Mechanical bone remodelling: Comparative study of distinct numerical approaches

Abstract

Bone is a complex living structure. Induced by its biomechanical environment, bone constantly adapts its internal and external structure, altering its mass and morphology. In this work, three distinct discretization techniques are combined with a mechanologic bone tissue remodelling algorithm, which describes the remodelling process by minimizing the strain energy density (SED) field. During an iterative remodelling process, bone tissue's mechanical properties are recurrently correlated with bone apparent density through a phenomenological law. The purpose of this study is to compare bone tissue remodelling solutions obtained with the Finite Element Method (FEM), the Radial Point Interpolation Method (RPIM) and the Natural Neighbour RPIM (NNRPIM). Thus, two numerical examples were analysed, namely a benchmark bone patch and a femur. On both examples, regardless the discretization technique, it was possible to accurately reproduce the trabecular bone architecture. Additionally, a comparison between each numerical method was performed. The model shown high adaptability, since, for every method, successful performances were obtained. Nevertheless, meshless solutions produced smoother and more accurate results, closer to real X-ray images.