Two-dimensional analysis of fluid motion in the cochlea resulting from compressional bone conduction

Fluid motion resulting from the compressional excitation of the cochlear capsule due to bone conduction is examined in this paper. Vibrations of the skull deform the shape of the cochlear capsule and give rise to motion the fluid. A two-dimensional channel having a height to length ratio equal to ε is used to model the cochlea. The cochlear pressure is expressed as an integral equation in the cochlear partition velocity. In the limit as ε approaches zero the integral equation is solved and the cochlear pressure is expressed as an asymptotic expansion in ε. Rapid spatial variation in the velocity of the cochlear partition requires one to treat high-order fluid modes within the cochlear fluid. Hence, evanescent pressure modes are included in the analysis. Asymmetry in the oval and the round window velocity is shown to give rise to a pressure gradient across the cochlear partition and basilar membrane displacement. The vibration amplitude of the cochlear partition is shown to depend on the value of the ratio of the oval and the round window impedance.