Accurately modeling resting-brain functional connectivity using hypergraph neural field-Fourier deep neural network.

Revealing the relationship between resting-state human brain structure and function is a central question for understanding brain cognition and neuropsychiatric disorders, while the problem still remains largely unanswered. Graph diffusion (GD) model predicts functional connectivity (FC) from structural connectivity (SC), which makes the assumption that current signals of each brain region conform to exponential decay once activated. However, information interaction between brain regions is ignored, resulting in none of negative correlations in FC. To overcome the challenge, we establish hypergraph neural field (HNF) model to depict information interaction between excitatory and inhibitory neurons between brain regions. Then, taking excitatory membrane potentials, calculate Pearson correlation coefficients between brain regions to get interactive connectivity (IC). Although the mean of Pearson correlation coefficients between IC and FC is relatively low (0.4), it is slightly higher than that achieved by the graph neural field model, and IC exhibits a non-negligible amount of negative correlations. Furthermore, we propose hypergraph neural field-Fourier deep neural network (HNF-FDNN) model, in which Fourier deep neural network (FDNN) integrates low- and high-frequency components spectral information, thereby enhancing HNF model in the representation of FC and significantly improving prediction accuracy. We test HNF-FDNN model on Human Connectome Project S1200 release including 90 regions of interests, which contains 100 train subjects and 100 test subjects. The mean value of Pearson correlation coefficients reaches 0.8168 in the 100 test subjects, exceeding GD model (0.5499). Meanwhile, HNF-FDNN model shows the stronger robustness and stability. The study emphasizes the potential of combining the brain activity signals and machine learning methods for modeling FC. It is beneficial for exploring formation of cognition and mechanism of neuropsychiatric disorders.