Abstract
This paper uses mathematical modelling and simulations to explore the dynamics that emerge in large scale cortical networks, with a particular focus on the topological properties of the structural connectivity and its relationship to functional connectivity. We exploit realistic anatomical connectivity matrices (from diffusion spectrum imaging) and investigate their capacity to generate various types of resting state activity. In particular, we study emergent patterns of activity for realistic connectivity configurations together with approximations formulated in terms of neural mass or field models. We find that homogenous connectivity matrices, of the sort of assumed in certain neural field models give rise to damped spatially periodic modes, while more localised modes reflect heterogeneous coupling topologies. When simulating resting state fluctuations under realistic connectivity, we find no evidence for a spectrum of spatially periodic patterns, even when grouping together cortical nodes into communities, using graph theory. We conclude that neural field models with translationally invariant connectivity may be best applied at the mesoscopic scale and that more general models of cortical networks that embed local neural fields, may provide appropriate models of macroscopic cortical dynamics over the whole brain.
Highlights
This paper is about modelling the dynamics in large scale brain networks with both realistic and analytic connectivity matrices
An approximation of a large scale connectivity matrix with a translationally invariant matrix has often been used to describe cortical activity. This amounts to replacing the realistic connectivity kernel in Eq (1) by a parsimonious analytic approximation of the sort used in the differential formulation of neural field models in continuous media
Dynamics resulting from such an approximation will, differ from realistic resting state dynamics: even if we choose the nonlinearity in Eq (2) carefully, so that both the realistic as well as the homogenous network have the same fixed-point solution; neglecting inhomogeneities in the connectivity results in omitting important features of cortical activity
Summary
This paper is about modelling the dynamics in large scale brain networks with both realistic and analytic connectivity matrices. The analysis of large connectivity datasets, using graph theory, considers brain networks as weighted graphs, whose nodes represent cortical sources of measurable activity and whose edges correspond to anatomical connections Each of these edges can be associated with a number corresponding to the weight that characterises the strength of the relevant connection; for example, as obtained through tracing studies. We examine the ability of the (local) clustering coefficient to predict patterns of resting state dynamics; in particular the eigenmodes of cortical activity Another widely-used graph theoretical metric is modularity, which characterises the organisation of a complex network into sub-modules or communities; these are distinguished by a high degree of connections between nodes of the same module, in comparison with the degree of connections of these nodes to network elements outside this module, reflecting a natural segregation within the network (Newman, 2003). We will use these matrices to exemplify the relation between resting state activity, anatomical modes and graph theoretical measures
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