Hydrodynamic analysis of a two-dimensional model for micromechanical resonance of free-standing hair bundles

To investigate the role of inner ear fluids and structures on mechanical stimulation of the hair bundles of hair cells, we analyzed a two-dimensional structure that consists of: a rectangular flap (which represents a hair bundle) attached to a flat basal plate (which represents the surface of the epithelium that contains the hair cells) with a spring-loaded hinge (that represents the compliant attachment of a hair bundle to the hair cell body) and surrounded by a viscous fluid (that represents endolymph). We computed the fluid velocity as well as the forces on and motion of the flap in response to sinusoidal vibration of the plate by numerical integration of the hydrodynamic equations, and--at asymptotically low and high frequencies--by analytic methods. The results suggest that: (1) the surface of the sensory epithelium, from which hair bundles project into fluid, plays an important part in the production of fluid forces on hair bundles; (2) both fluid inertia and viscosity play a key role in hair bundle mechanics; (3) passive mechanical resonances are likely to contribute to both frequency selectivity and frequency-to-place coding in the inner ear.