Developing 2D and 3D micropolar FEM models for porous GBR meshes in dentistry applications

In the present work, COMSOL® Multiphysics is used to implement 2D and 3D micropolar continuum models to address the multidisciplinary problem of modelling guided bone regeneration (GBR) meshes. GBR meshes are used in dentistry as mechanical barriers to isolate and protect the area of bone loss from the surrounding tissue while allowing for new bone growth. The micropolar theory is adopted to provide a homogenised and efficient mechanical model for the heterogeneous porous structure of the GBR mesh. The mechanical constants are derived based on the strain energy equivalence between a periodic porous plate and its equivalent micropolar model under prescribed boundary conditions. The effects of various architectural features, such as pore shapes, patterns, and sizes, on the material parameters are investigated. The results show that the micropolar theory can effectively predict the mechanical response of the GBR mesh with a more reliable performance compared to the classical Cauchy theory. The collected equivalent micropolar parameters are further used for GBR mesh design, considering both mechanical and biomedical requirements. As an example, different materials and arrangements are analysed to find micropolar constitutive parameters that are comparable to bone parameters reported in the literature. This allows the GBR mesh to possess the mechanical performance that matches the adjacent bones and avoid the stress-shielding phenomenon.