The reflectivity function of the cochlear transmission line

Abstract

The generation of evoked otoacoustic emissions is related, for each frequency, to the reflectivity function of the cochlear membrane near the correspondent resonant place. A formal analogy exists between the transmission line equation that is often used to model the propagation of sound along the cochlea and the Schroedinger equation describing the motion of an elementary particle in a one-dimensional potential. In this analogy, the cochlear region near the tonotopic place is equivalent to a negative potential well. Analytical solutions are available in quantum mechanics textbooks, which predict partial reflection of the incoming wave from such a potential well. The reflectivity is expected to be a slow quasi-periodic function of the well width and depth, e.g., of the quality factor of the cochlear resonance. This observation could be useful to predict the large-scale spectral structure of evoked otoacoustic emissions as a function of the cochlear tuning curve.