Age-related changes in modular organization of human brain functional networks

Abstract

Graph theory allows us to quantify any complex system, e.g., in social sciences, biology or technology, that can be abstractly described as a set of nodes and links. Here we derived human brain functional networks from fMRI measurements of endogenous, low frequency, correlated oscillations in 90 cortical and subcortical regions for two groups of healthy (young and older) participants. We investigated the modular structure of these networks and tested the hypothesis that normal brain aging might be associated with changes in modularity of sparse networks. Newman's modularity metric was maximised and topological roles were assigned to brain regions depending on their specific contributions to intra- and inter-modular connectivity. Both young and older brain networks demonstrated significantly non-random modularity. The young brain network was decomposed into 3 major modules: central and posterior modules, which comprised mainly nodes with few inter-modular connections, and a dorsal fronto-cingulo-parietal module, which comprised mainly nodes with extensive inter-modular connections. The mean network in the older group also included posterior, superior central and dorsal fronto-striato-thalamic modules but the number of intermodular connections to frontal modular regions was significantly reduced, whereas the number of connector nodes in posterior and central modules was increased.

Introduction

Modularity is a word with many meanings in neuroscience (Fodor, 1983, Zeki and Bartels, 1998, Redies and Puelles, 2001, Callebaut and Rasskin-Gutman, 2005). Here we are concerned with the topological organization of whole human brain functional networks and the partitioning of these networks into a set of modules, each module being defined by dense internal or intra-modular connectivity and relatively sparse external or inter-modular connectivity (Newman and Girvan, 2004); see Fig. 1. This pattern of complex network organization, also sometimes described as a community structure, is widespread in biochemical, social and infrastructural networks (Guimerà et al., 2005). A key advantage of modular organization, which may explain its ubiquity in diverse systems, is that it favours evolutionary and developmental optimization of multiple or changing selection criteria (Redies and Puelles, 2001, Slotine and Lohmiller, 2001, Kashtan and Alon, 2005, Pan and Sinha, 2007): a modular network can evolve or grow one module at a time, without risking loss of function in other modules.

Mathematical tools have recently been developed to quantify the modularity of any network that can be abstractly described as a set of nodes and links (Newman and Girvan, 2004, Newman, 2004a, Danon et al., 2005, Newman, 2006). Once the modules have been identified, this information can be further used to refine the definition of the topological role of any particular node. For example, the global air transportation network has a modular organization (Guimerà and Amaral, 2005b), broadly conforming to geopolitical constraints, which informed the assignment of distinct roles to the component nodes (cities) based on the ratio of intra- and inter-modular links (flights) connecting each node to the rest of the network. Thus a highly-connected city, like London, with many long-haul flights to other modules (different continents), was designated a connector hub; whereas a regionally important city, like Barcelona, with relatively few long-haul flights outside Europe and North Africa, was designated a provincial hub.

Here we extend the analysis of modularity and topological roles in functional brain networks, using tools drawn from the literature on physics of complex networks (Newman and Girvan, 2004, Guimerà and Amaral, 2005b) that have not been previously applied to analysis of human functional neuroimaging data. However, we note that there have been several prior studies using conceptually related multivariate or graph theoretical methods to explore the clustered or modular organization of mammalian cortex. Young (1992) applied non-metric multidimensional scaling (MDS) to anatomical connectivity matrices to demonstrate dorsal and ventral “streams” of inter-regional connectivity, and a predominance of local neighbourhood connections, in primate visual cortex. Scannell et al., 1995, Scannell et al., 1999 and Hilgetag et al. (2000) applied non-metric MDS, non-parametric cluster analysis (NPCA), and a novel evolutionary algorithm called optimal set analysis (OSA), to show that the anatomical connectivity of the cat and macaque cortices demonstrated relatively dense connections within groups of functionally related regions and much sparser connections between different groups of regions. Stephan et al. (2000) investigated neuronographic data, which mapped the propagation of epileptiform activity following local disinhibition of areas of the macaque cortex by topical application of strychnine, and showed that functionally connected regions of cortex tended to co-segregate in one of three major sub-systems (visual, somatomotor, or orbito-temporo-insular). Various forms of hierarchical cluster analysis were subsequently applied to human functional MRI data acquired in a no-task or resting state (Cordes et al., 2002, Salvador et al., 2005). For example, Salvador et al. (2005) showed that 90 cortical and subcortical regions defined by an anatomically parcellated template image were aggregated by cluster analysis into 6 major systems of anatomically and functionally related regions. More recently, using graph theoretical tools, the community structure of human brain networks has been investigated using structural MRI to infer anatomical connectivity between major cortical and subcortical regions (Chen et al., 2008). This study confirmed that the human brain anatomical network, derived from analysis of MRI data on a large group of healthy volunteers, had a modular organization which broadly conformed to known functional specialisations and the hierarchical cluster solution reported by Salvador et al. (2005); for example, many occipital regions specialised for visual processing were identified as members of the same anatomical module. There have also been a few recent graph theoretical studies of modularity of functional networks inferred from fMRI measurements on rodents (Schwarz et al., 2008) and healthy human adults (Ferrarini et al., in press).

In this context, the distinctive contributions of this paper are to apply a graph-theoretical measure of modularity (Newman and Girvan, 2004), and related concepts of the topological roles of individual nodes (Guimerà and Amaral, 2005b), to the analysis of human functional MRI data, with two main objectives: i) to further investigate the modular organization and topological roles of each regional node comprising large-scale human brain functional networks; and ii) to test the hypothesis that normal aging is associated with changes in the community structure of whole human brain functional networks.