Speaker
Description
The mammalian ear has a remarkable ability to distinguish sounds that differ only slightly in frequency, while at the same time amplifying these signals so that they can be converted into neural impulses. This fine-frequency tuning phenomenon is commonly attributed to some form of mechanical resonance within the fluid-filled cochlea (or inner ear), and more specifically to resonant oscillations in the basilar membrane (BM) that runs along the cochlear duct [2]. We extend a well-known immersed boundary model for fluid-structure interaction in the cochlea [1, 4] by incorporating a small-amplitude periodic internal forcing due to contractions of outer hair cells that are embedded within the BM structure and induce parametric resonance through periodic variations in the BM stiffness. A Floquet stability analysis demonstrates the existence of resonant (unstable) solutions for physical parameters typical of mammalian cochleas, and also exhibits travelling wave solutions that are consistent with other models and experiments [3]. We then describe more recent efforts to include the influence of Reissner's membrane, which is another much more flexible elastic structure that is typically ignored in other cochlear models. Numerical simulations validate the analytical results and support the hypothesis that fluid-mediated resonance may be a significant contributing factor in the active process that drives cochlear mechanics [5].
[1] Richard P. Beyer, Jr. A computational model of the cochlea using the immersed boundary method. Journal of Computational Physics, 98:145162, 1992.
[2] A. J. Hudspeth. Mechanical ampli cation of stimuli by hair cells. Current Opinion in Neurobiology, 7:480486, 1997.
[3] William Ko and John M. Stockie. An immersed boundary model of the cochlea with parametric forcing. SIAM Journal on Applied Mathematics, 75(3):10651089, 2015.
[4] Randall J. LeVeque, Charles S. Peskin, and Peter D. Lax. Solution of a two-dimensional cochlea model with uid viscosity. SIAM Journal on Applied Mathematics, 48(1):191213, 1988.
[5] Tobias Reichenbach and A. J. Hudspeth. The physics of hearing: Fluid mechanics and the active process of the inner ear. Reports on Progress in Physics, 77:076601, 2014.
