Summary
A Hodgkin-Huxley model for ventricular excitation is abstracted from electrophysiological data. A singular perturbation analysis of the 8-dimensional phase portrait of the model characterizes the role of calcium during the plateau phase of the ventricular action potential and demonstrates how the calcium refractory period prevents tetanization.
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References
Adelman, W. J., Jr.: Biophysics and Physiology of Excitable Membranes. New York: Van Nostrand Reinhold Co., 1971
Adelman, W. J., FitzHugh, R.: Solutions of the Hodgkin-Huxley equations modified for potassium accumulation in a periaxonal space. Federation Proc.34, 1322–1329 (1975)
Armstrong, C. M., Benzanilla, F.: Charge movement associated with the opening and closing of the activation gates of Na channels. J. Gen. Physiol.63, 533–552 (1973)
Bell, J., Cook, P.: A model of the nerve action potential. Submitted for publication, 1977
Bell, J., Cook, L. P.: On solutions of a nerve conduction equation. Siam J. on Appl. Math, in press (1978)
Carpenter, G. A.: A geometric approach to singular perturbation problems with applications to nerve impulse equations. J. Differential Equations23, 335–367 (1977)
Carpenter, G. A.: A revised Hodgkin-Huxley model (in preparation)
Carpenter, G. A.: Bursting phenomena in excitable membranes. Submitted for publication, 1976. SIAM J. on Appl. Math. (Subject to final revisions)
Carpenter, G. A.: Periodic solutions of nerve impulse equations. J. Math. Anal. Appl.58, 152–173 (1977)
DeMello, W. C. (editor): Electrical Phenomena in the Heart. New York: Academic Press, 1972
FitzHugh, R.: Thresholds and plateaus in the Hodgkin-Huxley nerve equations. J. Gen. Physiol.43, 867–896 (1960)
Frankenhaueuser, B., Hodgkin, A. L.: The action of calcium on the electrical properties of squid axons. J. Physiol.137, 218–244 (1957)
Gettes, L. S., Reuter, H.: Slow recovery from inactivation of inward currents in mammalian myocardial fibres. J. Physiol.240, 703–724 (1974)
Goldman, J.: Principles of Clinical Electrocardiography, 8th edition. Los Altos, California: Lange Medical Publications, 1973
Hodgkin, A. L., Huxley, A. F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol.117, 500–544 (1952)
Hoyt, R. C.: Sodium inactivation in nerve fibers. Biophys. J.8, 1074–1097 (1968)
Hoyt, R. C., Adelman, W. J., Jr.: Sodium inactivation: experimental test of two models. Biophys. J.10, 610–617 (1970)
Jakobsson, E.: The physical interpretation of mathematical models for sodium permeability changes in excitable membranes. Biophys. J.13, 1200–1211 (1973)
Jakobsson, E., Scudiero, C.: A transient excited state model for sodium permeability changes in excitable membranes. Biophys. J.15, 577–590 (1975)
Kohlhardt, M., Krause, H., Kubler, M., Herdey, A.: Kinetics of inactivation and recovery of the slow inward current in the mammalian ventricular myocardium. Pflügers Arch.355, 1–17 (1975)
Kuffler, S. W., Nicholls, J. G.: From Neuron to Brain. Sunderland, Ma.: Sinauer Associates, 1976
Moore, L. E., Jakobsson, E.: Interpretation of the sodium permeability changes of myelinated nerve in terms of linear relaxation theory. J. Theor. Biol.33, 77–89 (1971)
Noble, D., Tsien, R. W.: Outward membrane currents activated in the plateau range of potentials in cardiac Purkinje fibres. J. Physiol.200, 205–231 (1969).
Noble, D., Tsien, R. W.: Reconstruction of the repolarization process in cardiac Purkinje fibres based on voltage clamp measurements of membrane current. J. Physiol.200, 233–254 (1969)
Reuter, H.: Divalent cations as charge carriers in excitable membranes. Prog. in Biophys. and Molec. Bio.26, 1–43 (1973)
Reuter, H.: Exchange of calcium ions in the mammalian myocardium, Circulation Res.34, 599–605 (1974)
Trautwein, W., McDonald, T. F., Tripathi, O.: Calcium conductance and tension in mammalian ventricular muscle. Pflügers Arch.354, 55–74 (1975)
Trautwein, W.: Membrane currents in cardiac muscle fibers. Physiol. Reviews.53, 793–835 (1973)
Vender, A. J., Sherman, J. H., Luciano, D. S.: Human Physiology, 2nd edition. New York: McGraw-Hill, 1975
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Supported in part by the Undergraduate Research Opportunities Program, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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Carpenter, G.A., Knapp, V.R. An analysis of the mammalian ventricular action potential. J. Math. Biology 6, 305–316 (1978). https://doi.org/10.1007/BF02462996
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DOI: https://doi.org/10.1007/BF02462996