Analytic Formulas for the Clinical Issues of a UV-Light-Activated Corneal Crosslinking Device

Objective: Modeling the critical issues of the dynamics of UV-light-initiated crosslinking of corneal collagen including the new safety criteria, crosslinking time and the efficacy. Methods: A coupled dynamic equations is numerically solved and analytic formulas are derived for three critical parameters: the safety dose (E*), the cross linking time (T*) and the efficacy defined by the increase of corneal stiffness (S). The critical issues of corneal crosslinking is explored by nine parameters: the three extinction coefficients, concentration and diffusion depth of the riboflavin solution, the UV light dose, irradiation duration, the cytotoxic energy threshold of endothelial cells and the corneal thickness. Results: The safety dose (E*) has a wide range of 3.5 to 12 (J/cm2) for RF concentration of 0.1% to 0.2% and diffusion depth of 200 μm to 400 μm. It is shown that T* and E* are an exponentially increasing function of the riboflavin concentration, penetration depth and corneal thickness. E* is also proportional to the cytotoxic energy threshold of endothelial cells. Optimal photoinitiation rate and corneal stiffness increasing are found to be the result of the competing parameter between the UV light intensity and the initiator concentration. Higher light intensity and extinction coefficient lead to shorter surface cross linking time, while T* increases with corneal thickness (z). The conventionally proposed UV light dose 5.4 J/cm2 should be reduced to the optimal values of 1.0 to 2.0 J/cm2 for maximum corneal stiffness increasing or corneal crosslinking efficiency. Conclusions: This study demonstrates that the linear theory of Bunsen Roscoe law requires a nonlinear revision which shows optimal UV dose and concentration for maximum stiffness increasing. The analytic formulas provide useful guidance for the protocol design and optimization in corneal crosslinking.