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On mathematical modelling of solitary pulses in cylindrical biomembranes.

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Title: On mathematical modelling of solitary pulses in cylindrical biomembranes.
Authors: Engelbrecht, Jüri1, Tamm, Kert1, Peets, Tanel1 tanelp@cens.ioc.ee
Source: Biomechanics & Modeling in Mechanobiology. Jan2015, Vol. 14 Issue 1, p159-167. 9p.
Subjects: Biological membranes, Computer simulation, Nerves, Cylinder (Shapes), Microstructure, Solid mechanics
Abstract: The propagation of action potentials in nerve fibres is usually described by models based on the ionic hypotheses. However, this hypothesis does not provide explanation of other experimentally verified phenomena like the swelling of fibres and heat production during the nerve pulse propagation. Heimburg and Jackson (Proc Natl Acad Sci USA 102(28):9790-9795, , Biophys Rev Lett 2:57-78, ) have proposed a model describing the swelling of fibres like a mechanical wave related to changes of longitudinal compressibility of the cylindrical membrane. In this paper, the possible dispersive effects in such microstructured cylinders are analysed from the viewpoint of solid mechanics, particularly using the information from the analysis of the well-known rod models. A more general governing equation is proposed which satisfies the conditions imposed by the physics of wave processes. The numerical simulations demonstrate the influence of nonlinearities, the role of various dispersion terms and the formation and propagation of solitary waves along the wall together with the corresponding transverse displacement. It is conjectured that due to the coupling effects between longitudinal and transverse displacements of a cylinder, the transverse displacement (i.e. swelling) is related to the derivative of the longitudinal displacement. In this way, the correspondence between theoretical and experimental (Tasaki in Physiol Chem Phys Med NMR 20:251-268, ) results can be described. [ABSTRACT FROM AUTHOR]
Copyright of Biomechanics & Modeling in Mechanobiology is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: On mathematical modelling of solitary pulses in cylindrical biomembranes.
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  Data: <searchLink fieldCode="AR" term="%22Engelbrecht%2C+Jüri%22">Engelbrecht, Jüri</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Tamm%2C+Kert%22">Tamm, Kert</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Peets%2C+Tanel%22">Peets, Tanel</searchLink><relatesTo>1</relatesTo><i> tanelp@cens.ioc.ee</i>
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  Data: <searchLink fieldCode="JN" term="%22Biomechanics+%26+Modeling+in+Mechanobiology%22">Biomechanics & Modeling in Mechanobiology</searchLink>. Jan2015, Vol. 14 Issue 1, p159-167. 9p.
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  Data: <searchLink fieldCode="DE" term="%22Biological+membranes%22">Biological membranes</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+simulation%22">Computer simulation</searchLink><br /><searchLink fieldCode="DE" term="%22Nerves%22">Nerves</searchLink><br /><searchLink fieldCode="DE" term="%22Cylinder+%28Shapes%29%22">Cylinder (Shapes)</searchLink><br /><searchLink fieldCode="DE" term="%22Microstructure%22">Microstructure</searchLink><br /><searchLink fieldCode="DE" term="%22Solid+mechanics%22">Solid mechanics</searchLink>
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  Data: The propagation of action potentials in nerve fibres is usually described by models based on the ionic hypotheses. However, this hypothesis does not provide explanation of other experimentally verified phenomena like the swelling of fibres and heat production during the nerve pulse propagation. Heimburg and Jackson (Proc Natl Acad Sci USA 102(28):9790-9795, , Biophys Rev Lett 2:57-78, ) have proposed a model describing the swelling of fibres like a mechanical wave related to changes of longitudinal compressibility of the cylindrical membrane. In this paper, the possible dispersive effects in such microstructured cylinders are analysed from the viewpoint of solid mechanics, particularly using the information from the analysis of the well-known rod models. A more general governing equation is proposed which satisfies the conditions imposed by the physics of wave processes. The numerical simulations demonstrate the influence of nonlinearities, the role of various dispersion terms and the formation and propagation of solitary waves along the wall together with the corresponding transverse displacement. It is conjectured that due to the coupling effects between longitudinal and transverse displacements of a cylinder, the transverse displacement (i.e. swelling) is related to the derivative of the longitudinal displacement. In this way, the correspondence between theoretical and experimental (Tasaki in Physiol Chem Phys Med NMR 20:251-268, ) results can be described. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
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  Data: <i>Copyright of Biomechanics & Modeling in Mechanobiology is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – SubjectFull: Nerves
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              Text: Jan2015
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