**Purpose**:
To examine the biomechanical effects-induced wave-front aberrations after conventional laser refractive surgery.

**Methods**:
A finite element model of the human eye was established to simulate conventional laser refractive surgery with corrected refraction from –1 to –15 diopters (D). The deformation of the anterior and posterior corneal surfaces was obtained under the intraocular pressure (IOP). Then, the surface displacement was converted to wave-front aberrations.

**Results**:
Following conventional refractive surgery, significant deformation of the anterior and posterior corneal surfaces occurred because of the corneal biomechanical effects, resulting in increased residual wave-front aberrations. Deformation of the anterior surface resulted in a hyperopic shift, which was significantly increased with the increasing refractive correction. The residual high-order aberrations consisted of spherical aberration, vertical coma, and y-trefoil. Spherical aberration was significantly positively correlated to enhanced refraction correction. The effect of posterior corneal surface on induced wave-front aberration was less than the anterior corneal surface. The IOP slightly affects the postoperative defocus, coma, and spherical aberration. When treatment decentration occurred during the procedure, the hyperopic shift decreased as the eccentricity increased. Treatment decentration had a significant impact on the spherical aberration and the coma. In addition, the ocular tissue elasticity played a key role in hyperopic shift, whereas it had little effect on the other aberrations.

**Conclusions**:
Among the many factors that affect high-order aberrations after conventional laser refractive surgery, the alterations in corneal morphology caused by biomechanical effects must be considered, as they can lead to an increase in postoperative residual wave-front aberrations.

^{1}Vision correction is achieved by changing the curvature of the anterior surface of the cornea. LASIK involves the creation of a lamellar corneal flap, lifting of the flap, and ablation of the underlying stromal bed.

^{2}However, some clinical data have shown that LASIK could significantly increase the incidence of higher-order aberrations.

^{3}In fact, not only laser ablation profiles, but also the cosine effect of laser energy loss can result in an increase of higher-order aberrations. Even wave-front-guided refractive surgery cannot completely prevent the expansion nor the long-term, continuous increase of aberrations. Many studies have demonstrated that the increase in postoperative aberrations may be a result of biomechanical effects.

^{4}The tissue ablation of the stromal layer leads to biomechanical changes of the cornea, which in turn affects its shape,

^{5}resulting in increased incidence of residual wave-front aberrations. Therefore it is of great clinical significance to explore the biomechanical effects on the residual wave-front aberrations.

^{6}Although many studies have focused on the finite element model (FEM) of the cornea, little is known about the whole-eye three-dimensional (3D) model of LASIK, which accounts for the entire surface of the eye. Deenadayalu et al.

^{7}studied the effects of corneal elasticity, flap diameter and thickness, and intraocular pressure (IOP) on the refractive changes caused by LASIK corneal flap. Although the corneal topographic data of patients were used for curved surface simulation, the extrapolation of geometric points of the sclera caused obvious deviations.

^{7}Another study led by Roy and Dupps

^{6}focused on the effects of corneal elasticity on the deformation of the cornea before and after LASIK surgery and established an axisymmetric two-dimensional model of the whole eye. The same group also developed a 3D patient-specific FEM to theoretically compare the corneal stress distribution of LASIK with that of small-incision lenticule extraction (SMILE).

^{8}Bao et al.

^{9}developed and validated a numerical model of LASIK surgery by integrating the effects of corneal biomechanical behavior. Therefore finite element-based biomechanical models of the eye have become important in predicting the effects of LASIK.

^{10}

^{,}

^{11}and this relationship has been established by several studies. Woo et al.

^{12}obtained the nonlinear material properties of the complete cornea and sclera through experimental measurement, finite element analysis, and axisymmetric mathematical modeling. Bryant and McDonnell

^{13}demonstrated that the corneal biomechanical response was nonlinear. Furthermore, Anderson et al.

