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Abbreviations: CXL: Corneal
Collagen CrossLinking; SCXL: Standard CXL (intensity 3 mW/cm^{2});
ACXL: Accelerated CXL (intensity 9 to 45 mW/cm^{2}), BRL: Bunsen–Roscoe
Reciprocal Law; CCM: Riboflavin (Rf) ConcentrationControlled Method
Corneal collages crosslinking (CXL) is a
technology using riboflavin solution as the photosensitizer activated by a UVA
light (at 365 nm) to change the biomechanical properties of the corneal stroma.
CXL has been used clinically for various corneal conditions such as
keratoconus, keratitis, corneal ectasia and corneal ulcers. It has also been
used to preventively treat thin corneas, which carry a higher risk of ectasia
after LASIK vision correction. Other potential applications include the reduction
of postoperative regression in vision correction and scleral treatment in
malignant myopia, scleromalacia and low tension glaucoma. The first animal data
was reported by Wollensak in 2003 for the treatment of keratoconus [1].
Extensive review of CXL has been covered in detail in a recent book edited by
Hafezi and Randleman [2], This Editorial Review will first address the current
controversial issues with comments and resolutions. Then it will summarize the
principles/formulas of and define the key parameters influencing the efficacy
of CXL.
The controversial issues to be discussed
include:

Safety criteria (and the minimum corneal thickness)

Dynamic profiles and depletion of riboflavin

Validation of Bunsen Roscoe law (BRL)

Intensity cutoff maximum

The role of oxygen and pulsed mode

CXL efficacy (typeI and typeII)

