Coherent reflection in a two-dimensional cochlea: Short-wave versus long-wave scattering in the generation of...

The theory of coherent reflection filtering explains the empirical form of the cochlear reflectance by showing how it emerges from the coherent "backscattering" of forward-traveling waves by impedance perturbations in the mechanics of the cochlear partition. Since the theory was developed using the one-dimensional (1-D) transmission-line model of the cochlea, an obvious logical shortcoming is the failure of the long-wavelength approximation near the peak of the traveling wave, where coherent backscattering is purported to occur. Indeed, existing theory suggests that wave reflection may be strongly suppressed in the short-wave regime. To understand how short-wave behavior near the peak modifies the predictions of the long-wave theory, this paper solves the scattering problem in the 2-D cochlear model. The 2-D problem is reduced to a 1-D wave equation and the solution expressed as an infinite series in which successive terms arise via multiple scattering within the cochlea. The cochlear reflectance is computed in response-matched models constructed by solving the inverse problem to control for variations in mechanical tuning among models of different heights and dimensionality. Reflection from the peak region is significantly enhanced by the short-wave hydrodynamics, but other conclusions of the 1-D analysis--such as the predicted relation between emission group delay and the wavelength of the traveling wave--carry over with only minor modifications. The results illustrate the important role of passive hydromechanical effects in shaping otoacoustic emissions and cochlear tuning.