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Silvia Schumacher, Michael Mrochen, Jeremy Wernli, Michael Bueeler, Theo Seiler; Optimization Model for UV-Riboflavin Corneal Cross-linking. Invest. Ophthalmol. Vis. Sci. 2012;53(2):762-769. doi: 10.1167/iovs.11-8059.
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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.
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.
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.
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.
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