Efficacy S-formula and Kinetics of Non-oxygen-mediated (Type-I) and Oxygen-mediated (Type-II) Corneal Cross-linking

Abstract

Aims: To derive analytic formulas for the overall efficacy of corneal collagen crosslinking (CXL) based on coupled kinetic equations including both non-oxygen-mediated (NOM) and oxygen-mediated (OM) type-II mechanisms. Study Design:  modeling the kinetics of CXL. Place and Duration of Study: Taipei, Taiwan, between June, 2017 and January 2018. Methodology: Coupled kinetic equations are derived under the quasi-steady state condition for the 3-pathway mechanisms of CXL. For type-I CXL, the riboflavin triplet state [T3] may interact directly with the stroma collagen substrate [A] under NOM, or with the ground-state oxygen [O2] to form reactive oxygen species [O-] under OM. For type-II process, [T3] interacts with [O2] to form a singlet oxygen [1O2]. Both reactive oxygen species (ROS), [O-] and [1O2], can relax to [O2], or interact with the extracellular matrix (or the stroma substrate [A]) for crosslinking. Results: In the first 3 to 20 seconds, CXL efficacy is governed by both type-I and –II mechanisms, and after that period type-I, NOM is the predominant contribution, while oxygen for OM only plays a limited and transient role, in contrary to the conventionally believed OM-dominant mechanism. The riboflavin profile has a much slower depletion rate than that of oxygen profile. The ratio between NOM-type-I and OM depends on the relative initial concentration of [A] and [1O2] and their diffusion depths in the stroma. The overall CXL efficacy is proportional to the UV light dose (or fluence), the riboflavin, C (z, t), and oxygen, [O2], initial concentration, where efficacy is limited by the depletion of either C (z, t) or [O2]. Conclusion: Resupply of riboflavin and/or oxygen concentration under a controlled-concentration-method (CCM) during the UV exposure may improve the overall efficacy, specially for the accelerated CXL which has lower efficacy than the standard Dresden low-power (under non-controlled concentration).