Magnetoencephalography and Attractor Dimension: Normal Subjects and Epileptic Patients

Abstract

In recent years methods from nonlinear dynamics analysis have been applied to examine the human electroencephalogram (EEG) with respect to attractor dimensions, Lyapunov exponents, etc.; using the same methods, Röschke and Başar (1988) have performed an analysis of EEG activity in cortical and subcortical structures of chronically implanted cats with respect to the fractal dimension of an EEG attractor during slow wave sleep. For the human EEG, Babloyantz et al. (1985) were able to determine an attractor dimension for two sleep stages (stages 2 and 4) whereas for REM sleep and for the awake state no attractor dimension was quoted. The dimensions found for the two sleep stages were close to 5 (stage 2) and 4 (stage 4). The analysis was based on data for two and three subjects, respectively, the experimental data consisting of time series of 4000 points with a sampling time of 10 ms. Similarly, for the chronically implanted cats (electrode positions: acoustic cortex, hippocampus, and reticular formation), Röschke and Başar quote a value of 4–5 for the EEG attractor during slow wave sleep. Further works by Babloyantz and Destexhe (1986) and Layne et al. (1985) quote still other values for attractor dimensions obtained under a number of conditions: anesthetized subjects, epileptic patients, alpha traces, etc.