Modeling, assessment, and design of porous cells based on schwartz primitive surface for bone scaffolds

The design of bone scafolds for tissue regeneration is a topic of great interest, which involves diferent issues related to geometry of architectures, mechanical behavior, and biological requirements, whose optimal combination determines the success of an implant. Additive manufacturing (AM) has widened the capability to produce structures with complex geometries, which should potentially satisfy the diferent requirements. These architectures can be obtained by means of refned methods and have to be assessed in terms of geometrical and mechanical properties. In this paper a triply periodic minimal surface (TPMS), the Schwarz's Primitive surface (P-surface), has been considered as scafold unit cell and conveniently parameterized in order to investigate the efect of modulation of analytical parameters on the P-cell geometry and on its properties. Several are the cell properties, which can afect the scafold performance. Due to the important biofunctional role that the surface curvature plays in mechanisms of cellular proliferation and diferentiation, in this paper, in addition to properties considering the cell geometry in its whole (such as volume fraction or pore size), new properties were proposed. Tese properties involve, particularly, the evaluation of local geometrical-diferential properties of the P-surface. Te results of this P-cell comprehensive characterization are very useful for the design of customized bone scafolds able to satisfy both biological and mechanical requirements. A numerical structural evaluation, by means of fnite element method (FEM), was performed in order to assess the stifness of solid P-cells as a function of the changes of the analytical parameters of outer surface and the thickness of cell. Finally, the relationship between stifness and porosity has been analyzed, given the relevance that this property has for bone scafolds design.