Abstracts

Rationale: Although the timing of epileptic seizures can appear stochastic, in many cases it is modelable as a nonlinear dynamical system experiencing deterministic chaos. Applying dynamical analysis to interseizure interval (ISI) time series can aid in discriminating deterministic chaos from random noise. This information could be used to change the way seizures are treated, such as modifying medication timing according to their seizure cycle, or be further developed for forecasting implications. Furthermore, chaotic parameters such as the Largest Lyapunov exponent (LLE) can determine seizure chaosticity and calculate forecast horizon.We hypothesize that the majority of ISI time series from sampled epilepsy patients will display a statistically significant index of time dependence and be chaotic, having at least one positive Lyapunov exponent. Methods: Our study took a novel approach to characterizing seizure time dependencies by applying methods developed in chaos theory for analysis of nonlinear dynamical systems to ISI time series. These time series were taken from 1,000 patients with epilepsy, randomly sampled from seizure diary database SeizureTracker.Using the method of time delays, we constructed each individual's ISI in one to three phase space dimensions, and used the Savit-Green statistic (SGS) to quantify the degree of time dependence on each dimension. Bootstrapping was used to calculate the statistical significance of the SGS for each individual: the indices of each ISI time series were randomized to destroy any effect of temporal order on the SGS. We repeated this thirty times to generate a normal distribution for the randomized values and quantified the significance of the difference between SDS and randomized values. The resulting number was the index of time dependence, considered to be significantly time dependent at p<0.05 if >=0.95. We finally calculated the time dependence index artificially generated exponential distribution data distributed about the mean of the original time series to further contrast the original ISI time series with stochastic data.The LLE was also calculated for each ISI time-series. From there, the seizure forecast horizon was calculated based on the patient's LLE. Results: 52.9% of sampled patients showed a seizure pattern with high time dependence based on ISI time-series data compared to bootstrapped data, disproving the null hypothesis (p<0.05) that ISIs were independent and identically distributed (as would be expected for a stochastic system), suggesting the system was driven by deterministic dynamics. All patient ISIs were visualized via histogram.We also evaluated whether the index of time dependence varied significantly between patient populations of different epilepsy etiologies. Using an ANOVA test, we found there to be no significant difference in degree of seizure time dependence between different seizure etiology groups.We are looking at calculating the LLE for each time series to quantify the degree of chaoticity of the system and define a forecast horizon over which ISI may be predicted. Initial evaluation indicates promising results. Conclusions: Our results show that the detailed methods, derived from chaos theory, may be able to be applied to seizure forecasting efforts by determining a patient's seizure predictability. They show that a large portion of patients have a highly time dependent ISI pattern. Furthermore, Lyapunov exponents and the Savit-Green statistic may be useful in the development of seizure prediction algorithms. Funding: No funding