Faculty of Design, Kyushu University, 4-9-1 Shiobaru, Minamiku, Fukuoka 815-8540, Japan.
J Acoust Soc Am. 2021 Oct;150(4):2589. doi: 10.1121/10.0006533.
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 n 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 n 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.
提出了一种快速数值时域求解非线性三维（3D）耳蜗模型的方法。在动力系统中，时域解可以确定非线性响应，而人类的听觉能力取决于耳蜗微观结构器官的非线性行为。因此，时域 3D 建模可以帮助解释听觉。矩阵乘积，n 次运算，是耳蜗模型中时域求解过程的核心部分。为了更快地求解耳蜗模型，使用快速傅里叶变换（FFT），nlogn 次运算，来替代矩阵乘积。数值模拟结果验证了在粗网格设置下矩阵乘积和 FFT 的相似性。此外，由于所提出方法的计算复杂度从 n 降低到 nlogn，FFT 的应用将计算时间缩短了 100 倍。此外，该方法成功计算了在矩阵乘积无法解决的中等和精细网格设置下的 3D 模型。在时域模拟中，3D 耳蜗模型在各种增益分布下对纯音和点击呈现出非线性响应。因此，基于 FFT 的方法提供了快速数值解，并支持耳蜗力学的 3D 模型的发展。
