For citation:
Pavlov E. A., Osipov G. V. Modeling of cardiac activity on the basis of maps: ensembles of coupled elements. Izvestiya VUZ. Applied Nonlinear Dynamics, 2011, vol. 19, iss. 3, pp. 116-126. DOI: 10.18500/0869-6632-2011-19-3-116-126
Modeling of cardiac activity on the basis of maps: ensembles of coupled elements
The dynamics of coupled maps’ ensembles is investigated in the context of description of spatio-temporal processes in the myocardium. Particular, the dynamics of two coupled maps is explored as well as modeling the interaction of pacemaker (oscillatory) cell and myocyte (excitable cell), and the interation of two pacemakers. Setting of synchronous regime by increasing of coupling strength is considered through a coincidence of their characteristic time scales (characteristic frequencies). Effects of cluster and global synchronization in 1D and 2D lattices of oscillatory cells with a random distribution of individual frequencies are discussed. Impulse propagation in the chain of excitable cells has been observed. Analysis of 2D lattice of excitable elements with target and spiral waves has been made. The characteristics of the spiral wave have been analyzed in depending on the individual parameters of the map and coupling strength between elements of the lattice. Comparative results of computational efficiency with the mapbased model and original ODE model are presented.
- Pavlov EA, Osipov GV. Modeling of cardiac activity on the basis of maps: dynamics of single element. Izvestiya VUZ. Applied Nonlinear Dynamics. 2011;19(3):104–115 (in Russian). DOI: 10.18500/0869-6632-2011-19-3-104-115.
- Rohr S. Role of gap junctions in the propagation of the cardiac action potential. Cardiovasc. Res. 2004;62(2):309–322. DOI: 10.1016/j.cardiores.2003.11.035.
- Joyner RW, van Capelle FJ. Propagation through electrically coupled cells. How a small SA node drives a large atrium. Biophys. J. 1986;50(6):1157–1164. DOI: 10.1016/S0006-3495(86)83559-7.
- Jamaleddine RS, Vinet A, Roberge FA. New frequency entrainment scenario in a pair of cardiac cells coupled through a variable resistance. In: Proceedings of the 18th Annual International Conference of the IEEE Engineering in Medicine and Biology Society. 31 Oct.-3 Nov. 1996, Amsterdam, Netherlands. IEEE; 1996. P. 1270. DOI: 10.1109/IEMBS.1996.652806.
- Henriquez AP, Vogel R, Muller-Borer BJ, Henriquez CS, Weinggart R, Cascio WE. Influence of dynamic gap junction resistance on impulse propagation in ventricular myocardium: A computer simulation study. Biophys. J. 2001;81(4):2112–2121. DOI: 10.1016/S0006-3495(01)75859-6.
- Kleber AG, Rudy Y. Basic mechanisms of cardiac impulse propagation and associated arrhythmias. Physiol. Rev. 2004;84(2):431–488. DOI: 10.1152/physrev.00025.2003.
- Bernus O, Wilders R, Zemlin CW, Verschelde H, Panfilov AV. A computationally efficient electrophysiological model of human ventricular cells. Am. J. Physiol. 2002;282(6):H2296–H2308. DOI: 10.1152/ajpheart.00731.2001.
- 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.
- Cherry EM, Greenside HS, Henriquez CS. A space-time adaptive method for simulating complex cardiac dynamics. Phys. Rev. Lett. 2000;84(6):1343–1346. DOI: 10.1103/physrevlett.84.1343.
- Qu Z, Garfinkel A. An advanced algorithm for solving partial differential equation in cardiac conduction. IEEE Trans. Biomed. Eng. 1999;46(9):1166–1168. DOI: 10.1109/10.784149.
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