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Indentation Testing of the Optic Nerve Head and Posterior Sclera

The mechanical behavior of the optic nerve head (ONH) and the surrounding sclera play important roles in the development of optic neuropathy. We assessed the indentation behavior of the ONH and the surrounding sclera in unfixed human autopsy eyes from individuals between 27 and 87 years of age. Our testing device utilized a round-tipped 250 μm diameter stainless steel probe to measure the force applied in discrete 50 μm steps from the surface of the tissues to a depth of 400 μm. Thirteen eyes from eight individuals were indented in various locations within and around the ONH and the posterior sclera. Tissue thickness, force and depth were recorded at each position tested. Data was analyzed by evaluating the recorded force as a function of the depth of indentation. The data showed that, for both the sclera and the ONH, the force rose exponentially with increased depth of indentation. Apparent stiffness values were estimated using 2 different equations that assess soft biologic tissues. Results showed that significantly higher levels of force were required with aging to indent the posterior sclera, with a corresponding increase in stiffness values. However, no significant increase in indentation force as a function of age was noted for the ONH. Interestingly, the data suggests that some individuals have relatively large differences in the stiffness between the ONH and the posterior sclera, while others show less difference regardless of age. This data supports the notion that some individuals have relatively softer ONH tissue, and as the sclera becomes stiffer with age, this difference is magnified. This difference may be important in understanding the biomechanical contribution to the individually different susceptibility to glaucoma. KeywordsOptic Nerve Head; Sclera; Biomechanics; Lamina Cribrosa; Aging


I. INTRODUCTION
Primary open angle glaucoma (POAG) is a primary cause of vision loss in the world [1,2]. Glaucoma is defined as an irreversible damage to the optic nerve with characteristic changes in the morphology and structure of the optic nerve head (ONH) [3]. Elevations in IOP, a major risk factor for POAG, lead to glaucomatous signs, such as the vertical elongation of the optic cup and thinning of the neuroretinal rim tissue [4]. Elevated IOP has been shown to damage retinal ganglion cell (RGC) axons [5] and block axonal transport at the level of the lamina cribrosa (LC) [6,7]. The LC is composed of lamellar beams of connective tissue aligned to form 400 to 500 channels or pores where the axons of RGC transverse the sclera [8,9]. Past studies have demonstrated structural changes in the connective tissue of the LC and the posterior sclera in glaucomatous environments [10][11][12][13], while others have investigated the biomechanical behavior of the LC in response to elevated pressure [14,15]. Most of these biomechanical models suggest that the behavior of the LC is greatly affected by the material properties of the ONH and the posterior sclera [16][17][18] A few studies have calculated the elastic moduli of the posterior sclera and the ONH [19,20] using uniaxial stress-strain measurements to provide an averaged elastic modulus over enucleated specimens, which considers contributions by fibers orientated along the stretched axis. More recently, Eilaghi et al [21] provided stiffness values for regionally defined posterior scleral samples using biaxial tensile measurements. Unfortunately, given the small size of the ONH and its complex structure, differences in the elastic modulus at various regions within the ONH and the posterior sclera have not been established. At the same time, computational models have indicated that the material properties of both the posterior sclera and the LC significantly influence the ONH's response to pressure [18] The indentation method, which measures indenting force over displacement into the material, has surfaced as an alternative method to assess this material property in biologic materials [22][23][24]. For this study, we constructed an indentation device and then investigated the forces generated in a stepped indentation within the ONH and the posterior sclera as a function of age, region (superior, inferior, nasal and temporal) and fellow eyes.

A. Indentation Device
An indenting force measurement device was built using a 3D positioning control as described in a previous study [25]. In this study, a 250 µm diameter probe with a round tip was attached to the tip of the force transducer, and the z axis actuator was driven by hand ( Fig. 1).
-18 -DOI:10.5963/BER0301003 Fig. 1 Schematic of the indentation measurement system. Tissues were located on a XY positioning system composed of translation stages and indented using a round tip probe of 250 µm diameter. The probe was attached to a force transducer fixed on a translation stage placed ninety degrees to the sample. The indenting force from the transducer was recorded by a computer-controlled data acquisition system

B. Instrument Validation Studies
Polyacrylamide hydrogels were prepared as previously described by Peyton et al [26]. Briefly, acrylamide (Invitrogen, Carlsbad, CA) and bisacrylamide (Sigma-Aldrich, St. Louis, MO) were mixed at various concentrations (8:0.6%, 10: 0.8% and 12.5:1%) and polymerized between glass plates separated by 3 mm spacers with the addition of ammonium persulfate. The resulting 3 mm thick hydrogels were cut into shapes appropriate for testing.

