Solving cochlear mechanics problems with higher-order differential equations.

Abstract

Since most "exact" solution methods for cochlear models are rather unwieldy, they do not lend themselves to easy and multi-purpose application. In this paper a new solution method is described that is more flexible in this respect. A three-dimensional cochlear model is considered. It can be described by an integral equation in terms of the wavenumber k. The kernel Q (k) of that equation is approximated by a rational function of k and this makes it possible to reformulate the problem as a differential equation. The latter can be solved by a straightforward and well-known method. Results of computations with this technique are presented in two forms: an overview of the entire cochlear wave pattern and a detailed representation of the response peak. The method is also used to determine whether a discernible reflected wave is produced in the cochlea or not. For this purpose the wavenumber spectrum of the cochlear wave is studied: it is found to be a one-sided function of k. With surprisingly simple means it is thus shown that no appreciable reflection occurs from the inhomogeneity that is characteristic in cochlear wave propagation. This holds true for values of damping constant delta as low as 0.01, a factor of 5 smaller than is commonly used in cochlear modeling.