Cochlear macromechanics: time domain solutions

In this paper we report on a new method of solving a previous derived, two-dimensional model, integral equation for basilar membrane (BM) motion. The method uses a recursive algorithm for the solution of an initial-value problem in the time domain, combined with a fast Fourier transform (FFT) convolution in the space domain at each time step. Thus, the method capitalizes on the high speed and accuracy of the FFT yet allows the BM to have nonlinear mechanical properties. Using the new method we compute (linear) solutions for various choices of model parameters and compare the results to the experimental measurements of Rhode. [J. Acoust. Soc. Am. 49, 1218-1231 (1971)]. We also demonstrate the effect of including longitudinal stiffness along the BM and conclude that it is useful in matching the high-frequency slope as measured by Rhode.