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Re: Wasn't v. Helmholtz right?

Dear Eckard Blumschein and list:

I'm encouraged by your comments. I acknowledge that the traveling wave (TW) has become the dominant paradigm of cochlear mechanics, but as we are beginning to see, it has definite limitations. The TW is a useful shorthand for a description of how the cochlear partition appears to behave to an observer; the problem is that, as you say, in itself the TW has no causal power, it is an epiphenomenon. And yet people continue to call on the TW to do all sorts of things to stimulate hair cells. The misapprehension arises because the TW can be so easily modeled mathematically; however, the mathematics tends to make us lose sight of what quantities are driving which others: which parameters are descriptions and which are causally efficacious.

Von Bekesy, in one of his later papers with Wever and Lawrence, acknowledged that the TW could be seen as merely descriptive of the result of the action of oscillating acoustic pressure in the cochlea.

The reason I am promoting a resonance theory of hearing is that, as Helmholtz appreciated, resonance allows small stimuli, through successive cycles, to build up to have an appreciable effect. It is 'efficient', unlike the TW theory, which requires a large mass (the cochlear partition) to move and to carry forward its energy to successive hair cells. The problem is that we know the ear can detect sound energy of the order of electron volts; this is not enough energy to move the whole partition.

Our aim is therefore to have acoustic energy 'funnelled' to individual resonators in the cochlea. The question is, of course, what are the resonant elements? One desirable outcome might be to have the acoustic energy funnelled to just that one inner hair cell (in the cochlear frequency map) that represents the frequency concerned. But, we know from Gold that we should put the amplifier before the detector. Everyone seems pretty sure the cochlear amplifier resides with the active outer hair cells. So our aim should be to funnel precious acoustic energy into the OHCs, have it amplified, and detected by the IHCs.

How to funnel acoustic energy into OHCs? You seem to believe that the OHC stereocilia are the resonant elements, but I find it hard to see how that could happen. I would be interested to hear how you propose that the OHC stereocilia are stimulated.

I consider the body of the OHC to be a much more likely receptor of acoustic energy. Let me explain why.

My starting point was to create a theory that could explain spontaneous otoacoustic emissions. Here we observe sound coming out of the cochlea without any stimulation at all. That is, the cochlear partition is just sitting there, in the quiet of an anechoic chamber, and narrow-band signals are being produced. This was the phenomenon that got me into hearing research, and it seemed clear to me at the time that the TW theory, with its large moving mass and lack of sharp tuning, was not a good candidate for an explanation. I produced a paper for Hearing Research in 1992 (vol 58, pp 91-100) which examined the circadian and menstrual variations of SOAEs and came to the conclusion that it was intracochlear pressure that changed their frequency. Now, how can static pressure affect the activity of an OHC (the candidate element)?

It seemed to me that pressure must be affecting the body of an OHC. Such cells are under pressure, are compressible (Zenner 1992), contain pressure sensors in their cell walls, and are seen to respond to oscillating acoustic pressure in  vivo (when a pipette projecting an oscillating jet of water is directed at the body of an OHC, the cell responds). Moreover, I have argued in my MSc thesis (ANU, 1998) that the alternative explanation for pressure affecting SOAE frequency (involving changes of mass of the partition due to blood flow changes) is not convincing. Interestingly, early papers by Wilson recorded that static pressure could precipitate tinnitus and labile SOAEs. Any theory of cochlear mechanics needs to explain this susceptibility to static pressure.

The idea that oscillating acoustic pressure directly affects OHCs in a similar way is attractive because it means that acoustic energy is funneled straight to the OHCs. The OHCs are compressible elements immersed in incompressible fluid contained within rigid bone. All the available energy therefore goes straight to the OHC (and a portion to the round window). In this respect, it is noteworthy that OHCs are surrounded by the spaces of Nuel. To my knowledge, every other cell in the body is placed next to its companion cells without any other intervening space. In contrast, the body of OHCs are in direct contact with the cochlear fluids, as we would expect a pressure detector to be. Moreover, as we go from base to apex, the OHCs show a steady gradation in length: the OHCs are tuned (and examination of OHCs in vivo has shown this tuning explicitly).

