Directed fMRI-based Functional Connectivity Estimation using Physics-Informed Neural Networks

Estimating directed functional connectivity (dFC) within the brain is crucial for comprehending neural interactions. However, conventional methodologies encounter constraints in accuracy, scalability, and interpretation. The method presented here harnesses Physics-Informed Neural Networks (PINNs) to amalgamate the governing physical principles of brain dynamics, thereby improving dFC estimation from resting-state functional magnetic resonance imaging (rsfMRI) data. In particular, during the training phase, we derive the input weights from a long-short term memory (LSTM) network, which, within our framework, represent the influence of all other brain areas on the specific region under consideration. These input weights are then integrated into the nonlinear differential equation that models the rsfMRI time series within the specific brain area. Through the training of the PINN model, we simultaneously estimate, for each brain area, the biophysical parameters of the model, including the dFC parameters from all the remaining areas. We applied this methodology to both autism spectrum disorder (ASD) and neurotypical data, revealing significant sex-specific differences in connectivity patterns. These findings underscore the potential of PINNs in advancing our understanding of neural dynamics and emphasize the significance of directionality in brain connectivity research.