Proceedings of The Physiological Society

University College London 2006 (2006) Proc Physiol Soc 3, DC2


Viscous damping of acoustic resonance with a restricted zone of wall compliance

A R Gardner-Medwin1

1. Physiology, UCL , London, United Kingdom.

The basis of cochlear frequency analysis lies in the compliance of the basilar membrane, separating two fluid chambers that are subjected to acoustic pressure differences. Modelling of the viscous damping associated with resonances in this structure (Gold, 1948) has led to the widely accepted conclusion that passive resonance could not be sharp enough to be consistent with psychophysical and physiological measurements. Active mechanisms (capable of generating force), associated with outer hair cells, may therefore be critical in the establishment of sharp resonance. Though this account may be correct, it is not the only way in which active mechanisms could be relevant to acoustic function of the cochlea. For example, they could modulate rather than cancel the viscous damping, they might limit the resonant after-effects of brief transients, or they might somehow act to restrict and concentrate the energy absorption of the Organ of Corti in zones where it will have greatest effect. Gold's model was based on calculations treating a zone of the basilar membrane as analogous to a piano string immersed in water. An alternative is to consider a portion of the basilar membrane (responsive to a particular frequency), as a small compliant zone of the wall separating two chambers with otherwise relatively rigid walls. This begs the question of in what sense, or perhaps by what active mechanism, the rest of the basilar membrane could be considered rigid for the purposes of analysing the dynamics of a single zone, but it provides an alternative model for analysing the ultimate constraint that viscosity places on the sharpness of resonance in a cochlear structure. The model adopted here considers a circular compliant zone of membrane of radius R and zero mass, with a relatively large chamber on each side subjected to distant pressure variation. Resonance involves alternating transfer between potential energy associated with extension of the compliant membrane and kinetic energy (KE) of fluid movement towards and away from the membrane. The KE and viscous dissipation are both mainly in fluid within a radius of the membrane, where velocities are highest. Measurements with ×10 scale models and calculations with simplified flow patterns suggest that the time constant (T) for energy loss with a compliant zone of radius R = 0.1mm can exceed 2ms (yielding for example a 3 dB resonance bandwidth equal to 4% of a center frequency f = 2 kHz, Q3dB = 2πfT = 25). The value of T due to viscosity scales with R2/K (where K = kinematic viscosity, ca. 0.7 × 10-6 m2/s at 37°C). With plausible dimensions this would appear to be able to account passively for frequency selectivity substantially greater than is inferred at any frequency from physiological and psychophysical data (Moore, 2003). A key issue would be how energy could be directed to optimal vibration modes for maximum sensitivity and selectivity.

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