ArticlePDF Available

Non-Invasive and Non-Destructive Determination of Corneal and Scleral Biomechanics Using Vibrational Optical Coherence Tomography: Preliminary Observations

  • Placental Analytics, LLC, NY, USA
Materials Sciences and Applications, 2018, 9, 657-669
ISSN Online: 2153-1188
ISSN Print: 2153-117X
10.4236/msa.2018.97047 Jun. 29, 2018 657 Materials Sciences and Applications
Non-Invasive and Non-Destructive
Determination of Corneal and Scleral
Biomechanics Using Vibrational Optical
Coherence Tomography: Preliminary
Frederick H. Silver1*, Ruchit G. Shah2, Dominick Benedetto3
1Department of Pathology and Laboratory Medicine, Robert Wood Johnson Medical School, Rutgers, The State University of New
Jersey, Piscataway, NJ, USA
2Graduate Program in Biomedical Engineering, Rutgers, The State University of New Jersey, Piscataway, NJ, USA
3Morristown Ophthalmology Associates, Morristown, NJ, USA
Experimental measurements made in this study on human and porcine eyes
suggest that the resonant frequency for both cornea and sclera varies
from 130
to 150 Hz and increases slightly with increasing intraocular pressure. The va
ues of the moduli calculated using the experimental values of the thickness are
close to 2 MPa. Similar values of the modulus for cornea and sclera suggest
that there is very little stress concentration at the cornea-
scleral junction and
that any stress concentration that occurs probably resides at the scleral a
tachment laterally and posteriorly. These moduli are close to those measured
in vivo
on human skin suggesting
that the mechanism of tensile deformation
of skin, cornea and sclera are similar. Our results suggest that the modulus of
cornea and sclera can be measured non-invasively and non-destructively u
ing vibrational OCT. Results of these studies will assist cli
nicians to better
understand the influence of biomechanics on the outcome of corneal refra
tive surgery as well as
the pathogenesis of eye disorders such as glaucoma,
myopia and keratoconus.
Collagen, Cornea, Sclera, Skin, Biomechanics, Vibrational OCT, Optical
Coherence Tomography (OCT), Modulus, Resonant Frequency, Mechanical
Properties, Myopia, Keratoconus, Glaucoma
How to cite this paper:
Silver, F.H., Shah,
.G. and Benedetto, D. (2018) Non-
and Non
-Destructive Determination of Cor-
neal and Scleral
Biomechanics Using Vi-
brational Optical Coherence Tomography:
Preliminary Observations
and Applications
, 657-669.
April 24, 2018
June 26, 2018
June 29, 2018
Copyright © 201
8 by authors and
Research Publishing Inc.
This work is licensed under the Creative
Commons Attribution International
License (CC BY
Open Access
F. H. Silver et al.
10.4236/msa.2018.97047 658 Materials Sciences and Applications
1. Introduction
The cornea and its tear film form the anterior superficial structure of the eye.
The cornea functions both as a clear optical lens, focusing light on the retina and
a protective structure for the eye’s inner elements. It is an aspheric, prolate
(steeper centrally than peripherally), curved structure and the most significant
refractive element of the eye providing 45 diopters of the total 65 diopters of re-
fractive power for an average sized eye.
Corneal clarity is maintained by the uniform spacing of its stromal collagen
fibrils [1] which comprise 80% of the cornea’s structure and the majority of its
strength [2]. The biomechanics of the cornea has been studied extensively in an
attempt to understand and predict the response of the cornea to surgical and ex-
ternal trauma as well as its response to common systemic and corneal degenera-
tive diseases [3] [4] [5] [6].
Corneal incisions, laser reshaping procedures and systemic and corneal dege-
nerative diseases can weaken corneal structure. In some cases, these influences
can lead to unpredictable changes in corneal shape and clarity. Collagen cross
linking with UV activated riboflavin has the capability to stiffen and strengthen
the stroma [7].
Corneal biomechanics has been evaluated by
in vitro
studies of tensile proper-
ties of corneal samples, pressure displacement studies of inflated whole human
ocular samples, and
in vivo
measurements of corneal displacement by air puff
indentation [3]-[11]. The need for a standard method to calibrate ocular biome-
chanical measurements makes it difficult to interpret many of the studies re-
ported in the literature. For example, the reported moduli of the cornea vary
from 0.250 MPa [3] to over 35 MPa [9] [10]. This large variation in measure-
ment may be due to: 1) strain dependence of the mechanical behavior, 2)
strain-rate dependence 3) assumption that the tissue deforms at constant vo-
lume, and 4) difficulties in measuring the tangent to the stress-strain curve re-
quired to calculate the modulus [12].
The corneal stromal is composed of layers of collagen fibrils that are oriented
at different angles depending on the anatomic location. The stroma is reported
to be composed of 8% water, 15% collagen and 7% non-collagenous proteins and
provides the tensile resistance (stiffness also termed modulus) to deformation
[3] [4] [5].
A variety of methods have been used to evaluate the mechanical properties of
extracellular matrix (ECM) over the last 30 years including uniaxial and biaxial
tensile testing, indentation and rotational tests, ultrasound elastography (UE),
optical coherence tomography (OCT), optical coherence elastography (OCE),
and OCT combined with vibrational analysis [12] [13] [14] [15]. Some of these
techniques assume the following materials properties: that the material is linear
elastic, Poisson’s ratio is close to 0.5 (stretching occurs at constant volume) and
that viscoelasticity does not dramatically affect the resulting properties [12]. In
addition, ECMs are non-linear materials that have an upward curvature to the
F. H. Silver et al.
10.4236/msa.2018.97047 659 Materials Sciences and Applications
stress-strain curve. This makes determination of the stiffness (tangent to the
stress-strain curve) and other mechanical properties very difficult to quantify
since the tangent to the stress-strain curve is constantly changing [12] [13] [14]
We recently reported the use of OCT and vibrational analysis to image and
evaluate the mechanical properties of a number of ECMs including human skin,
decellularized human dermis, pig skin, human scar, bovine cartilage, and bovine
subchondral bone [12] [16] [17]. The correlation between modulus measure-
ments made on human dermis using standard tensile testing
in vitro
and vibra-
tional OCT
in vitro
suggests that the two methods give similar values of the
modulus [16] [17]. Beyond these calibration studies, vibrational OCT has been
in vivo
to image and report the differences in mechanical properties of
human skin and scar tissues [17]. In this paper, we report images and prelimi-
nary biomechanical observations of the elastic modulus of porcine and human
cornea and sclera using vibrational OCT measurements on whole eyes. The cal-
culated values of modulus are compared to values reported for other ECMs
composed of fibrous collagens.
