Abstract
With the dynamic differential equations of Beeler, G. W., and H. Reuter (1977, J. Physiol. [Lond.]. 268:177-210), we have studied the oscillatory behavior of the ventricular muscle fiber stimulated by a depolarizing applied current I app. The dynamic solutions of BR equations revealed that as I app increases, a periodic repetitive spiking mode appears above the subthreshold I app, which transforms to a periodic spiking-bursting mode of oscillations, and finally to chaos near the suprathreshold I app (i.e., near the termination of the periodic state). Phase resetting and annihilation of repetitive firing in the ventricular myocardium were demonstrated by a brief current pulse of the proper magnitude applied at the proper phase. These phenomena were further examined by a bifurcation analysis. A bifurcation diagram constructed as a function of I app revealed the existence of a stable periodic solution for a certain range of current values. Two Hopf bifurcation points exist in the solution, one just above the lower periodic limit point and the other substantially below the upper periodic limit point. Between each periodic limit point and the Hopf bifurcation, the cell exhibited the coexistence of two different stable modes of operation; the oscillatory repetitive firing state and the time-independent steady state. As in the Hodgkin-Huxley case, there was a low amplitude unstable periodic state, which separates the domain of the stable periodic state from the stable steady state. Thus, in support of the dynamic perturbation methods, the bifurcation diagram of the BR equation predicts the region where instantaneous perturbations, such as brief current pulses, can send the stable repetitive rhythmic state into the stable steady state.
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Selected References
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- Beeler G. W., Reuter H. Reconstruction of the action potential of ventricular myocardial fibres. J Physiol. 1977 Jun;268(1):177–210. doi: 10.1113/jphysiol.1977.sp011853. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Best E. N. Null space in the Hodgkin-Huxley Equations. A critical test. Biophys J. 1979 Jul;27(1):87–104. doi: 10.1016/S0006-3495(79)85204-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Chay T. R., Lee Y. S. Impulse responses of automaticity in the Purkinje fiber. Biophys J. 1984 Apr;45(4):841–849. doi: 10.1016/S0006-3495(84)84228-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Guttman R., Lewis S., Rinzel J. Control of repetitive firing in squid axon membrane as a model for a neuroneoscillator. J Physiol. 1980 Aug;305:377–395. doi: 10.1113/jphysiol.1980.sp013370. [DOI] [PMC free article] [PubMed] [Google Scholar]
- HODGKIN A. L., HUXLEY A. F. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol. 1952 Aug;117(4):500–544. doi: 10.1113/jphysiol.1952.sp004764. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Hoffman B. F., Rosen M. R. Cellular mechanisms for cardiac arrhythmias. Circ Res. 1981 Jul;49(1):1–15. doi: 10.1161/01.res.49.1.1. [DOI] [PubMed] [Google Scholar]
- Jalife J., Antzelevitch C. Pacemaker annihilation: diagnostic and therapeutic implications. Am Heart J. 1980 Jul;100(1):128–130. doi: 10.1016/0002-8703(80)90289-6. [DOI] [PubMed] [Google Scholar]
- Jalife J., Antzelevitch C. Phase resetting and annihilation of pacemaker activity in cardiac tissue. Science. 1979 Nov 9;206(4419):695–697. doi: 10.1126/science.493975. [DOI] [PubMed] [Google Scholar]
- Katzung B. G. Effects of extracellular calcium and sodium on depolarization-induced automaticity in guinea pig papillary muscle. Circ Res. 1975 Jul;37(1):118–127. doi: 10.1161/01.res.37.1.118. [DOI] [PubMed] [Google Scholar]
- Rinzel J. On repetitive activity in nerve. Fed Proc. 1978 Dec;37(14):2793–2802. [PubMed] [Google Scholar]
- Spear J. F., Moore E. N. Mechanisms of cardiac arrhythmias. Annu Rev Physiol. 1982;44:485–497. doi: 10.1146/annurev.ph.44.030182.002413. [DOI] [PubMed] [Google Scholar]