Re: mechanical cochlear model

["Richard F. Lyon" <DickLyon@xxxxxxx>]

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 
further.

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.

Dick