Numerical Simulation of Higher-Order Nonlinearity of Human Brain Functional Connectivity Using Hypergraph <i>p</i>-Laplacian

• Main Authors: Jichao Ma, Chunyu Du, Weifeng Liu, Yanjiang Wang
• Format: Article
• Language: English
• Published: MDPI AG 2021-09-01
• Series: Mathematics
• Subjects: brain connectivity; structure–function relation; graph Laplacian; hypergraph Laplacian; <i>p</i>-Laplacian
• Online Access: https://www.mdpi.com/2227-7390/9/18/2345

Unravelling how the human brain structure gives rise to function is a central question in neuroscience and remains partially answered. Recent studies show that the graph Laplacian of the human brain’s structural connectivity (SC) plays a dominant role in shaping the pattern of resting-state functional connectivity (FC). The modeling of FC using the graph Laplacian of the brain’s SC is limited, owing to the sparseness of the Laplacian matrix. It is unable to model the negative functional correlations. We extended the graph Laplacian to the hypergraph <i>p</i>-Laplacian in order to describe better the nonlinear and high-order relations between SC and FC. First we estimated those possible links showing negative correlations between the brain areas shared across subjects by statistical analysis. Then we presented a hypergraph <i>p</i>-Laplacian model by embedding the two matrices referring to the sign of the correlations between the brain areas relying on the brain structural connectome. We tested the model on two experimental connectome datasets and evaluated the predicted FC by estimating its Pearson correlation with the empirical FC matrices. The results showed that the proposed diffusion model based on hypergraph <i>p</i>-Laplacian can predict functional correlations more accurately than the models using graph Laplacian as well as hypergraph Laplacian.