when data are spatially transformed to a template, given the significant registration errorsthat can occur to small brainstem nuclei during whole-brain registration [121]. In addition, weutilized PLS to find the combination of PPN voxels on a subject-by-subject basis that maximallycorresponded with other ROIs. In effect, the first column of Q in Equation 2.1 represents asubject-specific spatial filter to focus the activity that maximally covaried with other ROIs.It is interesting that many of the abnormal connectivities that we detected are lateralized,when balance might be considered a midline function. Balance control and gait are asymmetricalin patients with PD, and gait asymmetries have been linked to the pathophysiology of FOG[23]. The symptoms of PD generally show an asymmetric onset and progression and it hasbeen proposed that this may lead to a degree of unbalanced motor function, such that FOG istriggered by a breakdown in the bilateral co-ordination underlying the normal timing of gait[135].38There are a few limitations in our study. We examined a relatively small number of PDpatients. However, by carefully selecting the PPN voxels via PLS on a subject-by-subject basis,we expect that we have significantly enhanced our effect size, thus increasing our statisticalpower. PLS is one of the most widely used blind source separation (BSS) approaches whichhave largely benefited the neuroscience studies [44, 45, 162, 208]. In the future studies, we areinterested to further explore the effective voxel selections using such data-driven approaches.We have shown GVS induced changes in PPN functional connectivity in people with mild tomoderate PD but not in healthy controls. We speculate an inverted-U shape of effectiveness ofGVS as a function of disease severity: in controls, GVS had minimal effect, in early/moderatePD, it had some effect (shown here), and in severe disease, degeneration in the PPN itselfmay prevent modulation of its connectivity. Future work is required to further investigatethe relationship between disease severity and PPN functional connectivity and determine thebehavioral significance of this altered PPN functional connectivity. We do note that we founda negative correlation between UPDRS scores and overall PPN functional connectivity, yet stillfound robust modulation of connectivity across all of our subjects.The relation between behavioral gait measures (e.g., gait variability) and ultimate falls risk- the most important issue for people with PD - is an active area of research. Conceivably,previously-described GVS improvements in balance may not ultimately translate into reducedfall risk but such determination would require a prospective trial in the future. We havefocused on the PPN because of its possible therapeutic implications, but gait disturbancesin PD likely involve several cortical and subcortical structures. For example, PD patientshave decreased activity of the SMA during gait [75], and PD individuals have diminished pre-movement electroencephalographic potentials originating from the SMA prior to step initiation[160]. Future studies to assess connectivity changes modified by GVS in other supra-spinallocomotion centers including SMA/pre-SMA may help to guide the development of optimalstimuli on a subject-specific basis.2.5 ConclusionIn this chapter, we proposed a novel framework for brainstem-cortical functional connectivityestimation. The proposed framework was applied to investigate the effect of GVS on PPNfunctional connectivity in PD. Our results suggested that GVS can enhance deficient PPN39functional connectivity seen in PD in a stimulus-dependent manner. This may provide a mech-anism through which GVS assists balance in PD, and may provide a biomarker to developindividualized stimulus parameters.40Chapter 3PLS-based Regional SignalRepresentation for PPN FunctionalConnectivity Estimation in PD:fMRI Effect of Walking ExerciseIn Chapter 2, we propose a novel framework to assess brainstem-cortical functional connectivity.By extension, in this chapter, we further apply the proposed framework to perform treatmentevaluation of another therapeutic intervention. Specifically, we investigate the effect of walkingexercise on PPN functional connectivity in PD (see Figure 1.5).3.1 IntroductionAs mentioned in Chapter 2, gait disturbances in Parkinson’s disease such as decreased stridelength and gait variability, and especially FOG, are associated with increased fall risk and hencea significant source of disability [152]. Falls have devastating impacts on the quality of life ofindividuals with PD, and often trigger a downward spiral of frailty and can lead to depression,social isolation, activity avoidance, and fear of falling [18]. Unfortunately, gait impairment,including FOG, falls and postural instability (PI) are currently largely untreatable in PD [133].New therapeutic approaches, as well as finding potentially new targets for intervention aredesperately needed.The neuropathological substrates underlying postural and gait impairment in PD are poorlyunderstood. Pre-motor, primary motor and supplementary motor cortical areas, and the cere-bellum and basal ganglia all modulate brainstem structures, such as the mesencephalic loco-motor center (MLC), that generate postural responses and influence equilibrium, balance and41gait [172]. A key component of the MLC is the PPN, a brainstem cholinergic structure withwidespread connectivity to other brain regions. PPN receives direct glutamatergic inputs fromthe motor cortex, and GABAergic inputs from substantial nigra, GPi, STN, and deep nucleiof the cerebellum. Ascending efferent projections from the PPN target GPi, substantia nigrapars compacta, and thalamus, and descending efferent projections target pontine and medullaryreticular formation and spinal cord vital for control of muscle tone and locomotion. Alteredconnectivity to/from the PPN is likely a factor in PD gait abnormalities such as FOG, asimpaired structural connectivity can be demonstrated between basal ganglia-PPN and othertracts in FOG [182]. As suggested in previous studies, significantly stronger functional con-nectivity between PPN-SMA [61] may have been found in FOG patients, reflecting possiblymaladaptive compensatory mechanisms. As the PPN is affected in PD [61], there has beenintense interest on how to modulate PPN activity, but results have been inconsistent. ThePPN is modestly affected by acetylcholinesterase inhibitors [79]. Multiple studies on PPN-DBShave suggested possible clinical improvement in PD patients, although results have been varied[86, 164]. Reasons for this response variability may be difficulties in determining precise DBSelectrode placement, and variability of functional and structural connectivities from and to thePPN. In Chapter 2, we have demonstrated that PPN functional connectivity can be modifiedby GVS in PD subjects, but not in controls, with changes in functional connectivity correlatingwith UPDRS score.Behaviorally, exercise, physiotherapy as well as other measures targeting stepping-in-placehave been shown effective interventions for PD gait impairment and in preventing falls [47], butthe effects of these interventions on PPN functional connectivity are unknown. Ambulosonois one such program, that uses an iPodTM for music via Bluetooth headphones, and in somecases, assessing stride length, and if this drops below an individually designated level, the musicstops playing. The music is designed to improve step automaticity [47], increase the physicalvigour of lower limb movements, and enhance voluntary and automatic motor control [112].In this chapter, we utilized resting-state fMRI to determine if functional connectivity be-tween the PPN and other cortical/subcortical brain regions could be modulated by Ambulosonoin PD patients with mild gait impairment. Since there is increasing recognition that a numberof cortical and subcortical regions may be important for gait difficulties in PD [61], we specifi-cally employed a hypothesis-driven approach examining PPN functional connectivities, becauseit is potential target in DBS and to prevent problems with massive multiple comparisons that42would be required for a fully exploratory approach. Similar to Chapter 2, careful care wastaken to ensure robust activation from PPN structures by analyzing the data in native space(without registration to a template) and utilizing subject-specific weightings of voxels withinthe PPN region. We hypothesized that PPN functional connectivity could be modified by amusic walking training approach, in a dose-dependent manner.3.2 Materials and Methods3.2.1 SubjectsTwenty-seven PD subjects (Table 3.1) with mild to moderate PD (HY I - III) and optimallytreated with PD medications were recruited from the Pacific Parkinson’s Research Centre atthe University of British Columbia (UBC). The study was approved by the UBC Ethics ReviewBoard, and all subjects gave written, informed consent prior to participation.Table 3.1: Demographic and clinical information on PD patientsClinical characteristicsStatistics(mean ± standard deviation)Age 64.5 ± 8.1Gender 17 males, 10 femalesDisease duration (years) 4.9± 4.0UPDRS III 23.9 ± 11.3H & Y 1.4 ± 0.5FES-I 20.1 ± 5.7FOG-Q 2.8 ± 4.0MoCA 27.0 ± 3.1Total number of walks 29.8 ± 17.2Total length of training (min) 1471.7 ± 849.4Average walking (m/min) 73.1 ± 18.5Total walking distance (km) 112.4 ± 71.7Values are given as mean standard deviation. UPDRS III= Unified Parkinson’s Disease Rating Scale-Part III; HY =Hoehn and Yahr stage; FES-I = Falls Efficacy Scale Interna-tional; FOG-Q = Freezing of Gait Questionnaire; MoCA =Montreal Cognitive Assessment.433.2.2 AmbulosonoThe Ambulosono device and protocol have been previously described at length [47]. In brief,music with high emotional salience and likeableness are chosen and used to induce a high levelof physiological arousal and as means to activate locomotor networks and heighten sensorimotorperception, awareness and self-efficacy during walking [42, 148]. Later, music play may be madecontingent upon the amplitudes of walking steps so that smaller walking steps, i.e., shuffling,can be prevented before it becomes an undesirable habit [47]. However, for the purposes ofthis study, we pooled the groups who listened to music with and without the contingency toincrease our sample size.The study timeline and protocol are shown in Figure 3.1. The walking program first startedwith a baseline walking of 4 weeks, two of which they walked with NO music followed by twoweeks of music listening while walking. Participants were instructed to walk a minimum of 20minutes/walk, 3 times per week or a total of 60 minutes/week, at their own preferred pace.During the training, participants were required to upload their walking files once a week viawireless internet connection to our online database. The statistics on the walking data is shownin Table 3.1.All 27 patients completed clinical assessments, including UPDRS-III, HY, the MoCA forgeneral cognitive functioning, and self-reported questionnaires including the FES-I survey forfear of falling, the FOG-Q for freezing at baseline, and then after Ambulosono training forcomparison of pre- and post-intervention. MRI was performed at baseline and 3 months post-music training. Patients were in medication ON state during the clinical assessment and MRIscan. Five patients did not have a repeat UPDRS-III at follow-up point. Therefore, they wereexcluded from the UPDRS-related analysis.3.2.3 fMRI Data Acquisition and PreprocessingThe parameters of data acquisition and fMRI preprocessing steps were the same as those inSection 2.2.3 and 2.2.4. The scan duration of each functional run was 8 mins at the resting-state.44Figure 3.1: Flowchart for the study protocol.3.2.4 Brainstem Regional Signal Representation and Brain RegionSelectionHere we basically used the same brainstem-cortical functional connectivity modelling frameworkas in Chapter 2 (Figure 2.2). Initially, 80 ROIs were included in this study as shown in Table 3.2.Additionally, two PPN ROIs (namely left PPN and right PPN respectively) as mentioned abovewere incorporated to conduct the PPN functional connectivity analysis. Prior to the functionalconnectivity estimation, PLS was utilized to select a subset of cortical/subcortical ROIs thatsignificantly covaried with PPN voxels [30]. The dominant component of PPN voxel datasetwas utilized to represent the PPN regional signal in the subsequent functional connectivityanalysis.3.2.5 Functional Connectivity AnalysesFunctional connectivity network structure was additionally assessed between the PPN andPLS-selected ROIs using the PCfdr algorithm [97], a conditional independence based network45Table 3.2: The PLS-selected ROIs (italic) from the 80 ROIs used inthis studyNo.Name No.Name1 Left-Cerebellum-Cortex 39 Right-Cerebellum-Cortex2 Left-Thalamus-Proper 40 Right-Thalamus-Proper3 Left-Caudate 41 Right-Caudate4 Left-Putamen 42 Right-Putamen5 Left-Pallidum 43 Right-Pallidum6 Left-Hippocampus 44 Right-Hippocampus7 Left-Amygdala 45 Right-Amygdala8 Left-Accumbens-area 46 Right-Accumbens-area9 ctx-lh-parahippocampal 47 ctx-rh-parahippocampal10 ctx-lh-insula 48 ctx-rh-insula11 ctx-lh-superiorfrontal 49 ctx-rh-superiorfrontal12 ctx-lh-rostralmiddlefrontal 50 ctx-rh-rostralmiddlefrontal13 ctx-lh-caudalmiddlefrontal 51 ctx-rh-caudalmiddlefrontal14 ctx-lh-G-front-inf-Opercular 52 ctx-rh-G-front-inf-Opercular15 ctx-lh-G-front-inf-Orbital 53 ctx-rh-G-front-inf-Orbital16 ctx-lh-G-front-inf-Triangul 54 ctx-rh-G-front-inf-Triangul17 ctx-lh-lateralorbitofrontal 55 ctx-rh-lateralorbitofrontal18 ctx-lh-medialorbitofrontal 56 ctx-rh-medialorbitofrontal19 