Mode conversion in the cochlea?

Abstract

The cochlea is the part of the ear where sound is analysed into frequencies. It is partitioned into two channels by a flexible membrane, whose effective density varies little along the length but whose stiffness reduces by a factor 104 from base to apex. Via the stapes near the base of the cochlea, the incoming sound excites travelling waves on the cochlear partition. The standard theory is that they travel to a frequency-dependent place where the cochlear partition is resonant with the sound frequency and thus is excited to relatively large amplitude there. The response to high frequencies peaks a short distance from the base, that for lower frequencies peaks towards the apex of the cochlea. Thus the cochlea separates frequencies by location of the peak response along the cochlear partition, from where they are transduced into neural signals to the brain. Mathematically, such a scenario falls into the class of critical-layer resonance models, well known in plasma physics, fluid dynamics and atmospheric science. It is suggested here, however, that the frequency selectivity of the ear may be based on mode conversion rather than critical-layer resonance. Mode conversion is a phenomenon discovered in plasma physics in which two modes of wave in an inhomogeneous medium completely interconvert. Waves entering in one mode travel to a frequency-dependent place where they turn round and travel back in the other mode. The wave amplitude grows to a peak at the turning point. Thus mode conversion is an equally good mechanism for frequency analysis. By comparing the theory with some of the wealth of experimental data, several inconsistencies of critical-layer resonance with the cochlea are pointed out, and it is found that they can be removed by mode conversion. Furthermore, critical-layer models are not robust to addition of higher derivatives: they generically deform to mode conversion or a case with no singularity. A proposal is made for a physiological mechanism for mode conversion to arise in the cochlea, based on forces produced by outer hair cells (which so far have primarily been invoked only to cancel damping). Other sources for mode conversion are possible too, however, notably two-membrane models. The analysis is carried out at the linearised level, though extension to incorporate nonlinear effects is an essential next step. The key result of this article is to highlight mode conversion as a highly plausible mechanism for the frequency selectivity of the cochlea, much more likely than critical-layer resonance, and to stimulate further investigation of this option.