Open Access
Cornea & External Disease  |   April 2023
Biomechanical Responses of Different Cap Thicknesses of Corneas After Small Incision Lenticule Extraction: Finite Element Analysis
Author Affiliations & Notes
  • Lihua Fang
    Key Laboratory of Nondestructive Test (Ministry of Education), Nanchang Hangkong University, Nanchang, China
  • Tianzi Jin
    Key Laboratory of Nondestructive Test (Ministry of Education), Nanchang Hangkong University, Nanchang, China
  • Yu Cao
    Key Laboratory of Nondestructive Test (Ministry of Education), Nanchang Hangkong University, Nanchang, China
  • Xuefeng Li
    Key Laboratory of Nondestructive Test (Ministry of Education), Nanchang Hangkong University, Nanchang, China
  • Jialin Hu
    Key Laboratory of Nondestructive Test (Ministry of Education), Nanchang Hangkong University, Nanchang, China
  • Xinheng Zhao
    Key Laboratory of Nondestructive Test (Ministry of Education), Nanchang Hangkong University, Nanchang, China
  • Yan Wang
    Tianjin Key Lab of Ophthalmology and Visual Science, Tianjin Eye Institute, Tianjin Eye Hospital; Nankai University Eye Institute, Nankai University; Clinical College of Ophthalmology, Tianjin Medical University, Tianjin, China
  • Correspondence: Yan Wang, Tianjin Key Lab of Ophthalmology and Visual Science, Tianjin Eye Institute, Tianjin Eye Hospital; Nankai University Eye Institute, Nankai University; Clinical College of Ophthalmology, Tianjin Medical University, Tianjin 300020, China. e-mail: wangyan7143@vip.sina.com 
Translational Vision Science & Technology April 2023, Vol.12, 5. doi:https://doi.org/10.1167/tvst.12.4.5
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      Lihua Fang, Tianzi Jin, Yu Cao, Xuefeng Li, Jialin Hu, Xinheng Zhao, Yan Wang; Biomechanical Responses of Different Cap Thicknesses of Corneas After Small Incision Lenticule Extraction: Finite Element Analysis. Trans. Vis. Sci. Tech. 2023;12(4):5. https://doi.org/10.1167/tvst.12.4.5.

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Abstract

Purpose: This study analyzed the biomechanical responses of different corneal cap thicknesses after small incision lenticule extraction (SMILE).

Methods: Individual finite element models of myopic eyes were constructed based on the clinical data. Then, four types of corneal cap thicknesses after SMILE were included for each model. The biomechanical effects of material parameters and intraocular pressure on corneas with different cap thicknesses were analyzed.

Results: When the cap thickness increased, the vertex displacements of the anterior and posterior corneal surfaces decreased slightly. The corneal stress distributions demonstrated little change. Regarding wave-front aberrations caused by the displacements of the anterior surface, the absolute defocus value decreased slightly, but the magnitude of primary spherical aberration increased slightly. The horizontal coma increased, and the levels of other low-order and high-order aberrations were small and demonstrated little change. The corneal vertex displacement and wave-front aberration were significantly affected by elastic modulus and intraocular pressure, whereas the corneal stress distribution was greatly affected by intraocular pressure. There were obvious individual differences in the biomechanical responses of human eyes.

Conclusions: The biomechanical difference of different corneal cap thicknesses after SMILE was small. The effect of corneal cap thickness was significantly less than that resulting from material parameters and intraocular pressure.

Translational Relevance: Individual models were constructed based on the clinical data. The elastic modulus was controlled by programming to simulate its heterogeneous distribution in the actual human eye. The simulation was improved to bridge the gap between basic research and clinical care.

Introduction
Recently, with the rising proportion of juvenile myopia, the incidence of refractive surgery has increased substantially. The types of refractive surgery are diverse. Small Incision Lenticule Extraction (SMILE) has attracted attention because of the advantages of small incisions, the absence of corneal flaps and the ability to keep the cornea intact.1 During SMILE, the corneal stromal layer is cut with a laser, and the refractive lenticule is obtained and removed to correct myopia.2 Because the cornea is cut, the corneal structure changes, and the corneal biomechanical strength and resistance to deformation are reduced.3 However, the corneal cap can still play a biomechanical role after SMILE.4-6 Because the elastic modulus of the corneal stromal layer at different depths is different, there are conflicting opinions on the cutting depth used for SMILE.6-9 
In China, the cap thickness range is commonly expanded to 110 to 130 µm according to the condition of myopic eyes (such as central corneal thickness and diopter). Thicker caps are widely used abroad.10 In contrast, there is a view that the corneal cap should be thicker and that the cutting depth should be increased. It is believed that this approach can retain more of the anterior corneal stromal layer with a larger elastic modulus and that the stability of corneal biomechanical properties will be maintained. In addition, an extra lenticule with a specific thickness should be considered to prevent the refractive lenticule from being too thin and difficult to remove smoothly. The safety standard of SMILE also needs to be considered. For example, the residual stromal thickness (RST) should not be thinner than 60% of the central corneal thickness (CCT). 
The finite element method (FEM) is a method of mathematical approximation. The FEM uses a limited number of simple and interactive elements to approximate a complex system. Then the satisfaction conditions of the whole domain (i.e., the approximate solution of the actual problem) are obtained. The FEM is often used to analyze the geometric structure and biomechanical properties because of its strong adaptability and high accuracy.11 In ophthalmology, three-dimensional models are established based on the condition of myopic eyes.12,13 Then the FEM can be used to accurately and conveniently simulate biomechanical responses. This method is good for making disease diagnoses and performing clinical analyses. 
In China, Li et al.14 analyzed the influencing factors of elastic wave velocity of cornea-like structures by the FEM. Wang et al.12 used the FEM to predict large optic nerve head strains. Fang et al.15 studied the biomechanics of laser-assisted in situ keratomileusis (LASIK) flap thickness by using the FEM. Abroad, Roy et al.11 established finite element models to analyze the effects of corneal elasticity on morphological changes before and after LASIK. Roy et al.16 constructed human eye models to explore the differences in corneal elasticity after different types of refractive surgery. Zvietcovich et al.17 used finite element simulation to verify corneal elastic imaging results. 
This study constructed three-dimensional individual finite element models of myopic eyes, and then the biomechanical responses of corneas with different cap thicknesses were determined. Furthermore, the influence of cap thickness on corneal biomechanics was explored, which had guiding significance in clinical practice. 
Methods
Individual Human Eye Geometric Model
The oculus dexter and oculus sinister of three patients were studied. Clinical data from myopic eyes before and after SMILE were obtained from the ophthalmic hospital. Unigraphics NX 12.0 (Siemens PLM Software, Plano, TX, USA) was used to establish six cases of three-dimensional individual human eye preoperative geometric models. The X-axis curvature and Y-axis curvature of the ellipsoid were, respectively, from Rf and Rs. The Rf and Rs were derived from corneal topographic maps, representing flat and steep corneal radius of curvatures. The Rf and Rs formed an angle of 90°, and Rs represented the radius of curvature of the maximum diopter. The center of the scleral sphere in the model was placed at the origin of the three-dimensional coordinate system. The direction from the center of the scleral sphere to the apex of the cornea was the positive direction of the Z-axis. The Z-axis corresponded to the anterior and posterior poles of the globe. As shown in Figure 1, the size of the model shown in the three-dimensional coordinate system was consistent with the size of the actual human eye. 
Figure 1.
 
