The effect of hair bundle shape on hair bundle hydrodynamics of inner ear hair cells at low and high frequencies

Abstract The relationship between size and shape of the hair bundle of a hair cell in the inner ear and its sensitivity at asymptotically high and low frequencies was determined, thereby extending the results of an analysis of hair bundle hydrodynamics in two dimensions (Freeman and Weiss, 1990. Hydrodynamic analysis of a two-dimensional model for micromechanical resonance of free-standing hair bundles. Hear. Res. 48, 37–68) to three dimensions. A hemispheroid was used to represent the hair bundle. The hemispheroid had a number of advantages: it could represent shapes that range from thin, pencil-like shapes, to wide, flat, disk-like shapes. Also analytic methods could be used in the high frequency range to obtain an exact solution to the equations of motion. In the low frequency range, where an approximate solution was found using boundary element methods, the sensitivity of the responses of hair cells was mainly proportional to the cube of the heights of their hair bundles, and at high frequencies, the sensitivity of the hair cells was mainly proportional to the inverse of their heights. An excellent match was obtained between measurements of sensitivity curves in the basillar papilla of the alligator and bobtail lizards and the model’s predictions. These results also suggest why hair bundles of hair cells in vestibular organs which are sensitive to low frequencies have ranges of heights that are an order of magnitude larger than the range of heights of hair bundles of hair cells found in auditory organs.