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Distinct sleep phases are related to different dynamical patterns in electroencephalogram (EEG) signals. In this article, the relationship between the sleep stages and nonlinear behavior of sleep EEG is explored. In particular, analysis of approximate entropy (ApEn) and the largest Lyapunov exponent is evaluated in patients with sleep apnea, which is defined as respiratory flow that is suspended or decreased for more than 10 s. The pathological sleep EEG signals for analysis were obtained from the MIT-BIH polysomnography database available online at the PhysioBank. The results show that for the both normal and apneic sleep epochs, ApEn decreased significantly as the sleep goes into deeper stages. Therefore, it indicated that as sleep becomes deeper, the brain function becomes less activated. Compared with normal sleep, the mean value of largest lyapunov exponents was also significantly lower than that of normal epochs during deep sleep stages. The results also show that the average largest lyapunov exponents of EEG signals increased in the REM state. Because during this stage of sleep, the cortex becomes more active and more neurons incorporate in the information processing. In conclusion, the nonlinear dynamical measures obtained from the nonlinear dynamical analysis such as the approximate entropy and largest lyapunov exponents can be useful for characterizing the physiological or pathological states of the brain

Nonlinear Evaluation of Electroencephalogram Signals in Different Sleep Stages in Apnea Episodes