October 2015
Volume 56, Issue 11
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Cornea  |   October 2015
Establishing Corneal Cross-Linking With Riboflavin and UV-A in the Mouse Cornea In Vivo: Biomechanical Analysis
Author Affiliations & Notes
  • Arthur Hammer
    Laboratory for Ocular Cell Biology, University of Geneva, Geneva, Switzerland
  • Sabine Kling
    Laboratory for Ocular Cell Biology, University of Geneva, Geneva, Switzerland
    Center for Applied Biotechnology and Molecular Medicine (CABMM), University of Zurich, Zurich, Switzerland
  • Marc-Olivier Boldi
    Research Center for Statistics, University of Geneva, Geneva, Switzerland
  • Olivier Richoz
    Laboratory for Ocular Cell Biology, University of Geneva, Geneva, Switzerland
  • David Tabibian
    Laboratory for Ocular Cell Biology, University of Geneva, Geneva, Switzerland
  • J. Bradley Randleman
    Department of Ophthalmology, Emory University, Atlanta, Georgia, United States
  • Farhad Hafezi
    Center for Applied Biotechnology and Molecular Medicine (CABMM), University of Zurich, Zurich, Switzerland
    Department of Ophthalmology, University of Southern California, Los Angeles, California, United States
    ELZA Institute, Dietikon/Zurich, Switzerland
  • Correspondence: Arthur Hammer, Laboratory for Ocular Cell Biology, University of Geneva, Rue Michel Servet 1, 1206 Geneva, Switzerland; arthur.hammer6@gmail.com
  • Footnotes
     AH and SK contributed equally to the work presented here and should therefore be regarded as equivalent authors.
Investigative Ophthalmology & Visual Science October 2015, Vol.56, 6581-6590. doi:10.1167/iovs.15-17426
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      Arthur Hammer, Sabine Kling, Marc-Olivier Boldi, Olivier Richoz, David Tabibian, J. Bradley Randleman, Farhad Hafezi; Establishing Corneal Cross-Linking With Riboflavin and UV-A in the Mouse Cornea In Vivo: Biomechanical Analysis. Invest. Ophthalmol. Vis. Sci. 2015;56(11):6581-6590. doi: 10.1167/iovs.15-17426.

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

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Abstract

Purpose: To establish corneal cross-linking (CXL) with riboflavin and UV-A in in the mouse cornea in vivo and to develop tools to measure the biomechanical changes observed.

Methods: A total of 55 male C57BL/6 wild-type mice (aged 5 weeks) were divided into 14 groups. Standard CXL parameters were adapted to the anatomy of the mouse cornea, and riboflavin concentration (0.1%–0.5%) and fluence series (0.09–5.4 J/cm2) were performed on the assumption of the endothelial damage thresholds. Untreated and riboflavin only corneas were used as controls. Animals were killed at 30 minutes and at 1 month after CXL. Corneas were harvested. Two-dimensional (2D) biomechanical testing was performed using a customized corneal holder in a commercially available stress-strain extensometer/indenter. Both elastic and viscoelastic analyses were performed. Statistical inference was performed using t-tests and specific mathematical models fitted to the experimental stress-strain and stress-relaxation data. Adjusted P values by the method of Benjamini and Hochberg are reported.

Results: For all CXL treatment groups, stress-relaxation showed significant differences (P < 0.0001) after 120 seconds of constant strain application, with cross-linked corneas maintaining a higher stress (441 ± 40 kPa) when compared with controls (337 ± 39 kPa). Stress-strain analysis confirmed these findings but was less sensitive to CXL-induced changes: at 0.5% of strain, cross-linked corneas remained at higher stress (778 ± 111 kPa) when compared with controls (659 ± 121 kPa).

Conclusions: Cross-linking was induced in the mouse cornea in vivo, and its biomechanical effect successfully measured. This could create opportunities to study molecular pathways of CXL in transgenic mice.

