Modeling Heart Pacemaker Tissue by a Network of Stochastic Oscillatory Cellular Automata

  • Danuta Makowiec
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7956)

Abstract

Computations performed by a system of cyclic cellular automata, designed to model the principal organization rules known for the tissue of the first cardiac pacemaker — the sinus node, are investigated in terms of Kuramoto order parameters of synchronization. We show that such description provides consistent quantification of stationary states in the model. Finally, the model is used to give possible explanations for changes observed in the sinus node rhythmicity caused by age.

Keywords

cellular automata synchronization multiscale modeling 

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References

  1. 1.
    Stumpf, M., Balding, D.J., Gorolami, M.: Handbook of Statistical Systems Biology. Wiley (2011)Google Scholar
  2. 2.
    Jalife, J., Delmar, M., Davidenko, J., Anumonwo, J., Kalifa, J.: Basic Cardiac Electrophysiology for the Clinician. Wiley-Blackwell (2009)Google Scholar
  3. 3.
    Klabunde, R.E.: Cardiovascular Physiology Concepts. accesible via, http://www.cvphysiology.com/Arrhythmias/A005.html
  4. 4.
    Saffitz, J.E., Lerner, D.L., Yamada, K.A.: Gap Junctions Distribution and regulation in the Heart. In: Zipes, D.P., Jalive, J. (eds.) Cardiac Elecrophysiology. From Cell to Bedside, pp. 181–191. Saunders Co., Philadelphia (2004)Google Scholar
  5. 5.
    Dobrzynski, H., Boyett, M.R., Anderson, R.H.: New Insights Into Pacemaker Activity: Promoting Understanding of Sick Sinus. Circulation 115, 1921 (2007)CrossRefGoogle Scholar
  6. 6.
    Mangoni, M.E., Nargeot, J.: Genesis and Regulation of the Heart Automaticity. Physiol. Rev. 89, 919 (2008)CrossRefGoogle Scholar
  7. 7.
    Aslanidi, O.V., Boyett, M.R., Dobrzynski, H., Zhang, H.: Mechanisms of transition from normal to reentrant electrical activity in a model of rabbit atrial tissue: interaction of tissue heterogeneity and anisotropy. Biophysical J. 96, 7989 (2009)CrossRefGoogle Scholar
  8. 8.
    Boyett, M.R.: ‘And the beat goes on’ The cardiac conduction system: the wiring system of the heart. Experimental Physiol. 94, 1035 (2009)CrossRefGoogle Scholar
  9. 9.
    Greenberg, J.M., Hastings, S.P.: Spatial patterns for discrete models of diffusion in excitable media. SIAM J. Appl. Math. 34, 515 (1978)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Berry, H., Fatés, N.: Robustness of the critical behaviour in the stochastic Greenberg-Hastings cellular automaton model. IJUC 7, 65 (2011)Google Scholar
  11. 11.
    Bub, G., Shrier, A., Glass, L.: Global Organization of Dynamics in Oscillatory Heterogeneous Excitable Media. Phys. Rev. Lett. 94, 028105 (2005)Google Scholar
  12. 12.
    Chang, M.G., Zhang, Y., Chang, C.Y., Xu, L., Emokpae, R., Tung, L., Marban, E., Abraham, M.R.: Spiral waves and reentry dynamics in an in vitro model of the healed infarct border. Circ. Res. 105, 1062 (2009)CrossRefGoogle Scholar
  13. 13.
    Makowiec, D.: Modeling the sinoatrial node by cellular automata with irregular topology. Int. J. Mod. Phys. C 21, 107 (2010)MATHCrossRefGoogle Scholar
  14. 14.
    Makowiec, D.: Phase-sensitive cellular automata on stochastic network as a model for cardiac pacemaker rhythmicity. Acta Phys. Pol. B Proc. Supp. 5, 85 (2012)CrossRefGoogle Scholar
  15. 15.
    Michaels, D.C., Matyas, E.P., Jalife, J.: Dynamic interactions and mutual synchronization of sinoatrial node pacemaker cells. Circ. Res. 58, 706 (1986)CrossRefGoogle Scholar
  16. 16.
    Anumonvo, J.M., Delmar, M., Vinet, A., Michaels, D.C., Jalife, J.: Phase resetting and entrainment of pacemaker activity in single sinus nodal cells. Circ. Res. 68, 1138 (1991)CrossRefGoogle Scholar
  17. 17.
    Watts, D.J., Strogatz, S.H.: Collective dynamics of ’small-world’ networks. Nature 393, 409 (1998)CrossRefGoogle Scholar
  18. 18.
    Makowiec, D.: Evolving network - simulation study. From a regular lattice to scale free network. EPJ B 48, 547 (2005)CrossRefGoogle Scholar
  19. 19.
    Kuramoto, Y.: Chemical Oscillations, Waves and Turbulence. Springer, Berlin (1984)MATHCrossRefGoogle Scholar
  20. 20.
    Acebron, J.A., Bonilla, L.L., Vicente, C.J.P., Ritort, F., Spigler, R.: The Kuramoto model: A simple paradigm for synchronization phenomena. Rev. Mod. Phys. 77, 137 (2005)CrossRefGoogle Scholar
  21. 21.
    Rose, A.: Keeping the clock ticking as we age: changes in sinoatrial node gene expression and function in the aging heart. Exp. Physiol. 96, 1114 (2011)Google Scholar
  22. 22.
    Alings, A.M., Bouman, L.M.: Electrophysiology of the ageing rabbit and cat sinoatrial node-a comparative study. Eur. Heart J. 14(9), 1278 (1993)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Danuta Makowiec
    • 1
  1. 1.Institute of Theoretical Physics and AstrophysicsUniversity of GdańskPoland

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