Analytic formulas and numerical simulations for the dynamics of thick and non-uniform polymerization by a UV light

Lin, Jui‐Teng; Wang, Kuan-Chen

doi:10.1007/s10965-016-0934-4

Cited by 13 publications

(49 citation statements)

References 9 publications

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“…The corneal model system [11, 12] consists of its epithelial layer and the underlying stroma collagen as shown in Fig 1A. The UV light is normally incident to the corneal surface.…”

Section: Methodsmentioning

confidence: 99%

“…(A) The epi-off case with the stroma surface defined as z = 0. (B) The initial (at t = 0) RF concentration distribution inside the stroma given by a distribution function F(z,D), having a diffusion depth (D) [11, 12]. …”

Section: Methodsmentioning

confidence: 99%

“…For comprehensive analytic formulas, various numerically fitting techniques are presented earlier [11]. In this study we will use the linear approximation of the light intensity I ( z , t ) given by the mean value of the initial (I 1 ) and steady intensity (I 2 ) defined by I ( z , t ) = 0.5[ I 1 ( z ) + I 2 ( z )] for t<T and I ( z , t ) = I 2 ( z ) + 0.5[ I 1 ( z )− I 2 ( z )] for steady-state, or t>T, where T is the steady-state cross-linking time given by T = m/(aI 0 ), with m = 12 fit numerically with the exact solution of Eq (2) [12]…”

Section: Methodsmentioning

confidence: 99%

“…Time integration of the light intensity, the effective dose (at z) Eq (3) becomes [12] where E 0 = I 0 t is the surface dose (at z = 0), and g is a correction factor for the transient state given by g = 0.5(I 2 –I 1 )(T/E 0 ), T = f/(aI 0 ), with the fit parameter f = 12. With ε 1 = 204 (%·cm) -1 , ε 2 = 102 (%·cm) -1 , Q = 13.9 (cm -1 ) and C 0 = 0.1%, we obtain an approximated value of the correction factor g = 0.97[exp(− A 2 z )−exp(− A 1 z )], which is about 10% to 25% correction to the steady-state when E 0 = 3.0 to 4.0 J/cm 2 and at z = 400 um.…”

Section: Methodsmentioning

confidence: 99%

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Modeling the efficacy profiles of UV-light activated corneal collagen crosslinking

Lin¹,

Cheng

2017

PLoS ONE

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160

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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 corneal model system [11, 12] consists of its epithelial layer and the underlying stroma collagen as shown in Fig 1A. The UV light is normally incident to the corneal surface.…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

See 2 more Smart Citations

Modeling the efficacy profiles of UV-light activated corneal collagen crosslinking

Lin¹,

Cheng

2017

PLoS ONE

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160

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“…Therefore, the kinetics of PPS becomes very complex and the process is governed by multiple factors. To improve the efficiency of PPS particularly in a thick system (>1.0 cm), we have presented the numerical results using a focused light [7] and two-beam approach for the case of uniform PS distribution [8] and analytic comprehensive modeling for the non-uniform case [9].…”

Section: Introductionmentioning

confidence: 99%

Modeling the Kinetics, Dynamic Profiles and Strategies for Optimal Efficacy of Photo-Polymerization in Thick Polymers

J¹,

Chen²,

H³

et al. 2018

Preprint

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The kinetics and optimal efficacy conditions of photoinitiated polymerization are theoretically presented. Analytic formulas are derived for the crosslink time, crosslink depth and efficacy function. The roles of photosensitizer (PS) concentration, diffusion depth and light intensity on the polymerization spatial and temporal profiles, for both uniform and non-uniform cases, are presented . For optimal efficacy, a strategy via controlled PS concentration is proposed, where re-supply of PS in high light intensity may achieve a combined-efficacy similar to low light intensity, but has a much faster procedure. A new criterion of efficacy based on the polymerization (crosslink) [strength] and [depth] is introduced.

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UV‐Curable Alkenyl Monomers and Oligomers – The Backbone Chemistry ofUVInkjet Inks

Baro¹,

Fleckenstein²

2022

Inkjet Printing in Industry

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Analytic formulas and numerical simulations for the dynamics of thick and non-uniform polymerization by a UV light

Cited by 13 publications

References 9 publications

Modeling the efficacy profiles of UV-light activated corneal collagen crosslinking

Modeling the efficacy profiles of UV-light activated corneal collagen crosslinking

Modeling the Kinetics, Dynamic Profiles and Strategies for Optimal Efficacy of Photo-Polymerization in Thick Polymers

UV‐Curable Alkenyl Monomers and Oligomers – The Backbone Chemistry ofUVInkjet Inks

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