Abbreviations: CXL: Corneal Collagen Cross-Linking; SCXL: Standard CXL (intensity 3 mW/cm²); ACXL: Accelerated CXL (intensity 9 to 45 mW/cm²), BRL: Bunsen–Roscoe Reciprocal Law; CCM: Riboflavin (Rf) Concentration-Controlled Method

Corneal collages cross-linking (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 (type-I and type-II)

-          Dresden vs. Modern protocols

Controversial Issues

Safety criteria

The UV light intensity increases from its initial value I(z,t)=I₀exp[-A₁z] to steady-state vale given by I(z,t)=I₀exp[-A₂z], with A₁= 2.3aC₀+Q, A₂=2.3bC₀+Q. For C₀=0.1%, a=204 (1/cm/%), b=50(1/cm/%), and Q=32 (/cm), we obtain A₁ =79 (1/cm), and A₂ =43.5 (1/cm), with an averaged value of 61 (1/cm), which are much larger than the RF-constant 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[mbC₀ + 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 C₀=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 photo-biological 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/cm². Validation of BRL has been challenged by Lin’s non-linear law and the S-formulas 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/cm². 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 concentration-controlled 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 oxygen-mediated (OM) and non-oxygen-mediated (NOM) 3-pathway processes, rather than the conventionally believed type-II only (oxygen-mediated) mechanism [12,13]. Both type-I and type-II 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 3-pathway kinetics maybe described as follows. For type-I, the riboflavin triplet state [T] may interact directly with the stroma collagen substrate [A] under NOM (with a rate constant k₈, pathway-1); or with the ground-state oxygen [³O₂] to form reactive oxygen species [O-] under OM; and in type-II process, [T] interacts with [³O₂] to form a singlet oxygen [¹O₂]. [T] mayalso relax to riboflavin ground state (with a rate constant k₅). Both reactive oxygen species (ROS), [O-] and [¹O₂], can either relax to [³O₂], or interact with [A] for crosslinking.

Schumacher, et al. [4] reported the NOM-type-I CXL, in contrast to Kling, et al.[5] claiming that oxygen-mediated type-II played the critical role of CXL efficacy. Furthermore, Kamaev, et al.[12] claimed that CXL is NOM-type-I dominant, while the OM-type-II 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 epi-on 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 non-controlled comparison of RF concentration during the UV exposure, based in Lin and Kamaev studies [12-14] that OM-type-II 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 Type-II efficacy. CXL efficacy (type-I and type-II)

CXL efficacydefined by Eff=1-exp(-S), where the S-function for type-I and type-II CXL are shown in Table 1. Our numerical calculations⁵ showed that S2 follows BRL and proportional to the light dose (E₀) and C[O₂]. In contrast, non-BRL feature occurs in type-I CXL (or S1) to be analyzed late. In contrast to the conventional belief that oxygen-mediated type-II plays the critical role of CXL, Kamaev et al [12] kinectic model showed that CXL is predominated by type-I, while oxygen (or type-II) only plays a limited and transient role. Lin’s 3-path-way model[14] showed mathematical details of the role of oxygen, supporting the claim of Kamaev et al.

For type-I CXL, the S-function (S1) is shown in Table 1, where F(z)C₀ is the initial (at t=0) Rf concentration (in the stroma) having a depth-profile defined by a diffusion depth (D), F(z)=1-0.5z/D. In contrast to type-II (S2), in which oxygen plays a transient but critical role, type-I (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/cm² for 30 minutes, delivering a fluence (dose) of 5.4 J/cm². 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 type-I) and oxygen (in type-II). Besides, the protocol procedures defining how the RF drops are applied pre-operatively and during the UV exposure are also important, because they define the initial, and intra-procedure 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 concentration-controlled 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/cm² intensity for 30 minutes exposure (or 2.7 J/cm² dose) has similar efficacy as that of 3 mW/cm² and 30 minutes exposure (5.4 J/cm² dose). This feature may be easily realized by our S-function which has an optimal dose predicted to be about 3 to 4 J/cm², and the 5.4 J/cm² (for 3 mW/cm²) is certainly higher than the optimal value [16].

