A tapered box model of the cochlea

Abstract

The complicated, three dimensional geometry of the fluid chambers in the cochlea is often represented in models of its mechanics by a box with a uniform area along its length. In this paper we use previous measurements of the variation in area of the two fluid chambers along the length of the cochlea in various mammals, to calculate the variation in the “effective area” that determines the 1D fluid coupling, which is given by the harmonic mean of the two chamber areas. The square root of this effective area is found to vary surprisingly linearly along the cochlea length in several mammalian species. This suggests a variation of the box model in which the width and height of the two fluid chambers are still equal, but now decrease linearly along its length. The width of the basilar membrane, BM, is assumed to increase linearly along the length of the model. The analytic form of the 1D fluid pressure distribution due to elemental BM motion is derived for this tapered box model. The added mass due to the near field acoustic coupling can also be computed, which surprisingly turns out to be almost constant along the length of the BM. The coupled response of the box model with a passive BM can then be readily calculated. Although the pressure distributions due to elemental fluid coupling are very different in the uniform and tapered box models, the distribution of the passive BM response in the coupled models are very similar in the two cases, although the overall level of the response in the tapered model is about 10 dB greater than that in the uniform model

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ORCID for Guangjian Ni: orcid.org/0000-0002-9240-3020

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