C. Indentation Measurements
The 25 mm diameter circles of hydrogel were placed on the measuring platform ( Fig.1). Force was recorded with displacement of the probe in discrete, 20 µm increments occurring at the center of the hydrogels. Stiffness values were calculated using Eq. 1 [27], referred to as the Hayes equation, which has been used in past studies of soft biologic tissues [28][29][30][31]. The values for each measurement were determined by averaging the values calculated over an indenting depth representing 5 -15% of the gel thickness.
where F: indenting force, ν: Poisson's ratio, δ: indenting depth, κ: is a correction factor determined by ν and the ratio of R (radius of indenter) to h (material thickness) The value of κ was derived from the table developed by Hayes et al [27] which considers the overall thickness of the hydrogels (3mm), the radius of the indenting tip (125um), and Poisson's ratio of the material. In past studies, most investigators use a range between 0.45 and 0.49 [32,33] as the assumed value of Poisson's for acrylamide hydrogels. Values for the LC have ranged from 0.49 to 0.5 [34] and 0.46 to 0.5 for the sclera [35]. In all calculations, the assumed value of Poisson's ratio was taken as 0.46 for hydrogels and 0.49 for human tissue. The stiffness value for each acrylamide hydrogel concentration was obtained by averaging the results from 10 independent hydrogels.

D. Measurement of Compressive Elastic Modulus
Hydrogels were cut into 5 × 5 mm squares and placed on a 13 × 13 mm fixed platform supported by a load cell (Futek, Irvine, CA). As shown in Fig. 2, the gels were compressed at a velocity of 1 mm/min by a computer-controlled moving platform using methods established in prior studies [36,37]. The stress (σ) -strain (ε) curve was fitted to a polynomial trend line using Excel (Microsoft, Redmond, WA), and the elastic modulus was calculated based on the definition, E = dσ / dε and determined as the average of 10 independent measurements for each hydrogel concentration.  Thirteen eyes from eight individuals (mean age = 60 +/-23) (range 27 -87) were obtained from the San Diego Eye Bank with the approval of the institutional review board and following the tenets established by the Declaration of Helsinki (Table 1). All eyes were preserved within 24 hrs. postmortem and received as whole globes in moist chambers. The Optic nerve was cut flush with the posterior sclera, and the retina and choroid were dissected from the posterior scleral shell (Fig. 3A). The tissue was then cut in a radial pattern to create relaxing incisions to allow flattening of the tissue on the platform, as shown in Fig. 3B. The tissue was fixed to the platform using another board with a central 12.7 mm window, positioning the scleral canal opening in the center of the window (Fig. 3C). The platform with the tissue was then attached to a translation stage, as described in Fig.1.

F. Measurement of Indenting Force in the ONH and Posterior Sclera
Tissue, attached to the testing device, was indented by a probe in a fixed pattern as demonstrated in Fig. 4. Four positions within the ONH were assessed, representing the superior, inferior, nasal, and temporal regions. Similarly, regions outside the ONH and 4mm away from the canal opening were assessed for the posterior sclera. At each position, the surface contact point was determined by carefully lowering the tip to the tissue surface, and when the signal from the force transducer deviated from zero, the transducer was stopped and its position noted. Tissue thickness at the test point was calculated as the distance between the surface contact point and the surface of the board in Fig.  3B. The indenting probe was lowered into the tissue in discrete 50 µm steps with continuous recording of the transducer force. The apparent stiffness values from indenting force measurements were estimated using two methods. The first estimate was calculated using the Hayes equation (1), which was also used to calculate values for the hydrogels. Secondly, Eq. 2, referred to as the Hertz equation and commonly used with data derived with atomic force microscopes, was also employed [38], (2) where δ: indenting depth, F: indenting force, ν: Poisson's ratio, R: radius of indenter, F: indenting force

G. Statistics
The differences in force values at various indentation depths were analyzed using a four way ANOVA (MATLAB, Mathworks, Natick, MA) to account for the variability in measurements by age, region, fellow eyes of the ONH and the posterior sclera. Then, the differences in the averaged values over four regions for each individual eye were also analyzed using a three way ANOVA (MATLAB) to assess for variability between age and fellow eyes. Regression analysis was performed using SigmaStat ver. 3.11 (Systat Software Inc, Point Richmond, CA). P values less than 0.05 were considered significant.

