Noninvasive Measurement of Scleral Stiffness and Tangent Modulus in Porcine Eyes

Abstract

Purpose.: We investigated an indentation technique to measure the scleral stiffness and tangent modulus of porcine eyes.

Methods.: The scleral load-displacement responses were measured with a universal testing machine as a function of IOP in 15 porcine eyes ex vivo using a 5-mm diameter cylindrical flat-punch indenter. The scleral radius of curvature and scleral thickness were measured using a DSLR camera (Alpha 900) and a camera-mounted stereomicroscope (M205C), respectively. The relationships between scleral stiffness, tangent modulus, and IOP were examined.

Results.: The mean local scleral radius of curvature and scleral thickness were 7.86 ± 0.49 and 1.03 ± 0.14 mm, respectively. The average scleral stiffness and scleral tangent modulus of porcine eyes were 0.13 ± 0.02 N/mm and 0.20 ± 0.04 MPa at 15 mm Hg, respectively. The scleral stiffness and scleral tangent modulus were correlated positively with IOP (scleral stiffness, 0.989 < r < 0.999, P < 0.001; scleral tangent modulus, 0.989 < r < 0.999, P < 0.001).

Conclusions.: The scleral indentation technique can provide a noninvasive approach to measure scleral stiffness and tangent modulus.

Introduction

The sclera constitutes over 70% of the outer envelope of the eyeball, has a complex multilayered structure, and has a central role in providing structural stability to the eye. The scleral biomechanical property is an important parameter characterizing the ocular structural integrity. The sclera has been shown to be more flexible and less load-bearing in myopes than in emmetropes. ^1–5 It also has been shown that increased ocular rigidity (a measure describing the relationship between the change in IOP and the change in eyeball volume) is associated with the development of glaucoma, ⁶ and that scleral stiffness is correlated with increased prevalence of glaucoma and age. ^7,8 While the importance of scleral properties is recognized, in vivo technique for measurement of the scleral properties is limited. Scleral properties, such as scleral stiffness and tangent modulus, are ascertained from load-displacement curves of the sclera. (Like other biological tissues, the sclera is a complex composite structure with many layers. In investigations of biomechanical properties, the detailed fine structures often are ignored, such that the properties measured are interpreted as the material property of the composite structure ^9–11 under small deformation linear elastic regime.) The loads generally are imposed onto the eye using inflation methods, ^9,12–17 and displacements are ascertained using speckle interferometry, ^9,12,13,17 digital camera imaging, ^15,16 or ultrasound speckle tracking. ¹⁴ These inflation-based methods are destructive to the eye, and are unsuited for use in clinical study on the human eye in vivo. 

Instead of inflation, surface wave elastometry also can be used to measured elastic properties of the cornea. In surface wave elastometry (Refs. 18 and 19; Dupps W, et al. IOVS 2005;46:ARVO E-Abstract 2758), the ultrasound surface wave propagation time between two points on the cornea is measured, but analysis of the elastic modulus from the propagation time requires an accurate model of wave propagation-properties of the individual eye. 

Alternately, scleral properties can be obtained from indentation ²⁰ load-displacement data using an elastic mechanics model. In indentation, the force is applied through-plane in the direction of the outwardly directed IOP, and the elastic properties can be delineated using standard elasticity models. Indentation on porcine eyes ex vivo and rabbit eyes in vivo showed that the corneal elastic properties can be obtained using indentation. ²⁰ In this study, indentation is used to measure noninvasively the scleral stiffness and scleral tangent modulus of the eye. 

Methods

Experiments were performed in accordance with the ARVO Statement for the Use of Animals in Ophthalmic and Vision Research. We examined 15 enucleated porcine eyes obtained from a local abattoir. The measurements of scleral stiffness and tangent modulus were conducted within 12 hours of the animals being killed, and the eyes were kept moist inside an insulated bucket with refrigerants at 4°C. The extraocular muscles and the extraneous fat were removed carefully before the measurement. 

