Re: mechanical cochlear model

[Matt Flax <flatmax@xxxxxxxx>]

The concept that the passive inner ear mechanism does not conduct energy
as a fast pressure wave (with long wavelength) may be true - however not
everyone agrees on this point. I believe that you are talking about the
coupling between the outer ear and the inner ear below - and thus the
passive action of the hearing system.

The concept that the active inner ear mechanism is an active travelling
wave seems a little impossible (from what people have discussed
previously - experimental evidence and theory) for any location other
then the base of the inner ear. I stand on record as the first for
claiming that the base is dominated by the active travelling wave and
the mid/apex is dominated by the active long pressure wave (my
compression wave cochlear-amplifier definition).

Matt

On Mon, 2010-03-08 at 07:52 -0800, Richard F. Lyon wrote:
> Alain, your "simple account" was "reasonably correct" whether you 
> mentioned the traveling wave or not, so I agreed with you.
> 
> I admit I don't see why you don't explicitly identify that account 
> with traveling waves.  Sinusoids in such a system are locally 
> described as cos(ometa*t - k*x), with some varying amplitude, where 
> the relations between omega and k locally obey the same kind of 
> dispersion relation (more or less) as gravity waves on water.
> 
> The real issue seems to be about where the energy is, and how it 
> propagates and gets detected.  The fast pressure wave is another 
> physical mode that really exists, but its wavelengths are all very 
> large compared to the cochlea, so the pressure due to this mode can 
> be viewed as equal throughout the cochlea; pushing on the stapes 
> immediately pushes out at the round window.  But this mode doesn't 
> carry much energy, as the middle ear leverage isn't nearly enough to 
> couple efficiently to it; there's also no efficient way to get energy 
> back out of this mode into a place and a form for which detectors are 
> known; the fast compression wave therefore carries pressure, but not 
> much energy.  The traveling wave mode, on the other hand, involves 
> much larger fluid displacements at the same pressures; it's a 
> differential mode between the scalae, propagated by the spring of the 
> BM instead of by fluid compression.  And the energy converges on the 
> BM as the wave slows down and the wavelength gets short, focusing the 
> energy into a small layer with large displacements at the BM.  There, 
> the hair cells, which evolved to detect fluid motion via cilia 
> bending, are well positioned to respond.
> 
> A wave has three kinds of delays:  phase, group, and wave-front.  In 
> typical models, the wave-front delay is essentially zero, and the 
> response latency can be made to approach zero as the level gets very 
> high.  The group delay depends on the damping, including negative 
> damping effects, and so varies a lot with level.  The phase delay is 
> in between, around a cycle and half, and pretty stable.  Pretty much 
> everything about it is as Lighthill described, in terms of energy 
> flow, except that there's not much BM mass so it's not really 
> significantly resonant, except for very high frequencies very near 
> the base where the accelerations are very high.  And except for some 
> positive feedback from outer hair cells that modifies the dispersion 
> relation, providing active gain instead of loss over some range of 
> wavelengths.
> 
> If it walks like a wave, and quacks like a wave, and transports 
> energy like a wave, why not call it a wave?
> 
> Dick