Re: Wasn't v. Helmholtz right? (Andrew Bell )

Subject: Re: Wasn't v. Helmholtz right?
From:    Andrew Bell  <bellring(at)SMARTCHAT.NET.AU>
Date:    Fri, 26 May 2000 13:28:13 +1000

Yes, Helmholtz was basically right, I believe. I have written a paper (called "The Underwater Piano", after the way Gold characterised the problem of explaining the ear's high Q) which offers a resonance theory of cochlear mechanics along the lines of Helmholtz. The abstract is below, and you can find a preprint at I would value the comment= s of members of this list. The paper proposes that the resonating elements are virtually invisible - they are not physical fibres, as Helmholtz thought, but resonant cavities. Reverberation takes place between rows of outer hair cells, which both generate, and detect, ripples on the surface of the gelatinous tectorial membrane in response to incoming sound. The resonant frequency therefore comes not from mass-compliance but from precise time delays afforded by slow wave propagation - ripples of some kind - on the surface of the tectorial membrane. (In this respect, the resonator is more like an organ pipe than a piano string). The time for a ripple to propagate from OHC1 to OHC3 is one period of the characteristic frequency at that point. In this way, the three sets of outer hair cells = act in concert like a standing acoustic wave (SAW) resonator. The result is the regenerative receiver posited by Gold, in which the thr= ee rows of OHCs employ positive feedback to set up a tuned system (another analogy is a laser cavity where light reflects to and fro within a mirror= ed cavity); incoming sound will change the gain of 'the acoustic laser', and the strength of the emerging 'laser beam' is detected by the nearby inner hair cells. As required by Gold, the sensing stage (IHC) is separated fro= m the detector stage (OHCs). Of particular note, the movement is a lateral = one in the plane of the cochlear partition, not perpendicular to it as in the conventional picture. Of course, at higher SPLs (above about 60 dB), vertical movement of the partition does begin, but only as a means of damping excessive motion. The theory and its resonant cavity idea were first developed as a way of explaining SOAEs (in which an SOAE is simply an overactive resonant cavit= y formed by a set of OHCs). However, what if we were to identify the cavity= as Helmholtz's resonant element? Such a proposal could give a novel account= of cochlear mechanics. A key idea is to realise that resonant cavities can f= orm not only between OHC1 and OHC3 (at right angles to the rows), but also at oblique angles. Now it is possible to understand why OHC stereocilia are arranged in a 'V' or 'W' (so that oblique cavities can form in both directions between the stereocilia arms of neighbouring OHCs) and why the OHCs sit in such a precise, almost crystalline, lattice configuration (to form sets of tuned cavities at each point along the length of the partition). With this picture, it is possible to explain not only isolated SOAEs but, significantly, linked bistable SOAEs (where two SOAEs share energy and ca= n even alternate). Moreover, the occurrence of the preferred frequency rati= os between multiple SOAEs - about 1.06 - can be explained by simple geometry= as the ratio between the length of the perpendicular cavity and the first oblique cavity. Indeed, measurements of OHC arrangements in published micrographs show that the most common angle between the perpendicular and first oblique is 19 degrees (and 1/cos19, the resulting length ratio, is then 1.06). One exciting step that follows comes from noticing that 1.06 is a semiton= e, and closer examination of OHC lattices shows that other musical ratios, including the octave, can appear at other cavity lengths. In other words, there could well be a physical basis for music. Helmholtz would be please= d! It would be possible to continue, detailing how the hypothesis generates = the typical cochlear tuning curve, and how it explains evoked OAEs and other auditory phenomena. However, I would suggest instead that you go to the W= eb address given and read the account there. The new proposal gives a full account of how the ear works, and answers m= any of the current unexplained problems in auditory theory. Its drawbacks? Th= e gel of the tectorial membrane must have special properties: the surface tension, or similar properties, must be such as to support a very low propagation speed of the ripples (or other wave propagation mode), so tha= t the microscopic distance involved, about 30 =B5m, can be tuned to acousti= c frequencies. Unfortunately relevant properties of the