(A) Postoperative geometric model. The upper part of the model was the cornea, and the lower part was the sclera. The inner circule shown in the upper part was the cutting surface. The positive half axis of the X-axis was perpendicular to the center of the incision. (B) Mesh generation of the postoperative geometric model.
Figure 1.
 
(A) Postoperative geometric model. The upper part of the model was the cornea, and the lower part was the sclera. The inner circule shown in the upper part was the cutting surface. The positive half axis of the X-axis was perpendicular to the center of the incision. (B) Mesh generation of the postoperative geometric model.
Figure 2.
 
Distribution of the corneal elastic modulus in Case One's postoperative model. The corneal elastic modulus in the XZ plane of three-dimensional coordinate system was extracted. The size of the human eye model was reflected by the X-axis and Y-axis (adopted the standard unit: meter), and the elastic modulus was reflected by the color axis (adopted the standard unit: Pa).
Figure 2.
 
Distribution of the corneal elastic modulus in Case One's postoperative model. The corneal elastic modulus in the XZ plane of three-dimensional coordinate system was extracted. The size of the human eye model was reflected by the X-axis and Y-axis (adopted the standard unit: meter), and the elastic modulus was reflected by the color axis (adopted the standard unit: Pa).
To fit the cutting surface and the incision, the point cloud data were used. The point cloud data were calculated according to parameters including the optical zone, the preoperative diopter, the actual refractive lenticule thickness, and the actual cap thickness. The point cloud data were imported into the corresponding established preoperative geometric model. In addition, there was a cavity at the cutting position after the refractive lenticule was removed. The maximum thickness of the cavity was only a few micrometers. Finally, individual human eye postoperative geometric models with the corresponding actual cap thicknesses were obtained. 
In addition to the established models with the corresponding actual cap thicknesses, other human eye models were respectively established. The concept of RST was introduced to unify the standard in this study. For the same human eye, the thicker the cap thickness was, the thinner the RST was. RSTs of 250 µm, 200 µm and 150 µm were considered. 
Table 1 shows the surgical simulation parameters of six cases of myopic eyes. In addition, Table 2 shows the ocular parameters of six cases of myopic eyes, such as the diopter of spherical lens, the diopter of cylindrical lens, and so on. 
Table 1.
 
The Surgical Simulation Parameters of Six Cases of Myopic Eyes
Table 1.
 
The Surgical Simulation Parameters of Six Cases of Myopic Eyes
Table 2.
 
The Ocular Parameters of Six Cases of Myopic Eyes
Table 2.
 
The Ocular Parameters of Six Cases of Myopic Eyes
Table 3.
 
The Normal Material Parameters and Intraocular Pressure Levels
Table 3.
 
The Normal Material Parameters and Intraocular Pressure Levels
Table 4.
 
The Other Material Parameters and Intraocular Pressure Levels
Table 4.
 
