A Two-Dimensional Nonlinear Nonlocal Feed-Forward Cochlear Model and Time Domain Computation of Multitone Interactions

Abstract

A two-dimensional cochlear model is presented, which couples the classical second order partial differential equations of the basilar membrane (BM) with a discrete feed-forward (FF) outer hair cell (OHC) model for enhanced sensitivity. The enhancement (gain) factor in the model depends on BM displacement in a nonlinear nonlocal manner in order to capture multifrequency sound interactions and compression effects in a time-dependent simulation. The FF mechanism is based on the longitudinal tilt of the OHCs in feeding the mechanical energy onto the BM. A numerical method of second order accuracy in space and time is formulated by reducing the unknown variables to the BM with the representation of eigenfunction expansions. Though the nonlinear coupling with OHCs created an implicit algebraic problem at each time step, the structure of the FF mass matrix is found to permit a decomposition into a sum of a time-independent symmetric positive definite part and the remaining time-dependent part. A fast iterative method is devised and shown to converge with only the inversion of the time-independent part of the mass matrix. The time-dependent computation is studied by comparing with steady state solutions (frequency domain solutions) in the linear regime and by a convergence study in the nonlinear regime. Results are shown on OHC amplification of BM responses, compressive output for large intensity input, and nonlinear multitone interactions such as tonal suppression, noise suppression, and distortion products. Qualitative agreement with experimental data is observed.