Statistical Approaches for Exploring Brain Connectivity with Multimodal Neuroimaging Data Pubblico

Abstract

Advances in neuroimaging technology provide a gateway for studying the function and structure of the human brain, which stands to improve our understanding of neural networks and yield important insights about brain disorders. The statistical analysis of neuroimaging data poses a challenge, because the data is high-dimensional and contains spatial and temporal correlations. The focus of this dissertation is to develop statistical methods for multimodal neuroimaging data that allow us to explore the relationship between functional and structural brain connectivity, and investigate how this relationship differs between healthy and diseased brains. A set of functionally connected brain networks can be estimated from fMRI data using independent component analysis (ICA). However, this approach ignores information about the underlying structural connections, which are believed to facilitate functional connectivity between remote brain regions. For the first topic, we propose a novel measure of the strength of structural connectivity (sSC) underlying these functional networks, by incorporating structural information from DTI data. To conduct inference on our sSC measure, we estimate a covariance term that considers spatial similarity between observations via a parametric semivariogram model with a novel distance metric. We demonstrate the performance of our proposed measure with simulation studies, and apply our method to an fMRI and DTI dataset. We find that sSC is associated with component reliability, demonstrating the benefit of leveraging information from structural data in the estimation of functional networks from fMRI data. The second and third topics propose statistical frameworks for modeling the relationship between functional and structural connectivity across the whole-brain network. The second topic presents a hierarchical model with a linear link function to describe the association at each edge in the network, and uses the EM algorithm to estimate the model parameters. We consider both correlation and partial correlation as measures of functional connectivity. The third topic considers a more flexible approach to modeling the function-structure association by using copulas. In this way, we can model the marginal distributions of functional and structural connectivity data, and separately, estimate their association using a copula function. For each method, we conduct simulation studies to evaluate performance, and apply the proposed methods to an fMRI and DTI dataset, demonstrating biologically meaningful findings.

Table of Contents

1. Introduction. 1

1.1 Overview. 2

1.2 Organization of the Human Brain. 3

1.3 Functional Neuroimaging. 5

1.3.1 Basic Principles of Magnetic Resonance Imaging (MRI). 6

1.3.2 Functional MRI (fMRI) data. 7

1.3.2.1 The fMRI BOLD signal. 7

1.3.2.2 fMRI data structure. 8

1.3.2.3 Resting State. 9

1.3.3 fMRI Preprocessing Pipeline. 10

1.3.4 Functional Connectivity (FC) Analysis. 11

1.3.4.1 Independent Component Analysis (ICA). 13

1.3.4.2 Network Modeling Methods for FC. 15

1.4 Structural Neuroimaging. 16

1.4.1 Diffusion Tensor Imaging (DTI) Data. 16

1.4.2 DTI Preprocessing Pipeline. 17

1.4.3 Tractography and Structural Connectivity (SC). 18

1.5 Combining Structure and Function. 20

1.5.1 Motivation. 20

1.5.2 Review of Existing Multimodal Methods. 20

1.6 Motivating Data Example. 22

1.6.1 Major Depressive Disorder (MDD). 22

1.6.2 Subjects. 23

1.6.3 Data acquisition and preprocessing. 23

1.7 Proposed Research. 24

1.7.1 Topic 1: Quantifying the strength of structural connectivity underlying functional brain networks. 25

1.7.2 Topic 2: A joint model for functional and structural connectivity across the whole-brain network. 25

1.7.3 Topic 3: Using copulas to model the structure-function relationship in the brain. 26

2. Topic 1: Quantifying the strength of structural connectivity underlying functional brain networks. 27

2.1 Introduction. 28

2.2 Data. 29

2.2.1 Identifying Functional Networks. 29

2.2.2 Determining Structural Connectivity. 30

2.3 Methods. 30

2.3.1 The strength of Structural Connectivity (sSC) measure. 30

2.3.2 Hypothesis testing based on the sSC measure. 35

2.3.3 Using sSC to inform reliability of components. 37

2.4 Simulation Studies. 38

2.5 Data Analysis. 41

2.6 Discussion. 45

3. Topic 2: A joint model for functional and structural connectivity across the whole-brain network. 47

3.1 Introduction. 48

3.2 Data. 49

3.2.1 Functional Connectivity (FC) Matrix Construction. 49

3.2.2 Structural Connectivity (SC) Matrix Construction. 52

3.3 Methods. 54

3.3.1 Joint model of SC and FC. 54

3.3.1.1 Level 1. 54

3.3.1.2 Level 2. 55

3.3.1.3 Level 3. 55

3.3.1.4 EM algorithm. 56

3.4 Simulation Studies. 59

3.5 Data Analysis. 63

3.5.1 Measuring the edgewise FC-SC relationship. 64

3.5.2 Group comparison. 69

3.6 Discussion. 69

3.6.1 Limitations and Future Considerations. 70

4. Topic 3: Using copulas to model the structure-function relationship in the brain. 72

4.1 Introduction. 73

4.1.1 Copulas. 74

4.1.1.1 Elliptical copulas. 77

4.1.1.2 Archimedian copulas. 78

4.2 Data. 79

4.3 Methods. 80

4.3.1 Marginal distribution specification for SC and FC data. 80

4.3.2 Using copulas to measure the FC-SC association for within- vs. between-module edges. 84

4.3.3 Using copulas to measure the edgewise FC-SC association. 85

4.4 Simulation Studies. 86

4.4.1 Simulation example. 86

4.4.2 Simulation Results. 88

4.5 Data Analysis. 91

4.5.1 Using copulas to measure the FC-SC association for within- vs. between-module edges. 91

4.5.2 Using copulas to measure the edgewise FC-SC association. 95

4.6 Discussion. 98

A Appendix for Chapter 2 (Topic 1). 100

B Appendix for Chapter 3 (Topic 2). 103

C Appendix for Chapter 4 (Topic 3). 110

Bibliography. 116

About this Dissertation

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School	Laney Graduate School
Department	Biostatistics
Degree	PhD
Submission	Dissertation
Language	English
Research Field	Biology, Biostatistics Biology, Neuroscience
Parola chiave	neuroimaging networks ICA
Committee Chair / Thesis Advisor	Bowman, F Dubois, Emory University Guo, Ying, Emory University
Committee Members	Mayberg, Helen S, Emory University Kang, Jian , Emory University

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