November 2009
Volume 50, Issue 11
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Glaucoma  |   November 2009
Anterior Chamber Angle Opening during Corneoscleral Indentation: The Mechanism of Whole Eye Globe Deformation and the Importance of the Limbus
Author Notes
  • From the Department of Biomedical Engineering, University of Minnesota, Minneapolis, Minnesota. 
  • Corresponding author: Victor H. Barocas, Department of Biomedical Engineering, University of Minnesota, 7–105 Hasselmo Hall, 312 Church Street, SE, Minneapolis, MN 55455; baroc001@umn.edu
Investigative Ophthalmology & Visual Science November 2009, Vol.50, 5288-5294. doi:10.1167/iovs.08-2890
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      Rouzbeh Amini, Victor H. Barocas; Anterior Chamber Angle Opening during Corneoscleral Indentation: The Mechanism of Whole Eye Globe Deformation and the Importance of the Limbus. Invest. Ophthalmol. Vis. Sci. 2009;50(11):5288-5294. doi: 10.1167/iovs.08-2890.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

Purpose.: To determine how mechanical interaction among iris, cornea, limbus, sclera, and IOP contribute to angle opening during indentation of the cornea or sclera.

Methods.: A finite-element model of the globe was developed. The model consisted of three elastic isotropic segments—iris, cornea, and sclera—and a two-component anisotropic segment representing the limbus. The model was tested against published in vitro experiments and then applied to angle opening during indentation in vivo. Indentation of the central cornea with a cotton bud, indentation with a small or large eyecup during ultrasound biomicroscopy, indentation with a gonioscopy lens, and scleral indentation during goniosynechialysis were modeled.

Results.: The anisotropic limbus model matched published data better than any isotropic model. Simulation of all clinical cases gave results in agreement with published observations. The model predicted angle opening during indentation by a cotton bud or small eyecup but angle narrowing when the sclera was indented by a large eyecup. The model of indentation gonioscopy showed narrowing of the angle on the indentation side and opening of the angle on the opposite side. Nonuniform opening of the angle was predicted when the scleral surface was indented.

Conclusions.: The two-component model of the stiff fibers embedded in a soft matrix captured the mechanical properties of the complex limbal region effectively. The success of this model suggests that, at least in part, corneoscleral mechanics drive angle opening rather than aqueous humor pressurization.

There are numerous instances in which intentional or unintentional pressure on the corneoscleral junction results in the opening of the anterior chamber angle. 
Indentation gonioscopy of angle-closure glaucoma 14 : In angle-closure, the trabecular meshwork maintains outflow facility, but anterior positioning of the iris blocks aqueous humor access to the trabecular meshwork, leading to increased intraocular pressure (IOP). The angle can be examined via gonioscopy, in which a mirrored contact lens (Fig. 1) is placed on the cornea. The examiner, by applying focal pressure to the lens opposite the region of interest (e.g., pressure in the superior region when viewing the inferior region), can induce opening of the angle. 
Figure 1.
 
Gonioscopy lens used to visualize the anterior chamber angle.
Figure 1.
 
