Abstracts

Modern methods for dynamical analysis of signals recorded from the brain (like EEG, field potentials, spike trains) involve the notion of a multi-dimensional state space and measure of the complexity and stability of the embedded system in the state space. So far, the foundation blocks of this approach had been the information content (e.g. Renyi information) and the rate of change of information content (e.g. Lyapunov exponents, Kolmogorov entropy). However, what is still missing is reliable measures of the direction and magnitude of information flow that could characterize the interactions and quantify the coupling of different parts of a system in the state space. Such measures will be of paramount importance in science in general, and epilepsy in particular. Results from the application of such a measure to epilepsy will be presented.
We introduce a new method to analyze the interactions between brain signals in the spatio-temporal domain. The thus defined cross short-term maximum Lyapunov exponent (CSTL^A,B max) measures the rate of information flow (bits/sec) from brain site A to B. We have applied this measure to: 1) data from dynamical models of coupled chaotic oscillators, 2) long-term multi-electrode EEG recordings from patients with focal epilepsy, and 3) intracellular and extracellular cell membrane potential recordings in [ldquo]seizures[rdquo] produced by hyperhermia in immature rat hippocampal slices.
In all simulation data, under different spatial configurations and type of oscillators, the CSTLmax correctly estimated the direction of flow of information. Its application to the human EEG data showed the following novel results: a) Correct (p[lt]0.01) lateralization and localization of the epileptogenic focus in both patients analyzed (our two most difficult cases) by identification of the driver electrode sites, b) Elevated, intermittent, dynamical driving of extrafocal sites by the focus in the preictal periods, and of the focus by the extrafocal sites in the postictal periods. Its application to the data from hippocampal slices showed prevalence of uni-directional information flow between extra and intra-cellular spaces before the accompanying spreading depression (SD) at low temperatures, and balanced bi-directional flow after SD (high temperatures). This last observation is in accordance with the physiological basis of the phenomenon [italic]( J Wu [amp] RS Fisher, J. Neurophysiol., :1355-1360, 2000)[/italic]
The newly introduced measure of cross Lyapunov exponents provides new insights into the epileptogenic process( see also [italic]L Iasemidis, IEEE Trans. Biomed. Engin., , 549-558, 2003)[/italic]. Results from the simulation (computer), clinical (in-vivo) and experimental (in-vitro) data used in this study support this conjecture The results from the new measure[apos]s application to hippocampal slices data suggest that CTLmax can also be a useful tool in studies of the basic mechanisms of epilepsy.
[Supported by: NIH, Whitaker Foundation]