A linearly tapered box model of the cochlea

Abstract

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 accounted 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 (BM) width is assumed to increase linearly along the model. An analytic form of the far-field fluid pressure difference due to BM motion is derived for this tapered model. The distributions of the passive BM 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.

An elemental approach to modelling the mechanics of the cochlea

“…The coupled BM responses are also shown in Fig. 3 , for comparison, when both area non-uniformity, assumed to be linearly tapered ( Ni et al., 2017 ), and 3D fluid dynamics are considered. The linear variation in the physical dimensions of the fluid chambers along the length of the cochlea is based on Thorne et al.…”

“…4 The pressure distribution along a uniform (grey lines) and non-uniform (black lines) cochlea due to excitation by the vibration of a single BM element, at x 0 in the case of 1D fluid coupling (dashed) and 3D fluid coupling (solid). In this example, the human cochlear geometrical data for the non-uniform model is the same as that used in Ni et al. (2017) .…”

“…It has been assumed above that the two fluid chambers have a uniform area along the length. This restriction can be removed by modifying equation (10) with incorporation of geometrical variations of the scala cross-sectional area, A ( x ), and the BM and cochlear partition width, B ( x ) and W ( x ) respectively ( Ni et al., 2017 ). Generalised solutions to the 1D fluid dynamics in a tapered cochlear model have been proposed and discussed by Shera et al.…”

“…Generalised solutions to the 1D fluid dynamics in a tapered cochlear model have been proposed and discussed by Shera et al. (2004) using the Green's functions and by Ni et al. (2017) using the elemental method.…”

“…If only a single BM element is excited by a velocity of v 0 , from x 0 − Δ to x 0 and zero elsewhere, and assuming the pressure difference cross the BM is zero at x = L, account for the helicotrema, the 1D, far-field, fluid dynamics can be given as where is dummy integration variable, A e ( x ) is the effective area, given by the harmonic mean of the upper and lower areas of the fluid chambers. It should be noted that equation (30) is for the pressure distribution basal to the excitation point and equation (31) is for the pressure distribution from the excitation point to the apex, as derived with more details in Ni et al. (2017) .…”