Wave front aberrations induced from biomechanical effects after customized myopic laser refractive surgery in finite element model

A customized myopic refractive surgery was simulated by establishing a finite element model of the human eye, after which we studied the wave front aberrations induced by biomechanical effects and ablation profile after wave front-guided LASIK surgery. Thirty myopia patients (i.e., 60 eyes) without other eye diseases were selected. Their ages, preoperative spherical equivalent, astigmatism, and wave front aberration were then obtained, in addition to the mean spherical equivalent error range − 4 to − 8D. Afterward, wave front-guided customized LASIK surgery was simulated by establishing a finite element eye model, followed by the analysis of the wave front aberrations induced by the surface displacement from corneal biomechanical effects, as well as customized ablation profile. Finally, the preoperative and induced aberrations were statistically analyzed. Comatic aberrations were the main wave front abnormality induced by biomechanical effects, and the wave front aberrations induced by the ablation profile mainly included coma and secondary coma, as well as sphere and secondary-sphere aberrations. Overall, the total high-order aberrations (tHOAs), total coma (C31), and sphere (C40\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{4}^{0}$$\end{document}) increased after wave front-guided customized LASIK surgery. According to our correlation analyses, coma, sphere, and tHOAs were significantly correlated with decentration. Additionally, the material parameters of ocular tissue were found to affect the postoperative wave front aberrations. When the material parameters of the sclera remained constant but those of cornea increased, the induced wave front aberrations were reduced. All biomechanical effects of cornea and ablation profile had significant effects on postoperative wave front aberrations after customized LASIK refractive surgery; however, the effects of the ablation profile were more notorious. Additionally, the characteristics of biomechanical materials have influence on the clinical correction effect.

Results Comatic aberrations were the main wave front abnormality induced by biomechanical effects, and the wave front aberrations induced by the ablation profile mainly included coma and secondary coma, as well as sphere and secondary-sphere aberrations. Overall, the total high-order aberrations (tHOAs), total coma (C 31 ), and sphere (C 0 4 ) increased after wave front-guided customized LASIK surgery. According to our correlation analyses, coma, sphere, and tHOAs were significantly correlated with decentration. Additionally, the material parameters of ocular tissue were found to affect the postoperative wave front aberrations. When the material parameters of the sclera remained constant but those of cornea increased, the induced wave front aberrations were reduced. Conclusion All biomechanical effects of cornea and ablation profile had significant effects on postoperative wave front aberrations after customized LASIK refractive surgery; however, the effects of the ablation profile were more notorious. Additionally, the characteristics of biomechanical materials have influence on the clinical correction effect.
Keywords Wave front aberrations Á LASIK refractive surgery Á Biomechanical effects Á Finite element model Á Displacement

