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