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

C. B. Muratov

doi:10.1016/S0006-3495(00)76526-X

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

C. B. Muratov

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

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.

Original language	English (US)
Pages (from-to)	2893-2901
Number of pages	9
Journal	Biophysical Journal
Volume	79
Issue number	6
DOIs	https://doi.org/10.1016/S0006-3495(00)76526-X
State	Published - Dec 2000

All Science Journal Classification (ASJC) codes

Biophysics

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10.1016/S0006-3495(00)76526-X

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title = "A quantitative approximation scheme for the traveling wave solutions in the Hodgkin-Huxley model",

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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N2 - 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.

AB - 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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JO - Biophysical Journal

JF - Biophysical Journal

IS - 6

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

Abstract

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