Three-dimensional numerical modeling for global cochlear dynamics.

A hybrid analytical-numerical model using Galerkin approximation to variational equations has been developed for predicting global cochlear responses. The formulation provides a flexible framework capable of incorporating morphologically based mechanical models of the cochlear partition and realistic geometry. The framework is applied for a simplified model with an emphasis on application of hybrid methods for three-dimensional modeling. The resulting formulation is modular, where matrices representing fluid and cochlear partition are constructed independently. Computational cost is reduced using two methods, a modal-finite-element method and a boundary element-finite-element method. The first uses a cross-mode expansion of fluid pressure (2.5D model) and the second uses a waveguide Green's-function-based boundary element method (BEM). A novel wave number approach to the boundary element formulation for interior problem results in efficient computation of the finite-element matrix. For the two methods a convergence study is undertaken using a simplified passive structural model of cochlear partition. It is shown that basilar membrane velocity close to best place is influenced by fluid and structural discretization. Cochlear duct pressure fields are also shown demonstrating the 3D nature of pressure near best place.