Customized Corneal Cross-Linking—A Mathematical Model

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Abstract

Purpose:

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.

Methods:

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.

Results:

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.

Conclusions:

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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