September 2024
Volume 65, Issue 11
Open Access
Glaucoma  |   September 2024
Iris Morphological and Biomechanical Factors Influencing Angle Closure During Pupil Dilation
Author Affiliations & Notes
  • Royston K. Y. Tan
    Singapore Eye Research Institute, Singapore National Eye Centre, Singapore
    Duke-NUS Medical School, Singapore
  • Gim Yew Ng
    Department of Biomedical Engineering, NUS College of Design and Engineering, National University of Singapore, Singapore
  • Tin A. Tun
    Singapore Eye Research Institute, Singapore National Eye Centre, Singapore
    Duke-NUS Medical School, Singapore
  • Fabian A. Braeu
    Singapore Eye Research Institute, Singapore National Eye Centre, Singapore
    Duke-NUS Medical School, Singapore
    Critical Analytics for Manufacturing Personalized-Medicine, Singapore-MIT Alliance for Research and Technology, Singapore
  • Monisha E. Nongpiur
    Singapore Eye Research Institute, Singapore National Eye Centre, Singapore
    Duke-NUS Medical School, Singapore
  • Tin Aung
    Singapore Eye Research Institute, Singapore National Eye Centre, Singapore
    Duke-NUS Medical School, Singapore
    Department of Ophthalmology, Yong Loo Lin School of Medicine, National University of Singapore and National University Health System, Singapore
  • Michaël J. A. Girard
    Singapore Eye Research Institute, Singapore National Eye Centre, Singapore
    Duke-NUS Medical School, Singapore
    Department of Biomedical Engineering, Georgia Institute of Technology/Emory University, Atlanta, Georgia, United States
    Department of Ophthalmology, Emory University School of Medicine, Atlanta, Georgia, United States
  • Correspondence: Michaël J. A. Girard, Department of Ophthalmology, Emory School of Medicine, Emory Clinic Building B, 1365B Clifton Road, NE, Atlanta, GA 30322, USA; mgirard@ophthalmic.engineering
Investigative Ophthalmology & Visual Science September 2024, Vol.65, 7. doi:https://doi.org/10.1167/iovs.65.11.7
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      Royston K. Y. Tan, Gim Yew Ng, Tin A. Tun, Fabian A. Braeu, Monisha E. Nongpiur, Tin Aung, Michaël J. A. Girard; Iris Morphological and Biomechanical Factors Influencing Angle Closure During Pupil Dilation. Invest. Ophthalmol. Vis. Sci. 2024;65(11):7. https://doi.org/10.1167/iovs.65.11.7.

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

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Abstract

Purpose: To use finite element (FE) analysis to assess what morphologic and biomechanical factors of the iris and anterior chamber are more likely to influence angle narrowing during pupil dilation.

Methods: The study consisted of 1344 FE models comprising the cornea, sclera, lens, and iris to simulate pupil dilation. For each model, we varied the following parameters: anterior chamber depth (ACD = 2–4 mm) and anterior chamber width (ACW = 10–12 mm), iris convexity (IC = 0–0.3 mm), iris thickness (IT = 0.3–0.5 mm), stiffness (E = 4–24 kPa), and Poisson's ratio (v = 0–0.3). We evaluated the change in (△∠) and the final dilated angles (∠f) from baseline to dilation for each parameter.

Results: The final dilated angles decreased with a smaller ACD (∠f = 53.4° ± 12.3° to 21.3° ± 14.9°), smaller ACW (∠f = 48.2° ± 13.5° to 26.2° ± 18.2°), larger IT (∠f = 52.6° ± 12.3° to 24.4° ± 15.1°), larger IC (∠f = 45.0° ± 19.2° to 33.9° ± 16.5°), larger E (∠f = 40.3° ± 17.3° to 37.4° ± 19.2°), and larger v (∠f = 42.7° ± 17.7° to 34.2° ± 18.1°). The change in angles increased with larger ACD (△∠ = 9.37° ± 11.1° to 15.4° ± 9.3°), smaller ACW (△∠ = 7.4° ± 6.8° to 16.4° ± 11.5°), larger IT (△∠ = 5.3° ± 7.1° to 19.3° ± 10.2°), smaller IC (△∠ = 5.4° ± 8.2° to 19.5° ± 10.2°), larger E (△∠ = 10.9° ± 12.2° to 13.1° ± 8.8°), and larger v (△∠ = 8.1° ± 9.4° to 16.6° ± 10.4°).