Corneal cross-linking with riboflavin and UV-A, initially introduced by Spoerl et al.,1,2 is a method to increase corneal stiffness and to arrest corneal ectatic disorders like keratoconus and ectasia after refractive laser surgery3 with a follow-up of several years.4,5 The procedure is based on the combination of the photosensitizer riboflavin and UV-A irradiation and has initially been tested in ex vivo porcine corneas.6 To analyze the potential phototoxic effect on the corneal endothelium at high UV doses and to adjust riboflavin concentration, CXL was subsequently tested in vivo on rabbit corneas.7 A few years only after successful introduction of CXL into clinical ophthalmology,8 the frequency of penetrating keratoplasties has been considerably reduced.9 
Although already used extensively in clinical practice, CXL remains a relatively new technique needing further optimization. A number of new clinical treatment protocols have emerged in the past few years and have rapidly been used clinically without proper laboratory validation. Accelerated CXL is based on the Bunsen-Roscoe law, which states that the photochemical effect is proportional to the irradiance multiplied by the time of irradiation. This may mean that irradiation time could be shortened when using a higher UV irradiance. The efficacy of this treatment option, however, is unclear, and accelerated CXL may be less effective than CXL using the original protocol.10 Corneal cross-linking is an oxygen-dependent process.11 Pulsed CXL represents yet another new protocol that tries to overcome low oxygen saturation during irradiation at high UV-A light irradiances.12 However, clinical and experimental evidence did not show significant differences between the pulsed and standard CXL protocol.1315 
These unsuccessful implementations show that there is a need for a better understanding of the cellular and molecular events occurring during CXL. 
Most approaches to determine CXL efficacy focus on analysis of corneal biomechanics. There are only few and rather inaccurate approaches to determine the biomechanical efficacy of CXL in vivo; thus, clinicians have to rely on indirect signs like corneal topography and pachymetry maps. For ex vivo measurements, there are more accurate but destructive methods available to determine the actual biomechanical properties of the corneal tissue. The golden standard technique consists of measuring the stress-strain curve and determining the Young's modulus.1,2,6,11,12,16 Viscoelastic testing, including creep and relaxation tests,1719 has recently emerged as an option. However, a methodologic problem with ex vivo testing is that the tissue is subjected to hydration and other degrading processes soon after enucleation. These changes and the preservation media both modify the biomechanical properties20 and affect accuracy of testing. 
The main problem of optimizing CXL treatment parameters is that the underlying working principle of CXL can only be vaguely assumed: CXL might cross-link collagen fibers and/or proteoglycans, but could also affect gene expression. The latter is supposed, as keratoconus shows a genetic component.2124 A better understanding of the cellular and molecular events occurring during CXL might help in establishing optimized treatment modalities. 
For this purpose, we established the biomechanical measurement after CXL in the mouse cornea in vivo, and tested whether the biomechanical effect can reliably be measured. The corneal cross-linking procedure in mice has been previously introduced.25 
Methods
Specimens
All procedures concerning animals in this study adhered to the ARVO statement for the Care and Use of Animals in Vision Research. A total of 55 male C57/BL6 mice aged 5 weeks (Charles River Laboratories, Chatillon-sur-Chalaronne, France) were divided into two sets and treated with specific CXL parameters (Tables 1, 2). 
Table 1
 
