A coupled boundary element/finite difference method for fluid–structure interaction with application to dynamic analysis of outer hair cells

Outer hair cells (OHC) in the inner ear, which resemble fluid-filled and fluid-surrounded cylinders, are known to exhibit motility and play a critical role in our keen sense of hearing. In this study, we investigate the OHC frequency response using a mathematical model of the OHC, which consists of a two-layered anisotropic cylindrical lateral wall, and both the intracellular and extracellular fluids. We use the boundary integral equations to model the intracellular and extracellular fluids, and these are coupled to the anisotropic cylindrical shell equations (discretized using the finite difference method). Since the geometry is axisymmetric, the dynamic analysis is performed by decomposing the motion into Fourier modes in the circumferential direction. For the boundary element method, this leads to two sequences of line integrals along the generator of the domain, and the singular kernels need to be evaluated with elliptic integrals. The coupled fluid–structure equations are solved for several modes of deformation (axisymmetric, cylindrical beam-bending, and pinched modes), and the frequency responses are obtained. The frequency response of the model with viscous fluid is found to be significantly different from that using inviscid fluid. For the small length scale of the OHC (which is of micron size), the viscosity of the fluid is found to have significant damping effects on the OHC frequency response.