Customized Corneal Cross-Linking—A Mathematical Model

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To improve the safety, reproducibility, and depth of effect of corneal cross-linking with the ultraviolet A (UV-A) exposure time and fluence customized according to the corneal thickness.


Twelve human corneas were used for the experimental protocol. They were soaked using a transepithelial (EPI-ON) technique using riboflavin with the permeation enhancer vitamin E–tocopheryl polyethylene glycol succinate. The corneas were then placed on microscope slides and irradiated at 3 mW/cm2 for 30 minutes. The UV-A output parameters were measured to build a new equation describing the time-dependent loss of endothelial protection induced by riboflavin during cross-linking, as well as a pachymetry-dependent and exposure time-dependent prescription for input UV-A fluence. The proposed equation was used to establish graphs prescribing the maximum UV-A fluence input versus exposure time that always maintains corneal endothelium exposure below toxicity limits.


Analysis modifying the Lambert–Beer law for riboflavin oxidation leads to graphs of the maximum safe level of UV-A radiation fluence versus the time applied and thickness of the treated cornea. These graphs prescribe UV-A fluence levels below 1.8 mW/cm2 for corneas of thickness 540 μm down to 1.2 mW/cm2 for corneas of thickness 350 μm. Irradiation times are typically below 15 minutes.


The experimental and mathematical analyses establish the basis for graphs that prescribe maximum safe fluence and UV-A exposure time for corneas of different thicknesses. Because this clinically tested protocol specifies a corneal surface clear of shielding riboflavin on the corneal surface during UV-A irradiation, it allows for shorter UV-A irradiation time and lower fluence than in the Dresden protocol.

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