Hydrodynamic forces on hair bundles at high frequencies

We have analyzed a model for the motion of hair bundles of hair cells at high 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 at high frequencies, fluid forces cause the rigid body to move as though it were attached to the plates with a system of levers. As a result, the angular displacement of the rigid body is proportional to the displacements of the plates even when there are no mechanical attachments of the body to the tectorial plate. This result is independent of both the size and the shape of the rigid body and independent of the presence and proximity of the tectorial plate, although the constant of proportionality depends upon these factors. Therefore, the mechanical stimulation of hair cells may be particularly simple at high frequencies where the structural differences in hair bundles and tectorial attachments--that have been shown to be important at low frequencies--play a less important role.