Optimization Model for UV-Riboflavin Corneal Cross-linking

PURPOSE: To develop a theoretical model for riboflavin ultraviolet-A cross-linking treatment that can predict the increase in stiffness of the corneal tissue as a function of the ultraviolet intensity and riboflavin concentration distribution, as well as the treatment time. METHODS: A theoretical model for calculating the increase in corneal cross-linking (polymerization rate) was derived using Fick's second law of diffusion, Lambert-Beer's law of light absorption, and a photopolymerization rate equation. Stress-strain experiments to determine Young's modulus at 5% strain were performed on 43 sets of paired porcine corneal strips at different intensities (3-7 mW/cm²) and different riboflavin concentrations (0.0%-0.5%). The experimental results for Young's modulus increase were correlated with the simulated polymerization increase to determine a relationship between the model and the experimental data. RESULTS: This model allows the calculation of the one-dimensional spatial and temporal intensity and concentration distribution. The total absorbed radiant exposure, defined by intensity, concentration distribution, and treatment time, shows a linear correlation with the measured stiffness increase from which a threshold value of 1.7 J/cm² can be determined. The relative stiffness increase shows a linear correlation with the theoretical polymer increase per depth of tissue, as calculated by the model. CONCLUSIONS: This theoretical model predicts the spatial distribution of increased stiffness by corneal cross-linking and, as such, can be used to customize treatment, according to the patient's corneal thickness and medical indication.