Bone Tissue Scaffolds Designed With A Porosity Gradient Based On Triply Periodic Minimal Surfaces Using A Parametric Approach.

Recently, the interest in porous scaffolds design for cell culture has increased. Because of the curvotaxis property of the cells, they can respond to the curvature of the substrate in which they are seeded, like changing their morphology, despite that, curvature is little explored within scaffold design. What is more, for bone regeneration, the scaffold should ideally have a porosity gradient corresponding to the transition between compact and cancellous bone. Various studies have focused on finding the best geometry to mimic it, being the triple periodic minimum structures (TPMS) the most promising ones. However, as they are mathematically complex, researchers have approximated them with implicit equations, no longer respecting their minimum curvature when they vary the pore size, deforming the original geometry. This work proposed to approach the TPMS with parametric equations, finding an exact fundamental patch. In this way showing its potential to make customized structures with a porous gradient, thanks to the acquisition of a constant of variation. This generates a friendly user interface for the design of scaffolds. The work also presents a comparison with the implicit structures, remarking the benefits of using the parametric approach. Finally, it presents examples of 3D printed designs.