Scale-free brain functional networks

Functional magnetic resonance imaging (fMRI) is used to extract {\em functional networks} connecting correlated human brain sites. Analysis of the resulting networks in different tasks shows that: (a) the distribution of functional connections, and the probability of finding a link vs. distance are both scale-free, (b) the characteristic path length is small and comparable with those of equivalent random networks, and (c) the clustering coefficient is orders of magnitude larger than those of equivalent random networks. All these properties, typical of scale-free small world networks, reflect important functional information about brain states.Comment: 4 pages, 5 figures, 2 table

Functional Complexity Measure for Networks

We propose a complexity measure which addresses the functional flexibility of networks. It is conjectured that the functional flexibility is reflected in the topological diversity of the assigned graphs, resulting from a resolution of their vertices and a rewiring of their edges under certain constraints. The application will be a classification of networks in artificial or biological systems, where functionality plays a central role.Comment: 11 pages, LaTeX2e, 5 PostScript figure

Fluctuations between high- and low-modularity topology in time-resolved functional connectivity

Modularity is an important topological attribute for functional brain networks. Recent studies have reported that modularity of functional networks varies not only across individuals being related to demographics and cognitive performance, but also within individuals co-occurring with fluctuations in network properties of functional connectivity, estimated over short time intervals. However, characteristics of these time-resolved functional networks during periods of high and low modularity have remained largely unexplored. In this study we investigate spatiotemporal properties of time-resolved networks in the high and low modularity periods during rest, with a particular focus on their spatial connectivity patterns, temporal homogeneity and test-retest reliability. We show that spatial connectivity patterns of time-resolved networks in the high and low modularity periods are represented by increased and decreased dissociation of the default mode network module from task-positive network modules, respectively. We also find that the instances of time-resolved functional connectivity sampled from within the high (low) modularity period are relatively homogeneous (heterogeneous) over time, indicating that during the low modularity period the default mode network interacts with other networks in a variable manner. We confirmed that the occurrence of the high and low modularity periods varies across individuals with moderate inter-session test-retest reliability and that it is correlated with previously-reported individual differences in the modularity of functional connectivity estimated over longer timescales. Our findings illustrate how time-resolved functional networks are spatiotemporally organized during periods of high and low modularity, allowing one to trace individual differences in long-timescale modularity to the variable occurrence of network configurations at shorter timescales.Comment: Reorganized the paper; to appear in NeuroImage; arXiv abstract shortened to fit within character limit

Density-dependence of functional development in spiking cortical networks grown in vitro

During development, the mammalian brain differentiates into specialized regions with distinct functional abilities. While many factors contribute to functional specialization, we explore the effect of neuronal density on the development of neuronal interactions in vitro. Two types of cortical networks, dense and sparse, with 50,000 and 12,000 total cells respectively, are studied. Activation graphs that represent pairwise neuronal interactions are constructed using a competitive first response model. These graphs reveal that, during development in vitro, dense networks form activation connections earlier than sparse networks. Link entropy analysis of dense net- work activation graphs suggests that the majority of connections between electrodes are reciprocal in nature. Information theoretic measures reveal that early functional information interactions (among 3 cells) are synergetic in both dense and sparse networks. However, during later stages of development, previously synergetic relationships become primarily redundant in dense, but not in sparse networks. Large link entropy values in the activation graph are related to the domination of redundant ensembles in late stages of development in dense networks. Results demonstrate differences between dense and sparse networks in terms of informational groups, pairwise relationships, and activation graphs. These differences suggest that variations in cell density may result in different functional specialization of nervous system tissue in vivo.Comment: 10 pages, 7 figure

Intact Bilateral Resting-State Networks in the Absence of the Corpus Callosum

Temporal correlations between different brain regions in the resting-state BOLD signal are thought to reflect intrinsic functional brain connectivity (Biswal et al., 1995; Greicius et al., 2003; Fox et al., 2007). The functional networks identified are typically bilaterally distributed across the cerebral hemispheres, show similarity to known white matter connections (Greicius et al., 2009), and are seen even in anesthetized monkeys (Vincent et al., 2007). Yet it remains unclear how they arise. Here we tested two distinct possibilities: (1) functional networks arise largely from structural connectivity constraints, and generally require direct interactions between functionally coupled regions mediated by white-matter tracts; and (2) functional networks emerge flexibly with the development of normal cognition and behavior and can be realized in multiple structural architectures. We conducted resting-state fMRI in eight adult humans with complete agenesis of the corpus callosum (AgCC) and normal intelligence, and compared their data to those from eight healthy matched controls. We performed three main analyses: anatomical region-of-interest-based correlations to test homotopic functional connectivity, independent component analysis (ICA) to reveal functional networks with a data-driven approach, and ICA-based interhemispheric correlation analysis. Both groups showed equivalently strong homotopic BOLD correlation. Surprisingly, almost all of the group-level independent components identified in controls were observed in AgCC and were predominantly bilaterally symmetric. The results argue that a normal complement of resting-state networks and intact functional coupling between the hemispheres can emerge in the absence of the corpus callosum, favoring the second over the first possibility listed above