The Other Material Parameters and Intraocular Pressure Levels
It should be noted that one myopic eye was one case (such as Case One). A case contained multiple finite element models, including different values of cap thickness, elastic modulus, intraocular pressure, and more. In addition, one type of elastic modulus and intraocular pressure was one group (such as Group A mentioned later). 
Material Parameters
The cornea is nonuniform. The corneal elastic modulus at different depths is generally different. However, the trend showed a decrease in the corneal elastic modulus from the anterior stromal layer to the posterior.18-20 Moreover, the biomechanical properties of the anterior stromal layer were better than those of the full-thickness cornea.21-24 
In this study, MATLAB R2019a (MathWorks, Natick, MA, USA) was used to realize programming control of material parameter distribution in the models. The Normal Corneal Elastic Modulus was 1 to 1.4 MPa as shown in Figure 2.25,26 The elastic modulus decreased linearly with the corneal depth from 1.4 MPa of the anterior corneal surface to 1 MPa of the posterior corneal surface. Because the refractive lenticule was removed, the elastic modulus of the cavity changed suddenly and obviously. The corneal density was 1076 kg/m³, and the Poisson ratio was 0.49. In addition, the normal scleral elastic modulus was 2.4 MPa, the density was 1243 kg/m³, and the Poisson ratio was 0.49.25,27 
Intraocular pressure affects various biomechanical responses, such as corneal elasticity and deformation.25 Generally, the normal intraocular pressure range of human eyes is 10 to 21 mm Hg.25 Considering the actual intraocular pressure of myopic eyes is also critical. Therefore the normal intraocular pressure was set to 15 mm Hg in this study as shown in Table 3
The elastic modulus among clinical individuals demonstrated differences.26 Therefore this study expanded the other elastic modulus range to one-tenth to ten times that of the normal elastic modulus. But the proportion of the corneal and scleral elastic modulus was unchanged. In addition, the intraocular pressure among clinical individuals differed.28,29 Therefore this study expanded the other intraocular pressure range to 10 to 40 mm Hg as shown in Table 4.25,30,31 
Biomechanical Analysis
COMSOL Multiphysics 5.6 (Comsol, Inc., Stockholm, Sweden) was used for finite element analysis of the corneal biomechanical responses before and after SMILE. The corneal shape stability and visual imaging quality have the corresponding characteristics. Displacement and stress distribution reflect shape stability, and wave-front aberration reflects visual imaging quality. This study analyzed vertex displacements, stress distributions, vertex stresses, and wave-front aberrations caused by the displacements. Therefore the biomechanical responses of corneas with different cap thicknesses were determined. In addition, because the wave-front aberration was caused by the displacement, the simulated wave-front aberration also needed to be calculated by MATLAB programming. 
In this study, the anterior and posterior corneal surfaces after SMILE were displaced because of intraocular pressure. More specifically, vertex displacements were the difference values between the postoperative and preoperative vertex displacements. However, these displacements did not include the corneal deformation caused by removing the refractive lenticule. In the clinic, the anterior corneal surface was displaced because the cornea was cut. This displacement included the corneal deformation caused by removing the refractive lenticule. In addition, the stress distributions to be analyzed were present on the intersecting lines between the anterior and posterior corneal surfaces and the XZ plane. It is worth mentioning that aberration values above the fourth-order were minimal.25 Therefore high-order aberrations referred to third- and fourth-order aberrations in this study. 
Results
Effects in Case One With Normal Elastic Modulus and Intraocular Pressure
The normal elastic modulus and intraocular pressure were set in Case One (A random example). Then, the postoperative models with different cap thicknesses were established. Finally, the finite element analysis was completed. Figure 3A shows the vertex displacements of the anterior and posterior corneal surfaces. Figure 3B shows the stress distributions of the intersecting line between the anterior corneal surface and the XZ plane. In addition, Figure 4 shows the aberrations caused by the displacements of the anterior and posterior corneal surfaces. 
Figure 3.
 
(A) The change of the vertex displacements of the anterior and posterior corneal surfaces with the cap thickness. (B) The stress distributions of the intersecting line between the anterior corneal surface and the XZ plane with different cap thicknesses.
Figure 3.
 
(A) The change of the vertex displacements of the anterior and posterior corneal surfaces with the cap thickness. (B) The stress distributions of the intersecting line between the anterior corneal surface and the XZ plane with different cap thicknesses.
Figure 4.
 
The change of the aberrations with the cap thickness caused by the displacements of the (A) anterior and (B) posterior corneal surfaces.
Figure 4.
 
The change of the aberrations with the cap thickness caused by the displacements of the (A) anterior and (B) posterior corneal surfaces.
As shown in Figure 3A, when the cap thickness increased, the vertex displacements of the anterior and posterior corneal surfaces decreased slightly. The change speed of vertex displacement of the anterior corneal surface was slower than that of the posterior corneal surface. Moreover, when the cap thickness was 120 µm, the vertex displacements of the anterior and posterior corneal surfaces were 11.246 µm and 11.345 µm. However, when the cap thickness increased by 149 µm (i.e., the cap thickness was 269 µm), these values decreased by 4.77% and 5.84%, respectively. In addition, when the cap was thinner than 240 µm, the vertex displacement of the anterior surface was smaller than that of the posterior surface. However, when the cap was thicker than 240 µm, the opposite was observed. 
As shown in Figure 3B, cap thickness had little effect on the stress distribution. When the cap thickness increased by 149 µm, the vertex stress of the anterior corneal surface decreased by 2.42%. However, it was worth mentioning that the postoperative stress was significantly higher than that before surgery. For example, the vertex stress of the anterior corneal surface increased by approximately 67.49% after surgery. In general, the stress peaked at the vertex and significantly decreased moving away from the vertex. Then the stress increased slightly at the corneal edge and significantly decreased when closed to the incision. 
As shown in Figure 4, cap thickness had a certain effect on the wave-front aberrations. The aberrations caused by the displacements of the anterior corneal surface were one order of magnitude larger than the aberrations caused by the displacements of the posterior corneal surface. In addition, the two were partially complementary. Regarding the wave-front aberrations caused by the displacements of the anterior corneal surface, when the cap thickness was 120 µm, the defocus was -0.8695 µm, the primary spherical aberration was 0.1699 µm, and the horizontal coma was 0.0080 µm. However, when the cap thickness increased by 149 µm (i.e., the cap thickness was 269 µm), the absolute defocus value decreased by 0.0614 µm, but the magnitude of primary spherical aberration increased by 0.0059 µm. The horizontal coma increased by 0.0327 µm, and the levels of other low-order and high-order aberrations were small and showed little change. 
In conclusion, when the cap thickness of SMILE increased, the vertex displacements of the anterior and posterior corneal surfaces decreased slightly. The cap thickness had little effect on the stress distributions, but the postoperative stresses were significantly larger than the preoperative stresses. The absolute defocus value decreased slightly, but the magnitude of primary spherical aberration increased slightly. The horizontal coma increased, and the levels of other low- and high-order aberrations were small and showed little change. 
Effects in Case One With Other Elastic Modulus and Intraocular Pressure
Various elastic modulus and intraocular pressure were set in Case One because of the differences of the parameters among clinical individuals. Then the postoperative models of Case One with different cap thicknesses were established. Finally, the finite element analysis was conducted. The biomechanical responses of all groups were compared. Therefore the effects of the elastic modulus and intraocular pressure on corneal biomechanics with different cap thicknesses were studied. 
Groupings and specific values are shown in Tables 5 and 6. For example, the elastic modulus was too small in Group D, but the intraocular pressure was normal. The elastic modulus was normal in Group H, but the intraocular pressure was too high. In addition, the elastic modulus and intraocular pressure were normal in Group E. Not all groups have clinical significance. The smaller the elastic modulus is, the softer and more deformable the cornea will be. The higher the intraocular pressure is, the larger the force on the cornea, and the more obvious the corneal deformation will be. If the values of displacements, stresses, or wave-front aberrations are too large, the corneas will not meet the conditions required for SMILE. 
Table 5.
 
