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

Abstract

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.