Abstracts

Rationale: Recently, several nonlinear systems methods for EEG analysis have been proposed. One of the most widely applied first steps in these analyses is the construction of a phase space representation of the time series. The evaluation of phase space plots often begins with visual inspection. The first and most fundamental question is whether there is any structure in the plot, hence any value to proceeding with more detailed analyses. The purpose of this poster is to propose an alternative method of visualizing the evolution of the phase space plot, which better reveals underlying structures.Methods: EEG records were obtained from pediatric aged patients undergoing evaluation for intractable epilepsy. Two phase space reconstruction methods were used. The first plots the amplitude of the voltage time series, V(t), against its first derivative , dV(t)/dt. The second is a time delay method in which the amplitude of the voltage time series is plotted versus its ampitude at a time delay from the initial time. A range of time delays were assessed and the method of minimum mutual information chosen. Such plots usually superimpose the trajectories of the entire analysis epoch. Also, movies of the development of the phase space trajectories were generated using Chaos Data Analyzer Pro and a shareware DOS-emulator DOSbox v0.65. This allowed variable rates of viewing and permitted capturing snapshots which were correlated to the EEG signal. This latter processing was performed in MatLab.Results: Fifteen seizures from six patients were analyzed. In each case the pre-ictal trajectory occupied a limited portion of the phase space, consistent with an attractor. With ictal onset the trajectory orbits expanded substantially and showed recurrent behavior, with a return to the intial attractor region. No instances of multistability were seen. In two patients no structure was apparent in the phase space plot when the trajectories for the entire analysis epoch were superimposed. When the evolution of the trajectories were seen in slow motion the underlying structures became visible. The underlying structures had been obscured by the superimposition of multiple semi-periodic recurrences whose geometric orientations shifted over time. Lyapunov exponsents were positive in all cases. Conclusions: The construction of two dimensional phase space plots of seizures in pediatric patients reveals a number of consistencies. However, the underlying structure in the phase space can be obscured and therefore overlooked unless the phase space analysis also includes an examination of the temporal evolution of the plots. Hence, we recomend that efforts to perform nonlinear time series analyses of seizures, using phase space plots, should include an evaluation of the evolution of these trajectories over time.