Parameter Estimation in Brain Dynamics Models from Resting-State fMRI Data using Physics-Informed Neural Networks

Conventional modeling of the Blood-Oxygen-Level-Dependent (BOLD) signal in resting-state functional Magnetic Resonance Imaging (rsfMRI) struggle with parameter estimation due to the complexity of brain dynamics. This study introduces a novel brain dynamics model (BDM) that directly captures BOLD signal variations through differential equations. Unlike dynamic causal models or neural mass models, we integrate hemodynamic responses into the signal dynamics, considering both direct and network-mediated neuronal activity effects. We utilize Physics-Informed Neural Networks (PINNs) to estimate the parameters of this BDM, leveraging their ability to embed physical laws into the learning process. This approach simplifies computational demands and increases robustness against data noise, providing a comprehensive tool for analyzing rsfMRI data. Leveraging the functional connectivity matrices scaled by the estimated parameters, we apply a state-of-the-art community detection method to elucidate the network structure. Our analysis reveals significant differences in the participation coefficients of specific brain regions when comparing neurotypical individuals to those with Autism Spectrum Disorder (ASD), with distinct patterns observed between male and female cohorts. These differences are consistent with regions implicated in previous studies, reinforcing the role of these areas in ASD. By integrating PINNs with advanced network analysis, we demonstrate a robust approach for dissecting the complex neural signatures of ASD, providing a promising direction for future research in neuroimaging and the broader field of computational neuroscience.