Cut-off maximum intensity

Validation of BRL for accelerated CXL has been studied by Wernli, et al. [11] by the Cutoff maximum intensity about 50 mW/cm² and a minimum crosslinking time about 2 minutes. These criteria may be derived by our S-function as follow. Taking a threshold value of S₀ (the minimum S for efficient crosslinking as that of Dresden 3 mW/cm²), or 4KC₀Fexp(Az)/(aqKI₀) > S₀², from our S-formula, which leads to a cutoff maximum intensity (on the corneal surface, z=0) given by I*=4KC₀/(aqKS^*2). For C₀=0.1%, q=0.5, K=7.8, K’=0.05, a=0.622, we obtain I*=201/S₀², or I*= (50.3,22.3) mW/cm², for S₀= (2,3), i.e., Ceff=1.exp(-S₀) = (0.86,0.95). these values predict what was reported by Wernli et al [11]. We should note that the S-formula is valid for the situation of non-controlled RF concentration, i.e., no extra RF drops were applied during the UV exposure (or Fdrop=0). A concentration-controlled methods (with Fdrop=1 to 3) was proposed to overcome the limitation of maximum intensity [10].

New standard for CXL efficacy

At steady-state (with bt>>1), S1 follows a nonlinear scaling law[10,16] that S1 is promotional to (C₀E₀/I₀)^0.5exp(0.5Az) showing that S1 is proportional to C₀^0.5 (for z=0) and stronger dependence of exp(0.5Az) C₀^0.5 (for z>0), noting that A is also proportional to C₀, A=290F(z)C₀+32 (in cm^-1). For example, at z=0, S1(for C₀=0.2%)=1.43 S1(for C₀=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 cross-linking effect, as also clinically indicated by O’Brart, et al. [17].

1.       Wollensak G, Spoerl E, Wilsch M, Seiler T (2003) Endothelial cell damage after riboflavin–ultraviolet-A treatment in the rabbit. J Cataract Refract Surg 29: 1786-1790.

2.       Hafezi F and Randleman JB (2016) Corneal collagen cross-linking.

3.       Mooren P, Gobin L, Bostan N, et al. (2016) Evaluation of UVA cytotoxicity for human endothelium in an ex vivo corneal cross-linking experimental setting. J Refract Surg 32: 4-46.

4.       Schumacher S, Mrochen M, Wernli J, Bueeler M, Seiler T (2012) Optimization model for UV-riboflavin corneal cross-linking. Invest Opthamol Vis Sci 53: 762-769.

5.       Kling S, Hafezi F (2017) An algorithm to predict the biomechanical stiffening effect in corneal cross-linking. J Refract Surg 32: 128-136.

6.       Lin JT (2016) Combined analysis of safety and optimal efficacy in UV-light-activated corneal collagen crosslinking. Ophthalmol Res 6: 1-14.

7.       Lin JT (2017) Efficacy and Z* formula for minimum corneal thickness in UV-light crosslinking. Cornea 36: 30-31.

8.       Bunsen RW, Roscoe HE (1862) Photochemical researches-Part V. On the measurement of the chemical action of direct and diffuse sunlight. Proc R SocLond 12: 306-312.

9.       Lin JT, Cheng DC (2017) Modeling the efficacy profiles of UV-light activated corneal collagen crosslinking. PloS One 12: e0175002.

10.    Lin JT (2018) A proposed concentration-controlled new protocol for optimal corneal crosslinking efficacy in the anterior stroma. Invest. Ophthalmol Vis Sci 59: 431-432.

11.    Wernli J, Schumacher S, Spoerl E, Mrochen M (2013) The efficacy of corneal cross-linking shows a sudden decrease with very high intensity UV light and short treatment time. Invest Ophthalmol Vis Sci 54: 1176-1180.

12.    Kamaev P, Friedman MD, Sherr E, Muller D (2012) Cornea photochemical kinetics of corneal cross-linking with riboflavin. Invest Ophthalmol Vis Sci 53: 2360-2367.

13.    Lin JT (2017) Photochemical Kinetic modeling for oxygen-enhanced UV-light-activated corneal collagen crosslinking. Ophthalmol Res 7: 1-8.

14.    Lin JT (2018) Efficacy S-formula and kinetics of oxygen-mediated (type-II) and non-oxygen-mediated (type-I) corneal cross-linking. Ophthalmol Res 8: 1-11.

15.    Kling S, Hafezi F (2017) Biomechanical stiffening: Slow low-irradiance corneal crosslinking versus the standard Dresden protocol. J Cataract Refract Surg 43: 975-979.

16.    Lin JT (2018) A critical review on the kinetics, efficacy, safety, nonlinear law and optimal protocols of corneal cross-linking. 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 cross-Linking using an enzymatic resistance model in porcine corneas. Invest. Ophthalmol Vis Sci 59: 1058-1065.