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Hydration related changes in tensile response of posterior porcine sclera
Journal Pre-proof Hydration related changes in tensile response of posterior porcine sclera Hamed Hatami-Marbini, Mohammad Pachenari PII:
S1751-6161(19)31235-4
DOI:
https://doi.org/10.1016/j.jmbbm.2019.103562
Reference:
JMBBM 103562
To appear in:
Journal of the Mechanical Behavior of Biomedical Materials
Received Date: 23 August 2019 Revised Date:
5 November 2019
Accepted Date: 26 November 2019
Please cite this article as: Hatami-Marbini, H., Pachenari, M., Hydration related changes in tensile response of posterior porcine sclera, Journal of the Mechanical Behavior of Biomedical Materials (2020), doi: https://doi.org/10.1016/j.jmbbm.2019.103562. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.
Hydration related changes in tensile response of posterior porcine sclera
Hamed Hatami-Marbini, Mohammad Pachenari Computational Biomechanics Research Laboratory, Mechanical and Industrial Engineering Department, University of Illinois at Chicago, Chicago, IL USA
Keywords: Sclera; biomechanics; uniaxial tensile experiments; hydration; porcine eyes
Corresponding Author: Hamed Hatami-Marbini, Ph.D. 2033 Engineering Research Center 842 W Tylor St Chicago, IL 60607
1
Abstract It has been shown that there exists significance dependence between hydration and biomechanical properties of hydrated tissues such as cornea. The primary purpose of this study was to determine hydration effects on mechanical properties of sclera. Sclera strips dissected from the posterior part of pig eyes along the superior-inferior direction were divided into four hydration groups by first drying them and then soaking them in PBS until their hydration reached to 75%, 100%, 150%, and 200%. The strips were subjected to ten consecutive cycles of loading and unloading upto 1 MPa. The response of samples at the tenth cycle was used to compute the tangent modulus, maximum strain, and hysteresis as a function of hydration. The experiments were done in oil in order to prevent hydration changes during the mechanical tests. The mechanical response of strips right after dissection, control group, was also measured. In general, significant softening of sclera strips was found with increasing hydration (p < 0.05). The stress-strain response of control group was between those of samples with hydration 150% and 200%. The experimental stress-strain data were successfully represented numerically with an exponential mathematical relation with R2 > 0.99. The present study showed that hydration would significantly alter the tensile response of sclera tissue. Thus, researchers interested in characterizing sclera biomechanical properties should control the hydration of specimens during the experimental measurements.
2
1. Introduction The sclera plays an important role in protecting internal components of the eyeball against external forces. It forms about 80% of the outer surface area of eye globe and is constantly subjected to intraocular pressure as well forces from extraocular muscles. The mechanical properties of sclera are extremely important for the proper functioning of the eye. Ocular diseases such as myopia and glaucoma have been found to be initiated or advance because sclera mechanical properties were compromised (Avetisov et al., 1982; Campbell et al., 2014; Coudrillier et al., 2015; Downs et al., 2001; Girard et al., 2011; Phillips and McBrien, 1995; Rada et al., 2006). Myopia is the most common of eye problem in which patients see distant objects blurry. This refractive error occurs because the eyeball is too long and light rays do not focus correctly on the retina. Significant changes in the mechanical properties of sclera have been observed during myopia development. In addition to myopia, the amount of damage of retinal ganglion cells at the optic nerve head in glaucoma eyes seems to be correlated with significant changes in biomechanical response of sclera.
Thus, it is of great interest to determine the mechanical
properties of sclera tissue. Previous reports on biomechanical properties of sclera show strong variation. In particular, the inflation, uniaxial testing, and unconfined compression give Young’s modulus varying from about 1 KPa to 50 MPa (Eilaghi et al., 2010; Friberg and Lace, 1988; Geraghty et al., 2012; Mortazavi et al., 2009; Schultz et al., 2008; Woo et al., 1972). This large variation is mainly because of differences in testing protocols as well as intrinsic differences in the mechanical response of scleral
3
samples from difference species. Furthermore, these previous studies show that the sclera is an anisotropic viscoelastic material whose biomechanical properties show regional variations that depend on the age of specimens (Curtin, 1969; Elsheikh et al., 2010; Geraghty et al., 2012; Girard et al., 2009; Grytz et al., 2014). For example, the stiffness of sclera increases gradually moving from the posterior regions to anterior parts. Furthermore, the sclera become significantly stiffer with higher age. Not controlling the hydration of samples during experimental studies might be another contributing factor to the existing variation in the mechanical repose of sclera. The extracellular matrix of sclera is primarily composed of collagen fibrils and proteoglycans (Watson and Young, 2004). The proteoglycans consist of a core protein to which sulfated glycosaminoglycans (GAGs) are covalently attached. The primary proteoglycans in human sclera are decorin and biglycan, which have only 1-2 GAG side chains. GAGs play a crucial role in the collagen fibrillogenesis and tissue hydration. The sulfated GAGs become negatively charged in the aqueous environment and attract cations, which subsequently attract water molecules inside the tissue. The negatively charged GAG chains also repel each other, which increases the volume of the solid skeleton, and attract water inside. It is found that hydration variation in sclera affects the solute diffusion and fluid movement (Boubriak et al., 2000). Specifically, increasing the hydration increases diffusion coefficients. Nevertheless, possible effects of hydration on biomechanical response of sclera have not yet been determined. Due to similarities between the extracellular matrices of the sclera and cornea and previous studies on the effect of hydration on mechanical response of the cornea (Hatami-Marbini, 2014; Hatami4
Marbini and Etebu, 2013; Hatami-Marbini and Rahimi, 2014b), we assumed that hydration would significantly influence the sclera biomechanical properties and play a role in their accurate characterization. In order to investigate the above assumption, we conducted tensile experiments on porcine sclera samples at different hydration levels in the present study. The samples were prepared from the region near the posterior pole of similar age porcine eyes in order to prevent known regional variations in the mechanical properties.