ctx-lh-caudalanteriorcingulate57 ctx-rh-caudalanteriorcingulate20 ctx-lh-rostralanteriorcingulate58 ctx-rh-rostralanteriorcingulate21 ctx-lh-entorhinal 59 ctx-rh-entorhinal22 ctx-lh-inferiortemporal 60 ctx-rh-inferiortemporal23 ctx-lh-middletemporal 61 ctx-rh-middletemporal24 ctx-lh-superiortemporal 62 ctx-rh-superiortemporal25 ctx-lh-G-occipital-sup 63 ctx-rh-G-occipital-sup26 ctx-lh-G-oc-temp-lat-fusifor 64 ctx-rh-G-oc-temp-lat-fusifor27 ctx-lh-G-oc-temp-med-Lingual65 ctx-rh-G-oc-temp-med-Lingual28 ctx-lh-inferiorparietal 66 ctx-rh-inferiorparietal29 ctx-lh-postcentral 67 ctx-rh-postcentral30 ctx-lh-posteriorcingulate 68 ctx-rh-posteriorcingulate31 ctx-lh-precuneus 69 ctx-rh-precuneus32 ctx-lh-cuneus 70 ctx-rh-cuneus33 ctx-lh-superiorparietal 71 ctx-rh-superiorparietal34 ctx-lh-G-pariet-inf-Angular 72 ctx-rh-G-pariet-inf-Angular35 ctx-lh-G-pariet-inf-Supramar73 ctx-rh-G-pariet-inf-Supramar36 L-M1 74 R-M137 L-SMA-proper 75 R-SMA-proper38 L-Pre-SMA 76 R-Pre-SMA39 L-PMd 78 R-PMd40 L-PMv 80 R-PMvstructure learning approach [72], and suitably modified to incorporate a false discovery rate(FDR) control procedure, which was set to be 0.05.We utilized a common structure approach [41], which imposes the same connectivity networkstructure on each subject, while allows the connectivity strength (coefficients) to be different46across subjects and tasks. The strength/coefficients of functional connectivity were estimatedby computing partial correlation coefficients on a subject-by-subject basis.3.2.6 Statistical AnalysesThe individual connection coefficients of PPN functional connectivity and the sum of absolutevalues of significant connectivity coefficients were compared between pre-exercise and post-exercise using a paired t-test. Associations between PPN functional connectivity and UPDRSscore and walking data were investigated using Pearson’s correlation.3.3 ResultsUsing PLS, a total of 74 ROIs were significantly covaried with the PPN (p < 0.01, FDRcorrected - Table 3.2). There was significant functional connectivity between the left caudateand left posterior cingulate and the left PPN (p < 0.05, FDR corrected). For the right PPN,significant functional connectivity with right hippocampus and left inferior parietal were found(p < 0.05, FDR corrected), as shown in Figure 3.2.3.3.1 PPN Functional Connectivity Changes after Ambulosono ExerciseAmbulosono significantly increased the magnitude of overall right PPN functional connectivity(Figure 3.3a, p = 0.02, FDR corrected), but showed a trend in decreasing the overall PPNfunctional connectivity at the left side (Figure 3.3a, p > 0.05). The connectivity between rightPPN and left inferior parietal was significantly increased (p = 0.03, FDR corrected, Figure 3.3b),and the right PPN functional connectivity with right hippocampus was moderately increased(p = 0.07, FDR corrected, Figure 3.3b).3.3.2 PPN Functional Connectivity Correlates with Clinical ScoresThere was a significant decrease in UPDRS-III score after Ambulosono exercise (p = 0.003,Figure 3.3c). The overall functional connectivity of left PPN positively correlated with thebaseline UPDRS score (Figure 3.3d, r = 0.36, p = 0.05). In addition, the magnitude of thedecreased left PPN functional connectivity by exercise strongly correlated with the improvementin UPDRS-III score (Figure 3.3d, r = 0.63, p = 0.001). In contrast, the right PPN functionalconnectivity was increased after Ambulosono. There was no clear correlation between the47increase in right PPN functional connectivity and the improvement in UPDRS, a trend, however,was seen that individuals with lower baseline UPDRS showed higher magnitude of increasein right PPN functional connectivity (not significant). There was a decrease in the left PPNfunctional connectivity that correlated with the total number of walks (Figure 3.3e, r = 0.43, p =0.02) and the total length of training (Figure 3.3f, r = 0.39, p = 0.03).3.4 DiscussionWe have shown that walking exercise affects PPN functional connectivity in PD, in a dose-dependent manner. Previously, it has been shown that PPN functional connectivity can bemodified under certain conditions. For instance, PPN connectivity can be activated by treadmilltraining [2]. Unilateral PPN-DBS during self-paced lower limb movements results in increasesin regional cerebral blood flow in interconnected structures of cerebello-thalamo-cortical circuit[11] including the PPN region. Chronic low frequency PPN-DBS can modify brain connectivityin FOG, resulting in reduction of corticopontine overactivity seen in the pre-stimulation pe-riod [155]. In our study we found multiple cortical, subcortical and brainstem structures thatsignificantly covaried with the PPN (Table 3.2), consistent with previous studies examiningfunctional and anatomic connectivity patterns [7, 30, 38, 183]. The demonstrated alterationof PPN functional connectivity by Ambulosono complements our observation in Chapter 2 ofGVS also modulating PPN functional connectivity in PD patients [30].We have demonstrated that Ambulosono improved PD motor symptoms as measured byUPDRS-III. This is compatible with prior observations that rhythmic auditory clues [8] andmental singing during walking may improve gait in PD [151], and numerous studies demon-strating overall benefits of physical activity in PD [50].In our study, left and right PPN connectivities were different at baseline, and were differentlyaffected by Ambulosono exercise. After exercise, we found significant increases in overall rightPPN functional connectivity, more or less independent of disease severity. In contrast, beforethe intervention, the functional connectivity of the left PPN positively correlated with thebaseline UPDRS-III score, so that even though overall left PPN functional connectivity wasreduced in the PD population, greater connectivity was seen in greater disease severity. Thereare two potential explanations for this apparent paradox. One is that the left PPN functionalconnectivity represents a compensatory response that increases with disease severity. Note that48with a compensatory mechanism, reduction of disease effects (as evidenced by the improvementin behavioral measures) will also result in a decrease in compensatory mechanisms. Anotherrelates to neural efficiency, whereby exercise results in less co-activation of ancillary brainregions, presumably due to more efficient recruitment of necessary resources to complete thetask of ambulation [122]. In contrast, with the right PPN, while connectivity with both theleft inferior parietal and right hippocampus were increased after exercise, this did not correlatewith changes in motor function. While it is still unclear whether there is a dominant PPN inhumans, especially in PD gait-impaired individuals, our result further supports an asymmetryin PPN functional connectivity, as has been suggested in Chapter 2.There have been several studies that have demonstrated altered connectivity between leftand right PPN. In PD patients with FOG, reduced white matter connectivity can be seen fromthe PPN to the cerebellar locomotor regions, thalamus, and multiple regions of the frontaland prefrontal cortex only in the right hemisphere of freezers [62]. Functional connectivityin postural instability gait difficulty (PIGD) subgroups have increased functional connectivitybetween the left PPN and the SMA-proper, while the right PPN is hyper-connected to the rightpremotor cortex and left M1. Tremor dominant (TD) subgroups have increased functionalconnectivity between the left PPN and the left premotor cortex, pre-SMA and SMA [183].Greater functional connectivity between the SMA and MLC can be positively correlated withfreezing severity in FOG [61]. The pattern of such enhanced connectivity does not appear tobehave like a useful compensatory role, but rather may contribute to FOG. It is difficult tocompare these results directly with ours, as the group of subjects described in this report didnot have FOG, given their relatively mild disease. However, even mild PD is associated withaltered gait, and our results suggest that the PPN functional connectivity patterns we observedcan be seen even in the early stages of disease.There are a few limitations in our study. Similar to Chapter 2, we studied a relatively smallnumber of PD patients. Still, by carefully selecting the PPN voxels via PLS on a subject-by-subject basis, we expect that we have significantly enhanced our effect size, thus increasing ourstatistical power. Furthermore, we would include patients with more advanced disease whengait and balance concerns are more prominent (i.e. with FOG). In severe disease, degenerationin the PPN itself may prevent modulation of its connectivity. In addition, combining withstructural connectivity studies, for instance with tractography, we may be able to establishimaging biomarkers to predict responders from non-responders to treatment interventions. We49did not have a control group; we believe there is ample evidence already showing the beneficialeffects of exercise, particularly walking, so we therefore examined the dose-response of such anintervention.3.5 ConclusionIn this chapter, we extended the application of the brainstem-cortical functional connectivityestimation framework proposed in Chapter 2, to investigate the effect of walking exercise onPPN functional connectivity in PD. We demonstrated that PPN functional connectivity can bemodulated by walking exercise in a dose-dependent manner. The results provided additionalevidence of altered functional connectivity of the locomotor network in PD patients, and furthersupported evidence of asymmetric PPN functional connectivity early in the disease course.The observed modification in PPN functional connectivity provided a potential mechanism toexplain how exercise may improve gait function, possibly by increasing neural efficiency.50Figure 3.2: The functional connectivity of the left and right PPN. The connected regions ofthe left PPN include left caudate and left posterior cingulate, and the connected regions of theright PPN include right hippocampus and left inferior parietal.51Figure 3.3: The PPN functional connectivity changes due to the Ambulosono exercise and re-lated relationships with the UPDRS score. (a) The Ambulosono exercise significantly increasedthe magnitude of overall right PPN functional connectivity, but showed a trend to decrease leftPPN functional connectivity. (b) For individual PPN functional connectivity, the Ambulosonoexercise significantly increased the right PPN functional connectivity with left inferior parietal,and also moderately increased the connectivity between the right PPN and right hippocampus.(c) The Ambulosono exercise significantly decreased the UPDRS score, suggesting an improve-ment in PD patients overall motor symptoms by the music walking exercise. (d) The baselineleft PPN functional connectivity correlated positively with UPDRS score, suggesting that thelower connectivity indicates a better overall motor function. Additionally, the decrease in theleft PPN functional connectivity strongly correlated with the improvement in UPDRS scoreafter Ambulosono training. (e) The decrease in the left PPN functional connectivity correlatedwith the number of walks. (f) The decrease in the left PPN functional connectivity correlatedwith the training time. (#p > 0.1, ∗p < 0.1, ∗ ∗ p < 0.05, ∗ ∗ ∗p < 0.005)52Chapter 4Constrained Canonical CorrelationAnalysis for Brain FunctionalConnectivity EstimationIn ROI-based brain functional connectivity, representing the signal in a given ROI is an im-portant issue. With most current approaches, the signals from same-ROI voxels are simplyaveraged, neglecting any inhomogeneity in each ROI and thus less optimally reflecting ongo-ing activity in the ROI. In this chapter, we develop a novel method of representing regionalsignal with local brain activity incorporated and estimating brain functional connectivity viaconstrained CCA method (see Figure 1.5). We then apply the proposed method to estimatecortical/subcortical functional connectivity using Human Connectome Project data.4.1 IntroductionInferring brain functional connectivity from fMRI data has advanced our understanding oflarge-scale functional coordination of the brain. As mentioned in Section 1.2, a key issue forassessing the ROI-based brain functional connectivity is how to represent the information ina given ROI. Although receiving relatively little attention (in large part due to the ease ofsimply taking the average signal from same-ROI voxels), regional signal representation is ageneral research problem worthy of careful investigation. This is because different ROI signalrepresentation strategies may significantly impact the subsequent results inferred from fMRIdata, as has been previously demonstrated [176]. Current methods include using average signal,PCA and selecting a “representative” voxel. However, these methods ignore the possible func-tional inhomogeneity of ROIs and may exhibit poor reliability [115, 150, 181]. Recently, it hasbeen suggested that connectivity analyses can be prone to inaccuracy when there is insufficient53spatial constraint to ensure that the voxels with concentrated activity within each ROI areappropriately emphasized [48]. Therefore, improved brain functional connectivity modellingmethods that incorporate both the regionally-specific nature of brain activation (in the con-text of relation to a specific ROI) and the appropriate assessment of representative voxels arerequired to guide the fMRI analysis.We propose a new method for the estimation of brain functional connectivity from fMRIdata, in which appropriate