Mathematical Models of the Mechanics of the Cochlea

Author: Neely, Stephen Taylor

Year: 1978

Degree: Engineer's thesis

Advisor: Pierce, John Robinson

Committee Member: Unknown, Unknown

Option: Electrical Engineering

DOI: 10.7907/EP0H-Z652

Abstract

A two-dimensional mathematical model of cochlear mechanics is developed, based on classical assumptions. The basilar membrane is represented by an acoustic admittance function with longitudinal coupling only through the cochlear fluid. The fluid is assumed to be inviscid and incompressible and all motion in the cochlea is assumed to be linear. The integral equations of Allen (1977) and Siebert (1974) are presented for the infinite cochlea and shown to be Fourier transforms of each other. A two-dimensional finite difference scheme based directly on the model equations is shown to be as accurate as Allen's published solutions, and requires only 1/100 the computation time. Numerical solutions are obtained by this direct method for parameters chosen to fit the cochlear map. Traveling-wave solutions are obtained even when the stapes is motionless and the cochlear walls vibrate instead. It is suggested that the initial 9 db/octave slope of the magnitude of the basilar membrane displacement could provide a mechanism for encoding loudness. A new one-dimensional model of the cochlea is proposed which assumes the properties of the basilar membrane to vary slowly along the length of the cochlea. The one-dimensional model provides a link between the two-dimensional model and other one-dimensional, long-wave models.

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