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Re: HC selectivity ... was Re: Physiological models of cochlea activity - alternatives to the travelling wave
Dear Andrew and list,
One picometer is a small displacement, but it's hardly unphysiologically
small. For a 0 dB SPL tone at 4 kHz, the free-field peak displacement
of air is about 2.5 picometers. Commercial OAE systems have microphones
that can sense sounds at least as low as -20 dB SPL, corresponding to
air displacements of 0.25 picometers. If, as Martin said, "there is no
known physics by which a mechanical signal of this magnitude could be
transported, let alone be detected," then these microphones - and our
ears - would be detecting phantoms.
As a further example, the company PI has recently announced a
positioning device that has (at least) 50 picometer positioning
The sensor they use to detect this position has an even higher
resolution still; from their graph on that web page (click on the plot
in the lower right), the sensor noise looks to be on the order of a
couple of picometers. So even man-made systems come close to achieving
the required sensitivity. It is hardly a stretch of the imagination to
believe that a micro-scale biological system can perform similarly well.
With regard to whether Brownian motion would preclude OHC amplification
of such small signals, so far I've seen a lot of hand-waving on both
sides of the issue, but few quantitative arguments. Since it's much
easier to show that something is possible than to show that it isn't,
the people who wish to argue that OHCs can't amplify these small signals
have a harder job here. Nonetheless, I would be interested to see
someone do this analysis carefully.
Finally, the traveling wave has been seen experimentally, is consistent
with a wide variety of other measurements, and has strong predictive
power. These facts, and not some blind faith in von Bekesy as Martin
suggests, are why the traveling wave concept has become firmly ingrained
in the field of cochlear mechanics. For any alternate model to become
as widely adopted, we would need either compelling evidence that the
traveling wave concept is wrong, or a model with more explanatory and
predictive power than the traveling wave. So far I have not seen either.
Andrew Bell wrote:
I'm pleased we now both see the 1 pm for what it is: the fundamental input
signal of the traveling wave theory at 0 dB SPL. You express faith that such
a signal is sufficient to give a 1 nm measurable displacement via a
traveling wave mechanism of some sort. Yes, the evidence is that the OHCs do
the work, but why do you assume it's via a 'traveling wave' mechanism? There
could be other mechanisms, could there not, and if an alternative one
happened to give LARGER input displacements than what the TW offers, it
would seem to make a better candidate for the effective stimulus.
Calling such an alternative a 'strawman' seems a pejorative term that
prejudges the issue. If AJ's calculation returned a value a thousand times
lower (0.001 pm) would you still have faith that the TW could dig below the
noise threshold and take care of everything? In other words, do you have a
threshold below which you think the traveling wave mechanism would have
For me, 1 pm is below my threshold of credibility, but I can rest a bit
easier with a pressure-induced motion of 100 pm. I have recently published a
cochlear model in which outer hair cells produce standing waves in the
subtectorial space (Bell, 2007), and in it that 100 pm figure could be used
as the input to a local, OHC-driven cochlear amplifier. So the TW need not
be the only theoretically possible amplifying mechanism.
Bell, A. (2007). Tuning the cochlea: wave-mediated positive feedback between
cells. Biological Cybernetics 96, 421-438.
Research School of Biological Sciences
The Australian National University
Canberra, ACT 0200, Australia
T: +61 2 6125 5145
F: +61 2 6125 3808
From: AUDITORY - Research in Auditory Perception
[mailto:AUDITORY@xxxxxxxxxxxxxxx] On Behalf Of Richard F. Lyon
Sent: Thursday, 4 October 2007 5:00 PM
Subject: Re: [AUDITORY] HC selectivity ... was Re: Physiological models of
cochlea activity - alternatives to the travelling wave
At 2:44 PM +1000 10/4/07, Andrew Bell wrote:
The point is that we are talking about the input signal to the cochlear
amplifier. There has to be a passive signal (the effective stimulus) on
which the positive feedback process can work. The BM displacement that
is measured in a normal cochlea is _after_ amplification has occurred
(remember that AJ's original figure of 1 pm was derived from Ruggero et
al. 1997 by looking at their post-mortem data).
So the fundamental question is, how can a normal cochlea detect 1 pm
and amplify it a thousand-fold (60 dB) so that we see a 1 nm
displacement? I agree with Martin that it can't, and there has to be
some other, larger, effective stimulus.
Yes, that is the fundamental question, sort of. It's not like
there's some element that detects an "input" of 1 pm and amplifies to
an "output" of 1 nm; rather, there's a distributed amplifier that
multiplies up the power of traveling waves. At the low end of the
range, everything behaves linearly. As long as the noises of the
many hair cells are reasonably uncorrelated, the system will be able
to work to orders of magnitude below the level that would cause a
"noticeable" effect in a single hair cell. Ultimately, the shot
noise of ion channels, averaged over many OHCs, is what will set the
sensitivity limits; there's no "threshold" below which amplification
stops working, the signal just gets down below the noise.
So I reiterate: it's a funny strawman to look at what the motion
would be in a dead cochlea and say that's too little for the OHCs to
work; they do work, and the result is that the motion is much greater.