Optimization model for UV-riboflavin corneal cross-linking.
OBJECTIVE
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.
IROC AG, Zurich, Switzerland.
Silvia
S
Schumacher
Michael
M
Mrochen
Jeremy
J
Wernli
Michael
M
Bueeler
Theo
T
Seiler
D000818:Animals; D001696:Biomechanical Phenomena; D003315:Cornea / Q000187:drug effects / Q000378:metabolism* / Q000528:radiation effects; D003432:Cross-Linking Reagents / Q000378:metabolism / Q000528:radiation effects*; D006801:Humans; D008962:Models, Theoretical; D058105:Polymerization / Q000528:radiation effects; D012256:Riboflavin / Q000493:pharmacokinetics*; D013552:Swine; D014466:Ultraviolet Rays
D003432:Cross-Linking Reagents; D012256:Riboflavin