In-vivo Estimation of Corneal Hyperelastic Material Properties from Clinical Tompography Data

  • Grytz, Rafael (University of Alabama at Birmingham)
  • Shirazi, Hadi (University of Alabama at Birmingham)
  • Hsu, Kuang-Tsan (Case Western Reserve University School of Med)
  • Dupps, William (Cleveland Clinic Lerner College of Medicine o)

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Laser-Assisted In Situ Keratomileusis (LASIK) is a widely performed refractive surgery that involves ablating stromal tissue to modify corneal curvature. Personalized Finite Element (FE) simulations have been proposed for improved surgical outcome and risk predictions. Hyperelastic material properties necessary for predictive FE models of the cornea are typically obtained from ex vivo experiments such as inflation testing. Here we propose to estimate population averaged material parameters from readily available in vivo clinical data. A retrospective dataset of 45 eyes (25-68 years) with pre- and post-LASIK tomography scans was utilized. Pre-operative tomography defined the FE geometry. Each LASIK procedure invokes a biomechanical perturbation reflected by corneal curvature changes that we utilize as fitting targets to estimate hyperplastic material properties. However, this perturbation is small and insufficient to derive the corneal hyperplastic response for a single dataset. Instead, we combine data of all 45 eyes into one cost function and use Bayesian optimization to estimate the population average hyperplastic response. The population-level cost function is minimized by iteratively updating a surrogate model and selecting parameter sets based on a balance between predicted error and model uncertainty. To assess the quality of the in vivo calibrated model, the root mean square error (RMSE) of the post-LASIK corneal curvature was compared against a model that was calibrated using ex vivo inflation data [1]. The in vivo population data was rich enough to solve the inverse problem and to estimate the overall hyperplastic properties. The in vivo fitted model outperformed the ex vivo model resulting in significantly lower RMSE (Insert in Fig.). The inflation response of both models was similar at low and high pressure levels but deviated at pressures where the nonlinear stiffening of the cornea occurred (Fig.). Our results suggest that in vivo tomography data can be utilized for hyperelastic property estimation and accurate LASIK surgery simulations.