A new numerical approach to mechanically analyse biological structures.

In this work, an advanced discretization meshless technique is used to study the structural response of a human brain due to an impact load. The 2D and 3D brain geometrical models, and surrounding structures, were obtained through the processing of medical images, allowing to achieve a realistic geometry for the virtual model and to define the distribution of the mechanical properties accordingly with the medical images colour scale. Additionally, a set of essential and natural boundary conditions were assumed in order to reproduce a sudden impact force applied to the cranium. Then, a structural numerical analysis was performed using the Natural Neighbour Radial Point Interpolation Method (NNRPIM). The obtained results were compared with the finite element method (FEM) and a solution available in the literature. This work shows that the NNRPIM is a robust and accurate numerical technique, capable to produce results very close to other numerical approaches. In addition, the variable fields obtained with the meshless method are much smoother than the FEM corresponding solution.

A Global Numerical analysis of the "central incisor/local maxillary bone" system using a meshless method.

In this work the maxillary central incisor is numerically analysed with an advance discretization technique--Natural Neighbour Radial Point Interpolation Method (NNRPIM). The NNRPIM permits to organically determine the nodal connectivity, which is essential to construct the interpolation functions. The NNRPIM procedure, based uniquely in the computational nodal mesh discretizing the problem domain, allows to obtain autonomously the required integration mesh, permitting to numerically integrate the differential equations ruling the studied physical phenomenon. A numerical analysis of a tooth structure using a meshless method is presented for the first time. A two-dimensional model of the maxillary central incisor, based on the clinical literature, is established and two distinct analyses are performed. First, a complete elasto-static analysis of the incisor/maxillary structure using the NNRPIM is evaluated and then a non-linear iterative bone tissue remodelling analysis of the maxillary bone, surrounding the central incisive, is performed. The obtained NNRPIM solutions are compared with other numerical methods solutions available in the literature and with clinical cases. The results show that the NNRPIM is a suitable numerical method to analyse numerically dental biomechanics problems.