Abstract
Purpose:
Aggregation of riboflavin (Rf) molecules into clusters may impede the efficacy of highly concentrated Rf solutions in corneal cross-linking (CXL). For a 0.1% solution, typically used for CXL, ~37% of Rf is in clusters (1). This fraction increases to ~72% for a 0.5% solution (1). The rate constants of aggregation and disaggregation processes are known but the effect of aggregation on light-induced transformations of Rf has not been evaluated. We present a mathematical model of aggregation kinetics of Rf exposed to UVA light. The goal is to evaluate Rf concentration effect on the yield of triplet riboflavin that initiates CXL.
Methods:
Our model includes UV light propagation in Rf solution with varying concentrations of regular and reduced Rf; optical excitation of Rf monomers with light; quantum transitions between ground, singlet, and triplet states; chemical reactions transferring regular Rf into the reduced form; and aggregation, disaggregation, and diffusion of both the Rf forms in water solution under anaerobic conditions. Mathematically, the model was formulated as a set of partial differential equations in 1D space and was solved with finite-element software (Comsol 5.0).<br /> In order to validate the model the bleaching process of Rf under anaerobic conditions was studied experimentally by irradiating Rf aqueous solutions (0.01, 0.05, 0.1, and 0.5%) in a 200 µm cuvette with a top-hat 365 nm beam, at 3 and 30 mW/cm2 for up to 6 min. The concentrations of regular and reduced Rf forms after light exposure was assessed by measuring transmittance of probe light at 365 and 450 nm.
Results:
The measured dependencies of Rf and RfH2 concentrations vs. light dose are in good agreement with calculated data for 0.01, 0.05, and 0.1% solutions. 0.5% solution calculated bleaching rate is slower than measured. If the aggregation process is neglected, the model shows appreciable inaccuracy for concentrations ³0.5%.
Conclusions:
Rf aggregation effect is substantial for CXL modeling in the typical Rf concentration range. The present model is accurate for concentrations less than 0.5%, usually the case for CXL procedures. At higher concentrations, disaggregation may be higher than assumed by the model.