March 2016
Volume 57, Issue 3
Open Access
Visual Psychophysics and Physiological Optics  |   March 2016
Corneal Biomechanical Response Following Collagen Cross-Linking With Rose Bengal–Green Light and Riboflavin-UVA
Author Affiliations & Notes
  • Nandor Bekesi
    Instituto de Optica Consejo Superior de Investigaciones Cientificas, Madrid, Spain
  • Irene E. Kochevar
    Wellman Center for Photomedicine, Massachusetts General Hospital, Harvard Medical School, Boston, Massachusetts, United States
  • Susana Marcos
    Instituto de Optica Consejo Superior de Investigaciones Cientificas, Madrid, Spain
Investigative Ophthalmology & Visual Science March 2016, Vol.57, 992-1001. doi:10.1167/iovs.15-18689
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      Nandor Bekesi, Irene E. Kochevar, Susana Marcos; Corneal Biomechanical Response Following Collagen Cross-Linking With Rose Bengal–Green Light and Riboflavin-UVA. Invest. Ophthalmol. Vis. Sci. 2016;57(3):992-1001. doi: 10.1167/iovs.15-18689.

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

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Abstract

Purpose: To compare the biomechanical corneal response of two different corneal cross-linking (CXL) treatments, rose bengal–green light (RGX) and riboflavin-UVA (UVX), using noninvasive imaging.

Methods: A total of 12 enucleated rabbit eyes were treated with RGX and 12 with UVX. Corneal dynamic deformation to an air puff was measured by high speed Scheimpflug imaging (Corvis ST) before and after treatment. The spatial and temporal deformation profiles were evaluated at constant intraocular pressure of 15 mm Hg, and several deformation parameters were estimated. The deformation profiles were modeled numerically using finite element analysis, and the hyperelastic corneal material parameters were obtained by inverse modeling technique.

Results: The corneal deformation amplitude decreased significantly after both CXL methods. The material parameters obtained from inverse modeling were consistent with corneal stiffening after both RGX and UVX. Within the treated corneal volume, we found that the elasticity decreased by a factor of 11 after RGX and by a factor of 6.25 after UVX.

Conclusions: The deformation of UVX-treated corneas was smaller than the RGX-treated corneas. However, the reconstructed corneal mechanical parameters reveal that RGX produced in fact larger stiffening of the treated region (100-μm depth) than UVX (137-μm depth). Rose bengal–green light stiffens the cornea effectively, with shorter treatment times and shallower treated areas. Dynamic air puff deformation imaging coupled with mechanical simulations is a useful tool to characterize corneal biomechanical properties, assess different treatments, and possibly help optimize the treatment protocols.

