Different models of the active cochlea, and how to implement them in the state-space formalism

Abstract

The state-space formalism [Elliott S. J., et al. (2007). J. Acoust. Soc. Am. 122, 2759-2771] allows one to discretize cochlear models in a straightforward matrix form and to modify the main physical properties of the cochlear model by changing the position and functional form of a few matrix elements. Feed-forward and feed-backward properties can be obtained by simply introducing off-diagonal terms in the matrixes expressing the coupling between the dynamical variables and the additional active pressure on the basilar membrane. Some theoretical issues related to different cochlear modeling choices, their implementation in a state-space scheme, and their physical consequences on the cochlear phenomenology, as predicted by numerical simulations, are discussed. Different schematizations of the active term describing the behavior of the outer hair cell's feedback mechanism, including nonlinear and nonlocal dependences on either pressure or basilar membrane displacement, are also discussed, showing their effect on some measurable cochlear properties.

Distortion products and backward-traveling waves in nonlinear active models of the cochlea

“…We considered two different models: an anti-damping diagonal model and a spatial feed-forward model. The response to pure-tone stimulation of these two models has already been discussed in detail in Sisto et al (2010).…”

“…The discretized model, its numerical properties and integration strategies are discussed in Bertaccini and Sisto (2011). The parameter values necessary to reproduce our results are given in Sisto et al (2010).…”

“…More details on the state-space formalism used in this solution scheme can be found in previous studies (Moleti et al, 2009;Sisto et al, 2010). The key feature, and most delicate part of the solution method, is the schematization of the nonlinear and the nonlocal active feedback mechanism mediated by the OHCs.…”

“…We refer here to a 1-D nonlinear nonlocal active cochlear model that has been extensively described in Moleti et al (2009) and in Sisto et al (2010), based on the state-space formalism, following and slightly modifying the state-space scheme proposed by Elliott et al (2007). The discretized model, its numerical properties and integration strategies are discussed in Bertaccini and Sisto (2011).…”

“…As regards the functional dependence of the cochlear amplifier gain on the BM displacement level, we have chosen a "universal" gain function (see Sisto et al, 2010 for more details) that can be tuned (using two parameters only, the active gain coefficient a 0 and the displacement threshold for nonlinear saturation of the active amplifier n s ) to approximately match the behavior experimentally observed in mammals, which is characterized by constant gain at both low and high BM displacements and a compressive regime at intermediate levels (Nobili and Mammano, 1996). At low BM displacement levels, an approximately cubic distortion term is present, similar to that of Eq.…”