Gonioscopy lens used to visualize the anterior chamber angle.
Inadvertent opening of the angle during ultrasound biomicroscopy (UBM) 5,6 : Ishikawa et al. 5 reported that pressure applied to the eyecup during UBM can produce artifactual opening of the angle if a small cup is used but not if a large cup is used. This effect was subsequently exploited deliberately 6 to design a new eyecup for indentation UBM gonioscopy. 
Manual indentation of the central cornea to open the angle 4,79 : The indentation of central region of the cornea either with the gonioscopy lens 4 or with other instruments 8,9 was used to alleviate acute angle-closure. Masselos et al. 7 recently reported that central corneal indentation with indenting instruments such as a squint hook, cotton bud, glass rod, and gonioprism led to a significant reduction in IOP in 6 of 7 acute angle-closure cases studied. 
Scleral indentation to improve angle visualization 10 : In Takanashi et al., 10 the sclera was indented 2 mm from the limbus. The technique, designed to improve visualization of the angle during goniosynechialysis, showed angle opening in both patients and healthy persons. 
Anterior drift of the iris when blinking is prevented 11,12 : In eyes with pigmentary glaucoma 11,12 or narrow angles 12 and in healthy control eyes, 12 it was found that when blinking was prevented by the presence of an eyecup for UBM examination, the iris bowed progressively more to the anterior (or, in the pigmentary glaucoma case, progressively less to the posterior), suggesting that blinking provides a mechanism to push the iris to the posterior. 
These observations, taken collectively, point to a complex mechanical system in which pressures applied in one location cause effects in others and in which the interaction among the cornea and sclera must be considered to understand the underlying mechanism for angle-opening during indentation. 
The purpose of this project was to determine how different indentation techniques alter the angle differently; this goal was accomplished by means of a unifying finite-element model of the corneoscleral shell during indentation. Although previous models have been developed with emphasis on the effect of IOP on lamina cribrosa 1318 or on corneal mechanics, 1921 the latter with a high degree of structural accuracy, to our knowledge no such model has been applied to indentation. 
In developing the model, particular attention had to be paid to the limbus, in which collagen fibers are highly aligned around the circumference of the cornea. 22,23 The obvious consequence of this alignment is that the limbus provides purse-string-like support and prevents expansion of the cornea when the IOP is increased. 21,2426 For the purpose of our studies, however, it must also be recognized that the high alignment of the fibers in the circumferential direction renders the limbus more compliant in the meridional direction. 27 That is, the structural anisotropy of the limbus produces mechanical anisotropy, which plays a role in the response of the angle. 
Methods
Study Design
A finite-element model of the corneoscleral shell was created as described in the next section. Three different sets of simulations were performed and are described here. 
Model Validation Studies Using Simulated Inflation of the Isolated (Human) Cornea and the Isolated (Porcine) Globe.
These studies were designed to test whether our model could match experimental observations regarding corneoscleral mechanics. Specifically, it has been reported that when the isolated cornea is inflated, the central cornea stretches considerably less than the limbus 28 and that when the whole (porcine) globe is inflated, the sclera changes curvature significantly but the cornea does not. 26 We simulated those two experiments to assess the validity of our model before continuing to our studies of indentation. 
Parametric Studies on the Support of the Posterior Eye.
The interaction between the eye and the surrounding tissue is complex, 29 but, because of our focus on the anterior segment, we simplified the posterior-segment model as a fixed boundary on part of the sclera. A series of simulations was performed to assess the effect of the size of the fixed boundary on the results. Because we found no significant effect on the results, we subsequently chose an intermediate value for the application studies. 
Application Studies on the Different Modes of Indentation.
We simulated the various indentation scenarios described in the introduction, calculating the amount of predicted angle opening in each case. It is noted here that the actual amount of angle opening would depend on interactions among the iris, aqueous humor, and lens. Aqueous humor-iris interaction and lens-iris interaction were not considered in the current model. Rather, we calculated the amount of angle opening that would arise at the iris root absent interaction with aqueous humor and lens and used that quantity as a measure of how strongly the indentation compels the angle to open. 
Finite-Element Simulation
A finite-element model of the corneoscleral shell was created using general purpose nonlinear finite element analysis software (Abaqus; Simulia, Providence, RI) and mechanical and geometric data from the literature (summarized in Table 1 and Table 2). The model consists of four sections: iris, cornea, sclera, and limbus (Fig. 2). The iris, cornea, and sclera were treated as homogeneous, elastic, nearly incompressible solids. 
Table 1.
 
Mechanical Properties
Table 1.
 
Mechanical Properties
Parameter Value Reference
Modulus of elasticity (MPa)
    Cornea 19.1 27, 30
    Sclera 6 31, 32
    Limbus
        Fiber 1 *
        Matrix 300 *
    Iris 0.027 33
Poisson's ratio
    Cornea 0.5 34
    Sclera 0.49 35
    Limbus
        Fiber 0.5 *
        Matrix 0.5 *
    Iris 0.5 33
Table 2.
 
