Basilar-membrane stiffness.

["reinifrosch@xxxxxxxxxx" <reinifrosch@xxxxxxxxxx>]

Dear colleagues,

On March 21, I posted a message containing two different values (based on a two-dimensional cochlear 
model) for the effective stiffness of the basilar membrane (BM) near the apex of the human cochlea (at 32 mm from base; 
BM length 35 mm), namely 1.4 * 10^7 N / m^3 (Bekesy's Fig. 11-73) and 6 * 10^5 N / m^3 (derived from Bekesy's Fig. 11-
43 via travelling-wave theory). The latter stiffness value agrees well with the exponential function given by de Boer 
(1996; book "The Cochlea").

Today I would like to point out that a direct observation of BM oscillations tends to give 
plausibility to the smaller of those two values: in Fig. 1 of Mammano and Ashmore (1993), "Reverse transduction 
measured in the isolated cochlea by laser Michelson interferometry", Nature 365, 838-841, damped guinea-pig BM 
oscillations at the beginning and end of rectangular current pulses are shown. The corresponding BM oscillation 
frequency is stated, on page 840, to be f = (2.30 +/- 0.15) kHz. If one assumes that about the same BM oscillation 
frequency would be observed without liquid above and below the partition, and that the effective BM surface mass 
density is M = 0.1 kg / m^2, then the resulting BM stiffness at the observed place (11 mm from base) is S = M * (2pi*f)
^2 = 2.1 * 10^7 N / m^3. The guinea-pig one-octave distance of 2.65 mm and the assumption of an exponential stiffness-
versus-place function valid for the whole guinea-pig BM lead to a BM stiffness near the apex, (32/35)*18.5 mm = 16.9 mm 
from base, of ~9.5 * 10^5 N / m^3, close to to the smaller of the two above-mentioned human values. The lower audible-
frequency limit of guinea pigs is slightly above that of humans.

Reinhart.

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 .