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

Abstract

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.

Keywords: Biomechanics; Cornea; Finite-element; Gaussian process; Prediction; Stress-free.