Mapping epileptic directional brain networks using intracranial EEG data.

The human brain is a directional network system, in which brain regions are network nodes and the influence exerted by one region on another is a network edge. We refer to this directional information flow from one region to another as directional connectivity. Seizures arise from an epileptic directional network; abnormal neuronal activities start from a seizure onset zone and propagate via a network to otherwise healthy brain regions. As such, effective epilepsy diagnosis and treatment require accurate identification of directional connections among regions, i.e., mapping of epileptic patients' brain networks. This article aims to understand the epileptic brain network using intracranial electroencephalographic data-recordings of epileptic patients' brain activities in many regions. The most popular models for directional connectivity use ordinary differential equations (ODE). However, ODE models are sensitive to data noise and computationally costly. To address these issues, we propose a high-dimensional state-space multivariate autoregression (SSMAR) model for the brain's directional connectivity. Different from standard multivariate autoregression and SSMAR models, the proposed SSMAR features a cluster structure, where the brain network consists of several clusters of densely connected brain regions. We develop an expectation-maximization algorithm to estimate the proposed model and use it to map the interregional networks of epileptic patients in different seizure stages. Our method reveals the evolution of brain networks during seizure development.