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Re: Cochlear mechanics.

At 12:08 PM +0000 8/25/06, reinifrosch@xxxxxxxxxx wrote: 
Dear colleagues,

In models of the basal region of the cochlea, the basilar-
membrane stiffness S is often assumed to depend on the
longitudinal coordinate x as follows:

S = S_0 * e^(-x/d) ,

Reinhart, I think it would be more fair to call that a convenient approximation more than an assumption. It's well known that for large enough d to get into a low-CF region, it decreases too slowly.

where d is about 3 mm.  Yesterday I found that absence
of significant reflections is predicted even for low
frequencies if a different function is used instead:

S = S_0 * [1 - x/(4d)]^4 .

The use of [1 - x/N]^N as an approximation for exp(-x) is often very useful, for example in approximating Gaussians or high powers of cosines, in my experience, but I had not looked at it in this particular application. It looks like a useful way to get the stiffness and CF to go to 0 for finite d while preserving the desired behaviour at low d.

What do you mean by "even for low frequencies"? That was true of the original function as well, right? So you just mean it doesn't mess up the no-reflections property?

I have written a text-file of about 1.5 pages giving details.
Please write if you want to receive that file.


Definitely would love to see it.

Thanks.

Dick


With many thanks, sincerely,

Reinhart Frosch.


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 .