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Re: Cochlea Amplifier models : a new list
Hello Dick Lyon and List,
The main point of my long note of Oct. 17 is that the present
state of cochlear mechanics is, in my opinion, not badly
confused, in spite of the impression generated (on me, at
least) be the posting of Matt Flax of Oct. 9 ("Cochlea
Amplifier models: a new list") and the many reactions to it.
Of the list (a, b, ... , f) presented in Matt's Oct.-9 posting,
last item ("active travelling wave amplifiers") appears to me
to be significantly more plausible than the others. One can
start with the Neely-Kim (1983) model, but one should
replace the "TM (tectorial membrane) suspended on two
springs" by a different second degree of freedom, namely
by the "Hensen cell" resonator (spring = OHC's and maybe
other nearby structures; mass = Hensen cells and other
nearby structure; angle formed by RL and BM varies in its
vibration). Fig. 1b of Mammano and Ashmore (1993) [see
point 3 of my Oct.-17 posting] yields that this resonator has
the required resonance frequency about one octave below the
resonance frequency of the BM-resonator at the same place.
The model builders should use the many admirable
physiological experiments which have been done on the
function of the inner-ear organs. I have not studied in detail
the complicated mathematics of the models involving
Andronov-Hopf bifurcations, but I fear that they tend to
disregard at least a part of the detailed information supplied
by those experiments, and I tend to agree with the
conclusions reached by G. Zweig (2003) in his paper "Cellular
Cooperation in Cochlear Mechanics" in the proceedings book
"Biophysics of the Cochlea", A. W. Gummer, ed.,
World Scientific, New Jersey, etc., 315-330:
"[...] the responses of these two systems [saccular bullfrog
hair cells, BM of the cochlea] have little in common, even
qualitatively. Nonlinear aspects of [mammal] hearing do not
arise from a cochlea poised near a Hopf bifurcation. [...]"
The passive peak and the active peak:
One should always state (I think) whether one uses the
panoramic view (fixed sine-tone frequency and sine-tone level
at the stapes, variable distance x_b from the base on the BM)
or the frequency domain (fixed x_b and stapes level, variable
sine-tone frequency). In the panoramic view, the function of
local BM vibration level (or "response", in dB) versus x_b of
the wave generated by a soft or medium-loud sine-tone indeed
shows a continuum (i.e., a profile) containing a broad passive
peak (which stays there if the OHC's die) and, at a location
x_b about 1.4 mm further apex-ward (for guinea pigs), an
active peak. At 15 kHz and 55 dB, for instance, the active peak
is (according to the mentioned data of Russell and Nilsen)
higher than the passive peak by a BM-displacement factor of
10, i.e., by 20 dB.
I shall reply separately to the points raised by Matt Flax.
P.S.: One more correction, to my note "Correction ..." sent
two hours ago: In line 9, replace "abscissa" by "ordinate".
Dr. phil. nat.,
r. PSI and ETH Zurich,
Phone: 0041 56 441 77 72.
Mobile: 0041 79 754 30 32.
E-mail: reinifrosch@xxxxxxxxxx .
Datum: 18.10.2007 02:38
An: <reinifrosch@xxxxxxxxxx>, <AUDITORY@xxxxxxxxxxxxxxx>
Betreff: Re: AW: Cochlea Amplifier models : a new list
I remain unclear on the point of your long note, interesting
though it was. Are you saying that the passive peak and the
active peak that are a half octave apart in cochlear mechanics
are distinct things, or are you saying that they are two ends
of a level-dependent continuum? I tend to believe the latter;
do the data you describe tend to push the interpretation one
way or the other?