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Characterization of sleep stages by correlations in the magnitude and sign of heartbeat increments

Jan W. Kantelhardt1, Yosef Ashkenazy1, Plamen Ch. Ivanov1,2, Armin Bunde3, Shlomo Havlin4,1,3, Thomas Penzel5, Jörg-Hermann Peter5, and H. Eugene Stanley1

  • 1Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215
  • 2Beth Israel Deaconess Medical Center, Harvard Medical School, Boston, Massachusetts 02215
  • 3Institut für Theoretische Physik III, Justus-Liebig-Universität, D-35392 Giessen, Germany
  • 4Gonda-Goldschmied-Center and Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
  • 5Klinik für Innere Medizin, Klinikum der Philipps-Universität, D-35033 Marburg, Germany

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Phys. Rev. E 65, 051908 – Published 8 May, 2002

DOI: https://doi.org/10.1103/PhysRevE.65.051908

Abstract

We study correlation properties of the magnitude and the sign of the increments in the time intervals between successive heartbeats during light sleep, deep sleep, and rapid eye movement (REM) sleep using the detrended fluctuation analysis method. We find short-range anticorrelations in the sign time series, which are strong during deep sleep, weaker during light sleep, and even weaker during REM sleep. In contrast, we find long-range positive correlations in the magnitude time series, which are strong during REM sleep and weaker during light sleep. We observe uncorrelated behavior for the magnitude during deep sleep. Since the magnitude series relates to the nonlinear properties of the original time series, while the sign series relates to the linear properties, our findings suggest that the nonlinear properties of the heartbeat dynamics are more pronounced during REM sleep. Thus, the sign and the magnitude series provide information which is useful in distinguishing between the sleep stages.

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Phys. Rev. E 65, 051908– Published 8 May, 2002
  • Received 18 December 2000

© 2002 American Physical Society

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