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Communication structure of cortical networks - PubMed

  • ️Sat Jan 01 2011

Communication structure of cortical networks

Luciano da Fontoura Costa et al. Front Comput Neurosci. 2011.

Abstract

Large-scale cortical networks exhibit characteristic topological properties that shape communication between brain regions and global cortical dynamics. Analysis of complex networks allows the description of connectedness, distance, clustering, and centrality that reveal different aspects of how the network's nodes communicate. Here, we focus on a novel analysis of complex walks in a series of mammalian cortical networks that model potential dynamics of information flow between individual brain regions. We introduce two new measures called absorption and driftness. Absorption is the average length of random walks between any two nodes, and takes into account all paths that may diffuse activity throughout the network. Driftness is the ratio between absorption and the corresponding shortest path length. For a given node of the network, we also define four related measurements, namely in- and out-absorption as well as in- and out-driftness, as the averages of the corresponding measures from all nodes to that node, and from that node to all nodes, respectively. We find that the cat thalamo-cortical system incorporates features of two classic network topologies, Erdös-Rényi graphs with respect to in-absorption and in-driftness, and configuration models with respect to out-absorption and out-driftness. Moreover, taken together these four measures separate the network nodes based on broad functional roles (visual, auditory, somatomotor, and frontolimbic).

Keywords: Markov chains; accessibility; complex networks; cortical networks.

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Figures

Figure 1
Figure 1

(A) A simple network with walks performed by three moving agents. (B) The frequency of visits by an infinite number of moving agents (shown by the gray-levels) corresponds to diffusion dynamics taking node A as source.

Figure 2
Figure 2

Example of directed networks. The numbers associated to the edges correspond to the transition probabilities. (A) Simple directed network defining a cycle with five nodes. (B) The network in (A) modified in order to include a new node (6), which defines a single network bifurcation.

Figure 3
Figure 3

The effect of deviations in a ring network (A). Unlike shortest path, absorption is not symmetric, as illustrated is cases (B,C).

Figure 4
Figure 4

The four absorption-related measurements plotted against the respective in- and out- degrees considering the cortical network without thalamic nodes: in- (A) and out-absorptions (B) and in- (C) and out-driftness (D). Significant correlation was obtained for the cases (A,C and D).

Figure 5
Figure 5

The absorption-related measurements obtained for the cat cortical matrix incorporating the thalamic connections against the respective degrees: in- (A) and out-absorptions (B) and in- (C) and out-driftness (D). Different from the case where cortical nodes are considered alone, a non-linear dependency is now obtained.

Figure 6
Figure 6

Scatterplot comparison of in-absorption (A,C) and in-driftness (B,D) against in-degrees between cortical networks with thalamic nodes disconnected (A,B) and connected (C,D). In all cases, the cortical networks differ from the E–R counterparts by presenting a wider dispersion along both axes.

Figure 7
Figure 7

Scatterplot comparison of out-absorption (A,C) and out-driftness (B,D) against out-degrees between cortical networks with thalamic nodes disconnected (A,B) and connected (C,D). A much wider separation between cortical and E–R networks is now observed, especially for the out-absorption.

Figure 8
Figure 8

Illustration of the one-dimensional Mahalanobis distance, or z-score. Hypothetical measurements against the degree for the cortical nodes and respective configurations nodes are shown in (A). In (B) the distribution of the cortical node measurement (filled stem) is shown along with the configuration measurements (empty stems) with their fitted normal distribution. The Mahalanobis distance is obtained by subtracting the measurement value from the average μ of the normal distribution and dividing this difference L by the corresponding standard deviation σ.

Figure 9
Figure 9

Histograms of the one-dimensional Mahalanobis distances obtained for the in- and out-absorptions with respect to the cat cortical network without (A,B) and with (C,D) thalamus and the percentages of nodes with Mahalanobis distance above 2.

Figure 10
Figure 10

The scatterplot obtained after PCA projection of the four measurements considered for the cat cortical network without (A) and with (B) thalamus. Well-defined clusters were obtained for the visual, auditory, and somatomotor functional groups for the cortical network without thalamus (A).

Figure 11
Figure 11

The scatterplot obtained after PCA projection considering the one-dimensional Mahalanobis distances with respect to all four measurements for the cat cortical network without (A) and with (B) thalamus.

Figure A1
Figure A1

Illustration of the nature of the absorption measurement with respect to a simple star network. In case the moving agent performing the random walk is left at the central node (i.e., node 5), it will take, on average, a relatively long path to reach a specific neighboring node. However, in case the moving agent is left at any of the surrounding nodes, it will reach the central node at the very first move. Therefore, the average absorption value reflects the branching structure of the network. Note also that this measurement is not symmetric, i.e., the absorption for moving from a node i to a node j is not necessarily equal to the respective measurement considering a walk from j to i.

Figure A2
Figure A2

The simple network in Figure A1 modified by eliminating all the connections departing from the absorbing node 5.

Figure A3
Figure A3

The simple network in Figure A1 modified by eliminating all the connections departing from the absorbing node 1.

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