Computational modelling of TPMS unit cells for bone scaffold

Bone scaffolds have emerged as a key solution in tissue engineering for the repair of bone defects, with the objective of replicating the morphological and mechanical properties of the native bone. Triply Periodic Minimal Surfaces (TPMS) unit cells, characterized by their smooth and continuous geometry, represent an excellent solution for the design of lattice structures for bone scaffolds. In this thesis a computational framework has been implemented to design bone scaffolds based on TPMS unit cells with different geometries and configurations. The framework was developed in Matlab and it is based on the open-source toolboxes “LatticeWorks” and “GIBBON,” integrated with “TetGen” for unit cell generation and tetrahedral mesh creation. The stiffness of the lattice structure has been evaluated through the homogenization theory implemented via the “3D Homogenization of Cellular Materials” toolbox, allowing the estimation of the equivalent elastic modulus of the structures as a function of porosity and of the material. Three TPMS configurations (Gyroid, Primitive, and Diamond) have been analyzed by varying the level-set parameter, which enables control of the porosity and pore diameter of the lattice structure. Two biocompatible polymers commonly used in biomedical applications, polycaprolactone (PCL) and polymethylmethacrylate (PMMA), were tested to assess their application. The results showed that PCL is not suitable for trabecular bone applications, due to its low elastic modulus. On the contrary, PMMA proved to be an excellent solution, enabling the design of bone scaffolds with stiffness values comparable to trabecular bone. Based on these findings, three cylindrical scaffolds were designed in PMMA for each of the investigated TPMS configuration by periodic repetition of the unit cells. The cylindrical structure was then exported in STL format and fabricated via stereolithography (SLA) 3D printing. The proposed framework therefore represents a versatile and customizable design tool for lattice structures, adaptable to different biological and mechanical requirements in bone regeneration applications.