On the adequacy of the Peterson-Bogert model and on the effects of viscosity in cochlear dynamics

Viergever, Max A.; Kalker, J. J.

doi:10.1007/bf02353617

Cited by 10 publications

(6 citation statements)

References 9 publications

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“…Strength of hydrodynamic coupling of partition number k acting on partition number j is described by the integration kernel D K C jk in Eq. (22). The solid graphs display D K C jk for different k (50, 100, 150, 200, and 250) depending on the cochlear partition number j, the position.…”

Section: Numericsmentioning

confidence: 99%

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A two-dimensional cochlear fluid model based on conformal mapping

Lüling

Franosch

Hemmen

2010

The Journal of the Acoustical Society of America

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Using conformal mapping, fluid motion inside the cochlear duct is derived from fluid motion in an infinite half plane. The cochlear duct is represented by a two-dimensional half-open box. Motion of the cochlear fluid creates a force acting on the cochlear partition, modeled by damped oscillators. The resulting equation is one-dimensional, more realistic, and can be handled more easily than existing ones derived by the method of images, making it useful for fast computations of physically plausible cochlear responses. Solving the equation of motion numerically, its ability to reproduce the essential features of cochlear partition motion is demonstrated. Because fluid coupling can be changed independently of any other physical parameter in this model, it allows the significance of hydrodynamic coupling of the cochlear partition to itself to be quantitatively studied. For the model parameters chosen, as hydrodynamic coupling is increased, the simple resonant frequency response becomes increasingly asymmetric. The stronger the hydrodynamic coupling is, the slower the velocity of the resulting traveling wave at the low frequency side is. The model's simplicity and straightforward mathematics make it useful for evaluating more complicated models and for education in hydrodynamics and biophysics of hearing.

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Section: Numericsmentioning

confidence: 99%

“…(3) is negligible. 22,23 Taking the divergence on both sides of Eq. (4) and using the incompressibility condition div t ¼ 0 we get the Laplace equation…”

Section: Theorymentioning

confidence: 99%

A two-dimensional cochlear fluid model based on conformal mapping

Lüling

Franosch

Hemmen

2010

The Journal of the Acoustical Society of America

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“…The second term v 2 in equation (2.3) is negligible [25,26] compared to the first term. Taking the divergence on both sides of equation (2.4) and using the incompressibility condition div v = 0, one obtains the Laplace equation…”

Section: A Novel Box Modelmentioning

confidence: 99%

Auditory Information Processing

Shi¹

2012

Intelligence Science

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“…From (70) it is seen that B D 0 so that the two conditions in (71) suffice to determine the remaining two constants.…”

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confidence: 96%

“…3 (65) E4xao I (x to find the resulting centerline deflection. For boundary conditions we have at the origin (70) ao(0) 0, a condition which stems from the first part of (59). At the apical end, where x L, the situation is quite complex, and three kinds of end supportshinged end, free end, and elastic endare investigated in the next section.…”

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confidence: 99%

Cochlear Dynamics: The Evolution of a Mathematical Model

Inselberg¹

1978

SIAM Rev.

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The evolution of a mathematical model designed to clarify the relationship between the structure and the function of the cochlea (inner ear) is traced. Starting from physical (rather than empirical) considerations, the mathematical description of each model is derived in terms of well-defined physical properties of the cochlea. Initially, the basilar membrane is modeled as a uniform simply supported beam vibrating in a viscous medium, and driven by a concentrated oscillating moment at the basal end. In such a system traveling and standing waves (transients) occur simultaneously. An analysis of the traveling waves reveals a place principle. The model has high and low frequency "thresholds" (i.e., at very high and very low frequencies, frequency discrimination diminishes). The model suggests that the fluid properties play a particularly important role at high frequencies, while the role of cochlear geometry becomes dominant at low frequencies. In the second stage, the beam is enclosed in a rectangular "cochlea" divided into two equal chambers and filled with viscous and incompressible fluid (the perilymph) communicating through a small opening at one end (the helicotrema). At the opposite end, the system is driven by a piston-like periodic forcing (i.e., the movement of the stapes in the middle ear). It is assumed that the oscillations of the basilar membrane have long wavelengthmcompared with the cochlear chamber heightmand that a thin unsteady boundary layer forms on all surfaces within the cochlea. In general, the results confirm and improve the results of the previous model. The place principle exhibited by this model corresponds well with experimental data at higher frequencies, but not at low frequencies. For good low frequency response, the model must be endowed with much of the cochlea's intricate geometry. This is done in the third model where the basilar membrane is represented by a wedge-shaped isotropic plate of constant thickness and enclosed by an arbitrary surface of revolution representing the cochlear shell. The plate is simply supported along its long edges while three different boundary conditions are considered for the support at the helicotrema. So as to emulate the presence of the cochlear duct (third cochlear chamber), a pressure difference in the fluid at the helicotrema is included. As in the second model, the cochlear fluids are taken to be viscous and incompressible, and the system is driven by periodic forcing at one end. The solution of the equations of motion as the input frequency tends to zero is obtained. The role of the basilar membrane taper, as well as cochlear cross-section's opposing taper, is delimited. The third chamber (cochlear duct) must be included in the model in order to utilize the full length of the basilar membrane for frequency discrimination. Consequently, the boundary conditions of the basilar membrane at the helicotrema can be analyzed, and it is shown that an elastic support (representing a "ligament") is required at the helicotrema.

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On the adequacy of the Peterson-Bogert model and on the effects of viscosity in cochlear dynamics

Cited by 10 publications

References 9 publications

A two-dimensional cochlear fluid model based on conformal mapping

A two-dimensional cochlear fluid model based on conformal mapping

Auditory Information Processing

Cochlear Dynamics: The Evolution of a Mathematical Model

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