Introduction
There are many forms of laser refractive surgery, and LASIK (laser-assisted in situ keratomileusis) is one of the them. LASIK is the most commonly performed laser refractive surgery due to its short recovery times and superior safety and efficacy [1]. Vision correction through this procedure is achieved by changing the curvature of the cornea. In a conventional LASIK procedure, a hinged flap is first created using a microkeratome. The flap is folded back, and the exposed stroma is photoablated using an excimer laser. The flap is then returned to its original place to cover the treated area [2]. Alió et al. [3] found that LASIK for myopia over -10 D is a safe procedure with myopic regression that slows down with time and a high rate of best spectacle-corrected visual acuity increase in the long-term. However, some patients that undergo LASIK surgery for moderate to severe myopia manifest optical sequelae including glares, halos, and monocular diplopia [4,5]. Moreover, many clinical studies have shown that LASIK surgery increases the likelihood of corneal higher-order aberrations [6,7].
Some studies have reported that the correction of higher-order aberrations can improve the visual quality [8]. Particularly, wave front-guided LASIK is a promising technique that offers the potential to correct refractive errors [9]. Schallhorn et al. [10] found that the wave front-guided (WFG) procedures rendered similar or better refractive accuracy and uncorrected visual acuity outcomes compared to conventional LASIK. Keir et al. [11] found that despite an increase in higher-order aberrations, wave front-guided LASIK yielded excellent visual acuity and contrast sensitivity. Moreover, SMILE and wave front-guided LASIK surgery (WFG-LASIK) were found to be efficacious and safe procedures for the correction of low and moderate cases; however, WFG-LASIK allows for more predictable outcomes and better aberrometric control [12]. The finite element method has been widely used in the study of human eye biomechanics. Di et al. [13] applied finite element analysis based on inflation test data from rabbit cornea to determine its material parameters. These parameters were then used to simulate corneal refractive surgery to study postoperative corneal deformations. Deenadayalu et al. [14] used a biomechanical finite element model to study the effects of corneal modulus elasticity, flap diameter, thickness, and intraocular pressure on the refractive changes induced by the cornea flap after LASIK surgery. Uchio et al. [15] developed a simulation model to determine the physical and mechanical conditions that caused intraocular foreign body injuries, and the simulations were solved via finite element analysis.
Pooja et al. [16] found that flap and cap incisions induced corneal biomechanical weakening in patients. Cornea biomechanical response to ablative surgery may significantly affect post-surgery outcomes and should be taken into account when planning customized procedures [17]. Voronin et al. [18] reported that the biomechanical properties of the cornea are important for the functioning of the ocular optical system. Dupps et al. [19] associated hyperopia shifts with significant thickening of the unablated peripheral stroma, and these biomechanical effects may affect the refractive outcomes of LASIK surgery. Therefore, discussing the wave front aberrations caused by the whole-eyeball biomechanical effects after LASIK surgery is critical.
This study sought to evaluate the wave front aberrations caused by biomechanical changes after customized LASIK surgery. A 3D finite element model of the human eye was developed to evaluate the wave front aberrations before and after wave frontguided LASIK surgery based on clinical measurement data. Importantly, the outcomes of this model were then compared with actual clinical results. In summary, our study proposes a novel approach to predict the effect of biomechanical changes on high-order aberrations after customized LASIK surgery, which will be of great significance for preoperative screening and postoperative visual quality optimization.