2. Methods
2.1. Sample Preparation
Human decellularized dermis was obtained from allograft tissue as described
previously and was tested after immersion in phosphate buffer solution as de-
scribed elsewhere [16] [17]. All samples were tested wet after soaking in phos-
phate buffer solution at pH 7.4 for at least 30 minutes. Processing and testing
steps were conducted at 22˚C.
Human and porcine whole eyes were tested
in vitro
to demonstrate the use of
the OCT and vibrational techniques to measure the modulus of ocular tissues
The porcine eyes were obtained from Spear Products (Coopersburg, Pa) and the
human eyes were obtained from Eversight Eye Bank (Chicago, IL).
2.2. Imaging
OCT images of cornea and sclera were made using a Lumedica OQ labscope
(Lumedica, Inc., Durham, NC) operating in the scanning mode. Sample thick-
nesses for cornea and sclera were measured from OCT images using the Lume-
dica device as well as the laboratory OCT [16] [17]. OCT images of the cornea
and sclera are shown in Figure 1.
2.3. Mechanical Testing
Incremental Stress-Strain Tensile Measurements
in Vitro
Calibration samples of decellularized human dermis were tested in uniaxial
tension at 22˚C by adding a strain increment and then measuring the load before
an additional strain step was added as described previously [16] [17]. Axial de-
formations were applied through adjustment of a graduated translation stage.
F. H. Silver et al.
10.4236/msa.2018.97047 660 Materials Sciences and Applications
Figure 1. Typical images of the cornea (right) and sclera(left) from a human eye bank eye
obtained using a Lumedica OQ Labscope at low intraocular pressure (7 mm Hg).
The resulting axial force was measured by the force gage and recorded for sub-
sequent calculations. Stress values were calculated from the force divided by the
cross-sectional area. Strains were calculated by dividing the change in length by
the original length based on the movement of the translational stage after each
strain increment was added. The tensile modulus was calculated from a tangent
drawn to the stress-strain curve at the strain increment used as described pre-
viously [16] [17].
2.4. Calibration Studies
A variety of samples made from silicone rubber, decellularized human dermis,
pig skin, and chemically modified decellularized dermis were tested in uniaxial
tension and using vibrational analysis to establish a calibration curve between the
moduli calculated from tensile measurements and those derived from vibrational
in vitro
. These results have been published elsewhere [16] [17].
The relationship between the modulus measured using vibrational and tensile
measurements was reported to be approximately linear and the equation of the
line was found to be:
1.026 0.0046Ev Et= +
are the moduli measured using vibrational and tensile mea-
surements, respectively and are in MPas. The correlation coefficient between
these moduli is 0.984 as previously reported [16] [17]. The relationship between
tensile and vibrational moduli was approximated using Equation (1). The ma-
terial behavior was reported to be reversible for strains less than about 14% and
for at least three cycles of tensile testing [16] [17]. At the resonant frequency, the
modulus measured is within 3% to 4% of being perfectly elastic [16] [17].
The viscous component was estimated from the driving frequency peak, by
dividing the change in frequency at the half height of the peak (
3 db down
from maximum peak in power spectrum) by the driving frequency. This method
is known as the half-height bandwidth method discussed by Paul Macioce
( [18].
2.5. Vibrational OCT Experiments in Vitro
Transverse forces were applied to the sample by positioning an acoustic loud-
F. H. Silver et al.
10.4236/msa.2018.97047 661 Materials Sciences and Applications
speaker (IntervoxS225RA-40) beneath the sample. A function generator (Agi-
lent) was used to drive the speaker with sinusoidal waveforms at varying ampli-
tudes and frequencies as described previously [16] [17].
Transverse sample displacement was measured by spectral-domain optical
coherence tomography (SD-OCT), a non-contact, interferometric technique as
discussed previously [16] [17]. The SD-OCT system uses a fiber-coupled super-
luminescent diode light source with 1325 nm center wavelength and 100 nm
bandwidth (full-width at half maximum) [16] [17].
The resonant frequency of each sample was initially estimated at a single point
by measuring the transverse displacement resulting from sinusoidal driving fre-
quencies ranging from 50 Hz to 1000 Hz, in steps of 50 Hz as described pre-
viously [16] [17]. Once the region where the maximum frequency was identified,
smaller steps of 10 Hz were used to more accurately identify the peak frequency
and the actual resonant frequency,
( )
The modulus, E, from
in vitro
vibrational studies was determined using Equa-
tion (2) where
are the sample mass, length and cross-sectional area.
The resonant frequency was determined after correction for the resonant fre-
quencies exhibited by the speaker and any interference due to line fluctuations.
2.6. In Vitro Determination of the Resonant Frequency of Cornea
and Sclera
In vitro
studies of the mechanical properties of cornea and sclera were conducted
by fixing the whole eye in a Styrofoam block using needles and then vibrating the
eye from beneath the block using the sinusoidal sound waves. The block dis-
placements as a function of frequency were measured without the eye in place
and were compared to the displacements measured in the presence of the eye.
The resonant frequency of the cornea and sclera were converted into a modulus
using Figure 2, a calibration curve of modulus times sample thickness versus re-
sonant frequency for decellularized human dermis, porcine tissues, bovine carti-
lage, and human skin. The sample thickness was determined from OCT images.
Corneas were inflated by injecting normal saline into the globe using a needle
and syringe. Human eyes were inflated to intraocular pressures of 7 mm Hg (low
pressure) and 60 mm Hg (high pressure); the pressure was measured using a
Schiotz Tonometer (Tiger Medical, Irvington, NJ). Eyes were mounted in a
support structure carved out of a block of Styrofoam that was clamped in place
using a compressive force applied by mechanical grips at either end of the block.
