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Re: Cochlear travelling wave. An epiphenomenon?

Andrew Bell wrote:
> Dear Antony Locke and list:
> Thank you for the opportunity to clarify what I mean by 'epiphenomenon'.
> By the term I meant to convey that the traveling wave, viewed by an outside
> observer as a moving wave packet on the CP, doesn't, by itself, DO anything.
> It is merely descriptive of the graded time delay in a continuously tuned
> bank of resonators that are simultaneously excited, just like the model
> Bekesy built where he had a series of pendulums (of graded lengths) hanging
> from a common rod that is suddenly jolted. An observer sees 'a traveling
> wave' moving along the array of pendulums, but the traveling wave in this
> case is an epiphenomenon because it doesn't carry any energy.

First the word "epiphenomenon" is defined in the dictionary, so we dont
need to redefine it. You are not defining this word, your are describing a wave
that is not a traveling wave, it is a correlated set of resonators driven by
a common source.

The exsistance of such a device, as described by Bekesy, does not prove that
the cochela is such a device. In my opinion, it is not.

> On the resonance theory of hearing, what happens is exactly like Bekesy's
> model. And so I believe the TW in the cochlea is an epiphenomenon because it
> doesn't carry energy from one tuned element to the next.

The difference between the cochlea and Bekesy's device is that the resonators
(each section of the CP) is coupled via the fluid. The end result is a true
traveling wave. This analysis is done in

   author = {Allen, J. B. and Sondhi, M. M.},
   title = {Cochlear macromechanics: {T}ime-domain solutions},
   journal = JASA,
   volume = {66},
   pages = {120-132},
   year = {1979}

where we show how the Green's function for the fluid filled box couples
the independent resonators together.
The end result is a wave-like equations rather than the device of Bekesy.
There is a clear mathematical difference here.

> You state that on your view of cochlear mechanics the TW does carry energy,
> and the energy of the TW is shared between the kinetic energy of the fluid
> and the potential energy of the CP. I call this the 'flicked rope'
> description of cochlear mechanics because it behaves in essence like a
> flicked rope, with one element causing the movement of the next (I realise
> that you include coupled fluid elements, but the situation is similar in
> that one element passes on energy to the next). The arrangement is very
> easily modeled by a transmission line, and many mathematical models have
> seized on this analogy (and lost sight of what is going on physically). On
> this flicked rope description, I would agree that the TW is not
> epiphenomenal (it does have causal power), but then I also think this view
> is mistaken.

Based on the Green's function analysis of the fluid in the box, mentioned
above, I would stand by the classical view. Energy IS being propagated.

> One of the key problems with this flicked rope description is that it relies
> on coupling between the resonators to carry the energy. One soon finds that
> the coupling is very inefficient, so that the energy becomes prematurely
> dissipated way before the wave reaches the CF place.

Is very efficently coupled via the fluid (the Greens function convolution term
in the Allen Sondhi paper mentioned above).

> A related problem is
> that because one is relying on coupling, each resonating element cannot act
> independently, and so it is extremely difficult to achieve the high Q's that
> the cochlea does (a spontaneous otoacoustic emission at 1500 Hz can have a
> bandwidth of less than 1 Hz (f/deltaf = 1500).

This just is not true. I dont want to get into it here.

> I have seen no TW model that
> can achieve such a high figure.

Then you haven't looked carefully enough.

> Even more difficulty arises when one tries
> to model a reverse traveling wave (needed in order to carry OAEs from their
> location on the partition to the ear canal): the energy losses are even more
> severe.

To the best we know, forward and reverse propagation are identical. There
is no evidence to the contrary.

> Another drawback is that near the threshold of hearing, we are
> dealing with minute quanties of energy (units of electron-volts), and how
> can the whole partition (at the base) be moved using such tiny energy, even
> if the energy is only 'on loan' and is passed on to subsequent CP locations
> and eventually to the required CF? Because of these difficulties, one can
> see why the OHCs have been called on to pump in energy to overcome these
> difficulties, but so far unsuccessfully, I believe.

This is not a solid argument. One must average the energy over an area
of correlation before saying how much energy is involved.  The cochlea
is not a quantum device, and quantum arguments do not apply here.

> For these reasons, I have sought to abandon the difficulties posed by
> conventional TW theory (defined as that where energy traveling along the CP
> is initiated by pressure differences across it) and to develop a true
> resonance theory in which outer hair cells sense the common-mode pressure in
> the cochlea. At the outset, I want to make it plain that in most practical
> respects I am not disputing the general observations of the TW theory: in
> particular, there _is_ a graded delay in response along the CP, the only
> major difference is that this graded delay is an _epiphenomenon_ (there is
> no traveling energy). And so, Antony, I would like you to recognise that I
> am not "disregard[ing] two established, and fundamental, observations of
> cochlear mechanics."

Andrew, IMO you have the minority view here.

> My resonance theory consists of two components: high level (>60 dB SPL) and
> low-level (<60 dB).

You are suggesting a very nonlinear theory, that is not supported by the
experimental evidence. There is an important 60 dB effect, but your theory
does not capture it.

> The low-level component is what my 'Underwater Piano'
> paper dwells on,

I suggest you submit your paper to JASA, and get it published. Then lets
talk about it. Your airing your untested concepts on a large number of
people, and it needs some quiet private time, not a public discussion.


> Andrew.

Jont B. Allen
AT&T Labs-Research, Shannon Laboratory, E161
180 Park Ave., Florham Park NJ, 07932-0971
973/360-8545voice, x7111fax, http://www.research.att.com/~jba