Gaussian process prediction of the stress-free configuration of pre-deformed soft tissues: Application to the human cornea.

Image-based modeling is a popular approach to perform patient-specific biomechanical simulations. One constraint of this technique is that the shape of soft tissues acquired in-vivo is deformed by the physiological loads. Accurate simulations require determining the existing stress in the tissues or their stress-free configurations. This process is time consuming, which is a limitation to the dissemination of numerical planning solutions to clinical practice. In this study, we propose a method to determine the stress-free configuration of soft tissues using a Gaussian process (GP) regression. The prediction relies on a database of pre-calculated results to enable real time predictions. The application of this technique to the human cornea showed a level of accuracy five to ten times higher than the accuracy of the topographic device used to obtain the patients' anatomy; results showed that for almost all optical indices, the predicted curvature error did not exceed 0.025 D, while the wavefront aberration percentage error did not overcome 5%. In this context, we believe that GP models are suitable for predicting the stress free configuration of the cornea and can be used in planning tools based on patient-specific finite element simulations. Due to the high level of accuracy required in ophthalmology, this approach is likely to be appropriate for other applications requiring the definition of the relaxed shape of soft tissues.

Biomechanical Modeling of Femtosecond Laser Keyhole endokeratophakia Surgery.

PURPOSE: To apply a finite element model to endokeratophakia and evaluate anterior and posterior corneal surface changes. METHODS: Spatial elevation data (Pentacam HR; Oculus, Wetzlar, Germany) were obtained for the front and back corneal surfaces of an eye prior to undergoing an endokeratophakia procedure. These were used to warp a spherical template finite element model of the cornea to create a patient-specific finite element mesh and the initial stress distribution was computed with an iterative approach. The finite element model (Optimeyes; Integrated Scientific Services, Biel, Switzerland) included non-linear elastic characteristics of the stroma. The endokeratophakia procedure was recreated in the model: a donor lenticule (-10.50 diopters [D], 5.75-mm zone, 127-µm thick) was inserted into a lamellar pocket (180-µm deep, 6.25-mm diameter) and two 2-mm small incisions were made at 150° and 330°. Anterior and posterior surfaces, computed by the finite element model, were compared to clinical data to assess accuracy and reliability of finite element modeling. RESULTS: The postoperative axial curvature produced by the model closely resembled the patient data; average curvature was 48.01 D clinically and 48.23 D in the simulation, and corneal astigmatism was 3.01 D clinically and 2.88 D in the simulation. The posterior best-fit sphere elevation map also matched the patient data, replicating inward bulging of the posterior surface by approximately 40 µm. Stress distribution modeling predicted a stress increase by 159.94% ± 73% in the cap and a stress decrease by 32.41% ± 21% in the stromal bed. CONCLUSIONS: Finite element modeling of the cornea reproduced the clinically observed anterior and posterior corneal surface changes following an endokeratophakia procedure. This case sets the stage for further study to refine and yield predictive finite element modeling for the evaluation of corneal refractive surgical procedures.