Relating the Sodium Current and Conductance to the Shape of Transmembrane and Extracellular Potentials by Simulation: Effects of Propagation Boundaries

IEEE Transactions on Biomedical Engineering

Volumn BME-32, Issue 10, 1985, Pages 743-755

  Spach, Madison S ^a   Kootsey, J Mailen ^a  

^a DUKE UNIVERSITY MEDICAL CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER ANALYSIS; COMPUTER SIMULATION; HEART; HEART MUSCLE CONDUCTION SYSTEM; HEART MUSCLE FIBER MEMBRANE CONDUCTANCE; HEART MUSCLE FIBER MEMBRANE POTENTIAL; NONBIOLOGICAL MODEL; NONHUMAN; SODIUM CURRENT; THEORETICAL STUDY;

ELECTRIC CONDUCTIVITY; EXTRACELLULAR SPACE; ION CHANNELS; MEMBRANE POTENTIALS; MODELS, CARDIOVASCULAR; PAPILLARY MUSCLES; SODIUM; SUPPORT, U.S. GOV'T, P.H.S.;

BIOLOGICAL MATERIALS - ELECTRIC PROPERTIES; ELECTRIC CONDUCTIVITY - MEASUREMENTS; ELECTRIC MEASUREMENTS - CURRENT; MEMBRANES; WAVEFORM ANALYSIS;

EXTRACELLULAR POTENTIAL; PROPAGATION BOUNDARIES EFFECTS; SODIUM CURRENT AND CONDUCTANCE; TRANSMEMBRANE SHAPE;

BIOMEDICAL ENGINEERING;

EID: 0022270352     PISSN: 00189294     EISSN: 15582531     Source Type: Journal    
DOI: 10.1109/TBME.1985.325489     Document Type: Article

References (33)