2. Materials and Methods Sclera
strips
were
excised
from
fresh
porcine
eyeballs
obtained
from
a
slaughterhouse within 2 hours of arrival to the laboratory. The strips with a width of about 5 mm were dissected using a double edge cutting device along the superiorinferior direction covering the posterior pole of the eyes, Fig. 1a. A precision analytical scale with 0.1 mg accuracy was used to measure the weight of strips immediately after dissection. Based on their hydration, strips were divided into four hydration groups of 75%, 100%, 150% and 200% using the following procedure. The hydration, H, of samples is defined as H (%) = (Ww - Wd) / Wd × 100
(1)
where Ww and Wd are the wet weight and dry weight, respectively. The strips were initially dried by placing them in a desiccator filled with silica gels at room temperature. After measuring their dry weight, dried strips were soaked in PBS solution at pH of about 7.4 until their wet weight becomes (1+H) Wd. A preliminary 5
swelling study was done in order to determine the swelling behavior of dried sclera strips and obtain an estimate for the required time for swelling them to a given hydration, i.e. dried specimens were allowed rehydrate while their wet weight was measured at regular intervals (Hatami-Marbini et al., 2013). This preliminary study was used to guide the swelling process and determine the approximate times at which samples should be removed from PBS solution. If samples have not reached their desired wet weight (as determined from the hydration group to which they belonged), they were returned to PBS solution. Furthermore, if their wet weight was larger than the required amount, they were air-dried at the room temperature. After measuring the dimension of scleral strips by a pachymeter (DGH Technology Inc., Pennsylvania) and a caliper, they were mounted in the RSA-G2 machine (TA instruments, Delaware) using sand papers. The chamber was filled with mineral oil in order to keep the hydration constant during the mechanical tests (HatamiMarbini and Rahimi, 2014a). The mechanical experiments began by applying a tare stress of 0.01 MPa in order to straighten the strips. This tare stress was approximately equal to the tensile stress in sclera based on Laplace law approximation, P r / 2t where P, r, and t represent intraocular pressure (IOP), radius, and thickness, respectively.
Samples were then subjected to ten
consecutive cycles of loading and unloading with a constant displacement rate of 10 µm/s and maximum tensile stress of 1 MPa, Fig. 1b. The first nine cycles were included in order to precondition the strips and create a recoverable state. The stress-strain response of samples at the tenth cycle was used for the data analysis. The stress, σ, was calculated from the dividing the experimentally measured force by the initial cross-section of the specimens. In order to characterize the 6
mechanical response of unaltered sclera strips, we prepared five more sclera strips and measured their mechanical response right after dissection using the same testing protocol. We also measured the tensile response of five sclera strips right after dissection in PBS solution, i.e. we filled the chamber with PBS instead of mineral oil, in order to assess possible role of testing in oil versus testing in PBS.
Fig. 1
The initial tangent modulus and maximum tangent modulus, defined as slopes of tangent lines to the stress-strain curves at 0.05 MPa and at 1.0 MPa stress, respectively, were calculated from experimental stress-strain measurements. The energy
dissipation
over
loading-unloading
cycles,
i.e.
hysteresis,
was
also
calculated using the trapezoidal integration method. Moreover, an exponential relation given by
σ = A ( e Bε − 1) + σ 0
(2)
was used to numerically represent the stress-strain behavior of scleral samples during the last loading cycle. In equation (2), σ0, and ϵ, are the applied tare stress, and strain, respectively. The unknown constants A and B were found from fitting the mathematical relation (2) into the experimental data using the Levenberge Marquardt algorithm. The behavior of different hydration groups were compared together by conducting the one-way analysis of variance (ANOVA) with a p-value of 0.05. 7
3. Results The average hydration of strips right after dissection was about 180%. Fig. 2 shows the effect of hydration on the tensile behavior of porcine scleral strips. This figure shows that the tensile response of sclera immediately after dissection was between those of 150% and 200% hydration groups. Furthermore, no significant difference was seen between the tensile behavior of freshly dissected strips in oil and PBS solution. The solid lines show numerical curve-fits of experimental measurements using the relation (2). The mean and standard deviation of A and B coefficients of the exponential relation is given in Table 1. Fig. 3a compares the maximum strain of different hydration groups. A clear trend of increasing maximum strain was seen as the level of hydration increased. The effect of hydration on initial and maximum tangent moduli is shown in Fig. 3b and Fig. 3c, respectively. Except for the initial tangent modulus of 150% and 200% hydration groups (p = 0.22) and the maximum tangent modulus of 75% and 100% hydration groups (p = 0.10), a significant difference was seen between the tangent moduli of all other hydration groups (P < 0.05). Finally, the energy released in the last loading-unloading cycle of scleral strips is shown in Fig. 3d. It is seen that the amount of hysteresis was inversely proportional to hydration.
Figs. 2-3 Table 1 8
4. Discussion The objective of the present study was to assess the importance of hydration in tensile properties of posterior scleral samples. To this end, porcine sclera strips were divided into four different hydration groups and their tensile behavior was characterized using the uniaxial tensile testing method. The sclera is primary composed of collagen fibers and negatively charged proteoglycans. Thus, it swells as it is placed in the water-based solution and it dries if it does not have access to water. It is known that hydration could have important effects on tensile response of soft tissues such as cornea (Hatami-Marbini, 2014; Hatami-Marbini and Etebu, 2013). Nevertheless, the relation between hydration and tensile properties of sclera has not yet been investigated. In this work, we used the uniaxial tensile technique to investigate the assumption that water content of sclera affects its biomechanical properties. The biomechanical properties of sclera may significantly change in myopia and glaucoma. Thus, sclera properties could play a significant role in the onset and progress of these diseases (Avetisov et al., 1982; Campbell et al., 2014; Coudrillier et al., 2015; Downs et al., 2001; Girard et al., 2011; Phillips and McBrien, 1995; Rada et al., 2006; Romano et al., 2017). The sclera is constantly subjected to the intraocular pressure and any reduction in its load bearing capacity could cause unwanted stresses and strains on other sensitive components of the ocular system. For instance, the large deformation of tissues surrounding the optic nerve head may damage retinal ganglion cells. The mechanical behavior of sclera plays a role in the 9
appearance of the above condition. The in vitro experiments such as uniaxial tensile and inflation tests have been used to explore the changes in mechanical properties of sclera due to ocular diseases such as glaucoma and myopia. Inflation experiments on peripapillary sclera samples from patients diagnosed with glaucoma have shown that these tissues had higher stiffness and lower creep rates (Coudrillier et al., 2012). The reports on effects of myopia on mechanical parameters of sclera include some variations. For instance, uniaxial tensile experiments showed that the tensile strength of sclera from myopic eyes was lower than that of the normal human sclera (Avetisov et al., 1982). Similarly, Romano et al. showed that sclera strips from myopic eyes are more compliant than emmetropic ones (Romano et al., 2017). However, another study reported little difference in the stress-strain response of myopic and normal sclera strips despite their obviously different load extension behaviors (Phillips and McBrien, 1995). Phillips and McBrien stated that this is because samples from myopic eyes were significantly thinner (Phillips and McBrien, 1995). Thus, accurate thickness information is required to make the correct conclusion about the effects of various parameters on the stress-strain behavior of sclera samples.