Adaptation of CXL Parameters to the Mouse Cornea
Table 1
 
Adaptation of CXL Parameters to the Mouse Cornea
Table 2
 
Determining the Threshold Fluence for Effective CXL in the Mouse
Table 2
 
Determining the Threshold Fluence for Effective CXL in the Mouse
In set 1 (n = 41 mice), CXL fluence and riboflavin (ribo) concentration parameters used in the human setting were applied and compared with settings that were adapted to the reduced thickness of the mouse cornea. 
In set 2 (n = 14 mice), the fluence was consecutively reduced to determine the threshold level for effective CXL in the mouse cornea. 
CXL Treatment Parameters
Since the mouse cornea is approximately five times thinner than the human cornea (100 μm26 vs. 530 μm27) the CXL treatment parameters were adapted to prevent endothelial damage. For this purpose, we performed riboflavin concentration series (0.1%–0.5%), UV irradiance series (3–18 mW/cm2), and UV irradiation time series (30 seconds to 30 minutes; Tables 1, 2). 
The Lambert-Beer law was used to ensure that in all cases the endothelium absorbed equal or less UV energy compared with standard CXL in humans:  where T is the transmittance, I0 the intensity of the incident light, I the intensity at the endothelium, c the concentration of the riboflavin, th the thickness of the cornea, and ε the absorptivity of riboflavin.  
Treatment Protocol
The mice were anesthetized with a mixture of ketamine 100 mg/kg (Ketalar; Pfizer AG, Zurich, Switzerland) and xylazine 10 mg/kg (Rompun; Bayer AG, Leverkusen, Germany), administered subcutaneously. Corneas were soaked with tetracaine 1% SDU Faure (Novartis Pharma Schweiz AG, Risch, Switzerland) for 2 minutes, and 35% alcohol for 2 additional minutes. The epithelium was removed using an ophthalmologic surgical sponge (Sugi-Saugkeil, 17 × 8 mm; Dosch, Medizintechnik, Heidelberg, Germany). Riboflavin (vitamin B2; Streuli Pharma AG, Uznach, Switzerland) was diluted to the desired concentration using PBS (Dulbecco's PBS; Sigma-Aldrich GmbH, Steinheim, Germany), and the photosensitizing solution applied on the de-epithelialized cornea for 20 minutes. The corneal cross-linking treatment was performed according to Table 1. After UV-A irradiation, ofloxacin ointment (Floxal; Bausch and Lomb Swiss AG, Zug, Switzerland) was applied. 
Customized Stress-Strain Extensometry
Due to the small size of the mouse eye, a custom holder was developed to fixate the mouse cornea circumferentially for biomechanical measurements (Fig. 1). The holder was made of steel with a small central hole of 1.6 mm. The cornea was then placed into the lower part over the central hole, and the upper part mounted by means of screws to fix the cornea. Circular indentations were milled into the surrounding of the central hole to prevent slippage. The holder was then mounted on the stress-strain extensometer/indenter (Z0.5; Zwick GmbH & Co., Ulm, Germany). A custom metal indenter with spherical surface (0.5-mm radius) was used to apply a three-dimensional force on the corneal surface through the central hole of the holder. The system was operated in compression mode with the corresponding software (testXpert II; Zwick GmbH & Co.). 
Figure 1
 
(A) Mouse undergoing CXL treatment, showing riboflavin fluorescence of the cornea. (B) Experimental setup: corneal holder mounted on the extensometer/indenter.
Figure 1
 
(A) Mouse undergoing CXL treatment, showing riboflavin fluorescence of the cornea. (B) Experimental setup: corneal holder mounted on the extensometer/indenter.
Biomechanical Analysis
For biomechanical analysis, mice were euthanized, eyes were enucleated, and the corneas excised circumferentially near the limbus, leaving a small scleral rim. Corneas were then fixed within the holder, and a drop of PBS was applied on top of the central hole to prevent dehydration during testing. 
The biomechanical analysis consisted of three steps: (1) pre-conditioning with three repetitions of stress-strain cycling between 0.05 and 0.4 N; (2) stress-relaxation testing during 120 seconds under the application of an initial force of 0.4 N, corresponding to a stress of 663 kPa; and (3) stress-strain extensometry with increasing force until specimen break. For stress relaxation testing, a constant strain was applied on the cornea and the decrease in stress recorded. For stress-strain testing, the indenter was moved downward at a constant speed, which applied an increasing force on the cornea and the corresponding stress measured. 
In this context, stress can be calculated by:    
where σ is stress, F is the applied force, R is the radius of the central hole in the corneal holder, and th is the corneal thickness. Within the maximal vertical indentation observed (Δmax), we can assume that the force applied by the indenter is orthogonal to the corneal surface and hence induces tensile stress as shown in Figure 2
Figure 2
 
Scheme of the experimental setup describing the applied tensile force onto the corneal surface using a customized indenter.
Figure 2
 
