Cochlear partition stiffness—a composite beam model

Abstract

A mathematical model of the human cochlear partition is developed to investigate the partition's stiffness. To date, no experiment has been performed on the partition to determine the difference between the dynamic and the statically measured stiffness. Nonlinearities observed in the partition's dynamic motions and dynamic stiffness measurements on bone and muscle tissue indicate that previous investigations of the cochlear partitions's stiffness may not be adequate. In this study the cochlear partition is modeled by a series of composite beams whose stiffness is due to linear bending rigidity at normal amplitudes of motion. At larger amplitudes (in the nonlinear range near the threshold of pain), the model's stiffness is increased, owing to the nonlinear stretching of the basilar membrane. The model also includes the increase in stiffness, above the static stiffness, due to dynamic loading, as observed in the studies of bone and muscle tissue. The dynamic cochlear partition stiffness predicted by this model increases approximately by a factor of 100 from apex to base. Except near the stapes, the model's stiffness in the linear range at 100 Hz is approximately the same as measured statically. At 10 000 Hz the model's stiffness in the linear range is nearly twice as large as the statically measured value.