Abstract
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.
Highlights
Computational modeling studies can help explain the processes underlying dynamical systems, and time-domain numerical methods are powerful tools for solving nonlinear models
The results of prior experiments suggest that complex mechanical motions of the cochlea through space lead to the nonlinearities; some disagreement remains on this point (Cooper et al, 2018; Dewey et al, 2019; Gao et al, 2014; He et al, 2018; Lee et al, 2015)
To develop a fast solution method for nonlinear timedomain cochlear models, in this study, we propose a method that replaces the direct solver in the method proposed by Diependaal et al (1987) with an fast Fourier transform (FFT)-based solver
Summary
Computational modeling studies can help explain the processes underlying dynamical systems, and time-domain numerical methods are powerful tools for solving nonlinear models. The results of prior experiments suggest that complex mechanical motions of the cochlea through space lead to the nonlinearities; some disagreement remains on this point (Cooper et al, 2018; Dewey et al, 2019; Gao et al, 2014; He et al, 2018; Lee et al, 2015). This fact suggests that time-domain three-dimensional (3D) modeling can help explain the mechanism of hearing because it can predict the nonlinear cochlear responses caused by motions of the microscopically structured organs
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