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Radha Pertaub, Marc D. Friedman, William A. Eddington, David Muller; Computer Modeling Study of Corneal Cross-Linking with Riboflavin. Invest. Ophthalmol. Vis. Sci. 2012;53(14):6814.
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To build a computational model of riboflavin (RF) diffusion and UVA absorption in the cornea during corneal cross-linking to investigate differences between standard cross-linking and various accelerated cross-linking protocols.
A finite element model is developed that uses equations governing RF in 20% dextran transport and its UVA absorption within the corneal stroma and solving them in a 2-D domain. Fick’s 2nd law of diffusion is used for riboflavin transport & Beer-Lambert’s law for RF/UVA absorption. Diffusion coefficient of RF in cornea and the UVA absorption coefficients of cornea and of RF are implemented in the numerical model. Corneal scattering of UVA was taken into account for the measurement of corneal absorption coefficient. RF/UVA absorption was measured in the lab and showed a linear proportionality to RF concentration. The model also has four adjustable parameters that determine the UVA absorption profile in the cornea: 1) RF concentration, 2) presoak time, 3) UVA irradiance, and 4) duration of UVA exposure.
The model shows the distribution of riboflavin in the stroma and computes the UVA dose absorbed by riboflavin. The one hour standard clinical protocol shows a high distribution gradient of riboflavin due to the long diffusion time of riboflavin both during pre-soak and UVA application. Accelerated cross-linking protocols with shorter pre-soak times have a comparable riboflavin concentration gradient in the anterior cornea but less riboflavin presence in the posterior part. This implies similar doses of UVA absorbed by riboflavin in the anterior cornea to give comparable cross-linking to standard cross-linking. However, a much lower concentration of riboflavin present in the posterior cornea absorbs a lower UVA dose during accelerated cross-linking making it safer close to the endothelium. The model shows that accelerated procedures with short soak times are safer despite the irradiance being greater.
The model efficiently predicts the riboflavin and UVA distribution within the stroma and can be used to compare various clinical protocols. The parameters of the model can be changed to investigate the best approach for a clinical protocol using high irradiance at shorter times and/or different formulations of riboflavin photosensitizer.
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