In normal corneas, the biomechanical strength of the corneal tissue is such that it provides mechanical integrity to the cornea and a suitable geometry leading to the optical properties required for vision. However, in certain diseases such as keratoconus, the corneal tensile strength is significantly reduced,1 leading to progressive corneal bulging and, consequently, reduced optical quality and visual degradation. 
Corneal cross-linking (CXL) has been proposed as an effective means of stabilizing the cornea biomechanically,24 and is increasingly used in the clinic to treat keratoconus. Corneal cross-linking is a photochemical method, using a photosensitizer and light irradiation to create covalent bonds in the collagen fibrils, therefore increasing corneal stiffness. 
The standard CXL method uses riboflavin (in dextran solution) as a photosensitizer and UVA light at 366 nm for photoactivation radiation. The dehydrating effect of dextran produces corneal thinning, setting limits to the minimum corneal thickness that can be treated5 or the maximum light exposure to avoid corneal endothelial damage. Modifications of the procedure involve the use of hypo-osmotic riboflavin solutions to keep6 or even increase7 the native corneal thickness during treatment, or reducing the treatment times at the expense of increasing irradiance.8,9 However, other potential drawbacks still remain, including cytotoxicity to keratocytes, or the fact that treatment still occurs across a relatively high percentage of the corneal thickness. 
A new CXL method has been recently proposed that overcomes some of these problems. The method uses a different photosensitizer, rose bengal and green light (532 nm, 0.25 W/cm2 irradiance). A photochemical procedure using rose bengal and green light has also been used to replace sutures,10 for photobonding amniotic membrane to the corneal surface as a form of photoactivated bandage,11 and more recently for photobonding capsular bag tissue to polymers in intraocular lens implant applications.12 Similar to these applications that involve intercollagen covalent bond formation across two different tissues, the rose bengal (RB)–green light CXL creates bonds in the stromal collagen fibrils, therefore stiffening the cornea, as shown for standard riboflavin UVA CXL. Both tensile uniaxial extensiometry and Brillouin microscopy revealed stiffening of corneal tissue in rabbit eyes treated ex vivo.13 Fluorescence measurements (measured 4 to 64 minutes after RB application) indicated that rose bengal penetrated approximately 100 μm into the corneal stroma, suggesting that this method may be used safely even in corneas thinner than 400 μm. 
The characterization of biomechanical properties of the cornea is necessary to evaluate the effects of different CXL methods. Corneal biomechanical properties (i.e., Young's modulus) are usually measured by extensiometry tests on corneal strips, where a strip of cornea is subjected to tensile loading. However, the cornea is an anisotropic material, thus its mechanical response depends on the orientation of the collagen fibers, which may vary not only between different samples but also along the length of the same sample strip. While strip extensiometry can still be useful to compare samples of similar size and orientation, 2-dimensional (2D) mechanical testing provides a more suitable approach to characterize corneal biomechanical properties. In particular, 2D flap extensiometry and corneal/eye inflation have been used to characterize the changes in the corneal biomechanical response following CXL.14 In general, these techniques rely on measurements of the corneal deformation, while the intraocular pressure (IOP) is increased in a chamber on which the cornea or 2D corneal flaps are mounted or in an ocular globe infused with saline solution.1517 Corneal deformation is assessed indirectly through aberrometry,14 or directly from Scheimpflug imaging,18 (Bekesi N, et al. IOVS 2015;56:ARVO E-Abstract 1135) or OCT imaging,19,20 and the mechanical properties typically estimated based on the thin-walled pressure vessel theory or using inverse finite element (FE) modeling. Air puff deformation imaging, while commercialized primarily as a tonometer, is also a promising technique to characterize biomechanical properties of the cornea in vivo. A short air pulse is emitted against the cornea and the deformation is monitored by an adequately fast imaging system (e.g., OCT13 or Scheimpflug18). The deformation response to the air puff depends on the mechanical properties of the cornea, among other factors.21 The use of cutting-edge mechanical numerical simulations makes it possible to reconstruct the mechanical parameters of the cornea from the corneal deformation pattern. Kling et al.18 used inverse modeling to retrieve material properties of normal and cross-linked porcine corneas. The corneas were modeled by finite elements and the pressure distribution of the air puff applied. The viscoelastic material parameters were changed in an iterative process to fit the deformations with the measured results. In this earlier study, we found a 2-fold increase in corneal stiffness following CXL, and a 6-fold increase in the relaxation time. 
In this study, we compared the air puff corneal deformation mechanical response in rabbit corneas following ex vivo riboflavin UVA-CXL (UVX) and rose bengal–green light CXL (RGX), as well as the inherent material properties reconstructed by inverse mechanical modeling. These findings allow us to understand the relative effectiveness of each treatment in stiffening the cornea. 
Methods
Two groups of excised intact rabbit eyes were cross-linked. One group received standard UVX and the other group received the new RGX treatment. Air puff corneal deformation was evaluated at different stages of the cross-linking procedure. Spatial and temporal corneal deformations were analyzed in order to characterize the mechanical changes induced by the treatments. Finite element inverse modeling was applied to retrieve the corneal biomechanical properties and analyze their change with both procedures. 
Experimental Procedures
Samples.
Twenty-four freshly enucleated eyes from New Zealand rabbits were obtained from a farm associated with the Complutense University Veterinary School, (Madrid, Spain). The procedures followed protocols approved by the institutional review boards and in accordance with the ARVO Statement for the Use of Animals in Ophthalmic and Vision Research. Rabbits were aged 3 months and weighed 2.5 to 3.5 kg at the time of euthanasia. The tests were performed less than 24 hours postmortem. 
Cross-Linking Treatments.
All corneas were de-epithelialized by 15-second immersion in 50% ethanol, followed by scraping. After de-epithelialization, the corneas were treated by one of the following treatments. 
Rose Bengal–Green Light CXL.
The rose bengal (RB) solution consisted of 0.1% RB in PBS. Green light CXL was performed using a custom-developed light source, which incorporated a 532-nm laser with an output irradiance of 0.25 W/cm2 (MGL-FN-532; Changchun New Industries, Changchun, China) with a collimating lens that provided an 11-mm Gaussian profile beam at the sample plane. The RGX protocol was: (1) 2-minute staining with RB, then irradiation for 200 seconds; (2) 30-second staining with RB, then green light irradiation again for 200 seconds (total fluence, 100 J/cm2). A total of 12 eyes were treated by RGX. All 12 eyes in the group were measured before (virgin) and after CXL (CXL). Eight of these eyes were measured in the intermediate stage, after photosensitizer instillation (RB). 
Riboflavin–UVA Light CXL.
The riboflavin (RF) solution consisted of 0.125% riboflavin-5-phosphate in 20% dextran T500. We performed UVX using a UVA lamp (370 nm, 3 mW/cm2; Institute for Refractive and Ophthalmic Surgery, Zurich, Switzerland). The protocol UVX was: (1) 30-minute staining with RF, with one drop applied every 5 minutes; (2) UVA irradiation for 30 minutes, with one drop of RF applied every 5 minutes. A total of 12 eyes were treated by UVX. All 12 eyes in the group were measured before (virgin) and after CXL (CXL). Ten of these eyes were measured in the intermediate stage, after photosensitizer instillation (RF). 
Air Puff Experimental Measurements.
Eyes were mounted in a custom-made, three-dimensional (3D) printed eye holder consisting of two movable semicircular parts that allowed holding the eye along its equator. After mounting the eye in the holder, a needle was inserted through the optic nerve head to control IOP, which was kept constant at 15 mm Hg. Air puff corneal deformation measurements were taken using a commercial Scheimpflug-based imaging system. 
Air Puff System.
A commercial system was used (Corvis ST; Oculus, Wetzlar, Germany) that combines air puff with high-speed Scheimpflug imaging. The Corvis ST system has an air compressor emitting a quick, controlled air puff. The release of the air puff is synchronized with an ultrafast Scheimpflug camera that captures 140 horizontal cross-sectional corneal images during the ∼30-ms deformation event (i.e., at a rate of approximately 4330 images/second) with a resolution of 640 × 480 pixels. The eye is positioned in front of the system at a distance of 11 mm between the apex and the air tube. After the eye is aligned and positioned to be in focus, the device emits the air pulse that deforms the cornea. The cornea becomes concave around the apex and then returns to the initial shape in 30 ms. 
Result Parameters.
The corneal apex displacement as a function of time (temporal corneal deformation) and the cross-section of deformed shape of the cornea at maximum concavity (spatial corneal deformation) were analyzed. The following parameters were retrieved (Fig. 1): (1) maximum deformation amplitude (DA), which is the displacement of the corneal apex at maximum deformation; (2) peak-to-peak distance (PD), which is the lateral distance between the two peaks in the corneal profile at maximum deformation; (3) radius of central concave curvature (R), which is the radius of curvature in the vicinity of the apex at maximum deformation; (4) central corneal thickness (CCT), which is the thickness of the cornea at the apex; (5) time of highest concavity (THC), which is the time of the maximum corneal deformation; (6) temporal symmetry factor (TS), which is the ratio of the two areas under the apex displacement versus time curve separated by the THC, and can be calculated from Equation 1,  where T0 is the starting time of the air puff, Tend is the ending time of the deformation event and ΔYapex (t) is the displacement of the apex at a given time.  
Figure 1
 
