Developing 2D and 3D micropolar FEM models for porous GBR meshes in dentistry applications
Porous guided bone regeneration (GBR) meshes are used in dentistry as a mechanical barrier to separate and protect the area of bone loss, providing space for new bone growth. An appropriate pore size can play a role, as important as its space-maintaining properties. The characteristics can be optimised by adjusting their microstructure, which affects their mechanical performance and is directly related to bone formation ability. This work models the GBR mesh as a porous material with an idealised periodic structure. The mechanical behaviour is analysed through an equivalent continuum approximation approach to find equivalent material parameters that properly consider the influence of the microstructure on the overall behaviour [1]. Elastic micropolar (Cosserat) theory, which has been implemented before for heterogeneous materials [2]–[4], was used here. First, the effective properties are obtained based on a parametric study of detailed porous models defined in COMSOL for various possible microstructures (shapes, patterns, and sizes of pores) based on a parametrized geometry [5]{Fig.1}. After finding the equivalent stiffness parameters {Fig.2}, the micropolar FEM models are developed based on the constitutive parameters in 2D and 3D to study the mechanical performance of such structures using the PDE weak form in COMSOL [5]. These equivalent models are used to study the performance of GBR implants in contact with bone and also in multiphysics analysis of the bone remodelling process. It has been shown through experiments that the micropolar theory provides better predictions of bone behaviour than Cauchy elasticity [6], [7]. Bone scaffolds should mimic the mechanical characteristics of the host bone in order to prevent a phenomenon known as stress shielding. Stress-shielding happens when an over-rigid implant reduces the stress in its adjacent bone cells [8]. For instance, being inspired by the natural functionally graded (FG) porous structure of the bone, a GBR mesh is suggested so that the central part possesses mechanical properties close to cancellous bone while providing a proper porosity and the part near fixing areas (the screw's location) is similar to compact bone to provide the required load-bearing capacities. {Fig.3} Currently, metallic GBR sheets are used as a mechanical barrier, and bone grafts are inserted into the space created by the barrier. After the healing period, it is necessary that patients undergo a second surgery for removal. To avoid this, biodegradable materials such as PLA are used. However, their suboptimal mechanical properties, such as low stiffness, have limited their application. A 3D FG design is proposed in which the microstructure evolves from the porous structure at the lower level to the compact structure at the top surface {Fig.4}. The porous structure can host bioactive agents for stimulating bone regeneration and provide faster biodegradation during the healing period, while the upper compact surface should withstand the mechanical loads and provide the required stiffness. By implementing this model, the distribution of both the internal structure and the material properties can be customised and optimised. For instance, bimodal materials like PLA+HA or nano-reinforcements can be used.
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