**Purpose**:
The effect of ultraviolet (UV)–riboflavin cross-linking (CXL) has been measured primarily using the strip extensometry technique. We propose a simple and reliable methodology for the assessment of CXL treatment by using an established rheologic protocol based on small amplitude oscillatory shear (SAOS) measurements. It provides information on the average cross-link density and the elastic modulus of treated cornea samples.

**Methods**:
Three fresh postmortem porcine corneas were used to study the feasibility of the technique, one serving as control and two receiving corneal collagen cross-linking treatment. Subsequently, five pairs of fresh postmortem porcine corneas received corneal collagen cross-linking treatment with riboflavin and UVA-irradiation (370 nm; irradiance of 3 mW/cm^{2}) for 30 minutes (Dresden protocol); the contralateral porcine corneas were used as control samples. After the treatment, the linear viscoelastic moduli of the corneal samples were measured using SAOS measurements and the average cross-linking densities extracted.

**Results**:
For all cases investigated, the dynamic moduli of the cross-linked corneas were higher compared to those of the corresponding control samples. The increase of the elastic modulus of the treated samples was between 122% and 1750%. The difference was statistically significant for all tested samples (*P* = 0.018, 2-tailed *t*-test).

**Conclusions**:
We report a simple and accurate methodology for quantifying the effects of cross-linking on porcine corneas treated with the Dresden protocol by means of SAOS measurements in the linear regime. The measured dynamic moduli, elastic and viscous modulus, represent the energy storage and energy dissipation, respectively. Hence, they provide a means to assess the changing physical properties of the cross-linked collagen networks after CXL treatment.

^{1–3}The cornea biomechanical properties are derived from the intricate and pseudo-regular matrix structure. The decrease of corneal mechanical stability has a critical role in the onset and progression of keratoconus and postlaser-assisted in situ keratomileusis (LASIK) ectasia.

^{4}Corneal collagen cross-linking (CXL) was first described by Wollensak et al.

^{5}and is the treatment of choice to stop the progression of keratoconus and ectatic disorders by increasing corneal stiffness.

^{5,6}(i.e., number of cross-links), but in corneal tissue, the nature of the participants has not been elucidated. The increase in the number of cross-links is directly reflected in elastic modulus increase of the corneal tissue.

^{7}

^{8}with a hyperelastic behavior even under low stress load. In this respect, mechanical parameters of corneal tissues have been studied via strip extensometry,

^{9–12}pressure inflation,

^{13}unconfined compression,

^{14}and inflation testing.

^{15,16}Technical challenges and reproducibility issues in particular limit strip extensometry. An inherent problem with this technique is alteration of physical properties during processing, particularly sectioning and hydration.

^{17–19}However, the full characterization of these rheologic measurements with regards to quantitative assessment of the degree of cross-linking of the corneal tissues has not been reported.

^{2}for 30 minutes (5.4 J/cm

^{2}). The treated porcine corneas (5) received isotonic solution of 0.1% riboflavin (vitamin B2) photosensitizer and 20% dextran in 1 × PBS buffer every 5 minutes for 30 minutes, and then exposed to the same total UVA irradiation energy by applying the same protocol used for the control cornea samples. All animals were treated in accordance with the ARVO Statement for the Use of Animals in Ophthalmic and Vision Research.

^{20}We measured the linear viscoelasticity of a disc-shaped cornea specimen (i.e., their mechanical response was not affected by the extent of imposed time-dependent deformation on the sample) by applying a sinusoidal oscillatory strain

*γ*(

*t*) =

*γsin*(

*ωt*)

*,*with

*γ*the strain amplitude and

*ω*the frequency of oscillation. The resulting stress response of the material was

*σ*(

*t*) =

*γ*[

*G'sin*(

*ωt*)

*+G''cos*(

*ωt*)], which provides the strain-independent (see below) storage (or elastic)

*G'*and loss (or viscous)

*G''*dynamic moduli that characterize the material's viscoelasticity and reflect its structure. For the particular case of network-like corneal tissue which is a viscoelastic solid, the storage modulus

*G'*is proportional to the Young's modulus and reflects the mechanical strength of the material.

^{7}the rubbery plateau modulus, i.e., the measured nearly frequency-independent storage modulus

*G'*here, of an elastic network is given by

*G*' =

*v*kT where

*v*is the number density of cross-links (junctions/m

^{3}), k is Boltzmann's constant (J*K

^{−1}) and T the absolute temperature (K). This theory is based on the entropic origin of chain elasticity and considers incompressible and uniform network, as well as affine deformation. The uniformity of the network is reflected in a constant cross-link density. For the present case of cornea physical network this is not necessarily true, hence the present simple analysis provides an estimate of an average cross-link density.