handling of within–ROI clusters of voxels are taken into account forconstructing the ROI representative signal, and the connections between ROIs are appropriatelyinferred. This method is implemented in two steps, where regional activity is first detectedby density clustering and then spatially–constrained canonical correlation analysis (CCA) isapplied to the identified regionally-specific activity structures. Density clustering [139] is arecently proposed algorithm that divides data into clusters based only on the distance (whichcan be defined in temporal and/or spatial domains) between data points. This method hasadvantages of fast speed and automatic detection of the number of clusters by finding densitypeaks. We utilize this density clustering algorithm to explore local brain activation patternswithin an ROI, dividing the voxels into several groups which maximize intra-group homogeneity.We then utilize a modified version of CCA, a well-known multivariate statistical method formaximizing the correlation relationship between two sets of variables and previously used infMRI [65]. Here we propose a novel approach, which we call local activity constrained CCA (LA-cCCA), by modifying the traditional CCA method from two aspects: first by including spatialdominance constraints on highly locally–connected voxels to ensure the results more accuratelyreflect the spatial data structure, and second, by imposing non-negativity constraints that onlyallows for non-negative combinations of voxels to ease interpretability. We utilize LA-cCCAto simultaneously construct ROI representative signals and estimate the connections betweenROIs.The remainder of this chapter is organized as follows: Section 4.2 introduces density cluster-ing and spatially constrained CCA algorithms, followed by the integration of the two algorithms.Section 4.3 demonstrates the results using both synthetic and real fMRI data, and our resultsare compared with two main ROI signal representation approaches, i.e., the average signalapproach and the PCA approach. Finally, Section 4.4 provides the discussion of the presentstudy.54Figure 4.1: A schematic overview of the proposed method. Take two ROIs as an illustration,each ROI is first divided into several functional sub-regions (painted by different colors) bydensity clustering, and meanwhile the most important voxel for each ROI is identified. Next, thedetected most important voxels and their neighbours (pink) are selected to delineate the ROIs.Finally, spatially constrained CCA is performed between the ROIs wherein the constructedROI representation signals (red) exhibit maximized correlation: the weights of the blue ones(non-selected voxels) are zero, and the weights show an increase from red to yellow. The mostimportant voxels have maximum weights (yellow).554.2 MethodsIn this section, we introduce the proposed LA-cCCA method — a schematic overview of themethod is shown in Figure 4.1. Given two ROIs, we first detect the regional brain activationpatterns by density clustering, and then apply spatially constrained CCA on the basis of theregionally-specific nature of brain activity to estimate the connection strength between the pairof ROIs. This is then repeated for all other pairs. In the next subsections, the method will bedescribed in detail. We start with the introduction of density clustering algorithm, followed bythe formulation of spatially constrained CCA for brain functional connectivity estimation, andfinally give a comprehensive description on the integration of the two algorithms.4.2.1 Density ClusteringRodriguez and Laio [139] introduced a novel clustering algorithm for fast location of densitypeaks, which we refer to here as density clustering. This algorithm considers cluster centers asexhibiting two properties: (1) higher density than their neighbouring data points and (2) largedistance from other data points with higher densities. For each data point, two core quantitiesare calculated on the basis of distance matrix between data points. One is the density value ρiof data point i, which is computed using a Gaussian kernel asρi = bN∑j=1exp(−(dij − c)2d2c) (4.1)where dij denotes the distance between two data points i and j, and dc is a pre-specified cutoffdistance. As suggested in [139], the parameters b and c are set to 1 and 0 respectively, anddc is chosen such that the average percentage of neighbours is 1%. It can be seen that thedata point with a high density value tends to have short distances to other data points. Inthis study, the distance is defined based on functional dissimilarity between voxels (describedbelow). Therefore, the voxel that is functionally similar to other voxels tends to have a highdensity value.The other measure, δi, is calculated as the minimum distance between the data point i andany other data point with higher densityδi = minj:ρi<ρj(dij) (4.2)56For the data point with the highest density, the corresponding δi is taken as δi = maxj(dij).It is noteworthy that δi tends to be larger for those data points corresponding to local or globalmaxima of density.Therefore, the cluster centers are identified as the data points with both high density ρand high distance δ. In this study, the distance matrix is defined based on functional con-nectivity (e.g., Pearson’s correlation as described below) between voxels, the cluster centersthus correspond to the voxels that are local connectivity hubs which maintain the strongestconnections over a neighbourhood. Then cluster assignment is performed by assigning eachof the rest data points to the cluster that its nearest neighbour of higher density belongs to.The advantages of this algorithm include fast speed, relatively simple implementation whereonly the distance matrix is required, a one-step cluster assignment (as opposed to an iterativemethod) and automatic detection of the number of clusters.Geodesic DistanceThe distance matrix used in the proposed method is based on geodesic distance [80]. In orderto obtain the geodesic distance, we first generated a weighted graph where each voxel withinan ROI corresponded to the vertices, and the edges were constructed between spatially neigh-bouring voxels (within a 3× 3× 3 cube) by computing the Pearson’s correlation distance. Thegeodesic distance is computed as the shortest path length through the weighted graph betweeneach pair of voxels. Therefore, both the functional dissimilarity and spatial distance betweenvoxels are reflected in the geodesic distance.Automatic Density Peak DetectionIn density clustering [139], cluster centers are manually selected from a decision graph - a scatterplot of the density value ρ and the distance δ (illustrated below). The data points correspondingto density peaks, i.e., the data points with both high ρ and large δ, are chosen as cluster centers.However, it is both time consuming and laborious to conduct manual selection, especially forbatch processing. Therefore, it is desirable to incorporate an automatic cluster center selectioninto the original algorithm. In this chapter, we performed automatic density peak detection viaoptimizing the silhouette index [187]. The criterion used for the automatic selection of clustercenters conforms with the aforementioned fact that the cluster centers correspond to the datapoints with high ρ and large δ, which are typically located in the upper right corner of the57decision graph. The specific procedure for the automatic density peak detection is described inAlgorithm 1.Algorithm 1 Automatic density peak detection1: Define a set C as possible values for the number of clusters cn, and a value α such that ραdenotes the α-th quantile of the density values.2: for n = 1, 2, · · · , N do3: Among the data points I = {i : ρi > ρα}, select the data points with the top cn highestdistance values δ as cluster centers;4: Perform cluster assignment as in Rodriguez and Laio’s algorithm [139];5: Calculate the average silhouette index sn;6: end for7: The clustering configuration with the maximum average silhouette index is the final clustermodel, including the number of clusters, the corresponding cluster centers and the clusterassignment.4.2.2 Spatially Constrained CCACCA is applied on two data sets and tries to maximize the correlation between them by lin-ear transformations. Specifically, given two sets of variables X = [x1, x2, · · · , xp] and Y =[y1, y2, · · · , yq], with the matrix dimension of t× p and t× q respectively where t is the numberof observations and p, q represent the number of variables, CCA seeks the weight vectors wxand wyx = wx1x1 + wx2x2 + · · ·+ wxpxp = Xwx (4.3)y = wy1y1 + wy2y2 + · · ·+ wyqyq = Y wy (4.4)so that x and y have the maximum correlation, as shown in Equation 4.5.maxwx,wyCx,y =w′xX′Y wy√w′xX′Xwx√w′yY′Y wy(4.5)This problem can be solved by the following eigenvalue problems:(X′X)−1(X′Y )(Y′Y )−1(Y′X)wx = C2x,ywx (4.6)58(Y′Y )−1(Y′X)(X′X)−1(X′Y )wy = C2x,ywy. (4.7)Therefore, the weight vectors wx and wy correspond to the eigenvectors associated with thelargest eigenvalues of (X′X)−1(X ′Y )(Y ′Y )−1(Y ′X) and (Y ′Y )−1(Y ′X)(X ′X)−1(X ′Y ) respec-tively.CCA has proved useful for examining neuronal activity in fMRI [48, 65]. In this chapter, weutilize the CCA method to find representative signals from brain ROIs. Based on the definitionsabove, suppose X and Y denote fMRI signals from two brain ROIs, then the linear combinationsXwx and Y wy obtained from the CCA method can be used as the ROI representation signals,in the way that the connections between them are detected in a sensitive way. Note that agiven ROI will have several weight vectors, corresponding to the other ROIs. This is consistentwith the notion that the very important voxels within a given ROI may be a function of whatother ROI is being considered in a pairwise interaction.Conventional CCA can result in both positive and negative weights, but the negative weightscan be difficult to interpret. We therefore imposed non-negativity constraints on the weight vec-tors so that the resulting representative signals Xwx and Y wy can be considered as a weightedmean of the original time series within the ROI. Besides the obvious non-negativity constraint,it is also critical to incorporate spatial constraints on the weight vectors to take into account theconnectome properties of voxels which ensures adequate spatial weighting of the most locally-connected voxels (i.e., the local connectivity hubs that maintain the strongest connections overa neighbourhood) to reduce sensitivity to artifact.The constraints that we imposed on the weight vectors in the CCA can be summarized as,wi ≥ maxj 6=iwj ≥ 0, (4.8)where wi represents the weights for the most locally-connected voxels within a ROI, and wjdenotes the weights for other voxels in the same ROI. The spatial constraint for one ROI, say X,can be written as Dxwx ≥ 0. For instance, suppose the voxel x1 be the most locally-connected59voxel, then the p× p matrix Dx can be defined asDx =1 0 0 · · · 01 −1 0 · · · 01 0 −1 · · · 0.......... . ....1 0 0 · · · −1(4.9)We further formulated this spatially constrained CCA as a constrained optimization problemmaxwx,wyCx,y = w′xX′Y wy (4.10a)s.t. Dxwx ≥ 0 (4.10b)Dywy ≥ 0 (4.10c)wx ≥ 0 (4.10d)wy ≥ 0 (4.10e)w′xX′Xwx = 1 (4.10f)w′yY′Y wy = 1 (4.10g)Note that we adapted the objective function in the CCA in the way that the denominator inthe definition of the correlation between x and y as in Equation 4.5 has been converted intothe normalization terms that have been incorporated in the equality constraints as Equations4.10f and 4.10g.We utilized interior point method to solve the spatially constrained CCA problem. Interiorpoint method is a certain class of algorithms used for solving constrained optimization problems,which has proven powerful for nonlinear programming [123]. By implementing the interiorpoint method, the original constrained optimization problem is converted to a sequence ofapproximate problems through a barrier function. Given the constrained minimization problem60minxf(x) (4.11a)s.t. h(x) = 0 (4.11b)g(x) ≤ 0 (4.11c)The approximate problem is written asminx,sf(x)− µ∑ilog si (4.12a)s.t. h(x) = 0 (4.12b)g(x) + s = 0 (4.12c)where µ is a positive scalar, which is called barrier parameter, and si is slack variables, thenumber of which is equal to that of inequality constraints. The logarithm term in Equation4.12a is called a barrier function. The interior point method consists of solving the approxi-mate problem for a sequence of positive barrier parameters {µk}. As µ decreases to zero, thesolution of the approximate problem should approach the solution of the original constrainedoptimization problem.The approximate problem of spatially constrained CCA in Equation 4.10 isminw,sf(w)−µ∑ilog si = minw,s−w′Zw − µ∑ilog si (4.13a)s.t. g1(w) + s1 = −Dw + s1 = 0 (4.13b)g2(w) + s2 = −w + s2 = 0 (4.13c)h1(w) = w′Aw − 1 = 0 (4.13d)h2(w) = w′Bw − 1 = 0 (4.13e)where w = [wTx , wTy ]T , s = [sT1 , sT2 ]T . The matrices Z, D, A and B can be defined accordinglyto be consistent with Equation 4.10.61The Lagrange function associated with the approximate problem is thenL(w, s, λ, γ) =− w′Zw − µ∑ilog si+∑iλi(gi(w) + si) +∑jγjhj(w)(4.14)where g(w) =g1(w)g2(w), h(w) =h1(w)h2(w), and λ, γ are Lagrange multiplier vectors associatedwith g(w) and h(w) respectively.The Karush-Kuhn-Tucker (KKT) conditions (i.e., the first-order necessary conditions for aconstrained optimization problem) are∇f(w) + JTg λ+ JTh γ = 0 (4.15a)Sλ− µe = 0 (4.15b)g(w) ≤ 0 (4.15c)h(w) = 0 (4.15d)λ ≥ 0 (4.15e)where Jg, Jh denote the Jacobian matrices of the constraint functions g and h, respectively,S is defined to be the diagonal matrix with diagonal entries