Effects of basilar membrane arch and radial tension on the travelling wave in gerbil cochlea

The basilar membrane velocity of gerbil cochlea showed discrepancy between theoretical model and experimental measurements. We hypothesize that the reasons of such discrepancies are due to the arch towards the scala tympani and radial tension present in the basilar membrane of the gerbil cochlea. The arch changes the bending stiffness in the basilar membrane, reduces the effective fluid force on the membrane and increases the basilar membrane's inertia. The existence of the radial tension also dampens the acoustic travelling wave. In this paper, the wave number functions along the gerbil basilar membrane are calculated from experimentally measured physical parameters with the theoretical model as well as extracted from experimentally measured basilar membrane velocity with the wave number inversion formula. The two wave number functions are compared and the effects of the tension and membrane arch on the wave number are studied based on various parameters of the model. We found that the bending stiffness across the gerbil basilar membrane varies (1-2 orders along the cochlea in the section 2.2 mm-3 mm from base) more than the calculated value in the flat basilar membrane model and the radial tension increases the damping of the travelling wave in gerbil cochlea significantly (5 times more than that without radial tension). These effects of arch and radial tension in the basilar membrane elucidate the discrepancy between previous theoretical model and experimental measurements in gerbil cochlea.