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INVITED REVIEW
Corneal biomechanics –a review
Sabine Kling
1
and Farhad Hafezi
1,2,3,4
1
CABMM, University of Zurich, Zurich, Switzerland,
2
ELZA Institute AG Dietikon, Zurich, Switzerland,
3
USC Roski Eye Institute –Keck School of
Medicine, Los Angeles, USA, and
4
Ophthalmology, University of Geneva, Geneva, Switzerland
Citation information: Kling S & Hafezi F. Corneal biomechanics –a review. Ophthalmic Physiol Opt 2017. doi: 10.1111/opo.12345
Keywords: corneal biomechanics, corneal
ectasia, extracellular matrix, numerical
simulation
Correspondence: Sabine Kling
E-mail address: kling.sabine@gmail.com
Received: 11 October 2016; Accepted: 15
November 2016
Abstract
Purpose: In recent years, the interest in corneal biomechanics has strongly
increased. The material properties of the cornea determine its shape and therefore
play an important role in corneal ectasia and related pathologies. This review
addresses the molecular origin of biomechanical properties, models for their
description, methods for their characterisation, techniques for their modification,
and computational simulation approaches.
Recent findings: Recent research has focused on developing non-contact tech-
niques to measure the biomechanical properties in vivo, on determining structural
and molecular abnormalities in pathological corneas, on developing and optimis-
ing techniques to reinforce the corneal tissue and on the computational simula-
tion of surgical interventions.
Summary: A better understanding of corneal biomechanics will help to improve
current refractive surgeries, allow an earlier diagnosis of ectatic disorders and a
better quantification of treatments aiming at reinforcing the corneal tissue.
Introduction
The corneal shape is a determinant of ocular refraction, but
is itself determined by its biomechanical properties. The
cornea needs to be soft enough to bulge out in an aspheric
half-sphere, but stiff enough to maintain its shape and
resist the intraocular pressure (IOP). At the same time, the
tissue needs to remain transparent, which requires a com-
plex interplay between the extracellular matrix (ECM)
components. Particularly, the attachment of proteoglycans
and glycosaminoglycans to collagen fibres, the organisation
of the collagen structure, the corneal swelling pressure and
the production/degradation of ECM components have
been identified as essential factors determining the material
properties of the corneal tissue.
Factors determining corneal biomechanical
properties
Extracellular matrix (ECM) components
Glycosaminoglycans (GAGs) and proteoglycans (PGs) play
an essential role in the assembly of the ECM and its
transparency. It is generally understood that keratan sulfate
proteoglycans regulate the diameter of collagen fibrils,
while dermatan sulfate proteoglycans determine the inter-
fibrillar spacing and lamellar adhesion properties.
1
GAGs
interfere with collagen electrostatically only
2
and therefore
hardly affect nucleation or growth, but GAGs are required
to sulfate PG core proteins. It has been suggested
3
that par-
ticularly de-glycosylated small leucine-rich repeat proteo-
glycan core proteins may modulate the collagen
fibrillogenesis and could play a role in several corneal ecta-
tic disorders: in keratoconus, pellucid marginal degenera-
tion and macular corneal dystrophy the amount of highly
sulfated keratan sulfate proteoglycans is reduced
4
or absent,
respectively.
4
Also, keratoconic corneas show a reduced
amount of highly sulfated chondroitin sulfate proteogly-
cans (CS-PGs) and an increased ratio of glucosaminogly-
cans: galactosaminoglycans.
5
The amount of acidic GAGs
directly correlates with the degree of collagen fibre organi-
sation along the human corneal stroma.
5,6
Differences in GAG and PG composition are concomi-
tant with physiological modifications.
7
The proportions
of GAGs and PGs are strongly dependent on the amount
©2017 The Authors Ophthalmic & Physiological Optics ©2017 The College of Optometrists 1
Ophthalmic & Physiological Optics ISSN 0275-5408
of available oxygen. Studies on cornea and cartilage con-
clude that KS, rather than CS, is produced in conditions
of O
2
deficiency.
8
This may explain why KS dominates in
the posterior stroma.
9
Also, in large animals with high
corneal thicknesses –such as cows, pigs or humans –the
KS-GAG proportion reaches up to 60–70%,
9
while in
small animals, such as mice, KS is completely absent.
