Comparison of the design maps of TPMS based bone scaffolds using a computational modeling framework simultaneously considering various conditions.

In recent years, the triply periodic minimal surface (TPMS)-based scaffolds have been served as one of the crucial types of structures for biological replacements, the energy absorber, etc. Meanwhile, the development of additive manufacturing (AM) has facilitated the production of TPMS scaffolds with complex microstructures. However, the design maps of TPMS scaffolds, especially considering the AM constraints, remain unclear, which has hindered the design and application of TPMS scaffolds. The aims of the present study were to develop an efficient computational modeling framework for investigating the design maps of TPMS scaffolds simultaneously considering the AM constraints, the biological requirements, and the structural anisotropy. To demonstrate the computational framework, five widely-used topologies of the TPMS-based scaffolds (i.e. the Diamond, the Gyroid, the Fischer-Koch S, the F-RD, and the Schwarz P) were used, whose design maps for the surface-to-volume ratio and the effective elastic modulus were also investigated. The results showed that as the porosities increase, the design ranges of the surface-to-volume ratios decreases for all the structures. Compared with the effect of the constraint for the pore size, the minimal structural thickness for AM constraint has a greater effect on the surface-to-volume ratio. Regarding the elastic modulus, in the region of low porosity (approximately 0.5-0.7), the range for the effective elastic modulus of Schwarz P is the widest (approximately 2.24-32.6 GPa), but the Gyroid can achieve both high porosity and low effective elastic modulus (e.g. 0.61 GPa at the porosity of 0.90). These results and the method developed in the present study provided important basis and guidance for the design and application of the TPMS-based porous structures.