One of the factors
affecting the thickness is the water content (hydration), which is often not considered when characterizing the mechanical response of sclera. Thus, it is important to investigate the influence of hydration-related thickness changes on the stress-strain response of sclera. The extracellular matrix of the sclera is composed of collagen fibers (about 90% of dry weight) and proteoglycans (about 2% of dry weight) (McBrien et al., 2001). Proteoglycans are macromolecular assemblies of repeated disaccharide chains, 10
referred to as glycosaminoglycans (GAGs), which are covalently attached to a core protein. Chondroitin sulfate and dermatan sulfate are the most prevalent GAGs in sclera. These negatively charged GAGs attract water inside the tissue, causing hydration and subsequently thickness to increase (at a constant dry weight). Diseased conditions could affect the sclera GAG content. For example, it is found that there is a significant reduction in the amount of GAGs in myopic eyes (Norton and Rada, 1995; Rada et al., 2000). Fig. 2 shows the effect of hydration on tensile response of porcine sclera. The exponential relation (2) was able to curve-fit the experimental data for all hydration groups. Hydration variation significantly influenced tensile properties, as characterized by the maximum strain, initial tangent modulus, maximum tangent modulus, and hysteresis in this study. Fig. 3 shows that the average maximum strain decreased by 1.8%, 1.0% and 1.4% when the hydration of samples increased from 75% to 100%, 100% to 150%, and 150% to 200%, respectively. This means that increasing the hydration caused specimens to show softer tensile properties. This conclusion was further confirmed by plotting the variation of initial and maximum tangent moduli with hydration, Fig. 3. Except for the initial tangent modulus of H=150% and H=200% groups (p = 0.22) and the maximum tangent modulus of H=75% and H=100% hydration groups (p = 0.10), the difference between maximum and tangent moduli of all other groups was significant. The samples with hydration 150% and 200% possibly behaved similarly in the beginning because the mechanisms responsible for hydration effects, as discussed in the next paragraph, become structurally important at higher tensile loads. The mechanical measurements of this study agreed with those in literature. Schultz et al., using an almost similar mechanical testing protocol, found that the
11
posterior scleral strips have an average strain energy absorbed of about 6.09 kJ/m3 and a tangent modulus of 2.6 MPa at 1% strain (Schultz et al., 2008). Furthermore, the maximum tangent modulus of posterior sclera was estimated about 30 MPa to 50 MPa using tensile experiments similar to the present work (Geraghty et al., 2012; Lari et al., 2012). Although none of these previous studies controlled hydration of their samples, the hysteresis and the tangent modulus that they reported are comparable with what we found here for samples in 150% and 200% hydration groups. This could be because the hydration of sclera right after dissection, as measured here, is about 175%-200% and these previous studies conducted their experiments at this hydration. This statement was further supported by experimental results obtained from testing specimens immediately after dissection, Fig. 2. The difference between the tensile behavior of these samples when tested in oil and PBS was insignificant, which is possibly because the swelling rate was slow enough such that testing in PBS did not cause significant swelling during the mechanical tests. Figs. 2-3 show that tensile properties of sclera depended on hydration and there was significant stiffening when sclera strips became dehydrated. The extracellular matrix of sclera behaves like a composite material composed of a proteoglycan matrix with collagen fiber reinforcements. X-ray diffraction studies revealed that certain similarities exist between collagen fiber and proteoglycan organizations inside sclera and tendon (Quantock and Meek, 1988). It is believed that GAG side chains of proteoglycans are distributed along collagen fibrils and, while playing a significant role in the collagen fibril organization, they could influence the mechanical response of tissues such as cornea, sclera, and tendon (Scott, 1991a, 12
b). GAG chains and their interactions with each other and collagen fibrils may have a mechanical function by considering them as tiny ropes holding collagen fibers together. With increasing hydration, the load bearing capacity of the matrix reduces because the relative distance between neighboring collagen fibers increases, which possibly causes GAG complexes connecting them together to break and their structural effectiveness to reduce, Fig. 4. Furthermore, and for the same reason, the friction between ECM fibers is expected to decrease as the amount of water inside the tissue increases. It is interesting to note that previous studies on swelling response of sclera have shown that hydration changes are directly proportional to the variation of intermolecular and interfibrillar spacing (Huang and Meek, 1999). These molecular level changes due to hydration are expected to affect the biomechanical response of sclera tissue, as reported in the present study. In this study we used hydration of 200% as the maximum hydration group. Fig. 5 shows the variation of hydration over time for porcine sclera samples. It is seen that hydration variation became negligible after 200 minutes of soaking. This observation agrees with previous reports, which gave average hydration of about 200% (Murienne et al., 2015). Fig. 5 does not provide any information about the long term swelling response of sclera when immersed in PBS. Furthermore, hydration of sclera samples is expected to show some regional variations. The present work did not characterize the relation between hydration and mechanical properties of human sclera; however, it is likely that human samples show hydration dependent response. The current data in the literature suggests that hydration of porcine sclera is slightly lower than the hydration of bovine and
13
human samples. It has been shown that the average hydration of bovine sclera depends on the ionic strength and pH levels of the bathing solution with a maximum hydration of about 300% (Huang and Meek, 1999). The in vitro hydration of human and porcine sclera samples has been reported to be around 250% and 200%, respectively (Lee et al., 2004; Murienne et al., 2015). The variation
in
the
hydration
is
possibly
related
to
the
extracellular
matrix
microstructure, i.e. the interweaving of collagen and elastin fibers limit the amount of scleral swelling, which slightly varies from a species to another. In addition to causing different hydration levels, microstructural differences in the sclera extracellular matrix are expected to result in different hydration mechanical properties. For instance, both inflation and uniaxial experiments showed that human sclera is significantly stiffer than the porcine sclera (Geraghty et al., 2012; Murienne, 2016; Murienne et al., 2016; Schultz et al., 2008). Finally, it is noted that the swelling behavior of sclera is different from what has been reported for cornea tissue, which could swell upto ten times of its thickness (Hatami-Marbini et al., 2013; Huang and Meek, 1999). Different swelling properties are again expected to be because of significant differences in the content and organization of extracellular matrices of cornea and sclera (Meek, 2008).
