A few weeks ago, there was a discussion on this List about the basilar membrane (BM) in the cochleae of mammals. Cochlear models imply that the stiffness (spring constant per BM surface unit, Newtons per cubic metre) decreases by several orders of magnitude from base to apex. Some published direct stiffness measurements yielded a much weaker stiffness decrease. In the (previously mentioned) MoH-2011 proceedings (Williamstown, "What Fire Is in Mine Ears") there is an interesting contribution, "Mechanics of the Unusual Basilar Membrane in Gerbil", by Kapuria, Steele, and Puria (pp. 333-339). The BM in Gerbil is unusual because the lower collagen band of the BM in the pectinate zone (i.e., in the outer zone, between outer pillar cells and spiral ligament) is strongly arched, so that this zone of the BM is very rigid. Also, the BM width changes relatively little with distance-from-base. Nevertheless, "the computed volume compliance produces the proper frequency-to-place map".
In the discussion of that paper(page339), the authors were asked: "What gives rise to the frequency map in the region of the gerbil cochlea where the width is almost constant? Is there an anatomical change in the bowed fiber layers?"
The authors replied: "[...] Fortunately,  [Schweitzer et al., Hear Res. 97 (1996) 84-94] deduced that the significant change is in the thickness of the collagen bands. [...]".
As mentioned last year, the stiffness due to beams with axis in the y-direction (where xy = plane of BM and x-axis points toward apex) does increase strongly with the beam thickness delta-z.