On the fluid-structure interaction in the cochlea

Abstract

The cochlea is known to be a nonlinear system that shows strong fluid-structure coupling. In this work, the monolithic state space approach to cochlear modeling [Rapson et al., J. Acoust. Soc. Am. 131, 3925-3952 (2012)] is used to study the inherent nature of this coupling. Mathematical derivations requiring minimal, widely accepted assumptions about cochlear anatomy provide a clear description of the coupling. In particular, the coupling forces between neighboring cochlear partition segments are demonstrated, with implications for theories of cochlear operation that discount the traveling wave hypothesis. The derivations also reaffirm the importance of selecting a physiologically accurate value for the partition mass in any simulation. Numerical results show that considering the fluid properties in isolation can give a misleading impression of the fluid-structure coupling. Linearization of a nonlinear partition model allows the relationship between the linear and nonlinear fluid-structure interaction to be described. Furthermore, the effect of different classes of nonlinearities on the numerical complexity of a cochlear model is assessed. Cochlear models that assume outer hair cells are able to detect pressure will require implicit solver strategies, should the pressure sensitivity be demonstrated. Classical cochlear models in general do not require implicit solver strategies.

Waves in the cochlea and in acoustic rainbow sensors

“…The phase shift of D is then only π/2 at the BM resonance, as associated with a isolated resonator. These results are in accordance with [33], where the relationship between the BM mass and the coupled response is discussed. The more complete analysis here illustrates the dependence of the form of the coupled response not just on the BM mass via µ, but on the more complicated nondimensional parameter, N .…”

“…If this parameter is small, the fluid-structural coupling is weak, and the elements of the basilar membrane respond independently, driven by the constant pressure in the fluid, generating an almost symmetrical frequency response function when plotted on a log scale. Although the phaseshift parameter that determines the shape of the response is proportional to the square root of the ratio of the mass per unit length of the fluid in the chambers to the mass per unit length of the BM [33], it also depends on the ratio of the characteristic length of the exponential decay in frequency along the cochlea to the effective height of the fluid chambers. Therefore, the mass ratio by itself only changes the amplitude and not the form of the response if the phase-shift parameter is kept constant and the characteristic length of the cochlea is varied accordingly.…”

Wave propagation in non-uniform waveguides

“…The modulus response is similar to that with respect to normalised frequency shown in Figure 4.11b. The effect of the response becoming symmetric for a large mass ratio with respect to position was also observed in [87].…”

“…The small phase shift along the cochlea is also observed here in Figure 4.11c. Values for the mass per unit area of the basilar membrane, m 0 , that lead to high mass ratios, however, are not reasonable given the cochlear physiology, while values for m 0 close to the nominal value used here are physiologically justified [87], so that normal cochlear functioning does involve a wave of the form described in Section 4.4.…”

“…The symmetric response, which in this case occurs for µ = 25µ nom and hence N c = 0.2N c,nom , where the subscript nom denotes the nominal value, corresponds to the high mass ratio scenario in [87]. As described in [87], the high mass ratio results in little coupling between the fluid in the chambers and the basilar membrane, which causes the pressure to be almost uniform throught the cochlea, so that the basilar membrane vibration corresponds to a driven single-degree-of-freedom system. The small phase shift along the cochlea is also observed here in Figure 4.11c.…”