The experimental setup for indentation is shown in Figure 1. The enucleated eye was held on a cylindrical test jig. The anterior chamber was cannulated, and connected to a manometer and a bottle filled with saline. The IOP was adjusted between 7 and 39 mm Hg by varying the bottle height for each scleral measurement. A needle pressure sensor (OPP-M400; Opsens, Inc., Quebec, Canada) was inserted into the anterior chamber to measure the IOP independently. 

Figure 1

 

Experimental setup for measuring scleral stiffness and tangent modulus of an enucleated porcine eye. One needle inserted to the anterior chamber of the porcine eye was connected to a manometer for IOP control, while the other one was embedded with a pressure transducer for IOP measurement.

In parallel, a 5-mm diameter cylindrical flat-punch indenter was mounted on a 10-N load cell (MTS 100-090-795; S-Beam type; load resolution, 0.0001 N). The indenter assembly was then screw mounted onto the crosshead of a universal testing machine (UTM; MTS Alliance RT/5; MTS Systems Corp., Eden Prairie, MN, USA). The prepared eye was placed underneath the indenter assembly such that the indenter was positioned approximately 10 mm away from the limbus at 12 o'clock along the superior sclera. After alignment, the UTM moves the crosshead-mounted indenter downward at a rate of 20 mm/min to indent the sclera to a depth of 1 mm. The load (F) − displacement (δ) data from the indentation were recorded during the indentation. The indentation can be divided into an initial partial contact regime and a second full contact regime when the indentation depth is greater than Display Formula /2R (Fig. 2). To simplify analysis, the full contact regime with constant contact area is used for determination of the scleral properties in this study (see Appendix for details). The load-displacement curve in the full contact regime is linear, and the tangent modulus,²⁰ a scleral property that describes the stress–strain curve at a specific stress for the sclera, can be used to characterize its elastic behavior. The sclera is a structure consisting of multiple tissue layers. The scleral tangent modulus describes the structural response of the sclera as a whole, and is not the properties of the stroma or individual layers within. In this study, a scleral tangent modulus, E|_IOP, defined as the slope of the stress-strain curve at fixed IOP,²¹ 

 

is used to describe the scleral indentation behavior. The details of the IOP independence in Equation 1 can be found in the Supplementary Material. In Equation 1, S|_IOP is the scleral stiffness derived from the slope of the load-displacement curve for an eye held at constant IOP, a is a geometric constant of the indentation, and ν is the Poisson's ratio of the sclera. The sclera was assumed to be incompressible such that v = 0.5. The value of a depends on μ (see Table), which, in turn, depends on the thickness and radius of curvature of the sclera as shown in Equation 2 (See Appendix for more details).  

Figure 2

 

Typical load-displacement data acquired during the indentation on the porcine sclera. The flat-punch indenter tip is fully contacting the sclera when δ > /2R.

Table

 

Relation Between μ and a From Study of Young et al.²¹

μ	0	0.1	0.2	0.4	0.6	0.8	1.0	1.2	1.4
a	0.433	0.431	0.425	0.408	0.386	0.362	0.337	0.311	0.286

In the Table, μ is determined by using,  

 

and Display Formula is determined by:  

 

where r_o is the radius of the cylindrical indenter.  

R is an effective radius for ellipsoidal sclera. Following the data of Lazarus et al, ²² R is defined as,  

 

where R_a and R_b are the local radii of the sclera underneath the indent before indentation was used in Equation 1 to account for the ellipsoidal geometry. To determine R_a and R_b , photos of the tested eyes were taken using a DSLR camera (Alpha 900; Sony Corporation, Tokyo, Japan). The major radius R_a and minor radius R_b of the sclera were obtained by fitting an ellipse onto the boundary (Fig. 3a) using Matlab (R2013a; The MathWorks, Natick, MA). The value of t is the scleral thickness at the indentation region, and was measured by a camera-mounted Leica M205C stereomicroscope (Leica Mircosystems, Wetzlar, Germany) after scleral sectioning (Fig. 3b). In clinical practice, sectioning is not used and the thickness is measured noninvasively using optical coherence tomography (OCT), pachymetry, or other ultrasound methods.  

Figure 3

 

Measurement of (a) scleral radius of curvature and (b) scleral thickness at the indentation region.