Figures 4-5
The present work used a testing protocol in which no recovery period existed between loading cycles. Although this protocol has been previously used in 14
characterizing the tensile response of sclera in the literature (Geraghty et al., 2012; Schultz et al., 2008), the absence of a recovery period may have caused previous loading/unloading cycles influenced the measurements (Carew et al., 2000). However, this drawback did not interfere with the primary objective of this study, which was to determine the relation between hydration and tensile properties of sclera. The uniaxial tensile tests have certain well-known limitations when they are used to characterize the mechanical response of ocular tissues such as cornea and sclera (Elsheikh and Anderson, 2005; Hatami-Marbini and Rahimi, 2014b). For example, some residual stress may exist in dissected strips as they need to be straightened before being stretched. Furthermore, the structural organization of the sclera extracellular matrix might have been altered during the strip excision. Because of clear limitations of the uniaxial testing technique, its estimates may not be an accurate representation of the true in vivo mechanical response of the sclera. Nevertheless, it is still an excellent method for conducting comparative studies like the present work, which focused on hydration effects. Another weakness could be that although the maximum tensile response was within the range of previous studies (Elsheikh et al., 2010; Schultz et al., 2008), it was relatively high as it was equivalent
to
50-100
times
the
physiologic
IOP
based
on
Laplace
law
approximation. The thickness and in general the microstructure of sclera show significant variation across the ocular globe (Norman et al., 2010). The present study limits the effects of such variations by obtaining specimens from the same location and using hydration instead of thickness to divide them into different groups. This is important because previous studies on cornea tissue used the thickness of samples, along with a hydration-thickness relation, to divide specimens
15
into distinct hydration groups. The use of thickness could introduce errors because samples within a group do not have exactly similar hydration (Hatami-Marbini and Rahimi, 2014b). Although the present study prevented this drawback, the initial drying step (in order to obtain the dry weight of strips) may have adversely influenced
their
tensile
response
because
of
potential irreversible structural
modification. Such effects are expected to be of second importance because the tensile properties were in agreement with previous works in the literature when hydration of samples was similar. In summary, the effects of hydration on tensile response of sclera tissue were discussed here. The uniaxial tensile experiments showed that the tensile response of sclera would vary significantly with hydration. The findings were numerically represented by an exponential function and were discussed in terms of hydration dependent changes in the sclera extracellular matrix. It is concluded that hydration of samples should be controlled when conducting comparative studies for characterizing the influence of various parameters on the biomechanical response of sclera tissue.
Acknowledgements: The authors would like to acknowledge the support in part by National Science Foundation: Grant No. 1351461
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Quantock, A.J., Meek, K.M., 1988. Axial electron density of human scleral collagen. Location of proteoglycans by x-ray diffraction. Biophys J 54, 159-164. Rada, J.A., Nickla, D.L., Troilo, D., 2000. Decreased proteoglycan synthesis associated with form deprivation myopia in mature primate eyes. Investigative ophthalmology & visual science 41, 2050-2058. Rada, J.A.S., Shelton, S., Norton, T.T., 2006. The sclera and myopia. Experimental eye research 82, 185-200. Romano, M.R., Romano, V., Pandolfi, A., Costagliola, C., Angelillo, M., 2017. On the use of uniaxial tests on the sclera to understand the difference between emmetropic and highly myopic eyes. Meccanica 52, 603-612. Schultz, D.S., Lotz, J.C., Lee, S.M., Trinidad, M.L., Stewart, J.M., 2008. Structural factors that mediate scleral stiffness. Investigative ophthalmology & visual science 49, 4232-4236. Scott, J.E., 1991a. Proteoglycan: collagen interactions and corneal ultrastructure. Portland Press Limited. Scott, J.E., 1991b. Proteoglycan: collagen interactions in connective tissues. Ultrastructural, biochemical, functional and evolutionary aspects. International journal of biological macromolecules 13, 157-161. Watson, P.G., Young, R.D., 2004. Scleral structure, organisation and disease. A review. Experimental eye research 78, 609-623. Woo, S.-Y., Kobayashi, A., Schlegel, W., Lawrence, C., 1972. Nonlinear material properties of intact cornea and sclera. Experimental eye research 14, 29-39.
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Hydration
Thickness (mm)
A (MPa)
B
R-squared
75%
0.7 ± 0.16
0.0436 ± 0.0077
64.8 ± 8.0
0.9989
100%
0.75 ± 0.18
0.0196 ± 0.0058
59.0 ± 2.6
0.9993
150%
1.11 ± 0.19
0.0200 ± 0.0047
50.7 ± 3.8
0.9995
200%
1.27 ± 0.14
0.0259 ± 0.0115
41.1 ± 5.4
0.9990
Table 1. The fit parameters of the exponential relation that were used to represent the stress-strain response of porcine sclera.
Figure 1. a) The location of extracted strips from porcine eyeballs. b) The testing protocol used for conducting the tensile experiments. Ten loading and unloading cycles were used and results from the tenth cycle were used for data analysis. The first nine cycles were preconditioning steps for creating a similar stress history in specimens. Figure 2. The effect of hydration on the stress-strain behavior of sclera strips excised from the posterior part of porcine eyes. Symbols show the experimental measurements and solid lines depict the numerical fits obtained from the exponential relation (1). The tensile response of sclera strips immediately after dissection tested in PBS or mineral oil is also shown. Figure 3. The effect of hydration on a) the maximum strain, b) initial tangent modulus, and c) maximum tangent modulus, and d) the average strain energy absorbed (hysteresis) of the last loading cycle. The initial and maximum tangent moduli are obtained from the slope of the stress-strain curves at 0.05 MPa and 1.0 MPa stresses. The symbol ● represents that the different was insignificant between the two groups but symbol ■ denotes significant difference (p < 0.05). The error bars show one standard deviation. Figure 4. A schematic plot showing the effect of hydration variation on the interaction between collagen fibrils and PGs in sclera ECM. The ECM can be considered as a composite domain in which PGs and their interaction with each other and collagen fibrils form the matrix domain. As the ECM becomes dehydrated, the relative distance between collagen fibrils reduces and PGs’ interweaving increases. Thus, the stiffness of the matrix domain increases, causing a significant increase in the stiffness of sclera ECM. Figure 5. The swelling response of porcine sclera samples when immersed in PBS solution at room temperature.
