Literature DB >> 11106597

A quantitative approximation scheme for the traveling wave solutions in the Hodgkin-Huxley model.

C B Muratov1.   

Abstract

We introduce an approximation scheme for the Hodgkin-Huxley model of nerve conductance that allows calculation of both the speed and shape of the traveling pulses, in quantitative agreement with the solutions of the model. We demonstrate that the reduced problem for the front of the traveling pulse admits a unique solution. We obtain an explicit analytical expression for the speed of the pulses that is valid with good accuracy in a wide range of the parameters.

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Year:  2000        PMID： 11106597      PMCID： PMC1301168          DOI： 10.1016/S0006-3495(00)76526-X

Source DB:  PubMed          Journal:  Biophys J        ISSN： 0006-3495            Impact factor:   4.033


  7 in total

1.  Ion movements during nerve activity.

Authors:  A F HUXLEY
Journal:  Ann N Y Acad Sci       Date:  1959-08-28       Impact factor: 5.691

2.  A quantitative description of membrane current and its application to conduction and excitation in nerve.

Authors:  A L HODGKIN; A F HUXLEY
Journal:  J Physiol       Date:  1952-08       Impact factor: 5.182

3.  Ultrafast traveling spike autosolitons in reaction-diffusion systems.

Authors: 
Journal:  Phys Rev Lett       Date:  1995-07-10       Impact factor: 9.161

4.  Impulses and Physiological States in Theoretical Models of Nerve Membrane.

Authors:  R Fitzhugh
Journal:  Biophys J       Date:  1961-07       Impact factor: 4.033

5.  The optimum density of sodium channels in an unmyelinated nerve.

Authors:  A Hodgkin
Journal:  Philos Trans R Soc Lond B Biol Sci       Date:  1975-06-10       Impact factor: 6.237

6.  Traveling wave solutions of a nerve conduction equation.

Authors:  J Rinzel; J B Keller
Journal:  Biophys J       Date:  1973-12       Impact factor: 4.033

7.  The dependence of impulse propagation speed on firing frequency, dispersion, for the Hodgkin-Huxley model.

Authors:  R N Miller; J Rinzel
Journal:  Biophys J       Date:  1981-05       Impact factor: 4.033
  7 in total
  2 in total

1.  Ionic mechanisms underlying history-dependence of conduction delay in an unmyelinated axon.

Authors:  Yang Zhang; Dirk Bucher; Farzan Nadim
Journal:  Elife       Date:  2017-07-10       Impact factor: 8.140

2.  Dynamics of diffusive cell signaling relays.

Authors:  Paul B Dieterle; Jiseon Min; Daniel Irimia; Ariel Amir
Journal:  Elife       Date:  2020-12-04       Impact factor: 8.140
  2 in total

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