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Re: Cochlea Amplifier models : a new list
Hello Matt Flax and List,
Answers to your posting of Oct. 18:
1) Fig. 14 of Robles and Ruggero (2001) shows data of
Russell and Nilsen (1997), "The location of the cochlear
amplifier: spatial representation of a single tone on the
guinea pig basilar membrane", Proc Natl Acad Sci USA 94:
2660-2664; (this PNAS paper can be downloaded freely).
Yes, animal was alive and sedated. BM displacements were
measured using "the self-mixing effect of a laser diode".
Light directly reflected from the BM. Fig. 1 of that PNAS
paper is similar to Fig. 14 of Robles and Ruggero (2001),
so you can look at the broad passive response peaks at
x_a = 15.85 mm and at the narrower active peaks at
x_a = 14.47 mm yourself. The phase measurements are
shown in Fig. 2B of the PNAS paper; the phase decreases
if x_b increases (where x_b = 19mm - x_a); this shows
that the wave travels from base to apex.
2) Fig. 1C of Ren et al. (2003), "Measurement of Basilar-
Membrane Vibration ...":
The mentioned book "Biophysics of the Cochlea" (2003) is
the proceedings of the international "Mechanics of Hearing"
symposium at Titisee (Germany), July 27 to August 1, 2002.
That book is certainly in many libraries. The mentioned
Fig. 1C of Ren et al. demonstrates the travelling wave in
the active-peak x_b-region especially clearly --- but the
fact that this travelling wave exists is proven already by the
PNAS paper mentioned under point 1 above (and by many
other papers with phase measurements of course). I do not
understand the part of your message from "Normally Ren's
papers ..." to "... common knowledge". In my opinion the
travelling wave is entirely passive from the stapes to the
small-x_b limit of the active-peak region. Only for x_b-values
between that limit and the top of the active peak do the
OHC's actively feed energy into the travelling wave, as
indicated, e.g., by the negative real part of the BM
impedance in Fig. 3 of de Boer and Nutall (1999), discussed
under my point 4. Would you please give me references for
"Ren's other papers"?
3) Fig. 1b of Mammano and Ashmore (1993), "Reverse
RL (Hensen-cell resonator) has a resonance frequency
deeper, by a factor of about (1 / 2.3), than the resonance
frequency of the BM-resonator at the same place:
Here we appear to agree then.
4) Fig. 3 of de Boer and Nuttall (1999), "The inverse
problem solved ...":
Section VII of that paper is entitled "Conclusions and
reasons for caution", and the first mentioned reason for
caution is: "Long-wave behavior is assumed at and near
(x=0)". Indeed, my calculations have yielded that for the
considered case (guinea pigs, 16.8 kHz) the long-wave
condition (k*H << 1; see, e.g., Section 4 of de Boer's
chapter in the book "The Cochlea", Springer, 1996) is
strongly violated. Possibly there are reasons to hope that
the results of de Boer and Nuttall are approximately correct
in spite of that violation.
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 05:53
An: <reinifrosch@xxxxxxxxxx>, <AUDITORY@xxxxxxxxxxxxxxx>
Betreff: Re: Cochlea Amplifier models : a new list
Dear Reinhart and list,
In a manner similar to Martin, Richard and others, I will go
through the examples you have pointed out.
I also am unsure of what these points are leading to.
I am very interested to hear your conclusion.
Results pointed out by Reinhart:
1) I can confirm that you are pointing out two peaks. I am
not sure about the particulars of the experiment - how
visualisation was accomplished. I assume that the animal
was alive and sedated. The locations pointed out using your
assumptions are that :
a] Active peak in an apical location to the passive peak
b] Passive peak in basal location to active peak.
2) I can not get this reference currently. Normally Ren's
papers are about delay. Ren's other papers have continuity
in that they point out delays are normally as fast or faster
then the travelling wave delay for OAEs. For this reason,
Ren points out that active processes are too quick to
maintain the active travelling wave hypothesis. We
have known this point since the eighties and it should now
be common knowledge.
3) I can confirm that in the dead animal, the RL responds in
a resonant manner below the BM frequency at the same
point of reference. The interpretation is that the RL is tuned
more then an octave below the BM at the same tonotopic
4) I can see the projected negative damping which is
calculated using inverse techniques. I trust your
interpretation of this image which is "the distance between
active and passive peaks is 1.4 mm and so corresponds to
half an octave." I would like to point out that inverse
solutions are numerical interpretations. Guiding numerical
points of view if you will. You further reference high level
perception of pitch "a perceived-pitch difference much
smaller that half an octave"
I trust that I have not mislead the readers and am repeating
your train of thought as confirmation for the list.
