Point-impedance characterization of the basilar membrane in a three-dimensional cochlea model.

In this paper we derive which impedance definition appropriately represents the basilar membrane in a simple three-dimensional model (de Boer's 'block model') of the cochlea. The starting point of our considerations is a system of parallel visco-elastic beams as characterization of the basilar membrane. It is possible to transform this representation into an impedance concept by observing that the membrane velocity is to a very good approximation distributed over the width as a centred half cosine function, independent of the pressure distribution. The ensuing impedance definition is more accurate than the one proposed by de Boer (Hearing Res. 4, 53-77, 1981). The improvement to the model solutions is moderate, however, as appears from numerical calculations of the basilar membrane velocity.