^{21–23}The model is based on linear viscoelastic response and the definition of modulus (thermal energy over volume). This volume is called correlation volume and represents the stress-carrying volume element in the network as discussed by de Gennes.

^{24}The additional assumption is that for networks we take an average value for almost homogeneous distribution of network junctions (crosslinks). For large macromolecules, as in the present case, this is a sound assumption and the model is universally validated.

^{21–23,25}They represent selected examples as the field is wide. However, we note that our approach is a first attempt at correlating these measures with the condition of the cornea tissues, and in this respect it is simplified (albeit useful, we believe). In a next step one should account for the stiffness of the particular tissues (persistence length) which may influence the viscoelastic response. Such an attempt has been made for collagen.

^{22,26}Note that here we have considered flexible tissues, which is a rough approximation but allows drawing useful correlations. Accounting for the stiffness will be the subject of future work.

^{27}To be consistent with previous studies,

^{17,28,29}320 grit sandpaper was used. Temperature control was achieved via a Peltier hood and the setup temperature was maintained at 25°C for all measurements. The risk of evaporation (of water from the corneal tissue) was minimized by means of a custom made trap around the measurement fixture, which created a saturated atmosphere of water vapor. The latter was achieved using a ring-shaped water channel mounted on the bottom plate of the rheometer. The level of water was checked every 30 minutes and maintained constant by refilling. This procedure has been applied successfully with volatile polymer solutions.

^{30}

^{27}The total normal force applied to the specimen during loading did not exceed 0.1 N. With this protocol, no water was expelled from the sample. The loading procedure typically takes 2 minutes and the specimen then is left to relax for another 15 or 30 minutes before the measurement is initiated for control and treated cornea samples, respectively. During this time the tare stress relaxed to zero and the resulting equilibrium thickness of specimens was taken as the loading gap. To obtain reliable measurements in the linear viscoelastic regime, first we performed dynamic strain sweep tests to determine the linear strain range to apply and tested the consistency of the measurements. Figure 1 depicts typical results of dynamic strain sweeps which allow determining the linear viscoelastic regime, as already mentioned. For the particular case of untreated cornea sample tested at a frequency of 1 rad/s,

*G'*and

*G''*are independent of the imposed strain amplitude (

*γ*), hence the response is linear in this range of γ (0.5%–5%). The subsequent SAOS measurements were performed at a chosen strain amplitude of 1% within a frequency window between 0.1 and 100 rad/s. Data collected between 100 and 10 rad/s were affected by either sample stiffness or wall slip. For this reason these data were not taken into account in our analysis. The consistency of the measurements, hence time–independent viscoelastic properties of the cornea specimens, is demonstrated in Figure 2. It depicts the frequency-dependent viscoelastic moduli for a cornea control sample measured at two different times with an interval of 30 minutes. The time of 30 minutes is the typical relaxation time for cornea control samples, corresponding to the relaxation of the normal force signal after specimen loading. The discrepancy of experimental data between the two tests is less than 5% (well within the measurement specifications). This meticulous protocol ensured high quality consistent measurements confirming that the sample's condition remained unchanged during testing. The analysis of the linear viscoelastic moduli is based on the theory of rubber elasticity

^{7}which is discussed in the materials and methods section.

**Figure 1**

**Figure 1**

**Figure 2**

**Figure 2**

*G'*as a function of frequency. The value of

*G'*at a frequency of 1 rad/s, is observed to change from 2 × 10

^{3}to 1.5 × 10

^{4}and to 3 × 10

^{4}Pa from the control cornea sample to treated 1 to treated 2 cornea samples, respectively. Since the thermal unit kT is kept constant by taking into account a single temperature value for all of the measurements,

*v*increases almost 10-fold from control to treatment 1 and then by a factor of 2 to treatment 2. The control sample at room temperature (25°C), has a value of 4.86 × 10

^{14}junctions/mm

^{3}. The typical distance between two junctions,

*ξ*, is estimated to be approximately 13 nm by considering ξ ≈ [kT/

*G'*]

^{1/3}.

**Figure 3**

**Figure 3**

*G*' which can be as high as a factor of 20 (sample 2), it is apparent that there is a nonnegligible variance (the lowest increase is factor of approximately 2.5 for samples 3 and 5). This result suggests that there is variability in the effect of the treatment. However, an unambiguous change can be measured reliably with the described technique.

**Figure 4**

**Figure 4**

**Table**

*G'*at 1 rad/s) of the treated corneal samples over the reference (untreated control sample). Results show the elastic modulus

*G'*increase at 1 rad/s. These simple metrics compare samples from different animals and demonstrate the range of variance, which should relate to the difference among animals, with the most likely factor being age.