Subjects
In this study, the eyes of 30 potential refractive surgery candidates for correction of myopia (i.e., 60 eyes in total) were examined. None of the patients had a previous history of other ocular diseases. In addition, the patients had no other eye surgery and systemic diseases. The age of the patients ranged from 18 to 41 years (mean 36 ± 5.34). Figure 1a shows the distribution of mean spherical equivalents (D indicates the diopter). The mean spherical equivalent error range was -7.75 to -3.75 D, of which ranges of -5.44 ± 1.07 D were observed in the right eyes and -5.40 ± 1.02 D in the left eyes. Figure 1b shows the astigmatic power as a scatter plot of the orthogonal components J 0 and J 45 . The average astigmatism of the right eyes was -0.72 ± 0.55 and that of the left eyes was -0.77 ± 0.53. After a complete ophthalmic examination and an explanation of the nature and possible consequences of the research, the written informed consent was obtained from all patients. The preoperative wave front aberrations of all eyes were measured using a Shack-Hartmann aberrometer under natural scotopic conditions. All measurements were repeated at least three times for each eye, and the average of the three most consistent measurements were used. Wave front aberrations were expressed as seventh-order Zernike polynomials. Patients that wore contact lenses were excluded from this study.
Human eye finite element model Cornea is located at the most front of the eyeball, accounting for about 1/6 of the outer fibrous membrane of the eye. The central corneal thickness (CCT) is 0.5 mm, the curvature radius of anterior corneal surface is 7.7 mm, and the curvature radius of posterior corneal surface is 6.8 mm. Refer to the methods of building entity model in the existing literature and the cornea and sclera 3D solid morphology models were constructed by using Siemens NX.
Then, there is the problem of material models. The biomechanical properties of cornea are not only related to the stable structure, but also to the materials, material model is very important. In an early study, Woo et al. [20] reported that the cornea and sclera exhibited nonlinear material properties. The strain energy potential can be expressed as described by Eq. (1): where W represents the strain energy potential, k p represents the deviatoric principal stretches defined as k p ¼ J À 1 3 k p , and k p indicated the principal stretches of the left Cauchy-Green tensor. J represents the determinant of the elastic deformation gradient. N; l p ; a p and d p are material constants.
The initial shear modulus l is defined as: The initial bulk modulus k is defined as follows: For the purposes of this study, experimentally derived stress versus strain data were fit to the abovedescribed material model. We chose n = 2 and n = 1 as corneal and scleral fitting orders, respectively. The corneal fitting parameters were l1 = 3535.7 pa, a1 = 103.51, l2 = 3535.7 pa, a2 = 103.61; the scleral fitting parameters were l1 = 30,224 pa, a1 = 182.73. When d 1 = 0, it was assumed that the cornea and sclera were largely indistinguishable.
By changing the thickness of residual bed, cutting depth and clinical measurement data, the finite element model corresponding to thirty myopia patients (i.e., 60 eyes) was constructed. The thickness and diameter of the corneal flap and optical zone were 100 lm, 8 mm, and 6 mm, respectively. In the calculation process, a fixed constraint was used at the bottom of sclera, the cornea and sclera were bound and connected to prevent separation and sliding, and the flap was naturally attached to the stromal layer. Cornea and sclera were divided into different-sized hexahedral meshes based on their shape and characteristics using finite element analysis and the Ansys software. Because our study focused on the cornea, the cornea meshing was relatively smaller than that of the sclera. Figure 2 illustrates the -4D(-4DS -0.5 DC 9 30) model in the left eyes after meshing. Moreover, the numbers of corneal nodes, corneal mesh cells, scleral nodes, and scleral mesh cells were 188,767, 55,854, 123,698, and 33,989, respectively.
Customized laser refractive surgery ablation profile Compared with conventional refractive surgery, wave front-guided ablation can reduce the preexisting higher-order aberrations and the new induced higherorder aberrations. According to the phase-conjugate principle, the ablation depth in the optical zone of any arbitrary point is given directly by the wave front data.
Dðx; yÞ ¼ À X p and q Wðx; yÞ=ðn À 1Þ ð 4Þ here, the parameter n represents the refractive index of the cornea in visible light; n is 1.376, and (x, y) depicts an arbitrary point in the optical zone on the cornea. Additionally, the wave front W is expressed as a Zernike polynomial expansion.C q p is the Zernike coefficient.
here, the parameters p and q are the radial integer index and meridional index, respectively. In this section, we aimed to structure an ablation profile for the transition zone. R represents the radius of the optical zone. If the width of the transition zone is R q , the internal radius of the transition zone is R, and therefore the outer radius is R(1 ? q). Here, q The ablation profile for the transition zone can be calculated as described by Eq. (6): where D a (x, y) represents a blend function. Further calculations are then preformed with Eq. (7). The function value is 1 at the boundary between the optical and transition zones, but the value changes to zero at the boundary between the transition zone and the untreated periphery.
In Eq. (8), D b (x, y) indicates the extended ablation depth in the transition zone, which is extended from the boundary value of the optical zone.
Monte Carlo simulating treatment decentration In this study, the Monte Carlo method was used to simulate treatment decentration. The treatment decentration number was randomly selected from a clinical study population [21]. Here, the mean transverse translation was 0.26 ± 0.12 mm (0.04-0.52 mm). As illustrated in Fig. 3, the mean transverse translations along the horizontal and vertical meridians in the right eyes were -0.16 ± 0.16 mm (-0.46 to ? 0.13 mm) and -0.05 ± 0.15 mm (-0.26 to 0.23 mm), respectively. On the other hand, the mean transverse translations along the horizontal and vertical meridians in the left eyes were 0.24 ± 0.12 mm (0.05 to 0.49 mm) and -0.06 ± 0.12 mm (-0.23 to 0.17 mm), respectively.

