Quasi-linear modelling of the coupled cochlea using the WKB method

Karlos, Angelis, Vignali, Dario, Lineton, Ben and Elliott, Stephen (2018) Quasi-linear modelling of the coupled cochlea using the WKB method. In To the Ear and Back Again - Advances in Auditory Biophysics: Proceedings of the 13th Mechanics of Hearing Workshop. vol. 1965, American Institute of Physics.. (doi:10.1063/1.5038457).

Abstract

The WKB method provides a convenient way of predicting the coupled response of the linear cochlea, given the distribution of the complex wavenumber along it. With one-dimensional (1D) fluid coupling, the local wavenumber can be calculated from the micromechanical admittance, which can be either passive or active. In practice, the degree of activity at some point along the cochlea will depend on the level of response at this point, due to the nonlinearity of the cochlear amplifier. Quasi-linear models have previously been used, by Kanis and de Boer for example, to estimate the response of a nonlinear cochlear model to single tones or combinations of tones, by iteratively solving for the coupled response and re-evaluating the effective gain of the cochlear amplifier along the length of the cochlea, using the Finite Difference (FD) method. In this paper we consider calculating the coupled response in such a quasi-linear model to single tones using the WKB method, instead of FD, thus gaining an analytical insightful solution. An even simpler quasi-linear model is also explored, in which only a single gain is assumed for the cochlear amplifier along the whole length of the cochlea. It is found that for single tones the coupled response predicted by this simplified quasi-linear model is very similar to that predicted by the quasi-linear model with a distribution of cochlear amplifier gains along the cochlea. The reasons for this similarity are explored and its implications discussed.

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Contributors

Author: Dario Vignali

Author: Ben Lineton

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