tectorial membrane = are presently unknown; nevertheless, this is a question that is amenable to testing (without sacrificing animals I would add). I hope this new theory generates fruitful discussion and life-affirming experiment. Your feedbac= k on the paper is welcome. Andrew Bell. ______________________________________ ABSTRACT: In 1857 Helmholtz proposed that the ear contained an array of sympathetic resonators, like piano strings, which served to give the ear = its fine frequency discrimination. Since the discovery that most healthy huma= n ears emit faint, pure tones (spontaneous otoacoustic emissions), it has b= een possible to view these narrowband signals as the continuous ringing of th= e resonant elements. But what are the elements? We note that motile outer hair cells lie in a precise crystal-like array with their sensitive stereocilia in contact with the gelatinous tectorial membrane. This paper therefore proposes that ripples on the surface of the tectorial membrane propagate = to and fro between neighbouring cells. The resulting array of active resonat= ors accounts for spontaneous emissions, the shape of the ear=92s tuning curve= , cochlear echoes, and could relate strongly to music. By identifying the resonating elements that eluded Helmholtz, this hypothesis revives the resonance theory of hearing, displaced this century by the traveling wave picture, and locates the regenerative receiver invoked by Gold in 1948. -----Original Message----- From: AUDITORY Research in Auditory Perception [mailto:AUDITORY(at)LISTS.MCGILL.CA]On Behalf Of Eckard Blumschein Sent: Monday, 22 May 2000 9:54 To: AUDITORY(at)LISTS.MCGILL.CA Subject: Wasn't v. Helmholtz right? Dear list, The recent edition of Auditory Perception by Richard M. Warren provides a= n excellent review of Mechanics for Stimulation within the Inner Ear. Unfortunately, the author preferred to leave some conclusions and possibl= y some notorious errors to the reader. He wrote correctly: The speed of sou= nd in the cochlear liquids is very much faster ((than velocity of the traveling wave)), about 1,600 m/sec (this difference is of significance i= n determining whether the traveling wave or the sound pressure is the stimulus for receptor cell transduction...). He did not, however, mention the question whether or not the traveling wave is the result of energy transmission basilar from base to apex inside basilar membrane or it migh= t rather be an epi-phenomenon, i.e. an attendant symptom of local resonance. Referring to Lewis, Leverence, and Bialek (1985), and also to de Boer and Nutall (1996), Dancer, Avan, and Magnan (1997) tried to belittle this discrepancy by calling the traveling wave a leitmotiv. Recio, Rich, Narayan, and Ruggero (1998) rejected this point of view. Can anybody poin= t me to the final outcome of that discussion? Possibly, I am simply not yet aware of the latest news since I did neither attend a concerning conferen= ce in Japan last year nor the ARO meeting this year. >>>>>>>snip>>>>>>>>>>> P.S. The answer to Recio et al (1998) is that they only measured the vertical component of the BM motion. This demonstrates that one only measures what one sets out to measure, and illustrates why more can be learned from cooperating with living things. (A.B.) >>>>>>>snip>>>>>>>>>>>> It is my gut feeling that v. Helmholtz was pretty right with his idea of local resonance. Otherwise, I was wrong with my speculations on physiolog= y of the inner ear of some animals, explanation of equivalence of net laten= cy and 1/CF, problems with understanding of DPOAE, etc. I also realized evidence for the longitudinal coupling being fairly weak. Local resonance does neither exclude the appearance of a traveling wave nor the applicati= on of a modified transmission line model (with a nearly common upper potenti= al along the whole length). I additionally imagine an additional oscillating motion back and forth in radial direction due to motility of the outer ha= ir cells. Radial component of velocity was reported ten times larger than th= e longitudinal one. Once again, may I ask for hints to the ultimate elucidation? As Dancer et al. stated, the two positions should have implications in signal processing. Suggesting that psychoacoustics may be the touchstone for theories, I would be curious if it will really be possible to compensate for the traveling wave delay. Thank you very much, Dr. Eckard Blumschein Inst. of Electronics, Signal Processing, and Telecommunication Otto von Guericke Univ. Magdeburg, GERMANY

This message came from the mail archive
maintained by:
DAn Ellis <>
Electrical Engineering Dept., Columbia University