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Re: mechanical cochlear model
sorry for not using the special mailing list yet, but I was asked a
question which I have not yet answered. Some people may be waiting for
the answer. I'll keep it short.
The question was by Michael Rapson and was about a model of the cochlea
consisting of weights suspended on strings in a fluid.
The difference is that in this case the weights do not constitute a
boundary. All I have said about the traveling wave was based on a fluid
with a flexible boundary which has a restoring force. If the fluid is
moved, in this case you will always get a traveling wave.
(In reponse to Martin Barun: mathematically there is no limit or
threshold, physically the threshold would be there were the assumption
of a continuous fluid breaks down, that is the molecular level.)
In the model with weights suspended in fluid the weights do not form a
boundary and fluid can move around the weights freely. In this case
there is still a coupling of movement between the weights through the
fluid, but I'm afraid more complex stuff like boundary layers due to
viscosity come into play. So the dimensions of the weights and the
distances between them then become important. I would not hazard any
guess as to traveling wave behavior in such a model although I would
certainly not rule it out.
My statement about a traveling wave always resulting from movement of
the fluid, is restricted to the case where there is a fluid with a
flexible boundary with a restoring force. This I believe is a good
representation of the cochlea and therefore I believe there are
traveling waves in the cochlea.
In response to Martin Braun I have a question how there can be a motion
of fluid without a pressure change, or a sound wave without a pressure
change? The fluid mechanics I know (Bernoulli etc) states that any
motion of fluid is always linked to a pressure gradient, therefore
pressure difference, and I thought a sound wave was defined as pressure
differences traveling. But perhaps you're refering to some average
pressure? This discussion can be continued on the separate list at
if you'd like...
All the best,
Martin Braun schreef:
> Richard F. Lyon wrote Tuesday, March 16, 2010 4:10 PM:
>>>>> ...... 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
>>>> 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.
>>> No problem. In their often referenced review "Mechanics of the
>>> Mammalian Cochlea" Robles and Ruggero (2001) write as follows:
>>> "Pressure waves reaching the eardrum are transmitted via vibrations
>>> of the middle ear ossicles to the oval window at the base of the
>>> cochlea, where they create pressure differences between scala tympani
>>> and the other scalae, thus displacing the BM in a transverse
>>> direction." http://physrev.physiology.org/cgi/content/full/81/3/1305
>> I can agree with Robles and Ruggero here, but they are not supporting
>> your concept "that a displacement of fluid volume via the cochlear
>> windows was a precondition of a basilar membrane traveling wave." They
>> are not ruling out rocking motion creating a pressure difference
>> across the membrane via a traveling wave.
> It is not "my concept", but that of Bekesy, here adopted by Robles and
> Ruggero. When these authors write "pressure differences between scala
> tympani and the other scalae" they say that in scala tympani there must
> be a pressure that is different from that in the other scalae. This
> means that stapes motion must change the pressure in scala tympani. A
> piston-like motion of the stapes, with a sufficient amplitude, does
> this. A rocking-like motion does not do it. A rocking-like motion,
> however, causes a sound wave ("compression wave") in scala tympani,
> without changing the pressure in this scala.
> Again, Bekesy, Robles and Ruggero, and some others, consider a pressure
> change in scala tympani as a precondition of a hair cell response. The
> data of Huber et al. (2008), as quoted earlier in this thread, and
> several other sets of data have disproved this view. Hair cells do
> respond without a pressure change in scala tympani.
> Just some examples of the other data sets:
>>>> ..,,,,,. The notion of "sufficient energy" is peculiar in this
>>>> context, as if below some threshold something would not move.
>>> Not "peculiar", but self-evident. Everything that is moved by
>>> external forces has a threshold. Below this threshold it is not
>>> moved. The thinnest branches of a tree may have a threshold of 0.5
>>> m/s wind speed, whereas the thickest branches of the same tree may
>>> have a threshold of 20 m/s wind speed. You are not trying to tell us
>>> that everything that moves in the cochlea has got the same
>>> sound-level threshold, are you?
>> This "threshold" concept is to me "peculiar", as a person trained in
>> linear systems. Do you have some sources for it where I can try to
>> understand it?
> The "threshold concept" is a central one in most empirical auditory
> research. In particular, in recent years the differential motion of
> mechanical elements within the cochlea has been in the focus of
> empirical research of the inner ear. For example, the lab of Alfred
> Nuttall reported that at the same characteristic frequency (CF) place
> the basilar membrane and the reticular lamina moved independendly from
> each other.
> F. Chen, J. Zheng, N. Choudhury, S. Jaques, A.L. Nuttall (2009) Organ of
> Corti micromechanics with local electrical stimulation. In: NP Cooper,
> DT Kemp (eds) Concepts and Challenges in the Biophysics of Hearing.
> World Scientific Publishing, Singapore, pp. 135-140.
>> There is a gain in energy from the entrance of the cochlea to the hair
>> cells. That's what the cochlear amplifier is about.
> The gain takes place within the outer hair cells (OHCs), which are the
> motors of the cochlear amplifier. The amplification of a by-passing
> basilar membrane traveling wave by OHCs is physically impossible,
> because the motor activity of these cells has a latency. Even a delayed
> secondary traveling wave produced by OHC activity has never been
> observed. The data from the labs of Russell and Ren show no basilar
> membrane motion between the stapes and the characteristic frequency (CF)
> hair cell excitation area.
> Martin Braun
> Neuroscience of Music
> S-671 95 Klässbol
> email: nombraun@xxxxxxxxx
> web site: http://www.neuroscience-of-music.se/index.htm
dr. ir. Peter van Hengel
Fraunhofer Institut Digitale Medientechnologie (IDMT)
Project Group Hearing, Speech and Audio Technology
Haus de Hörens - Marie-Curie-Strasse 2 - 26129 Oldenburg - Germany
T: +49 (0) 441 2172 436
F: +49 (0) 441 2172 450