Variable Geometry Cochlear Model at Low Input Frequencies: A Basis for Compensating Morphological Disorders
by A. Inselberg
The implementation of an algorithm suitable for interactive experimentation with a mathematical model of the cochlea is described. In the model, the cochlea’s exterior shell is represented by a surface of revolution. Internally, the cochlea is partitioned symmetrically into two chambers (the scalae) by a midplane representing the basilar membrane with its bony supports together with the “collapsed” cochlear duct (third chamber). The two chambers are filled with a viscous and incompressible fluid and communicate through a small opening (the helicotrema), at the cochlea’s apex. The system is driven by the piston-like movement with frequency ω of the stapes at the cochlea’s basal end. An isotropic sectorial plate widening toward the apex represents the basilar membrane. Some of the effects of the cochlear duct are considered through a provision for nonzero net pressure at the basilar membrane’s apical end. The behavior of this system in the neighborhood of the low-frequency threshold, where the effects of cochlear geometry are most pronounced, is described from the solutions of the equations of motion for ω → 0.