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

Published electronically:
July 18, 2016

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Abstract | References | Similar Articles | Additional Information

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