Modeling Volatility Characteristics of Epileptic EEGs using GARCH Models

Abstract

Objective: To determine if there was a difference in the volatility characteristics of seizure and non-seizure onset channels in the intracranial electroencephalogram (EEG) in a patient with temporal lobe epilepsy. Methods: The half-life of volatility for the different EEG channels was determined using Autoregressive Moving Average–Generalized Autoregressive Conditional Heteroscedasticity (ARMA–GARCH) models; confidence intervals were constructed using the delta method and an asymptotic method for comparing the half-lives. Results: Clinically determined seizure onsets occurred over strip electrodes named RAST (Right Anterior Subtemporal) and RMST (Right Mid Subtemporal), at locations 2, 3 and 4, on the strip electrodes. The half-lives of volatility for two of the three seizure channels, RAST3 and RAST4, were found to be significantly lower the rest of the channels for six one-minute EEG segments prior to seizure onset and nine one-minute EEG segments of an awake state. The half-lives of volatility for RAST3 and RAST4 were not significantly different to the non-seizure channels for ten one-minute segments of sleep and ten one-minute segments of sleep-to-awake states. The estimates for the half-lives were consistent for randomly selected one-minute EEG segments. Conclusions: The use of GARCH models may be a useful tool in determining hidden properties in epileptiform EEGs that may lead to better understanding of the seizure generating process.