Dimensional Analysis of No‐Task Human EEG Using the Grassberger‐Procaccia Method

Abstract

A method developed by Grassberger and Procaccia allows estimation of the dimensional complexity of the state-space attractor of a time series. Saturation of dimensional-complexity estimates with increasing values of embedding dimension is considered a strong indication that the time series is governed by deterministic chaos. The present investigation employed the Grassberger-Procaccia method to estimate EEG dimensional complexity in a multi-subject, factorial experiment. Twelve subjects were tested under two no-task conditions (eyes closed and open), with the block of two conditions being repeated four times. EEG was recorded from the nineteen 10-20 loci. Dimensional complexity declined across Blocks 1-3 and then leveled off, and was higher in the eyes-open than in the eyes-closed condition. Condition also interacted with locus in that the increase in dimensional complexity associated with opening the eyes was greater over occipital loci. Comparison with the results of Fourier analysis indicated that a similar but not identical pattern of effects was obtained for alpha (8-12 Hz) power. Further, across the entire data set, if alpha power exceeded a value of about 70 microV2, dimensional complexity was uniformly low, a finding in concert with previous results indicating that the eyes-closed, occipital alpha rhythm possibly represents deterministic chaos of relatively low dimension.