September 2018
Volume 59, Issue 11
Open Access
Letters to the Editor  |   September 2018
The Role of Riboflavin Concentration and Oxygen in the Efficacy and Depth of Corneal Crosslinking
Author Affiliations
  • Jui-teng Lin
    New Vision, Inc., Taipei, Taiwan
Investigative Ophthalmology & Visual Science September 2018, Vol.59, 4449-4450. doi:10.1167/iovs.18-24437
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      Jui-teng Lin; The Role of Riboflavin Concentration and Oxygen in the Efficacy and Depth of Corneal Crosslinking. Invest. Ophthalmol. Vis. Sci. 2018;59(11):4449-4450. doi: 10.1167/iovs.18-24437.

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      © ARVO (1962-2015); The Authors (2016-present)

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The recent article of O'Brart et al.1 discussed the roles of riboflavin concentration (in the stroma) on the efficacy of corneal collagen crosslinking (CXL). Clinical studies of Ng et al.2 showed that accelerated CXL (ACXL) had less efficacy than standard CXL (SCXL) for the same fluence (dose) based on Bunsen–Roscoe reciprocal law (BRL). To overcome this intrinsic drawback of ACXL, Lin3 recently proposed a new protocol called riboflavin (Rf) concentration-controlled method (CCM) to improve the efficacy of ACXL by supplemental Rf during the UV exposure to compensate the fast depletion of Rf by UV light. 
This letter analyzes the role of Rf concentration and its limitation by a CXL depth formula. A new criterion of CXL efficacy based on crosslinking [strength] × [depth] is introduced for optimal protocol. In addition, the role of oxygen in both type-I and type-II CXL is briefly summarized. 
CXL efficacy4,5 defined by Eff = 1 − exp(−S), where the S-function for type-I and type-II CXL is shown in the Table. Our numerical calculations5 showed that S2 follows BRL and is 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, the kinetic model of Kamaev et al.6 showed that CXL is predominated by type-I, whereas oxygen (or type-II) plays only a limited and transient role. Lin's 3-pathway model5,7 showed mathematical details of the role of oxygen, supporting the claim of Kamaev et al.6 Moreover, a recent clinical study of Lombardo et al.8 showed a simple-exponential temporal profile of Rf concentration that implied that, in ambient environment, non–oxygen-mediated type-I mechanism is predominant. 
Table
 
Abbreviations and Key Parameters4,5
Table
 
Abbreviations and Key Parameters4,5
For type-I CXL, the S-function (S1) is shown in the Table, 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.48 
At steady-state (with btX>>1), S1 follows a nonlinear scaling law4 that S1 is proportional to (FC0/I0)0.5 exp(0.5Az), or S1α[C0]0.5 (for z = 0) and stronger dependence of S1α[C0exp(Az)]0.5 (for z > 0), because A is also proportional to C0. For example, on corneal surface (or z = 0), when C0 is doubled (from 0.1% to 0.2%), S1 increases by a factor of 1.43. The Figure shows the theoretical Rf dose-curve (or S1 versus C0) comparing to the data of O'Brart et al.1 (their Fig. 3A, normalized, and fit at 0.1%); both show the nonlinear feature of S1αC00.5
Figure
 
CXL efficacy versus Rf concentration shows the nonlinear feature, where theoretical curve (red curve) is compared with the clinical data (bars) of O'Brart et al.1
Figure
 
CXL efficacy versus Rf concentration shows the nonlinear feature, where theoretical curve (red curve) is compared with the clinical data (bars) of O'Brart et al.1
CXL depth (defined by when S1 is maximal) is given by7 z* = ln(NE0)/A, with N being a numerically fit constant given by N = 0.16 (for D >>1 cm) and N = 0.224 (for D = 500 μm). For example, when C0 is doubled (from 0.1% to 0.2%), A increases and z* is reduced by 1.48 times. The z*-formula shows that higher Rf concentration results in an increased (or larger S1), but more superficial (or small z*) crosslinking effect, as also indicated by O'Brart et al.1 Our formulas lead to a new criterion of CXL efficacy based on the product of CXL [strength] (or S1) and [depth] (or z*), that is, the [volume] of stroma being cross-linked. For a given C0, deeper CXL may be achieved by larger fluence (E0). However, to achieve clinically acceptable CXL efficacy by a minimal E0, one requires an optimal range of C0. For example, C0 = 0.15% to 0.3%, and E0 = 3.5 to 4.5 J/cm2, such that [depth], z* = 200 to 300 μm, and [strength], S1 = 1.5 to 2.0, or CXL efficacy Eff = 1 − exp(−S1) = 0.78 to 0.86. Our formulas also demonstrate that epi-on CXL (having a smaller D and C0) is less efficient than epi-off CXL, as clinically reported. To conclude, the author would like to see further basic, clinical investigations to support the presented formulas, as suggested by the reviewers. 
References
O'Brart NAL, O'Brart DPS, Aldahlawi NH, Hayes S, Meek KM . 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. 2018; 59: 1058– 1065.
Ng AL, Chan TC, Cheng AC. Conventional versus accelerated corneal collagen cross-linking in the treatment of keratoconus. Clin Exp Ophthalmol. 2016; 44: 8– 14.
Lin JT. A proposed concentration-controlled new protocol for optimal corneal crosslinking efficacy in the anterior stroma. Invest Ophthalmol Vis Sci. 2018; 59: 431– 432.
Lin JT, Cheng DC. Modeling the efficacy profiles of UV-light activated corneal collagen crosslinking. PLoS One. 2017; 12: e0175002.
Lin JT. Efficacy S-formula and kinetics of oxygen-mediated (type-II) and non-oxygen-mediated (type-I) corneal cross-linking. Ophthalmology Research. 2018; 8: 1– 11.
Kamaev P, Friedman MD, Sherr E, Muller D. Cornea photochemical kinetics of corneal cross-linking with riboflavin. Invest Ophthalmol Vis Sci. 2012; 53: 2360– 2367.
Lin JT. A critical review on the kinetics, efficacy, safety, nonlinear law and optimal protocols of corneal cross-linking. J Ophthalmol Vis Neurosci. 2018; 3: 017.
Lombardo G, Villlan V, Micali N, et al. Non-invasive optical method for real-time assessment of intracorneal riboflavin concentration and efficacy of corneal cross-linking. J Biophotonics. 2018; 11: e201800028.
Figure
 
CXL efficacy versus Rf concentration shows the nonlinear feature, where theoretical curve (red curve) is compared with the clinical data (bars) of O'Brart et al.1
Figure
 
CXL efficacy versus Rf concentration shows the nonlinear feature, where theoretical curve (red curve) is compared with the clinical data (bars) of O'Brart et al.1
Table
 
Abbreviations and Key Parameters4,5
Table
 
Abbreviations and Key Parameters4,5
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