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Re: mechanical cochlear model
Martin, I think you're changing your story. You had said that the
community had always maintained that a (net) displacement of fluid
volume via the cochlear windows was a precondition of a basilar
membrane traveling wave. What you've pointed out is that the
community knows that the traveling wave involves both localized
displacements and localized pressure differences across the BM. We
agree on that part.
The mathematical physics of wave propagation is not hard to
understand; it's clear that a rocking motion will propagate as waves,
as all disturbances will, but it may not be the most efficient
coupling to stimulate the hair cells, especially at low frequencies.
On the other hand, it may very well be the most effective way to
drive the traveling wave at high frequencies (starting above 4 kHz in
humans is where they say the stapes motion starts toward the rocking
mode), where the wavelength of the TW in the 3D shape of the
vestibule and basal region of the cochlea would be pretty short, so
you wouldn't want to try to drive it the same way as you'd drive it
in the long-wave region. This would be a great topic to explore
At least we can all agree with what Robles and Ruggero wrote.
Re the "threshold concept," it is fine in empirical auditory
research, especially psychophysical work. I've never seen anything
like it in physics, though. I don't see how the Nuttall paper
relates to what you're trying to say about a threshold. Typically, a
threshold is something set by the experimenter, such as a neural rate
threshold for finding a tuning curve, in which the experimenter sets
a threshold of 2 spikes per second over spontaneous rate (say); or in
psychophysics, where the experimenter's threshold is 75% correct on a
2AFC test. Given these thresholds, the stimulus parameters needed to
reach threshold can be measured and plotted. None of this suggests
that the system under test has a threshold inherent in it. But given
a response threshold, one can measure the stimulus intensity needed
to reach threshold.
I searched for Nuttall papers that mention a threshold, and found one
that might confuse (1991 Laser doppler velocimetry of basilar
membrane vibration), where he says "Thus the realistic minimum
velocity recorded by a lock-in amplifier using a 1 s time constant is
about 10 pm/s. This level is less than the anticipated threshold of
motion for the basilar membrane (Patuzzi et al., 1983)." I'm pretty
sure that what he means by "the anticipated threshold of motion for
the basilar membrane" is the amount of motion (velocity) that
corresponds to a neural rate threshold, and that his apparatus noise
is low enough to resolve that -- not that he thinks the wave motion
will jump from 0 to something above 10 pm/s at some stimulus level.
The latter concept has no place in mathematical physics; even quamtum
effects, which have discrete "jump" manifestations, are not
describable with a "threshold" in most cases, and those aren't the
releavant effects here.
The gain takes place within the outer hair cells (OHCs), which are
the motors of the cochlear amplifier. The amplification of a
by-passing basilar membrane traveling wave by OHCs is physically
impossible, because the motor activity of these cells has a latency.
Even a delayed secondary traveling wave produced by OHC activity has
never been observed. The data from the labs of Russell and Ren show
no basilar membrane motion between the stapes and the characteristic
frequency (CF) hair cell excitation area.
This is a common misconception, so it's good that you brought it up.
The energy for the gain comes from the OHCs, but to say the gain
takes place within them is to ignore the traveling wave. What you
say is physically impossible is what most of us think is going on:
amplification of a by-passing basilar membrane traveling wave by
OHCs. There's plenty of evidence and modeling work that shows how it
is possible. There are many experiments that show what you're saying
Russell and Ren do not show: BM wave motion between the base and the
best place. Of course, at low levels it's hard to show, as the wave
motion before amplification is too feeble to overcome the noise in
the experimental apparatus. But there's ample evidence that it's
linear in this region, so the low-level wave is easy to estimate from
measurements at higher levels.
My apologies to anyone who doesn't want me yakking so much to the list.