A tapered box model of the cochlea

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 nea...