title: An Algorithm to Predict the Biomechanical Stiffening Effect in Corneal Cross-linking.
abstract: OBJECTIVE
  To develop an algorithm to predict the stiffening effect of CXL and to verify the accuracy with results obtained from experimental measurements.
  
  
  METHODS
  The algorithm considers different variables: the reaction kinetics of riboflavin diffusion and riboflavin photodegradation to determine the effective riboflavin concentration in different stromal layers; the oxygen diffusion and ultraviolet (UV) absorption to determine the amount of reactive oxygen species as a function of time and stromal depth. For the experimental comparison, corneas were deepithelialized, followed by riboflavin instillation for 30 minutes and UV irradiation. Different pulsed and continuous-light conditions were analyzed with irradiances ranging from 3 to 100 mW/cm2and irradiation times from 8 to 30 minutes. Stress-relaxation measurements were performed in fresh-enucleated porcine (n = 66) and rabbit (n = 2) eyes directly after treatment, using a load of 0.6 MPa.
  
  
  RESULTS
  A clear linear relationship was observed between the concentration of newly induced cross-links and the experimentally observed stiffening factor (R2= 0.9432). An additional 1 mol/m3of cross-links increased the mechanical stress resistance of the cornea by 50.4%. The efficacy of standard CXL in murine, lapine, and porcine corneas was inversely related to corneal thickness. The stiffening effect after CXL decreased by 4.1% per 100 µm (R2= 0.9961).
  
  
  CONCLUSIONS
  The proposed model, supported by data in porcine, murine, and lapine corneas, suggests a possibility of also predicting the biomechanical CXL efficacy in human corneas. The biomechanical efficacy of CXL may be increased by prolonged UV irradiation at reduced irradiances or by a higher oxygen pressure in the environment. Pulsed CXL does not accelerate CXL or increase its efficacy when compared to standard CXL of the same irradiation duration. This model might be used to calculate customized irradiation settings for high-risk cases, but also topography-guided CXL treatments. [J Refract Surg. 2017;33(2):128-136.].
authors.forename: Sabine
authors.initials: S
authors.lastname: Kling
authors.forename: Farhad
authors.initials: F
authors.lastname: Hafezi
mesh_terms: D000465:Algorithms; D000818:Animals; D001696:Biomechanical Phenomena; D003094:Collagen / Q000378:metabolism; D003315:Cornea / Q000187:drug effects / Q000378:metabolism / Q000503:physiopathology*; D003319:Corneal Stroma / Q000378:metabolism; D003432:Cross-Linking Reagents; D004548:Elasticity / Q000502:physiology*; D008297:Male; D051379:Mice; D008962:Models, Theoretical; D017319:Photosensitizing Agents / Q000494:pharmacology*; D011817:Rabbits; D017382:Reactive Oxygen Species / Q000378:metabolism; D012256:Riboflavin / Q000494:pharmacology*; D013314:Stress, Mechanical; D013552:Swine; D014466:Ultraviolet Rays
chemical_list: D003432:Cross-Linking Reagents; D017319:Photosensitizing Agents; D017382:Reactive Oxygen Species; D003094:Collagen; D012256:Riboflavin