The whole eye was held in place by inserting three or more needles through the
scleral insertion of the ocular rectus muscles anchoring them to the Styrofoam.
The resonant frequency of the cornea and sclera were converted into values of
the modulus using Figure 2 and the experimentally measured sample thickness
determined from OCT images.
F. H. Silver et al.
10.4236/msa.2018.97047 662 Materials Sciences and Applications
Figure 2. Calibration curve showing the relationship between the product of the modulus (E) times the tissue thickness versus
resonant frequency measured using vibrational OCT for diffferent tissues. The calibration curve includes points from pig fat and
elastic tissue, human decellularized dermis at different strains, chemically modified decellularized dermis, and bovine femoral
3. Results
Stress-strain curves for inflated eyes obtained from the literature [18] were
compared to those of decellularized human dermis previously published [16]
[17] as shown in Figure 3. The stress-strain curves for decellularized human
dermis are similar in shape to the curves for porcine and human eyes consistent
with other tissues containing fibrous collagen networks [15]. These curves show
increased slopes with increasing strains. The tensile stress-strain curves of de-
cellularized human dermis and inflated eyes are composed of low and high
modulus regions consistent with previous reports on mechanical measurements
on human dermis and skin [15] [16] [17]. The difference in the length of the low
modulus region is related to the strain required to recruit the collagen fibrils and
fibers along the tensile direction [15]. The similarity in the shape of the
stress-strain curves between human and porcine eyes and decellularized dermis
indicate that the stress-strain behavior has a similar mechanism in these tissues,
e.g., at low strains the collagen fibrils and fibers are only partially recruited in the
loading direction and become fully recruited at high strains increasing the value
of the modulus.
Vibrational OCT was used to measure the mechanical properties of porcine
and human corneas and scleras
in vitro
. The results of previously published data
on decellularized human dermis, human skin, pig skin, human scar, and bovine
cartilage were used to calibrate and interpret the
in vitro
studies. The resonant
frequencies of human cornea and sclera were measured from vibrational OCT
studies at both low (7 mm Hg) and high (50 mm Hg) intraocular pressures as
shown in Figure 4. Resonant frequencies were obtained by determining the fre-
F. H. Silver et al.
10.4236/msa.2018.97047 663 Materials Sciences and Applications
quency at which the maximum displacement was observed based on measure-
ments at a single point about 14 μm in diameter. The resonant frequencies and
calculated moduli for porcine cornea and sclera and human cornea and sclera
from whole eye measurements are listed in Table 1. The calculated values of the
modulus for cornea and sclera were determined using Figure 2 and are about 2
MPas (Table 1) similar to those reported for decellularized human dermis and
human skin [16] [17]. Note the viscous loss reported for cornea and sclera at the
resonant frequency is between 2% and 3% (Table 1).
Table 1. Resonant frequency and calculated modulus for central cornea, corneal-scleral
junction, and sclera at low (7 mm Hg) and high (50 mm Hg) intraocular pressures. The
viscous response is presented as a percent of the elastic response.
Resonant Frequency
Viscous %
Human Cornea Center 7 130 1.84 2.14
50 140 2.07 1.97
Human Corneal Junction 7 130 1.84 2.59
50 140 2.07 2.24
Human Sclera 7 130 1.8 3.15
50 150 2.27 2.97
Porcine Cornea 7 150 2.37 3.22
Porcine Corneal Junction 7 140 2.07 3.02
Porcine Sclera 7 130 1.85 3.34
Figure 3. Tensile stress-strain curve for decellularized dermis obtained from tensile stress-strain measurements [16] [20] and
human eyes from inflation tests [19]. Note the similarity between the shapes of the stress-strain curve for decellularized dermis
composed largely of type I collagen and that of whole eyes. The upward curvature involves increased recruitment of collagen fibers
with the loading direction with increasing strain and leads to the increased slope of the stress-strain curve.
F. H. Silver et al.
10.4236/msa.2018.97047 664 Materials Sciences and Applications
Figure 4. Weighted displacement versus frequency for human cornea (a) (b) and sclera (c), (d) at low (7 mm Hg) and high (50
mm Hg) pressures. The resonant frequency is determined as the frequency at which the maximum displacement occurs. Note
peaks from the Styrofoam blocks and line noise were removed. The resonant frequency changes are small with increased pressure.
The increased moduli at higher pressures are listed in Table 1.
4. Discussion
The limited ability of researchers and clinicians to correlate changes in OCT
images of cornea and sclera with the biomechanics of the ECM underscores the
need to develop new non-invasive methods to understand and diagnose the na-
ture of common eye disorders and surgical interventions [6]. While the me-
F. H. Silver et al.
10.4236/msa.2018.97047 665 Materials Sciences and Applications
chanical properties of ECMs are complex, much progress has been made in un-
derstanding the strain-rate dependence, non-linearity and compressibility of
these tissues [15] [16] [17]. By calculating the modulus at the resonant frequency
it is possible to eliminate the viscous contribution to the mechanical properties
[20]. By pulsing tissues with a series of sinusoidal sound waves as a function of
the frequency, the viscous contribution can be shown to almost disappear at the
resonant frequency [20]. The viscous contribution of skin has been shown to as
high as 25% at low strains and strain-rates [15] and as low as 3% to 4% at high
strains and strain-rates [20]. However, measurements made at the resonant fre-
quency simplify the analysis since they are independent of strain-rate.
The correlation between modulus measurements on decellularized human
dermis made using standard tensile testing
in vitro
and vibrational OCT suggest
that measurements made using vibrational OCT give results that are consistent
with tensile testing, a “gold standard method” for measuring mechanical proper-
ties of ECMs [15] [16] [17]. Without comparison to a standard technique, mod-
uli measurements made with new methods such as vibrational OCT cannot be
validated [12].
Tensile incremental and constant rate-of-strain measurements made on tis-
sues have been the gold standard for determination of the mechanical properties
of tissues for decades [13] [14] [15]. Many techniques require the assumption
that the tissue density is near 1.0 and that Poisson’s ratio is 0.5 (stretching with-
out a change in volume). The later has been shown to vary between 0.38 and 0.75
for decellularized dermis [21]. The assumption that Poisson’s ratio is 0.5 will
lead to errors in modulus calculations. However, by measuring the modulus at
the resonant frequency using vibrational analysis and OCT and using Equations
(1) and (2), the elastic modulus can be calculated for ECMs without the need to
make any assumptions.
