Numerical solution of coupled transport equations applied to corneal hydration dynamics

Abstract

1. A quantitative basis for the currently accepted theory on the regulation of corneal hydration was derived using the technique of finite element analysis to integrate a set of coupled flow equations. The model was based on non-equilibrium thermodynamics and incorporated the transport and permeability properties of the corneal epithelium and endothelium as well as the gel properties of the central connective tissue layer. 2. Considerable errors were introduced in the prediction of corneal hydration dynamics (unsteady-state behaviour) unless allowance was made for the development of trans-stromal gradients in pressure and solute concentration. 3. Thickness of in vitro rabbit corneal epithelium and stroma were measured with an automatic specular microscope during responses to changes in the osmolarity of the tear-side bathing medium. The time course of these experiments was fitted with the mathematical model to obtain a set of membrane phenomenological coefficients and transport rates. 4. The model with the redetermined membrane parameters was tested by predicting the influence of other variations in boundary conditions with excellent match to several well-documented experimental observations, including an explanation for the slight stromal swelling observed in hibernating mammals. 5. The regulation of corneal stromal hydration can be explained accurately by balance between the dissipative flows across the serial array of corneal layers and the active HCO3 transport by the endothelium, supporting the earlier 'pump-leak' hypothesis. 6. It was found that stromal retardation of fluid flow, as well as gradients in solute concentration, significantly influences the dynamics of corneal stroma hydration. Tissue gel properties may be a more important factor in coupled transport across cell layers than generally appreciated.