Of course, this tuning is not as sharp as we observe SOAEs: less than 1 Hz in some cases. Here is where positive feedback comes in, and I have posited that reverberation arises between triplets of OHCs via ripples generated on the tectorial membrane (in which the stereocilia are embedded), since it is known that stimulation of the OHC causes movement of the stereocilia, as well as the reverse. The attraction of this concept is that it makes use of the properties of a reversible transducer, explains why OHCs occur in triplets in a quasi-crystalline arrangement, and, in addition, gives a prominent role to that much overlooked structure, the tectorial membrane (TM). The peculiar elastic properties of this gelatinous body are here called on to support slow-propagating ripples. It is therefore important that the stereocilia are embedded in the membrane so that movement of the stereocilia can generate ripples.

I have hypothesised ripples because they are isotropic, and the surface of the TM appears to be covered with an amorphous substance. This arrangement fits in with my measurements of the OHC 'crystal lattice' whereby the L1 resonator (relative length 1.06) sits well placed with respect to the other resonators to produce musically significant ratios (particularly the L5 resonator at length 2.0). Of course, other wave propagation modes within the TM are possible; Rayleigh waves are one example, but it is not clear that the TM properties would be such as to give a Rayleigh wave with a sufficiently low wave propagation speed to tune the three rows of OHCs to a whole wavelength. By contrast, surface-tension borne ripples are known to already have, on water, a low propagation speed (30-40 mm/sec), and it would be expected that the corresponding speed on the interface of a gel immersed in water would be even lower.

My hypothesis has shown up a lack of physical data on the TM, but in offering a hypothesis that can be tested, my hope is that hearing science will be advanced. I have suggested a transverse wave propagating in a radial direction, and I am not sure if your hypothesis calls for a longitudinal wave propagating in the radial direction, or something else. I am happy to entertain a longitudinal wave propagation mode if its speed can be made sufficiently low to tune the cavity to a whole wavelength. The presence of fibres within the TM opens up the possibility of many different propagation modes. However, it seems to me that capillary waves (ripples) present the simplest mechanism with which to get the hypothesis off the ground.

I will finish here for now. My answers to your individual queries are interspersed between your text below.

At this point, I wish to thank you for your constructive comments. I believe that a resonance theory of some sort is the only way to answer the requirements of the ear's high Q (as so perceptively demonstrated by Gold and Pumphrey). The hypothesis that I have proposed is able to fulfil that requirement; it is also able to explain most of the hearing phenomena that I know of. As a person trained in physics, I wanted to present a 'big picture' perspective based on fundamental physical principles that would give a satisfying synthesis of how the ear works. For that reason, it potentially covers the whole of the field (a lot for a single paper), and naturally some areas will not be covered in enough detail to satisfy everyone. Nevertheless, I hope this theory points in the right direction and suggests some worthwhile modeling and experiment.


Andrew Bell.


P.S. If you are having trouble viewing my paper at http://cogprints.soton.ac.uk/abs/bio/200005001  you may need to upgrade your Acrobat Reader to the latest version.


-----Original Message-----
From: AUDITORY Research in Auditory Perception
[mailto:AUDITORY@LISTS.MCGILL.CA]On Behalf Of Eckard Blumschein
Sent: Thursday, 1 June 2000 2:11
Subject: Re: Wasn't v. Helmholtz right?

Dear Andrew Bell,

I very much agree with some important ideas you outlined in your intriguing
paper on the underwater piano.
In particular we share the opinion that the traveling wave is just an
epiphenomenon, but most likely the stereocilia of the outer hair cells act
as the primary sensory elements.


how can the stereocilia resonate to acoustic energy?


