Mathematically defined gradient porous materials

Here we propose an effective and succinct method to generate graded porous material architectures in a mathematical way. Pores with gradient pore sizes, types, orientations and porosities can be integrated to create a single architecture. The resulting structures can be readily produced by using additive manufacturing (AM) techniques for medical applications. We give relevant examples of constructing several kinds of gradient porous scaffolds and discuss their respective characteristics for use in cell culture studies.