Meshless, Bone Remodelling and Bone Regeneration Modelling

In this chapter, it is presented an extensive bibliographic survey about meshless methods, bone remodelling and bone regeneration modelling. Here, the regeneration and remodelling processes are shown with detail and, in addition, it is presented a description of the mathematical models approaching both regeneration and remodelling processes. Three different classifications of models are presented, the mechanoregulated models, the bioregulated models and the mechanobioregulated models. The literature shows that the combination of remodelling models with meshless techniques allows to numerically achieve more realistic trabecular distributions. Thus, in this chapter, an introduction to meshless methods is presented, with a special focus on radial point interpolation meshless methods, such as the radial point interpolation method (RPIM) and the natural neighbour RPIM (NNRPIM).