Toward Three-Dimensional Analysis of Cochlear Structure

Abstract

Recent results from a three-dimensional model of the cochlea are summarized. The features include physically realistic values of basilar membrane stiffness, mass, and fluid viscosity. The simple ‘feed-forward’ principle for the active process yields results in qualitative agreement with recent mesurements in the cochlea. The limitation is a simplified representation of the organ of Corti, with two degrees of freedom representing the motion of the pectinate and arcuate zones of the basilar membrane. However, the inner sulcus fluid flow is included. The new feature presented in this paper is an approach to treat all the structural detail of the organ of Corti, with the sole input to the calculation in a form easily understood by anyone familiar with the cochlea. Specific results are shown for the Pakistani water buffalo, since a fairly complete anatomical description of this cochlea is available. The static stiffness from the calculation, based on only the anatomy and known values for the protein elastic moduli, are in remarkable agreement with recent measurements in the gerbil cochlea. Only preliminary results for the dynamic response with inviscid fluid are reported. Of interest, however, are the propagation modes related to significant fluid displacement and pressure in the different compartments of the organ of Corti.

A wave finite element analysis of the passive cochlea

“…The results of the full finite element model are thus in reasonable agreement with those predicted using only the slow wave up to about x=22 mm. The less rapid fall off in the results of the full finite element model just apical of the peak, compared those using the WKB method, has also been noted by Steele andTaber (1979), de Boer andViergever (1982) and Watts (2000), as discussed above.…”

“…(29), and so  m , and the corresponding distribution of pressures and fluid displacements, must be an eigenvalue, and the corresponding eigenvector, of the transfer matrix for this segment. Using the wave finite element method, the wavenumbers are thus obtained directly from the eigenvalues of the transfer matrix for the 3D finite element model of the segment, rather than eigenvalue problem for a finite element model of a 2D slice of the cochlea being used to deduce a polynomial dispersion equation, which then has to be solved to give the wavenumber (Fuhrmann et al, 1987;Chadwick et al, 1996;Steele, 1999). The analysis of a 2D slice is called the semi-analytic finite element method in the engineering literature, which dates back to the 1970's, as discussed by Bartoli et al (2006) for example, or the spectral finite element method (Finnveden, 2004), and has also been extended to deal with fluidstructural problems, by Nilsson and Finnveden (2008) for example.…”

“…It is noted that some roots represent non-propagating waves and a single wavenumber is chosen for a given model to represent the propagating wave in their asymptotic formulation. Steele (1999) also describes how multi-chamber models give rise to multiple modes. Cai et al (2003Cai et al ( , 2004 discuss how a more detailed numerical model of slices of the cochlea can be used to describe wave propagation.…”

The cochlear amplifier: augmentation of the traveling wave within the inner ear

“…The stereocilia are closer to the stapes than is the base of the cell. Thus, the force created by an OHC in response to having its stereocilia deflected acts in a "feed-forward" mechanism to deliver energy to a more apical section of the cochlea, slightly ahead of the traveling wave [17][18][19].…”

Can Outer Hair Cells Actively Pump Fluid into the Tunnel of Corti?

“…Some cochlear models have attempted to account for the CA by means of multiple modes of longitudinal coupling [6,7,15]. In [7], a traveling wave amplifier (TWamp) model shows that two wave modes can interfere constructively to create amplification such as that desired in the CA.…”