Conclusions: The morphology of the iris (IT and IC) and its innate biomechanical behavior (E and v) were crucial in influencing the way the iris deformed during dilation, and angle closure was further exacerbated by decreased anterior chamber biometry (ACD and ACW).

Angle closure is characterized by the closure of the anterior chamber (AC) angle between the iris and the cornea, blocking aqueous outflow through the trabecular meshwork.1,2 This may occur due to mechanisms such as pupillary block and plateau iris or conditions that affect the anatomy such as cataracts or ciliary body tumors. Angle narrowing occurs especially when the pupil dilates, pushing the iris toward the periphery and blocking the AC angle. The factors associated with primary angle closure glaucoma (PACG) have been extensively explored through imaging techniques such as optical coherence tomography3 and ultrasound biomicroscopy4 to determine the significance of each anterior segment biometric parameter. Among these are several morphologic parameters associated with angle closure glaucoma (ACG)1,5,6: shallow AC depth (ACD), smaller AC width (ACW), larger iris thickness (IT) (i.e., IT500, IT750, IT2000, and ITM), thicker lens vault, and shorter axial length. But given that angle closure is a very dynamic process, it is also plausible to suspect that the biomechanics of the iris would play a significant role. 
However, thus far, no studies have investigated the iris morphologic and biomechanical factors influencing angle closure during pupil dilation. The iris is a highly robust tissue, with constant fluid exchange through its pores7,8 when responding to nerve inputs, and the knowledge of its biomechanical behavior may help us understand why angle closure occurs. An approach to depicting this alteration in volume involves using Poisson's ratio,9 where a higher ratio indicates reduced fluid mobility. This is reflected in an increased iris thickness, which had been reported to be one of the factors associated with angle closure eyes.1012 It is our belief that angle closure occurrence is contributed by both morphologic and biomechanical factors. In fact, past studies had shown differences in iris biomechanical properties between normal individuals and patients with PACG,13 including increased stiffness and decreased permeability.3 These observations could be explained by alterations in densities of collagen type I and III,10,14,15 which would increase the tissue stiffness, and an increase in extracellular matrix would in turn decrease the porosity of the iris tissue. 
To conduct a thorough investigation into the impact of iris biomechanics, it would be necessary to capture images of a vast and varied cohort of individuals undergoing pupil dilation. Accomplishing this task in a real-world setting presents significant difficulties. Nonetheless, the advent of digital twin technology offers a viable alternative to study an extensive range of hypothetical patient profiles.16 Specifically, in this research, our aim was to employ finite element (FE) analysis to determine which morphologic and biomechanical attributes of the iris and AC are most important in inducing angle closure when the pupil dilates. 
Methods
A total of 1344 FE models were manually constructed and evaluated for the AC and angles before and after pupil dilation with varying anterior chamber parameters. Each finite element model was designed as a quadrant of an axisymmetric AC across two planes, with the assumption of a perfectly spherical eye. The model was first constructed using SolidWorks and exported into Abaqus for meshing. Finally, the meshed geometry was imported into FEBio for analysis in all scenarios. For this study, we varied four AC parameters and two iris biomechanical parameters for analysis: ACD, ACW, IT, iris convexity (IC), iris stiffness (E), and iris Poisson's ratio (v). A flowchart for processing an FE model is shown in Figure 1
Figure 1.
 
The flowchart for processing the FE models.
Figure 1.
 
The flowchart for processing the FE models.
Three-Dimensional Model
The AC model consisted of the cornea, sclera, lens, iris (consisting of the stroma, sphincter muscle, and dilator muscle), and ciliary body. The model, created with SolidWorks (2022; Dassault Systèmes, Vélizy-Villacoublay, France), was designed based on literature values: cornea thickness of 0.50 mm,17,18 cornea radius of curvature of 7.50 mm,19 sclera radius of curvature of 12.00 mm,20 and only the anterior lens of radii of 1.4 mm and 5.00 mm (Figs. 2A, 2B). The cornea and sclera were combined as a single tissue since the stiffness of the tissues was similar and far greater than the iris (essentially a rigid body). The trabecular meshwork region was also combined with the cornea and sclera and angled 15° from the cornea at a small curvature (Figs. 2B, 2C). The lens, intended to be a rigid body for iris sliding during pupil dilation, was simplified as a shell with a thickness of 0.10 mm and an inner diameter of 2.00 mm. 
Figure 2.
 
