A meshless microscale bone tissue trabecular remodelling analysis considering a new anisotropic bone tissue material law.

In this work, a novel anisotropic material law for the mechanical behaviour of the bone tissue is proposed. This new law, based on experimental data, permits to correlate the bone apparent density with the obtained level of stress. Combined with the proposed material law, a biomechanical model for predicting bone density distribution was developed, based on the assumption that the bone structure is a gradually self-optimising anisotropic biological material that maximises its own structural stiffness. The strain and the stress field required in the iterative remodelling process are obtained by means of an accurate meshless method, the Natural Neighbour Radial Point Interpolation Method (NNRPIM). Comparing with other numerical approaches, the inclusion of the NNRPIM presents numerous advantages such as the high accuracy and the smoother stress and strain field distribution. The natural neighbour concept permits to impose organically the nodal connectivity and facilitates the analysis of convex boundaries and extremely irregular meshes. The viability and efficiency of the model were tested on several trabecular benchmark patch examples. The results show that the pattern of the local bone apparent density distribution and the anisotropic bone behaviour predicted by the model for the microscale analysis are in good agreement with the expected structural architecture and bone apparent density distribution.