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AW: Cochlea Amplifier models : a new list

Hello Matt and List,

Because of a nice one-week stay in Montreal (CAA-2007 conference) 
this reaction to your posting of Oct. 9 is very late. After having 
read the many answers to your cochlear-amplifier question, however, I 
would like to suggest to some of the contributors to look at the 
following figures in journals and books. Some of my remarks on these 
four figures are very tentative of course.

1) L. Robles and M. A. Ruggero (2001), "Mechanics of the Mammalian 
Cochlea", Physiological Review 81, 1306-1352; the upper part of Fig. 
14 shows data of Russell and Nilsen on guinea-pig BM displacement 
versus cochlear longitudinal position x_a in response to 15-kHz 
sinusoidal tones; x_a, the distance from the apex, ranges from 13.5 
to 17 mm; BM length is about 19 mm; so x_b, the distance from the 
base, ranges from about 2 to 5.5 mm. At sound pressure levels (SPL) 
of 15, 20, 25, ... , 60, 70 dB there is an active peak at about x_a = 
14.47 mm. At SPL = 55, 60, ... , 90, 100 dB there is a passive peak 
at about x_a = 15.86 mm. At SPL < 55 dB no data are shown in the 
passive-peak x_a-region. 

2) T. Y. Ren et al. (2003), "Measurement of Basilar-Membrane 
Vibration Using a Scanning Laser Interferometer", in the book 
"Biophysics of the Cochlea", A. W. Gummer, ed., World Scientific, New 
Jersey, etc., 211-219; Fig. 1C shows gerbil BM velocity versus 
distance x_b from the base in response to a sinusoidal tone of 16 kHz 
and 40 dB (SPL). There are four curves, measured at times T/8, T/4, 
3T/8, and T/2, where T = (1second) / 16000 is the wave period; x_b 
ranges from 2.1 to 3 mm; a hint of the passive peak is visible at x_b 
= 2.1 mm; the active peak is at x_b = 2.6 mm and has a full width at 
half maximum of 0.25 mm. The four curves in Fig. 1C show that there 
is a wave travelling on the BM, in the +x_b-direction (i.e., from 
base to apex), across the active-peak x_b-region. At the active-peak 
centre (x_b = 2.6 mm) the phase velocity of the travelling wave (e.
g., the speed of a wave zero) is 3.2 m/s.

3) F. Mammano and J. F. Ashmore (1993), "Reverse transduction 
measured in the isolated cochlea by laser Michelson interferometry", 
Nature, 838-841. Fig. 1b shows the motion of aluminium-coated glass 
beads placed on the BM and on the Hensen-cell region of the RL 
(reticular lamina) of post-mortem guinea-pigs in response to 4-
millisecond-long rectangular electric-current pulses. Of interest 
here are the damped oscillations at the beginning and at the end of 
these current pulses, since they allow the determination of the 
resonance frequency (i.e., the frequency that the oscillations would 
have without damping) of the resonators to which the observed spots 
belong. At the observed place, the resonance frequency of the BM-
resonator (spring = BM fibres; mass = organ of Corti) was found to be 
2.3 kHz, and that of the "Hensen-cell" resonator (spring = outer hair 
cells and maybe elastic parts of the the Deiters cells; mass = Hensen 
cells and other nearby structures) was 1.0 kHz. I suspect that this 
Hensen-cell resonator (oscillating so that the angle formed by the RL 
and the BM varies) is the "second degree of freedom", rather than the 
tectorial membrane (TM) suspended on two springs mentioned, e.g., in 
Section 7.1 of E. de Boer's chapter in the book "The Cochlea" 
(Springer, 1996).

4) E. de Boer and A. L. Nuttall (1999), "The 'inverse problem' 
solved for a three-dimensional model of the cochlea. III. Brushing-up 
the solution method.", JASA 105, 3410-3420; the lower panel of Fig. 3 
shows the guinea-pig BM impedance (across-BM pressure difference 
divided by BM velocity) versus location x_b (expressed in percent of  
6 mm) for a sine-tone of 16.8 kHz and 20 dB (SPL). In the region from 
67 to 84 percent, i.e., from x_b = 4.0 to x_b = 5.0 mm, the real part 
of the impedance is negative; that implies "negative damping"; i.e., 
it implies that in this x_b-region the outer hair cells (OHC's) feed 
energy into the travelling wave. At locations x_b < 4.0 mm, the 
resonance-peak frequency region of the Hensen-cell resonator (see 
point 3 above) is above 16.8 kHz so that these resonators are not 
excited significantly by the wave. At x_b = 4.0 mm, the low-frequency 
limit of the just mentioned resonance-peak frequency region is at 
16.8 kHz, so that from that location onwards the resonator is 
excited, and the motor proteins in the OHC walls are caused to 
operate, maybe both via modulation of the electric current into the 
OHC hairs and via direct mechanical stimulation of the OHC walls. At 
x_b > 5.0 mm, the Hensen-cell-resonator's resonance-peak region is 
below 16.8 kHz, so that the OHC's do not feed energy into the 
travelling wave. The highest point of the active peak, shown in the 
upper panel of Fig. 3, (i.e., the characteristic place of the 16.8-
kHz-20-dB wave) is at that last-mentioned position of x_b = 5.0 mm. 
Extrapolation of the short-dashed curve in the lower panel yields 
that the imaginary part of the BM-impedance vanishes at about x_b = 
130 percent = 7.8 mm; thus the resonance frequency of the BM-
oscillator (see point 3 above) at x_b = 7.8 mm is 16.8 kHz. The 16.8-
kHz travelling wave does not reach that point. According to the upper 
panel, the passive peak (same wave, dead OHC's) is at about x_b = 60 
percent = 3.6 mm. Thus the distance between active and passive peaks 
is 1.4 mm and so corresponds to half an octave. In the case of two 
similar, but lower-frequency waves in human ears, e.g. 1kHz,20dB and 
1kHz,100dB, there is a similar x_b-difference but (since mostly time-
information is used) a perceived-pitch difference much smaller than 
half an octave; see, e.g., Chapter 6 of "An Introduction to the 
Psychology of hearing" by B. C. J. Moore, Academic Press, Amsterdam 
etc., 5th ed., 2003.

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: 09.10.2007 11:35
An: <AUDITORY@xxxxxxxxxxxxxxx>
Betreff: Cochlea Amplifier models : a new list


After our discussion last week, I have made a new list of possible 
physiological Cochlea Amplifiers (some of these are weakly 
physiologically based). [...]