(A) Deformed shape of the cornea at maximum concavity (spatial deformation profile). (B) Apex displacement as a function of time (temporal deformation profile) and definition of Time to Highest Concavity (THC).
Figure 1
 
(A) Deformed shape of the cornea at maximum concavity (spatial deformation profile). (B) Apex displacement as a function of time (temporal deformation profile) and definition of Time to Highest Concavity (THC).
Repeatability and Reproducibility.
A set of air puff tests were performed on a pair of virgin ex vivo eyes from the same rabbit, in order to evaluate the repeatability and reproducibility of the data. Eleven measurements per eye were obtained under the same conditions. The nominal distance between the apex of the cornea and the opening of the air tube is 11 mm. The air puff tests were repeated in three positions, within ± 1 mm of the best focused image. The effect of orientation was studied by rotating the eyes by 90° along their axes, by rotating the entire holder together with the eye. The eyes remained mounted during the measurements, The average standard deviations for repeated measurements in the same conditions were 2.18%, 3.85%, 9.76%, 2.08% of the average values of DA, PD, R and THC respectively. No statistically significant differences were found between the results at different distances or at different orientations. 
Finite-Element Model Analysis
In order to compare the inherent mechanical properties of the cornea following RGX and UVX, numerical simulations were performed, using an inverse modeling approach similar to that presented by Kling et al.18 
Inverse Modeling Process.
Figure 2A shows the block diagram of the inverse modeling process. Input parameters in the optimization model include the spatio-temporal characteristics of the air-pulse obtained as described in a previous publication,18 corneal and scleral geometry, including corneal thickness, scleral mechanical properties obtained from the literature,22 and a set of assumed initial set of corneal material parameters. In the first step, the time-dependent material properties were determined. The deformation history of the apex node is iteratively compared with the experimental temporal profile until the minimum of the sum of the square differences between the measured and the simulated temporal profiles is reached. The optimization was performed by first screening the variables with larger steps; then, after finding the global minimum, a downhill simplex algorithm was applied to find the minimum in finer steps. The Prony constants of the viscoelastic model obtained in the prior step were used in a subsequent step in which the measured and the simulated deformed shapes at highest concavity (spatial corneal deformation profiles) are compared and fitted by changing the five parameters of the hyperelastic model. 
Figure 2
 
