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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 
transduction ...": 
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.

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: 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, 
however, I 
> 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 
x_a = 
> 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 
to be 
> 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 
the RL 
> 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 
Fig. 3 
> 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
> Hello,
> 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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