A symmetry suppresses the cochlear catastrophe

When the independent spatial variable is defined appropriately, the empirical finding that the phase of the cochlear input impedance is small Lynch et al., J. Acoust. Soc. Am. 72, 108-130 (1982)] is shown to imply that the wavelength of the pressure wave in the cochlea changes slowly with position near the stapes. As a result, waves traveling in either direction through the basal turn undergo little reflection, and the transfer of energy between the middle and inner ears remains efficient at low frequencies. The slow variation of the wavelength implies that the series impedance Z and shunt admittance Y of the cochlear transmission line are approximately proportional at low frequencies and thus requires that the width of the basilar membrane and the cross-sectional areas of the cochlear scalae taper in opposite directions. Maintenance of the symmetry between Z and Y is both necessary and sufficient to ensure that the spatial derivative of the wavelength, and hence the phase of the cochlear input impedance, remains small. Although introduced in another context, the model of Zweig "Finding the impedance of the organ of Corti," J. Acoust. Soc. Am. 89, 1229-1254 (1991)] manifests the symmetry between Z and Y. In other transmission-line models of cochlear mechanics, however, that symmetry is absent, and the spatial derivative of the wavelength diverges at low frequencies--the "cochlear catastrophe." Those models therefore contradict the impedance measurements and predict little transfer of energy between the middle and inner ears.