An active model for the basilar membrane and the outer hair cells

A model for the joint motion of the basilar membrane (BM) and the outer hair cells (OHC) in the cochlea is presented. The model consists of two one-imensional mass distributions, one along the OHC and outer hair bundle (OHB) interface, and one along the BM. The motion of these masses is driven by the forces exerted on them by the elastic bodies connecting them and by the pressure difference in the fluids separated by the BM. The model includes a nonlinear motility of the OHC and its coupling with the vibrations of the BM. The model implies a Hopf bifurcation for the dynamical system governing the two coupled distributed oscillators. It is shown that when the system operates near the bifurcation point the BM motion is amplified up to a saturation level. The model provides very sharp frequency decomposition of the incident audio signal according to the place principle. It also acts as a powerful filter that distinguishes pure tones even in the presence of louder noisy background. In addition to simulations of the model, the unusual role played by the OHC friction is studied. Energy estimates are derived for the model functions.