Mathematical Model of the Cupula-Endolymph System with Morphological Parameters for the Axolotl (Ambystoma tigrinum) Semicircular Canals

By combining mathematical methods with the morphological analysis of the semicircular canals of the axolotl (Ambystoma tigrinum), a system of differential equations describing the mechanical coupling in the semicircular canals was obtained. The coefficients of this system have an explicit physiological meaning that allows for the introduction of morphological and dynamical parameters directly into the differential equations. The cupula of the semicircular canals was modeled both as a piston and as a membrane (diaphragm like), and the duct canals as toroids with two main regions: i) the semicircular canal duct and, ii) a larger diameter region corresponding to the ampulla and the utricle. The endolymph motion was described by the Navier-Stokes equations. The analysis of the model demonstrated that cupular behavior dynamics under periodic stimulation is equivalent in both the piston and the membrane cupular models, thus a general model in which the detailed cupular structure is not relevant was derived.