Characterising group-level brain connectivity: a framework using Bayesian exponential random graph models

Abstract

The brain can be modelled as a network with nodes and edges derived from a range of imaging modalities: the nodes correspond to spatially distinct regions and the edges to the interactions between them. Whole-brain connectivity studies typically seek to determine how network properties change with a given categorical phenotype such as age-group, disease condition or mental state. To do so reliably, it is necessary to determine the features of the connectivity structure that are common across a group of brain scans. Given the complex interdependencies inherent in network data, this is not a straightforward task. Some studies construct a group-representative network (GRN), ignoring individual differences, while other studies analyse networks for each individual independently, ignoring information that is shared across individuals. We propose a Bayesian framework based on exponential random graph models (ERGM) extended to multiple networks to characterise the distribution of a entire population of networks. Using resting-state fMRI data from the Cam-CAN project, a study on healthy ageing, we demonstrate how our method can be used to characterise and compare the brain's functional connectivity structure across a group of young individuals and a group of old individuals.Brain connectivity analysis aims to understand how spatially distinct regions of the brain interact with each other. The use of networks to model whole-brain connectivity has become increasingly popular in recent years [5]: by treating distinct regions as nodes and the connections between them as edges, researchers have gained new insights into both the structure and function of the brain. To determine the salient features of the brain's connectivity structure, it is necessary to identify which of those are common across individuals. Given the complex interdependencies inherent in network data, however, it is not a trivial task to consider connectivity structure across multiple individuals; how best to combine connectivity information across participants remains a key challenge.1 Many existing methods aim to construct a (single) group-representative network (GRN) across (multiple) individuals. There have been several methods proposed for constructing GRNs. For example, Achard et al. [2] constructed a group-representative network using mean functional connectivity (mean-GRN) by first taking the mean of the individuals' functional connectivity matrices and then thresholding the resulting matrix. Song et al. [38] took a similar approach using the median of the individuals' functional connectivity matrices (i.e. median-GRN). Sinke et al. [36] constructed a grouprepresentative structural connectivity network from Diffusion Tensor Imaging (DTI) data by keeping those edges which are present in at least 35% of the individuals' networks (i.e. minimal-GRN). These edge-based GRN methods are computationally convenient, since each individual is processed separately and the subsequent analysis is based on a single network. However, these methods ignore higher-order ...

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