Also, environmental modifications –such as the wear of
contact lenses –have the potential to increase the propor-
tion of keratan sulfate proteoglycans at the cost of chon-
droitin sulfate proteoglycans. Keratan sulfate
proteoglycans are generally understood to stabilise colla-
gen fibrils on the short-range, while chondroitin sulfate/
dermatan sulfate proteoglycans stabilize several fibrils as
far as lamellae.
10
Therefore, a decrease in chondroitin sul-
fate proteoglycans potentially weakens the cornea and
facilitates the development of corneal ectasia.
Collagen lamellae organisation
Collagen fibril orientation determines corneal transparency,
as well as direction-dependent material properties, and cor-
relates with visual acuity across species.
11
Crystallography
studies in ex vivo tissue show that the human collagen fibres
are orthogonally oriented in the centre and circumferen-
tially towards the limbus.
12
Orthogonal orientation pro-
vides the highest visual acuity and is expected to best
maintain the corneal shape, followed by vertical orientation
(marmoset, horse, cow) before circumferential orientation
(pig, rabbit mouse). It has been suggested that differences
in the stromal collagen arrangement may result from spe-
cies-specific eye movements, which activate the extraocular
rectus muscles in a certain way and evoke counteracting
forces to which the collagen fibres align.
11
In the human cornea, the fibres are more densely packed
in the peripupillary cornea.
13
Also, non-linear optical
microscopy found a stronger interweaving and steeper
angles of the collagen fibres in the anterior than in the pos-
terior cornea,
14
which correlates with an increased shear
stress in the anterior cornea when compared to the poste-
rior cornea.
15
Collagen organisation is disturbed in certain
degrading pathologies such as keratoconus,
16
demonstrat-
ing their importance for maintaining corneal shape.
Hydration/osmotic pressure
The degree of corneal hydration not only affects its trans-
parency, but also its elastic modulus: the more hydrated the
corneal tissue, the lower its elastic modulus,
17,18
which
potentially arises from an altered collagen attachment to
the proteoglycans an/or glycosaminoglycans based on their
ionic interaction. The swelling properties of the corneal tis-
sue are not purely osmotic pressure driven, but also arise
from electrolyte exclusion due to the collagen fibril
volume.
19
At 666 lm thickness, porcine corneas show
a hydration of 3.36 mg
H2O
/mg
dry_weight
and a swelling
pressure of 52 mmHg.
20
Corneal layers and their importance for biomechanical
properties
Due to the different collagen orientation and density, each
corneal layer contributes to a greater or lesser extent to the
overall biomechanical resistance. The epithelium and
endothelium as pure cell layers do not directly contribute
to corneal stiffness. Elsheikh et al
21
showed in human
donor eyes that the contribution of the epithelium to cor-
neal stiffness is much lower than that of the stroma and
therefore can most likely be neglected. These cell layers
may, however, indirectly affect corneal stiffness by regulat-
ing its hydration. In Bowman’s membrane, the collagen
lamellae are most densely packed, and it is considered to be
of major importance for corneal stability after laser ablative
surgery.
22
The stroma represents the largest part of the cor-
nea and is therefore the layer mainly defining the biome-
chanical properties of the cornea. In studies where the
cornea has been assumed a non-layered material, these typ-
ically refer to the stroma. The pre-descemet membrane,
also known as Dua’s layer, has been discovered only
recently.
23
Due to its mechanical strength, it is has been
postulated to contribute significantly to corneal stiffness.
Yet, more scientific evidence is required.
Diseases associated to corneal biomechanical properties
Several systemic diseases are known to alter the corneal
stiffness. Diabetic mellitus patients have a higher corneal
resistance factor as measured by the ocular response anal-
yser.
24,25
Also, diabetes has a protective effect on the inci-
dence rate
26
and severity
27
of degrading corneal diseases
such as keratoconus. It is assumed that the presence of
advanced glycation end products
28
in diabetic corneas leads
to an increased non-enzymatic cross-linking of the corneal
tissue that provides additional stiffness.
In contrast, the ECM of the keratoconic cornea is dispro-
portionally degraded leading to a loss of collagen fibril orien-
tation,
16
biomechanical weakening
29–32
and out-bulging of
the cornea into a conical shape. A susceptibility to kerato-
conus has been reported with Trisomy 21, Leber’s congential
amaurosis, Ehler-Danlos syndrome and osteogenesis imper-
fecta.
33
The latter two diseases directly affect collagen synthe-
sis, and the corneal ectasia potentially arises from an instable
collagen network. In Trisomy 21 and Leber’s congenital
amaurosis, the origin of corneal degradation however is still
unclear. Several studies have suggested that both genetic pre-
disposition and environmental factors are required for the
manifestation of keratoconus.