(A) Anterior chamber parameters for the models, with the analyzed parameters highlighted in red. (B) The computer-aided design (CAD) model of the anterior chamber was designed to align with anatomic measurements. (C) Simplification of the model by combining the trabecular meshwork, cornea, and scleral regions since they did not affect the final results. (D) The iris was designed with a 0.20-mm root, sphincter muscle at two-fifths of the thickness and a 0.80-mm radius, and the dilator muscle at one-tenth the iris thickness beginning from the mid-radius of the sphincter muscle to the iris root.
Figure 2.
 
(A) Anterior chamber parameters for the models, with the analyzed parameters highlighted in red. (B) The computer-aided design (CAD) model of the anterior chamber was designed to align with anatomic measurements. (C) Simplification of the model by combining the trabecular meshwork, cornea, and scleral regions since they did not affect the final results. (D) The iris was designed with a 0.20-mm root, sphincter muscle at two-fifths of the thickness and a 0.80-mm radius, and the dilator muscle at one-tenth the iris thickness beginning from the mid-radius of the sphincter muscle to the iris root.
The iris was attached to the sclera at the root, which was kept consistent for all cases at 0.20 mm. Iris tissue thickness was defined as the thickness from the iris margin to mid-periphery, and it decreased from the mid-periphery to the iris root. The iris tissue was rounded at the margin and consisted of the sphincter muscle at two-fifths of the thickness and a 0.80-mm radial length. The dilator muscle was located at the posterior of the iris, with a thickness one-tenth that of the iris. The dilator muscle spanned from the mid-portion of the sphincter muscle to the iris root (Fig. 2D). A ciliary body was included for illustration purposes and did not influence the simulation results. 
Mesh and Convergence
The three-dimensional (3D) model was exported from SolidWorks as a STEP file (AP203) and imported into Abaqus FEA (2021; Dassault Systèmes) for meshing. Eight-node hexahedral elements were predominantly used for each model, unless otherwise stated. 
A convergence study was performed on an average model with mesh sizes of 6800, 23,730, 53,120, and 344,960, and a convergence test showed that the selected mesh density was <0.8% of the most refined mesh results and was deemed numerically acceptable. 
Biomechanical Properties
The finite element model contained six parts with the following material parameters: the corneo-scleral shell was described with an incompressible neo-Hookean formulation with a Young's modulus of 500 kPa.21 The lens was described as a rigid body and fixed for all scenarios. The sphincter and dilator muscles were described as incompressible neo-Hookean materials with a Young's modulus of 40 kPa assigned to both. The dilator muscle was represented using the solid mixture material model comprising a prescribed active uniaxial muscle contraction force and a passive hyperelastic modulus. Since the active muscle contraction force required was different in each model, we ran each model manually with 100 time steps and extracted data for the AC angles for the time step that coincided with 1.1-mm ± 0.1-mm dilation. The direction of contraction was in the iris radial direction, which was specified using the element local coordinates. Finally, the iris stroma was also described as a neo-Hookean material with varying biomechanical properties according to our sensitivity study described below. Of note, the neo-Hookean formulation was selected primarily for its stability and accuracy when performing large deformations in FEBio. 
Boundary Conditions
Constraints along the axisymmetric planes of the quadrant AC model were enforced, and a zero-friction contact interface was assumed between the iris and lens, as well as between the iris and the corneal endothelium surface. The lens was fixed, and so was the outer boundary of the corneo-scleral shell. 
Varying the Parameters—FE Sensitivity Study
