Background: Bone repair needs porous hierarchical scaffolds, which should match the natural bone tissue and provide suitable mechanical support and permeability to allow cell activities, mass transport and bone ingrowth. Mechanical properties and permeability of scaffolds conflict as their porosity varies, then, based on one- and two-level periodic hierarchical scaffolds, the scaffolds are optimized to balance the two physical properties.

Method: The representative volume cell (RVC) of the one-level scaffold is formed by subtracting three small cuboids from a large cube, and the obtained transverse isotropic structure is denoted by β = b⁽¹⁾/a⁽¹⁾, where a⁽¹⁾ and b⁽¹⁾ are side lengths of the pores, respectively. The RVC of the two-level scaffold is self-similarly formed by assembling 20 new RVCs, not cubic, obtained through lengthening l_y⁽¹⁾ with β = l_y⁽¹⁾/l_x⁽¹⁾, where l_y⁽¹⁾ and l_x⁽¹⁾ are side lengths of the first-level RVCs and the self-similarity means that the second and the first-level RVCs share a common β. Considering four transverse anisotropic structures (β = 1.00, 1.06, 1.10, 1.15), their strain-stress curves, Young’s moduli, E, and yield stress are simulated by a commercial finite software (Abaqus); the permeable process are simulated by a software (Fluent), and Darcy’s law is employed to calculate the permeability, K, of the structures. The normalized mechanical properties and permeability are analyzed to get the optimal structure.

Results: For both one-level and two-level scaffolds, the Young’s moduli is approximately inversely proportional to the scaffold porosity when β is constant. As β increases, the Young’s moduli of the structure shows a big difference in y-direction and x-direction. The mechanical anisotropy in one-level scaffold is higher than that in two-level scaffold, and larger β leads to a higher anisotropy in both levels. The same trend has been observed for the yield stress of the one-level and two-level models. The permeability has an opposite trend in the one-level and two-level structure, showing a quasi-linear positive correlation with porosity in both directions, when β is constant. However, the permeable anisotropy in two-level is higher than that in one-level, and larger β leads to a lower anisotropy in both levels. As for an optimal structure, E_y⁽¹⁾ around 1300MPa ~1700MPa and K_y⁽¹⁾ around 5000DC~6000DC are obtained in one-level while the porosity is around 0.78~0.84; E_y⁽²⁾ around 1025MPa ~1065MPa and K_y⁽²⁾ around 8680DC~9680DC are obtained in two-level while the porosity is around 0.83~0.86.

Conclusion: The study shows that β has a great influence on the anisotropy of the mechanics and the permeability. An optimal structure is obtained for medical reference, as well.