The scleral tangent modulus was examined as a function of the in-plane biaxial stress in the sclera. When a spherical shell is pressurized, the in-plane biaxial stress in the membrane σ_s is described by the Laplace's Law, ¹⁵  

 

where t is the thickness and R is the effective radius. The two principal stresses are identical and are defined as σ_s for ellipsoid with locally spherical pole.  

The scleral stress in the pressurized sclera is determined using this relation. ¹⁵  

Results

The mean scleral radius of curvature R and scleral thickness t (n = 15) were 7.86 ± 0.49 and 1.03 ± 0.14 mm, respectively. Figure 2 shows a typical load-displacement curve obtained from the scleral indentation on a porcine eye measured ex vivo. The curve was linear and the slope represented the scleral stiffness S| _IOP . 

The scleral tangent modulus E| _IOP of the eye was then computed by Equation 1. The S| _IOP and E| _IOP of all the 15 enucleated porcine eyes were measured and plotted in Figures 4 and 5 as a function of IOP, respectively. Both plots show that the S| _IOP and E| _IOP were correlated positively with IOP (S| _IOP , 0.989 < r < 0.999, P < 0.001; E| _IOP , 0.989 < r < 0.999, P < 0.001). The mean scleral stiffness and scleral tangent modulus were 0.13 ± 0.02 N/mm and 0.20 ± 0.04 MPa at 15 mm Hg, with a range between 0.10 and 0.16 N/mm and between 0.14 and 0.27 MPa, respectively. The mean scleral stiffness and scleral tangent modulus increased at a rate of 0.0065 ± 0.0010 N/mm per mm Hg and 0.011 ± 0.0025 MPa per mm Hg with IOP, respectively. 

Figure 4

 

Relation between scleral stiffness and IOP. The lines represent experimental data from different porcine eyes (n = 15).

Figure 5

 

Relation between scleral tangent modulus and IOP. The lines represent experimental data from different porcine eyes (n = 15).

The E| _IOP as a function of the in-plane biaxial stress σ_s was plotted in Figure 6. The sclera was a stress-dependent material and E| _IOP was correlated linearly with σ_s (0.989 < r < 0.999, P < 0.001). 

Figure 6

 

Relation between scleral tangent modulus and in-plane stress in the sclera. The lines represent experimental data from different porcine eyes (n = 15).

Discussion

This study showed that scleral stiffness and scleral tangent modulus can be noninvasively determined using an indentation technique. The scleral stiffness and scleral tangent modulus increased linearly with IOP (Figs. 3, 4). Similar to other biological tissue structure, the sclera is less distensible at a high stress (Fig. 6). This behavior is in line with the findings from the uniaxial tensile strip tests in which the sclera was shown to have a higher tangent modulus when stressed. ^23–25  

The scleral tangent modulus measured in this study (E| _IOP = 0.20 MPa at 15 mm Hg) was approximately twice that of the corneal tangent modulus measured in our previous study (E| _IOP = 0.12 MPa at 15 mm Hg) using the same indentation technique. ²⁰ This suggested that the sclera is stiffer than the cornea, providing key structural support to the eye. The scleral tangent moduli of porcine eyes measured in this study are comparable to the results reported by Pierscoionek et al. ²⁶ using the inflation test (0.2–0.5 MPa, the testing IOP ranged from 15–50 mm Hg). However, they are significantly less than those measured with the tensile test reported by Wollensak and Spoerl ²⁵ (5.95 MPa at 8% strain). This may be due to the difference in stress borne by the sclera between the studies. In the present study, the IOPs were controlled between 7 and 39 mm Hg, and the scleral stress (σ_s ) was found to have varied from 0.003 to 0.03 MPa. The scleral stress reported in the tensile test was 0.25 MPa, ²⁵ which was significantly larger than the scleral stress in indentation. Since the tangent modulus varies with stress, the tangent modulus from tensile tests reported by Wollensak and Spoerl ²⁵ would be higher than ones from indentation. 

Nayar et al. ²⁷ measured the mechanical properties of porcine sclera using nanoindentation. The tangent modulus was 0.023 MPa (converted from the reduced tangent modulus), which was significantly less than the tangent modulus measured using indentation in this study. Since they used sectioned scleral samples that were not pressurized, the data would be regarded as data from the low stress regime and the modulus would be expected to be lower. 

