New computational model of corneal hydration dynamics

Purpose. Establishment of a moving boundary model of the whole corneal hydrodynamic system, including unstirred free solution boundary layers, epithelial and endothelial membranes and the intervening swelling stromal tissue, to aid in the accurate assessment of the effect of unstirred layers on the dynamics of corneal thickness changes. Methods. The nonequilibrium thermodynamics-based membrane transport equations of Kedem and Katchalsky and the Fatt and Goldstick corneal gel empirical relations were modified to derive a 1-dimensional set of moving boundary equations capable of modeling swelling stromal tissue. This set of highly non-linear partial differential equations was coupled through the discrete membrane equations of Kedem and Katchalsky to free solution diffusion equations that represent the epithelial and endothelial unstirred concentration boundary layers or standing gradients. The system of equations is non-dimensionalized, yielding a set of descriptive physical parameters including free solution and gel Peclet numbers, which relate the solute diffusion time scale to the solute convection time scale. The equation sets are sequentially solved using a method-of-lines diffusion equation solver (DMOLCH from IMSL). Results. As predicted by the Peclet numbers, two-phase modeling including epithelial and endothelial membranes showed that the unstirred layers at the membranes displayed little variance from the bulk solution concentration at steady-state. Perturbation of the bulk solution concentrations show dynamic gradient development and rapid (tau=70 seconds) dissipation in the external unstirred layer. Conclusions. This approach is seen as a powerful new technique to model the hydration dynamics of the cornea as well as to test unstirred layer assumptions as they relate to the characterization of membrane permeability.