According to population studies and estimates, the anterior chamber biometry can vary considerably, even among healthy individuals. This study aimed to understand the extent of influence of AC parameters in angle closure. To do so, we used a design of experiments22 approach to investigate how the variations in ACD, ACW, IT, IC, E, and v could influence the final AC angle and change in AC angle during pupil dilation. ACD was defined as the distance between the cornea endothelium and the lens, IT was defined as the thickness at mid-periphery, and IC was defined by the perpendicular distance of the line joining the iris base and the iris tip at midpoint (Fig. 2A). Instead of the horizontal distance between the scleral spurs, ACW was defined as the distance between the points where the cornea and sclera radii intersected (Fig. 2A). Each parameter was assigned either 3 or 4 values using the design of experiments method, including the lower and upper limits: ACD = 2, 3, and 4 mm2325; ACW = 10, 11, and 12 mm24,26; IT = 0.3, 0.4, and 0.5 mm11,12,27; IC = 0, 0.1, 0.2, and 0.3 mm12,28; E = 4, 8, 14, and 24 kPa3,29; and v = 0, 0.1, 0.2, and 0.3.3,30,31 
FE Processing to Predict Anterior Chamber Angles
All FE models were solved using FEBio (FEBio Studio v1.8.2, University of Utah, Salt Lake City, UT, USA), a nonlinear FE solver designed for biomechanical studies. The AC angles were determined using the coordinates of the nodes at the scleral spur and its adjacent nodes to calculate the initial and final angles, and we reported the change in AC angles (∆∠) as well as the final AC angles (∠f). For each parameter, ∆∠ and ∠f were reported as the average and standard deviation of all the scenarios with the parameter value, and the P-values were determined using the two-sample t-test assuming unequal variances. The cases were classified based on the final AC angle: open angles had final AC angles of ∠f > 20°, narrow angles had final AC angles of 0° < ∠f < 20°,26,32 and angle closure cases had final AC angles of ∠f = 0°. Multiple linear regression analysis was performed to rank the effects of each evaluated parameter. We normalized each parameter from 0 to 1 and reported the results as the coefficients ± standard errors. The multiple linear regression was governed by the following equation:  
\begin{eqnarray} && y = \left( {\frac{{{\rm{ACD}} - 2}}{2}} \right){x_{{\rm{ACD}}}} + \left( {\frac{{{\rm{ACW}} - 10}}{2}} \right){x_{{\rm{ACW}}}} + \left( {\frac{{3\, *\, {\rm{IC}} }}{{10}}} \right){x_{{\rm{IC}}}} \nonumber \\ && + \left( {\frac{{10\, *\,{\rm{IT}} - 3}}{2}} \right){x_{{\rm{IT}}}} + \left( {\frac{{E - 4}}{{20}}} \right){x_E} + \left( {\frac{{10\,{\rm{*}}\, v}}{3}} \right){x_v} + c\end{eqnarray}
(1)
where y is the independent variable (∆∠, ∠f or percentage ∆∠), x is the coefficient of the dependent parameter, and c is the constant. Since the variance of the parameters was skewed for angle closure cases (∠f ≥ 0°), we performed statistical analysis using the Wilcoxon rank-sum test and employed the Bonferroni correction. 
Results
Classification and Angle Changes
Of the 1344 simulated cases of pupil dilation, 61 (4.54%) ended up with angle closure, 160 (11.9%) had narrow angles, and 1123 (83.56%) maintained open angles. During pupil dilation, the AC angle width decreased for all scenarios, but the magnitude of change varied based on the parameter, without influencing the final AC angle (Figs. 3 and 4). When ACD decreased from 4 to 2 mm, the ∠f decreased following pupil dilation (53.4° ± 12.3° to 21.3° ± 14.9°; P < 0.001), even though ∆∠ decreased (15.4° ± 9.3° to 9.37° ± 11.1°; P < 0.001). Similarly, when ACW decreased from 12 to 10 mm, the ∠f decreased following pupil dilation (48.2° ± 13.5° to 26.2° ± 18.2°; P < 0.001), and ∆∠ increased (7.4° ± 6.8° to 16.4° ± 11.5°; P < 0.001). The largest changes were seen when IT increased from 0.3 to 0.5 mm, where ∠f decreased the most (52.6° ± 12.3° to 24.4° ± 15.1°; P < 0.001), and ∆∠ increased (5.3° ± 7.1° to 19.3° ± 10.2°; P < 0.001). When IC increased from 0 to 0.3 mm, the ∠f decreased following pupil dilation (45.0° ± 19.2° to 33.9° ± 16.5°; P < 0.001), even though ∆∠ decreased (19.5° ± 10.2° to 5.4° ± 8.2°; P < 0.001). The smallest changes were seen in stroma stiffness E, when increased from 4 to 24 kPa, the ∠f decreased following pupil dilation (40.3° ± 17.3° to 37.4° ± 19.2°; P = 0.0644), and ∆∠ increased (10.9° ± 12.2° to 13.1° ± 8.8°; P < 0.001). When Poisson's ratio v increased from 0 to 0.3, the ∠f decreased following pupil dilation (42.7° ± 17.7° to 34.2° ± 18.1°; P < 0.001), and ∆∠ increased (8.1° ± 9.4° to 16.6° ± 10.4°; P < 0.001) (Table). 
Figure 3.
 
