An advanced method to design graded cylindrical scaffolds with versatile effective cross-sectional mechanical properties

The selection of the most-suited bone scaffold for a given clinical application is challenging, and has motivated numerous studies. They are mostly based on the characterization of cellular structures, generated from the threedimensional repetition of a unit cell. However, the interest of circular graded bone scaffolds has been emphasized since they facilitate nutrient transport from the periphery to the core of the scaffold. In the present contribution, we present an advanced and versatile method to design graded circular porous 2D structures based on the conformal mapping of unit cells. We propose a method to generate 3D porous scaffolds by a multilayer repetition of the circular cross-section, resulting in tunable anisotropy depending on the clinical application. We then analyze the link between the porosities of the obtained structures and their effective elastic mechanical crosssectional properties, making use of a novel and computationally efficient method allowing exhaustive parametric studies. The comparison of various conformal transformations and unit cell designs emphasizes the extent of mechanical properties and porosities that may be reached for a given constitutive material, including nonstandard mechanical properties that open large perspectives towards the development of self-fitting scaffolds.