Evaluating induced wave front aberrations
Refractive surgery can cause ocular biomechanical changes, which result in significant displacements of the anterior and posterior cornea surface due to corneal biomechanical effects. These effects can ultimately alter the refractive state of the cornea (i.e., induced wave front aberrations after customized LASIK refractive surgery). However, the transition zone was combined with the optic zone to simulate the refractive surgery based on the ablation profile. In this study, we first discussed the wave front aberrations caused by LASIK surgery-associated biomechanical effects on the cornea. We then studied the wave front aberrations induced by the ablation profile of customized refractive surgery. Finally, we compared and analyzed preoperative and induced wave front aberrations.

Wave front aberration population statistics
Our study first analyzed the preoperative wave front aberrations of the subjects. Figure 4 shows the signed Zernike coefficients in the 60 eyes studied herein (i.e., 30 left eyes and 30 right eyes), including mean values and standard deviation (SD). In our study, terms like C with both subscript and superscript were used some places, while C with two subscripts were used elsewhere. Zernike polynomial functions are often referred to by their common names-magnitude/axis form.
Moreover, the formula can be used to obtain the magnitude/axis of the wave front aberrations. As illustrated in Fig. 4, although slightly higher primary astigmatism (C 2 2 ) and sphere (C 0 4 ) values were observed (C 2 2 in the right and left eyes was -0.411 ± 0.514 lm and -0.434 ± 0.442 lm, respectively; C 0 4 in the right and left eyes was 0.091 ± 0.094 lm and 0.093 ± 0.103 lm, respectively), both the mean and standard deviation of the other Zernike terms were close to zero. It is worth noting that, Fig. 5 also indicates that the average and SD of the Zernike terms are similar in the right and left eyes.

Wave front aberrations induced by biomechanical effects after customized refractive surgery
This study was based on wave front aberration data from preoperative clinical measurements. First, the corneal ablation depths in the optical and transition zones were calculated from the customized surgical ablation profile. The corneal flap and corneal stromal surfaces were then acquired by simulating corneal stromal ablation via refractive surgery. Finally, a finite element model of the human eye was constructed. Partial corneal stroma ablation leads to decreases in  The anterior and posterior surface of the cornea was displaced by loading the intraocular pressure, which resulted in corneal refractive state alterations. Under the influence of 15 mmHg of intraocular pressure (IOP), the displacement of the anterior and posterior surfaces of the cornea was corrected. The induced wave front aberrations after refractive surgery were computed as the differences between the postoperative and preoperative wave front aberrations from the displacement of the corneal surface. Moreover, the Zernike coefficients were obtained via mathematical fitting. The aberrations induced by the anterior surface were dominant, and those induced by the posterior surface were generally mild. Therefore, we concluded that the aberrations induced by the displacement of the anterior surface were the whole corneal surfaceinduced wave front aberrations after refractive surgery. Figure 5 illustrates the aberrations induced by biomechanical effects on the corneal surface of 60 eyes. Figure 5 shows that almost all Zernike coefficients were low in both eyes, with mean values that were close to zero. Apart from the obvious differences in comatic aberrations (C 1 3 in the right and left eyes was -0.08 ± 0.038 lm and 0.021 ± 0.040 lm, respectively), the distributions of the other wave front aberrations were largely similar.
Effects of the ablation profile on induced wave front aberrations after customized refractive surgery Using the methods described above, preoperative clinical measurement data were used to calculate the ablation depth of the corneal ablation zone, taking treatment decentration into account. The wave front aberrations induced by the ablation profile can then be obtained by subtracting the preoperative wave front aberrations from the optical path difference corresponding to the ablation depth. Figure 6 displays the ablation profile-induced wave front aberrations in 60 eyes.
The diagram shows that, with the exception of the x-coma (C 1 3 ) and x-secondary coma (C 1 5 ) (C 1 3 in the right and left eyes was 0.07 ± 0.104 lm and -0.120 ± 0.115 lm, respectively; C 1 5 in the right and left eyes was 0.091 ± 0.099 lm and -0.130 ± 0.087 lm, respectively), there was no significant difference in the distribution of other wave front aberrations. In addition to sphere (C 0 4 ), x-coma (C 1 3 ), x-secondary coma (C 1 5 ), and C 0 6 values were slightly higher (C 0 4 in the right and left eyes was 0.135 ± 0.113 lm and 0.158 ± 0.100 lm, respectively; C 0 6 in the right and left eyes was 0.101 ± 0.067 lm and 0.120 ± 0.059 lm, respectively), the rest of the wave front aberrations were close to 0 lm.

