Uncertainty quantification on a chemical poroelastic coupled problem: Mechanobiology of implant healing

Abstract

The fixation of a bone implant is related to the quality of tissue in the vicinity thereof. A numerical model is relevant to improve the understanding of mechanobiological events involved and to guide the implantation surgery. To build a robust model that integrates a large number of biomechanical parameters that are subject to variability, uncertainty propagation is analysed. In this work, a numerical model coupling of biochemistry and poroelasticity is proposed and it is applied to canine model. The model includes a nondimensionalization with control of the time and a stochastic modelling. The deterministic part of the model produces the bone density field, corresponding to the quantity of interest, at the end of the healing after several weeks. In particular, it takes into account the influence of external mechanical excitations on the healing process. To limit the costs of computing and development, the stochastic analysis is chosen by the non- intrusive method of probabilistic collocation with development of the polynomial chaos. The results obtained include the effect of coupling between the different sources of uncertainty and allow the influence of biochemical and mechanical parameters such as the applied displacement on the quality of the periprosthetic tissue healing to be quantified.