Subject: Basilar-membrane stiffness. From: "reinifrosch@xxxxxxxx" <reinifrosch@xxxxxxxx> Date: Sat, 27 Mar 2010 11:06:52 +0000 List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>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@xxxxxxxx .