©2017 The Authors Ophthalmic & Physiological Optics ©2017 The College of Optometrists2
Corneal biomechanics –a review S Kling and F Hafezi
Hormonal fluctuations
Changes in corneal stiffness have also been associated with
hormonal fluctuations: Increased oestrogen levels during
the menstrual cycle correlated with an increase in corneal
thickness,
34
a decrease in corneal hysteresis and a decrease
in the corneal resistance factor
35
as measured with the ocu-
lar response analyser. Also, pregnancy
36–38
and pathologi-
cally-reduced levels of thyroid hormones
39
have been
reported in context with the onset or progression of corneal
ectasia. Oestrogen administration to ex vivo corneas
reduces the biomechanical stiffness by 36%.
40
Environmental factors
Little is known on the influence of environmental effects
on corneal biomechanics. While eye-rubbing has been asso-
ciated to keratoconus,
41,42
ageing
43,44
and smoking
45,46
have both been reported to stiffen the corneal tissue and to
reduce the incidence of keratoconus.
45
Eye-rubbing induces
ocular trauma and may trigger inflammation increasing the
degradation of the ECM. In contrast, ageing leads to the
accumulation of glycation end products and cigarette
smoke contains aldehydes, which both induce non-
enzymatic cross-links between collagen molecules provid-
ing additional stiffness.
47
Mechanical description of corneal properties
Similar to most biological tissues, the cornea has viscoelas-
tic properties. Here, elasticity refers to the static properties
of a material and arises from the tensile characteristics of
the collagen microstructure. Viscosity refers to the dynamic
(i.e. time-dependent) properties and arises from the non-
covalent rearrangements of the ECM, such as from water
diffusion and electrostatic interactions between GAGs and
collagen.
Elastic properties
Elastic properties describe the immediate deformation
response to the application of a mechanical stress and
mainly result from the collagen fibres. When applying a
load on the non pre-stressed corneal tissue, in the begin-
ning the collagen fibres are crimped resulting in a toe
region in the stress-strain diagram,
48
see Figure 1a. Only
when the fibres become straight, the tissue deforms
Figure 1. (a) Stress-strain curve for an elastic material. (b) Stress-strain curve for a viscoelastic material. (c) Creep and stress-relaxation in a viscoelastic
material. (d) Phase lag between stress and strain in a viscoelastic material.
©2017 The Authors Ophthalmic & Physiological Optics ©2017 The College of Optometrists 3
S Kling and F Hafezi Corneal biomechanics –a review
elastically. It is assumed that the physiological state lies
between the end of the toe region and the beginning of the
elastic region. When a higher load is applied and the elastic
region surpassed, permanent plastic deformation occurs
and finally the tissue ruptures.
The standard elastic parameter is the static elastic modu-
lus, also known as Young’s modulus. It is defined as the
slope of the tangent in the stress-strain diagram.
E¼Dr
De ð1Þ
Linear elastic materials have a constant elastic modulus,
while in non-linear elastic materials –such as the cornea –
the elastic modulus is a function of strain. However, for
very small deformation, even non-linear elastic materials
deform linearly. Measurements of the corneal elastic modu-
lus range from 1.3 MPa
49
–5 MPa
50,51
in humans and
from 1.5 MPa
49
–3 MPa
52
in pigs.
Viscoelastic properties
Viscoelastic material properties describe the dynamic
deformation response. Time-dependent tissue properties
arise from molecular rearrangement, but also from osmotic
diffusion as a response to the application of a mechanical
load. Viscoelastic deformation is completely reversible with
time. In the stress-strain diagram a hysteresis (Figure 1b)is
observed between the loading and unloading cycle, whose
area represents the energy lost during the viscous
deformation (e.g. heat).
One possibility to define viscoelastic properties is to use
the dynamic modulus, which is composed of the loss and
storage modulus. The dynamic modulus E*is based on the
fact that stress and strain are out of phase in a viscoelastic
material, see Figure 1d. Therefore testing at different fre-
quencies is required. The storage (elastic) modulus E’ and
the loss (viscous) modulus E’’ are then defined by the phase
lag dbetween stress rand strain e:
E0¼ro
eo
:cos dð2aÞ
E00 ¼ro
eo
:sin dð2bÞ
The dynamic modulus can then be calculated by:
E
*
=E0+iE″This kind of viscoelastic characterisation
demonstrated that in porcine corneas the storage modulus
(2–8 kPa) was dominant over the loss modulus
(0.3–1.2 kPa).
