Additively manufactured (AM) lattice structures based on triply periodic minimal surfaces (TPMS) offer desirable structure-property relationships for bone tissue engineering (BTE) due to their biomimetic design. However, increasingly complex morphologies raise the question of structural integrity. Topology optimization (TO) could be a powerful tool in the design process, but existing approaches are mostly limited to a single design parameter and a single load case. 

Therefore, in the present study, multiscale TO, which involves optimization of both density distribution and unit cell design, is applied to TPMS based bone substitutes. Here, various load cases relevant to BTE are considered numerically using finite element method (FEM). Shear loading is found to induce biomimetic center-periphery differentiation of material distribution. In contrast, compression loading leads to a strut alignment similar to cancellous bone according to the principal stress trajectories. Furthermore, the selection of the design clearance proves to be a suitable adjusting screw for the compromise between morphology conservation and performance optimization. Here, the greater the design clearance, the greater both the performance gain and the morphological alteration.
Selected optimized Gyroid and I-WP based lattices are fabricated from biocompatible alloy Ti-42Nb using laser powder bed fusion (LPBF). The experimental results indicate a significant potential for coupling TO and AM processed lattice structures. Specifically, an increase in compressive stiffness of up to 80% and in strength of up to 61% compared to the standard design is experimentally demonstrated, while maintaining the inherent morphology of TPMS. Given a stiffness of about 1.5-2.0 GPa and a yield strength of 40-55 MPa, the optimized lattices exhibit excellent suitability for bone implants. Therefore, the proposed multiscale TO approach could be a key factor to exploit the composite of biocompatible Ti-42Nb alloy and TPMS based biomimetic design for future implant applications.