Advertisement

Quantification of Cardiorespiratory Interactions Based on Joint Symbolic Dynamics

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

Abstract

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.

Keywords

Heart Heart rate variability Coupling Breathing frequency Respiratory sinus arrhythmia 

Notes

Acknowledgments

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

Conflict of Interest

There is no conflict of interest.

References

  1. 1.
    Akselrod, S., S. Eliash, O. Oz, and S. Cohen. Hemodynamic regulation in SHR: investigation by spectral analysis. Am. J. Physiol. Heart Circ. Physiol. 253:H176–H183, 1987.Google Scholar
  2. 2.
    Baier, V., M. Baumert, P. Caminal, M. Vallverdu, R. Faber, and A. Voss. Hidden Markov models based on symbolic dynamics for statistical modeling of cardiovascular control in hypertensive pregnancy disorders. IEEE Trans. Biomed. Eng. 53:140–143, 2006.PubMedCrossRefGoogle Scholar
  3. 3.
    Bartsch, R., J. W. Kantelhardt, T. Penzel, and S. Havlin. Experimental evidence for phase synchronization transitions in the human cardiorespiratory system. Phys. Rev. Lett. 98:054102, 2007.PubMedCrossRefGoogle Scholar
  4. 4.
    Baselli, G., S. Cerutti, S. Civardi, D. Liberati, F. Lombardi, A. Malliani, and M. Pagani. Spectral and cross-spectral analysis of heart rate and arterial blood pressure variability signals. Comput. Biomed. Res. 19:520–534, 1986.PubMedCrossRefGoogle Scholar
  5. 5.
    Baumert, M., V. Baier, S. Truebner, A. Schirdewan, and A. Voss. Short- and long-term joint symbolic dynamics of heart rate and blood pressure in dilated cardiomyopathy. IEEE Trans. Biomed. Eng. 52:2112–2115, 2005.PubMedCrossRefGoogle Scholar
  6. 6.
    Baumert, M., T. Walther, J. Hopfe, H. Stepan, R. Faber, and A. Voss. Joint symbolic dynamic analysis of beat-to-beat interactions of heart rate and systolic blood pressure in normal pregnancy. Med. Biol. Eng. Comput. 40:241–245, 2002.PubMedCrossRefGoogle Scholar
  7. 7.
    Berens, P. CircStat: a Matlab toolbox for circular statistics. J. Stat. Softw. 31:1–21, 2009.Google Scholar
  8. 8.
    Bernardi, L., C. Porta, A. Gabutti, L. Spicuzza, and P. Sleight. Modulatory effects of respiration. Auton. Neurosci. Basic Clin. 90:47–56, 2001.CrossRefGoogle Scholar
  9. 9.
    Berntson, G. G., J. T. Cacioppo, and K. S. Quigley. Respiratory sinus arrhythmia: autonomic origins, physiological mechanisms, and psychophysiological implications. Psychophysiology 30:183–196, 1993.PubMedCrossRefGoogle Scholar
  10. 10.
    Buchheit, M., H. A. Haddad, P. B. Laursen, and S. Ahmaidi. Effect of body posture on postexercise parasympathetic reactivation in men. Exp. Physiol. 94:795–804, 2009.PubMedCrossRefGoogle Scholar
  11. 11.
    Caminal, P., B. Giraldo, M. Vallverdú, S. Benito, R. Schroeder, and A. Voss. Symbolic dynamic analysis of relations between cardiac and breathing cycles in patients on weaning trials. Ann. Biomed. Eng. 38:2542–2552, 2010.PubMedCrossRefGoogle Scholar
  12. 12.
    Caminal, P., M. Vallverdu, B. Giraldo, S. Benito, G. Vazquez, and A. Voss. Optimized symbolic dynamics approach for the analysis of the respiratory pattern. IEEE Trans. Biomed. Eng. 52:1832–1839, 2005.PubMedCrossRefGoogle Scholar
  13. 13.
    Censi, F., G. Calcagnini, S. Lino, S. Seydnejad, R. Kitney, and S. Cerutti. Transient phase locking patterns among respiration, heart rate and blood pressure during cardiorespiratory synchronisation in humans. Med. Biol. Eng. Comput. 38:416–426, 2000.PubMedCrossRefGoogle Scholar
  14. 14.
    Censi, F., G. Calcagnini, S. Strano, P. Bartolini, and V. Barbaro. Nonlinear coupling among heart rate, blood pressure, and respiration in patients susceptible to neuromediated syncope. Ann. Biomed. Eng. 31:1097–1105, 2003.PubMedCrossRefGoogle Scholar
  15. 15.
    Cysarz, D., H. Bettermann, S. Lange, D. Geue, and P. van Leeuwen. A quantitative comparison of different methods to detect cardiorespiratory coordination during night-time sleep. Biomed. Eng. Online 3:44, 2004.PubMedCrossRefGoogle Scholar
