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Re: mechanical cochlear model
At 8:36 PM +0100 3/15/10, Martin Braun wrote:
Dear Peter, and others,
>Any fluid motion (such as caused by a rocking stapes) will cause
>a travelling wave. Even the minute fluid displacements in a
>compession wave will cause a traveling wave.
Now I see what you mean. This is surely an original view, which
would be totally new to the community of Bekesy's followers, who
have always maintained that a displacement of fluid volume via the
cochlear windows was a precondition of a basilar membrane traveling
wave.
Martin, if anyone has maintained such a thing as a precondition, in
such a strong form, it would be good have a reference to it.
It's likely that "Bekesy's followers" have sometimes neglected other
modes than the piston or long-wave mode at the base, since these
modes aren't central to modeling the normal mode of operation. I'm a
little surprised by what the authors that you quoted (Huber et al.)
wrote: "The collected data of the presented study cannot be explained
by the current theory of hearing." Not exactly wrong, but perhaps a
narrow view of "the current theory of hearing". As I understand it,
the current theory is that the sound energy gets to the hair cells
via a hydromechanical traveling wave, and it seems clear that the
result is "explainable", if not yet "explained", within that theory.
According to this paper:
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2538349/#CR27
the old "piston" assumption was abandoned 10 or more years ago, and
several groups have been studying stapes modes in detail, before and
after that time. Perhaps the advances in knowledge of the middle ear
have not yet been fully integrated into 3D hydrodynamic models of the
inner ear. That doesn't mean there's an inherent impossibility in
doing so.
In the book version of the Huber paper (Sequeira et al. 2004)
http://books.google.com/books?id=xLbueVsCKCwC&pg=PA35&lpg=PA35&dq=stapes-footplate+rocking+piston+traveling-wave&source=bl&ots=TJF15nIl4c&sig=WS80xYSTWpf3qAYfXbkoeqmLzXg&hl=en&ei=1KSeS8LkAoHkswPwusm_Aw&sa=X&oi=book_result&ct=result&resnum=4&ved=0CBsQ6AEwAw#v=onepage&q=stapes-footplate%20rocking%20piston%20traveling-wave&f=false
they state that "the effective stimulus to the cochlea is thought to
be the pressure difference between the oval and round windows",
citing a paper "Is the pressure difference between the oval and round
windows the effective acoustic stimulus for the cochlea?" by Voss et
al. 1996. However good a model this may be of normal cochlear
operation, based only on measurements outside the windows, it is a
trivialization of the 3D traveling wave that generates the actual
effective stimulus, bending of hair-cell cilia.
In general, the response in the cochlea will be a superposition of
waves from different points on the oval and round windows. Something
close to piston mode is probably most efficient for moving the
basilar membrane, at least at low enough frequencies that the basal
region is in long-wave mode, and is the only source geometry usually
analyzed. But other patterns will propagate with the same 3D wave
equations. All the math still works, with (nearly) linear
superposition. At high enough frequencies, where the wave is not
long-wave near the oval window, a rocking motion will likely be more
effective than a piston motion at moving the membrane.
For any particular frequency and place, there will be certain stapes
motion geometries that will yield a zero response. Finding these
would give some detailed constraints on the traveling wave, though it
might be hard interpret these with respect to the detailed 3D
geometry.
This search:
http://www.google.com/search?q=stapes-footplate+rocking+piston+traveling-wave
suggests that several papers have investigated the relationship of
cochlear traveling waves to rocking motion of the stapes, and
suggests that the rocking mode was described first by von Bekesy.
Follow up and get the papers from Elsevier if you want to know what's
behind the snippets, but I doubt that you'll be able to continue to
say that these issues are "totally new to the community of Bekesy's
followers." Rather, they come from, and are studied by, the
community of hearing researchers, including those who respect Bekesy
for his contributions.
I see a question mark with your view, though. The basilar membrane
clearly is "harder" or "stiffer" than the cochlear fluids.
I'd say the opposite, if anything. The fluid is very hard
(incompressible); it just has mass (and a negligible compliance).
The membrane has spring (compliance). Like inductors and capacitors,
these (mass and compliance) can't be compared on the same scale.
They interact to make frequency and wavelength characteristics.
Would this not imply that on the low-level side of sound input we
are likely to have range where the energy is sufficient to move the
fluids ("compression wave") but not sufficient to move the basilar
membrane ("traveling wave")?
Energy is not the issue. Pressure is needed; the fast compression
wave needs much higher pressures than the slow BM wave. That
impedance mismatch also makes coupling energy into the compression
wave much less efficient, so it doesn't usually get nearly as much
energy as the slow traveling wave does.
Martin, I'm puzzled by your frequent resort to "low sound level" as
if the behavior there is not (approximately) a linear extrapolation
downward from the behaviors that we see at higher levels. Of course
we know there are differences due to the nonlinear cochlear
amplifier, especially near the peak, but in the tails at least, and
generally anything not right near the peak, the system is pretty
linear. The notion of "sufficient energy" is peculiar in this
context, as if below some threshold something would not move. An
understanding of the mathematics of distributed linear systems would
go a long way to clearing up your difficulties with the current
theory of hearing, I suspect.
Would it not be reasonable to assume that in this range of energy
input there could be enough energy to move hair cell cilia, but not
enough energy to move the much, much "harder" or "stiffer" basilar
membrane?
No, not reasonable.
Dick