Bayesian Inference of Directional Brain Network Models for Intracranial EEG Data

The human brain is a network system in which brain regions, as network nodes, constantly interact with each other. The directional effect exerted by one brain component on others is referred to as directional connectivity. Since the brain is also a continuous-time dynamic system, it is natural to use ordinary differential equations (ODEs) to model directional connections among brain regions. We propose a high-dimensional ODE model to explore directional connectivity among many small brain regions recorded by intracranial EEG (iEEG). The new ODE model, motivated by the physical mechanism of the damped harmonic oscillator, is effective for approximating neural oscillation, a rhythmic or repetitive neural activity involved in many important brain functions. To produce scientifically interpretable network results, we assume the sparse structure for the ODE model parameters that quantify directional connectivity among regions. We consider two types of sparse structure: 1. a modular network structure consisting of several functionally independent subnetworks/clusters of lower dimensions which provides an intuitive interpretation of functional specialization of brain regions in different clusters, 2. a small-world network structure consisting of several subnetworks with dense connections within the same cluster and sparse connections between different clusters which reflects two principles of the brain's functional organization: functional integration and segregation, resulting in two ODE models. We develop two Bayesian methods to estimate the model parameters of the proposed ODE models and to identify clusters of strongly connected brain regions. We compare the two proposed ODE models through simulation studies and analysis of iEEG data collected from a patient with medically intractable epilepsy and examine the patient's brain networks around the seizure onset.