Multi-scale community organization of the human structural connectome and its relationship with resting-state functional connectivity

Richard F Betzel,Alessandra Griffa,Jean-Philippe Thiran,Andrea Avena-Koenigsberger,Olaf Sporns,Patric Hagmann,Joaquín Goñi

doi:10.1017/nws.2013.19

Abstract

AbstractThe human connectome has been widely studied over the past decade. A principal finding is that it can be decomposed into communities of densely interconnected brain regions. Past studies have often used single-scale modularity measures in order to infer the connectome's community structure, possibly overlooking interesting structure at other organizational scales. In this report, we used the partition stability framework, which defines communities in terms of a Markov process (random walk), to infer the connectome's multi-scale community structure. Comparing the community structure to observed resting-state functional connectivity revealed communities across a broad range of scales that were closely related to functional connectivity. This result suggests a mapping between communities in structural networks, models of influence-spreading and diffusion, and brain function. It further suggests that the spread of influence among brain regions may not be limited to a single characteristic scale.

Highlights

Many complex networks exhibit community structure, defined for example by clustered edge distributions such that vertices in the same community preferentially link to one another (Guimera & Amaral, 2005; Girvan & Newman, 2002; Newman & Girvan, 2004)
Examples of community structure can be found in society as groups of friends, workplaces, cities, and states (Moody & White, 2003; Freeman, 2004); in protein interaction networks as groups of co-functioning proteins (Jonsson et al, 2006); and in the World Wide Web (WWW) as webpages sharing many hyperlinks (Albert et al, 1999; Flake et al, 2002)
The previous section described a procedure for identifying the connectome’s multiscale community structure using the partition stability framework. The association between this structure and observed functional connectivity was assessed by correlating it with resting-state functional connectivity (rsFC) and, separately, by measuring how well consensus communities modularized the rsFC matrix

Summary

Introduction

Many complex networks exhibit community structure, defined for example by clustered edge distributions such that vertices (nodes) in the same community preferentially link to one another (Guimera & Amaral, 2005; Girvan & Newman, 2002; Newman & Girvan, 2004). Examples of community structure can be found in society as groups of friends, workplaces, cities, and states (Moody & White, 2003; Freeman, 2004); in protein interaction networks as groups of co-functioning proteins (Jonsson et al, 2006); and in the World Wide Web (WWW) as webpages sharing many hyperlinks (Albert et al, 1999; Flake et al, 2002). One of the most widely used methods is to identify the vertex partition that maximizes the modularity quality function, defined as the difference between observed and expected intra-community edge density (Newman, 2006). Modularity analysis suffers from several drawbacks: maximization is NP-hard and identifying the optimal partition is often practically impossible (Fortunato, 2010); solutions are sometimes degenerate, with multiple partitions corresponding to the maximum modularity (Good et al, 2010); and a resolution limit renders modularity “blind” to communities below some characteristic scale (Fortunato & Barthelemy, 2007)

Objectives

Methods

Results

Discussion

Conclusion