Experimental measurements made on human and porcine eyes suggest that
the resonant frequency for human and porcine cornea and sclera vary from 130
to 150 Hz and increase slightly with increasing pressure. The values of the mod-
uli calculated from Figure 3 using the experimental values of the thickness are
about 2 MPa and fall in the low modulus region of the stress-strain curve
[Figure 3] which is similar to the value found for the modulus of skin
in vivo
[17]. Similar values of the modulus for cornea and sclera suggest that there is
very little stress concentration at the cornea-scleral junction and that any stress
concentration that occurs would probably reside at the scleral attachment lateral-
ly.It has been noted that blunt trauma causes scleral rupture by suddenly elevating
intraocular pressure. Ruptures are most commonly observed at the insertions of
the intraocular muscles or at the limbus, where the sclera is thinnest [22].
These measured values of modulus are similar to values reported
in vivo
skin using vibrational OCT [16] [17]. The similarity between normal values of
the moduli of skin, cornea and sclera suggest that the resting tension in these
tissues is likely to be similar
in vivo
and this tension may act as a baseline for
F. H. Silver et al.
10.4236/msa.2018.97047 666 Materials Sciences and Applications
maintaining normal mechanotransduction. Increased or decreased tension (and
moduli) may signal the up- or down regulation of mechanotransduction [23]
that may ultimately lead to tissue fibrosis in skin, increased tension in glaucoma
or tissue atrophy as observed in keratoconus.
The fact that the modulus calculated from different ECMs including skin, car-
tilage, cornea, sclera and dermis all are similar (Figure 5) suggests that fibrous
collagen is the load bearing macromolecule in these tissues and other tissue
components are in parallel with the collagen and do not limit tissue deformation
or prevent premature mechanical failure [23]. In some vessel walls, other ma-
cromolecular networks such as smooth muscle are in series with the collagen
network lowering the modulus of these tissues [24].
5. Conclusion
Our results indicate that the modulus of cornea and sclera can be measured
non-invasively and non-destructively using vibrational OCT. This will assist cli-
nicians to better understand the influence of biomechanics on the outcome of
refractive surgery [25] and some common eye diseases such as glaucoma
[26]-[32], myopia [33], and keratoconus [34] [35] [36]. It has been observed that
the modulus of keratoconus corneas is lower than that of normal tissue [7] and
that scleral stiffening occurs in glaucoma [37] associated with increased collagen
alignment and birefringence [38]. Future studies with vibrational OCT will focus
Figure 5. Plot of vibrational modulus versus the ratio of the resonant frequency per unit thickness for human decellularized
dermis, human skin and scar, bovine cartilage, porcine fat and human cornea and sclera. The modulus for fat is about 0.03 MPa,
elastic tissue 0.4 to 0.8 MPa, and collagen 2.0 to 7.0 MPa. Normal skin has a modulus of about 2 MPa and scar of about 7 MPa.
Normal cornea and sclera have moduli of about 2 MPa at low and high intraocular pressures very similar to normal skin. Note
that softening or stiffening of the ECMs found in ocular tissues would lead to lower (chemically treated dermis) or higher (scar)
values of the moduli, respectively that would be measureable using vibrational OCT.
F. H. Silver et al.
10.4236/msa.2018.97047 667 Materials Sciences and Applications
in vivo
measurements of corneal and scleral biomechanics to study how col-
lagen structure is altered in ocular diseases.
[1] Benedict, G. (1971) Theory of Transparency of the Eye.
Applied Optics
, 10, 459-
[2] Jue, B. and Maurice, D.M. (1986) The Mechanical Properties of the Rabbit and
Human Cornea.
Journal of Biomechanics
, 19, 847-853.
[3] Andreassan, T.T., Simonsen, A.H. and Oxlund, H. (1980) Biomechanical Properties
of Keratoconus and Normal Corneas.
Experimental Eye Research
, 31, 435-441.
[4] Roberts, C.J. (2014) Concepts and Misconceptions in Corneal Biomechanics.
nal of Cataract & Refractive Surgery
, 40, 862-869.
[5] Dupps Jr., W.J. and Wilson, S.E. (2006) Biomechanics and Wound Healing in the
Experimental Eye Research
, 83, 709-720.
[6] Ruberti, J.W., Roy, A.S., Cynthia, J. and Roberts, C.J. (2011) Corneal Biomechanics
and Biomaterials.
Annual Review of Biomedical Engineering
, 13, 269-295.
[7] Wollensak, G. and Iomdina, E. (2009) Biomechanical and Histological Changes af-
ter Corneal Crosslinking with and without Epithelial Debridement.
Journal of Cat-
aract & Refractive Surgery
, 35, 540-546.
[8] Ambekara, R., Kimani, C., Toussaint Jr., B. and Johnson, A.W. (2011) The Effect of
Keratoconus on the Structural, Mechanical, and Optical Properties of the Cornea.
Journal of the Mechanical Behavior of Biomedical Materials
, 4, 223-236.
[9] Nash, I.S., Peter, R., Green, P.R. and Foster, C.S. (1982) Comparison of Mechanical
Properties of Keratoconus and Normal Corneas.
Experimental Eye Research
, 35,
[10] Elsheikh, A. and Alhasso, D. (2009) Mechanical Anisotropy of Porcine Cornea and
Correlation with Stromal Microstructure.
Experimental Eye Research
, 88, 1084-1091.
[11] Elsheikh, A., Geraghty, B., Alhasso, D., Knappett, J., Campanelli, M. and Rama, P.
(2010) Regional Variation in the Biomechanical Properties of the Human Sclera.
Experimental Eye Research
, 90, 624-633.
[12] Silver, F.H. and Shah, R. (2016) Measurement of Mechanical Properties of Natural
and Engineered Implants.
Advances in Tissue Engineering and Regenerative Medi-
, 1, 1-9.
