FEA is a popular method to analyze complex systems. The benefits of using an FEA on complex problems are that geometry can be precisely defined58. It is very sensitive to measure even a subtle change in geometry, which is otherwise difficult to pick up with the current instruments59. Since FEA uses the static equilibrium and theories of elasticity, it is possible to assess a physical system subjected to multiple external forces with regard to stresses, deformation and strain60. Hence FEA was chosen as the analytical tool.
A computer with 2.80GHz CPU and 8GB RAM was used for this experimental study. COMSOL Multiphysics® (v5.2, COMSOL AB, Stockholm, Sweden), an FEA tool was used for the construction and analysis of the human eye model. The COMSOL Multiphysics® was used for the FEA because of its ability to provide accurate FE simulation results. The flow of procedure for the FEA includes,
- Modeling of the geometry
- Assigning the material properties
- Meshing
- Setting boundary conditions
- Parametric sweep analysis
- Post-processing of the results
Ocular parameters of various structures and their material properties were obtained from previous works of literature done on Indian eyes. Linear static analysis was carried out ignoring gravity.
- Modeling
It is unrealistic to consider a single eye geometry since the dimensions of the human eye vary from person to person. Here we have used the average value of each of the ocular parameters of the Indian eyes obtained through a thorough literature search.
The human eye model, which closely resembles the dimensions of the actual human eye, was constructed in 2D (Figure 7A) and was converted into a solid 3D model (Figure 7B). For simplicity, the human eye was assumed to be rotationally symmetrical along the optic axis. The eye model comprises of the following structures: Lid wiper, cornea, anterior chamber, vitreous cavity, sclera, optic nerve and optic nerve head. The anteroposterior (transverse) diameter of the eye model is approximately 24 mm, and the vertical (sagittal) diameter is approximately 23 mm61.
The asymmetrical nature of the optic nerve was ignored. The dimensions used in the construction of each structure of the human eye are as shown in Table 1.
Table 1: Dimensions of ocular structures and contact lens used in the finite element modeling
Part of the eye
|
Value (mm)
|
Lid wiper thickness
|
0.8
|
Corneal thickness
|
0.5
|
Corneal diameter
|
12
|
Anterior corneal curvature
|
7.8
|
Posterior corneal curvature
|
6.5
|
Scleral thickness
|
0.5
|
Scleral radius
|
11.5
|
Diameter of the contact lens
|
15
|
Base curve of the contact lens
|
8.6
|
Thickness of the contact lens
|
0.08
|
Since eyelid, conforms to the curvature of the ocular surface while blinking, we have assumed the curvature of the inner lid wiper to be the curvature of the anterior cornea. The thickness of the lid wiper was considered to be as 0.8mm with reference to the literatures62. The contact width between the lid wiper and cornea was 1mm63. The entire simulated model consisting of the eyeball and the lid wiper can be seen in Figure 7C.
Different soft CL geometries have been explored, in the previous research64–66. Complete specifics of the exact contact lens geometries were not available in the literature. The center thickness, base curve and the diameter of the CL were made to be available in the literatures67. In general, a CL is thicker at the center than in the periphery and this ranges from 0.05-0.9mm. The radius of curvature of the back surface of the lens i.e. the base curve generally ranges from 7-9 mm and also the diameter of the CL ranges from 13.00 to 14.50mm.
In this study, based on the eye geometry the contact lens of 15 mm diameter (2-3mm greater than Corneal diameter) and 8.6mm base curve (0.8-1.0mm flatter than Corneal curvature) was fitted in the eye (Figure 7D). Contact lens parameters used in this study can be found as mentioned in Table 1.
Young’s modulus, Poisson’s ratio and Density were the important material properties considered. Human ocular tissues are generally viscoelastic and exhibit nonlinear material properties29. This nonlinear material property of the human eye ranges widely due to its complex nature. Hence, the material properties were assumed to be homogenous, isotropic and linearly elastic. As shown in Table 2 the material properties of the ocular structures were obtained from the previous works of literature. Young’s modulus of the human eyelid has not yet been investigated45. Hence a value of 0.42MPa which is the young’s modulus of the human skin was assumed45,68. The Poisson’s ratio of the aqueous humor, vitreous humor, retina, zonules, and optic nerve have not yet been investigated. Since soft biological tissues hold more amount of moisture, Poisson’s ratio was set to be less than 0.5 for these ocular structures29,69.
Table 2: Material properties of the ocular structures and contact lens used in the finite element modeling
Part of the eye
|
Young’s modulus (MPa)
|
Poisson’s ratio
|
Density (Kg/m3)
|
Lid wiper68, 70
|
0.42
|
0.49
|
999
|
Cornea60, 71,72
|
0.4
|
0.42
|
1400
|
Aqueous humor60,73
|
0.037
|
0.49
|
999
|
Vitreous humor60,73
|
0.042
|
0.49
|
999
|
Retina68,74,69,75
|
0.03
|
0.49
|
999
|
Optic nerve69,75,76
|
0.03
|
0.49
|
999
|
Comfilcon A contact lens59,77
|
0.82
|
0.49
|
1040
|
The material properties used for the contact lens are as shown in Table 2. Contact lens is a rubbery polymer and it is highly hydrated. Hence a Poisson's ratio of 0.49 was set which makes it incompressible. Density of the contact lenses was not directly available in the literature. But specific gravity was available for the contact lenses. Hence using the following formula, we have calculated the density of these contact lenses.
![](data:image/png;base64,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)
Where,
Density of the water at 40 C = 999.9778
Specific gravity of the contact lens = 1.0479
- Analysis
Mesh convergence study was carried out to analyze the proper number of finite elements. Figure 8 shows the result when a body load of 0.03N is applied on the surface of the lid wiper. It can be found that the von mises stress, barely change when the length of a side of the finite element is 0.259 mm or more. Hence, the value of 0.259 mm was used as the length of a side of the element during Finite Element Analysis.
All components of the FEM were meshed with the physics-controlled settings in the COMSOL Multiphysics®. The predefined size of each element was set as fine. Figure 9 shows the mesh-divided model of the eyeball with lid wiper (A) and the contact lens (B).
The outer surface of the sclera was fixed completely. During blink the lid wiper is in contact with the cornea. Hence a contact pair was created between these 2 surfaces. The dynamic friction coefficient of the contact surface between the cornea and the lid wiper was set to 0.1 with reference to the previous literatures80. The eyelid itself exerts some amount of force over the cornea during blink9. Hence a body load of 0.03N was applied at the surface of the lid wiper45.
Blink was simulated by making the lid wiper move over the cornea (Figure 7C). Parametric sweep analysis was carried out by displacing the lid wiper for every 100 i.e. from the superior to the inferior portion of the cornea. Linear static analysis dealing with the contact problem was carried out. The whole analysis along with the parametric sweep required approximately 12hrs to complete. Von Mises stress, deformation and displacement were obtained as the result of FEA. Stress is defined as “the ratio of internal force produced to the area over which the force acts”. In humans, it represents the feeling of pain. Displacement is the distance from which one object has moved from its original location when an external force is applied. These indicate the amount of biomechanical response in human tissues81. Surface plots were used to display the results of the analysis.