53
Another possibility to define viscoelastic properties is to
use an n-element Prony series. Typically, stress-relaxation
test are performed and the stress is fitted to the following
equation:
rðtÞ¼r/þXn
i¼1riet
sið3Þ
where r
/
is the infinite stress and r
i
the stress at a given
time point s
i
. Given that the strain e
0
is maintained con-
stant during stress-relaxation, the elastic moduli at a given
time point tcan be easily calculated by dividing r(t)bye
0
.
See also Figure 1c. This kind of viscoelastic definition has
been applied in a study to retrieve biomechanical parame-
ters from air-puff deformation.
54
Measuring corneal biomechanical properties
Table 1 summarises previously applied techniques to mea-
sure the biomechanical properties of the cornea.
Extensometry
Stress-strain extensometry is the gold standard method in
engineering to measure the macroscopic mechanical prop-
erties within a normalized setting. Tissue samples of a pre-
defined length and width are fixed within brackets. Then, a
pre-defined load is applied and the corresponding displace-
ment measured. For elastic testing, a slowly increasing load
is applied (stress-strain diagram).
49
For viscoelastic testing,
a one-step load is applied and maintained constant until
the end of the test (stress-relaxation test), or a one-step dis-
placement is applied and maintained constant (creep test).
Given that this kind of extensometry cannot be applied
in vivo nor in intact ex vivo eyes, modifications of the testing
procedure have been proposed. For ex vivo measurements,
corneal button and whole eye inflation set ups were
designed, where either the displacement of mercury dro-
plets,
55
graphite flakes,
56
the corneal apex
57
or curvature
changes
58
were recorded. For in vivo measurements, Pal-
likaris et al.
59
developed a protocol, where the whole eye is
inflated during surgery and the corresponding rise in IOP
measured in order to determine ocular rigidity. Lam et al.
60
used a flat surface cylinder to perform indentation measure-
ments and estimated corneal stiffness from the inward dis-
placement. A problem inherent to whole eye globe
measurements is that the corneal deformation cannot be
separated from scleral deformation and the average macro-
scopic corneal stiffness can only be roughly estimated.
Brillouin microscopy
Brillouin microscopy offers the possibility to record a spa-
tially resolved map of corneal stiffness. The macromolecu-
lar, quasi-static non-contact measurement is based on
©2017 The Authors Ophthalmic & Physiological Optics ©2017 The College of Optometrists4
Corneal biomechanics –a review S Kling and F Hafezi
Brillouin scattering, which arises from a non-linear interac-
tion between an optical and acoustic wave, in which the
material is compressed by the electromagnetic field. The
resulting density variation has the effect of an index grating
that partially reflects the incident light. By measuring the
frequency shift of the backscattered light, information about
the mechanical properties of the material can be obtained:
M0¼qk2X2
4n2
M00 ¼qk2X2DX2
4n2
where M0is the elastic modulus, M″is the viscous modulus,
qis the mass density, kis the optical wavelength, Ωis
the frequency shift DΩis the line width and nis the
refractive index. The viscoelastic modulus is defined as
M*=M0+iM″, analogous to the dynamic elastic modu-
lus E*. Nevertheless, it is unknown how the Brillouin mod-
ulus compares to the static elastic modulus.
Although Brillouin scattering has been known since the
1920s
61
until recently only single-point measurements were
possible. In 2008, Scarcelli et al.
62
presented the first scan-
ning system that allowed to measure the cross-section of
intraocular and crystalline lenses. Meanwhile, Brillouin
microscopy has also been applied to perform measure-
ments in human eyes in vivo,
63
to quantify the stiffening
effect of cross-linking
64
and to identify weakened regions in
keratoconus corneas.
65
The Brillouin modulus M0of an
untreated porcine cornea roughly falls between 2.75 and 2.5
GPa (anterior and posterior) and increases to 2.95 and 2.5
GPa after CXL treatment.
64
Air-puff tonometry and related systems
Initially, air-puff tonometers have been developed to mea-
sure the intraocular pressure (IOP) by non-contact.
66
The
required air pressure to applanate the corneal curvature was
considered to be equivalent to the IOP. The ocular response
analyser
67
was the first device that tried to related the
dynamic deformation response of the cornea with
biomechanical parameters.