(A) Flowchart of the inverse modeling process. (B) Schematic diagram of the generalized Maxwell model used in the finite element simulations; a hyperelastic five-parameter MR model is attached to a three-term viscoelastic model. (C) Finite element mesh with the applied loads and boundary conditions.
Figure 2
 
(A) Flowchart of the inverse modeling process. (B) Schematic diagram of the generalized Maxwell model used in the finite element simulations; a hyperelastic five-parameter MR model is attached to a three-term viscoelastic model. (C) Finite element mesh with the applied loads and boundary conditions.
Finite Element (FE) Model.
A parametric model of the rabbit cornea was built assuming axial symmetry. Corneal thickness was modeled from the corresponding average experimental data (from the Scheimpflug images) in each condition, namely 364, 334, and 286 μm for virgin, RB, RGX; and 383, 226, 206 μm for virgin, RF, and UVX corneas, respectively. Rose bengal–green light CLX and UVX have been shown to produce stiffening in a different relative corneal depth. Cherfan et al.13 reported that RGX affects the top 100 μm of the corneal stroma. Riboflavin-UVA CLX has been shown to affect 300 μm of the human cornea23 and approximately 400 μm of the porcine cornea. A recent study24 suggests that the anterior cross-linked to total stromal thickness ratio of 2/3 is valid in rabbits. In accordance with these reports, we modeled different material properties in the top 100 and the top 137 μm of the rabbit cornea in RGX and UVX, respectively. 
Material Models.
The mechanical behavior of the cornea was described by a nonlinear, hyperelastic Mooney-Rivlin (MR) material model with five parameters along with a Prony-series viscoelastic model, as shown in the schematic diagram of Figure 2B. The strain energy density function (W) for an incompressible Mooney-Rivlin material is (Equation 2):  where Display FormulaImage not available and Display FormulaImage not available are the first and the second invariant of the left Cauchy–Green deformation tensor; C10, C01, C20, C11, C02 are material parameters. The five Mooney-Rivlin material parameters were the design variables of the optimization in the inverse modeling process.  
The virgin corneas were modeled first with uniform material properties. After retrieving the material parameters of the virgin corneas, the RGX and UVX corneas were modeled with two different materials corresponding to the anterior (treated) and posterior (untreated) part of the stroma. The posterior part was modeled with the result of the virgin eye and the material parameters of the anterior part were the variable set in the optimization. 
The limbus and the sclera were modeled as isotropic elastic materials with Young's moduli Elimbus = 1.76 MPa and Esclera = 3.52 MPa, respectively. 
Loads and Boundary Conditions.
Figure 2C shows the FE mesh with the loads and boundary conditions. The inside of the eye was modeled with incompressible fluid elements with a density of 1060 kg/m3. A pressure of 2000 Pa (∼15 mm Hg) was applied on these fluid elements as initial condition in order to model the IOP. The nodes along the equator were fixed, modeling the grip of the eye holder. The pressure from the air puff was modeled as an edge load on the top of the surface elements of the cornea as a function of location and time (as described in detail by Kling et al.18). 
Statistical Analysis
Statistical analysis was carried out on the result parameters using 1-way ANOVA in a spreadsheet program (Excel, v. 2007; Microsoft Corp, Redmond, WA, USA). Comparisons were made between parameters in the same eye tested in different conditions (virgin, after application of photosensitizer and after CXL), between groups of virgin and treated eyes, and between groups treated with RGX and UVX. The significance level was set at P < 0.05. 
Results
Air-Puff Corneal Deformation Imaging
Spatial Deformation Profiles.
Treatments with RGX and UVX produced changes in the spatial deformation profiles at maximum corneal deformation. Figure 3 shows examples of the initial and deformed shape of the same eye before and after application of photosensitizer and irradiations (Figs. 3A, after application of rose bengal and after green light CXL; 3B, after application of riboflavin and after UVA-CXL). The highest deformation occurs in the virgin condition, consistent with the lowest stiffness; the cornea after photosensitizer instillation and particularly after CXL deformed less in both treatments. 
Figure 3
 
Examples of initial corneal profile and maximum spatial deformation profile in virgin eyes, after application of photosensitizer and after CXL treatments. (A) RGX (eye number RGX10); (B) UVX (eye number UVX9). Error bars: represent standard deviations of repeated measurements.
Figure 3
 
Examples of initial corneal profile and maximum spatial deformation profile in virgin eyes, after application of photosensitizer and after CXL treatments. (A) RGX (eye number RGX10); (B) UVX (eye number UVX9). Error bars: represent standard deviations of repeated measurements.
Temporal Deformation Profiles.
Treatment with RGX and UVX produced changes in the temporal apex displacement. Figure 4 shows average temporal apex displacement profiles of untreated and CXL eyes, (Figs. 4A, RGX averaged across 12 eyes; 4B, UVX averaged across 12 eyes). 
Figure 4
 
