Phase space topography and the Lyapunov exponent of electrocorticograms in partial seizures

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Abstract
Summary Electrocorticograms (ECoG's) from 16 of 68 chronically implanted subdural electrodes, placed over the right temporal cortex in a patient with a right medial temporal focus, were analyzed using methods from nonlinear dynamics. A time series provides information about a large number of pertinent variables, which may be used to explore and characterize the system's dynamics. These variables and their evolution in time produce the phase portrait of the system. The phase spaces for each of 16 electrodes were constructed and from these the largest average Lyapunov exponents (L's), measures of chaoticity of the system (the larger the L, the more chaotic the system is), were estimated over time for every electrode before, in and after the epileptic seizure for three seizures of the same patient. The start of the seizure corresponds to a simultaneous drop in L values obtained at the electrodes nearest the focus. L values for the rest of the electrodes follow. The mean values of L for all electrodes in the postictal state are larger than the ones in the preictal state, denoting a more chaotic state postictally. The lowest values of L occur during the seizure but they are still positive denoting the presence of a chaotic attractor. Based on the procedure for the estimation of L we were able to develop a methodology for detecting prominent spikes in the ECoG. These measures (L*) calculated over a period of time (10 minutes before to 10 minutes after the seizure outburst) revealed a remarkable coherence of the abrupt transient drops of L* for the electrodes that showed the inital ictal onset. The L* values for the electrodes away from the focus exhibited less abrupt transient drops. These results indicate that the largest average Lyapunov exponent L can be useful in seizure detection as well as a discriminatory factor for focus localization in multielectrode analysis.

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