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Corrected version, Re: Cochlea Amplifier models : a new list.

Hello Matt Flax and List,

At first I thought that your newest posting ("Thank you 
Reinhart ...", see below) was meant ironically -- but
a later private message from you convinced me that
you earnestly, and probably in contradiction to me,
consider a "compression amplifier".

I would now like to discuss a "DPOAE" (distortion-
product oto-acoustic emission) mentioned in T. Ren
et al., "Backward propagation of otoacoustic emissions
in the cochlea", in "Auditory Mechanisms" = Portland 2005 
proceedings, World Scientific, 2006: 79-85,
in order to show that these data are not in conflict
with "my" cochlear model (involving the "HC-resonator").

Cochleae of young and healthy gerbils. Two simultaneous
70-db (SPL) sine-tones, f_2 = 17 kHz, f_1 = 14 kHz.
The active peak of the f_2-wave is at about x_b(2) = 2.30 mm,
and that of the f_ 1-wave is at about x_b(1) = 2.75 mm.
The (-10dB)-width of these active peaks is about 0.4 mm.
Because of the comparatively high level (70dB), the f_1-wave
BM-displacement amplitude at x_b(2) = 2.30 mm is
fairly large, so it is in the region ranging  from about
x_b = 2.1 mm to x_b = 2.5 mm that a soft "cubic 
combination tone" is  generated, because the waveform
(displacement versus time) of the two waves is
slightly flat-topped rather than exactly sinusoidal. (See
Appendix XII of Helmholtz's "On the sensations of tone").

This cubic combination tone is also called "distortion
product" and has the frequency f(DP) = 2f_1 - f_2 = 11 kHz.
An additional travelling wave (TW) with that frequency of
11 kHz is generated at and near x_b = 2.3 mm and travels,
on the BM, apex-ward, gaining in amplitude, to the 11-kHz
active-peak location, x_b(DP) = 3.3 mm, then dies at about
x_b = 3.7 mm. That 11-kHz wave is passive from 2.3 to
about 2.9 mm, where the 11-kHz active peak and the
energy generation by the OHC's begin. A similar (i.e., slow)
TW also travels from x_b = 2.3 mm base-ward; this wave
can be predicted by time-reversal of an 11-kHz wave
starting at the base and having the correct amplitude at 
x_b = 2.3 mm; thus the BM-displacement amplitude
of that that base-ward 11-kHz wave will be small at 2.3 mm
and even smaller on approaching the base.

The strongest 11-kHz BM vibration (amplitude at least 10 
times larger than at 2.3 mm) will occur at 3.3 mm. On the
basal side of that active 11-kHz peak, from about 2.9 to 
3.3 mm, the Hensen-Cell resonators vibrate strongly, i.e.,
the angle between RL and BM in that 0.4 mm long
x_b-region oscillates at 11 kHz. I now conjecture 
that the part of the organ of Corti containing the IHC's, 
the IP-cells, the inner tunnel, the OP-cells, the OHC's, 
Deiters cells, the outer tunnel, and the Hensen cells 
has a fairly tight wall around it, so that in the mentioned
0.4-mm x_b-section with strong HC-resonator vibration the
liquid pressure and the liquid volume oscillate at 11 kHz. 
That region is postulated to be the source of a liquid-
compression wave (i.e., an ordinary sound wave) which
spreads at c_s = 1500 m/s through the cochlear liquid and
causes the round window and the oval window to vibrate. 
The wavelength is c_s / f(DP) = 1500 / 11000 = 0.136 m =
136 mm, so at any given moment in time, the liquid
pressure is about equal at all points in the cochlear liquid. 
Thus that sound wave causes no across-BM pressure
difference and thus (I believe) no significant signals from
the IHC's to the brain, but it can, via the middle-ear 
ossicles and/or via air from the round window to the
eardrum, generate a signal in a microphone in the ear canal.

Reinhart Frosch.

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: flatmax@xxxxxxxx
Datum: 20.10.2007 19:02
An: <AUDITORY@xxxxxxxxxxxxxxx>
Kopie: "reinifrosch@xxxxxxxxxx"<reinifrosch@xxxxxxxxxx>
Betreff: Re: Cochlea Amplifier models : a new list

Thank you Reinhart. On behalf of the list.

You have finally walked a mind experiment which has led
you to your version of the Compression amplifier. [...]