Superposition of hydrodynamic forces on a hair bundle

Vertebrates sense sound, orientation, and motion by means of bundles of microscopic sensory hairs that protrude from the surfaces of receptor (hair) cells. To determine the effects of the sensory epithelium, tectorial structures, and fluids on the motions of hair bundles, we examine a class of mathematical models in which hair-cell organs are represented as a system of rigid mechanical structures surrounded by fluid. The epithelium and tectorial structures are represented by rigid basal and tectorial plates, respectively; the hair bundle by a rigid body hinged to the basal plate. When the displacements of these structures are small, the equations of motion for the fluid are predominately linear. Therefore, both the fluid velocity and the force of fluid origin on the body can be expressed as a sum of components; each component results from motion of a single structure while all others are stationary. This analysis leads to a network description of the motion of the rigid body in which hydrodynamic forces are segregated from mechanical forces. The separation of hydrodynamics and mechanics not only clarifies the effects of fluids on motion but also minimizes the number of hydrodynamic computations needed to analyze models of hair-bundle motion.