A Resonance Approach to Cochlear Mechanics

Abstract

BackgroundHow does the cochlea analyse sound into its component frequencies? In the 1850s Helmholtz thought it occurred by resonance, whereas a century later Békésy's work indicated a travelling wave. The latter answer seemed to settle the question, but with the discovery in 1978 that the cochlea emits sound, the mechanics of the cochlea was back on the drawing board. Recent studies have raised questions about whether the travelling wave, as currently understood, is adequate to explain observations.ApproachApplying basic resonance principles, this paper revisits the question. A graded bank of harmonic oscillators with cochlear-like frequencies and quality factors is simultaneously excited, and it is found that resonance gives rise to similar frequency responses, group delays, and travelling wave velocities as observed by experiment. The overall effect of the group delay gradient is to produce a decelerating wave of peak displacement moving from base to apex at characteristic travelling wave speeds. The extensive literature on chains of coupled oscillators is considered, and the occurrence of travelling waves, pseudowaves, phase plateaus, and forced resonance in such systems is noted.Conclusion and significanceThis alternative approach to cochlear mechanics shows that a travelling wave can simply arise as an apparently moving amplitude peak which passes along a bank of resonators without carrying energy. This highlights the possible role of the fast pressure wave and indicates how phase delays and group delays of a set of driven harmonic oscillators can generate an apparent travelling wave. It is possible to view the cochlea as a chain of globally forced coupled oscillators, and this model incorporates fundamental aspects of both the resonance and travelling wave theories.

Spatial asymmetries of resonant oscillations in periodically forced heterogeneous media

“…The analysis reported here can be extended to include spatial variations in additional parameters, e.g. µ, which is related to quality factors of the oscillator [50,51], or the coupling between the outer hair cell and the basilar membrane [41].…”

Fast Waves at the Base of the Cochlea

“…One property of traveling waves, first shown by von Békésy [ 1 ] and confirmed by other authors (e.g., [ 5 , 19 ]), can be observed in the phase curves in Fig 1B : there is a phase accumulation with frequency (as well as with distance along the BM). Another traveling wave property is the signal-front delay ([ 8 ]; see also comment by Peter Dallos in [ 20 ]). The 4-μs signal-front delay implied by the waveforms in Fig 1B approaches the delay of a wave traveling at the speed of sound in water, i.e., a compression wave.…”

“…In general, delays of mechanical or neural responses appear to increase with distance to the stapes and—at least at the base of cochlea [ 5 ]—are very short, in the order of a few tens of microseconds. Some authors have judged such signal-front delays as incompatible with a traditional (slow) traveling wave (e.g., [ 8 – 10 ]).…”

A fully coupled subwavelength resonance approach to filtering auditory signals

“…It is a significant observation that a simple graded-resonance model, with appropriate coupling between the resonators, predicts travelling wave behaviour in the acoustic pressure field, and that this has similar characteristics to that observed in the membrane motion. In some sense, these models represent the unification of Helmholtz' and Békésy's ideas [12,13].…”