III. RESULTS
Representative compressive (A) stress -strain curves and the indenting force -strain curve (B) for the 8%, 10%, and 12% acrylamide hydrogels are shown in Fig. 5. The data show that the stress/force at the same level of strain increased with increasing acrylamide concentrations. Stress-strain curves for each hydrogel were fitted to a second order polynomial curve for compressive measurements (Fig. 5A, r 2 >0.99).   Table 2 shows the stiffness values (mean (S.D.)) of the hydrogels determined by the two different testing methods over 5 -15% strain. The values obtained by indentation were generally equal to or larger than the values obtained by compression for all acrylamide concentrations. To assess the relationship between the values, linear regression analysis was performed.
As shown in Fig. 6, both testing methods gave similar results, and the only significant difference in values was within the 10% acrylamide group (P<0.05). This data confirmed that the indentation device performed reliably and provided information comparable to compressive testing in uniform hydrogels.   Fig. 7 shows a representative indenting force measurement profile with a displacement of a 50 µm step. It can be seen that the stepped indentation of the tip led to a rapid increase in force (point a), which then fell to a lower level (point b) that stabilized with time (point c). As this behavior is typical of a viscoelastic response and because the initial slope is rate dependent, forces were recorded after the response became stable and prior to another stepped indentation.   8 shows the representative material behavior of the tissue, indenting force over indentation depth, for both the posterior sclera and the ONH for a pair of eyes from a 72 year old sample. Much greater force was required to indent the posterior sclera than the ONH for each position tested. In all cases of each eye, the relationship between force and displacement was best characterized as an exponential curve. There was also significant difference in thickness between the scleral and the ONH positions (1047 +/-144 and 1357+/-172 µm, P< 0.003), which was more variable over the ONH (Fig. 9).  Due to the positional variation in tissue thickness, stiffness values were estimated using two methods. One of which considers thickness (Hayes), and the other does not (Hertz). The estimated stiffness values of the posterior and the ONH from all eyes are provided in Tables 3. By four way ANOVA, the estimated values for the posterior sclera were significantly higher than those obtained for the ONH (P<0.001). Additionally, there was significant variation with age (P<0.01) while no -23 -DOI:10.5963/BER0301003 significant differences were noted between left and right eyes from the same individual or regions within a single eye (superior, inferior, nasal, temporal) (P>0.05, not shown). This suggests that variations in estimated stiffness values from each measurement point for the same eye tissue could be represented by averaging values over the four regions tested. This was confirmed by a three way ANOVA analysis that showed a difference between the ONH, the sclera, and the age of the individual (P<0.05), regardless of the method used for estimating stiffness. Fig. 10 shows the estimated stiffness values plotted over age for the posterior sclera (A) and the ONH (B). Spearman rank correlation analysis was performed to assess the relationship between age and apparent stiffness. When considering scleral values, both estimates (Hayes and Hertz) gave r values of 0.93, P<0.0001, suggesting a strong correlation. When considering the values of the ONH, the correlation was less robust with r values of 0.8 (Hayes) and 0.76 (Hertz), P=0.001 (Hayes) and 0.002 (Hertz). Linear aggression analysis of the log-scaled stiffness values from (A); (B) shows a linear and statistically equivalent trend in both methods for the sclera (C), P=0.95; and, for the ONH (D), P=0.96. The goodness of fit was much higher (r 2 = 0.93) and with narrower confidence intervals for the scleral values (C) when compared to the estimated stiffness values for the ONH which were highly variable, r 2 =0.51 (Hayes) and 0.48 (Hertz), without statistical power higher than 80%, suggesting that no reliable regression line could be drawn. These comparisons suggest that the posterior sclera stiffens with age while no clear age effect is present in the ONH.