Scleral stiffness describes how the scleral shell behaves when it is subject to loading. For instance, an eyeball with a lower scleral stiffness potentially may be lengthened more than another with a stiffer sclera under the same environment and loading conditions (e.g., same level of IOP). This may be relevant to the development of myopia and glaucoma. 

Scleral tangent modulus is a structural property and is independent of the geometry of the sclera (e.g., scleral thickness and radius of curvature). It represents a structure characteristic and describes the mechanical behavior of the sclera with a particular composition and layered structure. When the structure has more crosslinked collagen, such as the sclera of an older individual, an older person would be expected to have tangent modulus larger than the sclera of a younger individual. Computation analysis showed that the scleral tangent modulus increases the stresses in the optic nerve head (ONH), ^28,29 and monitoring of the scleral modulus potentially may be an important parameter in managing ONH stresses and glaucoma. 

The measurement of scleral modulus at a specific IOP has been demonstrated, but the act of indentation itself may change the IOP. Indentation must be restricted to within a reasonable depth to limit the IOP effect to an acceptable level. In our tests, the indentation depths were limited to 1 mm and lower. For indentation depths under 1 mm, test data showed that the IOP change during indentation is less than 3 mm Hg/mm. This, in turn, corresponds to less than 3% effect on the scleral stiffness and tangent modulus for the porcine eyes in this study (see Appendix for details). Human sclera is expected to behave similarly as the porcine sclera, but tests are needed to determine the indentation effect on human scleral stiffness and tangent modulus before use. 

In addition to the indentation effect, further studies are needed on indentation locations on human eyes. In clinical practice, the human scleral equator is not easily accessible and scleral indentation may be limited to the area close to the limbus. Further studies on human eyes will be needed to examine the effect of indentation location on scleral mechanical property measurements. 

To summarize, the scleral stiffness and tangent modulus can be measured noninvasively with an indentation technique. They were correlated positively with the IOP and biaxial stress borne by the sclera. In vivo measurement of the biomechanical properties of the sclera may provide mechanistic insights into the development of glaucoma and myopia. 

Supplementary Materials

pdf S1 

pdf S2 

Acknowledgments

Supported in part by Grant its/362/09 from the Innovation and Technology Commission of the HKSAR, China. 

Disclosure: L.K.K. Leung, P; M.W.L. Ko, P; C. Ye, None; D.C.C. Lam, P; C.K.S. Leung, None 

Appendix: Indentation Analysis

The Goldmann Applanation Tonometry is derived from the modified Imbert-Fick Law, which is a force balance between the measured applied force F, surface tension force of the tear film s, pressure force A · IOP and material resistance force b, ³⁰  

 

where A is the applanation contact area. To determine the pressure, F is taken at the applanation area A.  

In instrumented indentation, the sclera is indented to pass δ = Display Formula /2R, where partial contact transits into full contact, to 1 mm where the indenter is in full contact with the sclera. The change in the contact force as a function of indentation depth δ can be obtained by differentiating Equation A1,  

 

 

The area of scleral contact does not change when indentation depth δ is greater than Display Formula /2R. Once full contact is reached, the applanation area A becomes constant and is independent of δ. In the full contact (denoted with subscript fc) regime, (dA/dδ)|_fc = 0, and the contact perimeter is constant. The change of surface tension with indentation depth also is constant such that (ds/dδ) = 0 and the load-displacement behavior in the full contact regime is linear (Fig. 2). As a result, Equation A2 can be simplified to,  

 

 

From experiments, (d/dδ)(IOP) in the full contact regime ranges from 1 to 3 mm Hg/mm. When combined with the indentation full contact area, that is A_fc · (d/dδ)(IOP), the contribution of this term is at most 3% of (dF/dδ)|_fc and can be ignored. Consequently, Equation A3 can be simplified to,  

 

where the term on the left is the slope of the load-displacement curve in the full contact regime S|_IOP = 0.20MPa. From the data of Young,²¹ the scleral resistant force b/δ can be written as,  

 

 

By combining Equations A4 and A5, Equation 1 can be obtained.