Statistical Methods for Brain Network Estimation Open Access

Lukemire, Joshua (Spring 2021)

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Functional Magnetic Resonance Imaging (fMRI) allows researchers to study neural activity by measuring changes in blood oxygen levels throughout the brain at rest or in response to experimental tasks/stimuli. In recent years, there has been great interest in using fMRI data to study brain networks. In this dissertation, we develop new statistical methods for providing reliable and robust estimation and characterization of brain networks across different cognitive states, subpopulations and imaging study designs.

In the first topic, we propose the Bayesian Joint Network Learning (BJNL) approach to joint brain network estimation that pools information across groups to estimate group-specific brain networks under a graph theoretic approach. BJNL uses information from multiple groups to estimate the probability of edges between nodes without forcing similarity in the edge strengths. The BJNL approach is shown to outperform other individual and joint estimation techniques in simulations. The technique is then applied to a Stroop fMRI data set.

Next, we propose a Sparse Bayesian Independent Component Analysis (SparseBayes ICA) for reliable estimation of individual differences in brain networks. We model the population-level ICA source signals for brain networks using a Dirichlet process mixture of Gaussians. To reliably capture individual differences on brain networks, we propose sparse estimation of the covariate effects in a hierarchical ICA model via a horseshoe prior. Through extensive simulation studies, we show our approach has improved performance in detecting covariate effects in comparison with the current group ICA methods. We then use it to perform an ICA decomposition of a motivating Zen meditation resting-state study.

In our third topic, we introduce a general framework of repeated measures Sparse Bayesian ICA (RM-SparseBayes ICA). This method provides a rigorous and much needed tool for investigating brain networks in imaging studies with complex study designs including longitudinal and/or multi-center studies. Through simulations, we show that the proposed method has considerably improved performance as compared to other potential approaches. We apply the RM-SparseBayes ICA to investigate brain network changes using the longitudinal multi-center Alzheimer’s disease data from the ADNI2 study.

Table of Contents

Introduction 1

Magnetic Resonance Imaging 2

Brain Networks 3

Bayesian Nonparametric Approaches 10

Research Topics 11

Bayesian Joint Network Learning 13

Introduction 14

Methods 19

Simulation 30

Stroop Task fMRI Analysis 38

Discussion 45

Sparse Bayesian Independent Component Analysis 50

Introduction 51

SparseBayes ICA 55

Posterior Computation 59

Simulation Studies 67

Zen Meditation Study 70

Discussion 75

Repeated Measures Sparse Bayesian Independent Component Analysis 78

Introduction 79

Methods 83

Posterior Computation 88

Simulation 93

ADNI2 Study 97

Discussion 102

Summary and Future Directions 105

Appendix for Chapter 2 108

Appendix for Chapter 3 110

Bibliography 111

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