  16. 16.
    Devaney, R. L. An Introduction to Chaotic Dynamical Systems. New York: Westview Press, 2003.Google Scholar
  17. 17.
    Galletly, D. C., and P. D. Larsen. Cardioventilatory coupling during anaesthesia. Br. J. Anaesth. 79:35–40, 1997.PubMedGoogle Scholar
  18. 18.
    Galletly, D. C., and P. D. Larsen. Relationship between cardioventilatory coupling and respiratory sinus arrhythmia. Br. J. Anaesth. 80:164–168, 1998.PubMedGoogle Scholar
  19. 19.
    Galletly, D. C., and P. D. Larsen. The determination of cardioventilatory coupling from heart rate and ventilatory time series. Res. Exp. Med. 199:95–99, 1999.CrossRefGoogle Scholar
  20. 20.
    Gilad, O., C. A. Swenne, L. R. Davrath, and S. Akselrod. Phase-averaged characterization of respiratory sinus arrhythmia pattern. Am. J. Physiol. Heart. Circ. Physiol. 288:H504–H510, 2005.PubMedCrossRefGoogle Scholar
  21. 21.
    Hayano, J., F. Yasuma, A. Okada, S. Mukai, and T. Fujinami. Respiratory sinus arrhythmia: a phenomenon improving pulmonary gas exchange and circulatory efficiency. Circulation 94:842–847, 1996.PubMedGoogle Scholar
  22. 22.
    Hoyer, D., O. Hader, and U. Zwiener. Relative and intermittent cardiorespiratory coordination. IEEE Eng. Med. Biol. Mag. 16:97–104, 1997.PubMedCrossRefGoogle Scholar
  23. 23.
    Hoyer, D., D. Kaplan, F. Schaaff, and M. Eiselt. Determinism in bivariate cardiorespiratory phase-space sets. IEEE Eng. Med. Biol. Mag. 17:26–31, 1998.PubMedCrossRefGoogle Scholar
  24. 24.
    Hoyer, D., U. Leder, H. Hoyer, B. Pompe, M. Sommer, and U. Zwiener. Mutual information and phase dependencies: measures of reduced nonlinear cardiorespiratory interactions after myocardial infarction. Med. Eng. Phys. 24:33–43, 2002.PubMedCrossRefGoogle Scholar
  25. 25.
    Kabir, M. M., H. Dimitri, P. Sanders, R. Antic, E. Nalivaiko, D. Abbott, and M. Baumert. Cardiorespiratory phase-coupling is reduced in patients with obstructive sleep apnea. PLoS One 5:e10602, 2010.PubMedCrossRefGoogle Scholar
  26. 26.
    Kabir, M. M., E. Nalivaiko, D. Abbott, and M. Baumert. Impact of movement on cardiorespiratory coordination in conscious rats. In: Engineering in Medicine and Biology Society (EMBC), 2010 Annual International Conference of the IEEE, 2010, pp. 1938–1941.Google Scholar
  27. 27.
    Kitchens, B. P. Symbolic Dynamics: One-Sided, Two-Sided and Countable State Markov Shifts. Berlin: Springer, 1998.Google Scholar
  28. 28.
    Kotani, K., K. Takamasu, Y. Ashkenazy, H. E. Stanley, and Y. Yamamoto. Model for cardiorespiratory synchronization in humans. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 65:051923, 2002.CrossRefGoogle Scholar
  29. 29.
    Krishnamurthy, S., X. Wang, D. Bhakta, E. Bruce, J. Evans, T. Justice, and A. Patwardhan. Dynamic cardiorespiratory interaction during head-up tilt-mediated presyncope. Am. J. Physiol. Heart Circ. Physiol. 287:H2510–H2517, 2004.PubMedCrossRefGoogle Scholar
  30. 30.
    Kurths, J., A. Voss, P. Saparin, A. Witt, H. J. Kleiner, and N. Wessel. Quantitative analysis of heart rate variability. Chaos Interdiscipl. J. Nonlinear Sci. 5:88–94, 1995.CrossRefGoogle Scholar
  31. 31.
    Lotric, M. B., and A. Stefanovska. Synchronization and modulation in the human cardiorespiratory system. Physica A 283:451–461, 2000.CrossRefGoogle Scholar
  32. 32.
    Moser, M., M. Lehofer, A. Sedminek, M. Lux, H. Zapotoczky, T. Kenner, and A. Noordergraaf. Heart rate variability as a prognostic tool in cardiology. A contribution to the problem from a theoretical point of view. Circulation 90:1078–1082, 1994.PubMedGoogle Scholar
  33. 33.
    Mrowka, R., L. Cimponeriu, A. Patzak, and M. G. Rosenblum. Directionality of coupling of physiological subsystems: age-related changes of cardiorespiratory interaction during different sleep stages in babies. Am. J. Physiol. Regul. Integr. Comp. Physiol. 285:R1395–R1401, 2003.PubMedGoogle Scholar
