Heterogeneous porous scaffold design for tissue engineering using triply periodic minimal surfaces

Recently, a paradigm shift is taking place in tissue engineering scaffold design from homogeneous porous scaffolds to functionally graded scaffolds that have heterogeneous internal structures with controlled porosity levels and architectures. This paper presents a new heterogeneous modeling methodology for designing tissue engineering scaffolds with precisely controlled porosity and internal architectures using triply periodic minimal surfaces. The internal architectures and porosity at the spatial locations of the scaffolds are determined based on a given distribution of architectures and porosity levels specified at a few selected points on the model. After generating the hexahedral elements for a 3D anatomical shape using the distance field algorithm, the unit cell libraries composed of triply periodic minimal surfaces are mapped into the subdivided hexahedral elements using the shape function widely used in the finite element method. By simply allocating parameter values related to the porosity and architecture type to the corner nodes in each hexahedral element, we can easily and precisely control the pore size, porosity, and architecture type at each region of the scaffold while preserving perfectly interconnected pore networks across the entire scaffold.