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Re: Wasn't v. Helmholtz right?

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
http://cogprints.soton.ac.uk/abs/bio/200005001. I would value the comments
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 three
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 mirrored
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 from
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 cavity
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 form
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

With this picture, it is possible to explain not only isolated SOAEs but,
significantly, linked bistable SOAEs (where two SOAEs share energy and can
even alternate). Moreover, the occurrence of the preferred frequency ratios
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 semitone,
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 pleased!

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 Web
address given and read the account there.

The new proposal gives a full account of how the ear works, and answers many
of the current unexplained problems in auditory theory. Its drawbacks? The
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 that
the microscopic distance involved, about 30 Ķm, can be tuned to acoustic
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 feedback
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 human
ears emit faint, pure tones (spontaneous otoacoustic emissions), it has been
possible to view these narrowband signals as the continuous ringing of the
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 resonators
accounts for spontaneous emissions, the shape of the earís 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@LISTS.MCGILL.CA]On Behalf Of Eckard Blumschein
Sent: Monday, 22 May 2000 9:54
Subject: Wasn't v. Helmholtz right?

Dear list,

The recent edition of Auditory Perception by Richard M. Warren provides an
excellent review of Mechanics for Stimulation within the Inner Ear.
Unfortunately, the author preferred to leave some conclusions and possibly
some notorious errors to the reader. He wrote correctly: The speed of sound
in the cochlear liquids is very much faster ((than velocity of the
traveling wave)), about 1,600 m/sec (this difference is of significance in
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 might
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 point
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 conference
in Japan last year nor the ARO meeting this year.

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.)


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 physiology
of the inner ear of some animals, explanation of equivalence of net latency
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 application
of a modified transmission line model (with a nearly common upper potential
along the whole length). I additionally imagine an additional oscillating
motion back and forth in radial direction due to motility of the outer hair
cells. Radial component of velocity was reported ten times larger than the
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