Vol. 2, No. 8, 2007

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Frequency and spatial response of basilar membrane vibration in a three-dimensional gerbil cochlear model

Yongjin Yoon, Sunil Puria and Charles R. Steele

Vol. 2 (2007), No. 8, 1449–1458

The cochlea of the inner ear presents severe difficulties for measurement and computation, and controversy exists on virtually every issue. However, the first in vivo measurement of the spatial distribution of elastic response for a fixed frequency is now available. This work compares experimental results and those from calculations with a three-dimensional model. This is a standard model that consists of a long, fluid-filled box with a partition, a portion of which is the elastic BM (basilar membrane). The BM velocity at a fixed point as a function of frequency and the spatial response for a fixed frequency are calculated. The model includes the three-dimensional viscous fluid and the pectinate zone of the elastic orthotropic BM with the gerbil dimensional and material property variation along its length. The radial BM thickness variation is, however, replaced by an equivalent constant thickness. The active process is represented by adding the motility of the OHCs (outer hair cells) to the passive model with a feed-forward approximation of the organ of Corti (OC). Asymptotic and numerical methods combined with Fourier series expansions are used to provide a fast and efficient iterative procedure that requires about one second on a desktop computer for obtaining the BM response for a given frequency. Our three-dimensional model results show the following agreement with the experimental measurements in various situations: (i) for map of place of maximum response to frequency — excellent; (ii) for the response at a fixed point as a function of frequency — excellent for amplitude, poor for phase; (iii) for the spatial distribution for fixed frequency — fair for amplitude and excellent for phase. The discrepancies in (ii) and (iii) remain to be clarified.

cochlear model, mechanical response, basilar membrane velocity, outer hair cell, gerbil
Received: 20 July 2006
Revised: 17 April 2007
Accepted: 20 April 2007
Published: 1 October 2007
Yongjin Yoon
Mechanics and Computation Division
Stanford University
496 Lomita Mall
Durand Building
Stanford, CA 94305-4035
United States
Sunil Puria
Department of Otolaryngology—Head and Neck Surgery
Stanford University
Stanford, CA 94305
United States
Charles R. Steele
Mechanics and Computation Division
Stanford University
496 Lomita Mall
Durand Building
Stanford, CA 94305-4035
United States