Model study of the spread of electrotonic potential in cardiac tissue

  • F. A. Roberge
  • L. Boucher
  • A. Vinet
Biomedical Engineering


This model study describes the electrotonic response of a cable model of cardiac tissue stimulated at one point. The stimulus is applied intracellularly in the form of a 2ms pulse of current of near threshold amplitude. The attenuation of the electrotonic potential with distance and its mode of propagation along the cable are compared for equivalent passive, continuous and discontinuous cables. The three structures have the same basic physical and electrical characteristic and they differ either with respect to being active or passive or to the presence or absence of intercellular gap junctions. In the continuous cable a just subthreshold stimulus produces a local active response which propagates more slowly and is attenuated less rapidly with distance than in a passive cable. The spatial decrement of the local response in a discontinuous cable is faster than in a continuous cable of equal average resistivity. It is suggested that the larger time constant of the foot of the action potential observed in the longitudinal direction in cardiac muscle could be due in part to the electrotonic spread of the local response from the site of stimulation.


Cable model Cardiac tissue Discontinuous propagation Electrotonic propagation Foot of the action potential 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Beeler, G. W. andReuter, H. (1977) Reconstruction of the action potential of ventricular myocardial fibers.J. Physiol. (London),268, 177–210.Google Scholar
  2. Drouhard, J. P. andRoberge, F. A. (1987) Revised formulation of the Hodgkin-Huxley representation of the Na current in cardiac cells.Comput. & Biomed. Res.,20, 333–350.CrossRefGoogle Scholar
  3. Fozzard, H. A. andSchoenberg, M. (1972) Strength-duration curves in cardiac Pukinje fibres: Effects of liminal length and charge distribution.J. Physiol. (London),226, 593–618.Google Scholar
  4. Henriquez, C. S. andPlonsey, R. (1987) Effect of resistive discontinuities on waveshape and velocity in a single cardiac fibre.Med. & Biol. Eng. & Comput.,25, 428–438.CrossRefGoogle Scholar
  5. Hodgkin, A. L. (1938) The subthreshold potentials in a crustacean nerve fibre.Proc. R. Soc. B.,126, 87–121.CrossRefGoogle Scholar
  6. Jack, J. J. B., Noble, D. andTsien, R. W. (1975)Electric current flow in excitable cells. Clarendon Press, Oxford.Google Scholar
  7. Joyner, R. W., Veenstra, R., Rawling, D. andChoro, A. (1984) Propagation through electrically coupled cells: effects of a resisting barrier.Biophys. J.,45, 1017–1025.Google Scholar
  8. Noble, D. andHall, A. E. (1963) The conditions for initiating “all-or-nothing” repolarization in cardiac muscle.,3, 261–274.CrossRefGoogle Scholar
  9. Noble, D. andStein, R. B. (1966) The threshold conditions for initiation of action potentials by excitable cells.J. Physiol. (London),187, 129–162.Google Scholar
  10. Noble, D. (1972) The relation of Rushton's liminal length for excitation to the resting and acting conductances of excitable cells.,226, 573–591.Google Scholar
  11. Norrie, D. H. andde Vries, G. (1978)An introduction to finite element analysis. Academic Press, New York.MATHGoogle Scholar
  12. Roberge, F. A., Vinet, A. andVictorri, B. (1986) Reconstruction of propagated electrical activity with a two dimensional model of anisotropic heart muscle.Circ. Res.,58, 461–475.Google Scholar
  13. Rudy, Y. andQuan, W. (1987) A model study of the effects of the discrete cellular structure on electrical propagation in cardiac tissue.,61, 815–823.Google Scholar
  14. Spach, M. S., Miller, W. T. III, Geselowitz, D. B., Barr, R. C., Kootsey, J. M. andJohnson, E. A. (1981) The discontinuous nature of propagation in normal canine muscle.,48, 39–54.Google Scholar
  15. Spach, M. S. andDolber, P. C. (1986) Relating extracellular potentials and their derivatives to anisotropic propagation at a microscopic level in human cardiac muscle.,58, 356–371.Google Scholar
  16. Tarr, M. andSperelakis, N. (1964) Weak electrotonic interaction between contiguous cardiac cells.Am. J. Physiol.,207, 691–700.Google Scholar
  17. Tille, J. (1966) Electrotonic interaction between muscle fibres in the rabbit ventricule.J. Gen. Physiol.,50, 189–202.CrossRefGoogle Scholar
  18. Weidmann, S. (1952) Electrical constants of Purkinje fibres.J. Physiol. (London),118, 348–360.Google Scholar
  19. Weidmann, S. (1970) Electrical constants of trabecular muscle from mammalian heart.,210, 1041–1054.Google Scholar
  20. Woodbury, J. W. andCrill, W. E. (1961) On the problem of impulse conduction in the atrium. InNervous inhibition.Florey, E. (Ed.), Plenum Press, New York, 124–135.Google Scholar

Copyright information

© IFMBE 1989

Authors and Affiliations

  • F. A. Roberge
    • 1
  • L. Boucher
    • 1
  • A. Vinet
    • 1
  1. 1.Institute of Biomedical EngineeringÉcole Polytechnique et Université de Montréal Faculty of MedicineMontrealCanada

Personalised recommendations