Geometric Parameters
Table 2.
 
Geometric Parameters
Parameter Value Reference
Thickness (mm)
    Cornea (average value) 0.55 36
    Human sclera
        Near the optic nerve head 1 37, 38
        Near the equator 0.5 38
        Near the limbus 0.65 38
    Porcine sclera
        Near the optic nerve head 0.8* 39
        Near the equator 0.8* 39
        Near the limbus 1.12* 39
        5 mm from the limbus 0.4* 39
    Limbus 0.65 39, 40
    Iris 0.34 41
Radius of curvature (mm)
    Cornea (average value) 7.8 36
    Human sclera 12.5 4244
    Porcine sclera 8.1* 39
Limbal length 2.8 40
Anterior chamber diameter (mm) 10.4 45
Anterior chamber angle (°) 25 41, 4648
Figure 2.
 
Model of globe deformation. (a) Axisymmetric model of the whole globe and nine different regions used as the supports on the sclera. Regions are cumulative. Region 7, for example, includes the entire posterior half of the globe. (b) Detailed fiber-matrix structure of the limbal section, showing the high-stiffness rings embedded in a low-stiffness matrix. The three-dimensional model geometry was specified by revolving the axisymmetric profile around the corneal axis. The angle was calculated using the three points marked with x's.
Figure 2.
 
