Department of Mathematics Colloquium

University of Idaho

Fall 2012

Thursday,  August 30, 3:30-4:20 pm, room TLC 149

Refreshments in Brink 305 at 3:00 pm

Dynamics of oxygen-dependent mechanisms during (Riboflavin/UV-A)-induced collagen-cross linking in the corneal stroma


Sergey Lapin

Department of Mathematics

Washington State University


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.