Assessing the behavior of a hybrid model of the knee with contact surrogate under parameter uncertainties

Modeling the knee is an important factor in increasing the quality of life of both healthy individuals and patients. Nevertheless, the intricate nature of the knee makes this problem complicated. In this study, an extension to an established planar knee joint model with Hertzian contact pairs is proposed with contact mechanics based on polynomial chaos expansion surrogate. Firstly, the finite element (FE) model is made representing a contact pair of sphere-to-plane type with two layers on both bodies, corresponding to the cartilage and the bone. Five variables corresponding to both geometry and material parameters are used to parametrize this model. Then, 128 distinct variants of the FE model are created based on a quasi-Monte Carlo sequence. This dataset is used to train and validate the surrogate. The trained surrogate is proven to have predictive capabilities with an average nRMSE of 0.2% in randomized test/train splits. When included in a model of the knee and tested under parameter uncertainties in Monte Carlo simulations, it results in nRMSE of 58% for angular coordinate compared to the original model with Hertzian pair. This signifies the high influence of contact formulation on the model output and the need for more physically based models in knee contact modeling.