Modelling the hydrodynamic behaviour of the cochlea: is the stiffness of the Reissner's membrane important for frequency selectivity?

The cochlea contains two membranes, the Reissner's membrane and the Basilar membrane. In most models of the cochlea only the Basilar membrane is considered. The displacement of the Basilar membrane is crucial for stimulating the sensory cells within the cochlea. The omission of the Reissner's membrane is often justified because it is believed to be floppy, and it makes the calculation of the travelling wave on the Basilar membrane analytically possible. In the present work we have looked into the influence of the stiffness of the Reissner's membrane on the frequency selectivity of the Basilar membrane with a finite-volume model of the cochlea. Simulations are performed with a logarithmic distribution of the Basilar membrane stiffness. Each segment of the Basilar membrane oscillates with an increasing amplitude for a different frequency of the stimulus (the local resonance frequency) and shows the expected frequency selectivity. Our simulations indicate that the local resonance frequency does not change with the stiffness of the Reissner's membrane as long as the sum of the stiffness of the Basilar membrane and the Reissner's membrane remains the same. Consequently, the division of stiffness over both membranes has no impact on the frequency selectivity of the Basilar membrane.