Scheme of the experimental setup describing the applied tensile force onto the corneal surface using a customized indenter.
Strain can be calculated by:    
where ε is strain and Δ is the vertical indentation measured. 
Appendix 1 provides more details about the derivation of Equations 2 and 3
Comparisons
Out of the different combinations of conditions, biomechanical tests, and postop times, we did four major comparisons: (1) stress-strain versus stress-relaxation analysis to determine if one technique is superior to the other, (2) different fluences to identify the lowest threshold for CXL, (3) immediate effect of CXL versus 1 month after to study if there are differences between short- and long-term, and (4) different irradiances at the same fluence to verify the validity of the Bunsen-Roscoe law. 
Statistical Analysis
Student's t-test (XLSTAT, version 2014.6.01; Addinsoft, Paris, France) was performed to compare the overall difference between CXL treatment and control groups: in the stress-strain analysis at 0.5% strain and in the stress-relaxation analysis at 120 seconds. 
The statistical analysis was further refined taking into account all points along the curves of the stress-strain and stress-relaxation measurements. For this purpose, the Research Center for Statistics at the University of Geneva used specific mathematical models that were fitted to the experimental stress-strain and stress-relaxation data. Unlike the Student's t-test or ANOVA, the approach of fitting a mathematical model to the experimental data allowed us to compare the entire curves additionally to individual points only. 
The Prony series is a physical model describing the stress-relaxation curves in a range between 0 and 119 seconds:  where F(t) is the force at time t, σ(t) is the stress at time t, σ is the asymptotic stress, σ1 and σ2 are the short-term stress and τ1 and τ2 are the corresponding relaxation times. The Prony series are typically expressed in terms of moduli, which is the case if Equation 4 is divided by the constant strain εconst that was applied during the measurement.  
For the statistical analysis, this basic physical model (Equation 4) was translated into a nonlinear mixed model.28 Like the repeated measure ANOVA, it extends the ANOVA taking into account for the correlations between repeated observations from the same subject. Nonlinear models generalize models in the same way.    
The index i is for the subject and j is for the treatment. All the random components are assumed independent and normally distributed (notation ∼N). In Equation 5, λ is the within-subject standard deviation, and λ, λ1, λ2, γ, γ1, γ2 are the between-subject standard deviations for each model parameter. The model is fitted to the observed stress series using a statistical computer program (package nlme v3.1-111 of R v3.0.2; The R Foundation for Statistical Computing, Vienna, Austria). The statistical comparison between groups was performed globally for the entire parameter set (σ, σ1, σ2, τ1, τ2). The interested reader can refer to Pinheiro et al.28 for detailed presentation of these models applied to several biological studies. 
For small deformations every material shows a linear stress-strain curve following the Hooke's law. We applied a linear model to describe the relation between stress and strain in a range of 0.05 to 0.5% of strain:  where F(t) is the force, σ(t) is the stress, ε the strain, α the intercept, and E the slope. Translated into a mixed linear model thus accounting for the within-subject correlation, the model can be formally written as    
Again, the index i is for the subject and j is for the treatment. All random components are independent and normally distributed. The statistical comparison between groups was performed only for parameter E, which represents the elastic modulus. 
Due to the large number of comparisons and the framework complexity, pairwise treatment comparisons were inspected independently using a likelihood ratio test. The P values were then adjusted (level of significance = 0.05) using the Benjamini and Hochberg method29 (Tables 36). 
Table 3
 
Significant Differences in Stress-Strain and Stress-Relaxation Tests Between CXL and Control Groups
Table 3
 
Significant Differences in Stress-Strain and Stress-Relaxation Tests Between CXL and Control Groups
Results
Stress-Strain Versus Stress-Relaxation
Both kinds of analysis demonstrated a significantly increased mechanical resistance after CXL. Stress-relaxation tests showed that cross-linked corneas maintained a higher stress (441 ± 40 kPa) than control corneas (337 ± 39 kPa) after 120 seconds of constant strain (Fig. 3). Stress-strain tests showed that cross-linked corneas presented a higher stress at 0.5% strain (778 ± 111 kPa) than control corneas (659 ± 121 kPa), which corresponds to a Young's modulus of 89.7 MPa and 70.9 MPa, respectively (Fig. 4). 
Figure 3
 
