Analysis of Medical Time Series: Long-Term Correlation and Phase Synchronization

Complex systems are often irreducibly complex, i.e. the complexity is lost, if they are separated into independently studied sub-systems. The complexity manifests itself in emerging properties of the complex systems, like long-term correlations (memory effects) and non-linear fluctuation behavior. Such behavior is studied by non-linear time series analysis. Taking the control of the human autonomous nervous system as an example, I will show how long-term correlations and phase synchronization measures applied to heartbeat and respiration signals reflect physiologically different states of the whole complex system. I will present techniques for the reliable quantification of these measures in real non-stationary data recordings.

Using the Detrended Fluctuation Analysis (DFA) we found that long-range correlations reminiscent to the wake phase are present only during REM (rapid eye movement) sleep, but not during non-REM (light and deep) sleep [1]. We also found that phase synchronization between heartbeat and respiration is enhanced during non-REM and reduced during REM sleep [2]. Studying brain waves from EEG recordings during the sleep phase, we analyze how the spatial and spectral inter-relations within the brain can be quantified. Very recently, we have developed amplitude and frequency phase synchronization techniques, which show interactions between amplitudes and frequencies of the (quasi-periodic) oscillations in different parts of the brain and in different frequency domains. I will also discuss briefly applications to climate data and climate models.

[1] Correlated and uncorrelated regions in heart-rate fluctuations during sleep, A. Bunde, S. Havlin, J. W. Kantelhardt, T. Penzel, J.-H. Peter und K. Voigt, Phys. Rev. Lett. 85, 3736 (2000).
[2] Experimental evidence for phase synchronization transitions in human cardio-respiratory system, R. Bartsch, J. W. Kantelhardt, T. Penzel und S. Havlin, Phys. Rev. Lett. 98, 054102 (2007).