Novel Equations for Permeability and Elastic Modulus of Triply Periodic Minimal Surface Scaffolds via Experimental and Numerical Analysis

Triply periodic minimal surface (TPMS) scaffolds are crucial in bone tissue engineering due to their significant impact on permeability, wall shear stress, and elastic modulus. However, optimizing both permeability and mechanical performance poses a challenge. This study presents an experimental and numerical investigation of three TPMS architectures: Primitive (P), Diamond (D), and Gyroid (G), featuring uniform and graded porosity distributions across various pore sizes. Graded porosity enhances the scaffolds’ ability to mimic the natural heterogeneity of bone tissue, improving biological functionality and mechanical compatibility. Novel empirical equations predict scaffold permeability as a function of pore size and normalized elastic modulus based on porosity percentage, allowing efficient early‐stage design without extensive prototyping. Analyses reveal complex relationships between scaffold geometry, porosity, and biological responses, including osteogenic potential. Eighteen uniform scaffolds with pore sizes of 600, 800, and 1200 μm and three gradient scaffolds are evaluated. The Primitive structure exhibits the highest permeability, while both Primitive and Gyroid architectures show superior elastic moduli. Importantly, increased porosity does not always lead to decreased wall shear stress. The results are validated through microstructural analysis and in vivo data, reinforcing the robustness of the proposed models for optimizing TPMS scaffolds in bone tissue regeneration.