Assessment of the effect of mesh density on the material property discretisation within QCT based FE models: a practical example using the implanted proximal tibia

A three-dimensional, quantitative computed tomography based finite element model of a proximal implanted tibia was analysed in order to assess the effect of mesh density on material property discretisation and the resulting influence on the predicted stress distribution. The mesh was refined on the contact surfaces (matched meshes) with element sizes of 3, 2, 1.4, 1 and 0.8 mm. The same loading conditions were used in all models (bi-condylar load: 60% medial, 40% lateral). Significant variations were observed in the modulus distributions between the coarsest and finest mesh densities. Poor discretisation of the material properties also resulted in poor correlations of the stresses and risk ratios between the coarsest and finest meshes. Little difference in Young's modulus, von Mises stress and risk ratio distributions were observed between the three finest models; hence, it was concluded that for this particular case an element size of 1.4 mm on the contact surfaces was enough to properly describe the stiffness, stress and risk ratio distributions within the bone. Poor convergence of the material property distribution occurred when the element size was significantly larger than the pixel size of the source CT data. It was concluded that unless there is convergence in the Young's modulus distribution, convergence of the stress field or of other parameters of interest will not occur either.