Biography
Biography: Jui-Teng Lin
Abstract
We will present a new analytic Z* formula for corneal cross linking (CXL). CXL safety the criteria for the validity of Bunsen-Roscoe law (BRL) for accelerated CXL and its comparison to the new nonlinear law will be discussed. New formulas for CXL efficacy for both type-I and type-II will be presented. The minimum corneal thickness given by a Z*-formula, Z*=(1/A’)ln(E*/Ed), where a steady state effective absorption constant given by A’=2.3[mï¥2G(z)C0+Q], where Ed is the endothelial cell’s cytotoxic damage energy threshold (Ed). CXL efficacy (for type-I) is given by Ceff=1-exp(-S) with S being the rate function. The Bunsen-Roscoe law (BRL) is based on the Beer-Lambert law for UV light intensity without RF depletion, such that S=akE, which is a linear function of the dose E=(tI). In comparison, using a time-dependent generalized Beer-Lambert law, we obtain S=√((4kCo/aIo) expâ¡(A^' z)) [1-expâ¡(-0.5aE)] which is a nonlinear function of E and has a steady-state proportional to √((Co/aIo)expâ¡(A^' z)). Our nonlinear law predicts that high UV intensity requires longer exposure time than what is calculated based on BRL. In addition, for the same dose, higher intensity depletes the RF faster and reaches a lower steady-state efficacy than that of lower intensity, consistent with the recent clinical data. The CXL efficacy (for type-II) is given by Ceff=1-exp(-S) with S is the time integral of the singlet oxygen concentration, given by S(z,t)=(k_7/k_4)b_1 V(z,t)[1-b_2 V(z,t)] , where V(z,t)=ln (1+Bt), with B=apqI(z)X0., where X0 is the initial oxygen concentration, p and q are the type-I and type-II quantum yield, respectively. The S formula provides the role of oxygen in type-II efficacy.