Abstract
Beat-to-beat alternation in action potential morphology (alternans) in individual cardiac cells may be important in the development of ventricular tachycardia and fibrillation. So far, it has been difficult to identify the cause for alternans at the ion channel level because computer models and experiments that display alternans also simultaneously exhibit other confounding rhythm patterns, including those attributable to short timescale memory effects. To address this difficulty, we have developed an eigenmode method to study the dynamics of detailed cardiac cell models under constant pacing. The method completely separates these effects from one another in the linear regime, allowing each to be studied individually. For the Beeler–Reuter ion channel model, the fundamental difference between the alternans and memory modes was found to be rooted in the difference in the relative phasings of the x_{1} and f gate perturbations associated with the slow outward and slow inward currents, respectively. The importance of this relative phasing was analyzed with the help of two new analytical methods. For the alternans case, the relative phasing produced constructive interference between the two currents large enough to reverse the perturbation in membrane potential from beat to beat. The opposite was true of the memory mode. © 2003 Biomedical Engineering Society.
PAC2003: 8716Uv, 8719Hh, 8717Aa, 8719Nn
Similar content being viewed by others
References
Bär, M., and M. Eiswirth. Turbulence due to spiral breakup in a continuous excitable medium. Phys. Rev. E48:R1635–R1637, 1993.
Beeler, G. W., and H. Reuter. Reconstruction of the action potential of ventricular myocardial fibers. J. Physiol. (London)251:1–59, 1975.
Courtemanche, M., and A. T. Winfree. Reentrant rotating waves in a Beeler–Reuter-based model of two-dimensional cardiac electrical activity. Int. J. Bifurcation Chaos Appl. Sci. Eng. 1:431–444, 1991.
Courtemanche, M. Complex spiral wave dynamics in a spatially distributed ionic model of cardiac electrical activity. Chaos6:579–600, 1996.
Davidenko, J. M., A. V. Pertsov, R. Salomonsz, W. Baxter, and J. Jalife. Stationary and drifting spiral waves of excitation in isolated cardiac muscle. Nature (London)355:349–351, 1992.
Dennis, J. E., and R. B. Schnabel. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Philadelphia, PA: SIAM, 1996, 378 pp.
Fenton, F. H., E. M. Cherry, H. M. Hastings, and S. J. Evans. Multiple mechanisms of spiral wave breakup in a model of cardiac electrical activity. Chaos12:852–892, 2002.
Fox, J. J., J. L. McHarg, and R. F. Gilmour. Ionic mechanism of electrical alternans. Am. J. Physiol. 282:H516–H530, 2002.
Fox, J. J., E. Bodenschatz, and R. F. Gilmour. Period-doubling instability and memory in cardiac tissue. Phys. Rev. Lett. 89:138101, 2002.
Gilmour, R. F., N. F. Otani, and M. A. Watanabe. Memory and complex dynamics in cardiac Purkinje fibers. Am. J. Physiol. 272:H1826–H1832, 1997.
Gray, R. A., J. Jalife, A. V. Panfilov, W. T. Baxter, C. Cabo, J. M. Davidenko, A. M. Pertsov, P. Hogeweg, and A. T. Winfree. Mechanisms of cardiac fibrillation. Science270:1222–1225, 1995.
Gray, R. A., J. Jalife, A. Panfilov, W. T. Baxter, C. Cabo, and A. M. Pertsov. Nonstationary vortex-like reentrant activity as a mechanism of polymorphic ventricular tachycardia in the isolated rabbit heart. Circulation91:2454–2469, 1995.
Guevara, M. R., G. Ward, A. Shrier, and L. Glass. Electrical alternans and period-doubling bifurcations. IEEE Computers in Cardiology. Silver Spring, MD: IEEE Computer Society, 1984, pp. 167–170.
Hall, G. M., S. Bahar, and D. J. Gauthier. Prevalence of rate-dependent behaviors in cardiac muscle. Phys. Rev. Lett. 82:2995–2998, 1999.
