Non-linear dynamics of alpha and theta rhythm: correlation dimensions and Lyapunov exponents from healthy subject's spontaneous EEG.
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 (F3, F4, Cz, P3, P4, O1 and O2) we calculated the so-called correlation dimension D2, 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.
Röschke
J
J
Department of Psychiatry, University of Mainz, Germany.
Fell
J
J
Mann
K
K
D000465:Algorithms; D000513:Alpha Rhythm / Q000706:statistics & numerical data*; D004569:Electroencephalography / Q000706:statistics & numerical data*; D006801:Humans; D017711:Nonlinear Dynamics; D012016:Reference Values; D013826:Theta Rhythm / Q000706:statistics & numerical data*