Mapping Multiplex Hubs in Human Functional Brain Networks

Abstract

Typical brain networks consist of many peripheral regions and a few highly central ones, i.e., hubs, playing key functional roles in cerebral inter-regional interactions. Studies have shown that networks, obtained from the analysis of specific frequency components of brain activity, present peculiar architectures with unique profiles of region centrality. However, the identification of hubs in networks built from different frequency bands simultaneously is still a challenging problem, remaining largely unexplored. Here we identify each frequency component with one layer of a multiplex network and face this challenge by exploiting the recent advances in the analysis of multiplex topologies. First, we show that each frequency band carries unique topological information, fundamental to accurately model brain functional networks. We then demonstrate that hubs in the multiplex network, in general different from those ones obtained after discarding or aggregating the measured signals as usual, provide a more accurate map of brain's most important functional regions, allowing to distinguish between healthy and schizophrenic populations better than conventional network approaches.

Keywords: brain fMRI; frequency bands; multiplex hubs; multiplex networks; schizophrenia.

Figure 1

Schematic illustration of brain multiplex functional network construction. (A) We measure the brain activity with a set of 264 ROIs (here, we only draw five ROIs, for simplicity), and estimate the coherence spectrum of signals between any pair of ROIs. (B) Averaged coherence values are calculated in 12 frequency bands (here we only show four bands, for simplicity), to quantify the strength of frequency-specific functional connectivity. The statistical significance of each connection is calculated (see Methods) and connections with Z-score smaller than 3 are discarded. (C) The remaining connections are used to build adjacency matrices, weighted by Z-scores, that constitute the layers of the multiplex functional network once interconnected. (D) Resulting single-layer and multiplex networks obtained from this procedure.

Figure 2

Frequency-dependent connectivity. Stacked histograms of structural descriptors where colors encode the contribution of each layer to each bin. The distribution of the average degree (left panels), average strength (central panels) and assortative mixing coefficient (right panels) are shown for healthy (top) and schizophrenic (bottom) subjects. For each panel, the dashed line indicates the median of the overall distribution (i.e., regardless of the frequency-dependent contribution).

Figure 3

Frequency-dependent clustering. As in Figure 2, showing the distribution of edge density (left panels), average weighted clustering coefficient (central panels) and modularity (right panels).

Figure 4

Frequency-dependent small-worldness. As in Figure 2, showing the distribution of average path length (left panels), average local clustering coefficient (central panels) and small-world index (right panels).

Figure 5

Structural reducibility of the multiplex functional network. (A) Schematic illustration of how the analysis structural reducibility of the network works: it allows to identify frequency bands providing redundant topological information and to verify the validity of the multiplex model with respect to conventional single-layer models. Global maxima in the quality function identify optimal structural reductions. (B) The median quality function is shown for healthy control (solid) and schizophrenic patients (dashed), with shaded areas indicating the standard deviation around each value. (C) Signal-to-noise ratio (SNR; see text for further details) for Jensen-Shannon distance calculated for each pair of layers, color-coded for both groups, and corresponding relative difference between the two groups.

Figure 6

Comparing centrality profiles of multiplex and conventional functional networks. Spearman's correlation coefficient between the centrality profiles obtained from multiplex, full-band and typical-band functional networks for (A) healthy and (B) patient groups.

Figure 7

Discrimination performance of the multiplex functional networks vs. conventional networks. (A) The statistical indicators of the discrimination between control and patient groups obtained from conventional network approaches (i.e., full-band and typical-band networks) are compared against the full multiplex functional network, which provides better overall discrimination. Note that the features are ROIs and their values are centrality scores. (B) Location of top 30 discriminating ROIs, obtained from multiplex analysis.

Figure 8

Brain regions playing the role of hubs in functional connectivity. The most central regions, i.e., hubs, identified in multiplex and conventional functional networks are shown (from top to bottom). Markers indicate their locations, whereas panels from left-hand to right-hand side show hubs found only in healthy controls (left), only in schizophrenic patients (center), or in both (right).