Nonlinear analysis of sleep EEG in depression: calculation of the largest lyapunov exponent

Conventional sleep analysis according to Rechtschaffen and Kales (1968) has provided meaningful contributions to the understanding of disturbed sleep architecture in depression. However, there is no characteristic alteration of the sleep cycle, which could serve as a highly specific feature for depressive illness. Therefore, we started to investigate nonlinear properties of sleep electroencephalographic (EEG) data in order to elucidate functional alterations other than those obtained from classical sleep analysis. The application of methods from nonlinear dynamical system theory to EEG data has led to the assumption that the EEG can be treated as a deterministic chaotic process. Chaotic systems are characterized by a so-called sensitive dependence on initial conditions. This property can be quantified by calculating the system's Lyapunov exponents, which measure the exponential separation of nearby initial states in phase space. For 15 depressive inpatients (major depressive episodes according to DSM-III-R criteria) and 13 healthy controls, matched in gender, age, and education, we computed the principal Lyapunov exponents L1 of EEG segments corresponding to sleep stages, I, II, III, IV, and rapid eye movement (REM), according to Rechtschaffen and Kales, for the lead positions CZ and PZ. We found statistically significant decreased values of L1 during sleep stage IV in depressives compared with a healthy control group.