HYDRO-ELASTIC WAVES IN A COCHLEAR MODEL: NUMERICAL SIMULATIONS AND AN ANALYTICALLY REDUCED MODEL

Confluentes Mathematici

HOLMES, WILLIAM R¹  RUBINSTEIN, JACOB¹  JOLLY, MICHAEL¹ 

[1] Department of Mathematics, Indiana University, 831 E. 3rd, Bloomington, IN 47401, USA

关键词: Ear model;    numerical simulation;    thin plate;    Dirichlet-to-Neumann operator;    cochlea;    reduced model;   

DOI  :  10.1142/S1793744211000382

学科分类：数学（综合）

来源: World Scientific Publishing Co. Pte. Ltd.

【 摘 要 】

A three-dimensional model of the hydro-elastic waves in the mammalian cochlea is presented along with numerical simulations. The cochlear fluid is treated as linear, incompressible, and inviscid. The cochlear partition is treated as a massless thin plate loaded by the fluid. This model is then reformulated by analytically removing the fluid variable with the use of a Dirichlet-to-Neumann operator. The resulting fifth-order nonlocal PDE for the motion of the partition is simulated using a novel implicit numerical scheme. Simulations demonstrate that this model exhibits traveling wave characteristics and a clear place principle. Asymptotic analysis in the small aspect ratio of the cochlea is performed on the given model equations with energetic concerns in mind. The results of simulations along with these asymptotic arguments suggest a relationship between the form and function of the cochlea which we compare to physiological data.

【 授权许可】

Unknown