Development of cochlear models with high computational efficiency by using spatial and parametric transformations

Abstract

Purpose: Our goal is to develop methods to improve the efficiency of computational models of the cochlea for applications that require the solution accurately only within a basal region of interest, specifically by decreasing the number of spatial sections needed for simulation of the problem with good accuracy. Approach: We design algebraic spatial and parametric transformations to computational models of the cochlea that are applied after the region of interest and allow for spatial preservation (spatial causality in the case study model), driven by the naturally absorptive characteristics of the cochlea. Objectives: The goal is to design, characterize and develop an understanding rather than optimization and globalization. Scope: Our scope is as follows: designing the transformations; understanding the mechanisms by which computational load is decreased for each transformation; development of performance criteria; characterization of the results of applying each transformation to a specific physical model and discretization and solution schemes. Case study: We explore the proposed methods for a case study physical model that is a linear, passive, transmission line model in which the various abstraction layers (electric parameters, filter parameters, wave parameters) are clearer than other models. This is conducted in the frequency domain for multiple frequencies using a second order finite difference scheme for discretization and direct elimination for solving the discrete system of equations. Performance: The performance is evaluated using two developed simulative criteria for each of the four transformations. For the increased dissipation transformation, we investigate individual deviation measures as part of constructing the corresponding transformation function. The nonsimulative process for this transformation is to stand as proof of concept for the remaining transformations. Conclusion: The developed methods serve to increase efficiency of a computational traveling wave cochlear model when spatial preservation can hold, while maintaining good correspondence with the solution of interest and good accuracy, for applications in which the interest is in the solution to a model in the basal region.