Skip to main content
Journal of Biological Physics logoLink to Journal of Biological Physics
. 1999 Jun;25(2-3):149–164. doi: 10.1023/A:1005119218136

Soliton-Like Regimes and Excitation Pulse Reflection (Echo) in Homogeneous Cardiac Purkinje Fibers: Results of Numerical Simulations

OV Aslanidi 1, OA Mornev 1
PMCID: PMC3455967  PMID: 23345694

Abstract

On the basis of numerical simulations of the partial McAllister-Noble-Tsien equations quantitatively describing the dynamics of electrical processes in conductive cardiac Purkinje fibers we reveal unusual – soliton-like – regimes of interaction of nonlinear excitation pulses governing the heart contraction rhythm: reflection of colliding pulses instead of their annihilation. The phenomenological mechanism of the reflection effects is that in a narrow (but finite) range of the system parameters the traveling pulse presents a doublet consisting of a high-amplitude leader followed by a low-amplitude subthreshold wave. Upon collisions of pulses the leaders are annihilated, but subthreshold waves summarize becoming superthreshold and initiating two novel echo-pulses traveling in opposite directions. The phenomenon revealed presents an analogy to the effect of reflection of colliding nerve pulses, predicted recently, and can be of use in getting insight into the mechanisms of heart rhythm disturbances.

Keywords: Excitable media, Nonlinear waves, Heart, Reflection, Limit cyclebifurcation

Full Text

The Full Text of this article is available as a PDF (133.0 KB).

References

  • 1.Zipes D.P., Jalife J., editors. Cardiac electrophysiology. Philadelphia: Sanders Co.; 1990. [Google Scholar]
  • 2.Khodorov B.I. General physiology of excitable membranes. Moscow: Nauka; 1975. [Google Scholar]
  • 3.Krinsky V.I., editor. Self-organization. Autowaves and structures far from equilibrium. Berlin: Springer; 1984. [Google Scholar]
  • 4.Howe J.F., Calvin V.H., Loeser J.D. Impulses reflected from dorsal root ganglia and from focal nerve injuries. Brain Res. 1976;116:139–144. doi: 10.1016/0006-8993(76)90255-9. [DOI] [PubMed] [Google Scholar]
  • 5.Antzelevich C., Jalife J., Moe G.K. Characteristics of reflection as a mechanism of reentrant arrythmias and its relationship to parasystole. Circulation. 1980;61:182–191. doi: 10.1161/01.cir.61.1.182. [DOI] [PubMed] [Google Scholar]
  • 6.Krinsky V.I., Kholopov A.V. Echo phenomenon in excitable tissue. Biofizika. 1967;12:524–528. [PubMed] [Google Scholar]
  • 7.Cabo C., Barr R.C. Reflection after delayed excitation in a computer model of a single fiber. Circ. Res. 1992;71:260–270. doi: 10.1161/01.res.71.2.260. [DOI] [PubMed] [Google Scholar]
  • 8.Ermentrout B., Rinzel J. Reflected waves in an inhomogeneous excitable medium. SIAM J. Appl. Math. 1996;56:1107–1128. [Google Scholar]
  • 9.Scott A.C., Chu F.Y.E., McLaughlin D.W. Solitons - a new concept in applied sciences. Proc. IEEE. 1973;61:1443–1483. [Google Scholar]
  • 10.Tuckwell H.C. Solitons in a reaction-diffusion system. Science. 1979;205:493–495. doi: 10.1126/science.205.4405.493. [DOI] [PubMed] [Google Scholar]
  • 11.Rotermund H., Jakubith S., Oertzen H., Ertl G. Solitons in a surface reaction. Phys. Rev. Lett. 1991;66:3083–3086. doi: 10.1103/PhysRevLett.66.3083. [DOI] [PubMed] [Google Scholar]
  • 12.Kobayashi R., Ohta T., Hayase Y. Self-organized pulse-generator in reaction-diffusion system. Phys. Rev. E. 1994;50:R3291–R3294. doi: 10.1103/physreve.50.r3291. [DOI] [PubMed] [Google Scholar]
  • 13.Petrov V., Scott S.K., Showalter K. Excitability, wave reflection and wave splitting in a cubic autocatalysis reaction-diffusion system. Phil. Trans. R. Soc. A. 1994;347:631–642. [Google Scholar]
  • 14.Kosek J., Marek M. Wave reflection in reaction-diffusion equations. Phys. Rev. Lett. 1995;74:2134–2137. doi: 10.1103/PhysRevLett.74.2134. [DOI] [PubMed] [Google Scholar]
  • 15.Mornev O.A., Aslanidi O.V., Aliev R.R., Chailakhyan L.M. Soliton regimes in the FitzHugh-Nagumo model: Reflection of colliding pulses of excitation. Doklady Biophys. 1996;346-348:21–23. [PubMed] [Google Scholar]
  • 16.Mornev O.A., Aslanidi O.V., Chailakhyan L.M. Solitonic mode in the FitzHugh-Nagumo equations: Dynamics of a rotating spiral wave. Doklady Biophys. 1997;352-354:29–32. [PubMed] [Google Scholar]
  • 17.Aslanidi O.V., Mornev O.A. Reflection of running excitation impulses. Biophysics. 1996;41:967–973. [Google Scholar]
  • 18.Aslanidi O.V., Mornev O.A. Can colliding nerve pulses be reflected? JETP Lett. 1997;65:579–585. [Google Scholar]
  • 19.McAllister R.E., Noble D., Tsien R.W. Reconstruction of the electrical activity of cardiac Purkinje fibres. J. Physiol. 1975;251:1–59. doi: 10.1113/jphysiol.1975.sp011080. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 20.Scott A.C. Neurophysics of a nerve fiber. Rev. Mod. Phys. 1975;47:487–555. [Google Scholar]
  • 21.Walton M.K., Fozzard H.A. Experimental study of the conducted action potential in cardiac Purkinje strands. Biophys. J. 1983;44:1–8. doi: 10.1016/S0006-3495(83)84272-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 22.Schechter E., Freenam C.C., Lazzara R. Afterdepolarizations as a mechanism for the long QT syndrome. J. Am. Coll. Cardiol. 1984;3:1556–1561. doi: 10.1016/s0735-1097(84)80296-x. [DOI] [PubMed] [Google Scholar]
  • 23.Wit, A.L. and Rosen, M.R.: Afterpolarizations and triggered activity, in H.A. Fozzard et al. (eds.), The Heart and the Cardiovascular System, Raven Press, 1986, pp. 1449–1490.
  • 24.DiFrancesco D., Noble D. A model of cardiac electrical activity incorporating ionic pumps and concentration changes. Phil. Trans. R. Soc. 1985;307:353–398. doi: 10.1098/rstb.1985.0001. [DOI] [PubMed] [Google Scholar]

Articles from Journal of Biological Physics are provided here courtesy of Springer Science+Business Media B.V.

RESOURCES