Analysis of the effective dose of ultraviolet light in corneal cross-linking

To analyze the efficacy of ultraviolet (UV) light initiating corneal cross-linking (CXL).

The time-dependent absorption of UV light due to the depletion of the initiator (riboflavin) was calculated. The effective dose of CXL with corneal surface covered by a thin layer of riboflavin was derived analytically. The cross linking time was calculated by the depletion level of the riboflavin concentration. A comprehensive method was used to derive analytic formulas.

The effective dose of CXL was reduced by a factor (R) which was proportional to the thickness (d) and concentrations (C0) of the riboflavin surface layer. Our calculations showed that the conventional dose of 5.4 J/cm(2) had a reduced effective dose of 4.3 and 3.45 J/cm(2), for d was 100 and 200 µm, respectively, and C0=0.1%. The surface cross linking time was calculated to be T*=10.75s, for a depletion level of 0.135 and UV initial intensity of 30 mW/cm(2). The volume T* was exponentially increasing and proportional to exp (bdC0), with b being the steady state absorption coefficient.

The effective dose of CXL is reduced by a factor proportional to the thickness and concentrations of the riboflavin surface layer. The wasted dose should be avoided by washing out the extra riboflavin surface layer prior to the UV light exposure.