given by the vector s, and e =(1, 1, . . . , 1)T .Applying Newton’s method to Equation 4.15, we obtain the variable update (∆w,∆s,∆λ,∆γ)H 0 JTh JTg0 SΛ 0 −SJh 0 I 0Jg −S 0 I∆w∆s−∆γ−∆λ = −∇f(w)− JTg λ− JTh γSλ− µehg + s (4.16)where H denotes the Hessian of the Lagrange function L, i.e., H = ∇2f(w) +∑i λi∇2g(w) +∑j γj∇2h(w), and Λ is the diagonal matrix with the diagonal entries given by the vector λ.We used backtracking line search to determine the step size α, which decreases the merit62functionφ(w, s; ν) = f(w)− µ∑ilog si + ν ‖g(w) + s‖1+ ν ‖h(w)‖1(4.17)where the penalty parameter ν may increase with the iteration number to ensure the solutiontowards feasibility [123]. The convergence criterion for each approximate problem (inner loop)and the overall optimization (outer loop) is measured using the following error function, whichis based on the fulfillment of the KKT conditions.E(w, s, λ, γ;µ) = max{∥∥∇f(w) + JTg λ+ JTh γ∥∥∞ ,‖Sλ− µe‖∞ , ‖h(w)‖∞ , ‖g(w) + s‖∞}(4.18)The interior point algorithm for spatially constrained CCA is described in Algorithm 2.Algorithm 2 The iterative algorithm of the line search interior point method1: Initialize w0, s0, λ0, γ0 and select the parameter σ ∈ (0, 1).2: while Convergence is false do3: while Convergence is false do4: Calculate the variable update (∆w,∆s,∆λ,∆γ) using Equation (4.16);5: Determine the step size α using backtracking line search and the merit function inEquation (4.17);6: Update (w+, s+, λ+, γ+)← (w + α∆w, s+ α∆s, λ+ α∆λ, γ + α∆γ);7: end while8: Set µ← σµ;9: end while4.2.3 Integration of Regional Activity Structure into Network ModellingThe proposed LA-cCCA method essentially integrates regional brain activity, via density clus-tering, into spatially constrained CCA for bivariate interaction estimation. Specifically, givena set of ROIs, our method can be summarized as follows (see Figure 4.1):1. Due to local functional segregation, one ROI can encompass several sub-ROIs. Therefore,we first utilized density clustering to detect regional activity on brain ROIs, dividingeach ROI into several functionally homogeneous and spatially contiguous sub-ROIs andidentifying the most important voxel (i.e., the voxel corresponding to the density peak)for each sub-ROI.632. To recognize the fact that the true fMRI activation tends to occur in spatially connectedclusters rather than a single voxel, and to avoid the arbitrary of the use of a single voxeland increase robustness, we include the neighbouring voxels around each density peak intothe analysis. In other words, we select a set of voxels (i.e., the heavily locally-connectedvoxels and their neighbours) to delineate each ROI.3. Based on the selected voxels, we perform spatially constrained CCA between ROIs, inwhich the spatial dominance constraint is imposed on the most important voxels and thenon-negativity constraint is introduced on all voxels. In this step, the ROI representativesignals are constructed and the connections between the ROIs are estimated.4.3 Results4.3.1 Synthetic Data SetWe validated our method on the synthetic data set by comparing the performance of theproposed method with that of two other popular correlation based brain functional connectivitynetwork estimation methods, which represent the ROI signal by either the PCA or the averagesignal.Two different scenarios were considered to test the performance of the proposed method.In the first scenario, we considered each ROI as having just one underlying signal, i.e., the ROIwas functionally homogeneous across all voxels. Three ROIs were generated for the connectivityassessment. In the second scenario, we considered the fact that one ROI can encompass severalfunctional sub-regions. In this case, we generated two ROIs, one with two functional sub-regions, and the other with just one underlying signal. In both scenarios, the underlying signalswere first generated from Gaussian distributions. Then signals for all voxels within the ROIwere generated according to the signal to noise ratio (SNR), which is defined asSNR =σ2signalσ2noise(4.19)where σ2 is the variance of the data.The correlation coefficients between the underlying signals were generated from a uniformdistribution on the interval [0,1]. The connectivity was identified as between those ROIs withsignificant correlations (p-value < 0.05). We then applied the proposed LA-cCCA, as well64as PCA and average-signal based correlation method to estimate the connectivity betweenthe generated ROIs. In each method, the significance of the connectivity was determined byperforming 5000 permutations, and setting the significance level to 0.05. The performance ofeach method was evaluated by the square root of mean square error (RMSE) as a function ofSNR. The RMSE is defined asRMSE =√√√√ 1nn∑i=1(vi − vˆi)2 (4.20)where v is the “true” connectivity vector with n elements, and vˆ is the estimated connectivityvector with the same length. To obtain a reliable assessment, the procedure was repeated 50times for each method. The average performance over 50 runs was compared between differentmethods.The results for the two scenarios on the synthetic data are shown in Figure 4.2 and 4.3. Foreach figure, the upper panel shows examples of the true connectivity matrix and the estimatedresults by the three methods, and the lower panel compares the performances of the differ-ent methods. As can be seen from the figures, in both cases, the proposed LA-cCCA modelperformed consistently better among the three methods across different SNRs. The averagesignal method exhibited a moderate performance, and the PCA method performed least well.As expected, the performance of each method was mostly improved with increased SNRs. Inthe second scenario, the advantage of LA-cCCA method was more apparent, suggesting theproposed method is more powerful in the case of the existence of sub-ROIs.4.3.2 Real fMRI Data SetSubjects and Data AcquisitionA total of 100 subjects from the Wu-Minn Human Connectome Project (HCP) [179] were em-ployed in this study. All subjects were healthy subjects aged 22-35 years. The MRI data fromall subjects were collected on a customized Siemens 3T “Connectome Skyra” scanner equippedwith a 32–channel head coil and a “body” transmission coil using HCP’s acquisition protocols[180]. Structural images were obtained with a three-dimensional MPRAGE T1-weighted se-quence with repetition time of 2400 ms, echo time of 2.14 ms, inversion time of 1000 ms andflip angle of 8◦. Two resting-state fMRI sessions were acquired on separate days while subjectswere fixed on a cross hair and asked to keep eyes open. The fMRI data scanning parameters65(a)(b)Figure 4.2: Simulation results for the first scenario. (a) The true connectivity matrix, as wellas the estimated connectivity matrices by average signal, PCA and LA-cCCA methods, wherethe blue entries correspond to the connectivities that are not considered in the analysis. (b)The performances of the three methods in terms of RMSE, as a function of SNR.66(a)(b)Figure 4.3: Simulation results for the second scenario. (a) The true connectivity matrix, as wellas the estimated connectivity matrices by average signal, PCA and LA-cCCA methods, wherethe blue entries correspond to the connectivities that are not considered in the analysis. (b)The performances of the three methods in terms of RMSE, as a function of SNR.67were as follows: repetition time of 720 ms, echo time of 33.1 ms, flip angle of 52◦, field of viewof 208 mm × 180 mm, matrix size of 104 × 90, 72 slices, 2 mm isotropic voxels and 1200 timepoints.Data PreprocessingThe data were processed by the HCP minimal preprocessing pipeline [71], including denoising,motion correction and alignment to standard space. FSL, FreeSurfer, and the ConnectomeWorkbench software packages were employed by this pipeline. Specifically, three pipelines,namely PreFreeSurfer, FreeSurfer and PostFreeSurfer were used to process the structural data,and two pipelines, namely fMRIVolumn and fMRISurface, were used to process the fMRI data.Furthermore, fMRI time series were de–meaned and linearly detrended, and the whole brainsignal was regressed out. Finally, the fMRI data were spatially smoothed by a 2 mm FWHMGaussian kernel and bandpass filtered at 0.01 Hz to 0.08 Hz.Table 4.1: The ROIs used in this studyNo. Label Name No. Label Name1 L1 Left Accumbens 2 R1 Right Accumbens3 L2 Left Amygdala 4 R2 Right Amygdala5 L3 Left Caudate 6 R3 Right Caudate7 L4 Left DiencephalonVentral8 R4 Right DiencephalonVentral9 L5 Left Hippocampus 10 R5 Right Hippocampus11 L6 Left Pallidum 12 R6 Right Pallidum13 L7 Left Putamen 14 R7 Right Putamen15 L8 Left Thalamus 16 R8 Right Thalamus“L” represents Left and “R” represents Right.Brain Functional Connectivity Network EstimationWe applied the proposed method to assess the brain functional connectivity network for eachsubject, utilizing the ROIs shown in Table 4.1. We first performed density clustering on eachROI, providing a decision graph that plotted δ as a function of ρ for each voxel within the ROI.The voxels located in the upper right corner of the decision graph were identified as densitypeaks. Instead of manual selection, the density peaks were automatically detected according toAlgorithm 1. Specifically, we set the candidate number of density peaks as C = {2, . . . , 6} andα = 10% to prevent the voxels with small ρ but high δ (i.e. outliers) being selected as density68peaks, as previously suggested [187]. The optimal number of density peaks was determinedby the maximum silhouette index. Figure 4.4 shows one example of the decision graph andthe process of determining the number of density peaks on the region of putamen. As can beseen from the decision graph, the density peaks should correspond to the two voxels in theupper right corner. Consistently, during the process of automatic density peak selection, themaximum silhouette index was found at the cluster number of 2, suggesting the voxels (withρi > ρα) with the top two largest δ as density peaks. As shown in Figure 4.5, the putamen wasfunctionally segregated into two sub-regions with associated density peaks.Figure 4.4: Example of decision graph (left) and the process of automatically determining thenumber of clusters (right).In the next step, we selected density peaks and their neighbours in each ROI for brainfunctional connectivity network estimation. Spatially constrained CCA was performed betweenROIs to assess the connectivity, with the spatial dominance constraint on density peaks andthe non-negativity constraint on all selected voxels. It should be mentioned that we initiallyestimated a fully connected brain network. Due to the relatively high computational cost,we did not perform a permutation test to determine the significance of the connectivity as in69(a) (b)(c)Figure 4.5: Density clustering on the Putamen. (a) The spatial distribution of subcorticalvolume in which 16 ROIs are included. (b) The region of Putamen. (c) Two functional sub-regions and their corresponding peak voxels detected by density clustering algorithm.70the simulation study. Instead, we determined the significant connectivity via a thresholdingstrategy (described below). Example of brain functional connectivity network estimated by theproposed method is shown in Figure 4.6.Figure 4.6: A fully connected brain network estimated by the proposed LA-cCCA method forone subject. (a)-(c) The sagittal, axial and coronal view of subcortical brain regions, whereeach node represents one ROI. (d) The estimated fully connected brain network, where the linesrepresent the connections between ROIs. The strength of the connection increases from blueto red.ReproducibilityTo demonstrate the performance of the proposed method, we compared the LA-cCCA methodwith the average signal and PCA method in terms of reproducibility of the estimated brainnetworks between two sessions. We hypothesized that the better the network modelling methodis, the more reproducible the estimated brain networks are. For the LA-cCCA method, the brainfunctional connectivity network was estimated as described above. For the other two methods,we first computed the average signal or the first principal component of each ROI to representthe ROI signal. The connectivity was then estimated by calculating the correlation coefficients71Figure 4.7: Comparison of estimated brain functional connectivity matrices between two ses-sions using different methods for one typical subject. The first row corresponds to the connec-tivity matrices (normalized) estimated during the first session, and the second row correspondsto the connectivity matrices (normalized) estimated during the second session.between ROIs using their ROI representative signals. For each subject, the brain functionalconnectivity network was assessed across two different sessions, each on separate days usingthe three methods (Figure 4.7). The connectivity matrices estimated by the LA-cCCA methodexhibited more consistent patterns between the two sessions, followed by the average signalmethod, but the PCA method performed the worst. The reproducibility was then quantifiedby measuring the Euclidean distance between the two connectivity matrices for each subject.The smaller the distance is, the more reproducible the connectivity pattern is. For the initiallyestimated fully connected networks, the LA-cCCA method demonstrated the most reproducibleresults, the average signal method showed a moderate reproducibility, and the PCA methodwas the least reproducible (Figure 4.8(a)). In real applications, we may need to determinethe significance of the estimated connectivity. Thresholding is a commonly used method fordetecting significant connectivities. Here