Additively manufactured metallic porous biomaterials based on minimal surfaces: A unique combination of topological, mechanical, and mass transport properties

The geometry of porous scaffolds that are used for bone tissue engineering and/or bone substitution has recently been shown to significantly influence the cellular response and the rate of bone tissue regeneration. Most importantly, it has been shown that the rate of tissue generation increases with curvature and is much larger on concave surfaces as compared to convex and planar surfaces. In this work, recent discoveries concerning the effects of geometrical features of porous scaffolds such as surface curvature, pore shape, and pore size on the cellular response and bone tissue regeneration process are reviewed. In addition to reviewing the recent experimental observations, we discuss the mechanisms through which geometry affects the bone tissue regeneration process. Of particular interest are the theoretical models that have been developed to explain the role of geometry in the bone tissue regeneration process. We then follow with a section on the implications of the observed phenomena for geometrical design of porous scaffolds including the application of predictive computational models in geometrical design of porous scaffolds. Moreover, some geometrical concepts in the design of porous scaffolds such as minimal surfaces and porous structures with geometrical gradients that have not been explored before are suggested for future studies. We especially focus on the porous scaffolds manufactured using additive manufacturing techniques where the geometry of the porous scaffolds could be precisely controlled. The paper concludes with a general discussion of the current state-of-the-art and recommendations for future research.

Triply-periodic minimal surfaces are shown to be a more versatile source of biomorphic scaffold designs than currently reported in the tissue engineering literature. A scaffold architecture with sheetlike morphology based on minimal surfaces is discussed, with significant structural and mechanical advantages over conventional designs. These sheet solids are porous solids obtained by inflation of cubic minimal surfaces to sheets of finite thickness, as opposed to the conventional network solids where the minimal surface forms the solid/void interface. Using a finite-element approach, the mechanical stiffness of sheet solids is shown to exceed that of conventional network solids for a wide range of volume fractions and material parameters. We further discuss structure-property relationships for mechanical properties useful for custom-designed fabrication by rapid prototyping. Transport properties of the scaffolds are analyzed using Lattice-Boltzmann computations of the fluid permeability. The large number of different minimal surfaces, each of which can be realized as sheet or network solids and at different volume fractions, provides design flexibility essential for the optimization of competing design targets.