68
It measures the pressure differ-
ence between the inward and outward applanation, the
so-called corneal hysteresis. The higher the pressure for the
inward and the lower the pressure for the outward
applanation, the higher is the viscous component. More
recently, air-puff tonometry was combined with high-speed
Scheimpflug
69–71
and OCT imaging,
72,73
which allowed for
the first time to capture both the complete temporal and
spatial deformation profile of the cornea during the air-puff
event.
While both systems are available for clinical use,
74
the
measured parameters are only geometrical and not directly
related to actual biomechanical parameters. Nevertheless,
several simulations have been suggested to extract biome-
chanically relevant parameters from these measure-
ments.
54,75,76
Air-puff systems have been used to analyse
differences between hyperopia and myopia,
77
between kera-
toconic and normal corneas
30,32,78
and in corneas with
induced swelling.
79
However in most studies only minor to
no changes could be detected demonstrating the need of a
more detailed analysis of the recorded deformation profile.
Elastography
Conventional ultrasound-based elastography is frequently
used in medicine for the diagnosis of pathologies related to
the viscoelastic material properties of tissue, such as breast
cancer or liver fibrosis. For ophthalmic applications,
51,80,81
ultrafast echo-graphic imaging is required due to the finer
structure of the eye and in order to allow high-resolution
acquisition.
82
For the measurement of the corneal tissue,
contact with a coupling liquid is needed. Ultrasonic shear
waves of 15 MHz are typically used to induce microscopic
strains in the tissue. The resulting shear wave is then
directly recorded by ultrasonic imaging. In large organs
where boundary conditions are negligible, the elastic mod-
ulus Ecan be calculated by:
E¼3qc2
s
where c
s
is the propagation speed of the induced shear
waves and qthe density of approx. 1000 kg m
3
. In the
Table 1. Summary of measurement techniques applied to determine the biomechanical properties of the corneal tissue
Static Dynamic Invasive Ex vivo In vivo Macroscopic Microscopic
Strip extensometry Yes Yes Yes Yes
49
–Yes –
Eye inflation Yes Yes Yes Yes
55–58
Yes
59
Yes –
Brillouin microscopy –Yes –Yes
64,65
Yes
63
–Yes
Air-puff systems –Yes Minimally Yes
70
Yes
74
Yes –
Ultrasound elastography –Yes Minimally Yes
51,80,81
Yes –Yes
OCT elastography –Yes Minimally Yes
85,86
Potentially –Yes
Enzymatic digestion Yes –Yes Yes
87–89
–Yes –
©2017 The Authors Ophthalmic & Physiological Optics ©2017 The College of Optometrists 5
S Kling and F Hafezi Corneal biomechanics –a review
cornea however the situation is more complex, as strong
reflections and mode conversions occur at the interfaces
(interiorly the aqueous humour, exteriorly the coupling liq-
uid).
82
The phase velocity c(w) in this context may be
approximated by a leaky Lamb wave:
cðwÞ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
wth cs
2ffiffiffi
3
p
s
where wis the angular frequency and th the local thickness
of the cornea. Corneal elasticity measured by this technique
is in the range of 50–190 kPa
82,83
for normal IOP and
increases to 890 kPa after CXL.
82
The drawback of ultra-
sound-based elastography is that contact is required mak-
ing it uncomfortable for the patient.
Therefore, more recently, non-contact elastography
based on OCT imaging has been developed.
84
Because light
has less impact on the corneal tissue than ultrasound, low-
amplitude elastics waves need to be induced using a differ-
ent source. The most recent research has applied a micro
air-pulse
85,86
for the induction of low-amplitude (<1lm)
elastic waves. The elastic moduli determined by optical
coherence elastography are in the range of 60 kPa for
untreated porcine corneal samples.
86
Enzymatic digestion
Although not a direct measure of corneal stiffness, enzymes
that degrade the ECM affect the biomechanical properties.
Therefore, the speed of digestion of a corneal sample can be
used to infer the original stage of cross-linking and estimate
corneal stiffness. Depending on the enzyme, certain chemi-
cal bonds will be degraded more efficiently than others.
Pepsin is a rather unspecific enzyme and degrades many
ECM components equally, which often makes it the
enzyme of choice for corneal digestion.
87–89
Other enzymes
that have been applied in this context are collagenases and
trypsin.
87
Although using selective enzymatic digestion
would allow studying the impact of certain ECM compo-
nents on the resulting biomechanical properties, these stud-
ies are still outstanding.
