Unraveling the mystery of hearing in gerbil and other rodents with an arch-beam model of the basilar membrane

The mammalian basilar membrane (BM) consists of two collagen-fiber layers responsible for the frequency-to-place tonotopic mapping in the cochlea, which together form a flat beam over at least part of the BM width. The mechanics of hearing in rodents such as gerbil pose a challenge to our understanding of the cochlea, however, because for gerbil the two layers separate to form a pronounced arch over the remaining BM width. Moreover, the thickness and total width normally thought to determine the local stiffness, and tonotopic mapping in turn, change little along the cochlear length. A nonlinear analysis of a newly developed model, incorporating flat upper and arched lower fiber layers connected by ground substance, explains the initial plateau and subsequent quadratic increase found in measured stiffness vs. deflection curves under point loading, while for pressure loading the model accurately predicts the tonotopic mapping. The model also has applicability to understanding cochlear development and to interpreting evolutionary changes in mammalian hearing.