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Dynamics of sleep-wake transitions during sleep.pdf

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Dynamics of sleep-wake transitions during sleep

Europhys. Lett., 57 (5), pp. 625–631 (2002) EUROPHYSICS LETTERS 1 March 2002 Dynamics of sleep-wake transitions during sleep C.-C. Lo1, L. A. Nunes Amaral1,2, S. Havlin3, P. Ch. Ivanov1,2, T. Penzel4, J.-H. Peter4 and H. E. Stanley1 1 Center for Polymer Studies and Department of Physics, Boston University Boston, MA 02215, USA 2 Cardiovascular Division, Beth Israel Deaconess Medical Center Harvard Medical School - Boston, MA 02215, USA 3 Gonda Goldschmid Center and Department of Physics, Bar-Ilan University Ramat Gan, Israel 4 Klinik fu?r Innere Medizin, Philipps-Universita?t Baldingerstrasse 1, Marburg D-35033, Germany (received 11 September 2001; accepted in final form 29 November 2001) PACS. 02.50.Ey – Stochastic processes. PACS. 05.40.Fb – Random walks and Levy flights. PACS. 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion. Abstract. – We study the dynamics of the awakening during the night for healthy subjects and find that the wake and the sleep periods exhibit completely different behavior: the durations of wake periods are characterized by a scale-free power law distribution, while the durations of sleep periods have an exponential distribution with a characteristic time scale. We find that the characteristic time scale of sleep periods changes throughout the night. In contrast, there is no measurable variation in the power law behavior for the durations of wake periods. We develop a stochastic model which agrees with the data and suggests that the difference in the dynamics of sleep and wake states arises from the constraints on the number of microstates in the sleep-wake system. In clinical sleep centers, the “total sleep time” and the “total wake time” during the night are used to evaluate sleep efficacy and to diagnose sleep disorders. However, the total wake time during a long period of nocturnal sleep is actually comprised of many short wake intervals (fig. 1). This fact suggests that the “total wake time” during sleep is