Statistical analysis of the preoperative and induced wave front aberrations
Given that the other orders had little influence on the results, we mainly recorded total high-order aberrations (3-6 orders) RMS (HOARMs), y-astigmatism (C À2 2 ), x-astigmatism (C 2 2 ), y-trefoil (C À3 3 ), x-trefoil (C 3 3 ), y-coma (C À1 3 ), x-coma (C 1 3 ), total coma (C 31 ), and sphere (C 0 4 ). The statistical values of the preoperative and induced wave front aberrations are shown in Table 1. ''I'' in the table represents the preoperative wave front aberrations, ''II'' refers the wave front aberrations induced by the biomechanical effects, ''III'' represents the wave front aberrations induced by the customized refractive surgery ablation profile, ''IV'' represents the induced aberrations (i.e., the main component of the postoperative wave front aberrations). Statistical analyses were performed with the SPSS 25.0 software, and a P value \ 0.05 was considered to indicate a significant difference between preoperative and induced wave front aberrations.
As indicated in Table 1, the right and left eye wave front aberrations induced by the biomechanical effects on the corneal surface mainly manifested as increases in x-coma (C 1 3 ). Moreover, the wave front aberrations induced by the ablation profile mainly manifested as xcoma (C 1 3 ) and sphere (C 0 4 ) increase. Based on the induced aberration results, tHOAs, total coma (C 31 ), and sphere (C 0 4 ) were significantly increased compared with the preoperative wave front aberrations. In fact, the coma of II and III had a partial compensation relationship.

Treatment decentration and induced wave front aberration correlation analysis
During clinical surgery, the center of the pupil changed with different light conditions and sitting posture during examination and surgery, which results in laser ablation decentration. We discussed the correlation between aberrations induced by biomechanical effects and ablation profiles with decentration. Figure 7a illustrates a scatter diagram of the wave front aberrations induced by biomechanical effects on the corneal surface in 30 left eyes. Figure 7b shows the scatter diagram of wave front aberrations induced by ablation profiles. Because aberrations and decentration are two continuous variables which obey normal distribution so Pearson correlation coefficients were calculated, and the correlation between the two variables was described. Table 2 summarizes the correlation coefficient analysis between wave front aberrations and decentration, ''Sig \ 0.05'' indicates that the correlation coefficients for a given subject  were statistically significant (i.e., the variables were correlated). Figure 7a shows that there was no correlation between wave front aberrations and decentration, Table 0.2 also shows that the individual (i.e., per person) correlation coefficients between all of the wave front aberrations and decentration were not statistically significant. The results derived from the right eyes were similar to those of the left eyes, and therefore a scatter plot and correlation coefficients were not reported. As illustrated in Fig. 7b, there was an obvious correlation between some wave front aberrations and decentration, and the individual coefficients are detailed in Table 2. The individual (i.e., per person) coefficients between pentafoil and decentration were the lowest. Moreover, individual coefficients for trefoil, tetrafoil, and defocus were 0.698, 0.795, and 0.806, respectively, and were found to be statistically different from the decentration values. Finally, the individual coefficients of primary astigmatism, coma, secondary astigmatism, sphere, and total higher-order aberrations ranged from 0.84 to 0.96, and there was a highly significant difference between the aforementioned coefficients and the decentration values. Through calculation and analysis, it was found that the effects of decentration on aberrations were not significant difference to the left and right eyes.

