Hydrodynamic forces on hair bundles at low frequencies

We have analyzed a model for the motion of hair bundles of hair cells at low frequencies. In the model, hair-cell organs are represented as a system of rigid mechanical structures surrounded by fluid. A rigid body, that represents a hair bundle, is hinged to a vibrating plate that represents the sensory epithelium. These structures are surmounted by a second vibrating plate that represents a tectorial structure. The analysis shows that both viscous and inertial properties of the fluid are important even at asymptotically low frequencies. The relative importance of these properties depends critically on the presence and mode of motion of the tectorial plate. As a result, the angular displacement of the body at low frequencies can be proportional to basal plate displacement, velocity, acceleration, or to no simple integral of its motion; the functional relation depends upon the disposition of the tectorial plate.