Nonlinear analysis of sleep EEG data in schizophrenia: calculation of the principal Lyapunov exponent

The generating mechanism of the electroencephalogram (EEG) points to the hypothesis that EEG signals derive from a nonlinear dynamic system. Hence, the unpredictability of the EEG might be considered as a phenomenon exhibiting its chaotic character. The essential property of chaotic dynamics is the so-called sensitive dependence on initial conditions. This property can be quantified by calculating the system's first positive Lyapunov exponent, L1. We calculated L1 for sleep EEG segments of 13 schizophrenic patients and 13 control subjects that corresponded to sleep stages I, II, III, IV and REM (rapid eye movement), as defined by Rechtschaffen and Kales, for the lead positions Cz and Pz. During REM sleep, for both electrode positions, the principal Lyapunov exponent L1 was significantly increased in schizophrenic patients compared with control subjects. This finding points to altered nonlinear brain dynamics during REM sleep in schizophrenia.