Safety evaluation after LASIK surgery based on the linear creep property: a finite element analysis

Abstract

Aim: To investigate the effect of the percent tissue altered (PTA) on the safety after laser-assisted in situ keratomileusis (LASIK) based on linear creep characteristics.

Methods: The linear creep characteristics of the cornea were characterized by the generalized Kelvin-Voigt constitutive relationship with five parameters. Then, the displacement and stress distribution on the anterior and posterior surfaces of the cornea were analyzed by constructing the eye model with different PTA.

Results: When PTA was above 39%, the vertex displacements under physiological intraocular pressure (IOP, 15 mm Hg) exceeded that of the preoperative glaucoma under average IOP. That is, an excessively high displacement value was found. In addition, with the increase of PTA, the central cornea was stretched thinner and more obviously due to IOP. When PTA was above 39%, the stress at the center of the anterior surface of the residual stroma was more than 20% larger than that of the normal human eye. The residual stroma was forced to stretch more severely due to excessive stress on the anterior surface. This resulted in deformation of the stroma and induced corneal ectasia. Meanwhile, the postoperative vertex displacement increased with the decrease in viscosity ratio.

Conclusion: PTA less than 39% is the safe range for LASIK surgery. This study may provide a reliable numerical basis for postoperative corneal dilatation and the outcomes after refractive surgery.

Keywords: finite element; laser-assisted in situ keratomileusis; percent tissue altered; vertex displacement.

Figure 1. Curvature radius and finite element mesh

A: The diagram of corneal anterior surface curvature radius before and after refractive surgery; B: Finite element mesh of the personalized model of the human eye.

Figure 2. Construction and verification of creep constitutive equation

A: Five-element linear viscoelastic Kelvin-Voigt model; B: Comparison of uniaxial tension test and simulation results.

Figure 3. Creep experimental curves and vertex displacement under different viscosity ratios

A: Creep experimental curves for different viscosity ratios; B: The vertex displacement of the anterior and posterior surfaces under different viscosity ratios.

Figure 4. Relationship between IOP and PTA with vertex displacements

A: The anterior corneal surface; B: The posterior corneal surface; C: The vertex displacement difference between posterior surface and anterior surface of cornea. IOP: Intraocular pressure; PTA: Percent tissue altered.

Figure 5. The stress nephogram of the anterior corneal surface after refractive surgery (IOP was 15 mm Hg, PTA was 37%)

A: Corneal flap; B: Pedicle flap and the residual stroma. IOP: Intraocular pressure; PTA: Percent tissue altered.

Figure 6. The stress of the corneal surface under different PTA

A: Stress distribution curves of anterior surface in Y-axis direction under different PTA; B: The stress in the center of the anterior and posterior surfaces under different PTA. IOP: Intraocular pressure; PTA: Percent tissue altered.

Figure 7. The distribution map of corneal displacement

A: The distribution map of corneal displacement without creep characteristics; B: The distribution map of corneal displacement with creep characteristics.