**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/cm^{2}) 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.

^{1,2}is a method to increase corneal stiffness and to arrest corneal ectatic disorders like keratoconus and ectasia after refractive laser surgery

^{3}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}

^{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.

^{13–15}

^{1,2,6,11,12,16}Viscoelastic testing, including creep and relaxation tests,

^{17–19}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 properties

^{20}and affect accuracy of testing.

^{21–24}A better understanding of the cellular and molecular events occurring during CXL might help in establishing optimized treatment modalities.

^{25}

**Table 1**

**Table 2**

*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.

*n*= 14 mice), the fluence was consecutively reduced to determine the threshold level for effective CXL in the mouse cornea.

^{26}vs. 530 μm

^{27}) 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/cm

^{2}), and UV irradiation time series (30 seconds to 30 minutes; Tables 1, 2).

*T*is the transmittance,

*I*

_{0}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.

**Figure 1**

**Figure 1**

*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 (

*Δ*

_{max}), 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**

**Figure 2**

*ε*is strain and

*Δ*is the vertical indentation measured.

*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.

*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.

*F*(

*t*) is the force at time

*t*,

*σ*(

*t*) is the stress at time

*t*,

*σ*is the asymptotic stress,

_{∞}*σ*

_{1}and

*σ*

_{2}are the short-term stress and

*τ*

_{1}and

*τ*

_{2}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

*ε*

_{const}that was applied during the measurement.

^{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.

*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*,

_{∞}*λ*

_{1},

*λ*

_{2}, γ

_{∞},

*γ*

_{1},

*γ*

_{2}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*

_{∞},

*σ*

_{1},

*σ*

_{2},

*τ*

_{1},

*τ*

_{2}). The interested reader can refer to Pinheiro et al.

^{28}for detailed presentation of these models applied to several biological studies.

*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

*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.

**Table 3**

**Figure 3**

**Figure 3**

**Figure 4**

**Figure 4**

*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**

**Table 5**

**Table 6**

^{2}in either stress-relaxation or stress-strain tests.

^{2}, 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).

*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/cm

^{2}with an irradiance of 9 mW/cm

^{2}(

*P*= 0.1643). Only stress-strain tests indicated a significant difference (

*P*= 0.043), which was close to the level of significance (Table 6).

^{30}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 study

^{17}that viscoelastic testing approaches, such as stress-relaxation or creep tests, are more sensitive to measure the effect of CXL.

^{10,31}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.

^{2}. 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 μm

^{26}) compared with porcine (877.6 μm

^{32}) and human (530 μm

^{27}) corneas. The oxygen dependency of CXL in murine and porcine corneas

^{33}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.

**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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*Refract Surg**F*is applied. This means the flap has to resist a net force of 2·

_{flap}*F*, but at each end one cross-section of the flap has to withstand

_{flap}*F*. Therefore, the stress in the flap is defined as:

_{flap}*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·

*A*. Therefore, the stress in a flap with the 2D testing system is defined as

_{cross}*F*corresponds to the net force. The cross-sectional area resisting this force is here

_{flap}**Figure A1**

**Figure A1**