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S1751-6161(19)31235-4
DOI:
https://doi.org/10.1016/j.jmbbm.2019.103562
Reference:
JMBBM 103562
To appear in:
Journal of the Mechanical Behavior of Biomedical Materials
Received Date: 23 August 2019 Revised Date:
5 November 2019
Accepted Date: 26 November 2019
Please cite this article as: Hatami-Marbini, H., Pachenari, M., Hydration related changes in tensile response of posterior porcine sclera, Journal of the Mechanical Behavior of Biomedical Materials (2020), doi: https://doi.org/10.1016/j.jmbbm.2019.103562. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.
Hydration related changes in tensile response of posterior porcine sclera
Hamed Hatami-Marbini, Mohammad Pachenari Computational Biomechanics Research Laboratory, Mechanical and Industrial Engineering Department, University of Illinois at Chicago, Chicago, IL USA
Keywords: Sclera; biomechanics; uniaxial tensile experiments; hydration; porcine eyes
Corresponding Author: Hamed Hatami-Marbini, Ph.D. 2033 Engineering Research Center 842 W Tylor St Chicago, IL 60607
1
Abstract It has been shown that there exists significance dependence between hydration and biomechanical properties of hydrated tissues such as cornea. The primary purpose of this study was to determine hydration effects on mechanical properties of sclera. Sclera strips dissected from the posterior part of pig eyes along the superior-inferior direction were divided into four hydration groups by first drying them and then soaking them in PBS until their hydration reached to 75%, 100%, 150%, and 200%. The strips were subjected to ten consecutive cycles of loading and unloading upto 1 MPa. The response of samples at the tenth cycle was used to compute the tangent modulus, maximum strain, and hysteresis as a function of hydration. The experiments were done in oil in order to prevent hydration changes during the mechanical tests. The mechanical response of strips right after dissection, control group, was also measured. In general, significant softening of sclera strips was found with increasing hydration (p < 0.05). The stress-strain response of control group was between those of samples with hydration 150% and 200%. The experimental stress-strain data were successfully represented numerically with an exponential mathematical relation with R2 > 0.99. The present study showed that hydration would significantly alter the tensile response of sclera tissue. Thus, researchers interested in characterizing sclera biomechanical properties should control the hydration of specimens during the experimental measurements.
2
1. Introduction The sclera plays an important role in protecting internal components of the eyeball against external forces. It forms about 80% of the outer surface area of eye globe and is constantly subjected to intraocular pressure as well forces from extraocular muscles. The mechanical properties of sclera are extremely important for the proper functioning of the eye. Ocular diseases such as myopia and glaucoma have been found to be initiated or advance because sclera mechanical properties were compromised (Avetisov et al., 1982; Campbell et al., 2014; Coudrillier et al., 2015; Downs et al., 2001; Girard et al., 2011; Phillips and McBrien, 1995; Rada et al., 2006). Myopia is the most common of eye problem in which patients see distant objects blurry. This refractive error occurs because the eyeball is too long and light rays do not focus correctly on the retina. Significant changes in the mechanical properties of sclera have been observed during myopia development. In addition to myopia, the amount of damage of retinal ganglion cells at the optic nerve head in glaucoma eyes seems to be correlated with significant changes in biomechanical response of sclera.
Thus, it is of great interest to determine the mechanical
properties of sclera tissue. Previous reports on biomechanical properties of sclera show strong variation. In particular, the inflation, uniaxial testing, and unconfined compression give Young’s modulus varying from about 1 KPa to 50 MPa (Eilaghi et al., 2010; Friberg and Lace, 1988; Geraghty et al., 2012; Mortazavi et al., 2009; Schultz et al., 2008; Woo et al., 1972). This large variation is mainly because of differences in testing protocols as well as intrinsic differences in the mechanical response of scleral
3
samples from difference species. Furthermore, these previous studies show that the sclera is an anisotropic viscoelastic material whose biomechanical properties show regional variations that depend on the age of specimens (Curtin, 1969; Elsheikh et al., 2010; Geraghty et al., 2012; Girard et al., 2009; Grytz et al., 2014). For example, the stiffness of sclera increases gradually moving from the posterior regions to anterior parts. Furthermore, the sclera become significantly stiffer with higher age. Not controlling the hydration of samples during experimental studies might be another contributing factor to the existing variation in the mechanical repose of sclera. The extracellular matrix of sclera is primarily composed of collagen fibrils and proteoglycans (Watson and Young, 2004). The proteoglycans consist of a core protein to which sulfated glycosaminoglycans (GAGs) are covalently attached. The primary proteoglycans in human sclera are decorin and biglycan, which have only 1-2 GAG side chains. GAGs play a crucial role in the collagen fibrillogenesis and tissue hydration. The sulfated GAGs become negatively charged in the aqueous environment and attract cations, which subsequently attract water molecules inside the tissue. The negatively charged GAG chains also repel each other, which increases the volume of the solid skeleton, and attract water inside. It is found that hydration variation in sclera affects the solute diffusion and fluid movement (Boubriak et al., 2000). Specifically, increasing the hydration increases diffusion coefficients. Nevertheless, possible effects of hydration on biomechanical response of sclera have not yet been determined. Due to similarities between the extracellular matrices of the sclera and cornea and previous studies on the effect of hydration on mechanical response of the cornea (Hatami-Marbini, 2014; Hatami4
Marbini and Etebu, 2013; Hatami-Marbini and Rahimi, 2014b), we assumed that hydration would significantly influence the sclera biomechanical properties and play a role in their accurate characterization. In order to investigate the above assumption, we conducted tensile experiments on porcine sclera samples at different hydration levels in the present study. The samples were prepared from the region near the posterior pole of similar age porcine eyes in order to prevent known regional variations in the mechanical properties.
