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The Peculiarity of A Nervous Pulse Propagation

Published: 20 February 2013
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Abstract

In the work, transmission of nerve impulses along nerve fibers is simulated. Research is being conducted in the framework of the electrical theory of propagation of the action potential. The soliton approach is used. The numerical experiment on the evolution of the nerve impulse and the laws of motion is conducted. It is shown that the stable form of nerve impulses solitons is realized under different initial conditions. The threshold character of occurrence of nerve pulse is simulated. It is shown that the number of pulses produced changes depending on the degree of nonlinearity: with strong initial excitation of large amplitude soliton is unstable; it breaks up into a multitude number of solitons with small ampli-tudes. In this case, the greater the nonlinearity parameter, the greater the number of births of solitons. Unusual solitonlike regimes of interaction of nonlinear pulses excitations are illustrated; in certain anomalies, colliding nerve impulses are re-flected instead of their usual quenching. The possibility of the decay of the nerve impulse at the bifurcation of the nerve fibers or the appearance of heterogeneity of the passing of a nerve impulse (the presence of dissipation in the environment) is investigated. Physical modeling allows obtaining and studying the analytical results and elucidating the physical prin-ciples of biological processes.

Published in European Journal of Biophysics (Volume 1, Issue 1)
DOI 10.11648/j.ejb.20130101.11
Page(s) 1-5
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2013. Published by Science Publishing Group

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Keywords

Soliton, Nervous Pulse, Nonlinear, Korteweg De Vries Equation

References
[1] T.Heimburg A.D.Jackson. On Soliton propagation in bio-membranes and nerves. Proc.Nat1.Acad.Sci.USA, 102, 9790-9795, 2005.
[2] B.Lautrub, R. Appali, A.D.Jackson and T.Heimburg. The stability of Solitons in biomembranes and nerves.Eur.Phys.J E 34(6) (2011) 1-9.
[3] S.Rowlands. Is the Arterial Pulse a Soliton? J.Biol.Phys.v.10, p.199-200,1982.
[4] A.N. Kolmogorov, I.G.Petrowskij, N.C.Piskunov.Bull.of Moskow State University, 1,N6, 1937. R.A. Fisher. The wave of advance of advantageous genes// Annual Eugenics, 1937, v.7, p.255-369.
[5] Karl Lonngren, Alwyn Scott. Solitons in Action. Proceedings of a Workshop, 1977.
[6] Markin V S, Pastushenko V F, Chizmadzhev Yu A "Physics of the nerve impulse" Sov. Phys. Usp. 20 836–860 (1977)
[7] A.Hodgkin, A.Huxley, J.Physical.(LND), 117, 500, 1952.
[8] R.Appali, S. Petersen and van Rienen.A comparision of A.Hodgkin- A.Huxley and Soliton neural theorives. Adv.Radio Sci, 8,75-79, 2010.
[9] O.V.Aslanidi, O.A.Mornev, (1997), Can the colliding nerve pulses be reflected? Pis’ma Zh.Eksp.Teor.Fiz., 65,No.7, 553-558.
[10] O.V.Aslanidi, O.A.Mornev.Echo in excitable cardias Fi-bers.Mathematical Modelling Journal.v.11, No 9, p.3-22. 1999
[11] G.M.Aldonin. Soliton Models of Processes in Biostructures. Journal of Radio Electronics, N5, November 2006.
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  • APA Style

    Mileta Arakelyan, Hakob Kanoyan. (2013). The Peculiarity of A Nervous Pulse Propagation. European Journal of Biophysics, 1(1), 1-5. https://doi.org/10.11648/j.ejb.20130101.11

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    ACS Style

    Mileta Arakelyan; Hakob Kanoyan. The Peculiarity of A Nervous Pulse Propagation. Eur. J. Biophys. 2013, 1(1), 1-5. doi: 10.11648/j.ejb.20130101.11

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    AMA Style

    Mileta Arakelyan, Hakob Kanoyan. The Peculiarity of A Nervous Pulse Propagation. Eur J Biophys. 2013;1(1):1-5. doi: 10.11648/j.ejb.20130101.11

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  • @article{10.11648/j.ejb.20130101.11,
      author = {Mileta Arakelyan and Hakob Kanoyan},
      title = {The Peculiarity of A Nervous Pulse Propagation},
      journal = {European Journal of Biophysics},
      volume = {1},
      number = {1},
      pages = {1-5},
      doi = {10.11648/j.ejb.20130101.11},
      url = {https://doi.org/10.11648/j.ejb.20130101.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ejb.20130101.11},
      abstract = {In the work, transmission of nerve impulses along nerve fibers is simulated. Research is being conducted in the framework of the electrical theory of propagation of the action potential. The soliton approach is used. The numerical experiment on the evolution of the nerve impulse and the laws of motion is conducted. It is shown that the stable form of nerve impulses solitons is realized under different initial conditions. The threshold character of occurrence of nerve pulse is simulated. It is shown that the number of pulses produced changes depending on the degree of nonlinearity: with strong initial excitation of large amplitude soliton is unstable; it breaks up into a multitude number of solitons with small ampli-tudes. In this case, the greater the nonlinearity parameter, the greater the number of births of solitons. Unusual solitonlike regimes of interaction of nonlinear pulses excitations are illustrated; in certain anomalies, colliding nerve impulses are re-flected instead of their usual quenching. The possibility of the decay of the nerve impulse at the bifurcation of the nerve fibers or the appearance of heterogeneity of the passing of a nerve impulse (the presence of dissipation in the environment) is investigated. Physical modeling allows obtaining and studying the analytical results and elucidating the physical prin-ciples of biological processes.},
     year = {2013}
    }
    

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    AU  - Mileta Arakelyan
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    Y1  - 2013/02/20
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    DO  - 10.11648/j.ejb.20130101.11
    T2  - European Journal of Biophysics
    JF  - European Journal of Biophysics
    JO  - European Journal of Biophysics
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    AB  - In the work, transmission of nerve impulses along nerve fibers is simulated. Research is being conducted in the framework of the electrical theory of propagation of the action potential. The soliton approach is used. The numerical experiment on the evolution of the nerve impulse and the laws of motion is conducted. It is shown that the stable form of nerve impulses solitons is realized under different initial conditions. The threshold character of occurrence of nerve pulse is simulated. It is shown that the number of pulses produced changes depending on the degree of nonlinearity: with strong initial excitation of large amplitude soliton is unstable; it breaks up into a multitude number of solitons with small ampli-tudes. In this case, the greater the nonlinearity parameter, the greater the number of births of solitons. Unusual solitonlike regimes of interaction of nonlinear pulses excitations are illustrated; in certain anomalies, colliding nerve impulses are re-flected instead of their usual quenching. The possibility of the decay of the nerve impulse at the bifurcation of the nerve fibers or the appearance of heterogeneity of the passing of a nerve impulse (the presence of dissipation in the environment) is investigated. Physical modeling allows obtaining and studying the analytical results and elucidating the physical prin-ciples of biological processes.
    VL  - 1
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Author Information
  • Yerevan State University, Dept. of Physics, Yerevan, Armenia

  • Yerevan State University, Dept. of Physics, Yerevan, Armenia

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