Fast time-domain solution of a nonlinear three-dimensional cochlear model using the fast Fourier transform

A fast numerical time-domain solution of a nonlinear three-dimensional (3D) cochlear model is proposed. In dynamical systems, a time-domain solution can determine nonlinear responses, and the human faculty of hearing depends on nonlinear behaviors of the microscopically structured organs of the cochlea. Thus, time-domain 3D modeling can help explain hearing. The matrix product, an n² operation, is a central part of the time-domain solution procedure in cochlear models. To solve the cochlear model faster, the fast Fourier transform (FFT), an n log n operation, is used to replace the matrix product. Numerical simulation results verified the similarity of the matrix product and the FFT under coarse grid settings. Furthermore, applying the FFT reduced the computation time by a factor of up to 100 owing to the computational complexity of the proposed approach being reduced from n² to n log n. Additionally, the proposed method successfully computed 3D models under moderate and fine grid settings that were unsolvable using the matrix product. The 3D cochlear model exhibited nonlinear responses for pure tones and clicks under various gain distributions in a time-domain simulation. Thus, the FFT-based method provides fast numerical solutions and supports the development of 3D models for cochlear mechanics.