the threshold was chosen such that the connectiondensity (i.e., the number of existing connections divided by the maximum possible number ofconnections) reached a desired value. To fully evaluate the proposed method, we examinedthe performance using a range of connection densities. The results showed that the proposedLA-cCCA method consistently outperformed the other two methods across different density72(a)(b)Figure 4.8: Comparison of the reproducibility for different methods. (a) The reproducibility onthe fully connected brain networks. (b) The reproducibility across different levels of connectiondensity.73levels in terms of the reproducibility (Figure 4.8(b)).4.4 Discussion and ConclusionIn this chapter, we have proposed a novel approach for brain functional connectivity estimation,which simultaneously determines the optimal ROI representation signals when considered incontext of connectivity with another ROI. Application of this method on both simulated andreal fMRI data set resulted in higher accuracy of brain network estimation and/or a morereproducible connectivity pattern.We utilized density clustering to investigate the local activity within the ROI. There are twoparameters in the algorithm: a cutoff distance dc for calculating the density and a threshold αfor preventing the outliers (ρi < ρα) being selected as density peaks. The parameters in thischapter were chosen according to heuristics suggested in previous studies [139, 187], althoughwe observed that mild perturbation in the parameter values didn’t appear to have a significantimpact on the results. The proposed method has advantage of detecting functional sub-regionsin the ROI and incorporates such local activity into the brain functional connectivity estimation.For a fair comparison with the other two methods, we didn’t split each sub-region in the realdata application. However, this advantage could facilitate potential analysis of sub-networkinteractions in the brain.We consider “reproducibility” as one key metric to evaluate the brain network models in thisstudy. Our results suggest that the proposed method outperformed the average-signal and PCAbased correlation methods in terms of the reproducibility. Previous studies on the comparisonsof different ROI signal representation methods suggested the PCA method tended to be moresensitive to functional inhomogeneity and exhibited a worse reproducibility than the averagesignal method [181], consistent with our current work. We utilized the Euclidean distance as thereproducibility measure in this study, which could be expanded for a comprehensive comparisonof different metrics in future work.One of the advantages of the LA-cCCA method is that we adaptively learn the weight vectorfor a single ROI according to its paired ROI. ROIs, especially if they are defined anatomically,may, and likely will, exhibit functionally inhomogeneous activations, depending upon neuralcontext. Therefore, we specifically allow, with the same spatial constraints, different weightvectors for the same ROI depending upon which other ROIs are being considered. This inherent74flexibility will ameliorate any concerns about functional heterogenity within an ROI. As anillustration, we analyzed the relationship between the variation in the weight vector of each ROIand the size of the ROI. The variation in the weights was characterized by the average standarddeviation over all voxels, and the size of the ROI was measured by the number of voxels in theROI. Unsurprisingly, the result showed that the variation in the weights was positively correlatedwith the ROI size (Figure 4.9, correlation coefficient = 0.73, p-value = 0.04), suggesting that thelarger the ROI is, the more heterogeneous the regional activation is, and likewise, the smallerthe ROI is, the more homogeneous the regional activation tends to be.Figure 4.9: Correlation between the variation in the weights and the size of ROI.In summary, the proposed method provides a potential method for regional activity rep-resentation and presents a more reliable model for connectivity network estimation. In thefuture studies, quantification of brain functional connectivity networks via graph theoreticalmeasures could further facilitate interpretations. Extension of the method to dynamic analysesmay also be of interest, and application to the neurological diseases could reveal disease relatedconnectivity patterns, providing potential biomarkers.75Chapter 5Graph Theory Method for DynamicBrain Functional ConnectivityAnalysisIn Chapter 2, 3 and 4, we have addressed the problems of regional signal representation andbrain functional connectivity modelling associated with ROI-based brain functional connectiv-ity. After estimating brain functional connectivity networks, a consequent challenging problemis how to summarize the information from the inferred brain functional connectivity networks,particularly in the dynamic setting which contains rich spatiotemporal information. In this chap-ter, we propose the use of dynamic graph theoretical measures to extract useful informationfrom time-varying brain functional connectivity networks as potential MRI-related biomarkers(e.g., the newly introduced graph spectral measure, Fiedler value, see Figure 1.5). Specifically,we apply the graph theory method to study the dynamics of cortical/subcortical functionalconnectivity in PD.5.1 IntroductionAs one of the most common degenerative neurological disorders, Parkinson’s disease affects alarge population worldwide, particularly in people over 50 years of age. It is characterized bythe cardinal motor features of tremor, rigidity, slowness of movement and postural instability,as well as various cognitive and behavioral problems, such as depression, sleep disturbancesand dementia. The relatively high prevalence and serious consequences of PD have a significantimpact on global health. Traditionally the diagnosis of PD has been clinical, because therecan be overlap with other conditions, and traditional structural imaging methods have beenrelatively uninformative, compared to other brain diseases (e.g. stroke, cancer).76Functional neuroimaging technologies, such as resting-state fMRI, may prove diagnosti-cally and prognostically useful for a number of brain diseases including PD. Due to its non-invasiveness, relatively high spatial resolution, and lack of requirement for the subject to engagein a task, resting-state fMRI has been adopted widely.If brain regions are considered as ‘nodes’ and the interactions between brain regions as‘edges’, graph theoretical analysis can be used to characterize the architecture and informationflow in brain networks [142]. Altered graph theoretical properties have been reported in neuro-logical diseases, such as AD and schizophrenia [14, 170], but a relative paucity of such studiesexist for PD [3, 131].In conventional functional connectivity analysis, brain networks are typically estimated uti-lizing the full time series under the assumption that connectivity is temporally stationary.However, even at the temporal resolution of fMRI, it is clear that different brain regions intrin-sically interact and coordinate in a dynamic manner [82], and functional connectivity dynamicproperties may provide insight into fundamental properties of brain networks [82, 99]. A bodyof literature has thus been dedicated to investigating dynamic functional connectivity, witha list of proposed network modelling methods that include a sliding window approach [82], achange point detection approach [49], time-frequency analysis [198] and hidden Markov models[136].Assessing the topological properties of these dynamic functional connectivity networks mayoffer a promising avenue for evaluating brain dynamics at a system level [63] as evidenced byrecent studies in schizophrenia and mild cognitive impairment [189, 202]. We suggest that theapplication of dynamic graph measures to PD will provide us deeper insights into the underlyingmechanisms of PD.The first aim of this study is to compare such dynamics in healthy controls (HCs) and PDsubjects by computing a range of graph measures over the time-varying functional connectivitynetworks. To construct the time-varying functional connectivity networks that can reveal thedynamic brain functional connectivity patterns, we use the sliding window approach, whereinthe sparse inverse covariance matrix is computed from the windowed segments [4].The second aim is to investigate two promising graph spectral measures that have receivedlittle attention in the study of PD: the Fiedler value and the normalized Fiedler value. TheFiedler value, also known as algebraic connectivity, reflects the global connectivity of a graph[59, 134], and has been applied in network science as an indicator of how well connected the77network is [102]. The normalized Fiedler value is similar to the Fiedler value, but normalizedfor the node degree in a graph [134]. These two measures are derived from the spectral graphtheory, or often referred to as Laplacian eigenmaps. In the latest literature, the informationprovided by Laplacian eigenmaps, especially by the second smallest eigenvalue of the Laplacian(the Fiedler value), has been successfully applied for the brain parcellation [100, 106]. Twoother studies have utilized the Fiedler value to characterize structural connectivity networks[51, 134]. Here we are the first to explore the potential of Fiedler value for studying the dynamicsof functional connectivity in PD.The third aim is to examine the utility of dynamic graph measures as potential featuresfor contributing to an MRI biomarker of PD. Conventional analysis of fMRI data exploringgroup differences between healthy individuals and neurological patients have commonly usedunivariate approaches [30, 117]. However, these studies have limited practical usage, as theyonly show significances at a group level. Thus, there has been an increasing interest in alter-native forms of analysis – e.g., applying machine learning techniques to fMRI data for effectiveand accurate computer-aided disease diagnosis [87, 141, 209], that provide discriminative powerat the individual level. Previous studies that performed discriminative analysis of PD usingmachine learning methods have used features such as structural/functional connectivity, ALFF(amplitude of low-frequency fluctuations) or ReHo (regional homogeneity) [46, 103]. In thisstudy, we propose utilizing dynamic graph measures derived from a temporal series of func-tional connectivity networks. To the best of our knowledge, this is the first work to utilizedynamic graph measures, especially the Fiedler value, for PD classification.The remainder of this chapter is organized as follows: Section 5.2 provides an extensivedescription on the dataset and methods used in this study, including the dynamic functionalconnectivity estimation, graph theoretical analysis and statistical analysis. The classificationframework using dynamic graph measures is also presented in this section. Section 5.3 presentsthe dynamic graph theoretical analysis results, demonstrates the classification performance ofthe proposed framework, and provides discussion. Finally, section 5.4 provides a brief conclusionof the present study.78Table 5.1: Participant demographic and clinical characteristicsCharacteristicsPD subjects(mean ± std)Healthy controls(mean ± std)Age 60.0 ± 9.8 58.3 ± 7.5Gender 30 females, 39 males 13 females, 16 malesUPDRS motor score 37.2 ± 17.3 Not applicableDisease duration 6.8 ± 4.6 Not applicableHoehn and Yahr stage(H&Y) 2.3 ± 0.8 Not applicable5.2 Methods5.2.1 Subjects and Data AcquisitionIn total, 69 PD subjects and 29 age-matched healthy controls participated in this study. ThePD subjects had mild to moderate PD (Hoehn and Yahr stage I - III). All healthy controls haveno history of neurological disorders. Demographic and clinical information are listed in Table5.1. All participants were recruited from the Movement Disorders Clinic of Xuanwu Hospitalof Capital Medical University, and provided written, informed consent prior to participation.All studies were approved by the Institutional Review Board of Xuanwu Hospital of CapitalMedical University, Beijing, China.Resting-state data were collected on a SIEMENS Trio 3T scanner equipped with a 16–channel head coil. During the scanning, all the participants were instructed to be awake witheyes closed and earplugs were used to minimize the machine noise. PD subjects were scannedat the off-medication state (after a 12-hour period of medication withdrawal).High-resolution T1 weighted anatomical images were acquired using a sagittal magnetizationprepared rapid gradient echo three-dimensional T1-weighted sequence with repetition time of1970 ms, echo time of 3.9 ms, inversion time of 1100 ms and flip angle of 15◦. A radiologistassessed the images for all the participants to exclude those with space-occupying lesions andcerebrovascular diseases. BOLD contrast EPI T2*-weighted images were acquired with thefollowing specifications: repetition time of 2000 ms, echo time of 30 ms, flip angle of 90◦, fieldof view of 256 mm × 256 mm, matrix size of 64 × 64, voxel size of 3.0 mm × 3.0 mm × 4.0mm, axial slices of 33 layers and the scanning time of 8 mins.79The fMRI preprocessing steps were the same as those in Section 2.2.4. 