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Zh. Vychisl. Mat. Mat. Fiz., 2009, Volume 49, Number 9, Pages 1708–1723 (Mi zvmmf4762)  

This article is cited in 2 scientific papers (total in 2 papers)

A hydrodynamic model of human cochlea

V. P. Varin, A. G. Petrov

Institute of Applied Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, Moscow, 117526, Russia

Abstract: A two-compartment model of the human cochlea is proposed. When stretched out, the bony spiral tube looks like two chambers separated by a membrane. Both chambers are filled with viscous fluid called perilymph; they communicate with one another via a canal. Sound vibrations enter the cochlea through the oval window and cause periodic change of pressure in the perilymph, which, in turn, causes the membrane to vibrate. The motion of the fluid is described by hydrodynamic equations, which are supplemented with the membrane vibration equation. The equations are linearized in the amplitude of the vibrations, and their solution is sought in the form of Fourier harmonics with a given frequency. To determine the harmonics, a system of linear boundary value problems for ordinary differential equations with variable coefficients is obtained. The numerical solution of this system using finite difference method fails because it involves a large parameter and the problem is close to a singular one. We propose a novel numerical method without saturation that enables us to obtain solutions in a wide range of frequencies up to an arbitrary and controllable accuracy. The computations confirm the Bekesy theory stating that high-frequency sounds cause the membrane to bend near the apex of the cochlea, and low-frequency sounds cause it to bend near the base of the cochlea.

Key words: basilar membrane, cochlea, perilymph, endolymph, vibrations, frequency, Chebyshev polynomials, linear boundary value problems, system of ordinary differential equations, variable coefficients, numerical method without saturation.

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English version:
Computational Mathematics and Mathematical Physics, 2009, 49:9, 1632–1647

Bibliographic databases:

UDC: 519.634
Received: 23.12.2008

Citation: V. P. Varin, A. G. Petrov, “A hydrodynamic model of human cochlea”, Zh. Vychisl. Mat. Mat. Fiz., 49:9 (2009), 1708–1723; Comput. Math. Math. Phys., 49:9 (2009), 1632–1647

Citation in format AMSBIB
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\by V.~P.~Varin, A.~G.~Petrov
\paper A~hydrodynamic model of human cochlea
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2009
\vol 49
\issue 9
\pages 1708--1723
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\zmath{https://zbmath.org/?q=an:1177.74285}
\transl
\jour Comput. Math. Math. Phys.
\yr 2009
\vol 49
\issue 9
\pages 1632--1647
\crossref{https://doi.org/10.1134/S0965542509090176}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-70350126163}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. De Paolis A., Watanabe H., Nelson J.T., Bikson M., Packer M., Cardoso L., “Human cochlear hydrodynamics: A high-resolution CT-based finite element study”, J. Biomech., 50:SI (2017), 209–216  crossref  isi  scopus
    2. De Paolis A., Bikson M., Nelson J.T., de Ru J.A., Packer M., Cardoso L., “Analytical and Numerical Modeling of the Hearing System: Advances Towards the Assessment of Hearing Damage”, Hear. Res., 349:SI (2017), 111–128  crossref  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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