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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 

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 location.

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 wrote:
> 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 .
> ----Ursprüngliche 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). [...]

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