Hypergraph Laplacian Diffusion Model for Predicting Resting Brain Functional Connectivity from Structural Connectivity

The relationship between the structure and function of the human brain is of immense importance in neuroscience and cognitive science, but little is known about how the brain structure shapes the function. Recent studies have shown that the graph Laplacian of structural connectivity (SC) plays an important role in generating functional connectivity (FC) in the resting state. However, the graph Laplacian can only simulate part of function due to the sparseness of the structural connection matrix. Additionally, it fails to model the negative functional correlations since it ignores the connection type information (excitatory or inhibitory) between brain regions. In this paper, we generalize the graph Laplacian to the hypergraph Laplacian, which can build relations between structurally unconnected brain regions, thus better results are obtained. Further, in order to simulate the negative correlations, we extract a sign matrix from the FC matrices of the first two subjects and then incorporate it into the model. We test the model on one empirical connectome dataset with 246 regions of interest (ROI) and the results show that the proposed hypergraph Laplacian model can describe FC with more accuracy than the graph Laplacian model.