On Geometric and Algebraic Properties of Human Brain Functional Networks

Duy Duong-Tran, Purdue University

Abstract

It was only in the last decade that Magnetic Resonance Imaging (MRI) technologies have achieved high-quality levels that enabled comprehensive assessments of individual human brain structure and functions. One of the most important advancements put forth by Thomas Yeo and colleagues in 2011 [1] was the intrinsic functional connectivity MRI (fcMRI) networks which are highly reproducible and feature consistently across different individual brains. This dissertation aims to unravel different characteristics of human brain fcMRI networks, separately through network morphospace and collectively through stochastic block models. The quantification of human brain functional (re-)configurations across varying cognitive demands remains an unresolved topic. Such functional reconfigurations are rather subtle at the whole-brain level. Hence, we propose a mesoscopic framework focused on functional networks (FNs) or communities to quantify functional (re-)configurations. To do so, we introduce a 2D network morphospace that relies on two novel mesoscopic metrics, Trapping Efficiency (TE) and Exit Entropy (EE). We use this framework to quantify the Network Configural Breadth across different tasks. Network configural breadth is shown to significantly predict behavioral measures, such as episodic memory, verbal episodic memory, fluid intelligence and general intelligence. To properly estimate and assess whole-brain functional connectomes (FCs) is among one of the most challenging tasks in computational neuroscience. Among the steps in constructing large-scale brain networks, thresholding of statistically spurious edge(s) in FCs is the most critical. State-of-the-art thresholding methods are largely ad hoc. Meanwhile, a dominant proportion of the brain connectomics research relies heavily on using a priori set of highly-reproducible human brain functional sub-circuits (functional networks (FNs)) without properly considering whether a given FN is information-theoretically relevant with respect to a given FC. Leveraging recent theoretical developments in Stochastic block model (SBM), we first formally defined and subsequently quantified the level of information-theoretical prominence of a prioriset of FNs across different subjects and fMRI task conditions for any given input FC. The main contribution of this work is to provide an automated thresholding method of individuals’ FCs based on prior knowledge of human brain functional sub-circuitry.

Degree

Ph.D.

Advisors

Wachs, Purdue University.

Subject Area

Mathematics|Medical imaging|Neurosciences

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