Vertex Displacements of the Anterior Corneal Surface
Table 5.
 
Vertex Displacements of the Anterior Corneal Surface
Table 6.
 
Vertex Displacements of the Posterior Corneal Surface
Table 6.
 
Vertex Displacements of the Posterior Corneal Surface
Tables 5 and 6 show the vertex displacements with different cap thicknesses with other elastic modulus and intraocular pressure. Figure 5A shows the stress distributions of the intersecting line between the anterior corneal surface and the XZ plane with different cap thicknesses in Group D and Group H. Figure 5B shows the vertex stresses with a cap thickness of 120 µm (the actual cap thickness) in Group A to Group I. Figures 6 and 7, respectively, show the wave-front aberrations caused by the displacements of the anterior corneal surface with different cap thicknesses in Group D and Group H. Figure 8 shows the results with a cap thickness of 120 µm in Group A to Group I. 
Figure 5.
 
(A) The change of the stress distributions of the intersecting line between the anterior corneal surface and the XZ plane with the cap thickness in Group D and Group H. (B) The vertex stresses with a cap thickness of 120 µm in Group A to Group I.
Figure 5.
 
(A) The change of the stress distributions of the intersecting line between the anterior corneal surface and the XZ plane with the cap thickness in Group D and Group H. (B) The vertex stresses with a cap thickness of 120 µm in Group A to Group I.
Figure 6.
 
The change of the (A) low-order and (B) high-order aberrations caused by the displacements of the anterior corneal surface with the cap thickness in Group D.
Figure 6.
 
The change of the (A) low-order and (B) high-order aberrations caused by the displacements of the anterior corneal surface with the cap thickness in Group D.
Figure 7.
 
The change of the (A) low-order and (B) high-order aberrations caused by the displacements of the anterior corneal surface with the cap thickness in Group H.
Figure 7.
 
The change of the (A) low-order and (B) high-order aberrations caused by the displacements of the anterior corneal surface with the cap thickness in Group H.
Figure 8.
 
The (A) low-order and (B) high-order aberrations caused by the displacements of the anterior corneal surface with a cap thickness of 120 µm in Group A to Group I.
Figure 8.
 
