Application of graph theoretical methods to the functional connectome of human brain.

Abstract

During the past decade, there has been a great interest in creating mathematical models to describe the properties of connectivity in the human brain. One of the established tools to describe these interactions among regions of the brain is graph theory. However, graph theoretical methods were mainly designed for the analysis of single network which is problematic for neuroscientists wishing to study groups of subjects. Specifically, studies using the Rich Club (RC) graph measure require cumbersome methods to make statistical inferences. In the first part of this work, we propose a framework to analyse the inter-subject variability in Rich Club organisation. The proposed framework is used to identify the changes in RC coefficient and RC organisation in patients with schizophrenia relative to healthy control. We follow this work by proposing a novel method, named Rich Block (RB), which is a combination of the tradition Rich Club and Stochastic Block Models (SBM). We show that using RBs can not only facilitate an inter-subject statistical inference, it can also account for differences in profile of connectivity, and control for subject-level covariates. We validate the Rich Block approach by simulating networks of different size and structure. We find that RB accurately estimates RC coefficients and RC organisations, specifically, in network with large number of nodes and blocks. With real data we use RB to identify changes in coefficient and organisation of highly connected sub-graphs of hub blocks in schizophrenia. In the final portion of this work, we examine the methods used to define each edge in networks formed from resting-state functional magnetic resonance imaging (rs-fMRI). The standard approach in rs-fMRI is to divide the brain into regions, extract time series, and compute the temporal correlation between each region. These correlations are assumed to follow standard results, when in fact serial autocorrelation in the time series can corrupt these results. While some authors have proposed corrections to account for autocorrelation, they are poorly documented and always assume homogeneity of autocorrelation over brain regions. Thus we propose a method to account for bias in interregion correlation estimates due to autocorrelation. We develop an exact method and an approximate, more computationally efficient method that adjusts for the sampling variability in the correlation coefficient. We use inter-subject scrambled real-data to validate the proposed methods under a null setting, and intact real-data to examine the impact of our method on graph theoretical measures. We find that the standard methods fail to practically correct the sensitivity and specificity level due to over-simplifying the temporal structure of BOLD time series, while even our approximate method is substantially more accurate