The role of scalae geometry in cochlear mechanical responses: Pressure focusing in two and three dimensions

This paper illustrates effects of model dimensionality, and of common simplifying assumptions, regarding the geometry of the scalae, on the solution of cochlear mechanical models. We extend a previous theoretical framework from Duifhuis [(1988). Auditory Function: Neurological Bases for Hearing (Wiley, New York), pp. 189-212] to study differences between models that consider three-dimensional (3D) and two-dimensional (2D) fluid motion in the scalae, and how these differences depend on the assumed cochlear geometry. Our results show that, while cochlear mechanical responses obtained in 2D and 3D are nearly identical over the mid- and apical cochlear turn, they are significantly different in the base-where the basilar membrane (BM) is narrow-especially in the presence of active amplification. Our analysis reveals that a narrower BM intensifies the 3D short-wave "pressure-focusing" effect, which boosts the vibration of the sensory tissue at locations tuned to the stimulus frequency. Importantly, these 3D short-wave effects can be accounted for in carefully constructed 2D models, by appropriately projecting the cochlear 3D geometry in 2D. Our work shows that the cochlear 3D geometry plays a major role to high-frequency cochlear amplification-a phenomenon with a straightforward explanation and that can be included in more tractable 2D theories.