Hastings, H. M., F. H. Fenton, S. J. Evans, O. Hotomaroglu, J. Geetha, K. Gittelson, J. Nilson, and A. Garfinkel. Alternans and the onset of ventricular fibrillation. Phys. Rev. E62:4043–4048, 2000.
Holden, A. V., and A. V. Panflov. Spatiotemporal chaos in a model of cardiac electrical activity. Int. J. Bifurcation Chaos Appl. Sci. Eng. 1:219–225, 1991.
Jalife, J., R. A. Gray, G. E. Morley, and J. M. Davidenko. Self-organization and the dynamical nature of ventricular fibrillation. Chaos8:79–93, 1998.
Janse, M. J., F. J. G. Wilms-Schopman, and R. Coronel. Ventricular fibrillation is not always due to multiple wavelet reentry. J. Cardiovasc. Electrophysiol. 6:512–521, 1995.
Karma, A. Spiral breakup in model equations of action potential propagation in cardiac tissue. Phys. Rev. Lett. 71:1103–1106, 1993.
Karma, A. Electrical alternans and spiral wave breakup in cardiac tissue. Chaos4:461–472, 1994.
Koller, M. L., M. L. Riccio, and R. F. Gilmour. Dynamic restitution of action potential duration during electrical alternans and ventricular fibrillation. Am. J. Physiol. 275:H1635–H1642, 1998.
Luo, C., and Y. Rudy. A dynamic model of the cardiac ventricular action potential. Circ. Res. 74:1071–1096, 1994.
Nolasco, J. B., and R. W. Dahlen. A graphic method for the study of alternation in cardiac action potentials. J. Appl. Physiol. 25:191–196, 1968.
Otani, N. F., and R. F. Gilmour. Memory models for the electrical properties of local cardiac systems. J. Theor. Biol. 187:409–436, 1997.
Panfilov, A. V. Spiral breakup as a model of ventricular fibrillation. Chaos8:57–64, 1998.
Pastore, J. M., S. D. Girouard, K. R. Laurita, F. G. Akar, and D. S. Rosenbaum. Mechanism linking T-wave alternans to the genesis of cardiac fibrillation. Circulation99:1385–1394, 1999.
Press, W. H., B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling. Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. Cambridge: Cambridge University Press, 1992, 994 pp.
Qu, Z., J. Weiss, and A. Garfinkel. Cardiac electrical restitution properties and stability of reentrant spiral waves: A simulation study. Am. J. Physiol. 276:H269–H283, 1999.
Qu, Z., A. Garfinkel, P. Chen, and J. N. Weiss. Mechanisms of discordant alternans and induction of reentry in simulated cardiac tissue. Circulation102:1664–1670, 2000.
Tolkacheva, E. G., D. G. Schaeffer, D. J. Gautheir, and W. Krassowska. Condition for alternans and stability of the 1:1 response pattern in a “memory” model of paced cardiac dynamics. Phys. Rev. E67:031904, 2003.
Vinet, A. Memory and bistability in a one-dimensional loop of model cardiac cells. J. Biol. Syst. 7:451–473, 1999.
Watanabe, M. A., F. H. Fenton, S. J. Evans, H. M. Hastings, and A. Karma. Mechanisms for discordant alternans. J. Cardiovasc. Electrophysiol. 12:196–206, 2001.
Weiss, J. N., A. Garfinkel, H. S. Karagueuzian, Z. Qu, and P. Chen. Chaos and the transition to ventricular fibrillation: A new approach to antiarrhythmic drug evaluation. Circulation99:2819–2826, 1999.
Winfree, A. T. When Time Breaks Down. Princeton, NJ: Princeton University Press, 1987, 339 pp.
Zipes, D. P., and H. J. J. Wellens. Sudden cardiac death. Circulation98:2334–2351, 1998.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Li, M., Otani, N.F. Ion Channel Basis for Alternans and Memory in Cardiac Myocytes. Annals of Biomedical Engineering 31, 1213–1230 (2003). https://doi.org/10.1114/1.1616930
Issue Date:
DOI: https://doi.org/10.1114/1.1616930