Customized Corneal Cross-Linking-A Mathematical Model

Cornea. 2017 May;36(5):600-604. doi: 10.1097/ICO.0000000000001160.

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/cm 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/cm for corneas of thickness 540 μm down to 1.2 mW/cm 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.

MeSH terms

  • Collagen / drug effects
  • Collagen / radiation effects
  • Cornea / drug effects*
  • Cornea / radiation effects*
  • Cross-Linking Reagents / pharmacology*
  • Humans
  • Models, Theoretical
  • Photochemotherapy / adverse effects
  • Photochemotherapy / methods*
  • Photosensitizing Agents / pharmacology*
  • Photosensitizing Agents / therapeutic use*
  • Reproducibility of Results
  • Riboflavin / pharmacology*
  • Ultraviolet Rays*

Substances

  • Cross-Linking Reagents
  • Photosensitizing Agents
  • Collagen
  • Riboflavin