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 and 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.
PackardNHCrutchfieldJPFarmerJDShawRS. Geometry from a time series. Phys Rev Lett1980; 45: 712.
2.
FarmerJDOttEYorkA. The dimension of chaotic attractors. Physica1983; 7D: 153–180.
3.
LayneSPMayer-KressGHolzfußJ. Problems associated with dimensional analysis of electroencephalogram data. In: Mayer-KressG (ed). Dimensions and Entropies in Chaotic Systems. Berlin: Springer; 1985:246–251.
4.
BabloyantzANicolisCSalazarU. Evidence of chaotic dynamics of brain activity during the sleep cycle. Phys Left A1985;111:152–156.
5.
BabloyantzA. Chaotic dynamics in brain activity, in: BasarE (ed). Dynamics of Sensory and Cognitive Processing by the Brain. Berlin: Springer; 1988:196–202.
6.
MayRM. Simple mathematical models with very complicated dynamics. Nature1976; 261: 459–467.
7.
EckmannJP. Roads to turbulence in dissipative dynamical systems. Rev Mod1981; 53: part 1.
8.
ShawR. Strange attractors, chaotic behavior and information flow. Z Naturforsch1981; 36: 80–112.
9.
SchusterHG. Deterministic Chaos. An Introduction. Weinheim: Physik Verlag; 1984.
10.
ParkerTSShuaCO. Practical numerical algorithms for chaotic systems. New York Heidelberg: Springer; 1989.
11.
DestexheASepulchreJABabloyantzA. A comparative study of the experimental quantification of deterministic chaos. Phys Lett A1988; 132:101–106.
12.
PoolR. It is healthy to be chaotic. Science1989; 243:604–607.
13.
BabloyantzA. Evidence for slow brain waves: A dynamical approach. Electroencephalogr Clin Neurophysiol1991; 78: 402–405.
14.
BabloyantzADestexheA. The Creutzfeld-Jacob disease in the hierarchy of chaotic attractors. In: MarkusMMlerSNicolisG (eds). From Chemical to Biological Organisation. Berlin, Heidelberg, New York: Springer; 1987; 307–316.
15.
BabloyantzADestexheA. Low-dimensional chaos in an instance of epilepsy. Proc Natl Acad Sci USA1986; 83: 3513–3517.
16.
RöchkeJAldenhoffJB. Estimation of the dimensionality of sleep: EEG data in schizophrenics. Eur Arch Psychiatry Clin Neurosci1993; 242:191–196.
17.
RöchkeJMannKFellJ. Nonlinear EEG dynamics during sleep in depression and schizophrenia. Intern J Neuroscience1994; 75: 271–284.
18.
RöchkeJAldenhoffJB. A nonlinear approach to brain function: Deterministic chaos and sleep EEG. Sleep1992; 15(2): 95–101.
19.
AchermannPHartmannRGunzingerAGuggenbuhlWBorbelyAA. Correlation dimension of the human sleep electroencephalogram: Cyclic changes in the course of the night. Euro J Neurosci1994; 6: 497–500.
20.
AchermannPHartmannRGunzingerAGuggenbuhlWBorbelyAA. All-night sleep EEG and artificial stochastic control signals have similar correlation dimensions. Electroencephalogr Clin Neurophysiol1994; 90: 384–387.
21.
RechtschaffenAKalesA. A Manual of Standardized Terminology, Technics and Scoring System for Sleep Stages of Human Subjects. Washington, DC: Public Health Services, US Government Printing Office; 1968.
22.
GrassbergerPProcacciaI. Measuring the strangeness of strange attractors. Physica1983; 9D: 189–208.
23.
RenyiA. Probability Theory. North Holland: Elsevier; 1970.
TakensF. Detecting strange attractors in turbulence. Lecture Notes in Mathematics 898. Berlin: Springer; 1981: 366–388.
26.
KobayashiTMisakiKNakagawaH. Correlation dimension of the human sleep EEG. Psychiatry Clin Neurosci2000;54:11–16.
27.
NiestrojESpiewegILoscherWMPfurtschellerG. On the dimensionality of sleep-EEG data: Using chaos mathematics and systematic variation of the parameters of the Corex program to determine the correlation exponents of sleep EEG segments. Neuropsychobiol1995; 31(3):166–172.
28.
RöchkeJBasarE. Correlation dimensions in various parts of cat and human brain in different states. In: BasarEBullockT, (eds). Brain Dynamics. Progress and Perspectives. Berlin: Springer; 1989:131–148.
29.
RöchkeJ. Eine Analyse der nichtlinearen EEG-Dynamik. Doctoral Dissertation. University of Gōttingen; 1986: 88–94.
30.
FreemanWJSkardaCA. Spatial EEG patterns, non-linear dynamics and preception: The Neo-Sherringtonian view. Brain Res Rev1985; 10:147–175.
31.
AzumiK. Sleep in the adult. In: The Japanese Society of Sleep Research. Handbook of Sleep Science and Sleep Medicine. 1998; 28–34.
32.
CrickFMitchisonG. The function of dream sleep. Nature1983; 304:111–114.
