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Ongoing cortical activity at rest: criticality, multistability, and ghost attractors - PubMed

  • ️Sun Jan 01 2012

Comparative Study

Ongoing cortical activity at rest: criticality, multistability, and ghost attractors

Gustavo Deco et al. J Neurosci. 2012.

Abstract

The ongoing activity of the brain at rest, i.e., under no stimulation and in absence of any task, is astonishingly highly structured into spatiotemporal patterns. These spatiotemporal patterns, called resting state networks, display low-frequency characteristics (<0.1 Hz) observed typically in the BOLD-fMRI signal of human subjects. We aim here to understand the origins of resting state activity through modeling via a global spiking attractor network of the brain. This approach offers a realistic mechanistic model at the level of each single brain area based on spiking neurons and realistic AMPA, NMDA, and GABA synapses. Integrating the biologically realistic diffusion tensor imaging/diffusion spectrum imaging-based neuroanatomical connectivity into the brain model, the resultant emerging resting state functional connectivity of the brain network fits quantitatively best the experimentally observed functional connectivity in humans when the brain network operates at the edge of instability. Under these conditions, the slow fluctuating (<0.1 Hz) resting state networks emerge as structured noise fluctuations around a stable low firing activity equilibrium state in the presence of latent "ghost" multistable attractors. The multistable attractor landscape defines a functionally meaningful dynamic repertoire of the brain network that is inherently present in the neuroanatomical connectivity.

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Figures

Figure 1.
Figure 1.

a, Neuroanatomical Connectivity matrix obtained by DSI and tractography after averaging across 5 human subjects. b, Empirical functional connectivity matrix of the BOLD activity averaged across the same 5 subjects during 20 min under resting state conditions (data from Hagmann et al., 2008).

Figure 2.
Figure 2.

Global cortical network. The network contains at each node (brain area) excitatory pyramidal cells (red triangles) and inhibitory interneurons (blue circles). Neurons are fully connected and clustered into excitatory and inhibitory populations (large circles). Black and yellow arrows indicate excitatory and inhibitory recurrent connections between neurons in a local brain area respectively, and red arrows indicate excitatory connections between neurons in different brain areas.

Figure 3.
Figure 3.

Mean-field analyses of the attractor landscape of the cortical spiking network as a function of the global inter-areal coupling strength. The dashed line plots the number of stable attractors, whereas the continued line shows the entropy of the attractors.

Figure 4.
Figure 4.

Fitting of empirical data as measured by the correlation between simulated and empirical functional connectivity as a function of the global coupling parameter W. The best fit is achieved at the edge of the bifurcation.

Figure 5.
Figure 5.

Detailed comparison between the neuroanatomical connectivity matrix, the empirical and the simulated functional connectivity for the working point W = Wc = 1.6 at the edge of the bifurcation. a, Left, Functional connectivity matrix based on the firing rates dynamics. Middle, Functional connectivity matrix based on the simulated BOLD signal. Right, Empirical functional connectivity. b, From left to right: neuroanatomical connections, empirical and simulated functional connectivity for the seed lPC. c, Pearson correlation between empirical and simulated functional connectivity for each individual seed (blue), and the corresponding p-value (red).

Figure 6.
Figure 6.

Simulated BOLD signal for 3 brain regions (lPC, green; lSF, blue and lST, red). lPC and lSF are part of the Default Mode network, whereas lST is part of the Attentional Network. Both in the empirical and in the simulated data, the functional connectivity between lPC and lSF is positive, while negative with lST. The temporal evolution of the signal shows this pattern of correlations.

Figure 7.
Figure 7.

p-values of the Kolmogorov–Smirnov test, the gof, and the estimated maximum-likelihood estimate of the scaling exponent (alpha), as a function of the global coupling parameter W. a plots the results taking into account all pairs, i.e., including also the interhemispherical, whereas b plots the results for single hemispheres, i.e., excluding interhemispherical pairs. The horizontal line in each subpanel corresponds to the value obtained for the empirical data.

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