^{14}studied the nonlinear response of the cornea through testing and mathematical analysis and applied the Ogden hyperelastic model to the cornea for simulation analysis. However, none of the earlier mentioned studies considered the material properties of the sclera based on the whole-eye 3D model. It is therefore necessary to consider the influence of the material properties of the cornea and sclera on the biomechanical properties after a patient undergoes LASIK.

^{15}demonstrated that the corneal ectasia after LASIK showed high-order aberrations dominated by coma on the anterior and posterior surfaces of the cornea. Agarwal et al.

^{16}found that, in patients with low myopia astigmatism, spherical aberration and total high-order aberrations increased by 0.085 µm and 0.13 µm, respectively, after wave-front-optimized LASIK. Hu et al.

^{17}discovered that the factor of IOP contributed to LASIK acting as a trigger for high-order aberrations, especially spherical aberration. The researchers also proposed that IOP should be integrated as a variable for laser surgery in the new algorithm to control high-order aberrations after LASIK.

^{17}In summary, researchers must consider the potentially significant influence of biomechanical factors in their study of corneal refractive surgery, which can be further accurately simulated by finite element analysis.

^{18}which was constructed in the software SIEMENS NX (Siemens PLM Software, Plano, TX, USA).

^{12}demonstrated that the cornea and sclera show nonlinear material properties. The properties of this nonlinear material can be summarized in a hyperelastic material model based on the Ogden strain energy function, which represents the hyperelastic, isotropic, and incompressible features of the cornea and sclera. The strain energy potential can be expressed as follows

^{19}:

*W*is the strain energy potential, \({\bar \lambda _p} = {J^{ - \frac{1}{3}}}{\lambda _P}\) is the deviatoric principal stretch,

*J*is the determinant of the elastic deformation gradient,

*λ*is the principal stretch of the left Cauchy–Green tensor, and

_{p}*N*,

*µ*,

_{i}*α*, and

_{i}*d*are material constants representing the tissue's hyperelasticity and compressibility.

_{k}*N*can provide a better fit to the exact solution. It may, however, cause numerical difficulties in fitting the material constants. For this reason, we choose

*N*= 2 and

*N*= 1 as corneal and scleral fitted parameters. The corneal fitted parameters are as follows:

*µ*= 0.003535 Mpa,

_{1}*α*= 103.51,

_{1}*µ*= 0.003535 Mpa, and

_{2}*α*= 103.61. The scleral fitted parameters are as follows:

_{2}*µ*= 0.030224 Mpa, and

_{1}*α*= 182.73. In addition,

_{1}*d*is set to 0 to account for the near incompressibility of the cornea and sclera.

_{1}^{20}The ablation depth of the cornea for myopic correction is given by:

*d*is the distance of any arbitrary point in the pupil plane to the center of the pupil, and

*R*represents the radius of curvature of the anterior corneal surface before refractive surgery.

_{1}*R*conveys the radius of curvature after refractive surgery.

_{f}*O*is the diameter of the optical zone.

*R*can be obtained as follows:

_{f}*D*depicts the myopic (hence negative) refraction in diopters;

_{s}*n*represents the refractive index of the cornea.

- a) The displacement (ΔX, ΔY, and ΔZ) of the corneal surface nodes under IOP before and after refractive surgery were obtained from the FEM.
- b) The optical path difference of any arbitrary point on the corneal surface before and after IOP loading was calculated from ΔX, ΔY, and ΔZ. Because the cornea is considered to be spherical, the value of Z of any point A (X, Y, Z) on the corneal surface was calculated using the following equation:

*n*is the refractive index of the cornea.

- c) Thus we obtained the preoperative Zernike coefficients by wave-front surface fitting from preoperative optical path difference. The same method can be used to obtain the Zernike coefficients after refractive surgery. The induced aberrations were obtained from the differences between the postoperative and preoperative wave-front aberrations, which were estimated as follows:

^{21}

^{,}

^{22}However, clinical studies have shown that the higher-order aberrations of the eyes significantly increase after refractive surgery, partly due to biomechanical effects of the cornea. Our study has shown that the higher-order aberrations caused by the displacement of the anterior and posterior corneal surfaces after refractive surgery mainly include spherical aberration, vertical coma, and y-trefoil, which is consistent with the clinical data published by Wu and Wang.

