ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Pavlov E. A., Osipov G. V. Modeling of cardiac activity on the basis of maps: dynamics of single element. Izvestiya VUZ. Applied Nonlinear Dynamics, 2011, vol. 19, iss. 3, pp. 104-115. DOI: 10.18500/0869-6632-2011-19-3-104-115

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Modeling of cardiac activity on the basis of maps: dynamics of single element

Pavlov Evgenij Aleksandrovich, Lobachevsky State University of Nizhny Novgorod
Osipov Grigorij Vladimirovich, Lobachevsky State University of Nizhny Novgorod

New computationally efficient model of cardiac activity is introduced. The model is a four-dimensional map based on well-known Luo–Rudy model. Capabilities of the model in replication of the basic cardiac cells’ properties are shown. Analysis of relationship between changes in individual parameters of the model and biophysical processes in real cardiac cells has been made. The model can reproduce two basic activity modes such as excitable and oscillatory regimes. Bifurcation mechanisms of transitions of between these regimes are investigated using phase space analysis. The dynamics of excitable cell on the external periodic action, including various types of synchronous response and hysteresis phenomenon, is investigated. 

  1. Hodgkin AL, Huxley AF. A quantitative description of membrane currents and its application to conduction and excitation in nerve. J. Physiol. 1952;117(4):500–544. DOI:
  2. Bonhoeffer KF. Modelle der Nervenerregung. Naturwissenschaften. 1953;40(11):301–311 (in German). DOI: 10.1007/BF00632438.
  3. Chialvo DR. Generic excitable dynamics on a two-dimensional map. Chaos, Solitons, Fractals. 1995;5(3–4):461–479. DOI: 10.1016/0960-0779(93)E0056-H.
  4. Noble D. A modification of the Hodgkin–Huxley equations applicable to Purkinje fibre action and pacemaker potential. J. Physiol. 1962;160(2):317–352. DOI: 10.1113/jphysiol.1962.sp006849.
  5. Beeler GW, Reuter H. Reconstruction of the action potential of ventricular myocardial fibers. J. Physiol. 1977;268(1):177–210. DOI: 10.1113/jphysiol.1977.sp011853.
  6. Di Francesco D, Noble D. A model of cardiac electrical activity incorporating ionic pumps and concentration changes. Phil. Trans. R. Soc. Lond. 1985;307(1133):353–398. DOI: 10.1098/rstb.1985.0001.
  7. Luo CH, Rudy Y. A model of the ventricular cardiac action potential, depolarization, repolarization and their interaction. Circ. Res. 1991;68(6):1501–1526. DOI: 10.1161/01.RES.68.6.1501.
  8. Ten Tusscher KH, Noble D, Noble PJ, Panfilov AV. A model for human ventricular tissue. Am. J. Physiol. 2004;286(4):H1573–H1589. DOI: 10.1152/ajpheart.00794.2003.
  9. Qu Z, Weiss JN, Garfinkel A. From local to global spatiotemporal chaos in a cardiac tissue model. Phys. Rev. E. 2000;61(1):727–732. DOI: 10.1103/physreve.61.727.
  10. Arce H, Lopez A, Guevara M. Triggered alternans in an ionic model of ischemic cardiac ventricular muscle. Chaos. 2002;12(3):807–818. DOI: 10.1063/1.1499275.
  11. Alonso S, Panfilov AV. Negative filament tension in the Luo–Rudy model of cardiac tissue. Chaos. 2007;17(1):015102. DOI: 10.1063/1.2430638.
  12. Kanakov OI, Osipov GV, Chan CK, Kurths J. Cluster synchronization and spatiotemporal dynamics in networks of oscillatory and excitable Luo–Rudy cells. Chaos. 2007;17(1):015111. DOI: 10.1063/1.2437581.
  13. Kurata Y, Hisatome I, Matsuda H, Shibamoto T. Dynamical mechanisms of pacemaker generation in IK1-downregulated human ventricular myocytes: Insights from bifurcation analyses of a mathematical model. Biophys. J. 2005;89(4):2865–2887. DOI: 10.1529/biophysj.105.060830.
  14. Silva J, Rudy Y. Mechanism of pacemaking in IK1-downregulated myocytes. Circ. Res. 2003;92(3):261–263. DOI: 10.1161/01.RES.0000057996.20414.C6.
  15. Carmeliet E, Vereecke J. Adrenaline and the plateau phase of the cardiac action potential. Pflugers Arch. 1969;313(4):300–315. DOI: 10.1007/bf00593955.
  16. Noble D, Noble SJ. A model of sino-atrial node electrical activity based on a modification of the DiFrancesco-Noble equations. Proc. R. Soc. Lond. B Biol. Sci. 1984;222(1228):295–304. DOI: 10.1098/rspb.1984.0065.
  17. Zhang H, Holden AV, Kodama I, Honjo H, Lei M, Varghese T, Boyett MR. Mathematical models of action potential in the periphery and center of the rabbit sinoatrial node. Am. J. Physiol. 2000;279(1):H397–H421. DOI: 10.1152/ajpheart.2000.279.1.h397.
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