[13] Yamada, H. and Evans, F.G. (1970) Strength of Biological Materials. University of
[14] Fung, Y.C. (1993) Biomechanics: Mechanical Properties of Living Tissue. 2nd Edi-
tion, Springer.
[15] Dunn, M.G. and Silver, F.H. (1983) Viscoelastic Behavior of Human Connective
Tissues: Relative Contribution of Viscous and Elastic Components.
Tissue Research
, 12, 59-70.
[16] Shah, R., Pierce, M.C. and Silver, F.H. (2017) A Method for Non-Destructive Me-
F. H. Silver et al.
10.4236/msa.2018.97047 668 Materials Sciences and Applications
chanical Testing of Tissues and Implants.
Journal of Biomedical Materials Research
Part A
, 105, 15-22.
[17] Shah, R.G., DeVore, D. and Silver, F.H. (2018) Biomechanical Analysis of Decellu-
larized Dermis and Skin: Initial
in Vivo
Observations Using Optical Cohesion To-
mography and Vibrational Analysis.
Journal of Biomedical Materials Research Part
, 106, 1421-1427.
[18] Papagiannopoulos, G.A. and Hatzigeorgiou, G.D. (2011) On the Use of the
Half-Power Bandwidth Method to Estimate Damping in Building Structures.
Dynamics and Earthquake Engineering
, 31, 1075-1079.
[19] Elsheikh, A., Alhasso, D. and Rama, P. (2008) Biomechanical Properties of Human
and Porcine Corneas.
Experimental Eye Research
, 86, 783-790.
[20] Shah, R.G. and Silver, F.H. (2017) Viscoelastic Behavior of Tissues and Implant
materials: Estimation of the Elastic Modulus and Viscous Contribution Using Opt-
ical Coherence Tomography and Vibrational Analysis.
Journal of Biomedical
Technology and Research
, 3, 105-109.
[21] Shah, R., DeVore, D. and Pierce, M.G. (2016) Morphomechanics of DermisA
Method for Non-Destructive Testing of Collagenous Tissues.
Skin Research and
, 23, 399-406.
[22] Prabhat, K.P. and Sanaz, A.L. (2007) Ocular Emergencies.
American Family Physi-
, 76, 829-836.
[23] Silver, F.H. and Silver, L.L. (2017) Gravity, Mechanotransduction and Healing.
Journal of Biomedical Engineering
, 3, 1023.
[24] Snowhill, P.B. and Silver, F.H. (2005) A Mechanical Model of Porcine Vascular
TissuesPart II: Stress-Strain and Mechanical Properties of Juvenile Porcine Blood
Cardiovascular Engineering
, 5, 157-169.
[25] Byun, Y., Kim, S., Lazo, M., Choi, M., Kang, M., Lee, J., Yoo, Y., Whang, W. and
Joo, C. (2018) Astigmatic Correction by Intrastromal Astigmatic Keratotomy dur-
ing Femtosecond Laser-Assisted Cataract Surgery: Factors in Outcomes.
Journal of
Cataract & Refractive Surgery
, 44, 202-208.
[26] Sun, L., Shen, M., Wang, J., Fang, A., Xu, A., Fang, H. and Lu, F. (2009) Recovery of
Corneal Hysteresis after Reduction of Intraocular Pressure in Chronic Primary An-
gle-Closure Glaucoma.
American Journal of Ophthalmology
, 6, 1061-1066.
[27] Pensyl, D., Sullivan-Mee, M., Torres-Monte, M., Halverson, K. and Qualls, C.
(2012) Combining Corneal Hysteresis with Central Corneal Thickness and Intra-
ocular Pressure for Glaucoma Risk Assessment.
), 10, 1349-1356.
[28] Zhang, C., Tatham, A.J., Abe, R.Y., Diniz-Filho, A., Zangwill, L.M., Weinreb, R.N.
and Medeiros, F.A. (2016) Corneal Hysteresis and Progressive Retinal Nerve Fiber
Loss in Glaucoma.
American Journal of Ophthalmology
166, 29-36.
[29] Medeiros, F.A., Meira-Freitas, D., Lisboa, R., Kuang, T.M., Zangwill, L.M. and
Weinreb, R.N. (2013) Corneal Hysteresis as a Risk Factor for Glaucoma Progres-
sion: A Prospective Longitudinal Study.
, 8, 1533-1540.
F. H. Silver et al.
10.4236/msa.2018.97047 669 Materials Sciences and Applications
[30] Park, J.H., Jun, R.M. and Choi, K.R. (2015) Significance of Corneal Biomechanical
Properties in Patients with Progressive Normal-Tension Glaucoma.
British Journal
of Ophthalmology
, 6, 746-751.
[31] Mansouri, K., Leite, M.T., Weinreb, R.N., Tafreshi, A., Zangwill, L.M. and Medei-
ros, F.A. (2012) Association between Corneal Biomechanical Properties and Glau-
coma Severity.
American Journal of Ophthalmology
, 3, 419-427.
[32] Vu, D.M., Silva, F.Q., Haseltine, S.J., Ehrlich, J.R. and Radcliffe, N.M. (2013) Rela-
tionship between Corneal Hysteresis and Optic Nerve Parameters Measured with
Spectral Domain Optical Coherence Tomography.
s Archive for Clinical and
Experimental Ophthalmology
, 7, 1777-1783.
[33] Chang, P.Y. and Chang, S.W. (2013) Corneal Biomechanics, Optic Disc Morpholo-
gy, and Macular Ganglion Cell Complex in Myopia.
Journal of Glaucoma
, 22,
[34] Martinez-Abad, A. and Pinero, D.P. (2017) New Perspectives on the Detection and
Progression of Keratoconus.
Journal of Cataract & Refractive Surgery
, 43,
[35] Vinciguerra, R., Ambrosio, R., Elsheikh, A., Roberts, C.J., Lopes, B., Morenghi, E.,
Azzolini, C. and Vinciguerra, P. (2016) Detection of Keratoconus with a New Bio-
mechanical Index.
Journal of Refractive Surgery
, 12, 803-810.
