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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.

Reinhart Frosch. 

P.S.: One more correction, to my note "Correction ..." sent 
two hours ago: In line 9, replace "abscissa" by "ordinate".

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 .

----UrsprÃngliche Nachricht----
Von: DickLyon@xxxxxxx
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?