ObjectiveAnalysis of the crosslink time, depth and efficacy profiles of UV-light-activated corneal collagen crosslinking (CXL).MethodsA 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.ResultsOptimal 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.ConclusionsThe 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.

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The levels in 74 » 76 Kr were studied with in-beam y-spectroscopy techniques and the j3 + decay of 7G Rb. The energies of the 2 t + states in 74,76 Kr deviate from smooth behavior compared with the higher spin levels. The yrast cascade B (E2)'s are highly collective. The 74 » 76 Kr ground states have unusually large deformation. The origin of this deformation and of shape coexistence in this region is described in terms of the protons driving the deformationo PACS numbers: 23.20. Ck, 23.20.Lv, 27.50. + e The 0 2 + energies have a deep minimum in 7O,72Q G an( j 72,74g e anc j are near or below the 2 X + energies. 1 These and other data have led to various suggestions of shape coexistence in these nuclei, where the low-lying 0 2 + states are more deformed than the ground states. 1 " 4 However, questions have been raised about shape coexistence and deformation in these nuclei, in part because well-developed, deformed bands built on the 0 2 + states in 70,72 Ge are not seen. 1 * 3 In this paper we suggest that the origin of shape coexistence for iV«38 nuclei is related to the number of protons which delicately controls whether a deformed shape or near-spherical shape is lowest in nuclei in this region. Our 74 » 76 Kr data give evidence that their ground states have remarkably large deformation.The origin of strong deformation and shape coexistence in this region can be attributed to the gaps in the single-particle spectrum seen in Fig. 1514

Kinetic equations for a modeling system with type-I radical-mediated and type-II oxygen-mediated pathways are derived and numerically solved for the photopolymerization efficacy and curing depth, under the quasi-steady state assumption, and bimolecular termination. We show that photopolymerization efficacy is an increasing function of photosensitizer (PS) concentration (C0) and the light dose at transient state, but it is a decreasing function of the light intensity, scaled by [C0/I0]0.5 at steady state. The curing (or cross-link) depth is an increasing function of C0 and light dose (time × intensity), but it is a decreasing function of the oxygen concentration, viscosity effect, and oxygen external supply rate. Higher intensity results in a faster depletion of PS and oxygen. For optically thick polymers (>100 um), light intensity is an increasing function of time due to PS depletion, which cannot be neglected. With oxygen inhibition effect, the efficacy temporal profile has an induction time defined by the oxygen depletion rate. Efficacy is also an increasing function of the effective rate constant, K = k′/kT0.5, defined by the radical producing rate (k′) and the bimolecular termination rate (kT). In conclusion, the curing depth has a non-linear dependence on the PS concentration, light intensity, and dose and a decreasing function of the oxygen inhibition effect. Efficacy is scaled by [C0/I0]0.5 at steady state. Analytic formulas for the efficacy and curing depth are derived, for the first time, and utilized to analyze the measured pillar height in microfabrication. Finally, various strategies for improved efficacy and curing depth are discussed.

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