On Wed, Oct 17, 2007 at 03:11:20PM +0000, reinifrosch@xxxxxxxxxx
> Hello Matt and List,
> Because of a nice one-week stay in Montreal (CAA-2007
> this reaction to your posting of Oct. 9 is very late. After
> read the many answers to your cochlear-amplifier question,
> would like to suggest to some of the contributors to look at
> following figures in journals and books. Some of my remarks on
> four figures are very tentative of course.
> 1) L. Robles and M. A. Ruggero (2001), "Mechanics of the
> Cochlea", Physiological Review 81, 1306-1352; the upper part of
> 14 shows data of Russell and Nilsen on guinea-pig BM
> versus cochlear longitudinal position x_a in response to 15-kHz
> sinusoidal tones; x_a, the distance from the apex, ranges from
> to 17 mm; BM length is about 19 mm; so x_b, the distance from
> base, ranges from about 2 to 5.5 mm. At sound pressure levels
> of 15, 20, 25, ... , 60, 70 dB there is an active peak at about
> 14.47 mm. At SPL = 55, 60, ... , 90, 100 dB there is a passive
> at about x_a = 15.86 mm. At SPL < 55 dB no data are shown in
> 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,
> 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
> and 40 dB (SPL). There are four curves, measured at times T/8,
> 3T/8, and T/2, where T = (1second) / 16000 is the wave period;
> ranges from 2.1 to 3 mm; a hint of the passive peak is visible at
> = 2.1 mm; the active peak is at x_b = 2.6 mm and has a full width
> half maximum of 0.25 mm. The four curves in Fig. 1C show that
> is a wave travelling on the BM, in the +x_b-direction (i.e.,
> base to apex), across the active-peak x_b-region. At the active-
> centre (x_b = 2.6 mm) the phase velocity of the travelling wave
> 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
> Nature, 838-841. Fig. 1b shows the motion of aluminium-coated
> 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
> here are the damped oscillations at the beginning and at the end
> these current pulses, since they allow the determination of the
> resonance frequency (i.e., the frequency that the oscillations
> have without damping) of the resonators to which the observed
> belong. At the observed place, the resonance frequency of the
> resonator (spring = BM fibres; mass = organ of Corti) was found
> 2.3 kHz, and that of the "Hensen-cell" resonator (spring = outer
> cells and maybe elastic parts of the the Deiters cells; mass =
> cells and other nearby structures) was 1.0 kHz. I suspect that
> Hensen-cell resonator (oscillating so that the angle formed by
> and the BM varies) is the "second degree of freedom", rather than
> tectorial membrane (TM) suspended on two springs mentioned, e.g.,
> 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.
> the solution method.", JASA 105, 3410-3420; the lower panel of
> shows the guinea-pig BM impedance (across-BM pressure
> divided by BM velocity) versus location x_b (expressed in percent
> 6 mm) for a sine-tone of 16.8 kHz and 20 dB (SPL). In the region
> 67 to 84 percent, i.e., from x_b = 4.0 to x_b = 5.0 mm, the real
> of the impedance is negative; that implies "negative damping"; i.
> it implies that in this x_b-region the outer hair cells (OHC's)
> energy into the travelling wave. At locations x_b < 4.0 mm, the
> resonance-peak frequency region of the Hensen-cell resonator
> point 3 above) is above 16.8 kHz so that these resonators are
> excited significantly by the wave. At x_b = 4.0 mm, the low-
> limit of the just mentioned resonance-peak frequency region is
> 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
> OHC hairs and via direct mechanical stimulation of the OHC walls.
> x_b > 5.0 mm, the Hensen-cell-resonator's resonance-peak region
> 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
> upper panel of Fig. 3, (i.e., the characteristic place of the
> kHz-20-dB wave) is at that last-mentioned position of x_b = 5.0
> Extrapolation of the short-dashed curve in the lower panel
> 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
> kHz travelling wave does not reach that point. According to the
> panel, the passive peak (same wave, dead OHC's) is at about x_b =
> percent = 3.6 mm. Thus the distance between active and passive
> is 1.4 mm and so corresponds to half an octave. In the case of
> similar, but lower-frequency waves in human ears, e.g. 1kHz,20dB
> 1kHz,100dB, there is a similar x_b-difference but (since mostly
> information is used) a perceived-pitch difference much smaller
> half an octave; see, e.g., Chapter 6 of "An Introduction to the
> Psychology of hearing" by B. C. J. Moore, Academic Press,
> 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
> physiological Cochlea Amplifiers (some of these are weakly
> physiologically based). [...]
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