Abstracts

Rationale: There have been many quantitative metrics proposed to provide insight into system behavior during an ictus. A consistent theme over previous years is that changes in these metrics and not their absolute values have been the most reliable indicators of seizure onset. We have already reported those changes for Kolmogorov entropy, correlation dimension, and others have demonstrated the same for synchronization and complexity. Others have previously reported the utility of stochastic techniques in epilepsy modeling. The unique aspect of this study is the focus on a finer grain temporal analysis through the application of moving windows and eigenvalue characterization of the Markov chain transition matrix. Methods: EEG records were obtained from pediatric aged patients undergoing evaluation for intractable epilepsy. The EEG data was discretized into a given number of states before the Markov chain transition matrix was generated. The effect of several time lags, variable number of states, and different methods for automatically determining state size were examined. Further analysis used 12 states and a time lag of 15 ms. State size was derived from the mean and standard deviation of the data in a given window. After selecting these parameters, temporal analysis of the seizure EEGs was performed using 30 second moving windows spaced one second apart. The Markov transition matrix was generated for each window, and the eigenvalues of the transition matrix were calculated. Data analysis was performed in Matlab. Results: The different methods for automatically determining state size showed only modest effects on the results. Varying the time lag and number of states (particularly for small numbers of states) resulted in substantial effects on the results. For pre-ictal data the transitional probabilities lie predominantly along the diagonal while this is not the case for the ictal transition probabilities. The eigenvalues of the pre-ictal probabilities lie along the real axis and extend to the unit circle. During the ictus the eigenvalues are complex and cluster near the origin. The most dramatic finding was that seizure onset was associated with a dramatic drop in the absolute value of the principal eigenvalue (from about .9 to .4). These results were consistent across several seizures from multiple patients. Conclusions: Results from this study reinforce the impression created from previously reported nonlinear systems analyses that seizure onset is associated with dramatic changes in system dynamics, and these changes in dynamics reflect a decrease in the impact of linear driving forces. These results imply the initiation of nonlinear driving functions for the Markov chain behavior. The clustering of the eigenvalues around the origin of the unit circle signifies increased synchronization and simplification of the system which is consistent with current models of epileptic brain behavior. To our knowledge this is the first report of the application of Markov chain modeling on pediatric EEGs.