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. 2010 Dec 8:4:200.
doi: 10.3389/fnins.2010.00200. eCollection 2010.

Modular and hierarchically modular organization of brain networks

David Meunier  1 , Renaud Lambiotte, Edward T Bullmore
Affiliations

Modular and hierarchically modular organization of brain networks

David Meunier et al. Front Neurosci. .

Abstract

Brain networks are increasingly understood as one of a large class of information processing systems that share important organizational principles in common, including the property of a modular community structure. A module is topologically defined as a subset of highly inter-connected nodes which are relatively sparsely connected to nodes in other modules. In brain networks, topological modules are often made up of anatomically neighboring and/or functionally related cortical regions, and inter-modular connections tend to be relatively long distance. Moreover, brain networks and many other complex systems demonstrate the property of hierarchical modularity, or modularity on several topological scales: within each module there will be a set of sub-modules, and within each sub-module a set of sub-sub-modules, etc. There are several general advantages to modular and hierarchically modular network organization, including greater robustness, adaptivity, and evolvability of network function. In this context, we review some of the mathematical concepts available for quantitative analysis of (hierarchical) modularity in brain networks and we summarize some of the recent work investigating modularity of structural and functional brain networks derived from analysis of human neuroimaging data.

Keywords: cortex; fractal; graph; near-decomposability; partition.

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Figures

Figure 1
Figure 1
Modular systems are small-world but not all small-world systems are modular. Many complex systems can be represented as graphs where the nodes correspond to the constitutive elements (people, websites, neurons, etc), and the links or edges to some type of interaction between nodes (friendships, hyper-links, synapses, etc.). The use of networks across disciplines allows for the formulation of generic organization principles, such as the small-world property. The small-world property is defined as the combination of high clustering and short path length and has originally been illustrated by the Watts–Strogatz model (A). Complex networks also have a tendency to exhibit a modular topology, where links are concentrated within modules (B). Another key type of organization is hierarchical or multi-scale modularity (C), where modules themselves are modular, thus leading to a nested or fractal topological hierarchy.
Figure 2
Figure 2
Many information processing networks have a fractal community structure of modules-within-modules. Dendrograms displaying significant modular and sub-modular structure for (A) a very large-scale integrated circuit, (B) Caenorhabditis elegans, (C) the human anatomical network estimated using MRI data on 259 normal volunteers, and (D) the human cortical network estimated using diffusion spectrum imaging (DSI) data on an independent sample of five volunteers. The modularity, m, at each level was estimated using the method of Blondel et al. (2008). The insets demonstrate hierarchical modularity in terms of the co-classification matrix of each system. Reproduced with permission from Bassett et al. (2010).
Figure 3
Figure 3
Age-related effects on modularity and topological roles of cortical regions in brain functional networks. Upper panel: intra-modular degree versus participation coefficient for each of the regional nodes in major posterior, central, and frontal modules of fMRI networks in younger (A) and older (B) participants. Connector nodes have large participation coefficients. Lower panel: topological representation of the average young (C) and older (D) brain networks with connector nodes located in a central ring to highlight their key role in inter-modular connectivity. Reproduced with permission from Meunier et al. (2009b).
Figure 4
Figure 4
Hierarchical modularity of a human brain functional network. (A) Cortical surface mapping of the community structure of the network at the highest level of modularity; (B) anatomical representation of the connectivity between nodes in color-coded modules. The brain is viewed from the left side with the frontal cortex on the left of the panel and occipital cortex on the right. Intra-modular edges are colored differently for each module; inter-modular edges are drawn in black; (C) sub-modular decomposition of the five largest modules (shown centrally) illustrates, for example, that the medial occipital module has no major sub-modules whereas the fronto-temporal module has many sub-modules. Reproduced with permission from Meunier et al. (2009a).
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