Learning image derived PDE-phenotypes from fMRI data.

Partial differential equations (PDEs) model various physical phenomena, such as electromagnetic fields and fluid mechanics. Methods such as sparse identification of nonlinear dynamics (SINDy) and PDE-Net 2.0 have been developed to identify and model PDEs on the basis of data via sparse optimization and deep neural networks, respectively. While PDE models are less commonly applied to fMRI data, they have the potential to uncover hidden connections and essential components in brain activity. Using the ADHD200 dataset, we applied canonical independent component analysis (CanICA) and uniform manifold approximation (UMAP) for dimensionality reduction of fMRI data. We then used sparse ridge regression to identify PDEs from the reduced data, and applied significant PDE features for classification achieving high accuracy in distinguishing individuals with attention deficit hyperactivity disorder (ADHD). This study demonstrates a novel approach for extracting meaningful features from fMRI data for neurological disorder analysis to understand the role of oxygen transport (delivery & consumption) in the brain during neural activity, which is relevant for studying intracranial pathologies.