2. Materials and Methods Sclera
strips
were
excised
from
fresh
porcine
eyeballs
obtained
from
a
slaughterhouse within 2 hours of arrival to the laboratory. The strips with a width of about 5 mm were dissected using a double edge cutting device along the superiorinferior direction covering the posterior pole of the eyes, Fig. 1a. A precision analytical scale with 0.1 mg accuracy was used to measure the weight of strips immediately after dissection. Based on their hydration, strips were divided into four hydration groups of 75%, 100%, 150% and 200% using the following procedure. The hydration, H, of samples is defined as H (%) = (Ww - Wd) / Wd × 100
(1)
where Ww and Wd are the wet weight and dry weight, respectively. The strips were initially dried by placing them in a desiccator filled with silica gels at room temperature. After measuring their dry weight, dried strips were soaked in PBS solution at pH of about 7.4 until their wet weight becomes (1+H) Wd. A preliminary 5
swelling study was done in order to determine the swelling behavior of dried sclera strips and obtain an estimate for the required time for swelling them to a given hydration, i.e. dried specimens were allowed rehydrate while their wet weight was measured at regular intervals (Hatami-Marbini et al., 2013). This preliminary study was used to guide the swelling process and determine the approximate times at which samples should be removed from PBS solution. If samples have not reached their desired wet weight (as determined from the hydration group to which they belonged), they were returned to PBS solution. Furthermore, if their wet weight was larger than the required amount, they were air-dried at the room temperature. After measuring the dimension of scleral strips by a pachymeter (DGH Technology Inc., Pennsylvania) and a caliper, they were mounted in the RSA-G2 machine (TA instruments, Delaware) using sand papers. The chamber was filled with mineral oil in order to keep the hydration constant during the mechanical tests (HatamiMarbini and Rahimi, 2014a). The mechanical experiments began by applying a tare stress of 0.01 MPa in order to straighten the strips. This tare stress was approximately equal to the tensile stress in sclera based on Laplace law approximation, P r / 2t where P, r, and t represent intraocular pressure (IOP), radius, and thickness, respectively.
Samples were then subjected to ten
consecutive cycles of loading and unloading with a constant displacement rate of 10 µm/s and maximum tensile stress of 1 MPa, Fig. 1b. The first nine cycles were included in order to precondition the strips and create a recoverable state. The stress-strain response of samples at the tenth cycle was used for the data analysis. The stress, σ, was calculated from the dividing the experimentally measured force by the initial cross-section of the specimens. In order to characterize the 6
mechanical response of unaltered sclera strips, we prepared five more sclera strips and measured their mechanical response right after dissection using the same testing protocol. We also measured the tensile response of five sclera strips right after dissection in PBS solution, i.e. we filled the chamber with PBS instead of mineral oil, in order to assess possible role of testing in oil versus testing in PBS.
Fig. 1
The initial tangent modulus and maximum tangent modulus, defined as slopes of tangent lines to the stress-strain curves at 0.05 MPa and at 1.0 MPa stress, respectively, were calculated from experimental stress-strain measurements. The energy
dissipation
over
loading-unloading
cycles,
i.e.
hysteresis,
was
also
calculated using the trapezoidal integration method. Moreover, an exponential relation given by
σ = A ( e Bε − 1) + σ 0
(2)
was used to numerically represent the stress-strain behavior of scleral samples during the last loading cycle. In equation (2), σ0, and ϵ, are the applied tare stress, and strain, respectively. The unknown constants A and B were found from fitting the mathematical relation (2) into the experimental data using the Levenberge Marquardt algorithm. The behavior of different hydration groups were compared together by conducting the one-way analysis of variance (ANOVA) with a p-value of 0.05. 7
3. Results The average hydration of strips right after dissection was about 180%. Fig. 2 shows the effect of hydration on the tensile behavior of porcine scleral strips. This figure shows that the tensile response of sclera immediately after dissection was between those of 150% and 200% hydration groups. Furthermore, no significant difference was seen between the tensile behavior of freshly dissected strips in oil and PBS solution. The solid lines show numerical curve-fits of experimental measurements using the relation (2). The mean and standard deviation of A and B coefficients of the exponential relation is given in Table 1. Fig. 3a compares the maximum strain of different hydration groups. A clear trend of increasing maximum strain was seen as the level of hydration increased. The effect of hydration on initial and maximum tangent moduli is shown in Fig. 3b and Fig. 3c, respectively. Except for the initial tangent modulus of 150% and 200% hydration groups (p = 0.22) and the maximum tangent modulus of 75% and 100% hydration groups (p = 0.10), a significant difference was seen between the tangent moduli of all other hydration groups (P < 0.05). Finally, the energy released in the last loading-unloading cycle of scleral strips is shown in Fig. 3d. It is seen that the amount of hysteresis was inversely proportional to hydration.
Figs. 2-3 Table 1 8
4. Discussion The objective of the present study was to assess the importance of hydration in tensile properties of posterior scleral samples. To this end, porcine sclera strips were divided into four different hydration groups and their tensile behavior was characterized using the uniaxial tensile testing method. The sclera is primary composed of collagen fibers and negatively charged proteoglycans. Thus, it swells as it is placed in the water-based solution and it dries if it does not have access to water. It is known that hydration could have important effects on tensile response of soft tissues such as cornea (Hatami-Marbini, 2014; Hatami-Marbini and Etebu, 2013). Nevertheless, the relation between hydration and tensile properties of sclera has not yet been investigated. In this work, we used the uniaxial tensile technique to investigate the assumption that water content of sclera affects its biomechanical properties. The biomechanical properties of sclera may significantly change in myopia and glaucoma. Thus, sclera properties could play a significant role in the onset and progress of these diseases (Avetisov et al., 1982; Campbell et al., 2014; Coudrillier et al., 2015; Downs et al., 2001; Girard et al., 2011; Phillips and McBrien, 1995; Rada et al., 2006; Romano et al., 2017). The sclera is constantly subjected to the intraocular pressure and any reduction in its load bearing capacity could cause unwanted stresses and strains on other sensitive components of the ocular system. For instance, the large deformation of tissues surrounding the optic nerve head may damage retinal ganglion cells. The mechanical behavior of sclera plays a role in the 9
appearance of the above condition. The in vitro experiments such as uniaxial tensile and inflation tests have been used to explore the changes in mechanical properties of sclera due to ocular diseases such as glaucoma and myopia. Inflation experiments on peripapillary sclera samples from patients diagnosed with glaucoma have shown that these tissues had higher stiffness and lower creep rates (Coudrillier et al., 2012). The reports on effects of myopia on mechanical parameters of sclera include some variations. For instance, uniaxial tensile experiments showed that the tensile strength of sclera from myopic eyes was lower than that of the normal human sclera (Avetisov et al., 1982). Similarly, Romano et al. showed that sclera strips from myopic eyes are more compliant than emmetropic ones (Romano et al., 2017). However, another study reported little difference in the stress-strain response of myopic and normal sclera strips despite their obviously different load extension behaviors (Phillips and McBrien, 1995). Phillips and McBrien stated that this is because samples from myopic eyes were significantly thinner (Phillips and McBrien, 1995). Thus, accurate thickness information is required to make the correct conclusion about the effects of various parameters on the stress-strain behavior of sclera samples.
