Evoked otoacoustic emissions as cochlear Bragg reflections

The reflection of cochlear waves is mathematically described for various assumptions about the dependence of the echo-generating mechanism on place and frequency, without requiring knowledge of the physical details of the mechanism. Any 'wave-related' reflections, caused by intrinsic features of the resonance or active-feedback mechanism, cannot explain long group delays in an approximately shift-similar basilar membrane (BM). Only 'BM related' scattering due to inhomogenities is a possible explanation then. Reflection at a fixed point of the BM could cause only narrow-band evoked otoacoustic emissions (EOAEs). Long group delays in a wider frequency band can be obtained by assuming Bragg reflection at an approximately periodic inhomogenity of BM parameters, possibly due to spatial variations of active undamping. This explains the long delays, about inversely proportional to frequency, the decreasing instantaneous frequency, the often found multi-packet or modulated structure of echoes (vanishing at higher SPL), the spectra of simultaneous and delayed EOAEs and their relation to the threshold of hearing. These phenomena do not necessarily require multiple reflection due to middle/inner-ear mismatch.