On the dimensionality of sleep-EEG data. Using chaos mathematics and a systematic variation of the parameters of the Corex program to determine the correlation exponents of sleep EEG segments.

Sleep-EEG data of 16 healthy subjects, classified according to the Rechtschaffen and Kales criteria, were taken to determine the correlation exponent (CE) or dimensionality (D2) of the data using the Corex program. We tested the applicability of this program to the analysis of sleep-EEG data changing systematically the embedding dimension (ED), the time lag (tau), the number of involved pairs of vectors and the EEG segment by split half. We could confirm the results of other authors according to which the complexity of the EEG signal decreases from stage 'awake, eyes closed' to sleep stages 1, 2, 3 and 4. The differences between the various sleep stages were significant. Stage REM could be differentiated from every stage but stage 1. The most important finding of our study was that the absolute value of the dimensionality depends on almost all the parameters tested: with increasing tau up to tau = 200 the CE increases, which means a 1.56-second shift. A higher number of pairs is needed when the signal is more complex. The ED is selected well between 6 and 11, that means reasonably higher or close to the dimensionalities for that purpose as presented in the literature. Different segments of one sleep stage in 1 subject led to different CE values, thus demonstrating that the EEG signal is not stationary over a segment of 2 min time. Although using chaos mathematics seems to be a useful tool in analyzing EEG data to explore their complexity, we could demonstrate the urgent need of calibrations and conventions to be able to interpret the absolute values.

Bivariate global frequency analysis versus chaos theory. A comparison for sleep EEG data.

Various quantitative descriptors for EEG data will be compared taking sleep as an example. In this contribution, Hjorth's mobility and complexity measures will be used to classify sleep stages. The results will be compared with those of a dimensionality analysis. Several authors have shown that the correlation exponent can describe the complexity of sleep EEG data and is able--with the exception of REM sleep--to distinguish significantly between sleep stages. The discriminative power of a bivariate global frequency analysis appears to be superior to that of the correlation exponent. Furthermore a very high statistical correlation between the estimator of fractal dimension and Hjorth's mobility was obtained.

[Periodic discharges of sleep spindles with placebo and zopiclone]. / Periodische Entladungen von Schlafspindeln unter Plazebo und Zopiclone.

According to our experiences (parietal) sleep spindles often show a periodical appearance. Successive sleep spindles in series have a distance of about four seconds. In 95% the duration of such series of sleep spindles is not longer than 40 s, so that there appears no more than ten successive periodical sleep spindles. In the present study ten subjects aged between 57 and 77 years were given Placebo and 7.5 mg Zopiclone. Under the effect of verum we found a doubling of sleep spindle series. However, the distance between the periodical spindles and the length of the spindle series remained unchanged. The variance in the ability to generate sleep spindle series was very high across subjects. One subject for example produced only one sleep spindle series in the Placebo-night (three under verum) and another subject on the other hand 95 (under verum 130). The results of the present study well corresponding to the results of a former investigation comparing Placebo, Pentobarbital, Methaqualon, Carbromal, Flunitrazepam, Triazolam and Lormetazepam.