Abstract
A model of cardiac cells incorporating the membrane potential and the intracellular calcium concentration as the two dynamical variables is developed. This model is applied to simple systems of cells to investigate its behavior as a function of the model parameters. Rational entrainment is observed in systems of two coupled pacemaker cells. The propagation of the membrane potential and intracellular calcium concentration through a sheet is simulated. Behavior suggestive of circus movement tachycardias is observed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bak P (1986) The Devil's staircase. Phys Today 39:38–45
Beeler GW, Reuter H (1977) Reconstruction of the action potential of ventricular myocardial fibres. J Physiol 268:177–210
Brown RF, Kimura J, Noble D, Noble SJ, Taupignon A (1984) The slow inward current, i si, in the rabbit sino-atrial node investigated by voltage clamp and computer simulation. Proc R Soc London B 222:305–328
DiFrancesco D, Noble D (1985) A model of cardiac electrical activity incorporating ionic pumps and concentration changes. Phil Trans R Soc London B 307:353–398
Hindmarsh AC (1980) LSODE and LSODI, two new initial value ordinary differential equation solvers. ACM-SIGNUM Newslett 15:10–11
Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117:500–544
Joyner RW, Picone J, Veenstra R, Rawling D (1983) Propagation through electrically coupled cells. Effects of regional changes in membrane properties. Circ Res 53:526–534
McAllister RE, Noble D, Tsien RW (1975) Reconstruction of the electrical activity of cardiac Purkinje fibres. J Physiol 251:1–59
Michaels DC, Matyas EP, Jalife J (1984) A mathematical model of the effects of acetylcholine pulses on sinoatrial pacemaker activity. Circ Res 55:89–101
Michaels DC, Matyas EP, Jalife J (1986) Dynamic interactions and mutual synchronization of sinoatrial node pacemaker cells. Circ Res 58:706–720
Moe GK, Rheinboldt WC, Abildskov JA (1964) A computer model of atrial fibrillation. Am Heart J 67:200–220
Plonsey R (1969) Bioelectric phenomena. McGraw-Hill, New York
Reuter H, Scholz H (1976) A study of the ion selectivity and the kinetic properties of the calcium-dependent slow inward current in mammalian cardiac muscle. J Physiol 264:17–47
Stranden NB, Stanfield PR (1982) A binding-site model for calcium channel inactivation that depends on calcium entry. Proc R Soc London B 217:104–110
Van Capelle FJL, Durrer D (1980) Computer simulation of arrhythmias in a network of coupled excitable elements. Circ Res 47:454–466
Wier WG, Cannel MB, Verlin JR, Marban E, Lederer WJ (1987) Cellular and subcellular heterogeneity of [Ca2+]i in single heart cells revealed by fura-2. Science 235:325–328
Yanagihara K, Noma A, Irisawa H (1980) Reconstruction of sinoatrial node pacemaker potential based on the voltage clamp experiments. Jpn J Physiol 30:841–857
Ypey DL, Van Meerwijk WPM, Ince C, Groos G (1980) Mutual entrainment of two pacemaker cells. A study with an electronic parallel conductance model. J Theor Biol 86:731–755
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lambert, M.H., Chay, T.R. Cardiac arrhythmias modelled by Cai-inactivated Ca2+ channels. Biol. Cybern. 61, 21–28 (1989). https://doi.org/10.1007/BF00204756
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00204756