Statistical Methods for Estimating and Analyzing Brain Functional Connectivity Pubblico
Higgins, Ixavier A. (Spring 2019)
Abstract
In recent years, network science has become an increasingly popular approach for investigating interdependencies between spatially distinct brain regions. The network based paradigm is particularly useful in neuroimaging applications because of the ease of representing complex spatiotemporal relationships via a finite set of regions. Analyses of functional and structural architecture have elucidated the mechanisms by which neurological disorders distort local and global functional organization, inhibiting normal brain processes.
In chapter two, we propose a Differential Degree Test (DDT) which detects regions of interest (ROIs) incident to a statistically significant number of edges that are differentially weighted across healthy and depressed populations. We achieve this by generating null networks in which edge weights match distributional properties of edges in the observed difference network. Extensive numerical studies demonstrate superior performance relative to popular network comparison methods. We apply the method to major depressive disorder patients and age-matched healthy controls. Our method selects ROIs commonly implicated in studies of depression.
In chapter three, we propose a structurally informed Gaussian Graphical Model (siGGM) that incorporate structural connectivity into the estimation of functional connections between all region pairs. Although the exact relationship between brain function and structure is not completely known, anatomical wiring certainly constrains cortical activity. Our multimodal approach requires rs−fMRI and diffusion tensor imaging (DTI) which maps the orientation of all white matter fiber tracks in the brain. Our efficient optimization algorithm admits a MAP solution of subject-specific functional brain networks. Numerical studies and an application to sixty-nine individuals in the Philadelphia Neurodevelopment Cohort demonstrate our method's superior performance to state of the art competitors.
In chapter four, we investigate rapidly changing functional connectivity. Recent work suggests that the brain utilizes a finite set of connectivity states that are common across all health conditions. We propose a semi-parametric dictionary learning method to simultaneously estimate the shared set of brain networks as well as classify individuals into disease groups based upon usage of the basis set. We assess the method’s performance on simulated data and detect biologically meaningful brain networks in a study of posttraumatic stress disorder.
Table of Contents
1 Introduction....1
1.1 Overview.................................. 2
1.1.1 Basics of functional magnetic resonance.........5
1.1.1.1 Resting state fMRI................... 8
1.1.2 Basics of Diffusion Tensor Imaging ............... 8
1.1.3 Brain structure and function................... 10
1.2 Brain Connectome ............................ 11
1.2.1 Static Functional connectivity Methods ............14
1.2.2 Dynamic functional connectivity Methods .............16
1.2.3 Challenges in functional connectivity ...............17
1.3 MotivatingData ............................. 18
1.3.1 Major Depressive Disorder dataset ..........19
1.3.2 Philadelphia Neurodevelopmental Cohort dataset .......20
1.3.3 Grady Trauma Project dataset ................. 22
1.4 ProposedResearch ............................ 23
1.4.1 Topic 1: Difference degree test for comparing brain networks....24
1.4.2 Topic 2: Anatomically informed estimation of brain functional networks.............................. 24
1.4.3 Topic 3: Semi-parametric Bayesian hierarchical dictionary learning................................. 25
2 Comparison of nodal differential degree centrality......26
2.1 Introduction................................ 27
2.2 Method .................................. 31
2.2.1 Brain network construction ................... 31
2.2.2 DifferentialDegreeTest ..................... 33
2.2.2.1 Difference Network Construction........... 33
2.2.2.2 Deriving p-value from between-group tests .........35
2.2.2.3 Null distribution generation.............. 36
2.2.2.4 An adaptive threshold selection method ............38
2.2.2.5 The DDT Test ..................... 40
2.3 Simulation................................. 41
2.3.1 Results .............................. 44
2.4 Data Application ............................. 48
2.4.1 Data................................ 49
2.4.2 Results............................... 50
2.5 Discussion................................. 55
3 Anatomically Informed Estimation of Functional Brain Networks .....57
3.1 Introduction................................ 58
3.2 Materials and methods.......................... 62
3.2.1 Gaussian graphical model for brain networks .......... 62
3.2.2 Structurally informed Bayesian Gaussian graphical model...64
3.2.3 Model Estimation......................... 68
3.3 Results and Discussion .......................... 70
3.3.1 Simulations ............................ 70
3.3.1.1 Simulation Setting ................... 70
3.3.1.2 Results ......................... 74
3.3.2 PNC Data Application...................... 79
