Investigating Instabilities in the Mammalian Cochlea Using a Stochastic Uncertainty Model

Abstract

We examine the problem of mean-square stability in a dynamical model of the mammalian cochlea with stochastically uncertain parameters. The cochlea is a mechanical spectrum analyzer with an adaptive gain amplification mechanism that gives it a very large dynamic range as an acoustic sensor. This adaptive gain mechanism has been conjectured to be responsible for occasional instabilities that can be clinically significant. We model the cochlea as a spatio-temporal dynamical system made up of a spatially distributed array of coupled oscillators incorporating an adaptive amplification mechanism. We consider settings where the cochlear amplifier has spatially and temporally varying stochastic parameters. It is shown that relatively small parameter variations (few orders of magnitude smaller than the nominal values) are sufficient to destabilize the dynamics and induce spontaneous oscillations. This extreme sensitivity of the cochlear dynamics appears to be due to a combination of the local cochlear amplification mechanism, as well as the spatial coupling of the distributed resonators. The analysis technique used in this work allows for a simulation-free prediction of the stability thresholds and the statistics of the spontaneous oscillations. Theoretical predictions are verified using full nonlinear stochastic simulations that demonstrate a good agreement with the theoretical predictions.