Recently great progress has been made in many areas of non-linear theory. Results of electroencephalogram (EEG) analysis by non-linear analysis have been reported of the 'awake' EEG as well as the sleep EEG during periods of the night. [1][2][3] The change of the correlation dimension over the whole night sleep EEG has not yet been reported, and the difference of the correlation dimension between each sleep cycle also has not yet been studied. We applied a correlation dimension which shows a flexibility in the time series in order to quantitatively study sleep EEG during the whole night, and compared the results of each sleep cycle. METHODSThe subject was a healthy male aged 22 years without a history of alcoholism. Polysomnography (PSG) was recorded from 23.00 to 07.30 h on the experiment night. The PSG was visually scored per 20 s according to the criteria of Rechtschaffen and Kales. 4 The attractors in the phase space were reconstructed from the data using a time shift method proposed by Takens. 5 The correlation dimensions of the EEG data were calculated as described by Grassberger and Procaccia. 6 These correlation dimensions were averaged for each sleep stage. We analyzed the whole night sleep EEG, and the correlation dimensions which were obtained each sleep cycle of the whole night sleep EEG recording, and compared them. Figure 1 represents the correlation dimensions of the whole night sleep EEG. Figure 2 shows the mean correlation dimensions for the 'awake' stage, sleep stages 1-3, and rapid eye movement (REM) sleep for each sleep cycle. Figure 3 illustrates the mean correlation dimensions versus the sleep stages for the entire sleep EEG. The mean correlation dimensions were 6.62 for 'awake', 5.91 for stage 1, 4.95 for stage 2, 3.88 for stage 3, and 6.13 for REM sleep. These values were statistically significant in each case. Figure 4 represents the smoothed correlation dimensions and sleep stages over the whole night sleep EEG. RESULTS DISCUSSIONWe calculated the correlation dimensions for the entire sleep EEG per 20-s epochs. The mean correlation dimensions decreased from the 'awake' stage to sleep stages 1-3 and increased at REM sleep. These results are generally consistent with the results reported by Roschke et al. 7 A change in the mean Psychiatry and Clinical Neurosciences (1999) AbstractA sleep electroencephalogram was analyzed by non-linear analysis. The polysomnography of a healthy male subject was analyzed and the correlation dimensions calculated. The correlation dimensions decreased from the 'awake' stage to sleep stages 1-3 and increased during rapid eye movement (REM) sleep. These results were seen during each sleep cycle. In each sleep cycle, the correlation dimensions decrease for slow wave sleep, and increase for REM sleep.

Sleep electroencephalogram (EEG) was analyzed by nonlinear analysis. Polysomnography of a healthy male subject was analyzed and the correlation dimension was calculated. The mean correlation dimensions decreased from stage 'awake' to stages 1, 2 and 3, and increased during rapid eye movement (REM) sleep. These results were also seen at every sleep cycle. During each sleep cycle the correlation dimensions decreased for slow wave sleep, then increased for REM sleep.The mean correlation dimension of the sleep EEG in the second half of the night was significantly higher than those in the first half of the night. A significant change was seen both during REM sleep as well as in sleep stage 2. Nonlinear analysis may be a useful method in the analysis of the entire sleep electroencephalogram.

Sleep electroencephalograms (EEG) were analyzed by non-linear analysis. Polysomnography (PSG) of nine healthy male subjects was analyzed and the correlation dimension (D2) was calculated. The D2 characterizes the dynamics of the sleep EEG, estimates the degrees of freedom, and describes the complexity of the signal. The mean D2 decreased from the awake stage to stages 1, 2, 3 and 4 increased during rapid eye movement (REM) sleep. The D2 during each REM sleep stage were high and those during each slow wave sleep stage were low, respectively, for each sleep cycle. The mean D2 of the sleep EEG in the second half of the night was significantly higher than those in the first half of the night. Significant changes were also observed during sleep stage 2, but were not seen during REM sleep and sleep stages 3 and 4. The D2 may be a useful method in the analysis of the entire sleep EEG.