To explore the fundamental biomechanics of sound frequency transduction in the cochlea, a two-dimensional analytical model of the basilar membrane was constructed from first principles. Quantitative analysis showed that axial forces along the membrane are negligible, condensing the problem to a set of ordered one-dimensional models in the radial dimension, for which all parameters can be specified from experimental data. Solutions of the radial models for asymmetrical boundary conditions produce realistic deformation patterns. The resulting second-order differential equations, based on the original concepts of Helmholtz and Guyton, and including viscoelastic restoring forces, predict a frequency map and amplitudes of deflections that are consistent with classical observations. They also predict the effects of an observation hole drilled in the surrounding bone, the effects of curvature of the cochlear spiral, as well as apparent traveling waves under a variety of experimental conditions. A quantitative rendition of the classical Helmholtz-Guyton model captures the essence of cochlear mechanics and unifies the competing resonance and traveling wave theories. 1. Introduction New data have created an opportunity to revisit central problem of audition: the function of the cochlea as a real-time frequency analyzer. This intellectual puzzle has attracted a large number of thinkers over the years, who have conducted extensive research in cochlear modeling [1–7]. Controversy continues, however, regarding which features of the various models are essential [8–11]. Most popular today are theories describing traveling waves that propagate longitudinally along the basilar membrane. However, criticisms of traveling wave models include suggestions that the traveling wave focusing is not sufficiently sharp and that computed peak displacements of the basilar membrane are on the order of one nanometer or less, perhaps too small to effectively stimulate hair cells [6, 12]. One path forward is to create increasingly detailed three-dimensional computational models [3, 4, 13]. The Cal Tech model of the cochlea, for example [3], uses the immersed boundary method to calculate the fluid-structure interactions at the San Diego Supercomputing Center. Six surfaces of immersed material in the cochlea are partitioned into 25 computational grids comprising 750,000 points. There is a fluid grid of 223 points [3]. In one report, the simulation of two milliseconds of time required approximately 18 hours of dedicated computation on a supercomputer [4]. The present paper takes a much
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