IV. DISCUSSION
Our indentation device was constructed to assess the stiffness of human tissues. As such, it was necessary to validate values calculated from indenting force measurements obtained by this device through comparison to those from bulk compression measurements. Polyacrylamide hydrogels were used for this validation in a manner similar to that used in past studies [29]. Reassuringly, high correlations (R 2 = 0.93) between stiffness values derived by the constructed device and those derived by conventional compressive measurements were obtained.
In this study, the relative stiffness of the human ocular tissue was estimated from indenting force measurements from the posterior sclera and the ONH without a tensile load. While the normal in vivo situation would provide a tensile stress to these tissues, we were unable to provide similar stresses ex vivo. However, the indenting force provided by a 250 micron radial tip should reflect the contributions of collagen fibers connected to the measurement point. While various models have been proposed to derive material properties from similar indentation measurements on soft tissues, most rely on the assumption that -24 -DOI:10.5963/BER0301003 the material is uniform and isotropic. Clearly, the tissues tested here are neither uniform nor isotropic and instead represent complex structures. Therefore, the actual deformation of the tissue under the indenting tip could be more complex than simply the depth of the probe into the tissue, making the estimate of strain difficult. Additionally, though relaxing incisions were placed to facilitate mounting the tissue on the testing device (Fig. 3B), the natural curvature of the sclera was bound by the fixing board 12.7mm from the scleral canal and could provide some undefined tensile stress. Therefore, the values reported here must be taken as an indication of the relative stiffness of the tissue, rather than as an estimate of Young's modulus. However, these values are useful when comparing different locations within a tissue or between individuals and have the ability to demonstrate relative behavior of the ONH and the sclera.
We acknowledge that tension is the principal load on the ONH and the posterior sclera, and indentation testing is more comparable to compression than tension. However, compression can also be a significant strain on the ONH, previously estimated to be 5 to 15% strain [39,40]. As discussed in recent reviews, tensile measurements of soft tissues routinely provide elastic moduli that are orders of magnitude larger than those obtained by indentation [41,42]. They suggest that tensile measurements are much larger due to the contribution of collagen fiber orientation and water constrained within the tissue. Obviously, stretching or compressing bulk tissue samples requires much larger forces than deforming a localized area [42]. With a small indenting probe, the water is free to move away from the measurement point and where force is not being exerted along the axis of the collagen fibers. Therefore, our data may provide only a few components (among many others) of the mechanical properties within and around the ONH. However, these measurements reflect parameters at defined positions, something not available through standard tensile and compression testing.
The standard deviation of the values presented here for the posterior sclera was quite large, and the variation within a single eye was often as large as the one between individual eyes. This suggests that regional differences in the posterior sclera within a single eye can be as large as the differences between individual eyes, which is in agreement with past studies [19,21]. However, in spite of the large variation, the data show that the right and left eyes from the same individual are quite similar, and a clear increase in scleral stiffness occurs with increasing age. The values for the ONH were even more variable, and though trending to indicate increasing stiffness with age, the correlation was not strong enough to be consistent regardless of analysis methods. Indeed, the data suggests that some eyes might have a softer ONH, independent of the surrounding sclera and not well correlated with age. This implies that some individuals might have relatively stiffer ONH tissue compared to other individuals, regardless of age.
Most importantly, our study reports the mechanical response in the specific tissues of the optic nerve where glaucomatous damage initially occurs. Elevated IOP applies stresses on the ONH resulting in compression of disc tissues, the LC and likely changes in the geometry of the scleral canal [43][44][45][46]. In a recent study, elastic moduli were measured using atomic force microscopy that ranged from 12.7 kPa to 22.0 kPa for the ONH and 101.9 kPa to 221.1 kPa for the posterior sclera from three individuals (64, 72 and 88 years) [47]. These values suggest a difference between ONH and sclera to vary from 5 to 20 fold, entirely consistent with the values we report here. As the magnitude of difference between the sclera and the ONH appeared to be widely different between individuals, this difference may contribute to the pathophysiology of glaucomatous damage, as suggested in the past study [48]. Clearly, further studies are needed to define the distribution of material properties within and around the ONH within a larger population to gain a better biomechanical understanding of the pathology of glaucoma.
V. ACKNOWLEDGMENT This study is supported by NIH grant EY019719, EY018665; Research to Prevent Blindness, Inc and Discovery Eye Foundation.