Clinical relevance of corneal biomechanics
Corneal stability after laser refractive surgery
Laser ablation has a considerable effect on the biomechani-
cal equilibrium of the cornea. The thinner the stromal bed
after surgery, the less tissue can resist the IOP and the
higher is the risk of the so-called postoperative ectasia.
90
Although eyes with an undiagnosed pre-operative ectatic
disorder are at the highest risk of developing postoperative
ectasia, healthy eyes are at risk if too much corneal tissue is
ablated or a thick flap is created.
91
It is difficult to predict
the maximal amount of corneal ablation necessary to pre-
vent postoperative ectasia for a given patient, as corneal
stiffness and thickness vary between individuals. Currently,
general safety limits such as a minimal required stromal
bed of 250 lm
92
are applied, but still cannot completely
prevent keratectasia.
93
However, the remaining risk might
potentially be reduced by combining laser ablation surgery
with CXL treatment.
94,95
Apart from corneal thickness, the
post-surgical refractive stability depends on the wound
healing process, and on the time-dependent relaxation
behaviour of the viscoelastic cornea.
22,96
Nevertheless, it
has been shown that the largest post-surgical change in
biomechanical parameters occurs within 1 week after
surgery.
97
Orthokeratology
Instead of direct refractive correction, the objective of
orthokeratology contact lenses (OK) is to induce a tempo-
rary shape change of the cornea, so that by day corneal
refraction is corrected, while by night,the OK is worn. OK
have a reversed geometry compared to normal contact
lenses. The working principle is based on the viscoelastic
properties of the corneal tissue, which allow maintaining a
deformation for limited time. However, rather than corneal
bending, a thinning of the central epithelium and a thick-
ening of the mid-peripheral corneal stroma were observed
with OK wear.
98
It can be assumed that the pressure
imposed by the OK induces an osmotic gradient that
removes liquid from the central epithelium. Due to individ-
ual differences in the corneal viscoelasticity however, OK
lenses are more challenging to fit than standard contact
lenses.
99
Corneal thickness and biomechanical properties
Corneal thickness and biomechanical properties are closely
related. On one hand, biomechanical properties determine
the extension of the corneal tissue under the load of the
IOP, which indirectly determines corneal thickness. On the
other hand, a thicker cornea can better resist the load of the
IOP than a thinner one and therefore can partially compen-
sate for a low biomechanical stiffness. Corneal thickness
plays an essential role in measurements depending on cor-
neal deformation, such as in tonometry.
Intraocular pressure and biomechanical properties
An accurate measurement of the intraocular pressure (IOP)
is essential in the diagnosis of glaucoma.
100
Due to limited
accessibility of the posterior chamber, the IOP is typically
measured via the cornea. While different contact and
©2017 The Authors Ophthalmic & Physiological Optics ©2017 The College of Optometrists6
Corneal biomechanics –a review S Kling and F Hafezi
non-contact systems exist, the obtained IOP values are
biased by the corneal thickness and its biomechanical prop-
erties: The thinner and the weaker the cornea, the lower the
value obtained. This constitutes an important problem in
the diagnosis of glaucoma, especially in patients after laser
refractive surgery. While nomograms have been developed
to correct the IOP reading for corneal thickness, the correc-
tion for corneal biomechanics is more complicated and is
currently not possible. In addition, corneal curvature also
has an impact on tonometric measurements.
101
The depen-
dency on many factors may explain why air-puff measure-
ments have a low sensitivity and specificity to detect a
difference between thin and keratoconic corneas.
78
Reinforcing corneal biomechanical properties
Corneal cross-linking (CXL) treatment
Corneal cross-linking
102,103
is a photodynamic method that
is based on the generation of oxygen radicals by means of
riboflavin and UV-A irradiation. While the interaction of
the oxygen radicals with the cornea tissue is not yet com-
pletely understood, ECM oxidation potentially leads to the
formation of additional cross-links. Experimental stud-
ies
49,58,83,104
report that corneal stiffness significantly
increased after CXL and clinical studies
105,106
could
demonstrate that the progression of keratoconus could be
stopped. CXL treatment induces keratocyte apoptosis in
the anterior cornea. Therefore, current endothelial safety
considerations restrict the treatment to corneal thicknesses
of >400 lm with the current irradiation settings used in
clinical practice.
107
One to two weeks post surgery a demar-
cation line can be observed in a depth of approximately
300 lm,
108
which potentially arises from a change in the
refractive index and may indicate the zone of effective cor-
neal stiffening.
