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Research Papers

# Patient-Specific Modeling of Corneal Refractive Surgery Outcomes and Inverse Estimation of Elastic Property Changes

[+] Author and Article Information
Abhijit Sinha Roy

Cole Eye Institute, Cleveland Clinic, Cleveland, OH 44195

William J. Dupps1

Cole Eye Institute, Department of Biomedical Engineering, and Transplant Center, Surgery Institute, Cleveland Clinic, Cleveland, OH; Department of Biomedical Engineering, Case Western Reserve University, Cleveland, OH 44195bjdupps@sbcglobal.net

1

Corresponding author.

J Biomech Eng 133(1), 011002 (Dec 22, 2010) (10 pages) doi:10.1115/1.4002934 History: Received February 11, 2010; Revised October 11, 2010; Posted November 02, 2010; Published December 22, 2010; Online December 22, 2010

## Abstract

The purpose of this study is to develop a 3D patient-specific finite element model (FEM) of the cornea and sclera to compare predicted and in vivo refractive outcomes and to estimate the corneal elastic property changes associated with each procedure. Both eyes of a patient who underwent laser-assisted in situ keratomileusis (LASIK) for myopic astigmatism were modeled. Pre- and postoperative Scheimpflug anterior and posterior corneal elevation maps were imported into a 3D corneo-scleral FEM with an unrestrained limbus. Preoperative corneal hyperelastic properties were chosen to account for meridional anisotropy. Inverse FEM was used to determine the undeformed corneal state that produced $<0.1%$ error in anterior elevation between simulated and in vivo preoperative geometries. Case-specific 3D aspheric ablation profiles were simulated, and corneal topography and spherical aberration were compared at clinical intraocular pressure. The magnitude of elastic weakening of the residual corneal bed required to maximize the agreement with clinical axial power was calculated and compared with the changes in ocular response analyzer (ORA) measurements. The models produced curvature maps and spherical aberrations equivalent to in vivo measurements. For the preoperative property values used in this study, predicted elastic weakening with LASIK was as high as 55% for a radially uniform model of residual corneal weakening and 65% at the point of maximum ablation in a spatially varying model of weakening. Reductions in ORA variables were also observed. A patient-specific FEM of corneal refractive surgery is presented, which allows the estimation of surgically induced changes in corneal elastic properties. Significant elastic weakening after LASIK was required to replicate clinical topographic outcomes in this two-eye pilot study.

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## Figures

Figure 1

(a) Stress-strain relationships along three meridia obtained from the experimental data of Elsheikh (29) and (b) a 3D corneoscleral model with finite element mesh and a superimposed map of displacements resulting from loading the undeformed pre-LASIK model (determined from inverse FEM) to clinically measured preoperative IOP. The paracentral and peripheral cornea exhibits greater displacements than the central zone (in mm).

Figure 6

Comparison of the corneal first-surface spherical aberration calculated from in vivo measurement and FEM prediction for (a) the right eye and (b) the left eye before and after LASIK: FEM preoperative, FEM1 postoperative (unchanged elastic properties), FEM2 postoperative (uniform reduction in elastic properties), and FEM3 postoperative (nonuniform reduction in elastic properties)

Figure 2

Maximum principal strain under applied IOP. The black dashed circle demarcates the corneal border. Differences in the strain are due to encoding experimentally derived meridional variations in hyperelastic properties of the cornea. Peak strains are predicted by the FEM along the oblique meridia.

Figure 3

(a) Clinical preoperative anterior axial power map of the right eye in diopters, (b) map of the ratio of the preoperative axial power predicted from the inverse FEM to the in vivo axial power for the right eye, (c) maps of the ratio (post-LASIK FEM/post-LASIK in vivo) of the postoperative anterior axial power assuming there was no change in elastic properties after LASIK, and (d) uniformly reduced elastic properties throughout the optical zone (diameter of 6.5 mm) after LASIK in the right eye

Figure 4

(a) Clinical preoperative anterior axial power map of the left eye in diopters, (b) map of the ratio of the preoperative axial power predicted from the inverse FEM model to the in vivo axial power for the left eye, (c) maps of the ratio (post-LASIK FEM/post-LASIK in vivo) of the postoperative anterior axial power assuming there was no change in elastic properties after LASIK, and (d) uniformly reduced elastic properties throughout the optical zone (diameter of 6.5 mm) after LASIK in the left eye

Figure 5

Patterns of radially nonuniform reduction in elastic properties in (a) the right eye (ΔE=0.35) and (b) the left eye (ΔE=0.5), where ΔE represents the factor multiplied with the preoperative property values to give the postoperative values and was determined for each case through an optimization process designed to maximize agreement between clinical and simulated postoperative anterior surface axial powers. Ratio of the predicted to actual anterior axial power (post-LASIK FEM/post-LASIK in vivo), assuming an ablation-depth dependent reduction in elastic properties within the ablation zone for (c) the right eye and (d) the left eye.

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