One of the factors
affecting the thickness is the water content (hydration), which is often not considered when characterizing the mechanical response of sclera. Thus, it is important to investigate the influence of hydration-related thickness changes on the stress-strain response of sclera. The extracellular matrix of the sclera is composed of collagen fibers (about 90% of dry weight) and proteoglycans (about 2% of dry weight) (McBrien et al., 2001). Proteoglycans are macromolecular assemblies of repeated disaccharide chains, 10
referred to as glycosaminoglycans (GAGs), which are covalently attached to a core protein. Chondroitin sulfate and dermatan sulfate are the most prevalent GAGs in sclera. These negatively charged GAGs attract water inside the tissue, causing hydration and subsequently thickness to increase (at a constant dry weight). Diseased conditions could affect the sclera GAG content. For example, it is found that there is a significant reduction in the amount of GAGs in myopic eyes (Norton and Rada, 1995; Rada et al., 2000). Fig. 2 shows the effect of hydration on tensile response of porcine sclera. The exponential relation (2) was able to curve-fit the experimental data for all hydration groups. Hydration variation significantly influenced tensile properties, as characterized by the maximum strain, initial tangent modulus, maximum tangent modulus, and hysteresis in this study. Fig. 3 shows that the average maximum strain decreased by 1.8%, 1.0% and 1.4% when the hydration of samples increased from 75% to 100%, 100% to 150%, and 150% to 200%, respectively. This means that increasing the hydration caused specimens to show softer tensile properties. This conclusion was further confirmed by plotting the variation of initial and maximum tangent moduli with hydration, Fig. 3. Except for the initial tangent modulus of H=150% and H=200% groups (p = 0.22) and the maximum tangent modulus of H=75% and H=100% hydration groups (p = 0.10), the difference between maximum and tangent moduli of all other groups was significant. The samples with hydration 150% and 200% possibly behaved similarly in the beginning because the mechanisms responsible for hydration effects, as discussed in the next paragraph, become structurally important at higher tensile loads. The mechanical measurements of this study agreed with those in literature. Schultz et al., using an almost similar mechanical testing protocol, found that the
11
posterior scleral strips have an average strain energy absorbed of about 6.09 kJ/m3 and a tangent modulus of 2.6 MPa at 1% strain (Schultz et al., 2008). Furthermore, the maximum tangent modulus of posterior sclera was estimated about 30 MPa to 50 MPa using tensile experiments similar to the present work (Geraghty et al., 2012; Lari et al., 2012). Although none of these previous studies controlled hydration of their samples, the hysteresis and the tangent modulus that they reported are comparable with what we found here for samples in 150% and 200% hydration groups. This could be because the hydration of sclera right after dissection, as measured here, is about 175%-200% and these previous studies conducted their experiments at this hydration. This statement was further supported by experimental results obtained from testing specimens immediately after dissection, Fig. 2. The difference between the tensile behavior of these samples when tested in oil and PBS was insignificant, which is possibly because the swelling rate was slow enough such that testing in PBS did not cause significant swelling during the mechanical tests. Figs. 2-3 show that tensile properties of sclera depended on hydration and there was significant stiffening when sclera strips became dehydrated. The extracellular matrix of sclera behaves like a composite material composed of a proteoglycan matrix with collagen fiber reinforcements. X-ray diffraction studies revealed that certain similarities exist between collagen fiber and proteoglycan organizations inside sclera and tendon (Quantock and Meek, 1988). It is believed that GAG side chains of proteoglycans are distributed along collagen fibrils and, while playing a significant role in the collagen fibril organization, they could influence the mechanical response of tissues such as cornea, sclera, and tendon (Scott, 1991a, 12
b). GAG chains and their interactions with each other and collagen fibrils may have a mechanical function by considering them as tiny ropes holding collagen fibers together. With increasing hydration, the load bearing capacity of the matrix reduces because the relative distance between neighboring collagen fibers increases, which possibly causes GAG complexes connecting them together to break and their structural effectiveness to reduce, Fig. 4. Furthermore, and for the same reason, the friction between ECM fibers is expected to decrease as the amount of water inside the tissue increases. It is interesting to note that previous studies on swelling response of sclera have shown that hydration changes are directly proportional to the variation of intermolecular and interfibrillar spacing (Huang and Meek, 1999). These molecular level changes due to hydration are expected to affect the biomechanical response of sclera tissue, as reported in the present study. In this study we used hydration of 200% as the maximum hydration group. Fig. 5 shows the variation of hydration over time for porcine sclera samples. It is seen that hydration variation became negligible after 200 minutes of soaking. This observation agrees with previous reports, which gave average hydration of about 200% (Murienne et al., 2015). Fig. 5 does not provide any information about the long term swelling response of sclera when immersed in PBS. Furthermore, hydration of sclera samples is expected to show some regional variations. The present work did not characterize the relation between hydration and mechanical properties of human sclera; however, it is likely that human samples show hydration dependent response. The current data in the literature suggests that hydration of porcine sclera is slightly lower than the hydration of bovine and
13
human samples. It has been shown that the average hydration of bovine sclera depends on the ionic strength and pH levels of the bathing solution with a maximum hydration of about 300% (Huang and Meek, 1999). The in vitro hydration of human and porcine sclera samples has been reported to be around 250% and 200%, respectively (Lee et al., 2004; Murienne et al., 2015). The variation
in
the
hydration
is
possibly
related
to
the
extracellular
matrix
microstructure, i.e. the interweaving of collagen and elastin fibers limit the amount of scleral swelling, which slightly varies from a species to another. In addition to causing different hydration levels, microstructural differences in the sclera extracellular matrix are expected to result in different hydration mechanical properties. For instance, both inflation and uniaxial experiments showed that human sclera is significantly stiffer than the porcine sclera (Geraghty et al., 2012; Murienne, 2016; Murienne et al., 2016; Schultz et al., 2008). Finally, it is noted that the swelling behavior of sclera is different from what has been reported for cornea tissue, which could swell upto ten times of its thickness (Hatami-Marbini et al., 2013; Huang and Meek, 1999). Different swelling properties are again expected to be because of significant differences in the content and organization of extracellular matrices of cornea and sclera (Meek, 2008).
