Subject: Re: mechanical cochlear model From: "Richard F. Lyon" <DickLyon@xxxxxxxx> Date: Mon, 15 Mar 2010 15:27:08 -0700 List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>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