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.
@article{CML_2011__3_3_523_0,
author = {Holmes, William R. and Jolly, Michael and Rubinstein, Jacob},
title = {Hydro-elastic waves in a cochlear model: {Numerical} simulations and an analytically reduced model},
journal = {Confluentes Mathematici},
pages = {523--541},
publisher = {World Scientific Publishing Co Pte Ltd},
volume = {3},
number = {3},
year = {2011},
doi = {10.1142/S1793744211000382},
language = {en},
url = {http://www.numdam.org/articles/10.1142/S1793744211000382/}
}
TY - JOUR AU - Holmes, William R. AU - Jolly, Michael AU - Rubinstein, Jacob TI - Hydro-elastic waves in a cochlear model: Numerical simulations and an analytically reduced model JO - Confluentes Mathematici PY - 2011 SP - 523 EP - 541 VL - 3 IS - 3 PB - World Scientific Publishing Co Pte Ltd UR - http://www.numdam.org/articles/10.1142/S1793744211000382/ DO - 10.1142/S1793744211000382 LA - en ID - CML_2011__3_3_523_0 ER -
%0 Journal Article %A Holmes, William R. %A Jolly, Michael %A Rubinstein, Jacob %T Hydro-elastic waves in a cochlear model: Numerical simulations and an analytically reduced model %J Confluentes Mathematici %D 2011 %P 523-541 %V 3 %N 3 %I World Scientific Publishing Co Pte Ltd %U http://www.numdam.org/articles/10.1142/S1793744211000382/ %R 10.1142/S1793744211000382 %G en %F CML_2011__3_3_523_0
Holmes, William R.; Jolly, Michael; Rubinstein, Jacob. Hydro-elastic waves in a cochlear model: Numerical simulations and an analytically reduced model. Confluentes Mathematici, Tome 3 (2011) no. 3, pp. 523-541. doi : 10.1142/S1793744211000382. http://www.numdam.org/articles/10.1142/S1793744211000382/
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