76 ROIs defined byDesikan-Killiany Atlas were selected in this study as shown in Table 5.2.Table 5.2: The 76 ROIs used in this studyIndex Name Index NameL1/R1 Left/Right-Cerebellum-CortexL20/R20 ctx-lh/rh-middletemporalL2/R2 Left/Right-Thalamus-ProperL21/R21 ctx-lh/rh-parahippocampalL3/R3 Left/Right-Caudate L22/R22 ctx-lh/rh-paracentralL4/R4 Left/Right-Putamen L23/R23 ctx-lh/rh-parsopercularisL5/R5 Left/Right-Pallidum L24/R24 ctx-lh/rh-parsorbitalisL6/R6 Left/Right-Hippocampus L25/R25 ctx-lh/rh-parstriangularisL7/R7 Left/Right-Amygdala L26/R26 ctx-lh/rh-pericalcarineL8/R8 Left/Right-Accumbens-areaL27/R27 ctx-lh/rh-postcentralL9/R9 ctx-lh/rh-caudalanteriorcingulateL28/R28 ctx-lh/rh-posteriorcingulateL10/R10 ctx-lh/rh-caudalmiddlefrontalL29/R29 ctx-lh/rh-precentralL11/R11 ctx-lh/rh-cuneus L30/R30 ctx-lh/rh-precuneusL12/R12 ctx-lh/rh-entorhinal L31/R31 ctx-lh/rh-rostralanteriorcingulateL13/R13 ctx-lh/rh-fusiform L32/R32 ctx-lh/rh-rostralmiddlefrontalL14/R14 ctx-lh/rh-inferiorparietal L33/R33 ctx-lh/rh-superiorfrontalL15/R15 ctx-lh/rh-inferiortemporalL34/R34 ctx-lh/rh-superiorparietalL16/R16 ctx-lh/rh-lateraloccipital L35/R35 ctx-lh/rh-superiortemporalL17/R17 ctx-lh/rh-lateralorbitofrontalL36/R36 ctx-lh/rh-supramarginalL18/R18 ctx-lh/rh-lingual L37/R37 ctx-lh/rh-transversetemporalL19/R19 ctx-lh/rh-medialorbitofrontalL38/R38 ctx-lh/rh-insula“L” represents Left and “R” represents Right.5.2.2 Dynamic Functional Connectivity EstimationWe used a sliding window approach to estimate the dynamic functional connectivity, where thesparse inverse covariance matrix was computed within each time window.80Sliding Window AnalysisDynamic functional connectivity analysis was performed for each subject with a sliding windowapproach. The sliding window approach is parameterized by a window length L and a step sizes. It decomposes the entire ROI time courses into multiple overlapping temporal windows oflength L. Specifically, given an entire ROI time courses with N time points, W = (N−L)/s+1is the number of temporal windows that can be generated by applying the sliding windowapproach. The functional connectivity metric is then calculated within each temporal window.In this study, we choose the window length L = 30 TRs (60s) and the step size s = 2 TRs aspreviously suggested [136].Sparse Inverse Covariance MatrixAs introduced in Section 1.3, the inverse covariance matrix (precision matrix) can be employedto infer brain functional connectivity. Under the assumed sparse nature of brain functionalconnectivity networks, a regularization strategy, such as LASSO, can be applied to the inversecovariance matrix. Functional connectivity is then indicated by the non-zero elements of thesparse inverse covariance matrix. This method is expected to be particularly useful when thenumber of the observations is limited, such as the limited number of time points in shorttemporal windows obtained from a sliding window approach.A sparse estimate of the inverse covariance matrix is obtained by minimizing the penalizednegative log likelihoodΘˆ = arg min {tr(SΘ)− log |Θ|+ λ‖Θ‖1} (5.1)where Θ is the inverse covariance matrix, S is the sample covariance matrix, ‖Θ‖1 is the element-wise L1-norm of Θ, and λ is the penalty parameter controlling the sparsity of the network. Anefficient algorithm has been found to solve this optimization problem [64]. We implementedthis sparse inverse covariance matrix estimation via the L1precision code 2.5.2.3 Graph Theoretical AnalysisGraph theoretical analysis was performed on the estimated dynamic functional connectivitynetworks. Graph measures, including characteristic path length, global efficiency, clustering2https://www.cs.ubc.ca/ schmidtm/Software/L1precision.html81coefficient, modularity and assortativity coefficient were calculated using the brain functionalconnectivity toolbox [142]. Additionally, we investigated two graph spectral measures that wehypothesized would be affected by PD (described below) but have received little attention inprevious studies. A list of graph measures used in this study are described in Table 5.3.Table 5.3: Description on graph measures used in this studyGraph Measures DefinitionCharacteristic path length The average of the shortest path lengthsover all pairs of nodes in a graph.Global efficiency The average inverse shortest path lengthof a graph.Clustering coefficient The number of connections existingamong the neighbours of a node, dividedby all possible connections (Average overall nodes to get an overall clustering coef-ficient of a graph).Modularity A statistic that quantifies the degree towhich the network can be subdivided intoindividual groups (modules).Assortativity The correlation coefficient between the de-grees of connected nodes.Fiedler value The second smallest eigenvalue of theLaplacian matrix of a graph.Normalized Fiedler value The second smallest eigenvalue of the nor-malized Laplacian matrix of a graph.The Fiedler value [59], also known as algebraic connectivity, is an indicator of global inte-gration of a network. The Fiedler value is computed as the second smallest eigenvalue of theLaplacian matrix of a graph G. The Laplacian matrix L(G) is defined as [60]:L(G) = D(G)−A(G) (5.2)where G is a graph with n nodes, D(G) is the degree matrix, an n-by-n diagonal matrix withthe elements of the diagonal equal to the degrees of the nodes in the graph G, and A(G) is theadjacency matrix, i.e., the connectivity matrix in this study.The other metric is the normalized Fiedler value, which is similar to the Fiedler value butnormalized for the number of edges in a graph. The normalized Fiedler value is computed asthe second smallest eigenvalue of the normalized Laplacian matrix. Given the ijth entry of the82Laplacian matrix Lij , and the degree of the ith node di, the ijth element of the normalizedLaplacian matrix Lnij is calculated as Lij/√didj .5.2.4 Statistical AnalysisTo examine whether the dynamic graph properties were different between HC and PD groups,statistical analyses were performed in each of the aforementioned graph measures using theWilcoxon rank sum test. For each subject, time-varying functional connectivity networks werefirst assessed with a sliding window approach, wherein the sparse inverse covariance matrixwas estimated within each temporal window. Graph measures were then calculated on theestablished temporal brain functional connectivity networks to get a series of dynamic graphmeasures. Finally, the Wilcoxon rank sum test was conducted on the standard deviations ofdynamic graph measures between HCs and PD subjects.In addition, an autoregressive (AR) model was employed to assess the dynamics in the graphmeasures. The AR model is a time series model that uses the observations from previous timesteps to predict the value at the next stepy(t) = c+p∑i=1aiy(t− i) + e(t) (5.3)where y is a time series vector, p is the order of the model, a1, a2, ..., ap are the parameters ofthe model, c is a constant, and e(t) is the white noise.Using the AR model, we examined the predictability of dynamic graph measures over time.The fitness of the AR model was assessed by the R2 coefficient of determination and comparedbetween HC and PD groups using the Wilcoxon rank sum test.Finally, CCA was employed to investigate the relationship between dynamic graph mea-sures and clinical features derived from PD subjects. When applying CCA to this study,dynamic graph measures and clinical information are the two sets of variables, that is, x =[x1, x2, . . . , xm]T , y = [y1, y2, . . . , yn]T , where xi(i = 1, 2, . . . ,m(= 7)) corresponds to thestandard deviation of each dynamic graph measure incorporated in the study, and yj(j =1, 2, . . . , n(= 5)) corresponds to each clinical information shown in the Table 5.1. We theninterrogated the loadings on dynamic graph measures and clinical information, which were de-fined respectively as the correlations between each dynamic graph measure xi and the canonicalvariable X, and between each clinical information yj and the canonical variable Y , to interpret83the relationship between dynamic graph measures and clinical information.5.2.5 Disease ClassificationTo evaluate the predictive ability of dynamic graph properties for disease identification, wecompared classification performance between HCs and PD subjects using different features. Afeature vector, with a large amount of features, is generated based on these dynamic time seriesof graph measures. With the high dimensionality of feature space, the complexity of the modelused for classification is dramatically increased and redundancy in features degrades classifi-cation performance. In order to avoid the effect of curse of dimensionality, feature extractionwas first performed by calculating 4 statistical indices, including the mean value, standard de-viation, minimum and maximum value, to characterize the time series of each graph measure,which led to a reduced feature dimension of 28 (4 statistics × 7 graph measures), and thenfeature selection was applied to the reduced feature set to obtain the most discriminative onesas the final feature set. Here a filter feature selection algorithm, i.e., the ReliefF algorithm[101], was used to sort the features based on their individual discriminative ability.Different supervised classifiers, including random forest, support vector machine (SVM),logistic regression, linear discriminant analysis (LDA) and na¨ıve Bayes, were used to examinethe discriminative power of dynamic graph measures. The random forest classifier was composedof 100 trees, and the SVM classifier was implemented with a radial base function (RBF) kernel.The same ten-fold cross validation strategy was performed for each of the five classifiers toevaluate classification performance. For each training set, we performed feature selection onthe training dataset and the classifier was trained using the selected features. We then appliedthe trained classifier to the testing dataset with the selected features to estimate classificationperformance. Final classification performance was obtained by averaging over all folds.In addition, to investigate the role of different dynamic graph measures in disease classifica-tion, we compared classification performances under different scenarios: with and without eachdynamic graph measure. Furthermore, we compared classification performance using station-ary graph measures (assessed by the mean value of temporal graph measures), dynamic graphmeasures (assessed by the standard deviation, minimum and maximum value of temporal graphmeasures), and a combination of stationary and dynamic graph measures.The overall framework proposed in this chapter is graphically shown in Figure 5.1. Giventhe extracted time series of each ROI, time-varying functional connectivity networks were es-84Figure 5.1: The proposed framework for the classification of Parkinson’s disease.timated using the sliding window approach. Graph measures were then calculated on eachtemporal network to generate a series of dynamic graph measures. Feature extraction and fea-ture selection were performed prior to proceeding to the classification step. Finally, differentclassifiers were applied to evaluate the classification performance.5.3 Experimental Results and Discussion5.3.1 Dynamic Graph Theoretical AnalysisOne example of the functional connectivity network at one time point is graphically shown inFigure 5.2. Graph theoretical analysis was applied to temporal functional connectivity networksto obtain a series of graph measures over time, quantitatively describing the dynamic topologicalproperties. In order to characterize the patterns of dynamic graph measures, the standarddeviation of each dynamic graph measure was calculated and compared between the two groups.The Wilcoxon rank sum test was performed on the standard deviations to determine if thechanging patterns of dynamic graph measures were statistically different between HCs and PDsubjects. The dynamic graph measures with significant differences between HC and PD groupsare shown in Figure 5.3. PD subjects exhibited lower standard deviation in the Fiedler value(p = 0.003, FDR (False Discovery Rate) corrected) and modularity (p = 0.04, FDR corrected),85Figure 5.2: Example of functional connectivity network at one time point. The red nodesrepresent brain regions, and the links represent functional connectivity between pairs of brainregions.suggesting both the global integration and local segregation of brain networks were less variablein PD. The standard deviation of the global efficiency was also found to be moderately smallerin PD subjects (p = 0.07, FDR corrected), suggesting a potential lack of variability in theparallel information transfer in brain networks of PD.In addition to the standard deviation of dynamic graph measures, an AR model was alsoemployed to explore the dynamics of the graph measures. Here a second order AR model wasfitted on each graph measure, and the R2 coefficient of determination was calculated and com-pared between HCs and PD subjects. Significant differences were found in the Fiedler value(p = 0.03, FDR corrected), characteristic path length (p = 0.03, FDR corrected), global effi-ciency (p = 0.03, FDR corrected) and modularity (p = 0.03, FDR corrected) with the Wilcoxonrank sum test, as shown in Figure 5.4. The higher coefficient of determination indicated thedynamic Fiedler value, characteristic path length, global efficiency and modularity were morepredictable over time in HCs, while PD subjects tended to exhibit a less deterministic dynamicpattern.Finally, CCA was performed on the dynamic graph measures and clinical information todetermine the relationship between them. Figure 5.5 shows the loadings (both positive andnegative) on dynamic graph measures and clinical information. One significant CCA component86Figure 5.3: The comparison of standard deviations between HC and PD groups with respectto the Fiedler value, modularity and global efficiency.