Dresden vs. Modern protocols
Controversial Issues
Safety criteria
Dynamic
profiles and depletion of RF
Conventional modeling [4,5] assumed a
constant RF concentration during the crosslink, which is true only under the
socalled Dresden protocol [1,2], in which the RF is constantly resupplied to
compensate its depletion. However, it also reduced the available effective dose
to approximately about 70% to 80% of the applied dose 5.4 J/cm^{2}. The
constantRF also underestimated the UV light intensity, which in general, is an
increasing function of time (when RF depletion is accurately included), given
by [6,7] I(z,t)=I_{0}exp[A(z,t)] with A(z,t) is a decreasing function
of time when C(z,t) is depleted, given by A(z,t)= 2.3[(ab)C(z,t)G(z)+bC_{0}]+Q,
where a,b and Q are, respectively, the absorption constant of RF, photolysis
product and stroma (without RF); G(z)=10.25z/D; and F(z)=10.5z/D is the initial RF distribution
defined by a diffusion constant (D) [6].
The UV light intensity increases from its
initial value I(z,t)=I_{0}exp[A_{1}z] to steadystate vale
given by I(z,t)=I_{0}exp[A_{2}z], with A_{1}= 2.3aC_{0}+Q,
A_{2}=2.3bC_{0}+Q. For C_{0}=0.1%, a=204 (1/cm/%),
b=50(1/cm/%), and Q=32 (/cm), we obtain A_{1} =79 (1/cm), and A_{2}
=43.5 (1/cm), with an averaged value of 61 (1/cm), which are much larger than
the RFconstant model with a value of 42.5 (1/cm). If one assumes Q=b=0, then A=46.9
(1/cm), which is smaller than our averaged value of 61 (1/cm). Numerical
simulation of Lin and Cheng [8], also showed another fit A=2.3[mbC_{0}
+ Q], with m=1.5 for b=50(1/%/cm), which is fit to the CXL efficacy (at steady
state). In this fitting, (for D=500 um), A=49 and 66 (1/cm) for C_{0}=0.1%
and 0.2%.
Validation of Bunsen Roscoe
law (BRL)
To shorten the CXL treatment duration while maintaining the similar CXL efficacy, various accelerated (AC) protocols to replace the SD protocol have been proposed based on the BRL of reciprocity [8] stating that the effect of a photobiological reaction is proportional only to the total irradiation dose (E=It), or the product of intensity (I) and exposure time (t). To achieve the same efficacy, the required exposure time based on BRL is given by t=E/I, which gives the protocol for AC; for example, t= (30, 10, 5, 3, 2) minutes for I= (3,9,18,30,45) mW/cm^{2}. Validation of BRL has been challenged by Lin’s nonlinear law and the Sformulas for CXL efficacy [7,9]. Wernli, et al. [11] also pointed out the limitation of BRL due to the sudden drop of efficacy at UV intensity around 50 mW/cm^{2}. To improve the CXL efficacy, extended exposure time and/or dose, has been proposed to compensate the drawback of exposure time predicted by BRL [9]. Moreover, a concentrationcontrolled method (CCM) was proposed by Lin [10] to improve the CXL efficacy by resupply of RF during the UV exposure.
The role of oxygen and pulsed
mode
CXL efficacy is governed by both oxygenmediated (OM) and nonoxygenmediated (NOM) 3pathway processes, rather than the conventionally believed typeII only (oxygenmediated) mechanism [12,13]. Both typeI and typeII reactions can occur simultaneously, and the ratio between these processes depends on the type of photosensitizers (PS) used, the concentrations of PS, substrate and oxygen, the kinetic rates involved in the process, and the light intensity, dose, PS depletion rate etc. The CXL 3pathway kinetics maybe described as follows. For typeI, the riboflavin triplet state [T] may interact directly with the stroma collagen substrate [A] under NOM (with a rate constant k_{8}, pathway1); or with the groundstate oxygen [^{3}O_{2}] to form reactive oxygen species [O] under OM; and in typeII process, [T] interacts with [^{3}O_{2}] to form a singlet oxygen [^{1}O_{2}]. [T] mayalso relax to riboflavin ground state (with a rate constant k_{5}). Both reactive oxygen species (ROS), [O] and [^{1}O_{2}], can either relax to [^{3}O_{2}], or interact with [A] for crosslinking.
Schumacher, et al. [4] reported the NOMtypeI CXL, in contrast to Kling, et al.[5] claiming that oxygenmediated typeII played the critical role of CXL efficacy. Furthermore, Kamaev, et al.[12] claimed that CXL is NOMtypeI dominant, while the OMtypeII only plays a limited and transient role, as shown by Figure 3. If Kling, et al. [5] were correct, then all the reported results of epion CXL would not be possible, since only limited and transient oxygen supply is available. Lin [13] proposed mathematically, model in supporting the claims of Kamaev, et al. Pulsed mode was claimed to have higher efficacy than CW mode [5]. This conclusion, I believe, is due to clinical measured errors and/or noncontrolled comparison of RF concentration during the UV exposure, based in Lin and Kamaev studies [1214] that OMtypeII only plays a limited and transient role. As shown by Figure 4, the role of oxygen resupply (and pulsed mode) take few minutes. Therefore, pulsing in few seconds would not help the TypeII efficacy. CXL efficacy (typeI and typeII)
CXL efficacydefined by Eff=1exp(S), where
the Sfunction for typeI and typeII CXL are shown in Table 1. Our numerical calculations^{5} showed that S2
follows BRL and proportional to the light dose (E_{0}) and C[O_{2}].
In contrast, nonBRL feature occurs in typeI CXL (or S1) to be analyzed late.
In contrast to the conventional belief that oxygenmediated typeII plays the
critical role of CXL, Kamaev et al [12] kinectic model showed that CXL is
predominated by typeI, while oxygen (or typeII) only plays a limited and
transient role. Lin’s 3pathway model[14] showed mathematical details of the
role of oxygen, supporting the claim of Kamaev et al.
For typeI CXL, the Sfunction (S1) is shown in
Table 1, where F(z)C_{0 }is the initial (at t=0) Rf concentration (in
the stroma) having a
depthprofile defined by a diffusion depth (D), F(z)=10.5z/D. In contrast to
typeII (S2), in which oxygen plays a transient but critical role, typeI (S1)
does not require oxygen and it is the predominant pathway of CXL efficacy.
Dresden
vs. Modern protocols
The standard Dresden (SD) protocol was
proposed by Wollensak et al [2] in 2003, where a UVA light (at 365 nm) was used
