State-Space Approaches for Mapping Brain Networks using iEEG Data

From a network perspective, neurons in the brain are interconnected upon performing functions during our everyday life. Seizures are network dysfunction phenomena, as abnormal neuronal activities within the seizure onset zone (SOZ) start to interrupt the normal brain network connectivity and propagate to otherwise healthy brain regions. In the current clinical practice, clinicians use multi-channel intracranial EEG (iEEG) recordings to visually localize SOZ in patients undergoing epilepsy surgery. Since iEEG recordings can be treated as high-dimensional time series resulting from the continuous directional network interactions across brain areas, it is thus reasonable to portray the dynamics of seizure network and localize the SOZ using statistical network connectivity approaches. Here, we have developed state-space multivariate autoregressive (SSMAR) models for identifying SOZ in patients with epilepsy. Using SSMAR, we first identify the connected brain areas (i.e., mapping the brain network) using estimated SSMAR parameters representing the directional connectivity within the network. To increase model estimation efficiency and to produce appropriate SOZ identification results, expert knowledge of the brain network’s cluster structure is also integrated during SSMAR parameter estimations.

Specifically, we first propose the modular state-space multivariate autoregressive (MSSMAR) model that features a cluster structure given by the Potts model, where the brain network consists of several clusters of densely connected brain regions. We develop a generalized expectation-maximization algorithm to estimate the proposed model and use it to map the inter-regional networks of epileptic patients in different seizure stages.

In addition, we propose the second model based on state-space multivariate autoregression, the Bayesian stochastic block model (BSBM) where a stochastic blockmodel-motivated approach is used for assigning clustered structures in the brain. Furthermore, in contrast to most existing network modeling approaches that were developed mainly for the observed network connections, we have subsequently developed a new network analysis framework using Bayesian approach for estimating the proposed high-dimensional model, inferring directional connections, and identifying clusters for unobserved network connections.

For both the proposed models, we show through simulation and real data analysis, 1) our SSMAR-based methods are robust to various deviations of the model assumptions and outperforms existing network methods on simulation iEEG data; 2) our SSMAR-based methods with their respective generalized expectation-maximization algorithm and Bayesian inference methodology applied to real iEEG data can reveal changes in brain network connectivity of the SOZ during seizure development.