The bone tissue remodelling analysis in dentistry using a meshless method

In this work a topology optimization model, based on deformation energy methods, is used to predict the bone density distribution in the vicinity of natural teeth and dental implants, both in the mandibular and the maxillary bones, due to natural external loads. Capable of maximizing the structural stiffness by itself, the bone tissue is an efficient and optimized anisotropic biological material. This work considers a recently developed anisotropic mathematical phenomenological law to predict the mechanical behaviour of the bone tissue. This law was developed based on experimental data available in the literature and permits to correlate the bone density with the obtained level of stress. In order to obtain the displacement and stress fields an advanced discretization technique is used: the Natural Neighbour Radial Point Interpolator Method (NNRPIM). The NNRPIM is an efficient and flexible meshless method, presenting various advantages in the topologic analysis comparing with other discrete numerical methods such as the Finite Element Method.