Non-linear analysis of the sleep EEG
Abstract
A 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.
INTRODUCTION
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.1–3 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.
METHODS
The 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.
RESULTS
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.
. Correlation dimension over the entire sleep electroencephalogram. REM, rapid eye movement; SWS, slow wave sleep; CD, correlation dimension.
. Mean correlation dimensions for stage ‘awake’, sleep stages 1–3, and rapid eye movement (REM) sleep for each sleep cycle. CD, correlation dimension.
and rapid eye movement (REM) sleep of entire sleep electroencephalogram. CD, correlation dimension.
. The smoothed correlation dimensions (CD) and sleep stages of entire sleep electroencephalogram. REM, rapid eye movement; SWS, slow wave sleep.
DISCUSSION
We 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 correlation dimension for each sleep stage was also recognized at every sleep cycle. These correlation dimensions may be used to score sleep stages in the future. For each sleep cycle, the correlation dimensions decreased during slow wave sleep (SWS), and increased during REM sleep. This similarity may exist for each sleep cycle. The correlation dimension shows the number of the independent variables in the time series. The sleep EEG during REM sleep and SWS have the independent variables of about 7 and 4 respectively, and these results have been identified over the entire sleep as well as at each sleep cycle.