Stress-relaxation curves with standard deviation of various treatment (plain lines) and control (dashed lines) groups. The standard deviations appear in green for the treatment groups and in gray for the control groups. (A) Stress-relaxation curves of the groups of the set 1 showing no superposition between treatment and control group standard deviations. (B) Stress-relaxation curves of the groups of the set 2 also showing no superposition between treatment and control groups standard deviations but with a reduced spacing.
Figure 3
 
Stress-relaxation curves with standard deviation of various treatment (plain lines) and control (dashed lines) groups. The standard deviations appear in green for the treatment groups and in gray for the control groups. (A) Stress-relaxation curves of the groups of the set 1 showing no superposition between treatment and control group standard deviations. (B) Stress-relaxation curves of the groups of the set 2 also showing no superposition between treatment and control groups standard deviations but with a reduced spacing.
Figure 4
 
Stress-strain curves with standard deviation of various treatment (plain lines) and control (dashed lines) groups. The standard deviations appear in green for the treatment groups and in gray for the control groups. (A) Stress-strain curves of the groups of the set 1 showing superposition between most of the treatment and control group standard deviations. (B) Stress-strain curves of the groups of the set 2 showing superposition between the treatment and control group standard deviations.
Figure 4
 
Stress-strain curves with standard deviation of various treatment (plain lines) and control (dashed lines) groups. The standard deviations appear in green for the treatment groups and in gray for the control groups. (A) Stress-strain curves of the groups of the set 1 showing superposition between most of the treatment and control group standard deviations. (B) Stress-strain curves of the groups of the set 2 showing superposition between the treatment and control group standard deviations.
Stress-relaxation tests thereby revealed higher significant differences (P < 0.0001) between average cross-linked and control conditions than stress-strain tests (P = 0.008). Stress-relaxation analysis also proved to be more sensitive in distinguishing minor differences, both between control and CXL treatment conditions, but also between different CXL treatment protocols, while stress-strain analysis was not sensitive enough (Table 4). 
Table 4
 
Higher Sensitivity of Stress-Relaxation Test Compared With Stress-Strain Test
Table 4
 
Higher Sensitivity of Stress-Relaxation Test Compared With Stress-Strain Test
Table 5
 
No Differences in Stress-Strain and Stress-Relaxation Tests Between Several CXL Treatment Conditions, or Between Riboflavin and Virgin Control Conditions
Table 5
 
No Differences in Stress-Strain and Stress-Relaxation Tests Between Several CXL Treatment Conditions, or Between Riboflavin and Virgin Control Conditions
Table 6
 
Significant Differences From Stress-Strain Analysis, Both Between CXL Treatment Conditions and Between Control Conditions
Table 6
 
