Resting brain activity emerges from wave propagating along spatiotemporal varying hyper-structural connectome

How spontaneous brain activities emerge from the structural connectivity (SC) has puzzled researchers for a long time. The underlying mechanism still remains largely unknown. Previous studies on modeling the resting-state human brain functional connectivity (FC) are normally based on the relatively static structural connectome directly and very few of them concern about the dynamic spatiotemporal variability of FC. Here we establish an explicit wave equation to describe the spontaneous cortical neural activities based on the high-order hypergraph representation of SC. Theoretical solution shows that the dynamic couplings between brain regions fluctuates in the form of an exponential wave regulated by the spatiotemporal varying Laplacian of the hyper-structural connectome (hSC), which orchestrates the cortical activities propagating in both space and time. Ultimately, we present a possible mechanism of how negative correlations emerge during the fluctuation of the hypergraph Laplacian of SC, which helps to further understand the fundamental role of SC in shaping the entire pattern of FC with a new perspective. Comprehensive tests on four connectome datasets with different resolutions confirm our theory and findings.