Cochlear wave mode transformations

Abstract

A three-dimensional “first filter” model, describing the transition from long to short cochlear traveling waves, contains no resonance. Amplitude maxima of middle- and low-frequency wave envelopes are calculated by this model to occur at the place where longitudinal wavelength equals 4πkb(x), where b(x) is the local width of the basilar membrane and k is the local (near unity) ratio of the longitudinal and lateral (dissipative) traveling-wave propagation velocities. These two wave modes share the same potential function and are thus tightly coupled; their phase relationship is established by both the curvature of the cochlea and the stiffening effects of the Arches of Corti near inner radius. The velocity-versus-boundary dimension methods used in constructing the above modeling are known collectively as normal-mode analysis. Normal-mode analysis also suggests many reasonable “second-filter” modes of vibration possibly operating within the Organ of Corti (which gelled material supports the bases of all hair cells). At high frequency, a vibration-absorber wave mode (squeeze of the Organ of Corti) can amplify the displacement of the traveling wave, especially at the inner hair cells, while simultaneously extinguishing (by well known force-balance processes) that traveling wave on the basilar membrane. At lower frequencies, where the Organ of Corti spans relatively less of the basilar membrane width, some constrained-sloshing wave modes in the gelled material also preferentially excite inner hair cells. Close agreement with published hydrodynamic cochlear wave observations is shown. Confirmation of any of these distinct (but theoretical) wave modes within the Organ of Corti awaits measurement of directional propagation velocities and elastic properties through the gelled material as it lies flooded and attached to the basilar membrane.