Causes of Propagation Failure in Excitable Media

  • J. P. Keener
Part of the Springer Series in Synergetics book series (SSSYN, volume 36)


In the cardiac conduction system, temporal order is related to spatial order and temporal disorder may very well be due to spatial disorder. For example, the normal heartbeat is initiated by a wave of excitation generated by the SA node which propagates across the atrium, through the AV node, down the His-Purkinje system and finally across the ventricles. However, if there is some disruption of the way action potentials propagate, it is possible that the normal sequence of events can change and lead to a disorder ot the EKG, that is, to a temporal disorder.


Excitable Medium Functional Block Propagation Failure Solitary Pulse Spatial Disorder 
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.
    E. G. Aronson, H. F. Weinberger: In Lecture Notes in Mathematics 446 5 (Springer, Berlin 1975)Google Scholar
  2. 2.
    G. E. Beeler, H. Reuter: J. Physiol. 268 177 (1977)Google Scholar
  3. 3.
    S. N. Chow, J. K. Hale, J. Mallet-Paret: J. Diff. Eqn. 31 351 (1980)MathSciNetCrossRefGoogle Scholar
  4. 4.
    P. F. Cranefield, The Conduction of the Cardiac Impulse (Futura Publ., New York 1975)Google Scholar
  5. 5.
    P. F. Cranefield, H. O. Klein B. F. Hoffmann: Circ. Res. 28 199 (1971)Google Scholar
  6. 6.
    P. Denes, D. Wu, R. C. Dhingra, F. Mat-y-Leon, C. Wyndham, K. M. Rosen: Circ. 51 244 (1975)Google Scholar
  7. 7.
    J. D. Dockery, J. P. Keener, J. J. Tyson: (to appear)Google Scholar
  8. 8.
    N. El-Sherif, R. R. Hope, B. J. Scherlag, R. Lazzara: Circ. 55 702 (1977)Google Scholar
  9. 9.
    P. C. Fife, J. B. McLeod: Arch. Rat. Mech. Anal. 65 333 (1977)MathSciNetCrossRefGoogle Scholar
  10. 10.
    C. Fisch, D. P. Zipes, P. L. McHenry: Circ. 48 714 (1973)Google Scholar
  11. 11.
    R. FitzHugh: Biophys. J. 1 445 (1961)CrossRefGoogle Scholar
  12. 12.
    A. L. Hodgkin, A. F. Huxley: J. Physiol. 177 500 (1952)Google Scholar
  13. 13.
    R. W. Joyner: Biophys. J. 35. 113 (1981)CrossRefGoogle Scholar
  14. 14.
    R. W. Joyner, J. Picone, R. Veenstra, D. Rawling: Circ. Res. 53 526 (1983)Google Scholar
  15. 15.
    M. Kawato, A. Yamanaka, S. Urushibara: J. Theor. Biol. (to appaer)Google Scholar
  16. 16.
    J. P. Keener: J. Math. Biol. 12 215 (1981)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    J. P. Keener: In Modelling of Patterns in Space and Time, ed. W. Jager and J. D. Murray (Springer, Berlin 1984)Google Scholar
  18. 18.
    J. P. Keener: SIAM J. Appl. Math. (to appear)Google Scholar
  19. 19.
    J. P. Keener: SIAM J. Appl. Math. (to appear)Google Scholar
  20. 20.
    J. P. Keener, J. J. Tyson: Physica D. (to appear)Google Scholar
  21. 21.
    R. E. McAllister, D. Noble, R. W. Tsien: J. Physiol. 251 1 (1975)Google Scholar
  22. 22.
    R. N. Miller: J. Math. Biol. 7 385 (1979)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    R. N. Miller, J. Rinzel: Biophys. J. 34 227 (1981)CrossRefGoogle Scholar
  24. 24.
    J. Moser: Stable and Random Motion in Dynamical Systems (Princeton University Press, Princeton 1973)Google Scholar
  25. 25.
    J. Nagumo, S. Arimoto, S. Yoshizawa: Proc. IRE 50 2061 (1962)CrossRefGoogle Scholar
  26. 26.
    D. Noble, S. J. Noble: Proc. Roy. Soc. Lond. B 222 295 (1984)ADSCrossRefGoogle Scholar
  27. 27.
    J. Pauwelussen: J. Math. Biol. 15 151 (1982)MathSciNetzbMATHCrossRefGoogle Scholar
  28. 28.
    J. P. Pauwelussen: Physica 4D, 67088 (1981)MathSciNetGoogle Scholar
  29. 29.
    J. Peon, G. R. Ferrier, G. K. Moe: Circ. Res. 43 125 (1978)Google Scholar
  30. 30.
    W. Rall: N. Y. Acad. Sci. 96 1071 (1952)ADSCrossRefGoogle Scholar
  31. 31.
    J. Rinzel: In Nonlinear Diffusion, ed. by W. E. Fitzgibbon and H. F. Walker (Pitman, 1977)Google Scholar
  32. 32.
    M. S. Spach, P. C. Dolber: In Cardiac Electrophysiology and Arrhythmias, ed. by D. P. Zipes and J. Jalife, (Grune and Stratton 1984)Google Scholar
  33. 33.
    K. Yanagihara, A. Noma, H. Irisawa: Japanese J. Phys. 30 841 (1980)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • J. P. Keener
    • 1
  1. 1.Department of MathematicsUniversity of UtahSalt Lake CityUSA

Personalised recommendations