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

Abstract

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 StudyMethodology: 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 [O 2 ], 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. D 2 O 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. Original Research Article

Dual-Wavelength (UV and Blue) Controlled Photopolymerization Confinement for 3D-Printing: Modeling and Analysis of Measurements

“…Although the mechanism for radical-mediated polymerization initiation and inhibition in dualwavelength system and the simple formulas for the associated printing speed and inhibition volume thickness [11] were reported, there is no detailed kinetics or the conversion efficacy have been theoretically reported in a dual-wavelength, thick polymer system. We have previously reported the kinetics and modeling of a single-wavelength radical-mediated photopolymerization in singleinitiator [12][13][14], two-initiator [15] and two-component system [16,17]. This study will extend our previous modeling to a 2-wavelength, 3-initiator system.…”

“…Using the short-hand notations for the concentration of various components: C1, C2, C3 for for the ground state concentration of PA, PB and PC, respectively, and [M] for the monomer, the kinetic equations for the dual-color and 5 radicals (R',R, [N], [X]) system are derived as follows [12,15,16]…”

“…For examples, in Eq. 7, k' is for the reaction of monomer and radical R, which has a relaxation rate k5; k12 is for the radical interaction of R' and R, and both have a bimolecular termination rate of kT; More detail derivation and definition of rate constants in g and g', have been previously published [12,15].…”

“…The dynamic light intensity of blue (I1) and UV (I2) are given by, when they are applied to the resin orthogonally and separately, [13,15]…”

“…Therefore, we expect a better fit if the spatial (zdependence) conversion profiles are included, as shown by our Eq. (15). However, most of the features and the roles of the key parameters presented based on surface layer should also apply to a volume conversion.…”