Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Reduced equations for the hydroelastic waves in the cochlea: The spring model

Authors: Lydia Peres Hari, Jacob Rubinstein and Peter Sternberg
Journal: Quart. Appl. Math. 74 (2016), 647-670
MSC (2010): Primary 92C10
DOI: https://doi.org/10.1090/qam/1443
Published electronically: July 18, 2016
MathSciNet review: 3539027
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Abstract: Hydroelastic waves in the cochlea are studied through modeling a passive basilar membrane as an elastic spring. A rigorous reduction of the three-dimensional equations for the fluid pressure and deflection of the basilar membrane to a one-
dimensional ordinary differential equation for the pressure jump across the membrane is derived. The one-dimensional reduced model is then critically examined and limits on its validity are discussed. An approximate solution of the reduced equations is in agreement with the experimental Greenwood formula for a proper selection of elastic parameters. The model is used to compute the effect of cochlear implants on the Place Principle governing the spectral decomposition of sound by the cochlea. Numerics are also carried out to see the effect of a cochlear implant on the mechanical response of the cochlea.

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Additional Information

Lydia Peres Hari
Affiliation: Department of Mathematics, Israel Institute of Technology, Haifa 32000, Israel
Email: lydia@fermat.technion.ac.il

Jacob Rubinstein
Affiliation: Department of Mathematics, Israel Institute of Technology, Haifa 32000, Israel
Email: koby@tx.technion.ac.il

Peter Sternberg
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: sternber@indiana.edu

DOI: https://doi.org/10.1090/qam/1443
Received by editor(s): December 18, 2015
Published electronically: July 18, 2016
Article copyright: © Copyright 2016 Brown University

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