Figures 4-5
The present work used a testing protocol in which no recovery period existed between loading cycles. Although this protocol has been previously used in 14
characterizing the tensile response of sclera in the literature (Geraghty et al., 2012; Schultz et al., 2008), the absence of a recovery period may have caused previous loading/unloading cycles influenced the measurements (Carew et al., 2000). However, this drawback did not interfere with the primary objective of this study, which was to determine the relation between hydration and tensile properties of sclera. The uniaxial tensile tests have certain well-known limitations when they are used to characterize the mechanical response of ocular tissues such as cornea and sclera (Elsheikh and Anderson, 2005; Hatami-Marbini and Rahimi, 2014b). For example, some residual stress may exist in dissected strips as they need to be straightened before being stretched. Furthermore, the structural organization of the sclera extracellular matrix might have been altered during the strip excision. Because of clear limitations of the uniaxial testing technique, its estimates may not be an accurate representation of the true in vivo mechanical response of the sclera. Nevertheless, it is still an excellent method for conducting comparative studies like the present work, which focused on hydration effects. Another weakness could be that although the maximum tensile response was within the range of previous studies (Elsheikh et al., 2010; Schultz et al., 2008), it was relatively high as it was equivalent
to
50-100
times
the
physiologic
IOP
based
on
Laplace
law
approximation. The thickness and in general the microstructure of sclera show significant variation across the ocular globe (Norman et al., 2010). The present study limits the effects of such variations by obtaining specimens from the same location and using hydration instead of thickness to divide them into different groups. This is important because previous studies on cornea tissue used the thickness of samples, along with a hydration-thickness relation, to divide specimens
15
into distinct hydration groups. The use of thickness could introduce errors because samples within a group do not have exactly similar hydration (Hatami-Marbini and Rahimi, 2014b). Although the present study prevented this drawback, the initial drying step (in order to obtain the dry weight of strips) may have adversely influenced
their
tensile
response
because
of
potential irreversible structural
modification. Such effects are expected to be of second importance because the tensile properties were in agreement with previous works in the literature when hydration of samples was similar. In summary, the effects of hydration on tensile response of sclera tissue were discussed here. The uniaxial tensile experiments showed that the tensile response of sclera would vary significantly with hydration. The findings were numerically represented by an exponential function and were discussed in terms of hydration dependent changes in the sclera extracellular matrix. It is concluded that hydration of samples should be controlled when conducting comparative studies for characterizing the influence of various parameters on the biomechanical response of sclera tissue.
Acknowledgements: The authors would like to acknowledge the support in part by National Science Foundation: Grant No. 1351461
16
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Downs, J.C., Ensor, M.E., Bellezza, A.J., Thompson, H.W., Hart, R.T., Burgoyne, C.F., 2001. Posterior scleral thickness in perfusion-fixed normal and early-glaucoma monkey eyes. Investigative ophthalmology & visual science 42, 3202-3208. Eilaghi, A., Flanagan, J.G., Tertinegg, I., Simmons, C.A., Brodland, G.W., Ethier, C.R., 2010. Biaxial mechanical testing of human sclera. Journal of biomechanics 43, 1696-1701. Elsheikh, A., Anderson, K., 2005. Comparative study of corneal strip extensometry and inflation tests. J R Soc Interface 2, 177-185. Elsheikh, A., Geraghty, B., Alhasso, D., Knappett, J., Campanelli, M., Rama, P., 2010. Regional variation in the biomechanical properties of the human sclera. Experimental eye research 90, 624-633. Friberg, T.R., Lace, J.W., 1988. A comparison of the elastic properties of human choroid and sclera. Experimental eye research 47, 429-436. Geraghty, B., Jones, S.W., Rama, P., Akhtar, R., Elsheikh, A., 2012. Age-related variations in the biomechanical properties of human sclera. Journal of the mechanical behavior of biomedical materials 16, 181-191. Girard, M.J., Suh, J.-K.F., Bottlang, M., Burgoyne, C.F., Downs, J.C., 2009. Scleral biomechanics in the aging monkey eye. Investigative ophthalmology & visual science 50, 5226-5237. Girard, M.J., Suh, J.-K.F., Bottlang, M., Burgoyne, C.F., Downs, J.C., 2011. Biomechanical changes in the sclera of monkey eyes exposed to chronic IOP elevations. Investigative ophthalmology & visual science 52, 5656-5669.
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21
Hydration
Thickness (mm)
A (MPa)
B
R-squared
75%
0.7 ± 0.16
0.0436 ± 0.0077
64.8 ± 8.0
0.9989
100%
0.75 ± 0.18
0.0196 ± 0.0058
59.0 ± 2.6
0.9993
150%
1.11 ± 0.19
0.0200 ± 0.0047
50.7 ± 3.8
0.9995
200%
1.27 ± 0.14
0.0259 ± 0.0115
41.1 ± 5.4
0.9990
Table 1. The fit parameters of the exponential relation that were used to represent the stress-strain response of porcine sclera.
Figure 1. a) The location of extracted strips from porcine eyeballs. b) The testing protocol used for conducting the tensile experiments. Ten loading and unloading cycles were used and results from the tenth cycle were used for data analysis. The first nine cycles were preconditioning steps for creating a similar stress history in specimens. Figure 2. The effect of hydration on the stress-strain behavior of sclera strips excised from the posterior part of porcine eyes. Symbols show the experimental measurements and solid lines depict the numerical fits obtained from the exponential relation (1). The tensile response of sclera strips immediately after dissection tested in PBS or mineral oil is also shown. Figure 3. The effect of hydration on a) the maximum strain, b) initial tangent modulus, and c) maximum tangent modulus, and d) the average strain energy absorbed (hysteresis) of the last loading cycle. The initial and maximum tangent moduli are obtained from the slope of the stress-strain curves at 0.05 MPa and 1.0 MPa stresses. The symbol ● represents that the different was insignificant between the two groups but symbol ■ denotes significant difference (p < 0.05). The error bars show one standard deviation. Figure 4. A schematic plot showing the effect of hydration variation on the interaction between collagen fibrils and PGs in sclera ECM. The ECM can be considered as a composite domain in which PGs and their interaction with each other and collagen fibrils form the matrix domain. As the ECM becomes dehydrated, the relative distance between collagen fibrils reduces and PGs’ interweaving increases. Thus, the stiffness of the matrix domain increases, causing a significant increase in the stiffness of sclera ECM. Figure 5. The swelling response of porcine sclera samples when immersed in PBS solution at room temperature.
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