Model of globe deformation. (a) Axisymmetric model of the whole globe and nine different regions used as the supports on the sclera. Regions are cumulative. Region 7, for example, includes the entire posterior half of the globe. (b) Detailed fiber-matrix structure of the limbal section, showing the high-stiffness rings embedded in a low-stiffness matrix. The three-dimensional model geometry was specified by revolving the axisymmetric profile around the corneal axis. The angle was calculated using the three points marked with x's.
Because of the special architecture and properties of the limbus, a two-component model was introduced (Fig. 2b), in which multiple high-stiffness (Young's modulus E ≈ 15 × Ecornea) rings were embedded in a more compliant (E ≈ 1/20 × Ecornea) surrounding matrix. The consequence of this geometry was that the limbus was stiff in circumferential loading because of the rings but compliant in meridional loading because of the matrix. Thus, the two-component limbus constituted a highly idealized simplification of the complex anatomy that captured the key feature for this study, the large degree of anisotropy in the limbus. The number and cross-sectional area of fibers and the compliance of the matrix and fiber network were designed using the theory of composite materials 49 to produce a model that matched the measured elasticity of the limbus. 27  
The boundary conditions on the inflation models were as follows. The interior surface of the corneoscleral shell was set to an elevated pressure (the IOP, which was published in the experimental studies 26,28 ), and the exterior surface was set to zero pressure. For corneal inflation, only the extreme anterior of the sclera was simulated, and the edge of it was fixed to simulate mounting in the testing apparatus. The pressure was increased progressively, and the finite-element solution was compared with the experimental data. For the corneal inflation case, 28 displacement was reported and easily compared between model and experiment. For the whole-globe inflation case, 26 the relationship among IOP, volume change, and curvature change was reported. IOP was the input parameter to our model; therefore, we had to calculate final volume and corneal and scleral radius of curvature. Volume change was determined by subdividing the interior space of the model into triangles (in axisymmetric cases) or tetrahedra (in nonsymmetric cases) and using standard geometric formulas to calculate the volume. Radii of curvature were calculated by fitting a circle to the final position of the exterior surface. In addition to the fiber-matrix model, in both cases the limbus was modeled as an isotropic section with different elastic moduli, and the results were compared with the experimental studies. 
For the indentation simulations, zero displacement was imposed over a region at the posterior of the sclera to represent the support from the surrounding tissue. As can be seen in Figure 2a, the size of the region was varied from very small (region 1) to just over half of the globe (region 9). The results were insensitive to the choice of region (<3% variation when different regions were fixed), so it was concluded that the approximation was acceptable; subsequent simulations were performed using regions 1 to 4. Exterior surfaces of the cornea and sclera that were not in the fixed region or directly under the indenter were set to zero pressure. 
In simulating indentation of the intact globe, we required that the volume of the globe remain unchanged. This stipulation was based on the incompressibility the material inside the eye and the relatively small amount of outflow. For a patient with a normal outflow facility of 0.2 μL/(mm Hg/min) and a “lid squeeze” IOP of 120 mm Hg, 50,51 the outflow rate would be only 0.4 μL/s; because indentation is typically on the order of a few seconds, only a few microliters of volume would be expected to be lost. 
To perform the simulations, we had to specify the IOP, the total force of indentation, or the total distance of indentation. Lacking good data on any of the three, we chose to specify an IOP of 120 mm Hg, a level measured during a hard lid squeeze. 50,51 In other words, we assumed that all modes of indentation produced roughly the same amount of IOP as a hard lid squeeze. Although this was a considerable simplification, it provided a consistent basis for the different models. Once the IOP was set, an initial indentation force was guessed, and the simulations were performed. The results were analyzed to determine the total volume, and the indentation force was modified, keeping the same indentation area, until the results gave a volume change of <2.5 μL. Once the appropriate indentation force had been determined, the results were further analyzed to calculate iris root rotation. Specifically, angle opening was calculated by taking the angle formed by the trabecular meshwork and two points, one on the anterior iris surface and one on the posterior cornea surface, 500 μm from the trabecular meshwork (Fig. 2b). 
The axisymmetric model was used in the central corneal, large UBM eyecup, and small UBM eyecup indentation simulations. To simulate central corneal indentation with a cotton bud, pressure was applied on a circle, 2.5 mm in diameter, centered on the corneal apex. The diameters of eyecups simulated were 13 and 18 mm. 5 To simulate the eyecup indentation, we applied pressure on a section, 0.35-mm wide, on the corneal or scleral surfaces 6.5 mm and 9 mm from the corneal axis. To simulate indentation gonioscopy with a Sussman lens (Dlens = 9 mm), we applied pressure on a section, 0.35 mm wide, 4.7 mm long, 4.5 mm from the corneal axis. To model the asymmetric scleral indentation, pressure was applied 2 mm from the limbus on a section 0.35 mm wide and 5.5 long. 
Results
Validation Studies
Figure 3 shows the results of model validation. Simulation of corneal inflation showed that when the posterior corneal surface was pressurized, the displacement of a point midway from the corneal apex to the limbus was 92% of the corneal apex displacement (Fig. 3a). Because very low pressures are not physiological, 28 we measured our displacements with 3 KPa (22 mm Hg) as the reference point. The results, shown in Figure 3a, compare favorably with Figure 9 of Boyce et al. 28 When the limbus was modeled as isotropic, the ratio of the midperiphery to apex displacement changed dramatically (Fig. 3b). When the limbus was made stiff (E = Ecornea, E = Esclera, or E = Efibers), the predicted displacement in the midperiphery dropped considerably. In the stiffest case (E = Efibers), the displacement of the midperipheral point was less than 40% of the apex displacement. In contrast, when the limbus was modeled as a compliant isotropic material (E = Ematrix), the midperipheral point moved as much as 95% of the apex. 
Figure 3.
 
Comparison of model with published experimental studies. (a) Simulated pressure-displacement profile for the corneal apex and a point midway from the limbus to the apex. (b) Ratio of the displacement of midperipheral point to the displacement of the corneal apex compared for different models of limbal section and published experimental data. 28 The limbus was modeled as isotropic (gray bars) with a modulus of either 300 MPa (stiff), 19.1 MPa (cornea), 6 MPa (sclera), or 1 MPa (soft) and as a fiber composite (striped bar) of stiff fibers embedded in a soft matrix. (c) Changes in the radius of curvature of cornea and sclera versus pressure obtained from simulation of a porcine model. (d) Ratio of changes in cornea radius of curvature to changes in sclera radius of curvature when pressure changed from 15 to 45 mm Hg for the different models of limbal section and published experimental data. 26
Figure 3.
 
