Subject: Re: mechanical cochlear model From: Matt Flax <flatmax@xxxxxxxx> Date: Tue, 9 Mar 2010 09:16:13 +1100 List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>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