[36] Ambrosio, R., Lopes, B.T., Faria-Correia, F., Salomeo, M.Q., Buhren, J., Roberts,
C.J., Elsheikh, A., Vinciguerra, R. and Vinciguerra, P. (2017) Integration of
Scheimpflug-Based Corneal Topography and Biomechanical Assessments for En-
hancing Ectasia Detection.
Journal of Refractive Surgery
, 7, 434-443.
[37] Huang, W., Fan, Q., Wang, W., Zhou, M., Laties, A.M. and Zhang, X. (2013) Colla-
gen: A Potential Factor Involved in the Pathogenesis of Glaucoma.
Medical Science
Monitor Basic Research
, 19, 237-240.
[38] Yamanari, M., Nagase, S., Fukuda, S., Ishii, K., Tanaka, R., Yasui, T., Oshika, T.,
Miura, M. and Yasuno, Y. (2014) Scleral Birefringence as Measured by Polariza-
tion-Sensitive Optical Coherence Tomography and Ocular Biometric Parameters of
Human Eyes
in Vivo
Optical Society of America
, 5, 1391-1402.
... 20,21 In vitro measurements of the tissue modulus of human and porcine corneas by VOCT are reported to be about 2 MPa. 22 In this pilot study, we report the in vivo use of VOCT to determine the elastic moduli of the corneas of healthy human volunteers. ...
... This equation was developed from previously published results of in vitro analyses of different human and porcine soft tissues using uniaxial tensile testing and VOCT analysis, as well as in vivo measurements on human skin. 19,22,24,25 This equation is employed under the assumption that most body soft tissues have a density close to 1.0. 26 ...
... 6,27 These networks may vary in stiffness and orientation depending on the location in the cornea, which may explain the presence of several unique peaks. 22,27,28 Results from previous VOCT studies also suggest that the modulus of peak 1 (approximately 1 MPa) may correspond to the cellular components in the cornea and the modulus of peaks 2 to 5 (approximately 2 to 7 MPa) to the fibrillar collagen in the lamellae and larger collagen fibers. 22,26 Age-dependent variability in moduli values was expected in the process of corneal biomechanical analysis, as reported by other authors. ...
Full-text available
Purpose: To determine the in vivo elastic modulus of the human cornea using vibrational optical coherence tomography (VOCT). Methods: Vibrational analysis coupled with optical coherence tomography (OCT) was used to obtain the resonant frequency (RF) and elastic modulus of corneal structural components. VOCT corneal thickness values were measured using OCT images and correlated with corneal thickness determined with Pentacam (Oculus, Wetzlar, Germany). Moduli were obtained at two locations: central cornea (CC) and inferior cornea (IC). Measurements were obtained with and without anesthetic eye drops to assess their effect on the modulus measurements. Results: VOCT thickness values correlated positively (R2 = 0.97) and linearly (y = 1.039x-16.89) with those of Pentacam. Five RF peaks (1-5) were present, although their presence was variable across eyes. The RF for peaks 1 to 5 in the CC and IC ranged from 73.5 ± 4.9 to 239 ± 3 Hz and 72.1 ± 6.3 to 238 ± 4 Hz, respectively. CC and IC moduli for peaks 1 to 5 ranged from 1.023 ± 0.104 to 6.87 ± 0.33 MPa and 0.98 ± 0.15 to 6.52 ± 0.79 MPa, respectively. Topical anesthesia did not significantly alter the modulus (P > 0.05 for all), except for peak 2 in the CC (P < 0.05). Conclusions: This pilot study demonstrates the utility of VOCT as an in vivo, noninvasive technology to measure the elastic modulus in human corneas. The structural origin of these moduli is hypothesized based on previous reports, and further analyses are necessary for confirmation. Translational relevance: This work presents VOCT as a novel approach to assess the in vivo elastic modulus of the cornea, an indicator of corneal structural integrity and health.
Full-text available
ABSTRACT PURPOSE: To present the Tomographic and Biomehanical Index (TBI), which combines Scheimpflugbased corneal tomography and biomechanics for enhancing ectasia detection. METHODS: Patients from different continents were retrospectively studied. The normal group included 1 eye randomly selected from 480 patients with normal corneas and the keratoconus group included 1 eye randomly selected from 204 patients with keratoconus. There were two groups: 72 ectatic eyes with no surgery from 94 patients with very asymmetric ectasia (VAE-E group) and the fellow eyes of these patients with normal topography (VAE-NT group). Pentacam HR and Corvis ST (Oculus Optikgeräte GmbH, Wetzlar, Germany) parameters were analyzed and combined using different artificial intelligence methods. The accuracies for detecting ectasia of the Belin/Ambrósio Deviation (BAD-D) and Corvis Biomechanical Index (CBI) were compared to the TBI, considering the areas under receiver operating characteristic curves (AUROCs). RESULTS: The random forest method with leave-oneout cross-validation (RF/LOOCV) provided the best artificial intelligence model. The AUROC for detecting ectasia (keratoconus, VAE-E, and VAE-NT groups) of the TBI was 0.996, which was statistically higher (DeLong et al., P < .001) than the BAD-D (0.956) and CBI (0.936). The TBI cut-off value of 0.79 provided 100% sensitivity for detecting clinical ectasia (keratoconus and VAE-E groups) with 100% specificity. The AUROCs for the TBI, BAD-D, and CBI were 0.985, 0.839, and 0.822 in the VAE-NT group (DeLong et al., P < .001). An optimized TBI cut-off value of 0.29 provided 90.4% sensitivity with 96% specificity in the VAE-NT group. CONCLUSIONS: The TBI generated by the RF/LOOCV provided greater accuracy for detecting ectasia than other techniques. The TBI was sensitive for detecting subclinical (fruste) ectasia among eyes with normal topography in very asymmetric patients. The TBI may also confirm unilateral ectasia, potentially characterizing the inherent ectasia susceptibility of the cornea, which should be the subject of future studies. [J Refract Surg. 2017;33(7):434-443.]
