Tetrahedron-Based Porous Scaffold Design for 3D Printing

Tissue repairing has been the ultimate goal of surgery, especially with the emergence of reconstructive medicine. A large amount of research devoted to exploring innovative porous scaffold designs, including homogeneous and inhomogeneous ones, have been presented in the literature. The triply periodic minimal surface has been a versatile source of biomorphic structure design due to its smooth surface and high interconnectivity. Nonetheless, many 3D models are often rendered in the form of triangular meshes for its efficiency and convenience. The requirement of regular hexahedral meshes then becomes one of limitations of the triply periodic minimal surface method. In this paper, we make a successful attempt to generate microscopic pore structures using tetrahedral implicit surfaces. To replace the conventional Cartesian coordinates, a new coordinates system is built based on the perpendicular distances between a point and the tetrahedral faces to capture the periodicity of a tetrahedral implicit surface. Similarly to the triply periodic minimal surface, a variety of tetrahedral implicit surfaces, including P-, D-, and G-surfaces are defined by combinations of trigonometric functions. We further compare triply periodic minimal surfaces with tetrahedral implicit surfaces in terms of shape, porosity, and mean curvature to discuss the similarities and differences of the two surfaces. An example of femur scaffold construction is provided to demonstrate the detailed process of modeling porous architectures using the tetrahedral implicit surface.