A MATHEMATICAL MODEL OF HUMAN COCHLEA
Alexander Petrov, Victor Varin
We suggest a two-chamber model of human cochlea. The motion of the uid is described by equations of hydrodynamics, which are supplemented by the equation of oscillations of the membrane. The equations are linearized and their solution is represented as Fourier harmonics with a given frequency. The harmonics satisfy a system of boundary value problems for ordinary differential equations with variable coe cients. Numerical solution of this system with a nite-dierence approximation is hardly possible due to a big parameter in the problem and a closeness of the problem to a singular one. We suggest a new numerical method without saturation, which allows to solve the problem in a wide range of frequencies with an arbitrary and controlled precision.
Computations con rmed Bekesy's theory. The low sound requencies cause the de ection of the membrane at the upper part of the cochlea, whereas high sound frequencies cause the deflection of the main volute of the cochlea.