Markov models for fMRI correlation structure: is brain functional connectivity small world, or decomposable into networks?

TL;DR

This paper investigates the structure of brain connectivity using Markov models on fMRI data, questioning whether the brain's functional network is best described as small-world or as decomposable into overlapping networks, and introduces a new method for analyzing such structures.

Contribution

It introduces a novel method for extracting strongly-connected cliques in large graphs and compares graph structures to better understand brain connectivity from fMRI data.

Findings

Markov models effectively identify brain connectivity structures.

Large, overlapping networks better explain the data.

Small-world properties are essential for accurate modeling.

Abstract

Correlations in the signal observed via functional Magnetic Resonance Imaging (fMRI), are expected to reveal the interactions in the underlying neural populations through hemodynamic response. In particular, they highlight distributed set of mutually correlated regions that correspond to brain networks related to different cognitive functions. Yet graph-theoretical studies of neural connections give a different picture: that of a highly integrated system with small-world properties: local clustering but with short pathways across the complete structure. We examine the conditional independence properties of the fMRI signal, i.e. its Markov structure, to find realistic assumptions on the connectivity structure that are required to explain the observed functional connectivity. In particular we seek a decomposition of the Markov structure into segregated functional networks using decomposable graphs: a set of strongly-connected and partially overlapping cliques. We introduce a new method to efficiently extract such cliques on a large, strongly-connected graph. We compare methods learning different graph structures from functional connectivity by testing the goodness of fit of the model they learn on new data. We find that summarizing the structure as strongly-connected networks can give a good description only for very large and overlapping networks. These results highlight that Markov models are good tools to identify the structure of brain connectivity from fMRI signals, but for this purpose they must reflect the small-world properties of the underlying neural systems.