The (A) low-order and (B) high-order aberrations caused by the displacements of the anterior corneal surface with a cap thickness of 120 µm in Group A to Group I.
As shown in Tables 5 and 6, various elastic modulus and intraocular pressure showed different results, but the variation trends of the results were the same. When the cap thickness increased, the vertex displacements of the anterior and posterior corneal surfaces decreased slightly. The variation trends were similar to those with normal elastic modulus and intraocular pressure. 
In addition, it was confirmed that elastic modulus and intraocular pressure had a substantial effect on corneal displacements. With a cap thickness of 120 µm, when the average value of the corneal elastic modulus decreased from 1.2 MPa to 0.12 MPa (Group E and Group D), the vertex displacements increased. To be more specific, the vertex displacements of the anterior and posterior corneal surfaces increased from 11.2456 µm and 11.3450 µm to 101.157 µm and 102.75 µm, respectively. However, when the intraocular pressure increased from 15 mm Hg to 40 mm Hg (Group E and Group H), the vertex displacements increased to 26.979 µm and 27.404 µm, respectively. 
As shown in Figure 5, the cap thickness had little effect on the stress distributions. In addition, the stresses after SMILE were significantly higher than those before surgery. The variation trends were similar to those with normal elastic modulus and intraocular pressure. In addition, it was confirmed that the elastic modulus had little effect on the stress distributions, but the intraocular pressure had a significant effect on them. The higher the intraocular pressure was, the larger the stresses of the anterior and posterior corneal surfaces were. For example, with a cap thickness of 120 µm, when the intraocular pressure increased from 10 mm Hg to 40 mm Hg (Group B and Group H), the vertex stress of the anterior corneal surface increased from 0.01124 MPa to 0.044927 MPa. 
As shown in Figures 6 to 8, when the cap thickness increased, the absolute defocus value decreased slightly, but the magnitude of primary spherical aberration increased slightly. The horizontal coma increased, and the levels of other low-order and high-order aberrations were small and demonstrated little change. The variation trends were similar to those with normal elastic modulus and intraocular pressure. 
In addition, it was confirmed that elastic modulus and intraocular pressure had a substantial influence on wave-front aberrations. For example, with a cap thickness of 120 µm, when the average value of the corneal elastic modulus decreased from 1.2 MPa to 0.12 MPa (Group E and Group D), the wave-front aberrations increased approximately 10-fold. However, when the intraocular pressure increased from 15 mm Hg to 40 mm Hg (Group E and Group H), the wave-front aberrations increased approximately 2.67-fold. 
In conclusion, the cap thickness of SMILE affected corneal biomechanics. However, the effect was significantly less than that resulting from material parameters and intraocular pressure. The corneal vertex displacements and wave-front aberrations were significantly affected by elastic modulus and intraocular pressure, whereas stress distributions were greatly affected by intraocular pressure. Moreover, in Group A, Group D, and Group G, the vertex displacements and wave-front aberrations were very large due to the soft cornea. In Group G, Group H, and Group I, the stresses were very large because of the high intraocular pressure. Therefore these groups of corneas did not meet the requirements for SMILE and had no clinical significance. 
Effects in Six Cases With Normal Elastic Modulus and Intraocular Pressure
The normal elastic modulus and intraocular pressure were set in the models of six cases of myopic eyes. Then, postoperative models with different cap thicknesses were established. Finally, the finite element analysis was performed. The biomechanical responses of all cases were compared to study the corneal biomechanics with different cap thicknesses. 
Figure 9A shows the vertex displacements with different cap thicknesses. Figure 9B shows the stress distributions of the intersecting line between the anterior corneal surface and the XZ plane with the actual cap thicknesses. Figure 10 shows the vertex stresses with different cap thicknesses. Figure 11 shows the aberrations caused by the displacements of the anterior corneal surface with the actual cap thicknesses. To unify the standard in this study, RST ≈ 300 µm in the figures represents the actual RST of the individual human eyes. All six cases showed different results, but the variation trends of the results were the same respectively, including the displacement, the stress and the wave-front aberration. 
Figure 9.
 
(A) The change of the vertex displacements of Case One to Case Six with the cap thickness. (B) The stress distributions of the intersecting line between the anterior corneal surface and the XZ plane of Case One to Case Six with the actual cap thicknesses.
Figure 9.
 
(A) The change of the vertex displacements of Case One to Case Six with the cap thickness. (B) The stress distributions of the intersecting line between the anterior corneal surface and the XZ plane of Case One to Case Six with the actual cap thicknesses.
Figure 10.
 
The change of the vertex stresses of Case One to Case Six with the cap thickness in the (A) anterior and (B) posterior corneal surfaces.
Figure 10.
 
The change of the vertex stresses of Case One to Case Six with the cap thickness in the (A) anterior and (B) posterior corneal surfaces.
Figure 11.
 
The (A) low-order and (B) high-order aberrations of Case One to Case Six caused by the displacements of the anterior corneal surface with the actual cap thicknesses.
Figure 11.
 
