Integrated mathematical model of the ear. I. Free-field pressure to basilar membrane displacements

In order to provide insight into the processes operative in the ear, especially at high sound pressure levels, an integrated mathematical model of the ear has been produced. The model’s electroacoustic elements are conformal with the strucure of the ear, which promotes physical insight. For maximum utility the model is menued to allow parameter changes by the user. Mathematically, the model is equations of motion formulated as a system of coupled ordinary differential equations, which allow both linear and nonlinear claculations in the time domain. The ‘‘Q’’ of the basilar membrane is not constant and the range is selectable. The systems are linear, except at very high SPLs (130+dB) where the stapes becomes nonlinear. Input to the model is any 4096-point free-field pressure or pressure at the ear drum. Outputs are standardly numerical files of stapes displacements and basilar membrane displacements at any number of evenly spaced user-selected places. As a final output the model makes a ‘‘movie’’ of the basilar membrane displacements coordinated with the pressure history, which shows the effect of each part of the waveform.