The basilar membrane as a uniformly loaded plate clambed on two spiral boundaries in a plane or on two helical-spiral boundaries: relevance of the species record

Abstract

The species record of the cochlea of the inner ear is examined, and the hypothesis is offered for numerical testing that the survival value of coiling is in protection of the high-frequency, or basal, end of the basilar membrane from low-frequency distortions due to vibrations of the apical end and vise versa. Crude estimates from figures given by von Békésy give one curve for the approximate relation of the radius of curvature to arc length r/ s versus angle of coiling θ as the spiral design used in all therian animals. A discussion of the model to be studied is given in [7]. It is important to remember that a complicated partial differential equation is to be solved involving variations with respect to two space variables (and time), not just with respect to one variable. The reaction of the basilar membrane as a whole must be considered together with its coiling. The experimental state of the art now clearly justifies undertaking computations in this context.