Kinetics of Enhancement for Corneal Cross-linking: Proposed Model for a Two-initiator System

Aims: To derive kinetic equations and analytic formulas for efficacy enhancement of corneal collagen crosslinking (CXL) in a 2-initiator system.

Study Design: Modeling the kinetics of CXL.

Place and Duration of Study: Taipei, Taiwan, between between January 2019 to June, 2019.

Methodology: Coupled rate equations are derived for two initiators system for a type-II process, consisting of a primary initiator (PA), and a co-initiator (PB) as an enhancer, having 3 cross linking pathways: Two radical-mediated (or electron transfer) pathways, and one oxygen-mediated (or energy transfer) pathway. For a type-II process, the triplet state T* interacts with the co-initiator, PB, to form the primary radicals R’, and an active intermediates radical, R, which could interact with the substrate [M] for crosslink, or be inhibited by oxygen [O2], or bimolecular termination. Rate equations, based on lifetime of triplet-state and oxygen singlet-state, are used to analyze the measured results in a rose-Bengal system with an enhanced initiator.

Results: Additive enhancer-monomer of arginine added to a rose Bengal photosensitizer may enhance the production of free radicals under a green-light CXL. D2O may extends the lifetime of oxygen singlet state and thus improve the efficacy. Our formulas predicted features are consistent with the measured results.

Conclusion: Efficacy may be improved by enhancer-monomer or extended lifetime of photosensitizer triplet-state or oxygen singlet state.