**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.

^{ 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.

*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.

^{ 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.

**Figure 1**

**Figure 1**

*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

*R*(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*|

*, defined as the slope of the stress-strain curve at fixed IOP,*

_{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*|

*is the scleral stiffness derived from the slope of the load-displacement curve for an eye held at constant IOP,*

_{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**

**Figure 2**

**Table**

**Table**

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 |

*μ*is determined by using, and

*r*is the radius of the cylindrical indenter.

_{o}*R*is an effective radius for ellipsoidal sclera. Following the data of Lazarus et al,

^{ 22 }

*R*is defined as, where

*R*and

_{a}*R*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

_{b}*R*and

_{a}*R*, photos of the tested eyes were taken using a DSLR camera (Alpha 900; Sony Corporation, Tokyo, Japan). The major radius

_{b}*R*and minor radius

_{a}*R*of the sclera were obtained by fitting an ellipse onto the boundary (Fig. 3a) using Matlab (R2013a; The MathWorks, Natick, MA). The value of

_{b}*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**

**Figure 3**

*σ*is described by the Laplace's Law,

_{s}^{ 15 }where

*t is*the thickness and

*R*is the effective radius. The two principal stresses are identical and are defined as

*σ*for ellipsoid with locally spherical pole.

_{s}^{ 15 }

*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}*E*|

*of the eye was then computed by Equation 1. The*

_{IOP}*S*|

*and*

_{IOP}*E*|

*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*

_{IOP}*S*|

*and*

_{IOP}*E*|

*were correlated positively with IOP (*

_{IOP}*S*|

*, 0.989 <*

_{IOP}*r*< 0.999,

*P*< 0.001;

*E*|

*, 0.989 <*

_{IOP}*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**

**Figure 4**

**Figure 5**

**Figure 5**

*E*|

*as a function of the in-plane biaxial stress*

_{IOP}*σ*was plotted in Figure 6. The sclera was a stress-dependent material and

_{s}*E*|

*was correlated linearly with*

_{IOP}*σ*(0.989 <

_{s}*r*< 0.999,

*P*< 0.001).

**Figure 6**

**Figure 6**

^{ 23–25 }

*E*|

*= 0.20 MPa at 15 mm Hg) was approximately twice that of the corneal tangent modulus measured in our previous study (*

_{IOP}*E*|

*= 0.12 MPa at 15 mm Hg) using the same indentation technique.*

_{IOP}^{ 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*) was found to have varied from 0.003 to 0.03 MPa. The scleral stress reported in the tensile test was 0.25 MPa,

_{s}^{ 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.

^{ 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.

^{ 28,29 }and monitoring of the scleral modulus potentially may be an important parameter in managing ONH stresses and glaucoma.

**L.K.K. Leung**, P;

**M.W.L. Ko**, P;

**C. Ye**, None;

**D.C.C. Lam**, P;

**C.K.S. Leung**, None

*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*.

*δ*=

*R*, 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,

*δ*is greater than

*R*. 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*)|

*= 0, and the contact perimeter is constant. The change of surface tension with indentation depth also is constant such that (*

_{fc}*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,

*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*)|

*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*

_{fc}*S*|

*= 0.20MPa. From the data of Young,*

_{IOP}^{21}the scleral resistant force

*b*/

*δ*can be written as,

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