Efficiency limit of nonuniform grid setting in two-dimensional cochlear model

In this study, a two-dimensional (2D) mechanical model of the cochlea, discretized by a nonuniform grid, is applied to investigate the mechanisms that limit the increase in the computational efficiency. To amount for experimental findings, cochlear models have become complicated. A cochlear model consists of micro- and macro mechanical models. Many types of micro mechanical model have been proposed. However, macro mechanical models are described by the Laplace equation and show various patterns of the cochlear response depending on the location. Therefore, an efficient step width depends on the location in the cochlea. To resolve this issue, a numerical calculation has been applied to divide the space of a cochlear model into a nonuniform grid and to achieve improved efficiency of the model. However, the limitation of this method remains unclear. To investigate this point, we develop a state space model for 2D cochlear mechanics with a nonuniform gird. Stability analysis and simulations are conducted for the cochlear model with nonuniform and uniform grids. As a result, the number of segments is reduced by 29%. In addition, the execution time is reduced by 10-fold. Therefore, it is shown that a nonuniform grid can efficiently divide the space for cochlear modeling.