Box plots of the angle changes with respect to the explored parameters. Note that the positive angle changes represent a decrease in the anterior chamber angle. There were statistical intergroup differences for the parameters ACD, ACW, IT, IC, and v, and E = 4 kPa and 24 kPa (P < 0.05).
Figure 3.
 
Box plots of the angle changes with respect to the explored parameters. Note that the positive angle changes represent a decrease in the anterior chamber angle. There were statistical intergroup differences for the parameters ACD, ACW, IT, IC, and v, and E = 4 kPa and 24 kPa (P < 0.05).
Figure 4.
 
Box plots of the final anterior chamber angles with respect to the explored parameters. There were statistical intergroup differences for the parameters ACD, ACW, IT, IC, and v (P < 0.05).
Figure 4.
 
Box plots of the final anterior chamber angles with respect to the explored parameters. There were statistical intergroup differences for the parameters ACD, ACW, IT, IC, and v (P < 0.05).
Table.
 
Change in AC Angle and Final AC Angles With Respect to Parameter Changes
Table.
 
Change in AC Angle and Final AC Angles With Respect to Parameter Changes
Multiple Linear Regression
The results of the multiple linear regression showed that, for change in AC angles (the AC angles always decrease after pupil dilation), the order of influence of the parameter coefficients was as follows: IT (14.0 ± 0.269, P < 0.001), ACW (–12.6 ± 0.315, P < 0.001), IC (–12.0 ± 0.301, P < 0.001), ACD (10.0 ± 0.326, P < 0.001), v (8.51 ± 0.295, P < 0.001), and E (1.90 ± 0.292, P < 0.001). The constant was 4.98 ± 0.347, and the adjusted R2 was 0.85. Note that the negative values indicate an inverse relationship (e.g., increase in IT results in larger decrease in AC angles, but increase in ACW results in lesser decrease in AC angles) (Fig. 5A). 
Figure 5.
 
Multiple linear regression of AC parameters with respect to (A) angle change, (B) final angles, and (C) percentage change from the initial angle. The green bars represent a positive correlation with the factor, while the red bars represent a negative correlation with the factor.
Figure 5.
 
