Otoacoustic emissions in time-domain solutions of nonlinear non-local cochlear models

Abstract

A nonlinear and non-local cochlear model has been efficiently solved in the time domain numerically, obtaining the evolution of the transverse displacement of the basilar membrane at each cochlear place. This information allows one to follow the forward and backward propagation of the traveling wave along the basilar membrane, and to evaluate the otoacoustic response from the time evolution of the stapes displacement. The phase/frequency relation of the response can be predicted, as well as the physical delay associated with the response onset time, to evaluate the relation between different cochlear characteristic times as a function of the stimulus level and of the physical parameters of the model. For a nonlinear cochlea, simplistic frequency-domain interpretations of the otoacoustic response phase behavior may give inconsistent results. Time-domain numerical solutions of the underlying nonlinear and non-local full cochlear model using a large number (thousands) of partitions in space and an adaptive mesh in time are rather time and memory consuming. Therefore, in order to be able to use standard personal computers for simulations reliably, the discretized model has been carefully designed to enforce sparsity of the matrices using a multi-iterative approach. Preliminary results concerning the cochlear characteristic delays are also presented.

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

“…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).…”

“…On the other hand, for a large number of discrete elements, timedomain solutions can be computationally expensive. The optimized numerical solution scheme used in this study (Moleti et al, 2009;Bertaccini and Sisto, 2011) permits accurate and reasonably fast solutions. We compare the predictions of a spatial feed-forward nonlinear and nonlocal cochlear model with those of "diagonal" models, as regards the DP phase behavior at a fixed BM, as a function of the stimulus frequency.…”

On the dependence of the BM gain and phase on the stimulus level

“…The matrices B E , C E , and D E are projection operators, defined in [1]. F is the discretized Laplace operator, S(t) represents a stimulus term applied to the stapes, the matrix A E is the system matrix containing the dynamics of the single tonotopic oscillator.…”

“…A fully nonlinear non-local model was used, which is described in detail in [1]. The cochlea is schematized by a box-model, with a tonotopic basilar membrane (BM) separating two volumes filled by a homogeneous incompressible fluid.…”

“…The BM excitation profile in the case of a single tone stimulus at f = 2 kHz was numerically calculated used the fully nonlinear model [1], with a nonlinear coupling = 0.999 and a passive tuning factor Q = 6. The stimulus level was changed from 0 dB to 90 dB in 10 dB steps.…”