^{23}In addition, Benito et al.

^{24}found that positive spherical aberration and coma were associated with a similar increase in corneal aberrations after myopic LASIK. Therefore the higher-order aberrations after LASIK partly resulted from the biomechanical effects of cornea.

^{7}showed that patient eyes (simulated) with an elastic cornea (modulus of elasticity = 2 MPa) could undergo a hyperopic shift as large as 2.0 D with just the introduction of the flap. However, in our study, the cornea ablation resulted in a 0.75 D hyperopic shift on refractive correction to –5 D. The different results may be due to differences in materials and models used in these studies.

^{20}analyzed the impact of refractive surgery on wave-front aberrations and found that significant higher-order aberrations were induced by the ablation profile based on a mathematical model of the anterior corneal surface. Therefore we concluded that these postoperative higher-order aberrations may be caused by the combination of laser ablation to the stromal bed and the anterior and posterior corneal surface displacement associated with the biomechanical weakness of the cornea.

^{15}

^{25}

^{26}Therefore effect of material parameters of the ocular tissue on wave-front aberrations from anterior corneal surface was studied. At present, some studies have suggested that the Young modulus of the sclera was approximately 3 to 5 times higher than that of the cornea.

^{27}In addition, it is worthwhile to consider the range of the elastic modulus of the cornea in normal human eyes, so eight cases were designed to support the effect of material parameters on the introduction of aberrations as shown in Table 1.

^{28}The material parameters of the cornea significantly affect the displacement of the anterior and posterior corneal surfaces. Moreover, once the scleral elasticity maintained a constant, with the increase of corneal elasticity, the maximum stress and maximum displacement moved toward the edge of the cornea. This finding was consistent with the studies published by Roy and Dupps.

^{6}Therefore further studies should focus on the effect of this result on the induced aberrations after refractive surgery. In addition, with the fixed material parameters of the cornea, the scleral material parameters still significantly affected the shape of the cornea. The material parameters of both the cornea and the sclera in this study were from previous publications. However, previous studies had shown significant individual differences in the corneal material parameters. The individual corneal material parameters was obtained by fitting a material model to experimental data of corneal tissue using the inverse finite element approach, but it had not been applied in clinical practice.

^{29}In fact, the proper in vivo measurement of the material parameters of cornea and sclera was required for the construction of a more precise and individual human eye FEM.

^{30}

^{31}found that higher deformations and stresses were observed within the residual stromal bed in flap-based cases than SMILE cases. In the Sinha Roy et al.

^{32}work, SMILE may present less biomechanical risk in the corneal residual bed than comparable corrections involving LASIK flaps. Second, another factor is the microstructure of the corneal tissue, such as the local micromechanical properties of different layers in the cornea,

^{33}and the distribution of physiological collagen fibers exhibiting nonlinear anisotropy.

^{34}Finally, the factor is the large differences among individuals in biomechanical property. The accuracy of simulation-based LASIK outcomes could be improved by the establishment of patient-specific simulation.

^{35}

^{36}

^{,}

^{37}Future research finding would be closer to clinical measurement data by using the ablation profiles for different surgical procedures and the individual eye models. Our goal is to simulate the clinical situation as much as possible. In follow-up work, the effect of refractive surgery on the biomechanical properties may be better evaluated by constructing individual FEM of the human eye combined with treatment decentration, transition zone, corneal flap, optical zone size, IOP, and other parameters.

^{38}In addition, we would also focus on the data of stress and strain in the results of the finite element analysis to better understand the biomechanical characteristics of the human eye. Finite element method can become a valuable tool to plan and design refractive surgery

^{39}and other ophthalmo-surgical procedures to optimize the refractive outcomes and the visual function.

^{40}

**L. Fang**, None;

**W. Ma**, None;

**Y. Wang**, None;

**Y. Dai**, None;

**Z. Fang**, None

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