(i.e., the first pair of canonical variables) was found (p < 0.05). Specifically, the dynamicFiedler value (its counterpart) and modularity loaded highly among all dynamic graph measures,and the H&Y score (a measure of overall disease severity) loaded highest among the clinicalinformation, suggesting a relationship between disease severity and the dynamics in the globalintegration and local segregation of brain networks.5.3.2 Classification PerformanceAlthough the statistical analysis results revealed group differences in the dynamic graph prop-erties between HCs and PD subjects, such group level differences have reduced applicability ina clinical setting, where a premium is placed on making inferences at an individual level. Tofurther examine the utility of dynamic graph measures as features for automatic diagnosis ofPD, we employed the classification technique to differentiate HCs and PD subjects based ontheir dynamic graph measures. In particular, we are interested in the role of dynamic graphmeasures, and especially, the Fiedler value for PD identification.87Figure 5.4: The comparison of coefficients of determination in the AR model between HC andPD groups.The classification performances across different classifiers are shown in Table 5.4. Two setsof experiments were done to examine the discriminative power of dynamic graph measures andthe role of the Fiedler value among all graph measures. In the first experiment, we first fed allother graph measures, including characteristic path length, global efficiency, clustering coeffi-cient, modularity and assortativity (in total, 4 statistics × 5 graph measures = 20 features),into the classifiers to obtain the classification performance as shown in the first row of Table 5.4.Then the Fiedler value and its counterpart (i.e., normalized Fiedler value) were added to theabove graph measures (in total, 4 statistics × 7 graph measures = 28 features) and fed intothe classifiers to examine the effect of the Fiedler value. The corresponding classification per-formance are shown in the second row of Table 5.4. In the second experiment, we applied theReliefF feature selection method to the settings of the first experiment. In each case, we selectedthe top 5 features as the input of the classifiers. We first applied feature selection to all othergraph measures without the Fiedler value to obtain the classification performance as shown inthe third row of Table 5.4, and then applied feature selection to all other graph measures withthe Fiedler value to obtain the classification performance as shown in the last row of Table 5.4.As can be seen from Table 5.4, in both cases (before and after feature selection), while all othergraph measures weakly differentiated HCs and PD subjects, the incorporation of the Fiedler88Figure 5.5: The loadings on dynamic graph measures and clinical information in the CCAanalysis.value significantly improved classification performance. When applying feature selection to all7 graph measures (the classification results in the last row of Table 5.4), the top 5 featurescorresponded to the statistics of the Fiedler value and normalized Fiedler value, suggesting theFiedler value played a more important role than other graph measures in disease classification.The top features among all other graph measures (i.e., characteristic path length, global ef-ficiency, clustering coefficient, modularity and assortativity) corresponded to the statistics ofmodularity and global efficiency, which also showed different levels of significance in the sta-tistical analysis. A best classification performance of 85.7% was achieved using random forest,suggesting the utility of dynamic graph measures as features for PD identification.The effect of each dynamic graph measure on the classification performance is graphicallyshown in Figure 5.6. The classification performance differences were minor for all other dynamic89Table 5.4: The classification performance of dynamic graph measuresGraph Measures RandomForestLogisticRegressionSVM LDA Na¨ıveBayesAll graph measureswithout Fiedler value64.3% 67.4% 69.4% 69.4% 62.2%All graph measureswith Fiedler value74.5% 71.4% 70.4% 74.5% 72.5%Feature selection with-out Fiedler value66.3% 70.4% 70.4% 69.3% 67.4%Feature selection withFiedler value85.7% 80.6% 79.6% 79.6% 78.6%graph measures. However, a significant improvement on the classification performance wasobserved by the inclusion of dynamic Fiedler value, supporting the important role of Fiedlervalue for disease identification.Classification performance using stationary graph measures, dynamic graph measures anda combination of stationary and dynamic graph measures were compared, as shown in Fig-ure 5.7. Inclusion of dynamic graph measures is important for the development of MRI-derivedbiomarkers for PD diagnosis.We compared our results with the current state-of-the-art in Table 5.5. The classificationperformance of our proposed work is comparable with previous studies in literature. Althoughthe performance is not among the best, we still consider it satisfactory considering the dramaticreduction in the number of features used for disease identification, and the larger sample sizeutilized here.5.3.3 DiscussionIn this chapter, we investigated the graph properties of time-varying functional connectivity inHCs and PD subjects derived from resting-state fMRI data. Dynamic functional connectivitynetworks were estimated by the sparse inverse covariance matrix across sliding windows, andgraph theoretical analysis was performed on the established time-varying functional connectivitynetworks to develop non-invasive biomarkers. The computed dynamic graph measures werefed into the classifier to evaluate their utility for automatic disease detection. All findingsdemonstrated the importance of including dynamic graph properties, especially fluctuations in90Table 5.5: Comparison between the proposed work and the state-of-the-artin PD classification.Work Subjects Modality Features # Classifier Acc[46] PD21/HC26fMRI Functionalconnectivity150 SVM 93.6%[103] PD19/HC27fMRIandsMRIALFF, ReHo,RFCS, GM,WM, CSF40 SVM 86.9%[137] PD30/HC30sMRI Values ofvoxels417 SVM 86.7%[95] PD123/HC85sMRIand DTIGM, CSF andFA10 SVM 83.3%[147] PD50/HC50DTI FA and MD 14 LogisticRegression77.2%Ours PD69/HC29fMRI Dynamicgraphmeasures5 RandomForest85.7%fMRI = functional MRI; sMRI = structural MRI; DTI = Diffusion TensorImaging; ALFF = Amplitude of Low-frequency Fluctuations; ReHo = Re-gional Homogeneity; RFCS = Regional Functional Connectivity Strength;GM = Gray Matter; WM = White Matter; CSF = Cerebrospinal Fluid;FA = Fractional Anisotropy; MD = Mean Diffusivity.91Figure 5.6: The classification performance differences between including and excluding eachdynamic graph measure.the Fiedler value, for the development of an MRI-related biomarker for PD.Graph theoretical analysis has been increasingly employed to study brain networks in avariety of neurological diseases, revealing significant altered graph properties in diseased brains[14, 170]. However, unlike the large number of graph theoretical analyses in diseases such asAD, limited studies have investigated graph properties in PD [3, 131]. Existing studies, utilizingstatic connectivity measures, suggested that topological properties of functional connectivitynetworks were altered in PD, with a decreased global efficiency and increased clustering coeffi-cient and modularity compared to HCs [10, 159]. In addition, another study investigated topo-logical properties of structural brain networks in PD, demonstrating aberrant cerebral networktopology with a larger characteristic path length and reduced global efficiency in comparisonwith HCs [131].The human brain is obviously a dynamically interactive system, and even at the relativelysluggish temporal resolution of fMRI, changes in connectivity patterns are evident [4, 142].Recent studies have examined the altered dynamics of functional connectivity in disease states[84, 145]. However, relatively few studies have explored dynamic graph measures of time-varyingfunctional connectivity networks (e.g., [89, 202]). In the current study, we analyzed dynamicgraph properties in PD using fMRI data. In a study that compared the graph measures with92Figure 5.7: The comparison of classification performance using stationary graph measures,dynamic graph measures and a combination of stationary and dynamic graph measures.different network densities, the values of graph measures were found to be dependent on thenetwork sparsity [25]. A low density without isolated nodes within the network was suggestedin graph theoretical analysis. We used a sparse inverse covariance matrix in our study. In thischapter, a fixed parameter with sparsity level as 20% was chosen. We found significant differ-ences between HCs and PD subjects in terms of the Fiedler value and modularity, suggestingabnormal dynamics in both global integration and local segregation of diseased brain networks.Further CCA analysis revealed such dynamics were closely related to disease severity. In addi-tion to the standard deviation which was mostly used to analyze dynamic patterns of features,an autoregressive model was further employed in this study to investigate the predictability ofdynamic graph measures over time. PD subjects had lower R2 of the model (indicating less pre-dictable) in dynamic Fiedler value, characteristic path length, global efficiency and modularity,suggesting less deterministic dynamics in disease states. In the current work, we included theFiedler value in the graph theoretical analysis, which has received little attention in previousstudies. We found PD subjects had an especially lower variability in dynamic Fiedler valueof brain networks. This is suggestive of a reduction in the variability of global integration ofdiseased brain networks, possibly due to the impaired cognitive flexibility in PD. Two priorstudies have applied the Fiedler value to studying structural connectivity network properties inpatients with AD [51, 134]. One study revealed a decreased Fiedler value in patients, suggest-ing a reduced network robustness as disease progressed, whereas the other study showed few93differences in the Fiedler value across diagnostic groups. In contrast, the current study appliedthe Fiedler value to time-varying functional connectivity networks, showing for the first timedisrupted temporal dynamics in global integration of brain networks in PD and its relation toseverity of the disease.In addition to the statistical group-wise analysis between HCs and PD subjects, we utilizedmachine learning techniques to make individual-based inferences using dynamic graph measures.There are several recent studies making use of graph measures for the diagnosis of neurologicaldiseases. For example, Khazaee et al. [87] used graph measures to identify patients with ADand mild cognitive impairment (MCI) from healthy controls. However, disease identificationstudies using dynamic graph properties remain scarce. In [189], Wee et al. employed, forthe first time, dynamic graph measure (i.e., clustering coefficient) for early MCI identification.With respect to PD, previous studies looking at MRI classification of PD have relied uponstatic features, such as structural/functional connectivity, ALFF or ReHo, with the accuracyranging from 39.53% to 93.6% [46, 103, 137]. To the best of our knowledge, this is the firstreport to explore the utility of dynamic graph measures for PD classification. A classificationaccuracy of 85.7% suggested good diagnostic power of dynamic graph measures. Although suchclassification performance is not the highest in the literature, we can still consider it satisfactorygiven the very low number of features used, and the relatively large sample size employed. Theclassification performance of the current work is higher than that of the early MCI identificationstudy using temporal clustering coefficients which yielded 79.6% classification accuracy [189].Promising classification results suggested that inclusion of dynamic graph measures, and inparticular, the Fiedler value, will be important for the development of MRI-related biomarkersfor PD.5.3.4 LimitationsWe have performed dynamic graph theoretical analysis of time-varying functional connectivitynetworks in PD, revealing the altered dynamic graph properties in diseased brains. However, theunderlying neurobiological underpinnings for such dynamics remain unclear. Future studies willbe required to advance our understanding of these temporal dynamics. In addition, the dynamicgraph measures were computed on time-varying functional connectivity networks which wereestimated by the sparse inverse covariance matrix across sliding windows. However, we cannotrule out the possibility that different graph creation methods may give varied results. As94suggested in [134], there has been little consistency in previous studies with respect to graphtheoretical analysis even though using the same image modality, in part due to the differentgraph creation methods. Therefore, future comprehensive studies using a wide range of graphcreation methods should be performed to verify the reliability of dynamic graph measures asbiomarkers for PD.5.4 ConclusionIn this chapter, we analyzed dynamic graph properties of time-varying functional brain func-tional connectivity in HCs and PD subjects. In particular, the Fiedler value, a novel graphspectral measure, was explored for studying the dynamics of functional connectivity. PD sub-jects had an altered variability in dynamic Fiedler value and modularity of brain networks,which was related to disease severity. The dynamics in Fiedler value, along with characteristicpath length, global efficiency and