The (A) low-order and (B) high-order aberrations of Case One to Case Six caused by the displacements of the anterior corneal surface with the actual cap thicknesses.
As shown in Figure 9A, when the cap thickness increased, the vertex displacements of the anterior and posterior corneal surfaces decreased slightly. In addition, it was confirmed that there were obvious differences in the corneal vertex displacements of different individual human eyes. The maximum differences reached 25.94% and 26.38%, respectively. As shown in Figures 9B and 10, cap thickness had little effect on stress distributions. The postoperative stress was significantly larger than that before surgery. In addition, it was confirmed that there were obvious differences in the corneal stress distributions of different individual human eyes. The maximum differences reached 12.20% and 12.48%, respectively. 
As shown in Figure 11, it was confirmed that there were obvious differences in the wave-front aberrations of different individual human eyes. In addition, the maximum differences of the defocus, the primary spherical aberration, and the horizontal coma reached 0.4320 µm, 0.1137 µm, and 0.0048 µm, respectively. 
In conclusion, the cap thickness of the six cases with normal elastic modulus and intraocular pressure affected corneal biomechanics. There were obvious differences in the biomechanical responses of different individual human eyes, but the variation trends of the results were the same, respectively. 
Discussion
In previous studies, Corvis ST was also used to analyze the effect of cap thickness. For example, Wu et al.32 used Corvis ST to analyze the biomechanical difference between cap thicknesses of 110 µm and 130 µm. Wu et al.33 used Corvis ST to analyze the influence of cap thickness on corneal curvature and corneal biomechanics. Liu et al.34 used Corvis ST to analyze the relationship between corneal biomechanical changes after SMILE and the intraoperative cutting thickness. However, the differences in cap thickness among the groups were not large enough. Thus a comprehensive conclusion was not obtained.35 
In this study, finite element models of six myopic eyes were constructed. One preoperative model and four postoperative models with different cap thicknesses were established for each eye. Each model was set with nine types of elastic modulus and intraocular pressures, respectively. This study involved 270 types of finite element models and yielded a large amount of data. The advantage of finite element analysis is that it can simulate extreme situations that cannot be realized in clinical or experimental situations. Although there are requirements for the range of RST in clinical practice, the range can be completely enlarged when conducting finite element analysis. This study analyzed the actual cap thickness and three types of RSTs (250 µm, 200 µm and 150 µm). Their corresponding proportions were 28.13% to 29.41%, 35.40% to 40.76%, 48.32% to 52.61%, and 61.24% to 64.45%, respectively. The extremely thick and thin corneal caps were analyzed, and the effects of cap thickness on corneal biomechanics were fully discussed. However, the conclusion was that cap thickness had little effect on corneal biomechanics. Therefore, in clinical surgery, under the premise of following the range requirements of RST, a smaller cutting range will have less effect on corneal biomechanics. 
In previous studies, the material parameter set for refractive surgery was relatively simple.12,25 For example, Fang et al.25 used the hyperelastic material model based on Ogden's strain-energy function to simulate corneas. However, in this study, the simulation of human eyes was improved by using MATLAB. Then, the results were more consistent with the findings in the actual human eyes. 
There were differences in the biomechanical responses of different individual human eyes. These differences may be caused by differences in the spherical lens, refractive lenticule thickness or other parameters, such as CCT, Cap, and cylindrical lens. For example, the biomechanical responses of Case Four in this study were the most pronounced and were obviously affected by the cap thickness. This situation of Case Four may be caused by the large proportion of the refractive lenticule thickness in the preoperative CCT. 
This study analyzed the biomechanical properties of the cornea with different cap thicknesses. Therefore, under the premise of ensuring calculation efficiency and simulation accuracy, other tissues were not added to the eye models, such as the crystalline lens and ciliary body. Their effect on corneal biomechanics hardly affected the accuracy of the results of this study. 
Conclusion
When the cap thicknesses increased, the vertex displacements of the anterior and posterior corneal surfaces decreased slightly. The corneal stress distributions showed little change, but the postoperative stresses were significantly larger than the preoperative stresses. In addition, regarding wave-front aberrations caused by the displacements of the anterior surface, the absolute defocus value decreased slightly, but the magnitude of primary spherical aberration increased slightly. The horizontal coma increased, and the levels of other low-order and high-order aberrations were small and showed little change. 
The corneal vertex displacement and wave-front aberration were significantly affected by elastic modulus and intraocular pressure, whereas the corneal stress distribution was greatly affected by intraocular pressure. If the values of displacements, stresses, or wave-front aberrations are too large, the corneas will not meet the conditions required for SMILE. Because of the differences in surgical parameters and geometric parameters, such as CCT, there were obvious individual differences among the biomechanical responses of human eyes. 
Therefore the biomechanical difference of different corneal cap thicknesses after SMILE was small, and the difference had little effect on the clinical surgery. In addition, the effect of corneal cap thickness was significantly less than that resulting from material parameters and intraocular pressure. 
Acknowledgments
The authors thank the participants of this multicenter study for their valuable contributions. The authors assume full responsibility for the analyses and interpretation of these data. 
Supported by the Natural National Science Foundation of China (NSFC) (62165010), The National Key Research and Development Program of China (2018YFE0115700). 
Disclosure: L. Fang, None; T. Jin, None; Y. Cao, None; X. Li, None; J. Hu, None; X. Zhao, None; Y. Wang, None 
References