Comparison of model with published experimental studies. (a) Simulated pressure-displacement profile for the corneal apex and a point midway from the limbus to the apex. (b) Ratio of the displacement of midperipheral point to the displacement of the corneal apex compared for different models of limbal section and published experimental data. 28 The limbus was modeled as isotropic (gray bars) with a modulus of either 300 MPa (stiff), 19.1 MPa (cornea), 6 MPa (sclera), or 1 MPa (soft) and as a fiber composite (striped bar) of stiff fibers embedded in a soft matrix. (c) Changes in the radius of curvature of cornea and sclera versus pressure obtained from simulation of a porcine model. (d) Ratio of changes in cornea radius of curvature to changes in sclera radius of curvature when pressure changed from 15 to 45 mm Hg for the different models of limbal section and published experimental data. 26
Figure 3c shows the changes in the radius of curvature of the cornea and the sclera when the whole globe was pressurized. Consistent with published experimental data (Fig. 3 of Pierscionek et al. 26 ), the corneal radius of curvature did not change dramatically, but the scleral radius of curvature changed by approximately 2 mm when the pressure increased from 15 to 60 mm Hg. Figure 3d shows the ratio of change in the corneal radius of curvature to change in the scleral radius of curvature when the pressures changed from 15 to 45 mm Hg. The ratio was very small for the experimental case (0.02), a result of the annular support from the limbus and the geometry of the porcine globe. The model with a stiff limbus (E = Efibers) and the anisotropic-limbus model gave relatively small ratios (the stiff model actually predicted that the corneal curvature would decrease), whereas the other models (E = Ecornea, E = Esclera, or E = Ematrix) did not give reasonable predictions for the curvature change ratio. 
In examining Figures 3b and 3d together, we see that only an anisotropic mechanical model of the limbus can capture both the meridional compliance (Fig. 3b) and the circumferential stiffness and resulting maintenance of corneal curvature (Fig. 3d). Thus, the anisotropic model was used for all simulations. 
Simulation of Indentation
Figure 4 shows the simulated eye globe before (Fig. 4a) and after (Figs. 4b-4f) each type of indentation studied. When indentation on the central cornea was simulated (Fig. 4b), the eye remained symmetric about the corneal axis, and the angle opened 8.2° as the cornea flattened and the sclera bulged slightly. The entire iris moved posteriorly, but we noted that the motion would be less pronounced in vivo because of the lens and zonules. This result is consistent with the well-established opening of the angle by central corneal indentation. 4,79  
Figure 4.
 
Simulation of indentation. (a) Undeformed whole globe. (b) Axisymmetric indentation in the central cornea. (c) Axisymmetric indentation with small eyecup. (d) Axisymmetric indentation with large eyecup. (e) Asymmetric indentation with a gonioscopy lens on the corneal surface. (f) Scleral indentation during goniosynechialysis. The arrows show the location of applied forces.
Figure 4.
 