Full-text available
Numerous tests have been used to elucidate the mechanical properties of tissues and implants including tensile, compressive, shear, hydrostatic compression and three-point bending in one or more axial directions. The development of a non-destructive test that could be applied to tissues and materials in vivo would promote the analysis of tissue pathology as well as the design of implant materials. In this paper, we review the methods that have been used to evaluate the mechanical properties of tissues and the invasiveness of these methods. There are several fairly new methods that have been evaluated in the literature such as magnetic resonance elastography (MRE), ultrasound elastography (UE), optical coherence tomography (OCT), ocular response analysis (ORA), optical coherence elastography (OCE) and OCT with vibrational analysis that are quite promising. Classical methods such as constant rate-of-strain deformation as well as incremental stress-strain analysis are useful but prove to be too destructive to tissue and therefore have limited value for measuring tissue properties in vivo. While these newer techniques are very useful, they must be modified to consider viscoelastic effects of polymer behavior and compressibility that may occur during deformation in order to provide accurate information about implants and tissues. Non-linear behavior, strain-rate dependence and volumetric effects that occur during mechanical loading of tissues and implants are very important considerations in the measurement of mechanical properties of tissues and implants. Mechanical testing results obtained using these new methods must be compared and be consistent with “gold standard” results obtained from constant rate-of strain experiments.
Full-text available
Purpose: To evaluate the ability of a new combined biomechanical index called the Corvis Biomechanical Index (CBI) based on corneal thickness profile and deformation parameters to separate normal from keratoconic patients. Methods: Six hundred fifty-eight patients (329 eyes in each database) were included in this multicenter retrospective study. Patients from two clinics located on different continents were selected to test the capability of the CBI to separate healthy and keratoconic eyes in more than one ethnic group using the Corvis ST (Oculus Optikgeräte GmbH, Wetzlar, Germany). Logistic regression was employed to determine, based on Database 1 as the development dataset, the optimal combination of parameters to accurately separate normal from keratoconic eyes. The CBI was subsequently independently validated on Database 2. Results: The CBI included several dynamic corneal response parameters: deformation amplitude ratio at 1 and 2 mm, applanation 1 velocity, standard deviation of deformation amplitude at highest concavity, Ambrósio's Relational Thickness to the horizontal profile, and a novel stiffness parameter. The receiver operating characteristic curve analysis of the training database showed an area under the curve of 0.983. With a cut-off value of 0.5, 98.2% of the cases were correctly classified with 100% specificity and 94.1% sensitivity. In the validation dataset, the same cut-off point correctly classified 98.8% of the cases with 98.4% specificity and 100% sensitivity. Conclusions: The CBI was shown to be highly sensitive and specific to separate healthy from keratoconic eyes. The presence of an external validation dataset confirms this finding and suggests the possible use of the CBI in everyday clinical practice to aid in the diagnosis of keratoconus. [J Refract Surg. 2016;32(12):803-810.].
Purpose: To evaluate the 6-month outcomes of femtosecond laser astigmatic keratotomy (AK) combined with femtosecond laser-assisted cataract surgery and identify factors affecting the efficacy of astigmatic correction. Setting: Seoul St. Mary's Hospital, Catholic University of Korea, Seoul, South Korea. Design: Retrospective case series. Methods: Femtosecond laser AK was performed during femtosecond laser-assisted cataract surgery. The keratometric astigmatism, refractive cylinder, corneal hysteresis (CH), and corneal resistance factor (CRF) were measured preoperatively and postoperatively at 1 week, 2 months, and 6 months. Vector analysis to evaluate the 6-month outcomes of femtosecond laser AK and univariable regression analysis to determine the factors influencing the correction index were performed. Results: The study enrolled 89 eyes of 89 patients. The stigmatism type, CH, CRF, and absolute angle of error showed significant correlations with the correction index (P = .041, P = .029, P = .044, and P < .001, respectively). There was a significant difference in the correction index and no difference in keratometric astigmatism between with-the-rule (WTR), against-the-rule (ATR), and oblique astigmatism (P = .044). The keratometric astigmatism with ATR and oblique astigmatism (0.66 diopter [D] ± 0.42 [SD] and 0.46 ± 0.27 D, respectively) was significantly lower than the refractive cylinder (0.92 ± 0.56 D and 0.78 ± 0.43 D, respectively) (P < .05); this was not the case for WTR astigmatism. Conclusions: The efficacy of femtosecond laser AK was affected by the biomechanical properties of the cornea and astigmatism type. Further studies incorporating the individual biomechanical properties of the cornea and total corneal astigmatism in a nomogram are recommended.
Measurement of the mechanical properties of skin in vivo has been complicated by the lack of methods that can accurately measure the viscoelastic properties without assuming values of Poisson's ratio and tissue density. In this paper, we present the results of preliminary studies comparing the mechanical properties of skin and scar tissue measured using a technique involving OCT and vibrational analysis. This technique has been reported to give values of the modulus that correlate with those obtained from tensile measurements made on decellularized dermis [1, 2]. The high correlation between moduli measured using vibrational studies and uniaxial tensile tests suggest that the modulus can be determined by measuring the natural frequency that occurs when a tissue is vibrated in tension. The results of studies on glutaric anhydride treated decellularized dermis suggest that vibrational analysis is a useful technique to look at changes in the properties of skin that occur after cosmetic and surgical treatments are used. Preliminary results suggest that the resonant frequency of scar tissue is much higher than that of adjacent normal skin reflecting the higher collagen content of scar. OCT in concert with vibrational analysis appears to be a useful tool to evaluate processes that alter skin properties in animals and humans as well to study the onset and pathogenesis of skin diseases such as cancer. This technique may be useful to evaluate the extent of wound healing in skin diabetic ulcers and other chronic skin conditions, scar tissue formation in response to implants, and other therapeutic treatments that alter skin properties. This article is protected by copyright. All rights reserved.
Laser refractive surgery has increased markedly in recent years, making the detection of corneal abnormalities extremely relevant. For this reason, an accurate diagnosis of clinical or subclinical keratoconus is critical. Corneal topography is the primary diagnostic tool for keratoconus detection, and pachymetry data and corneal aberrations are also commonly used. Recently, tomographic measurements using optical coherence tomography and corneal biomechanical indices have been used. In incipient and subclinical keratoconus, the use of a single parameter as a diagnostic factor is not sufficiently accurate. In these cases, the use of algorithms and predictive models is necessary. In addition, determining whether the disease will progress is crucial to selecting the most appropriate treatment. Some factors, such as age, keratometric indices, corneal elevation data, and corneal thickness, seem to be useful in predicting keratoconus progression.
