A Poroelastic Continuum Model of the Cupula Partition and the Response Dynamics of the Vestibular Semicircular Canal

Abstract

Using mixture theory, an axisymmetric continuum model is presented describing the response dynamics of the vestibular semicircular canals to canal-centered head rotation in which the cupula partition is modeled as a poroelastic mixture of interpenetrating solid and fluid constituents. The solid matrix of the cupula is assumed to behave as a linear elastic material, whereas the fluid constituent is assumed to be Newtonian. A regular perturbation analysis of the fluid dynamics in the canal provides a dynamic boundary condition, which acts across the cupula partition. Numerical solution of the coupled system of momentum equations provides the spatio-temporal displacement fields for both the fluid and solid constituents of the cupula. Results indicate that at frequencies above 1 Hz, the fluid constituent is dynamically entrained by the solid matrix such that their motions are bound as if to exist as a single component. The resulting high-frequency response is consistent with the macromechanical response predicted by single-component viscoelastic models of the cupula. Below 1 Hz, the dynamic coupling between the fluid and solid constituents weakens and the transcupular differential pressure is sufficient to force fluid through the mixture with little deformation of the solid matrix. Results are sensitive to the precise value of the cupular permeability. One of the most important distinctions between the present analysis and previous impermeable models of the cupula arises at the micromechanical level in terms of the local fluid flow that is predicted to occur within the cupula and around the ciliary bundles and sensory hair cells. Another important result reveals that the permeation dynamics predicted below 1 Hz gives rise to the same low-frequency macromechanical response as would occur with an impermeable viscoelastic structure having a much greater stiffness. Current estimates of the mechanical stiffness of the cupula, based solely on afferent nerve data, may therefore overestimate the true value intrinsic to the solid matrix by as much as an order of magnitude.