Digital solution of cochlear mechanics problems.
Several advantages are incurred when the greater part of the solution to a cochlear mechanics problem is carried out with an analytical method. Many cochlear mechanics problems can be formulated in such a way that they require solution of a specific integral equation in terms of the Fourier transform W(k) of the BM velocity w(x). An analytical solution for W(k) is possible for a certain class of impedance functions. In this paper it is shown how the Fourier transformation to the x domain can be carried out without producing aliasing errors. The impedance function Z(x) must be made periodic in x. For a particular choice of this function, one which puts the main emphasis on BM resonance, the solution to the integral equation can be found from a simple recurrence relation between the spectral components Wn of w(x). The method is illustrated for typical one-, two-, and three-dimensional cochlea models. It is proven that in the region of resonance for (nondigital) solution method published earlier produces nearly equivalent results. The digital method has a much wider scope of application.
D001696:Biomechanical Phenomena; D003051:Cochlea / Q000502:physiology*; D005583:Fourier Analysis; D008433:Mathematics; D008722:Methods; D008954:Models, Biological