Date Published: April 6, 2017
Publisher: Public Library of Science
Author(s): Jui-Teng Lin, Da-Chuan Cheng, Alexander V. Ljubimov.
Analysis of the crosslink time, depth and efficacy profiles of UV-light-activated corneal collagen crosslinking (CXL).
A modeling system described by a coupled dynamic equations are numerically solved and analytic formulas are derived for the crosslinking time (T*) and crosslinking depth (z*). The z-dependence of the CXL efficacy is numerically produced to show the factors characterizing the profiles.
Optimal crosslink depth (z*) and maximal CXL efficacy (Ceff) have opposite trend with respective to the UV light intensity and RF concentration, where z* is a decreasing function of the riboflavin concentration (C0). In comparison, Ceff is an increasing function of C0 and the UV exposure time (for a fixed UV dose), but it is a decreasing function of the UV light intensity. CXL efficacy is a nonlinear increasing function of [C0/I0]-0.5 and more accurate than that of the linear theory of Bunsen Roscoe law. Depending on the UV exposure time and depth, the optimal intensity ranges from 3 to 30 mW/cm2 for maximal CXL efficacy. For steady state (with long exposure time), low intensity always achieves high efficacy than that of high intensity, when same dose is applied on the cornea.
The crosslinking depth (z*) and the crosslinking time (T*) have nonlinear dependence on the UV light dose and the efficacy of corneal collagen crosslinking should be characterized by both z* and the efficacy profiles. A nonlinear scaling law is needed for more accurate protocol.
Photochemical kinetics of corneal collagen crosslinking (CXL) and the biomechanical properties of corneal tissue after CXL have been extensively explored in both animal and human models [1–5]. The dynamics of CXL and the safety and efficacy issues of CXL have been explored theoretically [6–13] and clinically [14, 15]. To increase the speed of CXL procedures, accelerated CXL using high UV power (9 to 45 mW/cm2) are also reported . However, the accelerated CXL based on the linear theory of Bunsen Roscoe law (BRL)  to shorten the irradiation time is still a debating issue. More recent clinical studies have indicated that the efficacy based on BRL is actually lower than the non-BRL [18, 19]. Prior modeling work of Schumacher et al. The study in  assumes a constant riboflavin concentration during the UV light exposure time. This assumption ignoring the dynamic of the riboflavin concentration leads to major errors in the calculations of the UV light intensity profile (both spatial and temporal), the rate of photopolymerization and the increase of stiffness. The CXL efficacy is characterized by multiple factors including the concentration and diffusion profile of the RF in the stroma, the absorption constant of the photolysis products and the quantum yield of the CXL process.
Unless specified, the following calculated results are based on the measured parameters [17, 20] of ε1 = 204(%·cm)-1 and Q = 13.9 cm-1 and the assumed quantum yield ϕ = 0.5 and ε2 = 50 (%·cm)-1.
To conclude the significance and new findings of this theoretical study of CXL are summarized as follows: