Stochastic analysis of a heterogeneous micro-finite element model of a mouse tibia

Finite element (FE) analysis can be used to predict bone mechanical environments that can be used for many important applications, such as the understanding of bone mechano-regulation mechanisms. However, when defining the FE models, uncertainty in bone material properties may lead to marked variations in the predicted mechanical environment. The aim of this study is to investigate the influence of uncertainty in bone material property on the mechanical environment of bone. A heterogeneous FE model of a mouse tibia was created from micro computed tomography images. Axial compression loading was applied, and all possible bone density-modulus relationships were considered through stochastic analysis. The 1st and 3rd principal strains (ε₁ and ε₃) and the strain energy density (SED) were quantified in the tibial volume of interest (VOI). The bounds of ε₁, ε₃, and SED were determined by the bounds of the density-modulus relationship; the bone mechanical environment (ε₁, ε₃, and SED) and the bone density-modulus relationship exhibit the same trend of change; the relative percentage differences caused by bone material uncertainty are up to 28%, 28%, and 21% for ε₁, ε₃, and SED, respectively. These data provide guidelines on the adoption of bone density-modulus relationship in heterogeneous FE models.