SHORT-WAVELENGTH INTERACTIONS BETWEEN OHCs: A "SQUIRTING" WAVE MODEL OF THE COCHLEAR AMPLIFIER

Abstract

A squirting wave model of the cochlear amplifier 1 5.1 Introduction 5.2 Squirting waves 5.3 SLR wave in the cochlea 5.4 Dispersion and tonotopic tuning 5.5 The cochlear amplifier as a standing wave 5.6 Derivation of equations governing squirting waves 5.7 Viscosity and the effects of hydrophobicity 5.8 Conclusions This chapter investigates the distinctive properties of symmetric Lloyd-Redwood (SLR) waves -known in ultrasonics as squirting waves -and describes how their unique characteristics make them well-suited for carrying positive feedback between rows of outer hair cells. This could provide standing-wave resonance -in essence a narrow-band cochlear amplifier. Based on known physical properties of the cochlea, such an amplifier can be readily tuned to match the full 10octave range of human hearing. SLR waves propagate in a thin liquid layer enclosed between two thin compliant plates or between a single such plate and a rigid wall, conditions found in the subtectorial space of the cochlea, and rely on the mass of the inter-plate fluid 1 Based on Bell, A. and N. H. Fletcher (2004). The cochlear amplifier as a standing wave: "squirting" waves between rows of outer hair cells? J. Acoust. Soc. Am. 116: 1016-1024.R 5 [2]interacting with the stiffness of the plates to provide extremely low phase velocity and high dispersion. The first property means SLR wavelengths can be as short as the distance between rows of outer hair cells, allowing standing wave formation; the second permits wide-range tuning using only an order-of-magnitude variation in cochlear physical properties, most importantly the inter-row spacing.Theoretically, viscous drag at the two surfaces should hinder SLR wave propagation at low frequencies, but by invoking hydrophobic effects this limitation might be overcome. R 5 [3]respond in unison. Furthermore, since the OHCs are arranged in three parallel rows, positive feedback at a resonance frequency related to the OHC spacing will occur and, as a result, will launch a 'radial' wave in a direction normal to the rows. This mechanism would operate effectively if the response sensitivity of the individual cells were adjusted neurally to be just below the threshold of oscillation.A major difficulty confronting this radial wave hypothesis, however, is the extremely low wave velocity and high dispersion required in order to have the wavelength match the separation between OHC rows over the full frequency range of the human cochlea. In this paper a wave type is identified that meets these requirements: a symmetric Lloyd-Redwood (SLR) wave, known in ultrasonics as a 'squirting' wave. This mechanism would provide the 'self-tuned critical oscillators' by which amplification of small signals takes place at a frequency where there is a dynamic instability (Hopf bifurcation) 5-9 . A feature of Hopf resonance ( §D 9.2/c) when applied to this system is that the tuning is governed by the frequencies of the oscillators, not the stiffness or inertia of the partition, and the oscillators will act as sharply tuned high-ga...

Tuning the cochlea: wave-mediated positive feedback between cells

“…1), and in this paper explicit wave equations are set up, and numerically evaluated, to see what the result would be if each cell in such a geometric pattern were simultaneously excited so that the resulting motion were communicated, via squirting waves, to nearby cells-which in turn also undergo electromotility, creating a positive feedback loop. The modelling builds on the work of Bell and Fletcher (2004) and is based on the author's Ph.D. thesis (Bell 2005). Independentally, Elliott et al (2005) have analytically examined the properties of squirting waves, explicitly including the effect of viscosity, and gone on to construct a basic feedback model of the cochlear amplifier.…”

“…In this respect, there is no fundamental difference between the standard model and the feedback model elaborated here. However, an alternative picture, and one favoured by considerations that go beyond what can be set out here (Bell 2003(Bell , 2004(Bell , 2005(Bell , 2007, is that the OHCs might be stimulated directly by the fast cochlear pressure wave that sweeps through the cochlear fluids at the speed of sound in water (some 1,500 m/s). Recent research indicates that a fast pressure wave is needed to explain a number of fast cochlear responses (Guinan et al 2005;Siegel et al 2005), and in this case no travelling wave excitation is required.…”

“…1). A spatial autocorrelation analysis (Bell 2005) of published OHC positions over Fig. 1 in which the outer hair cells have been reduced to a lattice of points.…”

“…The simplest case-two cells and non-dispersive propagation-will be examined first to demonstrate the general principle; this will be followed by the case of three rows of cells of some 20 cells each and dispersive squirting wave interactions. An intermediate case-a single row of cells-and other special cases (including non-dispersive ones) are given in Bell (2005).…”

“…Notwithstanding some question marks, this model provides a new perspective on how tuning in the cochlea might arise. A preliminary account of the model has been given in Bell (2006a).…”