On the fluid-structure interaction in the cochlea.

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.

Unification and extension of monolithic state space and iterative cochlear models.

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.