Simulation of indentation. (a) Undeformed whole globe. (b) Axisymmetric indentation in the central cornea. (c) Axisymmetric indentation with small eyecup. (d) Axisymmetric indentation with large eyecup. (e) Asymmetric indentation with a gonioscopy lens on the corneal surface. (f) Scleral indentation during goniosynechialysis. The arrows show the location of applied forces.
In the case of indentation with a small eyecup (Fig. 4c), the eye again remained symmetric, and the angle opened by as much as 24.5° as large rotations occurred at the iris root. This result is consistent with the experimental observation that indentation with a small eyecup opens the angle significantly. 5 When the large eyecup was simulated (Fig. 4d), however, the angle narrowed by 6.7°. The cited study 5 reported no change in the angle when a large eyecup was used. 
When corneal indentation with a Sussman gonioscope was simulated (Fig. 4e), the angle narrowed by 9.7° on the indentation side, and it opened by 12.5° on the opposite side. The opening of the opposite angle is observed clinically, but the narrowing at the indentation site is not observable because of the geometry of the gonioscope. 
Finally, in the case of scleral indentation 2 mm away from the limbus (Fig. 4f), the angle opened by a maximum of 6.7° at the point opposite the indentation site and by a minimum of 3.5° at a point nearest the indentation site. 
We also calculated the total force applied to the corneal (or scleral) surface during each of the indentation cases. As can be seen in Figure 5, the amount of force required to produce an IOP of 120 mm Hg varied greatly from just under 1 N (= 0.1 kg, or approximately 3.5 oz) in the case of asymmetric indentation by the gonioscope up to 7 N (= 0.7 kg, well over 1 pound) in the case of the large eyecup. 
Figure 5.
 
Net force was calculated for each case shown in Figure 4.
Figure 5.
 
Net force was calculated for each case shown in Figure 4.
Discussion
The first major conclusion of this work is that the limbus, by virtue of its unique circumferential fiber alignment, is a major determiner of the deformation of the cornea and sclera. We found that a simplified model using rings to represent the collagen fibers in the limbus was able to capture its mechanical behavior, particularly the kinematics during indentation and inflation, effectively. 
Turning to the simulations of indentation, the model correctly predicted angle opening under a variety of indentation scenarios. The largest amount of angle opening (24.5°) was observed during indentation with a small eyecup, followed by the asymmetric indentation of indentation gonioscopy (12.5° for the region of the angle directly opposite indentation site) and then central indentation (8.2°). Thus, if one's goal were to open the angle as much as possible with a minimum IOP increase, indentation with a small eyecup would appear to be the most effective method, but the potential advantage would have to be balanced against the inconvenience and mild patient discomfort of placing the eyecup. 
The difference in force needed to generate the same IOP in different cases, which arises primarily because of differences in the contact area, is important because the examiner feels the force, not the IOP. A force of 1 N applied to one quadrant of the cornea during indentation gonioscopy would be sufficient to produce a high IOP and a significant change in the angle. The same force, however, would have only a small effect if applied to a large eyecup. Thus, it is important that the examiner be aware that different indentation strategies can produce different IOPs and different amounts of angle opening with the same applied force. It is also possible that cushioning from saline or gel could affect the results. 
Although it is known that prevention of blinking leads to anterior drift of the iris, the mechanism by which this effect occurs is not known. The mechanics of blinking are extremely complex, and the force applied to the cornea or sclera by the lid is not well understood; therefore, we did not attempt to model blinking per se. Rather, we observed that in all cases studied, application of pressure to the central or midperipheral cornea led to opening of the angle, and we concluded that it is highly likely that blinking causes posterior rotation of the iris by a similar mechanism. Further studies are necessary to refine our understanding of blinking and how the pressure from the lid changes the contour of the iris. 