Significant Differences From Stress-Strain Analysis, Both Between CXL Treatment Conditions and Between Control Conditions
Different Irradiances at the Same Fluence
No significant differences were observed for different irradiances at a fluence of 5.4 J/cm2 in either stress-relaxation or stress-strain tests. 
Different Fluences
All corneal cross-linking treatment groups showed a significant difference compared with their corresponding control groups, according to stress relaxation and nonlinear mixed model analysis. Stress-strain tests confirmed this finding in approximately half of the treatment groups (Tables 3, 4). 
Stress relaxation could furthermore detect significant differences between certain CXL treatment protocols. Below a fluence of 5.4 J/cm2, the increase in corneal stiffness after CXL was significantly reduced (Table 4). An unexpected significant difference between control groups was observed in stress-strain testing (Table 6). 
Immediate Effect of CXL Versus 1 Month After
The application of the photosensitizer solution affected significantly the biomechanical response on the short term, as riboflavin control conditions were significantly different when compared at 30 minutes and at 1 month after treatment. A higher stress after relaxation remained at 30 minutes than at 1 month after riboflavin treatment (0.5% ribo versus 0.5% ribo 1 month; P < 0.0001 for stress-relaxation and P = 0.0027 for stress strain; Table 3). In contrast, the effect of CXL was less affected by the short-term effect of riboflavin: Stress-relaxation tests showed no significant differences for a fluence of 5.4 J/cm2 with an irradiance of 9 mW/cm2 (P = 0.1643). Only stress-strain tests indicated a significant difference (P = 0.043), which was close to the level of significance (Table 6). 
Discussion
We accurately measured the biomechanical properties of murine corneas at different degrees of in vivo CXL. Two-dimensional extensometry30 as applied in this study resembles the natural condition in a more realistic way than one-dimensional extensometry, which has been used for the biomechanical analysis of porcine, rabbit, and human corneas.6,16 We could confirm the finding of a previous study17 that viscoelastic testing approaches, such as stress-relaxation or creep tests, are more sensitive to measure the effect of CXL. 
Although both elastic (stress-strain) and viscoelastic (stress-relaxation) testing showed significant differences between CXL treated and control groups, these differences are distinctly more obvious in the stress-relaxation than in the stress-strain test. This may explain why previous studies10,31 analyzing the stress-strain of ex vivo porcine corneas required a higher number of samples to obtain significance. A main fact is that for detecting differences between CXL treatment protocols the stress-relaxation test should be preferred. 
The stress-strain testing procedure applied in the current study might not be directly comparable with standard stress-strain extensometry. An important difference is that stress was applied in three dimensions instead of uniaxially, which implies that a higher force is required to induce a similar extension. 
Given that even the lowest fluence in our study showed a significant increase in stress resistance after relaxation, the minimal necessary fluence for effective CXL in murine corneas is smaller or equal to 0.09 J/cm2. Even when considering the thinner corneal thickness of mice (1/5), this is lower than expected, when compared with CXL in humans, where the fluence is 60 times higher. We did not observe a decrease in the biomechanical CXL effect when increasing irradiance with constant fluence, as previously reported in ex vivo porcine corneas.10 This might be explained by a higher oxygen diffusion, and hence higher oxygen availability, in the mouse cornea (100 μm26) compared with porcine (877.6 μm32) and human (530 μm27) corneas. The oxygen dependency of CXL in murine and porcine corneas33 and other parameters (Kling S, Hammer A, Conti A, Hafezi F, unpublished data, 2015), including keratocyte apoptosis and the overall healing process, are the subject of two parallel studies from our group. 
Using a mouse model to study the effect of CXL will create opportunities to investigate the effect of gene modification on the biomechanical changes after CXL, and may help developing new and more efficient treatment protocols. 
Acknowledgments
Supported by the Swiss National Science Foundation (OR, AH), and the Gelbert Foundation (DT). 
Disclosure: A. Hammer, None; S. Kling, None; M.-O. Boldi, None; O. Richoz, None; D. Tabibian, None; J.B. Randleman, None; F. Hafezi, None 
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Appendix
Stress
Stress σ was calculated starting from the standard equation:  where F is the force applied and Image not available is the cross-sectional area orthogonal to the applied force.  
For a better understanding, we consider first a standard flap test. Typically one end of the flap in fixed, while at the other end a given force Fflap is applied. This means the flap has to resist a net force of 2·Fflap, but at each end one cross-section of the flap has to withstand Fflap. Therefore, the stress in the flap is defined as:    
with    
Considering now a flap within an entire cornea in 2D testing (see Fig. A1A, yellow area): Here a given force F is applied at the center of the flap, which is in this case also the net force. The corresponding area that has to withstand this force is 2·Across. Therefore, the stress in a flap with the 2D testing system is defined as    
with    
Considering now the entire cornea in 2D testing: As before, the applied force Fflap corresponds to the net force. The cross-sectional area resisting this force is here 
Figure A1
 
Parameters used for the calculation of (A) stress and (B) strain.
Figure A1
 
Parameters used for the calculation of (A) stress and (B) strain.
and, hence, corneal stress is defined as    
Strain
For the calculation of corneal strain we considered the sketch shown in Figure A1B. 
The assumption was made that at each indentation Δ the cornea adapts the shape of an ideal sphere with radius X. The arc-length LΔ is then defined by    
where α is the angle of the circular sector. Applying trigonometry, α and X can be expressed as a function of indentation Δ and radius of the holder R:     
Strain is defined as the relative change in length of the tested cross-section and can hence be calculated by    
Figure 1
 