Average temporal deformation profiles in virgin eyes, after application of photosensitizer and after CXL treatments. (A) RGX. (B) UVX. Error bars: indicate standard deviation across 12 eyes.
Figure 4
 
Average temporal deformation profiles in virgin eyes, after application of photosensitizer and after CXL treatments. (A) RGX. (B) UVX. Error bars: indicate standard deviation across 12 eyes.
Corneal Deformation Parameters: Average Data
Figure 5 compares average corneal deformation parameters in the two groups of eyes (RGX and UVX) in three stages of the procedure; virgin, 12 eyes in each group; after photosensitizer application, 8 eyes with RB and 10 eyes with RF; and after irradiation, 12 eyes after RGX and 12 eyes after UVX). 
Figure 5
 
Average corneal deformation parameters in virgin eyes after application of photosensitizer (RB and RF) and after CXL (RGX and UVX). Blue bars: indicate virgin eyes (n = 12 in each group). Pink bars: indicate data after RB application (n = 8). Yellow bars: after RF application (n = 10). Green bars: indicate data after green light application (n = 12). Purple bars: indicate data after UVA application (n = 12). Error bars: indicate standard deviations across eyes. (A) DA. (B) THC. (C) PD. (D) TS. (E) R. (F) CCT. *P < 0.05 between virgin and CXL data. **P < 0.001 between virgin and CXL data.
Figure 5
 
Average corneal deformation parameters in virgin eyes after application of photosensitizer (RB and RF) and after CXL (RGX and UVX). Blue bars: indicate virgin eyes (n = 12 in each group). Pink bars: indicate data after RB application (n = 8). Yellow bars: after RF application (n = 10). Green bars: indicate data after green light application (n = 12). Purple bars: indicate data after UVA application (n = 12). Error bars: indicate standard deviations across eyes. (A) DA. (B) THC. (C) PD. (D) TS. (E) R. (F) CCT. *P < 0.05 between virgin and CXL data. **P < 0.001 between virgin and CXL data.
Figure 5A shows average values of corneal DA in each group. On average, corneal deformation amplitude of the virgin group was 1.32 ± 0.17 mm. Application of photosensitizer (both RB or RF) decreased corneal deformation. Treatment with RGX decreased corneal deformation amplitude by 11% and UVX by 33%. Both treatments produced statistically significant differences in corneal deformation compared with the untreated condition (P = 0.0436 and 0.0006, for RGX and UVX, respectively). The difference in corneal deformation amplitude between RGX and UVX treatments was statistically significant (P = 0.0052). 
Figure 5B shows the time to highest concavity (THC). Application of the photosensitizer produced the largest increase in THC for RF (P = 0.0008) and CXL (P = 0.0006), although the change seems to be primarily associated with the photosensitizer. The difference in THC between RGX and UVX treatments was statistically significant (P = 0.0002). 
Figure 5C shows that the peak-to-peak distance in the spatial corneal deformation profile at maximum deformation (PD) decreased after application of the photosensitizer (for both RB and RF) and decreased further after CXL (5% and 12% for RGX and UVX, respectively). The difference in PD between virgin and CXL corneas was statistically significant for UVX (P = 0.0144), but did not reach statistical significance for RGX (P = 0.19). The difference in PD between RGX and UVX treatments was not statistically significant (P = 0.1299). 
Figure 5D shows the temporal symmetry factor (TS). Application of the photosensitizer shifts the TS significantly toward 1 (symmetry), more for RF (30%, P < 0.0001) than RB (4%, P = 0.18). Both treatments produced statistically significant differences in TS compared with the untreated condition (P = 0.028 and P < 0.0001, for RGX and UVX, respectively). The difference in TS between RGX and UVX treatments was statistically significant (P = 0.011). 
Figure 5E shows the radius of central concave curvature at maximum deformation. Application of RF increased R by 15%, UVX by 8%. Rose bengal decreased R by 8% and RGX by 2%. The differences were not statistically significant. 
Figure 5F shows CCT for all conditions. Application of a photosensitizer decreases CCT, RB by 8% (P = 0.55) and RF by 41% (P < 0.0001). Cross-linking decreases CCT further in both procedures. Cross-linked corneas are significantly thinner than virgin corneas (P = 0.0298 and P < 0.0001 for RGX and UVX, respectively). The difference in CCT between RGX and UVX treatments did not reach statistical significance (P = 0.095). 
Relative Changes in Corneal Deformation: Average Data
Figure 6 shows individual DA for each eye measured in virgin, photosensitized and CXL conditions, both for RGX (Fig. 6A) and UVX (Fig. 6B). The values of DA were normalized to the virgin value to allow a better comparison. In most cases, the application of the photosensitizer decreased the DA, which then decreased further following irradiation. The slopes of the curves are higher in the UVX eyes than in the RGX eyes. 
Figure 6
 