It is noted that some of the deformations in Figure 4 appear large and produce odd shapes in the simulated globe. These pronounced effects may be in part attributed to variations in indentation technique, with the note that our model assumed an IOP of 120 mm Hg in all cases. The asymmetric scleral indentation (Fig. 4f), for example, agrees reasonably well with the ultrasound image shown in Takanashi's paper 10 on the technique. On the other hand, Figure 4d clearly shows an artifact near the equator from our assumption about the supporting boundary condition, and the deformations of Figure 4e seem extremely pronounced. A more detailed and accurate account would require monitoring of force, contact area, or IOP during the indentation, and the results of Figure 4 should be taken primarily as qualitative guides to the effect of indentation on the angle. 
It is important to recognize that the model described here is consistent with all observations about indentation and angle opening without invoking a pressure drop between the anterior and posterior chambers. That is, the model predicts that the angle can open because of mechanical driving forces generated in the cornea and sclera, not because of aqueous humor being forced into the angle and opening it up. A mechanism involving aqueous humor and an effect similar to reverse pupillary block is certainly possible, perhaps even likely, but we conclude that the opening of the angle does not require an elevated aqueous humor pressure on the anterior surface of the iris. This prediction could be tested experimentally by repeating the Ishikawa study 5 on patients who underwent successful peripheral iridotomies, eliminating any possible aqueous humor pressure difference across the iris. 
Although the model described a number of experimental observations well, there are still further considerations in our attempts to understand the mechanics of the globe. As mentioned in the introduction, other investigators 1318 have attempted to explore globe mechanics to understand the mechanical environment of the optic nerve head at elevated IOP; the current model did not account for the different mechanical properties of the lamina cribrosa, 17,18 for example, because we would expect different properties in the lamina to change the shape of the extreme posterior eye considerably but not to affect the angle. Perhaps more important, the mechanical contributions of the lens, zonular fibers, and ciliary body were not included in the model. Given that the combination of the lens, zonular fibers, and ciliary body creates an internal mechanical constraint on the deformation of the eye globe, adding them to the model could cause changes in the iris root rotation calculated by the current method. The importance of lens/zonule mechanics has been demonstrated experimentally 52 and clinically. 53 We would expect the tension in the zonules to act similarly to that in the limbus, resisting radial expansion but allowing anterior-posterior stretch. 
Although we assumed that the volume of the globe was constant during the corneoscleral indentation, the intraocular blood volume changes when the IOP rises above arterial perfusion pressure. When the IOP approaches 120 mmHg, the ocular blood flow is significantly reduced 54 and the intraocular blood volume diminishes. Based on published data, 55 we estimated the intraocular blood volume to be 2% of the total globe volume. To assess the importance of the ocular blood loss, we reran the central corneal indentation simulation. The same force was applied on the corneal surface, but this time 2% of the globe volume was allowed to be lost. We found that the increase in the IOP was considerably lower (60 vs. 120 mm Hg), but the kinematics of the iris root rotation, the primary concern of our study, changed only slightly (approximately 20% of the calculated value) with no qualitative change (i.e., the angle remained widened). 
Another considerable simplification was the assumption that the complex interaction between the globe and the surrounding muscle, bone, and fat can be modeled as a fixed boundary around a certain region of the posterior eye. Based on the small variations in our parametric studies and the success of the current model in describing the clinical and experimental observations, we conclude that detailed models of the surrounding tissue are necessary only if one wishes to understand specific, local interactions. 
Footnotes
 Supported by National Institutes of Health Grant R01 EY15795. Computations were facilitated by a supercomputing resources grant from the University of Minnesota Supercomputing Institute for Digital Simulation and Advanced Computation.
Footnotes
 Disclosure: R. Amini, None; V.H. Barocas, None
Footnotes
 The publication costs of this article were defrayed in part by page charge payment. This article must therefore be marked “advertisement” in accordance with 18 U.S.C. §1734 solely to indicate this fact.
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Figure 1.
 