1. A. L. Hodgkin and A. F. Huxley, “A quantitative description of membrane current and its application to conduction and excitation in nerve,” J. Physiol (Lond.), vol. 117, pp. 500–544, 1952.
2. T. J. Colatsky, “Voltage clamp measuremennts of sodium channel properties in rabbit cardiac Purkinje fibres,” J. Physiol. (Lond.) vol. 305, pp. 215–234, 1980.
3. L. Ebihara, N. Shigeto, M. Lieberman, and E. A. Johnson, “The initial inward current in spherical clusters of chick embryonic heart cells,” J. Gen. Physiol., vol. 75, pp. 437–456, 1980.
4. L. Ebihara and E. A. Johnson, “Fast sodium current in cardiac muscle. A quantitative description,” Biophys. J., vol. 32, pp. 779–790, 1980.
5. A. M. Brown, K. S. Lee, and T. Powell, “Sodium current in single rat heart muscle cells,” J. Physiol. (Lond.), vol. 318, pp. 479–500, 1981.
6. B. I. Khodorov and E. N. Timin, “Nerve impulse propagation along nonuniform fibres (investigations using mathematical models),” Prog. Biophys. Mol Biol, vol. 30, pp. 145–184, 1975.
7. S. S. Goldstein and W. Rail, “Changes of action potential shape and velocity for changing core conductor geometry,” Biophys. J., vol. 14, pp. 731–757, 1974.
8. R. FitzHugh, “Computation of impulse initiation and saltatory conduction in a myelinated nerve fiber,” Biophys. J., vol. 2, pp. 11–21, 1962.
9. J. J. Jack, D. Noble, and R. W. Tsien, Electric Current Flow in Excitable Cells. Oxford, U.K.: Clarendon, 1975, ch. 4, pp. 67–82.
10. S. Weidmann, “The effect of the cardiac membrane potential on the rapid availability of the sodium-carrying system,” J. Physiol. (Lond.), vol. 127, pp. 213–224, 1955.
11. M. Bear, P. M. Best, and H. Reuter, “Voltage-dependent action of tetrodotoxin in mammalian cardiac muscle,” Nature, vol. 263, pp. 344–345, 1976.
12. L. M. Hondeghem and B. G. Katzung, “Time- and voltage-dependent interactions of antiarrhythmic drugs with cardiac sodium channels,” Biochimica et Biophysica Acta, vol. 472, pp. 373–398, 1977.
13. M. S. Spach, R. C. Barr, G. A. Serwer, J. M. Kootsey, and E. A. Johnson, “Extracellular potentials related to intracellular action potentials in the dog Purkinje system,” Circ. Res., vol. 30, pp. 505– 5019 1972.
14. M. S. Spach, W. T. Miller, III, E. Miller-Jones, R. B. Warren, and R. C. Barr, “Extracellular potentials related to intracellular action potentials during impulse conduction in anisotropic canine cardiac muscle,” Circ, Res., vol. 45, pp. 188–204, 1979.
15. M. S. Spach, R. C. Barr, G. A. Serwer, E. A. Johnson, and J. M. Kootsey, “Collision of excitation waves in the dog Purkinje system. 'Extracellular identification,” Circ. Res., vol. 29, pp. 499–511, 1971.
16. M. S. Spach, W. T. Miller, III, P. C. Dolber, J. M. Kootsey, J. R. Sommer, and C. E. Mosher, Jr., “The functional role of structural complexities in the propagation of depolarization in the atrium of the dog. Cardiac conduction disturbances due to discontinuities of effective axial resistivity,” Circ. Res., vol. 50, pp. 175–191, 1982.
17. G. A. Langer, “Sodium exchange in dog ventricular muscle. Relation to frequency of contraction and its possible role in the control of myocardial contractility,” J. Gen. Physiol, vol. 50, pp. 1221–1239, 1967.
18. H. D. Glitsch, H. Reuter, and H. Scholtz, “The effect of the internal sodium concentration on calcium fluxes in isolated guinea-pig auricles,” J. Physiol. (Lond.), vol. 209, pp. 25–43, 1970.
19. E. Jakobsson, “Interactions of cell volume, membrane potential, and membrane transport parameters,” Amer. J. Physiol, vol. 238, pp. C196–C206, 1980.
20. H. A. Fozzard and J. A. Wasserstrom, “Voltage dependence of intracellular sodium and control of contraction,” in Cardiac Electrophysiology and Arrhythmias, D. P. Zipes and J. Jalife, Eds. Orlando, FL: Grune & Stratton, 1985, pp. 51–57.
21. M. Lieberman, T. Sawanobori, J. M. Kootsey, and E. A. Johnson, “A synthetic strand of cardiac muscle. Its passive electrical properties,” J. Gen. Physiol, vol. 65, pp. 527–550, 1975.
22. C. F. Gerald, Applied Numerical Analysis. Reading, MA: Addison-Wesley, 1970, pp. 250–288.
23. J. Crank and P. Nicolson, “Practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type,” in Proc. Cambridge Phil. Soc., vol. 43, 1947, pp. 50–67.
24. A. L. Hodgkin, “A note on conduction velocity,” J. Physiol (Lond.), vol. 125, pp. 221–224, 1954.
25. M. S. Spach, R. C. Barr, E. A. Johnson, and J. M. Kootsey, “Cardiac extracellular potentials. Analysis of complex wave forms about the Purkinje networks in dogs,” Circ. Res., vol. 33, pp. 465–473, 1973.
26. H. Jenerick, “Phase plane trajectories of the muscle spike potential,” Biophys. J., vol. 3, pp. 363–377, 1963.
27. H. Jenerick, “An analysis of the striated muscle fiber action current,” Biophys. J., vol. 4, pp. 77–91, 1964.
28. A. L. Hodgkin and B. Katz, “The effect of sodium ions on the electrical activity of the giant axon of the squid,” J. Physiol (Lond.), vol. 108, pp. 37–77, 1949.
29. C. J. Cohen, B. P. Bean, and R. W. Tsien, “Maximal upstroke velocity as an index of available sodium conductance. Comparison of maximal upstroke velocity and voltage clamp measurements of sodium current in rabbit Purkinje fibers,” Circ. Res., vol. 54, pp. 636–651, 1984.
30. M. S. Spach, J. D. Sloan, and J. M. Kootsey, “Reconstruction of propagating depolarization in cardiac muscle based on voltage clamp data,” Biophys. J., vol. 45, p. 278a, 1984.
31. A. M. Scher and A. C. Young, “Pathway of ventricular depolarization in the dog,” Circ. Res., vol. 4, pp. 461–469, 1956.
32. D. Durrer, R. T. Van Dam, G. E. Freud, M. J. Janse, F. L. Meijler, and R. C. Arzbaecher, “Total excitation of the isolated human heart,” Circulation, vol. 41, pp. 899–912, 1970.
33. R. Horn and C. A. Vandenberg, “Statistical properties of single sodium channels,” J. Gen. Physiol., vol. 84, pp. 505–534, 1984.