Changes of DA in all eyes after application of photosenzitiser and after CXL treatment relative to the value for each virgin eyes. (A) RGX. (B) UVX. Error bars: represent standard deviations of repeated measurements.
Figure 6
 
Changes of DA in all eyes after application of photosenzitiser and after CXL treatment relative to the value for each virgin eyes. (A) RGX. (B) UVX. Error bars: represent standard deviations of repeated measurements.
Finite-Element Simulations
Reconstructed Material Parameters.
Figure 7 summarizes the material parameters of Equation 2 resulting from the inverse modeling for the virgin cornea, UVX and RGX, using average experimental corneal deformations. The material parameters (of the CXL section of the cornea) increased by a factor of 10.8 on average in RGX corneas and by 5.7 in UVX corneas compared with the virgin condition. The parameters of the RGX cornea are 2.2 times higher on average than the UVX. The viscoelastic relative moduli of the virgin corneas were 0.31, 0.06, and 0.4851 with relaxation times 2, 20, and 200 μs, respectively. The treatment of RGX changed only the last relative modulus by 8%. While UVX cornea were modeled without the viscous part in the material model, as the Prony constants were decreased to an extent that it practically did not make any difference in the results. 
Figure 7
 
Inherent hyperelastic material parameters of the anterior part of RGX and UVX corneas.
Figure 7
 
Inherent hyperelastic material parameters of the anterior part of RGX and UVX corneas.
Simulated Air Puff Corneal Deformation.
Figure 8 shows the simulated deformed shapes of the corneas post-RGX (Fig. 8A) and post-UVX (Fig. 8B) at highest deformation, using the reconstructed material parameters, where 100 μm of anterior cornea and for RGX and 137 μm of the anterior cornea for UVX were stiffened. Note that in the models the difference in CCT between the RGX and UVX eyes was also considered. 
Figure 8
 
Simulated maximum spatial corneal deformation from the estimated biomechanical models. (A) RGX. (B) UVX. Color plot represents deformation in mm.
Figure 8
 
Simulated maximum spatial corneal deformation from the estimated biomechanical models. (A) RGX. (B) UVX. Color plot represents deformation in mm.
Simulated Strain–Stress Curves.
Figure 9 shows a simulation of a tensile test using reconstructed material parameters, assuming isotropic hyperelastic corneal strips of 3 × 12 × 0.1 mm cut in the anterior (stiffened part of the CXL corneas) and a virgin cornea. Although the effect of RGX on corneal deformation parameters is lower than that of UVX (Figs. 36), the actual changes in the material parameters in the stiffened part of the cornea are larger for RGX than UVX (Fig. 7). As a consequence, the stress-strain curves are consistent with a higher stiffening of the treated cornea in RGX. Treatment of UVX affects a larger volume of the cornea; however, RGX seems to stiffen the cornea more, but in a thinner layer. From these graphs, the Young's modulus (defined as the slope of the stress-strain in their initial part) is 56.3 MPa for RGX and 32 MPa for UVX. 
Figure 9
 
Simulated stress-strain curves from the reconstructed biomechanical parameters for virgin, RGX, and UVX materials.
Figure 9
 