Comparison with previous clinical studies
Based on the finite element model, this study mainly analyzed the influence of biomechanical effects and ablation profile on the induction of wave front aberrations. According to the preoperative and induced aberration comparison, the biomechanical effects of corneal surface alterations led to wave front aberrations changes, and many studies have shown that refractive surgery can increase ocular wave front aberrations. Our simulation results also indicated that tHOAs, total coma (C 31 ), and sphere (C 0 4 ) were increased compared with preoperative data. Cynthia Roberts et al. [17] suggested that the corneal biomechanical response to ablative surgery may significantly affect outcomes. Dupps et al. [19] found that the aberrations was associated with significant thickening of the unablated peripheral stroma, and these biomechanical effects may affect the refractive outcome of LASIK surgery. Lihua et al. [23] also reported that among the factors affecting the incidence of higherorder aberrations after conventional laser refractive surgery, changes in corneal morphology caused by biomechanical effects had to be taken into account. Therefore, our results indicate that corneal biomechanical alteration is an important factor that influences postoperative aberrations after refractive surgery. Additionally, the wave front aberrations caused by the ablation profile after refractive surgery should also not be ignored. These aberrations are mainly caused by the mismatch between the treatment decentration and the optical and pupil regions. According to our preoperative and induced aberrations comparison, the wave front aberrations induced by the ablation profile were mainly manifested as an increase in total coma. Additionally, higher-order aberrations such as x-coma (C 1 3 ) and sphere (C 0 4 ) also increased. According to Table 2, after customized myopic laser refractive surgery, the correlation coefficients of treatment decentration and postoperative higher-order aberrations such as primary astigmatism, coma, secondary astigmatism, sphere, and total higher-order aberrations all exhibited remarkable statistical significance. Rong et al. [24] indicated that total higher-order aberrations and coma aberrations increased significantly due to ablation-induced decentration after LASIK surgery, and they believed that decentration was among the main factors leading to vision distortion after LASIK surgery. Similar to others' report, our study indicated that treatment decentration was the main factor that led to higher-order aberrations after customized refractive surgery.
This study mainly analyzed 3rd to 6rd order higherorder aberrations, and higher-order aberrations can affect wave front aberrations, of which Zernike aberration coefficients are mostly affected. Moreno-Barriuso et al. [25] also reported that ocular aberrations (3rd order and above) have a great impact on image quality. Therefore, our results were consistent with the clinical results.

Influence of material parameters on the induced wave front aberrations
The material parameters of biological tissue are key determinants of biomechanical effects. Studies have shown that the material parameters of cornea and sclera vary greatly among individuals [26]. In order to demonstrate the influence of material parameters on the wave front aberrations of the corneal surface, we designed eight different cases and assigned different material parameters for cornea and sclera (Table 3) and the cornea and sclera were modeled with nonlinear materials. Some studies have shown that the Young's modulus of the sclera was approximately 3-5 times higher than that of the cornea [27]. From case 1-4, the elastic range of the cornea ranged from 0.1 to 3.0 MPa, and the elastic range of the sclera ranged from 0.3 to 8.0 MPa. However, the change of corneal and scleral material parameters at the same time can only show that the material parameters have an impact on aberration, the results of cornea and sclera alone cannot be explained. So, from case 5 to 8, the material parameters of the sclera remained constant, whereas that of the cornea ranged from 0.49 to 3.9 MPa. Therefore, the material parameters determined herein were consistent with the true values. We first selected a representative eye model from the 30 study subjects. The wave front aberrations were then calculated using the different material parameters from the eight cases. Finally, the displacement of the corneal surface and the Zernike coefficients was obtained. Here, C 20 is defocus, C 22 is primary astigmatism, C 33 is trefoil, C 31 is primary coma, C 44 is tetrafoil, C 42 is secondary astigmatism, C 40 is sphere, C 55 is pentafoil, C 53 is secondary trefoil, and C 51 is secondary coma. All calculations are described in Sect. 3.4, and the results are summarized in Table 4. Table 4 summarizes the induced wave front aberrations derived from corneal surface displacement that were shown in the eight studied cases. Material parameters had a significant influence on hyperopic shift; however, the effects on higher-order aberrations were less than 0.19 lm. From case 1 to case 4, we concluded that the elastic modulus of the cornea and sclera increased simultaneously, the low-order aberrations decreased after refractive surgery, and the hyperopic shift (C 20 ) decreased rapidly. From case 5 to case 8, when scleral elasticity remained constant and corneal elasticity increased, the hyperopic shift, astigmatism, and coma decreased, and the variation in spherical aberrations was also decreased. Roy et al. [28] found that differences in the corneoscleral stiffness relationship affect simulated outcomes and may be a source of individual variation in refractive surgery outcomes. Therefore, we believe that changes in ocular tissue material parameters will likely affect the occurrence and characteristics of postoperative residual wave front aberrations.

