Fast numerical solution of nonlinear nonlocal cochlear models

Self Cite

This study explores the phenomenology of distortion products in nonlinear cochlear models, predicting their amplitude and phase along the basilar membrane. The existence of a backward-traveling wave at the distortion-product frequency, which has been recently questioned by experiments measuring the phase of basilar-membrane vibration, is discussed. The effect of different modeling choices is analyzed, including feed-forward asymmetry, micromechanical roughness, and breaking of scaling symmetry. The experimentally observed negative slope of basilar-membrane phase is predicted by numerical simulations of nonlinear cochlear models under a wide range of parameters and modeling choices. In active models, positive phase slopes are predicted by the quasi-linear analytical computations and by the fully nonlinear numerical simulations only if the distortionproduct sources are localized apical to the observation point and if the stapes reflectivity is unrealistically small. The results of this study predict a negative phase slope whenever the source is distributed over a reasonably wide cochlear region and/or a reasonably high stapes reflectivity is assumed. Therefore, the above-mentioned experiments do not contradict "classical" models of cochlear mechanics and of distortion-product generation.

Section: The Discretized Model and Its Numerical Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Sisto

Moleti

Botti

et al. 2011

Self Cite

“…The state space model, i.e., the formulation of the cochlear dynamics through a set of coupled, first-order differential equations, can be applied to a large family of cochlear models (Elliott et al, 2007), and it has been used by Bertaccini and Sisto (2011) in conjunction with a hybrid solver for fast numerical simulations. The connection between the method proposed by Diependaal et al (1987) and the state space model has recently been discussed by Rapson et al (2012).…”

Section: Introductionmentioning

confidence: 99%

Transmission line cochlear models: Improved accuracy and efficiency

Altoè

Pulkki

Verhulst

2014

This paper presents an efficient method to compute the numerical solutions of transmission-line (TL) cochlear models, and its application on the model of Verhulst et al. The stability region of the model is extended by adopting a variable step numerical method to solve the system of ordinary differential equations that describes it, and by adopting an adaptive scheme to take in account variations in the system status within each numerical step. The presented method leads to improve simulations numerical accuracy and large computational savings, leading to employ TL models for more extensive simulations than currently possible.

“…The MSS method, in turn, has been developed further by Bertaccini and Sisto (2011). A major benefit of this approach is that it allows the eigenvalues (which show stability) of a linear cochlear model to be computed easily.…”

Section: Introductionmentioning

confidence: 99%

“…Ultimately, however, our aim is not to argue that any of the three approaches discussed is superior, but to note their specific strengths and weaknesses. We derive an identity that not only allows the differences between the methods to be summarized, but also offers insight into the numerical stiffness problems mentioned in Sisto et al (2010) and Bertaccini and Sisto (2011). Since the MSS method is a relative newcomer to cochlear modeling, we believe that describing its relationship to the established approach will assist users of cochlear models to understand their options.…”

Section: Introductionmentioning

confidence: 99%

Unification and extension of monolithic state space and iterative cochlear models

Rapson

Tapson

Karpul

2012

Time domain cochlear models have primarily followed a method introduced by Allen and Sondhi [J. Acoust. Soc. Am. 66, 123-132 (1979)]. Recently the "state space formalism" proposed by Elliott et al. [J. Acoust. Soc. Am. 122, 2759-2771 (2007)] has been used to simulate a wide range of nonlinear cochlear models. It used a one-dimensional approach that is extended to two dimensions in this paper, using the finite element method. The recently developed "state space formalism" in fact shares a close relationship to the earlier approach. Working from Diependaal et al. [J. Acoust. Soc. Am. 82, 1655-1666 (1987)] the two approaches are compared and the relationship formalized. Understanding this relationship allows models to be converted from one to the other in order to utilize each of their strengths. A second method to derive the state space matrices required for the "state space formalism" is also presented. This method offers improved numerical properties because it uses the information available about the model more effectively. Numerical results support the claims regarding fluid dimension and the underlying similarity of the two approaches. Finally, the recent advances in the state space formalism [Bertaccini and Sisto, J. Comp. Phys. 230, 2575-2587 (2011)] are discussed in terms of this relationship.