Abstract

We use ordinary differential equations (ODE) to model the directional interactions among brain regions and their dynamic activities. In contrast to existing ODE models that focus on the directional connections among only a few brain regions, we propose a high-dimensional ODE model motivated by statistical considerations to explore connectivity among a large number of brain regions. To characterize the brain’s oscillatory activity, we extend the classical one-dimensional Harmonic oscillator equation to a set of high-dimensional oscillators, each describing one brain region’s oscillation and interaction with other regions. The new ODE model also features the high-dimensional brain network in a small network structure, which consists of clusters of densely connected brain regions. We develop a unified Bayesian framework to quantify uncertainty in the assumed ODE model, identify clusters, select strongly connected brain regions, and make statistical comparison between brain networks under different conditions.  We use the developed methods to study the brain networks of epileptic patients by analyzing their brain activity measurements.