Quantification of Cardiorespiratory Interactions Based on Joint Symbolic Dynamics

  • Muammar M. KabirEmail author
  • David A. Saint
  • Eugene Nalivaiko
  • Derek Abbott
  • Andreas Voss
  • Mathias Baumert


Cardiac and respiratory rhythms are highly nonlinear and nonstationary. As a result traditional time-domain techniques are often inadequate to characterize their complex dynamics. In this article, we introduce a novel technique to investigate the interactions between R–R intervals and respiratory phases based on their joint symbolic dynamics. To evaluate the technique, electrocardiograms (ECG) and respiratory signals were recorded in 13 healthy subjects in different body postures during spontaneous and controlled breathing. Herein, the R–R time series were extracted from ECG and respiratory phases were obtained from abdomen impedance belts using the Hilbert transform. Both time series were transformed into ternary symbol vectors based on the changes between two successive R–R intervals or respiratory phases. Subsequently, words of different symbol lengths were formed and the correspondence between the two series of words was determined to quantify the interaction between cardiac and respiratory cycles. To validate our results, respiratory sinus arrhythmia (RSA) was further studied using the phase-averaged characterization of the RSA pattern. The percentage of similarity of the sequence of symbols, between the respective words of the two series determined by joint symbolic dynamics, was significantly reduced in the upright position compared to the supine position (26.4 ± 4.7 vs. 20.5 ± 5.4%, p < 0.01). Similarly, RSA was also reduced during upright posture, but the difference was less significant (0.11 ± 0.02 vs. 0.08 ± 0.01 s, p < 0.05). In conclusion, joint symbolic dynamics provides a new efficient technique for the analysis of cardiorespiratory interaction that is highly sensitive to the effects of orthostatic challenge.


Heart Heart rate variability Coupling Breathing frequency Respiratory sinus arrhythmia 



The research was supported by the Australian Research Council (grant # DP 110102049).

Conflict of Interest

There is no conflict of interest.


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Copyright information

© Biomedical Engineering Society 2011

Authors and Affiliations

  • Muammar M. Kabir
    • 1
    • 2
    Email author
  • David A. Saint
    • 1
    • 3
  • Eugene Nalivaiko
    • 4
  • Derek Abbott
    • 1
    • 2
  • Andreas Voss
    • 5
  • Mathias Baumert
    • 1
    • 2
  1. 1.Centre for Heart Rhythm DisordersThe University of AdelaideAdelaideAustralia
  2. 2.School of Electrical and Electronic EngineeringThe University of AdelaideAdelaideAustralia
  3. 3.School of Medical SciencesThe University of AdelaideAdelaideAustralia
  4. 4.School of Biomedical Sciences and PharmacyUniversity of NewcastleCallaghanAustralia
  5. 5.Department of Medical Engineering and BiotechnologyUniversity of Applied Sciences JenaJenaGermany

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