105
CXL has been shown to stabilise corneal
ectasia on the long-term.
106
In an ex vivo study,
49
corneal
stiffness increased by 329% in human and by 72% in por-
cine corneas after CXL treatment.
Proteoglycan treatment
Proteoglycans are an essential requisite for the interaction
and mutual binding of ECM components. Decorin is an
important regulatory element of the collagen fibril assem-
bly. Studies on decorin-null mice presented a disrupted col-
lagen fibril structure and organisation especially in the
posterior cornea.
109
Crystallography analysis of corneal
samples with a truncated decorin mutation confirmed this
finding.
110
The administration of decorin core protein to a
keratoconic cornea therefore might have the potential to
re-establish the physiologic collagen structure and halt the
progressing ectasia. A recent experimental study showed
that decorin application induced a stiffening of 92% in
porcine eyes.
111
Compared to CXL with a 72% stiffening in
porcine eyes,
49
decorin core treatment does not require de-
epithelialisation nor UV irradiation and therefore might be
less invasive. It is yet however unclear how long the stiffen-
ing effect will last and if the same results can be obtained
in vivo.
SMILE lenticule implantation
SMILE lenticule implantation aims at correcting hyper-
opia. It requires a donor lenticule from a patient undergo-
ing a high-dioptre myopic SMILE surgery, which
subsequently is implanted in the previously created cor-
neal pocket of the recipient eye. The central tissue addi-
tion allows then to correct the refraction.
112,113
While the
primary objective of this surgery is clearly refractive, add-
ing tissue locally also has a biomechanical effect: An
increased corneal thickness reduces the longitudinal stress,
which in turn leads to a flattening of the corneal curva-
ture. This unintended flattening acts contrary to the
desired central steepening, and might explain why only
50% of the expected refractive correction were achieved
after SMILE lenticule implantation.
112
Animal models for corneal biomechanics
Most species present a lower corneal stiffness and a higher
viscoelastic creep behaviour than humans, which might be
attributed to differences in the fibrillar collagen
arrangement.
11
For ex vivo experiments, freshly enucleated porcine cor-
neas are often used
49,58,64,70,87,88,111
because of their similar
anatomy compared to the human cornea. In view of
anatomical differences only a less developed or absent Bow-
man’s membrane
114–116
and a higher corneal thickness
(666 lm centrally)
117
becomes apparent in the porcine
cornea. In view of biomechanical properties
52
however,
porcine corneas have different stress-relaxation properties
and are less stiff than human corneas.
118,119
Nevertheless –
considering their abundant availability –porcine eyes are
widely accepted as a model for biomechanical studies of the
cornea.
For in vivo studies, rabbit corneas are widely used due to
their large corneas –with a diameter of 13.2 mm and a cor-
neal radius of 7.3 mm.
120
In view of biomechanical proper-
ties, at low IOP rabbit corneas deform non-linearly, while
human corneas do not deform at all –at higher IOP the
stress-strain relation is more similar and linear in both spe-
cies.
50
Recently, our group has established a corneal biome-
chanics model in the mouse eye.
121
We observed a linear
stress-strain relation similar to rabbit corneas, which could
make the mouse an attractive model for studies addressing
the molecular origin of biomechanical parameters.
©2017 The Authors Ophthalmic & Physiological Optics ©2017 The College of Optometrists 7
S Kling and F Hafezi Corneal biomechanics –a review
Computational modelling of corneal biomechanics
Before any prediction of reinforcing treatments or refrac-
tive surgical interventions can be performed, it is important
to construct a representative model of the intact eye. While
analytical models are less demanding computationally, they
only offer limited flexibility and are not suitable to individ-
ual patient modelling. Most biomechanical simulations in
ophthalmology therefore use numerical approaches.
Depending on the relevant characteristics and the desired
degree of accuracy, the model may consider species-specific
input data such as collagen fibril orientation
122
and
patient-specific
123
topography and pachymetry data. For
this purpose, fibril orientation may be defined by using an
anisotropic material and corneal elevation coordinates can
be directly used to define the nodes of a finite element
model. A more difficult issue is to account for the IOP.
Typically, the model is defined for the stress-free geometry
–which however is unknown for the cornea. To overcome
this issue, inverse modelling needs to be performed: Either
the IOP-induced stress is computed step-wise until the ini-
tial stress state of the cornea is determined,
124
or the pro-
voked deformation is calculated step-wise and subtracted
from the stressed geometry in order to obtain the stress-free
geometry.
