Learning Image Derived PDE-Phenotypes from fMRI Data

TL;DR

This paper introduces a novel method for deriving PDE-based features from fMRI data to classify ADHD, revealing insights into brain oxygen transport during neural activity.

Contribution

It applies PDE modeling to fMRI data using dimensionality reduction and sparse regression, a novel approach for neurological disorder analysis.

Findings

High accuracy in ADHD classification

Effective PDE feature extraction from fMRI data

Insights into oxygen transport in brain activity

Abstract

Partial Differential Equations (PDEs) model various physical phenomena, such as electromagnetic fields and fluid mechanics. Methods like Sparse Identification of Nonlinear Dynamics (SINDy) and PDE-Net 2.0 have been developed to identify and model PDEs based on data using sparse optimization and deep neural networks, respectively. While PDE models are less commonly applied to fMRI data, they hold the potential for uncovering 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, achieving high accuracy in classifying attention deficit hyperactivity disorder (ADHD). The study demonstrates a novel approach to 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 relevant for studying intracranial pathologies.