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Re: mechanical cochlear model

Reinhart, Lina, Sunil, Douglas, and list:

We need to consider that a bank of resonators, when simultaneously excited,
create something that _looks_like_ a traveling wave. I have no doubt that
Ren et al. show increasing phase delay with distance, but the fundamental
question is: what causes it - traveling wave or resonance?

I have tried to disentangle the semantics by classifying a resonant system
as one where the stimulus is applied _in_parallel_ (like when thumping a
piano with the sustain pedal down), whereas a traveling wave (TW) system is
one where the stimulus moves through the system _in_series_ (like a ripple
on a pond). Douglas points us to Bekesy's bank of pendulums, where the
distinction is nicely made: resonance is when all the pendulums are excited
simultaneously, and a traveling wave, when the pendulums are coupled via an
elastic thread. Both give rise to a moving wavefront, but in the first case
the wavefront carries no energy, whereas in the second it does.

On this basis, the University of Utah model is really a resonance model, for
it is a bank of independent resonators - tubes which are isolated from each

Remove the tubes and we get coupling, something close to a traveling wave
model. But according to de Boer's analysis of traveling waves (p. 277), we
require "a fairly large mass term, one that is larger than can be accounted
for by the mass of the fluid contained in the organ of Corti". Section 5.4
is headed "A Dilemma", and says, troublingly, that either the amplitude of
the peak remains too low or the phase variations too fast.

I'm not clear where your energy figures come from, but the physical model
constructed by Sunil doesn't appear to be particularly efficient. Fig. 10
shows membrane displacements of about 1 nm/Pa, whereas sensitivity of the
organ of Corti is measured as about 0.1 nm/20 uPa (live cochlea) and about
50 nm/Pa for a dead one. Karl Grosh's cochlea shows a similar sensitivity
problem, with a response of about 0.02 nm/Pa, and that's with one side
facing air.

My thinking is that the differential pressure needed to drive a traveling
wave is insufficient for the task. It can't produce the responses observed,
and we should look elsewhere for the effective cochlear stimulus. The
common-mode pressure is my preferred candidate. A pressure wave spreads
rapidly through the cochlear fluids, and the outer hair cells can
simultaneously sense it (they seem to be piezoelectric
voltage-to-displacement converters) which then gives rise to the motion we
see. The idea is set out in my PhD thesis where I construct a resonance
model of the cochlea and discuss drawbacks of the conventional TW theory:
Bell, A. (2005) The Underwater Piano: A Resonance Theory of Cochlear
Mechanics http://thesis.anu.edu.au/public/adt-ANU20080706.141018/index.html
Bell, A. (2007) Detection without deflection? A hypothesis for direct
sensing of sound pressure by hair cells. Journal of Biosciences 32, 385-404
(open access).

Can the cochlea resonate? When I listen to the recording of the sound picked
up by a microphone in the ear canal, it sure sounds like a highly tuned
structure is resonating.


Andrew Bell
Research School of Biology (RSB)
College of Medicine, Biology and Environment
The Australian National University
Canberra, ACT 0200, Australia
T: +61 2 6125 5145
Mob:  0410 403 341
F: +61 2 6125 3808

> -----Original Message-----
> From: AUDITORY - Research in Auditory Perception 
> [mailto:AUDITORY@xxxxxxxxxxxxxxx] On Behalf Of reinifrosch@xxxxxxxxxx
> Sent: Wednesday, 3 March 2010 11:38 PM
> To: AUDITORY@xxxxxxxxxxxxxxx
> Subject: [AUDITORY] AW: Re: mechanical cochlear model
> Dear Andrew,
> Many others would be better qualified to comment on your 
> posting, but since they have not done so up to now, here goes:
> The travelling cochlear wave is well established, I think. 
> Even at the "characteristic place", i.e., at the low-level 
> "active peak", the travelling wave has been experimentally 
> demonstrated; see, e.g., Fig. 1 of Ren et al. (2003), 
> "Measurement of Basilar-Membrane Vibration Using a 
> Scanning Laser Interferometer", Biophysics of the Cochlea 
> (Titisee Proceedings), World Scientific, New Jersey, pp. 211-219.
> The mechanical-energy transfer from fluid to partition is 
> efficient. For instance, in slices dx near the base of a 
> passive two-dimensional model 
> as described by de Boer (1996) in Chapter 5 of "The Cochlea" 
> (Springer, New York), the pure-tone-wave mechanical energy is 
> predominantly in the liquid; in a slice dx 
> at the "passive peak", however, 30 percent of the energy is 
> in the "upper-half-channel" liquid, 40 percent in the 
> partition, and 30 percent in the "lower-half-channel" liquid.
> The construction of a corresponding mechanical model may 
> indeed be difficult: the direct longitudinal coupling between 
> neighboring elements dx of the partition 
> must be negligibly small, but the liquid must be prevented 
> from penetrating through 
> the partition.
> Reinhart Frosch,
> Dr. phil. nat.,
> r. PSI and ETH Zurich,
> Sommerhaldenstr. 5B,
> CH-5200 Brugg.
> Phone: 0041 56 441 77 72.
> Mobile: 0041 79 754 30 32.
> E-mail: reinifrosch@xxxxxxxxxx .