Abdelhalim N. Corneal topographic and biomechanical changes after Small Incision Lenticule Extraction (SMILE) In Myopic Eyes. Egypt J Hosp Med. 2019; 74: 558–563. [CrossRef]
Reinstein DZ, Shah R, Moshirfar M, et al. Small-incision lenticule extraction. J Cataract Refr Surg. 2015; 41: 652–665.
Chen XG, Shen M, Wang Y, et al. Finite element analysis of corneal deformation and stress after LASIK. Chin J Optom Ophthalmol Vis Sci. 2019; 21(2): 7.
Dupps WJ, Wilson SE. Biomechanics and wound healing in the cornea. Exp Eye Res. 2006; 83: 709–720. [CrossRef] [PubMed]
Sefat SMM, Wiltfang R, Bechmann M, et al. Evaluation of changes in human corneas after femtosecond laser-assisted LASIK and small-incision lenticule extraction (SMILE) using non-contact tonometry and ultra-high-speed camera (Corvis ST). Curr Eye Res. 2016; 41: 917–922. [CrossRef] [PubMed]
Khamar P, Shetty R, Vaishnav R, et al. Biomechanics of LASIK flap and SMILE cap: A prospective, clinical study. J Refract Surg. 2019; 35: 324–332. [CrossRef] [PubMed]
Pallás H, Elies D, Gris O, et al. Advantages and disadvantages of different cap thicknesses. Cham: Springer; 2015: 113–119.
El-Massry AAE, Goweida MBB, Shama AE, et al. Contralateral eye comparison between femtosecond small incision intrastromal lenticule extraction at depths of 100 and 160 µm. Cornea. 2015; 34: 1272–1275. [CrossRef] [PubMed]
Damgaard IB, Ivarsen A, Hjortdal J. Refractive correction and biomechanical strength following SMILE with a 110 or 160 µm cap thickness, evaluated ex vivo by inflation test. Invest Ophthalmol Vis Sci. 2018; 59: 1836–1843. [CrossRef] [PubMed]
Ganesh S, Brar S, Pereira S. A comparison of safety and clinical outcomes of 100 µm versus 160 µm cap in patients undergoing ReLEx-Small Incision Lenticule Extraction (SMILE). Int Ophthalmol. 2021; 41: 2657–2665. [CrossRef] [PubMed]
Roy AS, Dupps WJ. Effects of altered corneal stiffness on native and postoperative LASIK corneal biomechanical behavior: A whole-eye finite element analysis. J Refract Surg. 2009; 25: 875–887. [CrossRef] [PubMed]
Wang XF, Rumpel H, Lim W, et al. Finite element analysis predicts large optic nerve head strains during horizontal eye movements. Invest Ophthalmol Vis Sci. 2016; 57: 2452–2462. [CrossRef] [PubMed]
Li H, Chen M, Zhou Q, et al. Biomechanical effects of deep anterior lamellar keratoplasty and penetrating keratoplasty for keratoconus: A finite element analysis. Transl Vis Sci Techn. 2021; 10(9): 15. [CrossRef]
Li H, Chen M, Zhou Q, et al. Analysis of the effects of curvature and thickness on elastic wave velocity in cornea-like structures by finite element modeling and optical coherence elastography. Appl Phys Lett. 2015; 106(23): 233702. [CrossRef] [PubMed]
Fang LH, Wang Y, Yang RZ, et al. Effects of the LASIK flap thickness on corneal biomechanical behavior: A finite element analysis. BMC Ophthalmol. 2020; 20: 67. [CrossRef] [PubMed]
Roy AS. Patient-specific modeling of corneal refractive surgery outcomes and inverse estimation of elastic property changes. J Biomech Eng. 2011; 133(1): 11002. [CrossRef]
Zvietcovich F, Pongchalee P, Meemon P, et al. Reverberant 3D optical coherence elastography maps the elasticity of individual corneal layers. Nat Commun. 2019; 10: 1–13. [CrossRef] [PubMed]
Labate C, Lombardo M, Santo MPD, et al. Multiscale investigation of the depth-dependent mechanical anisotropy of the human corneal stroma. Invest Ophthalmol Vis Sci. 2015; 56: 4053–4060. [CrossRef] [PubMed]
Mikula ER, Jester JV, Juhasz T. Measurement of an elasticity map in the human cornea. Invest Ophthalmol Vis Sci. 2016; 57: 3282–3286. [CrossRef] [PubMed]
Randleman JB, Dawson DG, Grossniklaus HE. Depth-dependent cohesive tensile strength in human donor corneas: Implications for refractive surgery. J Refract Surg. 2008; 24(1): S85. [PubMed]
Komai Y, Ushiki T. The three-dimensional organization of collagen fibrils in the human cornea and sclera. Invest Ophthalmol Vis Sci. 1991; 32: 2244–2258. [PubMed]
Elsheikh A, Alhasso D, Rama P. Assessment of the epithelium's contribution to corneal biomechanics. Exp Eye Res. 2008; 86: 445–451. [CrossRef] [PubMed]
Sara CL, Luis CS, Mónica LR, et al. Corneal biomechanics in unilateral keratoconus and fellow eyes with a scheimpflug-based tonometer. Optom Vis Sci. 2018; 95: 608–615. [PubMed]
Bueno JM, Gualda EJ, Artal P. Analysis of corneal stroma organization with wavefront optimized nonlinear microscopy. Cornea. 2011; 30: 692–701. [CrossRef] [PubMed]
Fang LH, Ma WW, Wang Y, et al. Theoretical analysis of wave-front aberrations induced from conventional laser refractive surgery in a biomechanical finite element model. Invest Ophthalmol Vis Sci. 2020; 61(5): 34. [CrossRef] [PubMed]
Ma JN, Wang Y, Wei P, et al. Biomechanics and structure of the cornea: Implications and association with corneal disorders. Surv Ophthalmol. 2018; 63: 851–861. [CrossRef] [PubMed]
Huseynova T, Waring GO, Roberts C, et al. Corneal biomechanics as a function of intraocular pressure and pachymetry by dynamic infrared signal and Scheimpflug imaging analysis in normal eyes. Am J Ophthalmol. 2014; 157: 885–893. [CrossRef] [PubMed]
Mohammad-Ali J, Firooz MG, Monirsadat M, et al. Steroid induced ocular hypertension following myopic photorefractive keratectomy. J Ophthal Vis Res. 2008; 3(1): 42.
Krag S, Larsen D, Albertsen BK, et al. Risk of ocular hypertension in children treated with systemic glucocorticoid. Acta Ophthalmol. 2021; 99(8): e1430–e1434. [CrossRef] [PubMed]
Mohamed H, Fayrouz A, Hoda ES, et al. Comparison of different intraocular pressure measurement techniques in normal eyes and post small incision lenticule extraction. Clin Ophthalmol. 2017; 11(1): 1309–1314. [PubMed]
Tauste A, Salvestrini P, Fernandez J, et al. New parameters for evaluating corneal biomechanics and intraocular pressure after small-incision lenticule extraction by Scheimpflug-based dynamic tonometry. J Cataract Refract Surg. 2017; 43: 803–811. [PubMed]
Wu F, Yin H, Yang Y. Contralateral eye comparison between 2 cap thicknesses in small incision lenticule extraction: 110 Versus 130 µm. Cornea. 2019; 38: 617–623. [CrossRef] [PubMed]
Wu D, LIU CL, LI B, et al. Influence of cap thickness on corneal curvature and corneal biomechanics after SMILE: A prospective, contralateral eye study. J Refract Surg. 2020; 36: 82–89. [CrossRef] [PubMed]
Liu J, Wang Y, Zou H, et al. Relation between corneal biomechanical alteration after small incision lenticule extraction and intraoperative cutting thickness. Chin J Ophthalmol. 2021; 57: 104–112.
Güell JL, Verdaguer P, Mateu-Figueras G, et al. SMILE procedures with four different cap thicknesses for the correction of myopia and myopic astigmatism. J Refract Surg. 2015; 31: 580–585. [CrossRef] [PubMed]
Figure 1.
 
