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. 1996 Nov;71(5):2427–2439. doi: 10.1016/S0006-3495(96)79436-5

A quasi-one-dimensional theory for anisotropic propagation of excitation in cardiac muscle.

J Wu 1, E A Johnson 1, J M Kootsey 1
PMCID: PMC1233732  PMID: 8913583

Abstract

It has been shown that propagation of excitation in cardiac muscle is anisotropic. Compared to propagation at right angles to the long axes of the fibers, propagation along the long axis is faster, the extracellular action potential (AP) is larger in amplitude, and the intracellular AP has a lower maximum rate of depolarization, a larger time constant of the foot, and a lower peak amplitude. These observations are contrary to the predictions of classical one-dimensional (1-D) cable theory and, thus far, no satisfactory theory for them has been reported. As an alternative description of propagation in cardiac muscle, this study provides a quasi-1-D theory that includes a simplified description of the effects of action currents in extracellular space as well as resistive coupling between surface and deeper fibers in cardiac muscle. In terms of classical 1-D theory, this quasi-1-D theory reveals that the anisotropies in the wave form of the AP arise from modifications in the effective membrane ionic current and capacitance. The theory also shows that it is propagation in the longitudinal, not in the transverse direction that deviates from classical 1-D cable theory.

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Selected References

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  1. Beeler G. W., Reuter H. Reconstruction of the action potential of ventricular myocardial fibres. J Physiol. 1977 Jun;268(1):177–210. doi: 10.1113/jphysiol.1977.sp011853. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Clerc L. Directional differences of impulse spread in trabecular muscle from mammalian heart. J Physiol. 1976 Feb;255(2):335–346. doi: 10.1113/jphysiol.1976.sp011283. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Diaz P. J., Rudy Y., Plonsey R. A model study of the effect of the intercalated discs on discontinuous propagation in cardiac muscle". Adv Exp Med Biol. 1983;161:79–89. doi: 10.1007/978-1-4684-4472-8_5. [DOI] [PubMed] [Google Scholar]
  4. Ebihara L., Johnson E. A. Fast sodium current in cardiac muscle. A quantitative description. Biophys J. 1980 Nov;32(2):779–790. doi: 10.1016/S0006-3495(80)85016-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. HODGKIN A. L., HUXLEY A. F. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol. 1952 Aug;117(4):500–544. doi: 10.1113/jphysiol.1952.sp004764. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. HODGKIN A. L., KATZ B. The effect of sodium ions on the electrical activity of giant axon of the squid. J Physiol. 1949 Mar 1;108(1):37–77. doi: 10.1113/jphysiol.1949.sp004310. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Henriquez C. S., Plonsey R. Simulation of propagation along a cylindrical bundle of cardiac tissue--II: Results of simulation. IEEE Trans Biomed Eng. 1990 Sep;37(9):861–875. doi: 10.1109/10.58597. [DOI] [PubMed] [Google Scholar]
  8. Hoyt R. H., Cohen M. L., Saffitz J. E. Distribution and three-dimensional structure of intercellular junctions in canine myocardium. Circ Res. 1989 Mar;64(3):563–574. doi: 10.1161/01.res.64.3.563. [DOI] [PubMed] [Google Scholar]
  9. Johnson E. A., Sommer J. R. A strand of cardiac muscle. Its ultrastructure and the electrophysiological implications of its geometry. J Cell Biol. 1967 Apr;33(1):103–129. doi: 10.1083/jcb.33.1.103. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Joyner R. W. Effects of the discrete pattern of electrical coupling on propagation through an electrical syncytium. Circ Res. 1982 Feb;50(2):192–200. doi: 10.1161/01.res.50.2.192. [DOI] [PubMed] [Google Scholar]
  11. Joyner R. W., Ramón F., Morre J. W. Simulation of action potential propagation in an inhomogeneous sheet of coupled excitable cells. Circ Res. 1975 May;36(5):654–661. doi: 10.1161/01.res.36.5.654. [DOI] [PubMed] [Google Scholar]
  12. Leon L. J., Roberge F. A. Structural complexity effects on transverse propagation in a two-dimensional model of myocardium. IEEE Trans Biomed Eng. 1991 Oct;38(10):997–1009. doi: 10.1109/10.88445. [DOI] [PubMed] [Google Scholar]