Other thoughts
In this study, the finite element model was based on classical Gullstrand eye model and the Munnerlynnbased profile, in which the individual clinical data of 30 potential refractive surgery candidates were not considered. But, our results represent the average of 30 patients. Additionally, the effects of hinge chord length were considered and we set it to a constant value of 4 mm, but this size of hinge chord length may not be optimal. In fact, some studies have shown that the hinge chord length had an effect on the higherorder aberrations after LASIK surgery. Additionlly, the model without considering the epithelial layer and transitional zone but the epithelial layer plays an important role in the biomechanical properties of cornea, Sano et al. [29] indicated that the protrusion of abnormal substance in corneal elastic layer after PRK may be due to the destruction of corneal epithelial integrity.
In addition, the material parameters of cornea and sclera were from previous publications. Our study found that the material properties of eye tissues had an important effect on the biomechanical properties. Chaitanya Deenadayalu et al. [30] also found that the elastic modulus had a great influence on the hyperopic shift. In our study, although the material parameters of the sclera were set to be three times that of the cornea, the actual relationship of scleral and corneal material parameters must be different from this situation. Furthermore, previous studies have shown that there were remarkable individual differences in the material parameters of eye tissue. Therefore, it is very important to measure the material parameters of eye tissue in vivo for the finite element analysis. The corneal surface displacement included not only the displacement through the Z-axis, but also the displacement through both the X-and Y-axis. In this research, these displacements were all considered and the calculation of wave front aberrations was guaranteed to be accurate. Additionally, the individual differences in intraocular pressure were not considered. During the simulation, the intraocular pressure was set to be a constant value of 15 mmHg, the prestressing stress of zero intraocular pressure is not discussed. We also did not discuss the aberrations of low and high intraocular pressure loading, respectively.
After customized LASIK refractive surgery, the wave front aberrations of clinical measurements may be derived from the postoperative recovery, wound healing, and other external factors. Ikuko Toda et al. [31] indicated that patients undergoing LASIK develop dry eye with compromised tear function for at least 1 month after surgery, this may also be related to postoperative wave front aberrations. Additionally, there are many factors that affect the postoperative biomechanical properties including the microstructure of corneal tissue and different surgical procedures.
In fact, the simulation results of refractive surgery may deviate slightly from the actual clinical results, our goal is to simulate the clinical situation as much as possible and reduce this bias. In follow-up work, a personalized finite element eye model was constructed based on the clinic data and material parameters measured in vivo. Then, the biomechanical effects of hinge chord length, material parameters and, intraocular pressure on induced wave front aberrations should be quantitatively analyzed. Therefore, the finite element analysis results will be more accurate, and the biomechanical characteristics of human eye were better understood.

Conclusion
In this study, a human eye finite element model was used to simulate customized LASIK refractive surgery. Moreover, we studied the wave front aberrations induced by the biomechanical effects on the anterior and posterior corneal surfaces and the ablation profile. Our results demonstrated that corneal biomechanical alteration resulted mainly in comatic aberrations. Moreover, the wave front aberrations induced by ablation profiles mainly included coma, secondary coma, sphere, and secondary-sphere aberrations. Overall, the total high-order aberrations (tHOAs), total coma (C 31 ), and sphere (C 0 4 ) were increased after customized LASIK surgery. Additionally, our statistical analyses demonstrated that coma, sphere, and tHOAs were significantly correlated with decentration. Furthermore, the material's parameters of ocular tissue can affect the postoperative wave front aberrations, and the harder the cornea, the smaller the aberrations. Specifically, the induced wave front  aberrations were ameliorated when the material parameters of the sclera remained constant while those of the cornea increased. Both corneal biomechanical effects and ablation profile have significant effects on postoperative wave front aberrations after customized LASIK refractive surgery; however, the effects associated with ablation profile are more notorious.