to treat cornea 9 mm zone at an intensity of 3.0 mW/cm^{2} for 30
minutes, delivering a fluence (dose) of 5.4 J/cm^{2}. Modern protocols,
named as CCM by Lin [10], used a limited resupply of RF to eliminate the extra
blocking effect due to over resupplied RF in Dresden protocol.
CXL efficacy is influenced by multiple
factors including, the UV light intensity, exposure period and dose, the
initial concentration profiles of RF and oxygen, the quantum yield of the RF
triplet state, the kinetic rate constants of RF (in typeI) and oxygen (in
typeII). Besides, the protocol procedures defining how the RF drops are
applied preoperatively and during the UV exposure are also important, because
they define the initial, and intraprocedure RF concentration profiles (or
diffusion depth). For example, the frequency of RF drops (Fdrop) applied on the
cornea after the UV is turned on, and the waiting period (Twait) for each RF
drops instillation during the UV exposure. In the conventional Dresden
protocol, Fdrop is about 5 to 10 times and Twait=0. In contrast, our proposed
concentrationcontrolled method (CCM) uses Fdrop is about 1 to 3 times (for RF
replenishment) and Twait is 1 or 2 minutes (for enough diffusion depth, with
D>150 um).
Kling, et al. [15] recently reported the use of
1.5 mW/cm^{2} intensity for 30 minutes exposure (or 2.7 J/cm^{2 }dose)
has similar efficacy as that of 3 mW/cm^{2} and 30 minutes exposure (5.4 J/cm^{2 }dose). This
feature may be easily realized by our Sfunction which has an optimal dose
predicted to be about 3 to 4 J/cm^{2}, and the 5.4 J/cm^{2}
(for 3 mW/cm^{2}) is certainly higher than the optimal value [16].
Cutoff
maximum intensity
Validation of BRL for accelerated CXL has
been studied by Wernli, et al. [11] by the Cutoff maximum intensity about 50
mW/cm^{2} and a minimum crosslinking time about 2 minutes. These
criteria may be derived by our Sfunction as follow. Taking a threshold value
of S_{0 }(the minimum S for efficient crosslinking as that of Dresden 3
mW/cm^{2}), or 4KC_{0}Fexp(Az)/(aqKI_{0}) > S_{0}^{2},
from our Sformula, which leads to a cutoff maximum intensity (on the corneal
surface, z=0) given by I*=4KC_{0}/(aqKS^{*2}). For C_{0}=0.1%,
q=0.5, K=7.8, K’=0.05, a=0.622, we obtain I*=201/S_{0}^{2}, or
I*= (50.3,22.3) mW/cm^{2}, for S_{0}= (2,3), i.e.,
Ceff=1.exp(S_{0}) = (0.86,0.95). these values predict what was
reported by Wernli et al [11]. We should note that the Sformula is valid for
the situation of noncontrolled RF concentration, i.e., no extra RF drops were
applied during the UV exposure (or Fdrop=0). A concentrationcontrolled methods
(with Fdrop=1 to 3) was proposed to overcome the limitation of maximum
intensity [10].
New
standard for CXL efficacy
At steadystate (with bt>>1), S1
follows a nonlinear scaling law[10,16] that S1 is promotional to (C_{0}E_{0}/I_{0})^{0.5}exp(0.5Az)
showing that S1 is proportional to C_{0}^{0.5} (for z=0) and
stronger dependence of exp(0.5Az) C_{0}^{0.5 }(for z>0),
noting that A is also proportional to C_{0}, A=290F(z)C_{0}+32
(in cm^{1}). For example, at z=0, S1(for C_{0}=0.2%)=1.43
S1(for C_{0}=0.1%), i.e., S1 increases by a factor of 1.43 when the Rf
concentration (in the stroma) is doubled. Our formulas show that higher Rf
concentrations result in an increased but more superficial crosslinking
effect, as also clinically indicated by O’Brart, et al. [17].
CONCLUSION
1. Wollensak G, Spoerl E, Wilsch M, Seiler T
(2003) Endothelial cell damage after riboflavin–ultravioletA treatment in the
rabbit. J Cataract Refract Surg 29: 17861790.
2. Hafezi F and Randleman JB (2016) Corneal
collagen crosslinking.
3. Mooren P, Gobin L, Bostan
N, et al. (2016) Evaluation of
UVA cytotoxicity for human endothelium in an ex vivo corneal crosslinking
experimental setting. J Refract Surg 32: 446.
4. Schumacher S, Mrochen M, Wernli J, Bueeler
M, Seiler T (2012) Optimization model for UVriboflavin corneal crosslinking.
Invest Opthamol Vis Sci 53: 762769.
5. Kling S, Hafezi F (2017) An algorithm to
predict the biomechanical stiffening effect in corneal crosslinking. J Refract
Surg 32: 128136.
6. Lin JT (2016) Combined analysis of safety
and optimal efficacy in UVlightactivated corneal collagen crosslinking.
Ophthalmol Res 6: 114.
7. Lin JT (2017) Efficacy and Z* formula for
minimum corneal thickness in UVlight crosslinking. Cornea 36: 3031.
8. Bunsen RW, Roscoe HE (1862) Photochemical
researchesPart V. On the measurement of the chemical action of direct and
diffuse sunlight. Proc R SocLond 12: 306312.
9. Lin JT, Cheng DC (2017) Modeling the
efficacy profiles of UVlight activated corneal collagen crosslinking. PloS One
12: e0175002.
10. Lin JT (2018) A proposed
concentrationcontrolled new protocol for optimal corneal crosslinking efficacy
in the anterior stroma. Invest. Ophthalmol Vis Sci 59: 431432.
11. Wernli J, Schumacher S, Spoerl E, Mrochen M
(2013) The efficacy of corneal crosslinking shows a sudden decrease with very
high intensity UV light and short treatment time. Invest Ophthalmol Vis Sci 54:
11761180.
12. Kamaev P, Friedman MD, Sherr E, Muller D
(2012) Cornea photochemical kinetics of corneal crosslinking with riboflavin.
Invest Ophthalmol Vis Sci 53: 23602367.
13. Lin JT (2017) Photochemical Kinetic
modeling for oxygenenhanced UVlightactivated corneal collagen crosslinking.
Ophthalmol Res 7: 18.
14. Lin JT (2018) Efficacy Sformula and
kinetics of oxygenmediated (typeII) and nonoxygenmediated (typeI) corneal
crosslinking. Ophthalmol Res 8: 111.
15. Kling S, Hafezi F (2017) Biomechanical
stiffening: Slow lowirradiance corneal crosslinking versus the standard
Dresden protocol. J Cataract Refract Surg 43: 975979.
16. Lin JT (2018) A critical review on the
kinetics, efficacy, safety, nonlinear law and optimal protocols of corneal
crosslinking. J Ophthalmol Visual Neurosci.
17. O'Brart NAL, O'Brart DPS, Aldahlawi NH,
Hayes S, Meek KM (2018) An Investigation of the effects of riboflavin
concentration on the efficacy of corneal crossLinking using an enzymatic
resistance model in porcine corneas. Invest. Ophthalmol Vis Sci 59: 10581065.
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