Non-linear EEG measures during sleep: effects of the different sleep stages and cyclic alternating pattern. 
The objective of this work was to study the non-linear aspects of sleep EEG, taking into account the different sleep stages and the peculiar organization of its phasic events in ordered sequences (CAP) by applying a series of new non-linear measures (non-linear cross prediction or NLCP), which appear more reliable for the detection and characterization of non-linear structures in experimental data than the commonly used correlation dimension.  Eight healthy subjects aged 18-20 years participated in this study.  Polysomnography was performed in all subjects; signals were sampled at 128 Hz and stored on hard disk.  The C3 or C4 derivation was used for all the subsequent computational steps, which were performed on EEG epochs (4096 data points) selected from sleep stage 2 (S2) and slow-wave sleep (SWS), in both CAP and non-CAP (NCAP) conditions.  Also, epochs from sleep stage 1 (S1), REM and wakefulness preceding sleep were recorded.  The dynamic properties of the EEG were assessed by means of the non-linear cross-prediction test, which uses three different 'model' time series in order to predict non-linearly the original data set (Pred, Ama, and Tir).  Pred is a measure of the predictability of the time series, and Ama and Tir are measures of asymmetry, indicating non-linear structure.  The non-linear measures applied in this study indicate that sleep EEG tends to show non-linear structure only during CAP periods, both during S2 and SWS.  Moreover, during CAP periods, non-linearity can only be detected during the phase A1 subtypes (and partially A2) of CAP.  The A3 phases show characteristics of non-stationarity and bear some resemblance to wakefulness.  Based on the results of this study, sleep might be considered as a dynamically evolving sequence of different states of the EEG, which we could track by detecting non-linearity, mostly in association with CAP.  Our results clearly show that detectable non-linearity in the EEG is closely related to the occurrence of the phase A of CAP.