Reduced equations for an active model of the hydroelastic waves in the cochlea

TL;DR

This paper develops a reduced mathematical model of the cochlea incorporating active mechanisms, simplifying complex PDE systems to ODEs, and demonstrates its ability to amplify multi-frequency signals through numerical simulations.

Contribution

It introduces a novel active cochlear model with a rigorous dimension reduction from PDEs to ODEs, enabling efficient analysis of signal amplification.

Findings

Reduced model accurately captures active amplification

Model distinguishes multiple input frequencies

Numerical simulations validate the model's effectiveness

Abstract

Building upon our earlier passive models for the cochlea, here we enhance the model with an active mechanism. Starting with a one-chamber simplification leading to a system of a time-dependent PDE in two spatial variables for the pressure coupled to a PDE in one spatial variable for the oscillation of the basilar membrane, we rigorously establish the validity of a dimension reduction to a system to two ODE's. We then present numerical simulations demonstrating the ability of this reduced active system to distinguish and amplify multi-frequency input signals.