Simulated stress-strain curves from the reconstructed biomechanical parameters for virgin, RGX, and UVX materials.
Discussion
We evaluated the biomechanical changes produced by two different corneal cross-linking treatments, namely UVX and RGX, using air puff deformation imaging in rabbit eyes. The measured changes in corneal deformation parameters after cross-linking are consistent with corneal stiffening. Although the deformation parameters indicate greater stiffening after UVX than after RGX, the reconstructed biomechanical parameters from numerical finite element method simulations show that the cross-linked layer of the cornea is in fact stiffer after RGX that after UVX. This apparent conflict results from the thinner layer of stroma cross-linked by RGX than by UVX. 
The experimental results presented are, to our knowledge, the first application of air puff deformation imaging in rabbit eyes. Rabbit corneas are thinner than porcine and human corneas; thus, for similar IOP, it is expected that rabbit corneas will show higher DA in response to an air puff. The deformation amplitude in rabbit eyes (1.32 mm) was indeed higher than in porcine eyes (1.26 mm22) and in human eyes (0.85 mm for ex vivo eyes18 and 1.08 mm for in vivo measurements25). 
Since the measurements were obtained under a constant IOP, corneal thickness and the biomechanical viscoelastic properties of the cornea determine the temporal and spatial deformation profiles. In virgin corneas, we found a moderate correlation between CCT and DA (Pearson's r = 0.39). As the photosensitizer solutions alone modulate corneal thickness (especially due to the dextran in the riboflavin solution [Fig. 5F]26), some of the observed changes in corneal deformation parameters are likely influenced by changes in CCT. The dextran remains in the cornea during UVX and may also influence the deformation parameters after irradiation. However, RB is at least partially destroyed during RGX and might have less of an influence after irradiation. Interestingly, besides a decrease in corneal deformation amplitude, a significant decrease in the temporal symmetry (TS) factor was found both after RGX and UVX. Kling et al.18 suggested that THC and TS are associated with the viscoelasticity of the cornea and, therefore, CXL produced consistent changes in viscoelasticity. As found in a previous study,13 our results support the finding that RB alone, without irradiation, increases corneal stiffness. This may be explained by the fact that RB strongly associates with collagen in tissues and most cannot be washed away. These complexes may be responsible for the stiffening produced by RB. 
Finite element simulations showed that both CXL methods stiffened the corneas. In fact in the cross-linked layer (100 μm in RGX and 137 μm in UVX), RGX has a larger effect than UVX (Fig. 7). The simulations were performed assuming axial symmetry. Extending the models to 3D would help modeling asymmetries in geometry or in material distribution (e.g., eccentric keratoconus), or to incorporate anisotropic material models. Another assumption was modeling two different materials in two layers in the CXL corneas. In reality, the material properties change gradually from the anterior to the posterior part of the cornea,27,28 although showing a sharper transition at the penetration depth of the photosensitizer, which makes this simplification reasonable. The two-step optimization process first determined time-dependent material parameters, and then obtained the hyperelastic parameters.18 This assumption neglects the effects of the viscous component the material model on the spatial profile.21 This could be improved by joining the two optimization steps in one single process, although this approach would involve reconstruction of 11 design variables to fit both the temporal and the spatial profiles simultaneously, which would make the optimization challenging. 
The stress-strain curves shown in Figure 9 were developed from the retrieved material properties and can be compared to similar data from the literature. This comparison is complicated by differences in the studies in the dimensions of the cornea strips, postmortem time, hydration properties, time after CXL and section of the cornea cut for the uniaxial extensiometry measurements. Typically, the entire corneal thickness is used in extensiometry studies, and therefore our results may overestimate the corneal stiffening measured experimentally. Typical reports of Young's moduli from extensiometry measurements range from 6.8 to 11.9 MPa29 in virgin rabbit eyes, 19.1 to 31.7 MPa in UVX rabbit eyes,13 and 10.2 to 16.3 MPa in RGX rabbit eyes.13 Our simulated stress-strain curve of the virgin cornea is in good agreement with published data up to a strain level of 7%, the initial part of the curve that is generally used for the reported measurements on cornea. In this range, we found that RGX increased corneal stiffness by a factor of 11 and UVX by a factor of 6.25, within the ranges reported in the literature.2931 
An interesting finding in this study was the greater influence of UVX than RGX on measured air puff deformation parameters (Fig. 5), but the greater increase in inherent material properties after RGX than after UVX in the volumes occupied by the photosensitizers (Fig. 7). The greater increase in inherent material properties after RGX is consistent with a higher density (or more stiffening type) of covalent cross-links in a smaller volume of stroma since RB penetrates less deeply (∼100 μm) than riboflavin (∼137 μm). It is likely that different covalent cross-links could be produced by the two photosensitizers after irradiation since they are located at different molecular level sites in the stroma: when applied to the cornea, RB associates tightly with collagen,11 whereas riboflavin freely diffuses throughout the cornea. Rose bengal also produces a significantly lower reduction in corneal thickness than the standard riboflavin in dextran formulation that, along with the more shallow penetration of RB into stroma, indicate that RGX may be used to treat corneas less than 400 μm, the nominal limit. Increasing the penetration depth of RB in RGX would increase overall corneal stiffness and may be accomplished by changing the application time or other parameters. The optimal penetration depth that balances corneal treatment response and endothelial protection remains to be investigated. Finite element models, such as those presented in this study, may help in searching for these optimized parameters. 
This study advances our understanding of the features of different cornea cross-linking treatments by using air puff corneal deformation measurements and reconstruction of corneal biomechanical properties. The earlier ex vivo studies of RGX and UVX had used uniaxial extensiometry and Brillouin microscopy to measure changes in overall cornea stiffness. Since air puff corneal deformation measurements are now used in vivo in human eyes, reconstruction of biomechanical properties of cross-linked corneas several weeks after cross-linking can be accomplished under conditions that are not influenced by hydration/dehydration effects or any remaining photosensitizer. 
Acknowledgments
The authors thank Luis Revuelta (School of Veterinary Medicine, Universidad Complutense de Madrid) for help in facilitating access to rabbit eyes, as well as technical contributions from Pablo Pérez and Miriam Velasco (Instituto de Optica, CSIC) for technical help with the sample handling. We acknowledge Oculus for providing access to the Corvis ST system. 
Supported by the European Research Council under the European Union's Seventh Framework Program ERC Advanced Grant agreement no. 294099; Comunidad de Madrid and EU Marie Curie COFUND program (FP7/2007-2013/REA 291820); and the Spanish Government Grant FIS2014-56643-R. 
Disclosure: N. Bekesi, None; I.E. Kochevar, P; S. Marcos, None 
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Figure 1
 
