[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

Re: mechanical cochlear model

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?