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,
2–4
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 treated
5
or the maximum light exposure to avoid corneal endothelial damage.
Modifications of the procedure involve the use of hypo-osmotic
riboflavin solutions to keep
6 or even increase
7 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/cm
2 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.
15–17 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., OCT
13 or Scheimpflug
18). 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 Δ
Yapex (
t) is the displacement of the apex at a given time.
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.
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 cornea
23 and approximately 400 μm of the porcine cornea. A recent study
24
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 Formula
and
Display Formula 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/m
3. 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.
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).
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 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.
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.
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.
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. 3–
6), 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.
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 mm
22) and in human eyes (0.85 mm for ex vivo eyes
18 and 1.08 mm for in vivo measurements
25).
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 MPa
29 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.
29–31
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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