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

TL;DR

This work tackles the limitation of 1-D time-domain cochlear TL models in representing 2-D effects that amplify short-wave BM responses. It combines the physics-driven S-2D model with a time-domain V-1D framework by introducing a β gain-correction factor derived from autoregressive filtering, approximated via ridge and RBF-NN regressions and integrated into the V-1D BM admittance as a 32-tap filter. The resulting V^{ star} model partially decouples frequency selectivity from gain, delivering about 5 dB additional peak gain and extending the compressive regime by roughly 10 dB in gerbil-like simulations, while still facing limitations in reproducing human-like sharp tuning and apex behavior. The approach demonstrates a practical path to embedding wavelength-dependent 2-D effects into real-time TL simulations, with implications for translational cochlear modeling in small mammals and for studying nonlinear temporal processing in the auditory periphery.

Abstract

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.

Figures (7)

• Figure 1: Implementation strategy for the setup of the admittance correction.
• Figure 2: Implementation strategy at runtime (when running simulations).
• Figure 3: Characteristic responses of the initial V-1D model.A. BM velocity growth functions with respect to stimulus level at the place with CF=4 kHz (the stimulus is a CF tone). B to D. Frequency responses (magnitudes) of the V-1D model estimated by the BM velocity responses to a slow linear chirp presented at different sound levels. B Frequency response at the CF= 4 kHz place for the gerbil model (in color). Responses for the human model but at CF=5.5 kHz are also shown (in gray). C. Frequency response at the CF=20 kHz place. The color code for sound level is the same as in B. Vibration data from OCT measurements in gerbils He2022 are overlayed with dashed lines. For the experimental data, sound levels are in dB SPL and velocity is relative to motion at the stapes. D. Same as C., but with a model version with sharper tuning. Figures B. to D.: 're:snd level / re:max' indicates that the frequency responses were normalized to the the sound level and to the maximum peak magnitude of each curve set.
• Figure 4: Gain enhancement factor $\beta$ (A. gain and B. phase) for four different values of $G$ (strength of the active process). The target was calculated using the recursive procedure described in Sisto et al. for the S-2D model and the relation $\beta = \alpha/\alpha_0$ where $\alpha_0$ is the pressure focusing factor for $G_{REF}=0.7$ (reference value). The dashed curves correspond to the regressions used to approximate $\beta$ as a recursive all-pole filter. Dash-dotted: first regression (ridge regression). Dashed: second regression (RBF neural network). In the two panels, the vertical line corresponds to the BM characteristic frequency $\omega_{BM}/(2\pi)$.
• Figure 5: BM velocity magnitude normalized to sound level in response to tones for the $V^\star$ model (CF=20 kHz). The sound level goes from 20 to 80 dB in 10 dB steps (same color code as in Fig. \ref{['fig:initial_model']}). The responses for the V-1D model (gray lines) and real vibration data (dashed lines) are reproduced from Fig. \ref{['fig:initial_model']}.