Short-wave admittance correction for a time-domain cochlear transmission line model

Transmission line (TL) models implemented in the time domain can efficiently simulate basilar-membrane (BM) displacement in response to transient or non-stationary sounds. By design, a TL model is well-suited for an one-dimensional (1-D) characterization of the traveling wave, but the real configuration of the cochlea also introduces higher-dimensional effects. Such effects include the focusing of the pressure around the BM and transverse viscous damping, both of which are magnified in the short-wave region. The two effects depend on the wavelength and are more readily expressed in the frequency domain. In this paper, we introduce a numerical correction for the BM admittance to account for 2-D effects in the time domain using autoregressive filtering and regression techniques. The correction was required for the implementation of a TL model tailored to the gerbil cochlear physiology. The model, which includes instantaneous nonlinearities in the form of variable damping, initially presented insufficient compression with increasing sound levels. This limitation was explained by the strong coupling between gain and frequency selectivity assumed in the 1-D nonlinear TL model, whereas cochlear frequency selectivity shows only a moderate dependence on sound level in small mammals. The correction factor was implemented in the gerbil model and made level-dependent using a feedback loop. The updated model achieved some decoupling between frequency selectivity and gain, providing 5 dB of additional gain and extending the range of sound levels of the compressive regime by 10 dB. We discuss the relevance of this work through two key features: the integration of both analytical and regression methods for characterizing BM admittance, and the combination of instantaneous and non-instantaneous nonlinearities.