**Figure 5**

**Figure 5**

*E*was calculated as three times of the rubbery plateau modulus

*G'*according to the theory of linear viscoelasticity

^{27}and it was 11,011 ± 5947 Pa for the control corneal samples and 62,982 ± 26,740 Pa for the treated corneal samples. This difference is statistically significant with a

*P*value of 0.018 (paired

*t*-test). Values of average cross-linking density

*ν*and junction distance

*ξ*for control and CXL treated corneal samples are reported in the Table together with Young's modulus and its relative improvement.

*ν*and

*ξ*for control corneal samples do not have their original physical meaning of numbers of actively junction points per unit volume and distance between two adjacent junction points, respectively. They are material parameters for chemical cross-linked network systems. Stromal structure of control corneal samples consists of temporary bridges between collagen fibrils via proteoglycan chains in an antiparallel fashion.

^{31}For this reason values of

*ν*and

*ξ*for control corneal samples must be considered more qualitatively than quantitatively as reference point.

^{32}Strip extensometry involves cutting the corneal tissue in equal sized strips, then mounting it on an appropriately modified extensometer

^{9,12,33}and eventually measuring the Young modulus until the sample breaks up.

^{34}Although the technique is standardized, it can prove difficult to obtain consistent measurements due to several issues, such as ensuring equal tissue strip sizes to measure and avoiding slippage as the tissue is stretched.

^{12}Furthermore, measurements must be performed quickly enough to avoid dehydration of the corneal sample, which can alter the results of the measurement itself. Hence, two crucial issues are maintaining a constant water content of the sample and the nonlinear deformation imposed, leading to fracture. The former already has been addressed, whereas the latter affects the sample's microstructure significantly, as will be discussed further below.

^{18}and ultrasound microscopy.

^{35}Despite the fact that these techniques provide quantitative information about tensile/compressive material properties (such as Young's/Longitudinal modulus, Poisson ratio) of cornea and some of them can be applied even in vivo,

^{36,37}they have limitations and, moreover, they do not always yield consistent results.

^{38}Hence, a simple but reliable biomaterial-dedicated experimental procedure is needed.

^{39,40}

^{9,12}which, in our experience, can be challenging. It also requires a modification of the strip extensometer to mount the strips of tissue and prevent slippage. Moreover, the continuous deformation accumulates strain in the material and becomes nonlinear, hence affecting its microstructure, with the constituting collagen network constituents being oriented in the flow direction, stretched, and eventually broken (sample fracture).

^{19}The measurements were performed in bovine corneas. However, the corneal samples were cut into strips and preconditioned before the frequency sweep measurements were performed. Hence, no specific protocol was used aiming at preserving the original microstructure and water content of the cornea samples.

^{9,12}Our values under shear deformations are one order of magnitude smaller than those under small tensile deformations. Conversely, there is a good agreement for control corneal samples in terms of shear modulus between our work and Hatami and Marbini's study.

^{17}A possible explanation for the difference in corneal behavior in shear and tensile modes of deformation might be given in terms of the microstructure. The corneal extracellular matrix is composed of stacks of collagen lamellae with a parallel-to-the-surface distribution, each comprising bundles of thin collagen fibrils and proteoglycans. The gap between the collagen fibrils is filled with a network of proteoglycans which are responsible to maintain the uniform spacing of the fibrils.

^{1–3}In compression studies,

^{14}a difference of two orders of magnitude already was observed between in-plane (compressive) and out-of-plane (transverse) Young's modulus. From the same point of view, when subjected to uniaxial tensile strain in the strip testing method, the collagen lamellae are mainly loaded in tension. It is known that collagen fibrils have a nonlinear stress-strain behavior. Thus, a strain-hardening response (associated with collagen fibril stretching) is expected with increasing imposed deformation. In previous studies

^{12,13}the calculation of Young's modulus was made at different strains of a uniaxial extensional test where the stress-strain behavior of the cornea sample already was nonlinear (i.e., strain hardening was observed). On the other hand, when subjected to shear deformation the proteoglycan matrix mainly provides the shear stiffness. Adjacent lamellae just slide to each other and a lower shear stiffness is obtained. In summary, the described SAOS testing procedure ensured nearly equilibrium measurements of the viscoelasticity of the measured cornea samples while maintaining their microstructure and water content intact. Despite the above discussion, however, further studies will be needed to fully elucidate the physical origin of cornea's viscoelastic behavior and the issues raised.

**I.M. Aslanides**, None;

**C. Dessi**, None;

**P. Georgoudis**, None;

**G. Charalambidis**, None;

**D. Vlassopoulos**, None;

**A.G. Coutsolelos**, None;

**G. Kymionis**, None;

**A. Mukherjee**,

**T.N. Kitsopoulos**, None

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