Gonioscopy lens used to visualize the anterior chamber angle.
Figure 1.
 
Gonioscopy lens used to visualize the anterior chamber angle.
Figure 2.
 
Model of globe deformation. (a) Axisymmetric model of the whole globe and nine different regions used as the supports on the sclera. Regions are cumulative. Region 7, for example, includes the entire posterior half of the globe. (b) Detailed fiber-matrix structure of the limbal section, showing the high-stiffness rings embedded in a low-stiffness matrix. The three-dimensional model geometry was specified by revolving the axisymmetric profile around the corneal axis. The angle was calculated using the three points marked with x's.
Figure 2.
 
Model of globe deformation. (a) Axisymmetric model of the whole globe and nine different regions used as the supports on the sclera. Regions are cumulative. Region 7, for example, includes the entire posterior half of the globe. (b) Detailed fiber-matrix structure of the limbal section, showing the high-stiffness rings embedded in a low-stiffness matrix. The three-dimensional model geometry was specified by revolving the axisymmetric profile around the corneal axis. The angle was calculated using the three points marked with x's.
Figure 3.
 
Comparison of model with published experimental studies. (a) Simulated pressure-displacement profile for the corneal apex and a point midway from the limbus to the apex. (b) Ratio of the displacement of midperipheral point to the displacement of the corneal apex compared for different models of limbal section and published experimental data. 28 The limbus was modeled as isotropic (gray bars) with a modulus of either 300 MPa (stiff), 19.1 MPa (cornea), 6 MPa (sclera), or 1 MPa (soft) and as a fiber composite (striped bar) of stiff fibers embedded in a soft matrix. (c) Changes in the radius of curvature of cornea and sclera versus pressure obtained from simulation of a porcine model. (d) Ratio of changes in cornea radius of curvature to changes in sclera radius of curvature when pressure changed from 15 to 45 mm Hg for the different models of limbal section and published experimental data. 26
Figure 3.
 
Comparison of model with published experimental studies. (a) Simulated pressure-displacement profile for the corneal apex and a point midway from the limbus to the apex. (b) Ratio of the displacement of midperipheral point to the displacement of the corneal apex compared for different models of limbal section and published experimental data. 28 The limbus was modeled as isotropic (gray bars) with a modulus of either 300 MPa (stiff), 19.1 MPa (cornea), 6 MPa (sclera), or 1 MPa (soft) and as a fiber composite (striped bar) of stiff fibers embedded in a soft matrix. (c) Changes in the radius of curvature of cornea and sclera versus pressure obtained from simulation of a porcine model. (d) Ratio of changes in cornea radius of curvature to changes in sclera radius of curvature when pressure changed from 15 to 45 mm Hg for the different models of limbal section and published experimental data. 26
Figure 4.
 
Simulation of indentation. (a) Undeformed whole globe. (b) Axisymmetric indentation in the central cornea. (c) Axisymmetric indentation with small eyecup. (d) Axisymmetric indentation with large eyecup. (e) Asymmetric indentation with a gonioscopy lens on the corneal surface. (f) Scleral indentation during goniosynechialysis. The arrows show the location of applied forces.
Figure 4.
 
Simulation of indentation. (a) Undeformed whole globe. (b) Axisymmetric indentation in the central cornea. (c) Axisymmetric indentation with small eyecup. (d) Axisymmetric indentation with large eyecup. (e) Asymmetric indentation with a gonioscopy lens on the corneal surface. (f) Scleral indentation during goniosynechialysis. The arrows show the location of applied forces.
Figure 5.
 
Net force was calculated for each case shown in Figure 4.
Figure 5.
 
Net force was calculated for each case shown in Figure 4.
Table 1.
 
Mechanical Properties
Table 1.
 
Mechanical Properties
Parameter Value Reference
Modulus of elasticity (MPa)
    Cornea 19.1 27, 30
    Sclera 6 31, 32
    Limbus
        Fiber 1 *
        Matrix 300 *
    Iris 0.027 33
Poisson's ratio
    Cornea 0.5 34
    Sclera 0.49 35
    Limbus
        Fiber 0.5 *
        Matrix 0.5 *
    Iris 0.5 33
Table 2.
 
Geometric Parameters
Table 2.
 
Geometric Parameters
Parameter Value Reference
Thickness (mm)
    Cornea (average value) 0.55 36
    Human sclera
        Near the optic nerve head 1 37, 38
        Near the equator 0.5 38
        Near the limbus 0.65 38
    Porcine sclera
        Near the optic nerve head 0.8* 39
        Near the equator 0.8* 39
        Near the limbus 1.12* 39
        5 mm from the limbus 0.4* 39
    Limbus 0.65 39, 40
    Iris 0.34 41
Radius of curvature (mm)
    Cornea (average value) 7.8 36
    Human sclera 12.5 4244
    Porcine sclera 8.1* 39
Limbal length 2.8 40
Anterior chamber diameter (mm) 10.4 45
Anterior chamber angle (°) 25 41, 4648
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