  34. 34.
    Mrowka, R., A. Patzak, and M. Rosenblum. Quantitative analysis of cardiorespiratory synchronization in infants. Int. J. Bifurc. Chaos 10:2479–2488, 2000.Google Scholar
  35. 35.
    Neff, R. A., J. Wang, S. Baxi, C. Evans, and D. Mendelowitz. Respiratory sinus arrhythmia: endogenous activation of nicotinic receptors mediates respiratory modulation of brainstem cardioinhibitory parasympathetic neurons. Circ. Res. 93:565–572, 2003.PubMedCrossRefGoogle Scholar
  36. 36.
    Porta, A., S. Guzzetti, N. Montano, M. Pagani, V. Somers, A. Malliani, G. Baselli, and S. Cerutti. Information domain analysis of cardiovascular variability signals: evaluation of regularity, synchronisation and co-ordination. Med. Biol. Eng. Comput. 38:180–188, 2000.PubMedCrossRefGoogle Scholar
  37. 37.
    Robinson, C. Dynamical Systems: Stability, Symbolic Dynamics, and Chaos. Boca Raton: CRC Press, 1999.Google Scholar
  38. 38.
    Robinson, B. F., S. E. Epstein, G. D. Beiser, and E. Braunwald. Control of heart rate by the autonomic nervous system: studies in man on the interrelation between baroreceptors mechanisms and exercise. Circ. Res. 19:400–411, 1966.PubMedGoogle Scholar
  39. 39.
    Rosenblum, M. G., J. Kurths, A. Pikovsky, C. Schafer, P. Tass, and H. H. Abel. Synchronization in noisy systems and cardiorespiratory interaction. IEEE Eng. Med. Biol. Mag. 17:46–53, 1998.PubMedCrossRefGoogle Scholar
  40. 40.
    Rowell, L. B. Reflex control during orthostasis. In: Human Cardiovascular Control, edited by L. B. Rowell. New York: Oxford University Press, 1993, pp. 37–80.Google Scholar
  41. 41.
    Rybski, D., S. Havlin, and A. Bunde. Phase synchronization in temperature and precipitation records. Phys. A Stat. Mech. Appl. 320:601–610, 2003.CrossRefGoogle Scholar
  42. 42.
    Saul, J. P., R. D. Berger, P. Albrecht, S. P. Stein, M. H. Chen, and R. J. Cohen. Transfer function analysis of the circulation: unique insights into cardiovascular regulation. Am. J. Physiol. Heart Circ. Physiol. 261:H1231–H1245, 1991.Google Scholar
  43. 43.
    Schafer, C., M. G. Rosenblum, H. H. Abel, and J. Kurths. Synchronization in the human cardiorespiratory system. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscipl. Top. 60:857–870, 1999.Google Scholar
  44. 44.
    Schafer, C., M. G. Rosenblum, J. Kurths, and H. H. Abel. Heartbeat synchronized with ventilation. Nature 392:239–240, 1998.PubMedCrossRefGoogle Scholar
  45. 45.
    Stefanovska, A., H. Haken, P. V. E. McClintock, M. Hozic, F. Bajrovic, and S. Ribaric. Reversible transitions between synchronization states of the cardiorespiratory system. Phys. Rev. Lett. 85:4831–4834, 2000.PubMedCrossRefGoogle Scholar
  46. 46.
    Taha, B. H., P. M. Simon, J. A. Dempsey, J. B. Skatrud, and C. Iber. Respiratory sinus arrhythmia in humans: an obligatory role for vagal feedback from the lungs. J. Appl. Physiol. 78:638–645, 1995.PubMedGoogle Scholar
  47. 47.
    Tzeng, Y., P. Larsen, and D. Galletly. Cardioventilatory coupling in resting human subjects. Exp. Physiol. 88:775–782, 2003.PubMedCrossRefGoogle Scholar
  48. 48.
    Tzeng, Y. C., P. D. Larsen, and D. C. Galletly. Mechanism of cardioventilatory coupling: insights from cardiac pacing, vagotomy, and sinoaortic denervation in the anesthetized rat. Am. J. Physiol. Heart Circ. Physiol. 292:H1967–H1977, 2007.PubMedCrossRefGoogle Scholar
  49. 49.
    Voss, A., J. Kurths, H. J. Kleiner, A. Witt, N. Wessel, P. Saparin, K. J. Osterziel, R. Schurath, and R. Dietz. The application of methods of non-linear dynamics for the improved and predictive recognition of patients threatened by sudden cardiac death. Cardiovasc. Res. 31:419–433, 1996.PubMedGoogle Scholar
  50. 50.
    Zar, J. H. Circular distributions: hypothesis testing. In: Biostatistical Analysis, 4th ed., edited by T. Ryu. New Jersey: Prentice-Hall, 1999, pp. 616–663.Google Scholar

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

Personalised recommendations