The cochlear compromise.

Abstract

It is conjectured that the design of the cochlea is influenced by two conflicting requirements: (1) the cochlea should act as a precise frequency analyzer and (2) waves propagating along the basilar membrane should be transmitted without reflections. Accurate frequency analysis is possible only if the mechanical properties of the cochlea change rapidly with distance along the basilar membrane. Reflections of waves traveling on the basilar membrane will be negligible, however, only if these same mechanical properties change slowly. A compromise between these two requirements is possible if a loss constant δ related to the sharpness of response of the basilar membrane to a pure tone is related to the number N of wavelengths of the wave on the basilar membrane [N/(δ)1/2?1]. Furthermore, if sizable changes in the displacement occur only over distances larger than the width of a hair cell, then δ must be larger than the ratio of the width w of a hair cell to the distance d along the basilar membrane over which the characteristic frequency changes by an octave [δ≳4N (2δ)1/2 w/d]. These remarks are made explicit in a transmission-line model of cochlear mechanics. A simple closed-form solution of the equations, which agrees with a numerical solution, is given. The solution is compared with Mössbauer measurements of basilar membrane motion. Agreement with experiment is good if N and δ are chosen appropriately. These values are consistent with both of the conjectured relations and indicate that δ is the same order of magnitude as its lowest possible value. Subject Classification: [43]65.26, [43]65.35.