Department of Mathematics Colloquium
|The goal of the project is to numerically
simulate (Riboflavin/UV-A)-induced photochemical reactions in the
corneal stroma for prediction of depth-resolved variations in
collagen-cross linking (CxL) and potential for toxicity to the corneal
endothelium in response to controlled partial pressure of oxygen at the
surface of the cornea.
The model incorporates three state variables that govern CxL: oxygen (O2), riboflavin (Rf) and UV-A fluence. Riboflavin, instilled as a 20% dextran drop every 5 min on bare stroma, is assumed to form a dextran-Rf film of 40 um and then diffuse into the stroma. pO2, which can be controlled at the surface of the Rf film, is assumed to undergo depletion in the stroma and in the endothelium. After 30 min of exposure to Rf, stroma is exposed to UV-A at 3 mW/cm2. Light penetration is modeled by Beer-Lambert’s law. The ensuing photochemical reactions are assumed to follow biomolecular reaction kinetics of first order. The resulting system of partial differential equations (with depth and time as independent variables) for Rf and pO2, along with a set of algebraic equations involving short-lived intermediates (i.e., triplet Rf, singlet oxygen) were solved by employing finite difference based operator splitting method.