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Re: Laws of physics and old history; BM stiffness.

There are two modern sets of BM stiffness data, one from our lab, the other from the Northwestern group.

Naidu, R.C. and Mountain, D.C. (1998).  Measurements of the stiffness map challenge a basic tenet of cochlear theories.  Hear. Res. 124: 124-131. [PDF]
Emadi GRichter CPDallos P.  (2004) Stiffness of the gerbil basilar membrane: radial and longitudinal variations. J Neurophysiol. 2004 Jan;91(1):474-88

The problem with treating the basilar membrane as a beam is that there can be significant longitudinal coupling along the basilar membrane:

Naidu, R.C. and Mountain, D.C. (2001). Longitudinal coupling in the basilar membrane. J. Assoc. Res. Otolaryngol.  3:257-67. [PDF]

Also, both the tension and the amount of collagen in the basilar membrane changes with longitudinal location.

Naidu, R.C. and Mountain, D.C. (2007) Basilar membrane tension calculations for the gerbil cochlea. J. Acoust. Soc. Am. 121:994-1002 [PDF]

In the case of the gerbil, the BM dimensions vary in a manner contrary to the conventional wisdom.  With the exception of the hook region, the width of the basilar membrane changes little from base to apex and actually increases in thickness from base to apex.  On the other hand, in cetaceans, the width and thickness vary significantly from base to apex much as one would expect if the material properties were uniform and the beam equation applies.

On Fri, Nov 11, 2011 at 6:35 AM, reinifrosch@xxxxxxxxxx <reinifrosch@xxxxxxxxxx> wrote:


The following is a reaction to an earlier post of this thread:

As already posted some years ago, it appears possible to me that the stiffness S [Newtons per m^3] of the mammalian cochlear basilar membrane (BM) decreases by several orders of magnitude from base to apex. If the elements of the BM are treated as elastic beams, then the following formula for S is obtained:

S = n * Y * (delta-z)^3 / w^4,

where delta-z is the beam thickness, w is the beam length (equal to the BM width), and Y is Young's modulus of the beam material (elasticity modulus, Newtons per m^2); the integer n depends on the way in which the beams are fixed, at their ends, to the walls of the cochlear channel. If the beams are clamped, then n = 60, if not, then n = 10.

Fig. 11-73 of von Bekesy's book "Experiments in Hearing" (1960) yields a human BM stiffness decrease of only two orders of magnitude from base to apex. Has that experiment been re-done? 

Reinhart Frosch,
Dr. phil. nat.,
CH-5200 Brugg.
reinifrosch@xxxxxxxxxx .

----Ursprüngliche Nachricht----
Von: rsran@xxxxxxxxxxx
Datum: 09.11.2011 20:17
An: <AUDITORY@xxxxxxxxxxxxxxx>
Betreff: Re: Laws of physics and old history (A new paradigm?(On pitch and periodicity (was &quot;correction to post&quot;)))


David C. Mountain, Ph.D.
Professor of Biomedical Engineering

Boston University
44 Cummington St.
Boston, MA 02215

Email:   dcm@xxxxxx
Website: http://www.bu.edu/hrc/research/laboratories/auditory-biophysics/
Phone:   (617) 353-4343
FAX:     (617) 353-6766
Office:  ERB 413