Hello Peter,
Yes, the oscillating elastic beam is formed by the whole cochlear partition (CP), not only by the BM (basilar membrane). There appears to be longitudinal coupling of CP elements. According to the first of the papers mentioned yesterday by Prof. David Mountain, however, in gerbil the coupling range is only +-16.7 micro-m (1.6 mm from base) and +-34.5 micro-m (8.1 mm from base). These coupling ranges are small compared to the wavelength of the cochlear travelling wave (at least in most of the relevant cases), so it appears reasonable to treat the CP as a series of independent beams (oriented in the sideways direction). Because of the organ-of-Corti cells, the oscillations of the beams are expected to be strongly damped. This is confirmed to a degree, e.g., by Fig. 1 of the paper "Reverse transduction measured in the isolated cochlea by laser Michelson interferometry", by Mammano and Ashmore, Nature 365 (1993) 838-841. The oscillations at the beginning and at the end of the rectangular current pulse sent through the CP are strongly damped. The Q-value (resonance frequency divided by -3-dB resonance-peak width) of the Claudius-cell oscillation is about 4. A part of that damping is due to the generated oscillation of the liquid particles above and below the CP, but damping caused by CP structures is probably significant, too.
The dependance of the mammalian CP stiffness (at liquid-pressure differences across the CP so small that the CP centre-of-mass displacement is a few hundred nm or less) on distance-from-base is still not definitely known, I believe. In my contribution to the MoH-Workshop at Keele (2008), I tried to derive the gerbil CP stiffness from CP oscillation mesurements of Ren et al. I found:
S(x) = S_0 * exp(-alfa*x); S_0 = 4.16*10^10 N/m^3; alfa = 1260 m^-1. If that that formula (based on near-base data only) could be assumed to hold at larger distance-from-base x too, it would yield S(0) / S(10mm) = 3 * 10^5.
Reinhart Frosch,
CH-5200 Brugg.
reinifrosch@xxxxxxxxxx .
----UrsprÃngliche Nachricht----
Von: pwj.vanhengel@xxxxxxxxx
Datum: 14.11.2011 10:21
An: <AUDITORY@xxxxxxxxxxxxxxx>
Betreff: Re: Laws of physics and old history; BM stiffness.
Dear list,
just a word of caution: the stiffness term used in cochlea models
(transmission line models) should not be confused with the stiffness of
the BM fibers. The stiffness term in these models represents an overall
stiffness of the cochlear partition, and thus includes more than the
stiffness of the BM fibers. Relating the two directly, or even asssuming
they are the same, may lead to misinterpretation.
I do, however support the remark by dr Frosch that depending on the way
in which the beams are fixed at their ends, the stiffness of the BM may
decrease by several orders of magnitude from base to apex.
All the best,
Peter van Hengel