Review of Recent Mathematical Theories of Cochlear Dynamics

TLDR

Cochlear mechanics theories are grouped into two classes—long‑wave models reducible to a single differential equation and short‑wave boundary‑problem models lacking exact solutions—yet none fully satisfies current understanding. The comparative analysis shows convergence among theories and progress toward understanding cochlear dynamics, though no single model yet fully explains the system.

Abstract

An analysis of several theories of cochlear mechanics has been attempted on the basis of general hydrodynamic theory. The theories are divided into two classes according to the mathematical treatment. The first class assumes that transverse waves propagated along the cochlea are long in comparison to the cross-sectional dimension of the canal: all theories of this class can be deduced from one differential equation when the emphasis put on different factors. The second class assumes that the waves are relatively not long, and the mathematical treatment becomes a boundary problem to which no exact solution has yet been found. The analysis of the individual theories indicates a certain convergence of opinions, and it is clear that definite progress has been achieved toward an understanding of the dynamic behavior of the cochlea. In spite of this trend, however, no one of the theories seems entirely satisfactory.