Computer-aided Porous Scaffold Design for Tissue Engineering Using Triply Periodic Minimal Surfaces

Recently, computer aided geometric design of triply periodic minimal surfaces (TPMS) has received considerable attention in the area of computer aided nano design on account of its ability to efficiently construct a large number of complex surfaces. In this paper, a TPMS is described with periodic surfaces composed of simple trigonometric functions, thus enabling easy generation of TPMS for use in various mechanical, chemical, and physical applications. We first describe a TPMS with mesh surface using conventional marching cube algorithm. We then propose various related algorithms for generating complete solid model for various applications, ranging from thickened solid, through voxel solid, to complex-shaped solid. The validity of this new technique is demonstrated for a variety of TPMSs, including the P. G, D, I-WP, F-RD, L, and I(2)-Y** surfaces. Finally, a new control approach for pore size distribution in tissue scaffold design is presented based on the pore-making element composed of TPMS and conformal refinement of all-hexahedral mesh in order to show the practical applicability of the newly suggested modeling approach.