Nonlinear Analysis of Sleep Stages Using Detrended Fluctuation Analysis: Normal vs. Sleep Apnea

The purpose of this paper is to compare the characteristics of EEGs, which typically exhibit non-stationarity and long-range correlations, by calculating its scaling exponents in between sleep apnea and the normal conditions. Detrended fluctuation analysis (DFA), which is suitable for non-stationary time series, is used to analyze the fluctuation of the EEG dynamics by calculating its scaling exponents. As we classified the stages into REM (R: Rapid Eye Movement), Non-REM (N), and Waken (W), each mean scaling exponent was significantly (p<0.001) different from the other stages in both sleep apnea and normal conditions. Two groups show significant (p<0.001) differences in all the stages. While the sleep apnea group shows N>R>W by order of the mean scaling exponent value, the normal group shows N>W>R. The fact of the reversed order of R and W between two groups may be related to some characteristics of sleep apnea. It was also noted that monotonic increasing in the stage 1 to 4 in both groups. We conclude that the scaling exponents could be used to classify the sleep stages automatically, and give some evidence for the non-linear dynamics of the sleep stages that varies with the condition of the patients. Key-words: Detrended-Fluctuation-Analysis (DFA); Electroencephalogram (EEG); Sleep Apnea; Scaling Exponents; Non-linear Dynamics