Theory and Simulation of Stationary Wave Propagation



Stationary spiral wave phenomena, in simulated myocardium consisting of AP models, and their associated characteristics (such as rotational angular velocity, core radius, and wavefront morphology) are topics of major theoretical and practical interest. These topics will be discussed in this chapter within the framework of findings from Zykov [1], which are valid under the following assumptions: an unrestricted domain of spiral wave propagation only one spiral wave is initiated spiral wave rotation is stationary and the resultant period of circulation T = 2ω/π, is constant.


Spiral Wave Diastolic Interval Restitution Curve Unrestricted Domain Restitution Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Zykov, V.S., Simulation of wave process in excitable media. Nonlinear science: theory and applications, ed. A.V. Holden. 1987, Manchester and New York: Manchester University Press.Google Scholar
  2. 2.
    Kogan, B.Y., W.J. Karplus, B.S. Billet, and W. Stevenson, Excitation wave propagation within narrow pathways: geometric configurations facilitating unidirectional block and reentry. Physica D, 1992. 59: 275–296.MATHCrossRefGoogle Scholar
  3. 3.
    Courtemanche, M. and A.T. Winfree, Re-entrant rotating waves in a Beeler-Reuter based model of two- dimensional cardiac conduction. Int J Bifurc Chaos, 1991. 1: 431–444.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Panfilov, A.V. and A.V. Holden, Spatiotemporal irregularity in a two-dimensional model of cardiac tissue. Int J Bifurc Chaos, 1991. 1: 219–225.MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Qu, Z., J.N. Weiss, and A. Garfinkel, Cardiac electrical restitution properties and stability of reentrant spiral waves: a simulation study. Am J Physiol Heart Circ Physiol, 1999. 45: H269–H283.Google Scholar
  6. 6.
    Courtemanche, M., L. Glass, and J.P. Keener, Instabilities of a propagating pulse in a ring of excitable media. Phys Rev Lett, 1993. 70: 2182–2185.CrossRefGoogle Scholar
  7. 7.
    Shiferaw, Y., M.A. Watanabe, A. Garfinkel, J.N. Weiss, and A. Karma, Model of intracellular calcium cycling in ventricular myocytes. Biophys J, 2003. 85: 3666–3686.CrossRefGoogle Scholar
  8. 8.
    Kogan, B., S.T. Lamp, and J.N. Weiss, Role of intracellular Ca dynamics in supporting spiral wave propagation, in Modeling and Simulation, G. Bekey and B. Kogan, Editors. 2003, Kluwer Academic Publishers: Norwell, MA. p. 177–193.Google Scholar
  9. 9.
    Huffaker, R.B., J.N. Weiss, and B. Kogan, Effects of early afterdepolarizations on reentry in cardiac tissue: a simulation study. Am J Physiol Heart Circ Physiol, 2007. 292: H3089–H3102.CrossRefGoogle Scholar
  10. 10.
    Samade, R., Personal Communication. 2008.Google Scholar
  11. 11.
    Kogan, B.Y., W.J. Karplus, B.S. Billet, A.T. Pang, H.S. Karagueuzian, and S.S. Khan, The simplified Fitzhugh-Nagumo model with action potential duration restitution: effects on 2D-wave propagation. Physica D, 1991. 50: 327–340.MATHCrossRefGoogle Scholar
  12. 12.
    Pertsov, A.M., E.A. Ermakova, and A.V. Panfilov, Rotating spiral waves in a modified Fitz-Hugh-Nagumo model. Physica D, 1984. 14: 117–124.MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Davidenko, J.M., A.V. Pertsov, J.R. Salomonsz, W. Baxter, and J. Jalife, Stationary and drifting spiral waves of excitation in isolated cardiac muscle. Nature, 1992. 355: 349–351.CrossRefGoogle Scholar
  14. 14.
    van Capelle, F.J.L. and D. Durrer, Computer simulation of arrhythmias in a network of coupled excitable elements. Circ Res, 1980. 47: 454–466.Google Scholar
  15. 15.
    Kogan, B.Y., W.J. Karplus, and M.G. Karpoukhin. The Van Capelle and Durrer model of cardiac action potential generation and 2D propagation: modification and application to spiral wave propagation. in Proceedings of the Society of Computer Simulation. 1996. San Diego, CA. p. 106–112.Google Scholar
  16. 16.
    van Capelle, F.J.L., Propagation and reentry in two dimensions, in Cardiac Electrophysiology. From Cell to Bedside, D.P. Zipes and J. Jalife, Editors. 1990, WB Sauders Co: Philadelphia, PA. p. 175–182.Google Scholar
  17. 17.
    Landau, M., P. Lorente, J. Henry, and S. Canu, Hysteresis phenomena between periodic and stationary solutions in a model of pacemaker and nonpacemaker coupled cardiac cells. J Math Biol, 1987. 25: 491–509.MATHMathSciNetGoogle Scholar
  18. 18.
    Panfilov, A.V. and A.V. Holden, Computer simulation of re-entry sources in myocardium in two and three dimensions. J Theor Biol, 1993. 161: 271–285.CrossRefGoogle Scholar
  19. 19.
    Garfinkel, A., P.-S. Chen, D.O. Walter, H.S. Karagueuzian, B. Kogan, S.J. Evans, M. Karpoukhin, C. Hwang, T. Uchida, M. Gotoh, O. Nwasokwa, P. Sager, and J.N. Weiss, Quasiperiodicity and chaos in cardiac fibrillation. J Clin Invest, 1997. 99: 305–314.CrossRefGoogle Scholar
  20. 20.
    Chudin, E., A. Garfinkel, J. Weiss, W. Karplus, and B. Kogan, Wave propagation in cardiac tissue and effects of intracellular calcium dynamics (computer simulation study). Prog Biophys Mol Biol, 1998. 69: 225–236.CrossRefGoogle Scholar
  21. 21.
    Zeng, J., K.R. Laurita, D.S. Rosenbaum, and Y. Rudy, Two components of the delayed rectifier K+ current in ventricular myocytes of the guinea pig type. Theoretical formulation and their role in repolarization. Circ Res, 1995. 77: 140–152.Google Scholar
  22. 22.
    Chudin, E., J. Goldhaber, A. Garfinkel, J. Weiss, and B. Kogan, Intracellular Ca(2+) dynamics and the stability of ventricular tachycardia. Biophys J, 1999. 77: 2930-2941.CrossRefGoogle Scholar
  23. 23.
    Frenet, F., Sur les corbes a double courbure. J Math Pur Appl, 1852. 17: 437-447.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of California, Los AngelesLos AngelesUSA

Personalised recommendations