RegionTPMS — Region based triply periodic minimal surfaces (TPMS) for 3-D printed multiphase bone scaffolds with exact porosity values

Abstract With the advances in biocompatible materials for additive manufacturing (AM) methods, triply periodic minimal surface (TPMS) functions have been gaining grounds in design and development of bone scaffolds. Their promising results for cell proliferation, differentiation and physical characteristics in-vivo have drawn attention in both biomedical and engineering communities. In order to advance the current state-of-the-art, a region based TPMS scaffold generation algorithm is proposed, where the exact porosity values and explicitly described surface functions are used as the input parameters. Rather than adding thickness to the minimal surfaces, as being the common practice, regions are defined within the range of local minimum and maximum of the investigated surface functions in the present study. Therefore, it is possible to design and print the 3-D scaffolds with the exact desired porosity and also define interfaces for functionally graded scaffolds. In order to demonstrate the region-based scaffold concept, first, porous scaffolds based on different mathematical functions (Schwarz-D, Schwarz-P, Gyroid, Fischer–Koch S, Fischer–Koch Y, Lidinoid, I-WP, F-RD and Split-P surface functions) with the porosity values 0 . 2 , 0 . 3 , 0 . 4 , 0 . 5 , 0 . 6 , 0 . 7 were demonstrated. Secondly, multi-phase and multi-porous scaffolds based on the region ranges were presented. The related editable Mathematica notebooks and sample 3D printing files in the standard triangle language (STL) format were also made available for the community use at https://github.com/metudust/RegionTPMS under MIT license.