3.3.2.1 Data preprocessing................... 80
3.3.2.2 Results ......................... 80
3.4 Conclusion................................. 86
4 Semi-parametric Bayesian hierarchical dictionary learning......88
4.1 Introduction................................ 89
4.2 Methodology ............................... 93
4.2.1 Dictionary learning........................ 93
4.2.2 Bayesian Dictionary Learning (BayDiL) ..............94
4.2.3 PosteriorSampling ........................ 96
4.2.4 Subcase: Regional time series as Observed Signal .........98
4.3 Results and Discussion .......................... 100
4.3.1 Simulations ............................ 100
4.3.1.1 SimulationSetting ................... 100
4.3.1.2 Results ......................... 102
4.3.2 Posttraumatic Stress Disorder Data Application .............106
4.3.2.1 Results ......................... 106
4.4 Conclusion................................. 112
5 Summary and Future Directions .....115
A Appendix for Chapter 2 ....119
A.1 Proof for HQS procedure......................... 119
A.2 Tables ................................... 122
B Appendix for Chapter 3 ......123
B.1 Parameter Updates............................ 123
B.2 Hyperparameter Choice and Initial Values ...........125
B.3 Measure for computing between module differences ...........126
B.4 Calculation of ICC ............................ 126
B.5 Tables ................................... 127
B.6 NetworkMetrics ............................. 128
C Appendix for Chapter 4 .......130
C.1 Hyperparameter selection and initial values ............130
C.2 Figures................................... 132
Bibliography............135
List of Figures
1.1 The brain is composed of grey matter, white matter, and cerebrospinal fluid........................3
1.2 Communication between neurons in the brain.........11
1.3 Estimation of sliding windows correlations.......17
2.1 Comparison of eDDT, aDDT, t-test (T(10%) ),BinB) on simulated data with three differentially connected nodes incident to 4, 7, and 11 DWEs....................... 46
2.2 Performance of the methods as the network size increases with a fixed
density................................... 47
2.3 Performance of the methods in selecting DWEs .............48
2.4 DWEs detected by eDDT under four model assumptions ..........52
2.5 Heat map of chi-squared statistic....................... 54
3.1 FC and SC association observed in the data ................60
3.2 Distribution of ωjk as a function of hyperparameters and SC ...........67
3.3 Graphical illustration of the siGGM................... 68
3.4 Comparison of siGGM, G-Wishart, and aGlasso for p=100 regions ....76
3.5 Results for data simulated from non-Gaussian ICA model ...........77
3.6 siGGM computation time ........................ 77
3.7 Gender-stratified correlates of FCandSC ............81
3.8 Network estimates for females and males in the PNC data application ....82
3.9 Comparison of network features across males and females .............83
3.10 Reliability of network metrics estimated by siGGM, aGlasso, and glasso 86
4.1 Comparison of the the BayDiL and DL methods in recovering the basis signals when the signals share 1, 2 and 3 active regions in common.....104
4.2 BayDiL performance with misspecified number of atoms ......105
4.3 Covariance matrices of the five basis components estimated by the BayDiL method.............................. 108
4.4 Covariance matrices of the five basis components estimated by the DL method .................................. 108
4.5 Maps of co-activation in each atom for the BayDiL .........109
4.6 Posterior distributions of the length scale parameters for the BayDiL estimates.................................. 111
C.2.1Comparison of network estimates for Square Exponential Kernel simulations .................................. 132
C.2.2Comparison of network estimates for Sinusoidal simulations ...........133
C.2.3Twenty seven brain regions organized by functional module .........134
List of Tables
2.1 False positive and true positive rates for the Random, Small World, and Hybrid network structures considered.........45
2.2 Top 20 differentially connected nodes in the MDD data application ..... 51
2.3 Consistency of identified DWEs ..................... 53
3.1 Performance of SC-informed methods on simulated data ............78
3.2 Within- and between- module differences in FC between males and
females................................... 85
4.1 Dictionary atom recovery success rate in simulations ..........103
4.2 Average classification accuracy as measured by the adjusted rand index for
the BayDiL method. ............................ 104
4.3 Average score in the intrusion, avoidance/numbing, and hyperarousal domains. Reported values are the mean and standard deviation. . . . . . . 111
A.1 Within and between functional module DWE in the major depressive disorder study. Bolded values indicate statistically significant number of DWE between the respective functional modules ...................122
B.1 Performance of siGGM and SC naive approaches on simulated network data
with p=100 and 200 nodes. Eglob is the bias in global efficiency........127
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