An immersed boundary model for fluid-structure interaction in the cochlea

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 phenomenon is commonly attributed to some form of mechanical resonance within the fluid-filled cochlea (or inner ear), and more specifically to resonant oscillations of the basilar membrane that runs along the cochlear duct.  We develop an immersed boundary model of fluid-structure interaction in the cochlea that incorporates a small-amplitude periodic internal forcing due to contractions of outer hair cells that are embedded within the BM structure and can induce parametric resonance. 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. We also describe 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.

John Stockie is an applied mathematician with research interests that span scientific computing, fluid mechanics, partial differential equations and applications in engineering and biology. He received my PhD in Applied Mathematics from the University of British Columbia in 1997 after which he held a postdoctoral fellowship at Simon Fraser University. In 2000 he moved to Fredericton to take up a faculty position at the University of New Brunswick, and returned 3 years later to the Math Department at SFU where he has remained ever since. John's current research focuses on modelling of fluid-structure interactions arising in biological systems such as the cochlea (or inner ear) and suspensions of swimming organisms.