During the funding period a systematic reduction of the equations of motion for the cochlear amplifier will be carried out. The objective is to derive an effective surface approximation for the partition, after which multiple-scales will be used to derive an asymptotic approximation of the nonlinear waves propagating in the cochlea. The objective is to be able to achieve quantitative agreement with the known properties of these waves, including the apical shift in the tuning curve at low intensity levels, the decrease of the relative contribution of the amplifier with increasing stimulus level, the odd-order distortion tones, the observation that the temporal position of the zero-crossings on the basilar membrane remain largely unaffected by stimulus intensity, and the dearth of harmonic distortion in the basilar membrane response to pure tones at low to moderate sound pressure levels in the basal portion of the cochlea.
The fundamental open question in understanding how we hear concerns the role of a nonlinear feedback mechanism known as the cochlear amplifier. One of the reasons why progress in delineating the exact mechanism responsible for amplification is so slow is that it requires the solution of a three-dimensional, coupled, nonlinear, time-dependent system. The PI proposes to develop approximation methods that can be used to help study this problem, both the mechanistic basis for amplification as well as its effects on wave propagation in the cochlea. The results from this study will provide a rigorous framework to help answer the amplifier question.