Effects of geometry on fluid loading in a coiled cochlea

Despite its snail-shaped geometry, theoretical studies of the mammalian cochlea generally modeled it as a straight fluid-filled duct. Most people support the idea that the purpose of coiling is to pack the cochlea into a small space. However, attempts by researchers to establish the functional significance of the complex shape of the cochlea have been inconclusive. We study the effects of geometry on fluid loading in the cochlea and introduce helicoidal coordinates in order to describe cochlear geometry and fluid motion. The geometrical description takes into account curvature, partition width, basilar membrane (BM) width, and the height of the modiolus of a guinea pig cochlea. We assume a given mode, wavelength, and amplitude for the BM. We study the fluid equations within the WKB framework and numerically simulate the pressure in a plane containing the modiolar axis. We then compare numerical results for different geometrical parameters. We find that pressure on the BM increases with increasing BM width and decreasing cross-sectional area of the cochlear ducts. We also find that the net effect of curvature is to decrease the fluid pressure on the BM. When the cochlea spirals out of the plane, fluid loading is greater compared with the in-plane coiled case but smaller than in a straightened cochlea. These results suggest that the coiling helps to lower the fluid impedance, particularly at the apex, where BM curvature is greatest.