Graph slepians to probe into large-scale network organization of resting-state functional connectivity

Functional magnetic resonance imaging (fMRI) is providing large amounts of data about brain function. Measuring correlations between spontaneous activity time courses from resting-state fMRI has revealed large-scale network organization. In the graph-based approach for functional connectivity analysis, a graph is built where nodes are brain regions and edge weights are pairwise correlations between the associated time courses. Here, we propose to apply recent approaches from graph signal processing to analyze fMRI data. First, the graph is constructed from structural connectivity, then, the corresponding graph spectrum is obtained such that the graph Slepian design can be deployed. In particular, graph Slepians are band-limited (i.e., using only graph Laplacian eigenvectors with lowest eigenvalues) with optimal energy concentration in predefined subgraphs. The subgraphs selected here are default-mode network (DMN) and fronto-parietal network (FPN), known as task-negative and — positive networks, respectively. While their activity appears anti-correlated during resting-state, a much more complicated interplay has been suggested recently using dynamic and time-resolved approaches. Preliminary results using data from the Human Connectome Project show that the proposed framework can direct the analysis to specific parts of the network and bring to light interactions between local and global aspects of network organization that were hidden before.