Dear colleagues,
Please permit me one more posting on the stiffness S of the human CP [CP = cochlear partition = basilar membrane (BM) and cells attached to the BM; S = spring constant per CP surface unit, Newtons per metre-cubed].
According to the left ordinate scale of Fig. 11-73 of "Experiments in Hearing" by von Bekesy, the volume change per millimetre of length at distance-from-base x = 3 mm at an across-CP pressure difference of 1 cm of water is 7 * 10^-8 cm^3. For the local CP width of 0.15 mm, that translates into the following CP stiffness:
S(3 mm) = 2.1 * 10^8 N/m^3. (1)
If, however, the human CP stiffness is assumed to be as defined by Eq. (3.2.1) and by the caption of Fig. 5.2 of de Boer's chapter in the book "The Cochlea" (1996), then one obtains
S(3 mm) = 4.1 * 10^9 N/m^3, (2)
greater than the value in Eq. (1) by a factor of almost twenty.
A possible explanantion can be found with the help of Fig. 2.3B of Slepecki's chapter in "The Cochlea" (1996): The boundary, made by tight junctions, between perilymph and endolymph is not the BM, but rather the RL (reticular lamina) and the scala-media-side walls of the Hensen and Claudius cells. According to Figs. 11-71 and 11-72 of "Experiments in Hearing", the pressure in the scala tympani was reduced below the pressure in air and in scala vestibuli. According to the right scale of Fig. 11-73 and to the text above that diagram (maximum displacement 0.01 mm), the pressure difference delta-p applied for the measurement at x = 3 mm was as high as ~100 cm of water. The change from delta-p = 0 to delta-p = 100 cm of water was slow, so the (comparatively low) scala-tympani pressure presumably penetrated upwards through the BM, and up to the mentioned cell walls. Therefore Fig. 11-73 may show the stiffness of those cell walls, rather than that of the CP. Our Eq. (2), in contrast, gives the effective CP stiffness (across-CP pressure difference divided by displacement of the centre-of-mass of the local CP slice) valid at audio-frequency pressure oscillations.
Question to biologists: Do you agree with that (very preliminary) explanation?
Reinhart Frosch,
CH-5200 Brugg.
reinifrosch@xxxxxxxxxx .