  13. Lieberman M., Sawanobori T., Kootsey J. M., Johnson E. A. A synthetic strand of cardiac muscle: its passive electrical properties. J Gen Physiol. 1975 Apr;65(4):527–550. doi: 10.1085/jgp.65.4.527. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Mathias R. T., Ebihara L., Lieberman M., Johnson E. A. Linear electrical properties of passive and active currents in spherical heart cell clusters. Biophys J. 1981 Oct;36(1):221–242. doi: 10.1016/S0006-3495(81)84725-X. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Plonsey R. The active fiber in a volume conductor. IEEE Trans Biomed Eng. 1974 Sep;21(5):371–381. doi: 10.1109/TBME.1974.324406. [DOI] [PubMed] [Google Scholar]
  16. Pollard A. E., Hooke N., Henriquez C. S. Cardiac propagation simulation. Crit Rev Biomed Eng. 1992;20(3-4):171–210. [PubMed] [Google Scholar]
  17. Roberts D. E., Hersh L. T., Scher A. M. Influence of cardiac fiber orientation on wavefront voltage, conduction velocity, and tissue resistivity in the dog. Circ Res. 1979 May;44(5):701–712. doi: 10.1161/01.res.44.5.701. [DOI] [PubMed] [Google Scholar]
  18. Roth B. J. Action potential propagation in a thick strand of cardiac muscle. Circ Res. 1991 Jan;68(1):162–173. doi: 10.1161/01.res.68.1.162. [DOI] [PubMed] [Google Scholar]
  19. Rudy Y., Quan W. L. A model study of the effects of the discrete cellular structure on electrical propagation in cardiac tissue. Circ Res. 1987 Dec;61(6):815–823. doi: 10.1161/01.res.61.6.815. [DOI] [PubMed] [Google Scholar]
  20. Shiba H. Heaviside's "Bessel cable" as an electric model for flat simple epithelial cells with low resistive junctional membranes. J Theor Biol. 1971 Jan;30(1):59–68. doi: 10.1016/0022-5193(71)90036-1. [DOI] [PubMed] [Google Scholar]
  21. Shiba H., Kanno Y. Further study of the two-dimensional cable theory: an electric model for a flat thin association of cells with a directional intercellular communication. Biophysik. 1971;7(4):295–301. doi: 10.1007/BF01190241. [DOI] [PubMed] [Google Scholar]
  22. Shibata N., Chen P. S., Dixon E. G., Wolf P. D., Danieley N. D., Smith W. M., Ideker R. E. Influence of shock strength and timing on induction of ventricular arrhythmias in dogs. Am J Physiol. 1988 Oct;255(4 Pt 2):H891–H901. doi: 10.1152/ajpheart.1988.255.4.H891. [DOI] [PubMed] [Google Scholar]
  23. Sommer J. R., Scherer B. Geometry of cell and bundle appositions in cardiac muscle: light microscopy. Am J Physiol. 1985 Jun;248(6 Pt 2):H792–H803. doi: 10.1152/ajpheart.1985.248.6.H792. [DOI] [PubMed] [Google Scholar]
  24. Spach M. S., Dolber P. C., Heidlage J. F., Kootsey J. M., Johnson E. A. Propagating depolarization in anisotropic human and canine cardiac muscle: apparent directional differences in membrane capacitance. A simplified model for selective directional effects of modifying the sodium conductance on Vmax, tau foot, and the propagation safety factor. Circ Res. 1987 Feb;60(2):206–219. doi: 10.1161/01.res.60.2.206. [DOI] [PubMed] [Google Scholar]
  25. Spach M. S., Heidlage J. F., Darken E. R., Hofer E., Raines K. H., Starmer C. F. Cellular Vmax reflects both membrane properties and the load presented by adjoining cells. Am J Physiol. 1992 Dec;263(6 Pt 2):H1855–H1863. doi: 10.1152/ajpheart.1992.263.6.H1855. [DOI] [PubMed] [Google Scholar]
  26. Spach M. S., Kootsey J. M. The nature of electrical propagation in cardiac muscle. Am J Physiol. 1983 Jan;244(1):H3–22. doi: 10.1152/ajpheart.1983.244.1.H3. [DOI] [PubMed] [Google Scholar]
  27. Spach M. S., Miller W. T., 3rd, Geselowitz D. B., Barr R. C., Kootsey J. M., Johnson E. A. The discontinuous nature of propagation in normal canine cardiac muscle. Evidence for recurrent discontinuities of intracellular resistance that affect the membrane currents. Circ Res. 1981 Jan;48(1):39–54. doi: 10.1161/01.res.48.1.39. [DOI] [PubMed] [Google Scholar]
  28. Spach M. S., Miller W. T., 3rd, Miller-Jones E., Warren R. B., Barr R. C. Extracellular potentials related to intracellular action potentials during impulse conduction in anisotropic canine cardiac muscle. Circ Res. 1979 Aug;45(2):188–204. doi: 10.1161/01.res.45.2.188. [DOI] [PubMed] [Google Scholar]
  29. Spach M. S. The discontinuous nature of electrical propagation in cardiac muscle. Consideration of a quantitative model incorporating the membrane ionic properties and structural complexities. The ALZA distinguished lecture. Ann Biomed Eng. 1983;11(3-4):209–261. doi: 10.1007/BF02363287. [DOI] [PubMed] [Google Scholar]

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