Semirealistic models of the cochlea

Abstract

The aim of this paper is the introduction and comparison of consistent albeit passive mechanical models for the whole cochlea. A widely used transmission line filterbank, which hydrodynamically speaking is a long wave approximation (L model), suffers from a well-known inconsistency: its main modeling assumption is not valid within the resonance region, where most of the overall excitation takes place. In the present paper two approaches to overcome this inconsistency are discussed. One model is the average pressure (AP) model by Duifhuis, the other is obtained by a combination of a long and a short wave approximation (LS model). Considerable differences between the L and the LS model are observed. All models are compared by inserting them into the full integral equation obtained from the hydrodynamic equations and the boundary conditions. Here the LS model fares better than the AP model for small damping, whereas the opposite is true for higher damping. As expected, the L model fails badly in the resonance region.

Leibniz, Husserl, and the Brain

“…The physiological processes corresponding to the buildup of pitch can be described by means of mechanistic models of the inner ear (see, for example, Sieroka et al 2006). Since the basilar membrane varies in stiffness, each point of the cochlea is particularly sensitive to a different frequency, and the site-specific excitement then gets converted into an excitation of specific nerves connected to that site.…”

A two-dimensional cochlear fluid model based on conformal mapping

“…Both assumptions fail either near the resonance region or far away from it. 10 All these approximative theories have been reviewed by Wever 12 and, more recently, by Sieroka who additionally discusses a composition of the long-and short-wave approximation. 10 Beyond the above approximations there are attempts to solve cochlea partition motion equations in a stricter manner for different dimensions.…”

“…Besides practical efforts 1,2 to understanding cochlear mechanics, there are several mathematical approaches. [3][4][5][6][7][8][9][10][11] Not only are the mechanical properties of the cochlear partition the ones that need to be captured but also its intricate interaction with the fluids in which it is immersed. This makes the task a mathematically delicate one.…”

Auditory Information Processing

“…the place of maximal displacement of the cochlear partition, or far away from it [13]. All these approximative theories have been reviewed by Wever [15] and, more recently, by Sireoka, who additionally discusses a composition of the long-and short-wave approximation [13].…”

“…There were plenty of models put forward [6,7,8,9,10,11,12,13,14], many of which utilize the long-wave approximation [11] and short-wave approximation [10,12]. These theories assume the local wave length of the cochlear partition to be long or short, respectively, as compared to the duct's (scala vesibuli and ductus cochlearis together) height.…”