A general approach to modeling conduction and concentration dynamics in excitable cells of concentric cylindrical geometry

Journal of Theoretical Biology

Volumn 199, Issue 3, 1999, Pages 329-358

  Nygren, A ^a   Halter, J A ^b  

^a BAYLOR COLLEGE OF MEDICINE   (United States)

^b RICE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ION;

ACTION POTENTIAL; ARTICLE; CELL SHAPE; DIFFUSION; DYNAMICS; EXCITABLE MEMBRANE; HAIR CELL; HEART MUSCLE CELL; ION TRANSPORT; MATHEMATICAL MODEL; MYELINATED NERVE; NERVE CONDUCTION; NONMYELINATED NERVE; PRIORITY JOURNAL;

EID: 0033533180     PISSN: 00225193     EISSN: None     Source Type: Journal    
DOI: 10.1006/jtbi.1999.0962     Document Type: Article

References (31)

1. +)ATPase is continuous along the axolemma of unensheathed axons from spinal roots of 'dystrophic' mice. J. Neurocytol. 16:1987;239-248.
2. CHEN Y., DEHAAN R. L. Temperature dependence of embryonic cardiac gap junction conductance and channel kinetics. J. Mem. Biol. 136:1993;125-134.
3. FITZHUGH R. Computation of the impulse initiation and saltatory conduction in a myelinated nerve fiber. Biophys. J. 2:1962;11-21.
4. HALTER J. A., CLARK J. W. JR. A distributed-parameter model of the myelinated nerve fiber. J. theor. Biol. 148:1991;345-382.
5. HALTER J. A., KRUGER R. P., YIUM M. J., BROWNELL W. E. The influence of the subsurface cisternae on the electrical properties of the outer hair cell. NeuroReport. 8:1997;2517-2521.
6. HALTER J. A., ZUPAN B. An electrodiffusion model of the mammalian myelinated nerve fiber. Proc. 17th Annual Int. Conf. of IEEE Engineering in Medicine and Biology Society. 16:1995.
7. HOLM M., JOHANSSON R., BRANDT J., LÜHRS C., OLSSON S. B. Epicardial right atrial free wall mapping in chronic atrial fibrillation: documentation of repetitive activation with a focal spread - a hithereto unrecognised phenomenon in man. Eur. Heart J. 18:1997;290-310.
8. HUME J. R., GILES W. R. Active and passive electrical properties of single bullfrog atrial cells. J. Gen. Physiol. 78:1981;19-42.
9. KONINGS K. T. S., KIRCHHOF C. J. H. J., SMEETS J. R. L. M., WELLENS H. J. J., PENN O. C., ALLESSIE M. A. High-density mapping of electrically induced atrial fibrillation in humans. Circulation. 89:1994;1665-1680.
10. LIDE D. R. CRC Handbook of Chemistry and Physics. 1992;CRC Press, Cleveland.
11. LINDBLAD D. S., MURPHEY C. R., CLARK J. W., GILES W. R. A model of the action potential and underlying membrane currents in a rabbit atrial cell. Am. J. Physiol. 271:1996;H1666-H1691.
12. MASCAGNI M. V. Numerical methods for neuronal modeling. Koch, Segev. Methods in Neuronal Modeling: from Synapses to Networks. 1989;439-484 MIT Press, Cambridge.
13. +-ATPase in internodal axolemma of myelinated fibers of rat sciatic and optic nerve. J. Neurochem. 57:1991;184-192.
14. MURPHEY C. R., CLARK J. W., GILES W. R., RASMUSSON R. L., HALTER J. A., HICKS K., HOYT B. Conduction in bullfrog atrial strands: Simulations of the role of disc and extracellular resistance. Math. Biosci. 106:1991;39-84.
15. NICHOLSON C., PHILLIPS J. M. Ion diffusion modified by tortuosity and volume fraction in the extracellular microenvironment of the rat cerebellum. J. Physiol. 321:1981;225-257.
16. NOMA A., TSUBOI N. Dependence of junctional conductance on proton, calcium and magnesium ions in paired cells of guinea pig. J. Physiol. 382:1987;193-211.
17. NYGREN A. Mechanisms of repolarization and conduction in a mathematical model of electrophysiological responses in the human atrium. 1998;Rice University, Houston.
18. +currents in repolarization. Circ. Res. 82:1998;63-81.
19. PRESS W. H., TEUKOLSKY S. A., VETTERLING W. T., FLANNERY B. P. Numerical Recipes in FORTRAN: The Art of Scientific Computing. 1992;Cambridge University Press, Cambridge.
20. QIAN N., SEJNOWSKI T. J. An electro-diffusion model for computing membrane potentials and ionic concentrations in branching dendrites, spines and axons. Biol. Cybern. 62:1989;1-15.
21. RUSH S., LARSEN H. A practical algorithm for solving dynamic membrane equations. IEEE Trans. Biomed. Engng. 25:1978;389-392.
22. RÅDE L., WESTERGREN B. BETA Mathematics Handbook. 1990;Studentlitteratur AB, Lund.
23. SEVERS N. J. The cardiac gap junction and intercalated disc. Int. J. Cardiol. 26:1990;137-173.
24. SHAW R. M., RUDY Y. Electrophysiologic effects of acute myocardial ischemia: A mechanistic investigation of action potential conduction and conduction failure. Circ. Res. 80:1997;124-138.
25. SHUMAKER J. M., CLARK J. W., GILES W. R. Simulations of passive properties and action potential conduction in an idealized bullfrog atrial trabeculum. Math. Biosci. 116:1993;127-167.
26. STYS P. K., WAXMAN S. G., RANSOM B. R. Ion pumps and exchangers. Waxman. The Axon: Structure, Function, and Pathophysiology. 1995;296-310 Oxford University Press, New York.
27. VAN EGERAAT J. M., WIKSWO J. P. A model for axonal propagation incorporating both radial and axial ionic transport. Biophys. J. 64:1993;1287-1298.
28. VERHEULE S., VAN KEMPEN M. J. A., TE WELSCHER P. H. J. A., KWAK B. R., JONGSMA H. J. Characterization of gap junction channels in adult rabbit atrial and ventricular myocardium. Circ. Res. 80:1997;673-681.
29. WANG S., LEON L. J., ROBERGE F. A. Interactions between adjacent fibers in a cardiac muscle bundle. Ann. Biomed. Engng. 24:1996;662-674.
30. WAXMAN S. G. Voltage-gated ion channels in axons: Localization, function and development. Waxman. The Axon: Structure, Function, and Pathophysiology. 1995;218-243 Oxford University Press, New York.
31. ZUPAN B., HALTER J. A. A simulation and optimization environment for models in computational neurobiology. Breitenecker F., Husinsky I. EUROSIM'95. 1995;963-968 Elsevier, Amsterdam.