Boundary-integral modeling of cochlear hydrodynamics

Abstract

A two-dimensional model that captures the essential features of the vibration of the basilar membrane of the cochlea is proposed. The flow due to the vibration of the stapes footplate and round window is modeled by a point source and a point sink, and the cochlear pressure is computed simultaneously with the oscillations of the basilar membrane. The mathematical formulation relies on the boundary-integral representation of the potential flow established far from the basilar membrane and cochlea side walls, neglecting the thin Stokes boundary layer lining these surfaces. The boundary-integral approach furnishes integral equations for the membrane vibration amplitude and pressure distribution on the upper or lower side of the membrane. Several approaches are discussed, and numerical solutions in the frequency domain are presented for a rectangular cochlea model using different membrane response functions. The numerical results reproduce and extend the theoretical predictions of previous authors and delineate the effect of physical and geometrical parameters. It is found that the membrane vibration depends weakly on the position of the membrane between the upper and lower wall of the cochlear channel and on the precise location of the oval and round windows. Solutions of the initial-value problem with a single-period sinusoidal impulse reveal the formation of a traveling wave packet that eventually disappears at the helicotrema.