123
For final validation purposes, the model can be applied
to simulate an experiment. For inflation experiments, the
comparison of model predictions and experimental
measurements could previously confirm a good
performance.
125,126
Corneal ectasia and corneal cross-linking
Numerical simulations might be a helpful tool to predict
the individual success rate of CXL in stopping progression
of ectasia, but also to predict the associated corneal re-
shaping and hence refractive changes. Several in silico
(computational) studies have predicted the weakening pro-
file of a cornea presenting keratectasia
127
and the expected
response to CXL treatment.
123,127
These simulations could
confirm the clinically observed topographic flattening after
CXL,
127
but showed important inter-patient variability
indicating the need for patient-specific modeling.
123
In a
specific attempt to reduce astigmatism, the simulation of
patterned CXL has shown promising effects.
128
Refractive surgery
One of the major difficulties in refractive surgery is the
uncertainty how much tissue can be ablated from a
patient’s cornea without inducing postoperative ectasia.
Several years ago, computer models addressed the potential
of myopic and astigmatic correction by incision
surgery.
129,130
More recently, simulations are applied to
estimate the long-term impact of laser ablative surgery:
PRK surgery showed to increase the corneal stress by
approx. 25%,
131
while LASIK surgery was predicted to
induce a 55% corneal weakening.
132
A comparison between
LASIK and SmILE refractive surgery concluded that SmILE
increases the corneal stress to a lesser amount than
LASIK,
133
which also has been suggested theoretically.
134
Further simulations could show that the refractive outcome
after LASIK depends on the inherent corneal stiffness –not
only on the amount of tissue ablated,
135
and that tonome-
try underestimates the actual IOP following PRK or LASIK
surgery.
130
Intra-corneal ring segment (ICRS) implantation
ICRSs serve as a re-shaping and homogenising element in
highly distorted corneal surfaces.
136
They are used to
improve the visual outcome, but also to make the corneal
surface better suited for contact lens wear. The corneal
response to ICRS implantation is mostly geometrical and
to a minor extent mechanical: The arc length of the cornea
is reduced leading to a flatter corneal curvature and a
slightly shorter axial length of the eye.
137
The weaker tissue
regions will be deformed more strongly. While there are
few publications addressing the simulation of ICRS implan-
tation,
136–138
most of them only predict the average
response of the cornea and do not allow patient-specific
analyses: The thicker the ICRS, the higher the myopic
correction. Up to date, only one study presented a patient-
specific ICRS model, which however showed a consis-
tent overestimation compared to the actual post-surgical
outcome.
139
Disclosure
SK (none), FH (none).
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Sabine Kling is a postdoctoral researcher in the Ocular Cell Biology group at the
University of Zurich, Switzerland, and investigates the relationship between cor-
neal biomechanics and gene expression. She also develops models to optimise cor-
neal cross-linking and refractive surgeries. In 2009, Kling graduated in Physical
Engineering with honours from the University of Isny, Germany. She performed
her pre-doctoral studies at the Optics Institute of the Spanish Council for Scien-
tific Research in Madrid, where she investigated the measurement, modification
and simulation of corneal biomechanics. In 2011, she earned her MSc and in 2014
her PhD degree in Vision Sciences, both with honours from the University of Val-
ladolid, Spain. Kling’s scientific work has been cited more than 396 times, she has
a cumulative impact factor of 60, and an h-index of 10.
Farhad Hafezi is a Swiss eye surgeon and researcher. Hafezi holds professorships
at the University of Geneva and University of Southern California, Los Angeles.
He also serves as the chief medical officer of the ELZA Institute in Zurich,
Switzerland, where he conducts his surgical activities. Hafezi is internationally
recognized as a pioneer of corneal cross-linking (CXL) for treating keratoconus
and a pacemaker in translating CXL principles to new applications like infec-
tions. In both 2014 and 2016, he was voted by his peers onto the “PowerList
100.” This list comprises the 100 top most influential people in global ophthal-
mology. Clinically, Hafezi’s expertise includes corneal diseases, dystrophies and
degenerations as well as complication management related to refractive surgery.
His research is dedicated to understanding corneal diseases with a special
emphasis on ocular cell biology. Hafezi’s scientific work has so far been cited
more than 5300 times, he has a cumulative impact factor of 460, and an h-index
of 38.
©2017 The Authors Ophthalmic & Physiological Optics ©2017 The College of Optometrists 13
S Kling and F Hafezi Corneal biomechanics –a review
