Radial structure of traveling waves in the inner ear

We develop a hybrid approach for modeling the cochlea, in which we let the WKB method determine the axial propagation of waves and restrict the numerics to transverse planes, where we solve a fluid-solid interaction eigenvalue problem. The cochlear fluid is treated as viscous and incompressible. Viscous effects are confined to oscillatory boundary layers and the thin gap between the reticular lamina (RL) and the lower surface of the tectorial membrane (TM). Our model includes axial fluid coupling and also axial elastic coupling via a basilar membrane (BM) modeled as an orthotropic clamped plate. Three-dimensional (3D) flow is solved in two-dimensional (2D) domains, with interactions with 2D elastic domains representing the organ of Corti (OC) and the TM. The OC contains inhomogeneities representing discrete cellular structures. We have computed the interaction between the BM, TM, OC, and the cochlear fluid to find the complex-valued wavenumber-frequency relation and vibrational modes. The details of the cochlear fluid flow and pressure fields are calculated, along with displacements of the elastic structures. Simulation of passive radial modes in the apical region of a guinea pig cochlea for frequencies less than 1 kHz indicates monophasic vibration of the BM and a synchronous rotation of three rows of outer hair cell stereocilia induced by a shearing motion between the RL and TM.