Non-linear dynamics of alpha and theta rhythm: Correlation dimensions and Lyapunov exponents from healthy subject's spontaneous EEG

Author(s): Fell, J., Mann, K.

Journal/Book: Int J Psychophysiol. 1997; 26: PO Box 211, 1000 AE Amsterdam, Netherlands. Elsevier Science BV. 251-261.

Abstract: The aim of the present paper was to analyze some non-linear dynamic properties of the resting EEG from healthy subjects under eyes closed conditions. For this purpose we digitally filtered the spontaneous EEG in the theta (3-8 Hz) and alpha frequency range (8-13 Hz) and considered these independent rhythms as signals from a deterministic system. Under certain conditions non-linear dynamic systems are able to generate deterministic chaos, which means that similar causes do not produce similar effects. This phenomenon is called sensitive dependence on initial conditions. From different lead positions (F-3, F-4, C-2, P-3, P-4, O-1 and O-2) we calculated the so-called correlation dimension D-2, which is assumed to be an estimation of the system's complexity, and the Lyapunov exponent L, which appears to be a measure of the sensitive dependence on initial conditions. Our investigations revealed that the dimensionality of the theta- and alpha-rhythm varies within subjects across the experimental session in wide ranges. The degrees of freedom of the alpha and theta rhythms across the scalp are in the same order, indicating dynamic processes which can not be differentiated by applying the Grassberger-Procaccia algorithm. The Lyapunov-exponents, indicating 'how chaotic a deterministic process is', are in general smaller for the theta than for the alpha activity. Across the scalp there is no evidence for different dynamics of the theta rhythm. The dynamics of the alpha rhythm, on the contrary, appears to be different at various lead positions. It appears justified to state that the dynamics of the frontal alpha activity is functionally different from the alpha activity recorded at other topographic locations.

Note: Article Roschke J, Univ Mainz, Dept Psychiat, Untere Zahlbacher Str 8, D-55101 Mainz, GERMANY

Keyword(s): EEG; eyes closed conditions; deterministic chaos; correlation dimensions; Lyapunov exponents; STRANGE ATTRACTORS; TIME-SERIES; SLEEP EEG; CORTEX; CHAOS; LOCALIZATION; MODEL; STATE

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