A model for signal transmission in an ear having hair cells with free-standing stereocilia. III. Micromechanical stage

Abstract

Measurements have shown that the sound-induced motion of free-standing stereocilia of hair cells in the alligator lizard cochlea exhibits tonotopically organized frequency selectivity that is correlated with the geometry of the stereociliary tuft. We propose a model in which basilar-membrane motion causes vibration of the receptor organ which drags the stereocilia back and forth through the endolymph. The stereociliary tuft is represented as a rigid rod attached to the cuticular plate by a compliant hinge. Viscous and inertial forces exerted by the endolymph on the rod are computed approximately. A transfer function, H μ ( f ), is derived that relates rod angular displacement to basilar-membrane velocity. H μ ( f ) has low- and high-frequency slopes of 10 and -20 dB/decade, respectively. The resonant frequency of H μ ( f ) depends on the dimensions of the rod because this frequency is inversely proportional to the square root of the product of the moment of inertia of the rod, which depends on rod dimensions, and the compliance of the hinge, which does not. In most respects, measurements of frequency selectivity and tonotopic organization of hair cells and cochlear neurons in the alligator lizard, can be accounted for by an input transfer function, H I( f)= H m( f) H μ ( f) H a( f) where H m( f) is the macromechanical transfer function that relates sound pressure at the tympanic membrane to basilar-membrane velocity (Rosowski et al., 1985, Hearing Res. 20, 139–155), and H a( f) is a first-order lowpass filter. Mechanisms that could produce the additional lowpass filter process are discussed.