Background: Collagenous tissues store, transmit and dissipate elastic energy during mechanical deformation. In skin, mechanical energy is stored during loading and then is dissipated, which protects skin from mechanical failure. Thus, energy storage (elastic properties) and dissipation (viscous properties) are important characteristics of extracellular matrices (ECMs) that support the cyclic loading of ECMs without tissue failure. Methods: Uniaxial stress-strain measurements on decellularized human dermis have been made and compared to results of a non-destructive technique involving optical coherence tomography (OCT) combined with vibrational analysis. In addition, Poisson's ratio has been determined for tensile deformation of decellularized dermis. Results: The modulus of decellularized dermis measured using standard tensile stress-strain tests and that determined from calculations derived from natural frequency measurements give similar results. It is also observed that Poisson's ratio for dermis is between 0.38 and 0.63 after correction for changes in volume that occur during tensile deformation. These results suggest that the assumption that dermis and other ECMs deform at constant volume is incorrect and will lead to differences in the calculated modulus by conventional tensile stress-strain measurements. Conclusions: It is proposed that OCT in conjunction with vibrational analysis is a convenient way to non-destructively measure the modulus of decellularized dermis, ECMs and other materials that have a positive curvature to their stress-strain curves. Tensile deformation of dermis and possibly other ECMs is associated with an increase in Poisson's ratio consistent with a model of fluid expulsion from collagen fibrils during stretching. The value of Poisson's ratio should be considered in analyzing the mechanical properties of ECMs since at least dermis appears to be compressible during tensile deformation. Fluid expression during tensile deformation may play a role in mechanotransduction in skin in a similar manner to cartilage and bone tissue.
Purpose: To investigate the relationship between corneal hysteresis (CH) and progressive retinal nerve fiber layer (RNFL) loss in a cohort of patients with glaucoma followed prospectively over time. Design: Prospective observational cohort study. Methods: One-hundred and eighty-six eyes of 133 patients with glaucoma followed for an average of 3.8 ± 0.8 years, with a median of 9 visits during follow-up. The CH measurements were acquired using the Ocular Response Analyzer (Reichert Instruments, Depew, NY) and RNFL measurements were obtained at each follow up visit using spectral domain optical coherence tomography (SD-OCT). Random-coefficient models were used to investigate the relationship between baseline CH, central corneal thickness (CCT), average intraocular pressure (IOP) and rates of RNFL loss during follow up, while adjusting for potentially confounding factors. Results: Average baseline RNFL thickness was 76.4 ± 18.1 μm and average baseline CH 9.2 ± 1.8 mmHg. CH had a significant effect on rates of RNFL progression. In the univariable model, including only CH as a predictive factor along with time and their interaction, each 1 mmHg lower CH was associated with a 0.13 μm/year faster rate of RNFL decline (P=0.011). A similar relationship between low CH and faster rates of RNFL loss was found using a multivariable model accounting for age, race, average IOP and CCT (P=0.015). Conclusions: Lower CH was significantly associated with faster rates of RNFL loss over time. The prospective longitudinal design of this study provides further evidence that CH is an important factor to be considered in the assessment of the risk of progression in patients with glaucoma.
To investigate the clinical significance of corneal biomechanical properties assessed using an ocular response analyser in patients with progressing normal-tension glaucoma (NTG). In this retrospective study, we included 82 eyes of 82 NTG patients who had been receiving topical anti-glaucoma medications. Patients were allocated to two groups based on the mean value of corneal hysteresis (CH) and the status of progression. The assessment of progression was based on the trend analysis using mean deviation slope. Uni- and multivariable logistic analyses were constructed to identify factors associated with increased odds of progression, including CH, central corneal thickness (CCT), and retinal nerve fibre layer (RNFL) thickness. Forty-six eyes (56.1%) reached the progression criteria. Eyes with progression had lower CCT (530.2±38.6 vs 549.4±38.3 μm, p=0.03), thinner average RNFL thickness (70.6±16.1 vs 82.8±17.4 μm, p<0.01), lower CH (9.4±1.3 vs 10.8±1.4 mm Hg, p<0.01), and lower corneal resistance factor (9.3±1.3 vs 10.4±1.8 mm Hg, p<0.01) than eyes without progression. CH and CCT were significantly correlated (r=0.44, p<0.01). Upon multivariable analysis, CH (β (B)=0.32 per mm Hg lower, p<0.01) and average RNFL thickness (β=0.96 per μm lower, p=0.04) remained statistically significant. Corneal biomechanical properties are correlated and associated with the progression of visual field damage in NTG patients. These findings suggest that CH can be used as one of the prognostic factors for progression, independent of corneal thickness or intraocular pressure. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to
The relationship between scleral birefringence and biometric parameters of human eyes in vivo is investigated. Scleral birefringence near the limbus of 21 healthy human eyes was measured using polarization-sensitive optical coherence tomography. Spherical equivalent refractive error, axial eye length, and intraocular pressure (IOP) were measured in all subjects. IOP and scleral birefringence of human eyes in vivo was found to have statistically significant correlations (r = -0.63, P = 0.002). The slope of linear regression was -2.4 × 10(-2) deg/μm/mmHg. Neither spherical equivalent refractive error nor axial eye length had significant correlations with scleral birefringence. To evaluate the direct influence of IOP to scleral birefringence, scleral birefringence of 16 ex vivo porcine eyes was measured under controlled IOP of 5-60 mmHg. In these ex vivo porcine eyes, the mean linear regression slope between controlled IOP and scleral birefringence was -9.9 × 10(-4) deg/μm/mmHg. In addition, porcine scleral collagen fibers were observed with second-harmonic-generation (SHG) microscopy. SHG images of porcine sclera, measured on the external surface at the superior side to the cornea, showed highly aligned collagen fibers parallel to the limbus. In conclusion, scleral birefringence of healthy human eyes was correlated with IOP, indicating that the ultrastructure of scleral collagen was correlated with IOP. It remains to show whether scleral collagen ultrastructure of human eyes is affected by IOP as a long-term effect.