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Abstract:
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We use ordinary differential equations (ODE) to model the directional interaction, also called effective connectivity, among brain regions. In contrast to existing ODE models that focus on effective connectivity among only a few brain regions and that rely on strong prior belief of the existence and strength of connections, we propose a high-dimensional ODE model motivated by statistical considerations to explore connectivity among multiple small 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 cluster structure, which consists of modules 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 across different experimental trials. We apply the proposed method to electrocorticography (ECoG) datasets and evaluate brain networ
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