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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 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.