(A) Mouse undergoing CXL treatment, showing riboflavin fluorescence of the cornea. (B) Experimental setup: corneal holder mounted on the extensometer/indenter.
Figure 1
 
(A) Mouse undergoing CXL treatment, showing riboflavin fluorescence of the cornea. (B) Experimental setup: corneal holder mounted on the extensometer/indenter.
Figure 2
 
Scheme of the experimental setup describing the applied tensile force onto the corneal surface using a customized indenter.
Figure 2
 
Scheme of the experimental setup describing the applied tensile force onto the corneal surface using a customized indenter.
Figure 3
 
Stress-relaxation curves with standard deviation of various treatment (plain lines) and control (dashed lines) groups. The standard deviations appear in green for the treatment groups and in gray for the control groups. (A) Stress-relaxation curves of the groups of the set 1 showing no superposition between treatment and control group standard deviations. (B) Stress-relaxation curves of the groups of the set 2 also showing no superposition between treatment and control groups standard deviations but with a reduced spacing.
Figure 3
 
Stress-relaxation curves with standard deviation of various treatment (plain lines) and control (dashed lines) groups. The standard deviations appear in green for the treatment groups and in gray for the control groups. (A) Stress-relaxation curves of the groups of the set 1 showing no superposition between treatment and control group standard deviations. (B) Stress-relaxation curves of the groups of the set 2 also showing no superposition between treatment and control groups standard deviations but with a reduced spacing.
Figure 4
 
Stress-strain curves with standard deviation of various treatment (plain lines) and control (dashed lines) groups. The standard deviations appear in green for the treatment groups and in gray for the control groups. (A) Stress-strain curves of the groups of the set 1 showing superposition between most of the treatment and control group standard deviations. (B) Stress-strain curves of the groups of the set 2 showing superposition between the treatment and control group standard deviations.
Figure 4
 
Stress-strain curves with standard deviation of various treatment (plain lines) and control (dashed lines) groups. The standard deviations appear in green for the treatment groups and in gray for the control groups. (A) Stress-strain curves of the groups of the set 1 showing superposition between most of the treatment and control group standard deviations. (B) Stress-strain curves of the groups of the set 2 showing superposition between the treatment and control group standard deviations.
Figure A1
 
Parameters used for the calculation of (A) stress and (B) strain.
Figure A1
 
Parameters used for the calculation of (A) stress and (B) strain.
Table 1
 
Adaptation of CXL Parameters to the Mouse Cornea
Table 1
 
Adaptation of CXL Parameters to the Mouse Cornea
Table 2
 
Determining the Threshold Fluence for Effective CXL in the Mouse
Table 2
 
Determining the Threshold Fluence for Effective CXL in the Mouse
Table 3
 
Significant Differences in Stress-Strain and Stress-Relaxation Tests Between CXL and Control Groups
Table 3
 
Significant Differences in Stress-Strain and Stress-Relaxation Tests Between CXL and Control Groups
Table 4
 
Higher Sensitivity of Stress-Relaxation Test Compared With Stress-Strain Test
Table 4
 
Higher Sensitivity of Stress-Relaxation Test Compared With Stress-Strain Test
Table 5
 
No Differences in Stress-Strain and Stress-Relaxation Tests Between Several CXL Treatment Conditions, or Between Riboflavin and Virgin Control Conditions
Table 5
 
No Differences in Stress-Strain and Stress-Relaxation Tests Between Several CXL Treatment Conditions, or Between Riboflavin and Virgin Control Conditions
Table 6
 
Significant Differences From Stress-Strain Analysis, Both Between CXL Treatment Conditions and Between Control Conditions
Table 6
 
Significant Differences From Stress-Strain Analysis, Both Between CXL Treatment Conditions and Between Control Conditions
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