Modeling the Kinetics of Enhanced Photo-Polymerization under a Collimated and a Reflecting Focused UV Laser

Lin, Jui‐Teng; Liu, Hsia‐Wei; Cheng, Da‐Chuan

doi:10.3390/polym6051489

Cited by 9 publications

(11 citation statements)

References 18 publications

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“…In the modeling system shown in Fig 1B, the UV light intensity I ( z , t ) and RF concentration C(z,t) in the corneal stroma (for the epi-off case) may be described by a set of coupled first-order differential equations, or by the integral equations [8–11] as follows, with the time-dependent RF concentration given by, Where a = 83.6 λϕε 1 , with ϕ being the quantum yield and λ being the UV light wavelength; ε 1 and ε 2 are the extinction coefficients of RF and the photolysis product, respectively. I 0 is the initial UV light surface intensity, or I(z = t = 0) = I 0 .…”

Section: Methodsmentioning

confidence: 99%

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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Section: Methodsmentioning

confidence: 99%

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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“…For more realistic systems, the distribution of the photoinitiator is non-uniform and the UV light may still be absorbed by the photolysis product besides the absorption of the monomer. To improve the efficiency and spatial uniformity (in the depth direction) particularly in a thick system (>1.0 cm), we have presented the numerical results using a focused light [24] and two-beam approach [25] for the case of uniform PS distribution; and analytic and computer modeling for the non-uniform case [26]. Optimal efficacy in light-activated biomedical systems and nonlinear laws versus linear Beer-Lambert law were also reported by Lin [27].…”

Section: Introductionmentioning

confidence: 88%

Modeling the Dynamic Concentration Profiles and Efficacy of Type-I and Type-II Photopolymerization

J¹,

Cheng²,

Chen³

et al. 2018

Preprint

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The kinetics and efficacy profiles of photoinitiated polymerization are theoretically presented. For the same dose, lower light intensity achieves a higher steady-state-efficacy (SSE) in type-I; in contrast, type-II has an equal SSE. Higher light intensity has a faster rising efficacy, due to faster depletion of photoinitiator (PS) concentration. However, type-II process is also affected by the available oxygen. Higher light intensity produces more efficient singlet oxygen, resulting a higher transient efficacy, in which all intensities reach the same SSE when oxygen is completely depleted. With external oxygen, type-II efficacy increases with time, otherwise, it is governed only by the light dose, i.e., same dose achieves same efficacy. Moreover, type-II has an efficacy follows Bunsen Roscoe law (BRL), whereas type-I follows non-BRL. The measured type-I efficacy and gelation profile are analyzed by our analytic formulas. Schematics of the photocrosslinking stage defined by the availability of oxygen is developed, where both type-I and –II coexist until the oxygen is depleted. The overall efficacy may be enhanced by resupply of PS or oxygen during the light exposure. The roles of light dose and PS concentration on the efficacy of photoinitiated polymerization should be are governed a new concept of a volume efficacy (Ve), defined by the product of the crosslink (or gelation) depth (CD) and local [efficacy].

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“…5 i.e., the anterior portion always has less efficacy (gelation). Strategy using two-side illumination [6,8] and focused light [7] were proposed to improve the overall efficacy and uniformity of the GSP. For class (b), the PSCD profile is controlled by the diffusion time (or the value of D).…”

Section: Strategies For Optimal Efficacymentioning

confidence: 99%

“…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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Modeling the Kinetics of Enhanced Photo-Polymerization under a Collimated and a Reflecting Focused UV Laser

Cited by 9 publications

References 18 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 Dynamic Concentration Profiles and Efficacy of Type-I and Type-II Photopolymerization

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

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