The European Physical Journal Special Topics

, Volume 222, Issue 2, pp 487–500 | Cite as

Quantifying heart rate dynamics using different approaches of symbolic dynamics

  • D. Cysarz
  • A. Porta
  • N. Montano
  • P.V. Leeuwen
  • J. Kurths
  • N. Wessel
Regular Article Applications to Real World Time Series


The analysis of symbolic dynamics applied to physiological time series is able to retrieve information about dynamical properties of the underlying system that cannot be gained with standard methods like e.g. spectral analysis. Different approaches for the transformation of the original time series to the symbolic time series have been proposed. Yet the differences between the approaches are unknown. In this study three different transformation methods are investigated: (1) symbolization according to the deviation from the average time series, (2) symbolization according to several equidistant levels between the minimum and maximum of the time series, (3) binary symbolization of the first derivative of the time series. Furthermore, permutation entropy was used to quantify the symbolic series. Each method was applied to the cardiac interbeat interval series RR i and its difference ΔRR I of 17 healthy subjects obtained during head-up tilt testing. The symbolic dynamics of each method is analyzed by means of the occurrence of short sequences (“words”) of length 3. The occurrence of words is grouped according to words without variations of the symbols (0V%), words with one variation (1V%), two like variations (2LV%) and two unlike variations (2UV%). Linear regression analysis showed that for method 1 0V%, 1V%, 2LV% and 2UV% changed with increasing tilt angle. For method 2 0V%, 2LV% and 2UV% changed with increasing tilt angle and method 3 showed changes for 0V% and 1V%. Furthermore, also the permutation entropy decreased with increasing tilt angle. In conclusion, all methods are capable of reflecting changes of the cardiac autonomic nervous system during head-up tilt. All methods show that even the analysis of very short symbolic sequences is capable of tracking changes of the cardiac autonomic regulation during head-up tilt testing.


Tilt Angle European Physical Journal Special Topic Symbolic Sequence Permutation Entropy Interbeat Interval 
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Copyright information

© EDP Sciences and Springer 2013

Authors and Affiliations

  • D. Cysarz
    • 1
  • A. Porta
    • 2
  • N. Montano
    • 3
  • P.V. Leeuwen
    • 4
  • J. Kurths
    • 5
    • 6
  • N. Wessel
    • 5
  1. 1.Integrated Studies for Anthroposophic Medicine; Chair for Theory of Medicine, Integrative and Anthroposophic Medicine, Faculty for Health, University of Witten/HerdeckeHerdeckeGermany
  2. 2.Department of Biomedical Sciences for HealthGaleazzi Orthopedic Institute, University of MilanMilanItaly
  3. 3.Department of Biomedical and Clinical SciencesInternal Medicine II, L. Sacco Hospital, University of MilanMilanItaly
  4. 4.Department of Radiology and MicrotherapyFaculty for Health, University of Witten/HerdeckeHerdeckeGermany
  5. 5.Cardiovascular Physics, Department of Physics, Humboldt-Universität zu BerlinBerlinGermany
  6. 6.Potsdam Institute for Climate Impact ResearchPotsdamGermany

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