modularity, were less deterministic in PD. Promising clas-sification results provided support for including dynamic graph measures, especially dynamicFiedler value, for MRI assessment of PD.95Chapter 6Conclusion and Future Work6.1 ConclusionInferring brain functional connectivity from fMRI data can take place at the voxel or ROIlevel. In this thesis, we focus on the ROI-based brain functional connectivity study. From theapplication perspective, brain functional connectivity assessment can be broadly divided intotwo major categories: brainstem functional connectivity and cortical/subcortical brain func-tional connectivity. While the former is rarely studied and the latter is commonly studied, weinvestigate both of them in this thesis (for brainstem functional connectivity, we specificallyfocus on brainstem-cortical functional connectivity). From the methodological perspective, weaddress fundamental problems associated with ROI-based brain functional connectivity study,including regional signal representation, brain functional connectivity modelling and brain func-tional connectivity analysis. All the proposed methods have been applied to real fMRI data.The results revealed reliable brain functional connectivity estimation and/or indicated success-ful disease assessment and treatment evaluation. A summary of the thesis contributions andmajor findings are listed below.First, we proposed a novel framework for brainstem-cortical functional connectivity mod-elling where the regional signal of brainstem nuclei is appropriately represented by PLS and theconnections between brainstem nuclei and other cortical/subcortical brain regions are reliablyestimated by partial correlation. Since brainstem structures can be highly functionally inho-mogeneous, it may not be optimal to use average signal based regional signal representationstrategy. PLS is a reasonable alternative approach that represents regional signals by utilizingthe covariance relationship between brainstem nuclei and other cortical/subcortical brain re-gions. Additionally, considering the anatomical peculiarity of the brainstem, in our proposedframework, special care is taken in the preprocessing wherein a separate brainstem motioncorrection is performed. We applied the proposed framework to assess functional connectiv-ity of the PPN, a brainstem nucleus critical for locomotion control. Specifically, in Chapter962 and 3, we employed the proposed framework to examine the effect of two clinical interven-tions, namely GVS and walking exercise, on PPN functional connectivity. Our method reliablyassisted in the treatment evaluation of PD in terms of brainstem-cortical functional connec-tivity. The results demonstrated that PPN functional connectivity can be modulated by GVSin a stimulus-dependent manner as well as by walking exercise in a dose-dependent manner inPD, which may guide how these clinical interventions can induce functional plasticity and thusprovide insights into their underlying mechanism of disease treatment.Second, in Chapter 4, we proposed a novel method of representing regional signal andestimating brain functional connectivity with constrained canonical correlation analysis. Withmost ROI-based brain functional connectivity modelling approaches, the signals from same-ROI voxels are simply averaged, neglecting any inhomogeneity in each ROI. Our proposedmethod is able to take the regionally-specific nature of brain activity, the spatial location ofconcentrated activity, and activity in other ROIs into account for simultaneous regional signalrepresentation and brain functional connectivity estimation. Using the proposed method, weestimated brain functional connectivity between subcortical brain regions in healthy adults. Ourresults demonstrated that the proposed method is a robust model for assessing brain functionalconnectivity, yielding a more reproducible connectivity pattern.Finally, given the inferred brain functional connectivity network, further analysis to sum-marize network properties is of great importance, especially for dynamic brain functional con-nectivity which contains rich spatiotemporal information. In Chapter 5, we proposed the useof graph theory in a dynamic manner to extract useful information from brain functional con-nectivity network for the development of MRI-related biomarkers. In particular, a novel graphspectral metric, Fiedler value, was introduced for studying the dynamics of functional con-nectivity. When applied to studying brain dynamics in PD, we found altered dynamic graphproperties, including Fiedler value, in PD compared to healthy controls. In addition, we ob-tained promising classification performance using dynamic graph properties, and indicated thatFiedler value was the most important feature for improving the diagnosis power. Our findingsdemonstrated the importance of including dynamic graph properties, especially fluctuations inthe Fiedler value, for the development of an MRI-related biomarker for PD.976.2 Future Work6.2.1 Multi-task Brainstem-cortical Functional Connectivity AnalysisIn this thesis, we have proposed a framework for analyzing brainstem-cortical functional con-nectivity under one condition (e.g., resting-state or under stimuli). In clinical applications, theexperiment design could incorporate multiple tasks and it would be of interest to investigatethe differential effects of tasks. Therefore, we would like to extend the one-condition brainstem-cortical functional connectivity analysis to multi-task brainstem-cortical functional connectivityanalysis.Discriminant correlation analysis (DCA) [73] is a recently proposed approach for analyzingthe correlation relationship between two datasets. Similar to the CCA method, it maximizesthe correlation between two datasets, while the DCA method also incorporates the class as-sociations, wherein the between-class correlations within each dataset are eliminated and thecorrelation relationships are restricted to be within classes. Therefore, DCA is well suited formulti-task connectivity analysis, wherein each task is considered as one class. We are interestedin applying the DCA method to investigate the multi-task brainstem-cortical functional connec-tivity. By applying DCA, the two datasets correspond to the time courses of cortical/subcorticalROIs and the time courses of a brainstem area, and in each dataset, time courses correspondingto different tasks are incorporated.6.2.2 Regional Signal Representation with Constrained Multiset CanonicalCorrelation Analysis for Brain Functional Connectivity NetworkEstimationIn ROI-based brain functional connectivity estimation, a key issue is how to represent theinformation in a given ROI. Previous studies have suggested that different regional signal rep-resentation strategies may have a significant impact on the subsequent analysis inferred fromthe fMRI data. Most current studies take the average signal from same-ROI voxels for re-gional signal representation. Alternative strategies such as PCA-based approach have beenproposed in the literature. In Chapter 4, we propose a novel regional signal representationmethod using constrained CCA and demonstrate its superiority over average-signal and PCAbased approaches in terms of the accuracy of the estimated brain functional connectivity andthe reproducibility of the connectivity pattern. However, our proposed method is a pairwise98regional signal representation strategy which is conducted between pairs of ROIs. To facilitatethe computational speed and the large-scale analysis, it would be desirable to develop a jointregional signal representation method which could simultaneously assess representative signalsacross all ROIs.Multiset CCA (MCCA) [98] is a statistical method extended from the CCA to summarizethe correlation structure among different datasets. While CCA maximizes the correlation rela-tionships between two datasets via linear transformation, MCCA extends the CCA to multipledatasets in which the overall correlation among multiple (i.e., more than two) datasets is op-timized. By applying MCCA, the corresponding canonical variables from each dataset can bejointly obtained.Inspired by the potential of MCCA, we are interested in extending the pairwise to joint re-gional signal representation for brain functional connectivity estimation. Similar to the pairwiseregional signal representation with constrained CCA, spatial constraints will be incorporatedinto the MCCA for the joint regional signal representation. Given a set of ROIs, instead ofperforming constrained CCA on each pair of ROIs, MCCA will be carried out on all ROIs tojointly obtain the regional representative signals at one time. Meanwhile, the correlation matrixof representative signals will be available for brain functional connectivity estimation.6.2.3 Deep Clustering for Automated Brain ParcellationBrain parcellation refers to the division of the brain into a set of regions (or parcels) that sharecertain neurobiological characteristics. It is an active research area which provides insightsinto the underlying brain architecture. Appropriate brain parcellation is always a prerequisiteand of great significance for the subsequent quantitative analysis of the brain [19]. Whilemanual parcellation of the brain is laborious, subjective and time-consuming, automated brainparcellation is highly desired in practice for quantitative assessment.Many approaches have been proposed for the automated parcellation of the brain. Conven-tional strategies can be categorized into: (1) atlas-based registration, (2) data-driven methodssuch as ICA and clustering algorithms, and (3) machine learning with hand-crafted features.However, these conventional methods suffer from disadvantages including potential registrationerrors, dependence on manual feature engineering and shallow structures with limited power,especially for sophisticated high-dimensional features. Recently, with the emergence of deeplearning, researchers have leveraged this technique to perform brain parcellation, accounting for99the shortcomings of previous methods. Although significant improvements have been achievedvia deep learning, this technique highly depends on the labelled training data for supervisedlearning. Nevertheless, in the case of lacking labelled data and exploratory studies where theunderlying ground truth is not explicitly clear, we would be more interested in unsuperviseddeep learning.Most recently, efforts have been dedicated to adapting clustering algorithms to end-to-endlearning using the deep neural network, which we call Deep Clustering. It simultaneouslylearns feature representations and cluster assignments in an unsupervised manner. Differentalgorithms have been developed, including Deep Embedded Clustering (DEC) [196], Deep Em-bedded Regularized Clustering (DEPICT) [70], and DeepCluster [34], showing significant im-provements over traditional clustering algorithms. While deep clustering is a recently emergingmethod, its application to the medical area remains scarce. In the future work, we plan toapply deep clustering to brain parcellation. Specifically, we would like to conduct a voxel-wisebrain parcellation on the basis of brain functional connectivity, under the assumption that thepatterns of functional connectivity are of high dimension with complexly organized hierarchicalfeatures that could be extracted by deep neural network and used for partitioning the braininto distinct functional regions. An interesting application would be to investigate functionalregions contained in the brainstem, which could provide insights into the underlying functionalstructures of the brainstem and ultimately benefit clinical neuroscience.6.2.4 Application to Parkinson’s Disease StudiesAs one of the most common degenerative neurological disorders, Parkinson’s disease affects alarge population worldwide, particularly in people over 50 years of age. The relatively highprevalence and serious consequences of PD have a significant impact on global health. Whiletraditionally the diagnosis of PD has been clinical, and traditional structural imaging methodshave been relatively uninformative, fMRI may prove diagnostically and prognostically usefulfor PD.It has been suggested that neurological disorders including PD can be characterized asdysconnection syndromes. The study of brain functional connectivity from fMRI data couldprovide insights into the disease related connectivity abnormality, which may ultimately assistin the disease diagnosis and treatment assessment.In future work, we plan to investigate brain functional connectivity in PD, examining the100disease induced effect on connectivity patterns. In particular, we are interested in studying thebrainstem functional connectivity in PD. It would be interesting to examine functional connec-tions of different brainstem nucleus, evaluate the effects of various therapeutic interventions onbrainstem functional connectivity and characterize functional organizations of the brainstem.101Bibliography[1] Feridun Acar, Go¨ksemin Acar, Levent Sinan Bir, Bengi Gedik, and Attila Og˘uzhanog˘lu.Deep brain stimulation of the pedunculopontine nucleus in a patient with freezing of gait.Stereotactic and functional neurosurgery, 89(4):214–219, 2011.[2] L Adams, H Frankel, J Garlick, A Guz, K Murphy, and SJ Semple. The role of spinal cordtransmission in the ventilatory response to exercise in man. The Journal of physiology,355(1):85–97, 1984.[3] Federica Agosta, Marina Weiler, and Massimo Filippi. Propagation of pathology throughbrain networks in neurodegenerative diseases: from molecules to clinical phenotypes. 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