Solution using Lagrange's equation to the model of cochlear micromechanics

 

M. Jiménez Hernández

 

 

In this paper a new solution to micromechanical model of the cochlea developed by Neely and Kim is presented using Lagrange's equation. This solution has the advantage over previous methodologies to provide a mathematical model for the displacement exercised on the outer hair cells in the organ of Corti that only depends of the mechanical characteristics in the system and the value of the excitation frequency in the inner ear. For the evaluation of this new model the parameters developed by Ku are used and is considers that the amplitude of the excitation frequency is normalized. The model developed is satisfactorily compared with the impedance method and its numerical solution proposed by Neely and Kim, the state space analysis developed by Elliot, Ku and Lineton and the physiological measurements taken from Békésy.