(A) Postoperative geometric model. The upper part of the model was the cornea, and the lower part was the sclera. The inner circule shown in the upper part was the cutting surface. The positive half axis of the X-axis was perpendicular to the center of the incision. (B) Mesh generation of the postoperative geometric model.
Figure 1.
 
(A) Postoperative geometric model. The upper part of the model was the cornea, and the lower part was the sclera. The inner circule shown in the upper part was the cutting surface. The positive half axis of the X-axis was perpendicular to the center of the incision. (B) Mesh generation of the postoperative geometric model.
Figure 2.
 
Distribution of the corneal elastic modulus in Case One's postoperative model. The corneal elastic modulus in the XZ plane of three-dimensional coordinate system was extracted. The size of the human eye model was reflected by the X-axis and Y-axis (adopted the standard unit: meter), and the elastic modulus was reflected by the color axis (adopted the standard unit: Pa).
Figure 2.
 
Distribution of the corneal elastic modulus in Case One's postoperative model. The corneal elastic modulus in the XZ plane of three-dimensional coordinate system was extracted. The size of the human eye model was reflected by the X-axis and Y-axis (adopted the standard unit: meter), and the elastic modulus was reflected by the color axis (adopted the standard unit: Pa).
Figure 3.
 
(A) The change of the vertex displacements of the anterior and posterior corneal surfaces with the cap thickness. (B) The stress distributions of the intersecting line between the anterior corneal surface and the XZ plane with different cap thicknesses.
Figure 3.
 
(A) The change of the vertex displacements of the anterior and posterior corneal surfaces with the cap thickness. (B) The stress distributions of the intersecting line between the anterior corneal surface and the XZ plane with different cap thicknesses.
Figure 4.
 
The change of the aberrations with the cap thickness caused by the displacements of the (A) anterior and (B) posterior corneal surfaces.
Figure 4.
 
The change of the aberrations with the cap thickness caused by the displacements of the (A) anterior and (B) posterior corneal surfaces.
Figure 5.
 
(A) The change of the stress distributions of the intersecting line between the anterior corneal surface and the XZ plane with the cap thickness in Group D and Group H. (B) The vertex stresses with a cap thickness of 120 µm in Group A to Group I.
Figure 5.
 
(A) The change of the stress distributions of the intersecting line between the anterior corneal surface and the XZ plane with the cap thickness in Group D and Group H. (B) The vertex stresses with a cap thickness of 120 µm in Group A to Group I.
Figure 6.
 
The change of the (A) low-order and (B) high-order aberrations caused by the displacements of the anterior corneal surface with the cap thickness in Group D.
Figure 6.
 
The change of the (A) low-order and (B) high-order aberrations caused by the displacements of the anterior corneal surface with the cap thickness in Group D.
Figure 7.
 
The change of the (A) low-order and (B) high-order aberrations caused by the displacements of the anterior corneal surface with the cap thickness in Group H.
Figure 7.
 
The change of the (A) low-order and (B) high-order aberrations caused by the displacements of the anterior corneal surface with the cap thickness in Group H.
Figure 8.
 
The (A) low-order and (B) high-order aberrations caused by the displacements of the anterior corneal surface with a cap thickness of 120 µm in Group A to Group I.
Figure 8.
 
The (A) low-order and (B) high-order aberrations caused by the displacements of the anterior corneal surface with a cap thickness of 120 µm in Group A to Group I.
Figure 9.
 
(A) The change of the vertex displacements of Case One to Case Six with the cap thickness. (B) The stress distributions of the intersecting line between the anterior corneal surface and the XZ plane of Case One to Case Six with the actual cap thicknesses.
Figure 9.
 
(A) The change of the vertex displacements of Case One to Case Six with the cap thickness. (B) The stress distributions of the intersecting line between the anterior corneal surface and the XZ plane of Case One to Case Six with the actual cap thicknesses.
Figure 10.
 
The change of the vertex stresses of Case One to Case Six with the cap thickness in the (A) anterior and (B) posterior corneal surfaces.
Figure 10.
 
The change of the vertex stresses of Case One to Case Six with the cap thickness in the (A) anterior and (B) posterior corneal surfaces.
Figure 11.
 
The (A) low-order and (B) high-order aberrations of Case One to Case Six caused by the displacements of the anterior corneal surface with the actual cap thicknesses.
Figure 11.
 
The (A) low-order and (B) high-order aberrations of Case One to Case Six caused by the displacements of the anterior corneal surface with the actual cap thicknesses.
Table 1.
 
The Surgical Simulation Parameters of Six Cases of Myopic Eyes
Table 1.
 
The Surgical Simulation Parameters of Six Cases of Myopic Eyes
Table 2.
 
The Ocular Parameters of Six Cases of Myopic Eyes
Table 2.
 
The Ocular Parameters of Six Cases of Myopic Eyes
Table 3.
 
The Normal Material Parameters and Intraocular Pressure Levels
Table 3.
 
The Normal Material Parameters and Intraocular Pressure Levels
Table 4.
 
The Other Material Parameters and Intraocular Pressure Levels
Table 4.
 
The Other Material Parameters and Intraocular Pressure Levels
Table 5.
 
Vertex Displacements of the Anterior Corneal Surface
Table 5.
 
Vertex Displacements of the Anterior Corneal Surface
Table 6.
 
Vertex Displacements of the Posterior Corneal Surface
Table 6.
 
Vertex Displacements of the Posterior Corneal Surface
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