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How anatomy shapes dynamics: a semi-analytical study of the brain at rest by a simple spin model - PubMed

  • ️Sun Jan 01 2012

How anatomy shapes dynamics: a semi-analytical study of the brain at rest by a simple spin model

Gustavo Deco et al. Front Comput Neurosci. 2012.

Abstract

Resting state networks (RSNs) show a surprisingly coherent and robust spatiotemporal organization. Previous theoretical studies demonstrated that these patterns can be understood as emergent on the basis of the underlying neuroanatomical connectivity skeleton. Integrating the biologically realistic DTI/DSI-(Diffusion Tensor Imaging/Diffusion Spectrum Imaging)based neuroanatomical connectivity into a brain model of Ising spin dynamics, we found a system with multiple attractors, which can be studied analytically. The multistable attractor landscape thus defines a functionally meaningful dynamic repertoire of the brain network that is inherently present in the neuroanatomical connectivity. We demonstrate that the more entropy of attractors exists, the richer is the dynamical repertoire and consequently the brain network displays more capabilities of computation. We hypothesize therefore that human brain connectivity developed a scale free type of architecture in order to be able to store a large number of different and flexibly accessible brain functions.

Keywords: computational neuroscience; connectivity matrix; fMRI modeling; ongoing activity; resting state.

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Figures

Figure 1
Figure 1

Neuroanatomical connectivity data obtained by DSI and tractography after averaging across five human subjects (from Hagmann et al., and Honey et al., 2009). (A) A three-dimensional reconstruction of connectivity patterns and spatial relations among cortical areas. (B) The structural connectivity matrix.

Figure 2
Figure 2

Theoretical investigation of the activity in a simplified network of stochastic neural spins with Glauber dynamics: network architecture (see text for details).

Figure 3
Figure 3

Entropy of the attractors in an Ising-spin network reflecting human structural connectivity as a function of the global coupling strength. The rapid increase of entropy corresponds to the bifurcation. At the brink of this region resting state networks emerge.

Figure 4
Figure 4

Functional connectivity observed for the left and right hemisphere of empirical resting state data and spin glass model. The ordering of cortical areas corresponds to that of the underlying neuroanatomical connectivity matrix.

Figure 5
Figure 5

(A) Entropy of the attractors of Ising-spins networks of 20 nodes and 38 edges as a function of the global coupling strength. Scale free architectures are able to sustain a much richer dynamical repertoire as evidenced by the larger maximal value of the entropy of the attractors than the one corresponding to the small world, regular and random networks. (B) Evolution of the maximal entropy value obtained with the different architectures as a function of the number of nodes. The scale free network shows a much faster increase of the maximal entropy than small world type of networks. Importantly, the number of connections each node makes remains unchanged implying that sparsity of the network does not influence the results. (C) Distribution of the pair correlations for scale free networks of 20 nodes and 38 edges, and for different coupling values. At the edge of the bifurcation, i.e., when the entropy is maximal, the distribution of the pair correlations shows a power law.

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