A linearly tapered box model of the cochlea

A box shape with constant area is often used to represent the complex geometry in the cochlea, although variation of the fluid chambers areas is known to be more complicated. This variation is account for here by an "effective area", given by the harmonic mean of upper and lower chamber area from previous measurements. The square root of this effective area varies linearly along the cochleae in the investigated mammalian species. This suggests the use of a linearly tapered box model, in which the fluid chamber width and height are equal, but decrease linearly along its length. The basilar membrane width is assumed to increase linearly along the model. An analytic form of the far-field fluid pressure difference due to basilar membrane motion is derived for this tapered model. The distributions of the passive basilar membrane response are calculated using both the tapered and uniform models and compared with human and mouse measurements. The discrepancy between the models is frequency-dependent and becomes small at low frequencies. The tapered model developed here shows a reasonable fit to experimental measurements, when the cochleae are cadaver or driven at high sound pressure level and provides a convenient way to incorporate cochlear geometrical variations