I would merely recommend to not ignore the work of Hudspeth who has shown
that depolarization of the hair cells coincides with opening of ion
channels at surface of the stereocilia. Kiang and more recently Ruggero
gave evidence for immediate response to rarefaction whereas response to
condensation is delayed by half a period. So it would possibly be somewhat
misleading to understand OHCs as reacting to over-pressure.


I am not denying that something happens at the tips of stereocilia. I am
simply seeing OHC as reversible transducers. When the body of the OHC
is stimulated by acoustic pressure, that causes the stereocilia to bend;
conversely, when the stereocilia are bent, that causes the body of the OHC
to respond (see below).

What about your suggestions of reverberation between adjacent rows of hair
cells, resonant cavities like a laser cavity, etc. I would need much more
precise descriptions in order to be able and follow you. Surface acoustic
waves seems to me more realistic, in principle.
These are both analogies of the reverberation process that I envisage.
Both have a wave propagating from one end of a cavity to the other,
where it is reflected; the process is repeated and the wave is amplified,
resulting in an active resonant cavity with coherent wave energy
emerging at the end. If you have problems with the term 'acoustic
laser', then it might be better to keep to the analogy with the surface
acoustic wave resonator, which seems closer to what is happening in
the cochlea. To recapitulate, the body of the OHC detects sound
energy and causes its stereocilia to move, launching a ripple in the
TM. When the ripple encounters a neighbouring OHC, its
stereocilia are bent, depolarising the cell and causing the body of
the cell to react. The vital amplifiying mechanism at work is that the
OHC endeavours to return itself to its resting membrane potential.
The stereocilia therefore 'kick back', returning to their original
undeflected position faster than they were deflected away from it,
in the process consuming cellular energy and amplifying the
amplitude of the ripple. The ripple returns to the OHC where it
began, and the process repeats. It may help to imagine the
stereocilia 'connected'  to a molecular motor in the OHC's
cytoskeletal spring: when the stereocilia bend in one direction
(away from the basal body, for example) they cause the spring to
contract, and when the stereocilia bend in the other direction,
toward the basal body, the spring expands. An active servo
mechanism, a molecular motor of some sort, is continually at
work returning the spring to its resting position.
However, why did not you
deal with alternative radial oscillations, being already substantiated by
measurements which were published in several abstracts of previous ARO
As mentioned above, I am happy to entertain radial oscillations
if they are able to give a sufficiently low propagation speed that
the cavity is tuned to a whole wavelength.

How do you interpret that the tips of the stereocila of the OHCs are
obviously embedded in the tectorial membrane? I refer to N. Slepecky
(1997), "Anatomy of the cochlea and auditory nerve", chapter 107 in
Encyclopedia of Acoustics, p. 1350, Fig. 4.
The attachment is necessary so that the stereocilia can launch
a ripple in the TM when they move in response to acoustic
stimulation of the OHC body.

If neural fibers are able to rapidly convey ions, why not expect the same
inside TM? Because I am qualified an electrical engineer, I tend to makes
such exotic conjectures first.
You seem to be suggesting that the stereocilia convey charges to
the TM. Can you describe what happens next and how the IHC
finally respond?

Do not take me wrong, I would like to stress and acknowledge once again
that you pointed the list to the need for a serious revision of the present
doctrine. Even if the majority might have more problems than me with your
whole paper, I strongly support the publication of what I consider the very
point, i.e. prominent radial resonance. This holds on condition you are
ready to rigorously purify your reasoning from any speculative or
inappropriate stuff, no matter whether or not your models on lattice and
musical ratio could be correct.

Eckard Blumschein
I wanted my hypothesis to be comprehensive, showing how the
model could be extended to encompass the panorama of
hearing physics and psychophysics. At times I have had to be
speculative where data were lacking, but I believe the core of
the hypothesis is contained in the body of the paper, with the
speculative material residing chiefly in the appendix. I am
willing to consider suggestions from you or other list members
as to which material currently in the body should be sent to
the appendix, or vice versa.
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