Multiple linear regression of AC parameters with respect to (A) angle change, (B) final angles, and (C) percentage change from the initial angle. The green bars represent a positive correlation with the factor, while the red bars represent a negative correlation with the factor.
For the final AC angles, the order of influence of the parameter coefficients was as follows: IT (–28.2 ± 0.287, P < 0.001), ACD (26.0 ± 0.347, P < 0.001), ACW (11.6 ± 0.335, P < 0.001), v (–8.51 ± 0.314, P < 0.001), IC (–8.06 ± 0.321, P < 0.001), and E (–1.90 ± 0.311, P < 0.001). The constant was 45.9 ± 0.370, and the adjusted R2 was 0.944. Note that the negative values indicate an inverse relationship (e.g., increase in IT results in decrease in final AC angles) (Fig. 5B). 
For the percentage change in angles (with respect to the initial angle), the order of influence of the parameter coefficients is as follows: IT (41.3 ± 0.978, P < 0.001), ACW (–29.8 ± 1.14, P < 0.001), v (19.5 ± 1.07, P < 0.001), IC (–14.2 ± 1.09, P < 0.001), E (7.62 ± 1.06, P < 0.001), and ACD (–1.58 ± 1.18, P = 0.734). The constant was 9.44 ± 1.26, and the adjusted R2 was 0.71. Note that the negative values indicate an inverse relationship (e.g., increase in ACW results in a smaller percentage change in angle) (Fig. 5C). 
Discussion
Our study combined clinical knowledge with computational analysis to understand how AC dynamics could influence angle closure. Our models were able to predict cases of angle closure, revealing that the AC angle width always decreased during pupil dilation. The extent of this angle change varied based on the combination of parameters that had changed, with specific parameters such as iris thickness having a greater impact. 
Increased Iris Thickness, Convexity, Stroma Stiffness, and Poisson's Ratio Led to Narrower AC Angles
Existing literature was only able to report significance for individual factors that correlate with angle closure, and our FE predictions were able to highlight the disproportionate influence of the six investigated parameters in relation to the AC angle. It was clear from the results that the morphology of the iris (thickness and convexity) and its innate biomechanical behavior (stiffness and Poisson's ratio) were crucial in influencing the way the iris deformed during dilation, and angle closure was further exacerbated by decreased AC biometry (ACD and ACW). 
Our results showed that iris thickness had the largest effect on the narrowing of the chamber angle. This result corroborated literature findings, specifically reports of iris thickness at 750 µm, 2000 µm, and maximum (IT750, IT2000, and ITM)11,12 from the sclera spur. As the primary tissue involved in angle closure, it is unsurprising that iris morphology is directly related to narrower AC angles. 
Iris convexity had also been correlated with angle closure, with increased convexity reported in patients with ACG.12,33 This phenomenon is likely to be the result of muscle activity controlling pupil size, the biomechanical differences between the stroma and muscle, and the aqueous pressure that is induced between the anterior and posterior chambers when the dilator muscle contracts.34 Hence, iris convexity is influenced by the biomechanical equilibrium between the stroma and muscle states within the AC, and our results also indicated that the stiffness and Poisson's ratio of the stroma were correlated to angle closure. 
Our FE Model Was Able to Predict Cases of Angle Closure
In our study, we designed the AC to be accurate and robust, have few geometrical compromises, and be able to perform the high deformation simulations (Fig. 6). Our results showed that a small fraction (4.54%) of the cases had angle closure. Among these 61 scenarios, all of them had a shallow AC (ACD = 2 mm), 59 had a thick iris (IT = 0.5 mm), and 58 had a narrow AC width (ACW = 10 mm). It is important to note that this percentage of cases with angle closure applies to the prescribed dilator muscle contraction force dilating the pupil from 4.0 mm to about 5.1 mm, and we expect the number of scenarios for angle closure to increase when the iris is dilated further. Our FE presents an opportunity to develop a tool for angle closure, and we believe that clinical diagnosis could be improved by combining the knowledge from clinical imaging techniques and computational biomechanics to evaluate for angle closure. Using tools such as inverse FE,3 it may be possible to improve prognosis of angle closure, allowing potential candidates to take precautionary measures for the disease. 
Figure 6.
 
Comparing AC parameters with significant correlation: ACD, ACW, IT, IC, E, and v. For each AC figure, the left and right halves show the iris before and after dilator muscle contraction. The red and blue lines show the initial and final AC angles, and the dotted blue lines show the outline of the final iris shape. ∠f is presented as the mean ± SD of cases corresponding to the parameter.
Figure 6.
 
