Sensitivity analysis based on non-intrusive regression-based polynomial chaos expansion for surgical mesh modelling

The modelling of a system containing implants used in ventral hernia repair and human tissue suffers from many uncertainties. Thus, a probabilistic approach is needed. The goal of this study is to define an efficient numerical method to solve non-linear biomechanical models supporting the surgeon in decisions about ventral hernia repair. The model parameters are subject to substantial variability owing to, e.g., abdominal wall parameter uncertainties. Moreover, the maximum junction force, the quantity of interest which is worthy of scrutiny due to hernia recurrences, is non-smooth. A non-intrusive regression-based polynomial chaos expansion method is employed. The choice of regression points is crucial in such methods, thus we study the influence of this choice on the quantity of interest, and look for an efficient strategy. For this purpose, several aspects are studied : (i) we study the quality of the quantity of interest, i.e. accuracy of the mean and standard deviation, (ii) we perform a global sensitivity analysis using Sobol sensitivity indices. The influence of uncertainties of the chosen variables is presented. This study leads to the definition of an efficient numerical simulation dedicated to our model of implant.