(A) Deformed shape of the cornea at maximum concavity (spatial deformation profile). (B) Apex displacement as a function of time (temporal deformation profile) and definition of Time to Highest Concavity (THC).
Figure 1
 
(A) Deformed shape of the cornea at maximum concavity (spatial deformation profile). (B) Apex displacement as a function of time (temporal deformation profile) and definition of Time to Highest Concavity (THC).
Figure 2
 
(A) Flowchart of the inverse modeling process. (B) Schematic diagram of the generalized Maxwell model used in the finite element simulations; a hyperelastic five-parameter MR model is attached to a three-term viscoelastic model. (C) Finite element mesh with the applied loads and boundary conditions.
Figure 2
 
(A) Flowchart of the inverse modeling process. (B) Schematic diagram of the generalized Maxwell model used in the finite element simulations; a hyperelastic five-parameter MR model is attached to a three-term viscoelastic model. (C) Finite element mesh with the applied loads and boundary conditions.
Figure 3
 
Examples of initial corneal profile and maximum spatial deformation profile in virgin eyes, after application of photosensitizer and after CXL treatments. (A) RGX (eye number RGX10); (B) UVX (eye number UVX9). Error bars: represent standard deviations of repeated measurements.
Figure 3
 
Examples of initial corneal profile and maximum spatial deformation profile in virgin eyes, after application of photosensitizer and after CXL treatments. (A) RGX (eye number RGX10); (B) UVX (eye number UVX9). Error bars: represent standard deviations of repeated measurements.
Figure 4
 
Average temporal deformation profiles in virgin eyes, after application of photosensitizer and after CXL treatments. (A) RGX. (B) UVX. Error bars: indicate standard deviation across 12 eyes.
Figure 4
 
Average temporal deformation profiles in virgin eyes, after application of photosensitizer and after CXL treatments. (A) RGX. (B) UVX. Error bars: indicate standard deviation across 12 eyes.
Figure 5
 
Average corneal deformation parameters in virgin eyes after application of photosensitizer (RB and RF) and after CXL (RGX and UVX). Blue bars: indicate virgin eyes (n = 12 in each group). Pink bars: indicate data after RB application (n = 8). Yellow bars: after RF application (n = 10). Green bars: indicate data after green light application (n = 12). Purple bars: indicate data after UVA application (n = 12). Error bars: indicate standard deviations across eyes. (A) DA. (B) THC. (C) PD. (D) TS. (E) R. (F) CCT. *P < 0.05 between virgin and CXL data. **P < 0.001 between virgin and CXL data.
Figure 5
 
Average corneal deformation parameters in virgin eyes after application of photosensitizer (RB and RF) and after CXL (RGX and UVX). Blue bars: indicate virgin eyes (n = 12 in each group). Pink bars: indicate data after RB application (n = 8). Yellow bars: after RF application (n = 10). Green bars: indicate data after green light application (n = 12). Purple bars: indicate data after UVA application (n = 12). Error bars: indicate standard deviations across eyes. (A) DA. (B) THC. (C) PD. (D) TS. (E) R. (F) CCT. *P < 0.05 between virgin and CXL data. **P < 0.001 between virgin and CXL data.
Figure 6
 
Changes of DA in all eyes after application of photosenzitiser and after CXL treatment relative to the value for each virgin eyes. (A) RGX. (B) UVX. Error bars: represent standard deviations of repeated measurements.
Figure 6
 
Changes of DA in all eyes after application of photosenzitiser and after CXL treatment relative to the value for each virgin eyes. (A) RGX. (B) UVX. Error bars: represent standard deviations of repeated measurements.
Figure 7
 
Inherent hyperelastic material parameters of the anterior part of RGX and UVX corneas.
Figure 7
 
Inherent hyperelastic material parameters of the anterior part of RGX and UVX corneas.
Figure 8
 
Simulated maximum spatial corneal deformation from the estimated biomechanical models. (A) RGX. (B) UVX. Color plot represents deformation in mm.
Figure 8
 
Simulated maximum spatial corneal deformation from the estimated biomechanical models. (A) RGX. (B) UVX. Color plot represents deformation in mm.
Figure 9
 
Simulated stress-strain curves from the reconstructed biomechanical parameters for virgin, RGX, and UVX materials.
Figure 9
 
Simulated stress-strain curves from the reconstructed biomechanical parameters for virgin, RGX, and UVX materials.
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