Comparing AC parameters with significant correlation: ACD, ACW, IT, IC, E, and v. For each AC figure, the left and right halves show the iris before and after dilator muscle contraction. The red and blue lines show the initial and final AC angles, and the dotted blue lines show the outline of the final iris shape. ∠f is presented as the mean ± SD of cases corresponding to the parameter.
The Amount of Angle Change Does Not Reflect the Final AC Angle
Whether angle closure develops depends on the interaction with many parameters, and it is clear from the multiple linear regression coefficients that the correlations are not straightforward. For example, when IT increases from 0.3 to 0.5 mm, the ∆∠ increases and the ∠f decreases. However, when ACD increases from 2 to 4 mm, the ∆∠ increases and ∠f increases as well. This meant that a thicker iris contributed more to closing of the AC angle, yet a larger AC angle from a larger ACD was effective in resisting angle closure caused by the other factors. Therefore, the state of the final AC angle is dependent on the combination of all the factors, with the extreme cases (i.e., large IT, shallow ACD, small ACW, and high v) resulting in closure of the chamber angle. 
Anterior Chamber Interactions is Highly Complex
Several more parameters highlighted in the literature had strong correlations with angle closure.3538 Two such parameters are the anterior chamber area (ACA) and, by geometric transitive property (i.e., two-dimensional [2D] to 3D), the anterior chamber volume (ACV). These are dependent parameters from the cumulative effect of other AC biometry (i.e., cornea radius of curvature, sclera radius of curvature, ACD, ACW, IT, IC, lens thickness, etc.) influencing the residual ACA/ACV space. Likewise, the combined effect of iris biomechanical properties (i.e., E and v) could vary the ACA/ACV changes during pupil dilation. In fact, Foo et al.39 ranked determinants influencing AC angles and found ACA/ACV to be most significantly correlated, along with lens vault, which is also influenced by AC biometry (i.e., ACD, ACW, lens thickness, etc.). This implied that the dynamic interactions within the AC are immensely complex and likely to be a cumulative effect of all factors at disproportionate weightage, with interdependencies of parameters affecting one another. We believe more work is required in segregating and analyzing individual parameters to correlate them with angle closure. 
Additionally, while we analyze 2D images captured, it is important to remember that there are many concurrent processes happening, and the equilibrium state of the tissues within the AC can be difficult to ascertain. At the exterior, extraocular muscles are constantly changing the position of the globe, and saccadic eye movements create fluctuations of cellular stresses40 from the inertia of the aqueous humor, which in turn affects iris movements. During distance accommodation, ciliary muscle contraction pushes the ciliary body centrally and anteriorly to increase lens curvature and increases the lens vault.4144 This, in turn, pushes the iris anteriorly during near vision. During light accommodation, the iris dilator muscle constricts when light intensity decreases to increase pupil size, pushing the anterior border layer closer to the cornea. All these accommodative processes change not only the positions of the intraocular tissues but also the differential pressure between the anterior and posterior chambers of the anterior segment of the eye.34 The invention of laser peripheral iridotomy seeks to prevent angle closure by relieving pupil block and excessive iris anterior bowing.45 These anterior chamber interactions are highly complex and dynamic, and while we attempt to rationalize individual measurable parameters, it is important to remember these parameters often influence one another, and this parametric study represents the first step in gaining a clearer understanding of the development of angle closure. 
Limitations
As with all studies, the assumptions and design choices of this study had some drawbacks. First, we performed this study using the “design of experiments” method. This approach allowed us to systematically distribute cases among all the parameters. However, while this method provides a valuable framework for understanding the influence of each parameter, it does not reflect the distribution of these parameters in a human population, which is likely to follow a normal or skewed distribution.46 This implies that the design of experiments method could introduce higher result variance, potentially reducing the probability values in correlations that might have been significant. With a normal or skewed distribution, we also expect the cases of angle closure to be greatly reduced since the prevalence of these extreme cases is at the tail end of the population distribution. 
Second, our computational study examined the solid mechanics of soft tissues in the AC without involving the aqueous humor. The conditions in vivo could be affected by intraocular pressure (IOP), aqueous humor movement, dynamic interactions with the porous iris and outflow through the trabecular meshwork and ciliary body (conventional and unconventional pathways),47 and so on. In particular, pupillary block is an important observation in many angle closure subjects,48,49 and the difference in pressure between the chambers anterior and posterior to the iris had been hypothesized to influence iris convexity and AC angles.28,50 As the dilator muscle constricts, it slides outward and downward along the lens, exerting a force that prevents aqueous humor from escaping and creating a pupillary block.48,51 This is likely to exacerbate angle closure, resulting in a more pronounced convex iris often seen in patients. Hence, future models could include a biphasic pressurized anterior chamber model with IOP, iris stroma porosity, and solid–fluid interfaces to investigate the dynamics within a more physiologic anterior chamber. Additionally, other biometry parameters may be included to improve iris dynamics, including lens curvature, crypts, and furrows that would interact with the aqueous humor to affect how the pupil dilates. 
Third, research on iris biomechanics is lacking, especially at the microscopic level. The iris anterior border layer (ABL) has been investigated to reveal an intercrimp fiber pattern, with the fiber direction approximately 45° away from the radial direction. Below the ABL, the sparse collagen network is much less understood, with little information regarding the porosity and biomechanical properties of the stroma meshwork. This makes the model sensitive to inaccuracies in material properties, which could have an impact on the results. 
Finally, we generated models based on general geometric shapes, each with a smooth ABL and uniform iris curvature. The models were not able to account for variable features such as nonuniform iris thickness and curvature, iris crypts, and furrows. These features affect iris dilation movement and explain cases of short iridotrabecular contact cases52 and concave iris cases,53 further contributing to the incidence of angle closure. 
Conclusions
This study highlights the intricate role of AC biometry and biomechanics influencing angle closure, underscoring the importance of multiparameter analysis for the development of more accurate diagnostic techniques. While our study utilized “hypothetical” patients, combining this approach with optical coherence tomography imaging in a clinical scenario could enhance the identification of patients at risk of developing angle closure. Further research is essential to enhance the complexity of models, ultimately improving clinical prognosis for preventing the development of angle closure cases. 
Acknowledgments
The authors thank the donors of the National Glaucoma Research, a program of the BrightFocus Foundation, for support of this research (G2021010S [MJAG]); the NMRC-LCG grant “TAckling & Reducing Glaucoma Blindness with Emerging Technologies (TARGET),” award ID: MOH-OFLCG21jun-0003 (MJAG); and the SERI-Lee Foundation grant (LF0622-03). 
Disclosure: R.K.Y. Tan, None; G.Y. Ng, None; T.A. Tun, None; F.A. Braeu, None; M.E. Nongpiur, None; T. Aung, None; M.J.A. Girard, None 
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Figure 1.
 
