Excitation-Propagation in One Dimensional Fibers



The study of pulse propagation in one-dimensional (1D) fiber is of prime interest for the propagation through nerve fibers. For cardiac tissue, which is predominately 2D and 3D, this study presents chiefly methodological value. The exception is a type of the atrium flutter and observed circulation of excitation in atrium around vena cava.

It is worthwhile to consider two major cases: propagation along the fiber with open ends and propagation in a ring-shaped 1D fiber. For the first case we will consider the propagation of a solitary pulse and pulse sequences generated at one of the open ends.

The study of excitation wave propagation in a ring of cardiac tissue is a subject of significant practical and theoretical importance [1-3]. Methodologically it allows us to investigate the behavior of the cell in the fiber under different pacing rates by only changing the equivalent ring length. The study of excitation pulse propagation in a ring facilitates an understanding of mechanisms of many life-threatening cardiac tachyarrhythmias.


Pulse Propagation Action Potential Duration Passive Propagation Early Afterdepolarizations Ring Length 
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  1. 1.
    Karma, A., H. Levine, and X. Zou, Theory of pulse instability in electrophysiological models of excitable tissues. Physica D. 1994. 73: 113–127.MATHCrossRefGoogle Scholar
  2. 2.
    Chialvo, D.R., R.F.J. Gilmour, and J. Jalife, Low dimensional chaos in cardiac tissue. Nature, 1990. 343: 653–657.CrossRefGoogle Scholar
  3. 3.
    Ito, H. and L. Glass. Theory of reentrant excitation in a ring of cardiac tissue. Physica D. 1992. 56: 84–106.CrossRefGoogle Scholar
  4. 4.
    Frame, L.H. and M.B. Simson, Oscillations of conduction, action potential duration, and refractoriness. A mechanism for spontaneous termination of reentrant tachycardias. Circulation, 1988, 78: 1277–1287.Google Scholar
  5. 5.
    Fei, H., M.S. Hanna, and L.H. Frame, Assessing the excitable gap in reentry by resetting: implications for tachycardia termination by premature stimuli and antiarrhythmic drugs. Circulation, 1996. 94: 2268–2277.Google Scholar
  6. 6.
    Fei, H., D. Yazmajian, M.S. Hanna, and L.H. Frame, Termination of reentry by lidocaine in the tricuspid ring in vitro: role of cycle-length oscillation, fast use-dependent kinetics, and fixed block. Circ Res, 1997. 80: 242–252.Google Scholar
  7. 7.
    Rudy, Y. and W.L. Quan, A model study of the effects of the discrete cellular structure on electrical propagation in cardiac tissue. Circ Res, 1987. 61: 815–23.Google Scholar
  8. 8.
    Keener, J. and J. Sneyd, Mathematical Physiology. 2nd ed. 2001: Springer-Verlag.Google Scholar
  9. 9.
    Hodgkin, A.L. and A.F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol, 1952. 117: 500–544.Google Scholar
  10. 10.
    Sakmann, B. and E. Neher, eds. Single Channel Recording. 1983, Plenum Press: New York.Google Scholar
  11. 11.
    Panfilov, A.V. and A.V. Holden, eds. Computational Biology of the Heart. 1997, Wiley Publishing: New York.MATHGoogle Scholar
  12. 12.
    Nagumo, J., S. Arimoto, and S. Yoshizawa, An active pulse transmission line simulating nerve axon. Proceedings of the IRE, 1962. 50: 2061–2070.CrossRefGoogle Scholar
  13. 13.
    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
  14. 14.
    Kogan, B.Y., W.J. Karplus, and M.G. Karpoukhin, The third-order action potential model for computer simulation of electrical wave propagation in cardiac tissue., in Computer Simulations in Biomedicine, H. Power and R.T. Hart, Editors. 1995, Computational Mechanics Publishers: Boston.Google Scholar
  15. 15.
    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
  16. 16.
    Courtemanche, M., J.P. Keener, and L. Glass, A delay equation representation of pulse circulation on a ring of excitable media. SIAM J Appl Math, 1996. 56: 119–142.MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Franz, M.R., J. Schaefer, M. Schottler, W.A. Seed, and M.I.M. Noble, Electrical and mechanical restitution of the human heart at different rates of stimulation. Circ Res, 1983. 53: 815–822.Google Scholar
  18. 18.
    Kogan, B.Y., W.J. Karplus, M.G. Karpoukhin, I.M. Roizen, E. Chudin, and Z. Qu, Action potential duration restitution and electrical excitation propagation in a ring of cardiac cells. Comput Biomed Res, 1997. 30: 349–359.CrossRefGoogle Scholar
  19. 19.
    Chudin, E. and B. Kogan, Pulse propagation in a ring-shaped cardiac tissue model with intracellular Ca(2+) dynamics. (Computer simulation study), in Mathematics and Computers in Modern Science: Acoustics and Music, Biology and Chemistry, Business and Economics, N. Mastorakis, Editor. 2000, World Scientific and Engineering Society Press: Athens, Greece. p. 187–192.Google Scholar
  20. 20.
    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
  21. 21.
    Priori, S.G. and P.B. Corr, Mechanisms underlying early and delayed afterdepolarizations induced by catecholamines. Am J Physiol, 1990. 258: H1796-H1805.Google Scholar
  22. 22.
    Volders, P.G., A. Kulcsar, M.A. Vos, K.R. Sipido, H.J. Wellens, R. Lazzara, and B. Szabo, Similarities between early and delayed afterdepolarizations induced by isoproterenol in canine ventricular myocytes. Cardiovasc Res, 1997. 34: 348–359.CrossRefGoogle Scholar
  23. 23.
    Huffaker, R., S.T. Lamp, J.N. Weiss, and B. Kogan, Intracellular calcium cycling, early afterdepolarizations, and reentry in simulated long QT syndrome. Heart Rhythm, 2004. 1: 441–448.CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

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

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