The flowchart for processing the FE models.
Figure 1.
 
The flowchart for processing the FE models.
Figure 2.
 
(A) Anterior chamber parameters for the models, with the analyzed parameters highlighted in red. (B) The computer-aided design (CAD) model of the anterior chamber was designed to align with anatomic measurements. (C) Simplification of the model by combining the trabecular meshwork, cornea, and scleral regions since they did not affect the final results. (D) The iris was designed with a 0.20-mm root, sphincter muscle at two-fifths of the thickness and a 0.80-mm radius, and the dilator muscle at one-tenth the iris thickness beginning from the mid-radius of the sphincter muscle to the iris root.
Figure 2.
 
(A) Anterior chamber parameters for the models, with the analyzed parameters highlighted in red. (B) The computer-aided design (CAD) model of the anterior chamber was designed to align with anatomic measurements. (C) Simplification of the model by combining the trabecular meshwork, cornea, and scleral regions since they did not affect the final results. (D) The iris was designed with a 0.20-mm root, sphincter muscle at two-fifths of the thickness and a 0.80-mm radius, and the dilator muscle at one-tenth the iris thickness beginning from the mid-radius of the sphincter muscle to the iris root.
Figure 3.
 
Box plots of the angle changes with respect to the explored parameters. Note that the positive angle changes represent a decrease in the anterior chamber angle. There were statistical intergroup differences for the parameters ACD, ACW, IT, IC, and v, and E = 4 kPa and 24 kPa (P < 0.05).
Figure 3.
 
Box plots of the angle changes with respect to the explored parameters. Note that the positive angle changes represent a decrease in the anterior chamber angle. There were statistical intergroup differences for the parameters ACD, ACW, IT, IC, and v, and E = 4 kPa and 24 kPa (P < 0.05).
Figure 4.
 
Box plots of the final anterior chamber angles with respect to the explored parameters. There were statistical intergroup differences for the parameters ACD, ACW, IT, IC, and v (P < 0.05).
Figure 4.
 
Box plots of the final anterior chamber angles with respect to the explored parameters. There were statistical intergroup differences for the parameters ACD, ACW, IT, IC, and v (P < 0.05).
Figure 5.
 
Multiple linear regression of AC parameters with respect to (A) angle change, (B) final angles, and (C) percentage change from the initial angle. The green bars represent a positive correlation with the factor, while the red bars represent a negative correlation with the factor.
Figure 5.
 
Multiple linear regression of AC parameters with respect to (A) angle change, (B) final angles, and (C) percentage change from the initial angle. The green bars represent a positive correlation with the factor, while the red bars represent a negative correlation with the factor.
Figure 6.
 
Comparing AC parameters with significant correlation: ACD, ACW, IT, IC, E, and v. For each AC figure, the left and right halves show the iris before and after dilator muscle contraction. The red and blue lines show the initial and final AC angles, and the dotted blue lines show the outline of the final iris shape. ∠f is presented as the mean ± SD of cases corresponding to the parameter.
Figure 6.
 
Comparing AC parameters with significant correlation: ACD, ACW, IT, IC, E, and v. For each AC figure, the left and right halves show the iris before and after dilator muscle contraction. The red and blue lines show the initial and final AC angles, and the dotted blue lines show the outline of the final iris shape. ∠f is presented as the mean ± SD of cases corresponding to the parameter.
Table.
 
Change in AC Angle and Final AC Angles With Respect to Parameter Changes
Table.
 
Change in AC Angle and Final AC Angles With Respect to Parameter Changes
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