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

A flexible design framework to design graded porous bone scaffolds with adjustable anisotropic properties

“…In our recent work (Cheikho et al, 2022), we proposed a new method to design various scaffolds crosssections based on the 2D mapping of various UC's. The large range of reachable apparent mechanical properties of the generated cross-sections, depending on the selected UC and the chosen mapping, were particularly underlined.…”

“…The apparent elastic properties were calculated using the strain energy based-method (Mindlin, 1964), based on the established relationship between the strain energy of the structure and that of the homogenized equivalent model under specific boundary conditions. The technique has been largely described elsewhere (Cheikho et al, 2022;Goda and Ganghoffer, 2015) and consists in applying elementary kinematic loadings to the structure using a Finite Element (FE) analysis, in order to compute the resulting total elastic Strain Energy (SE) and to determine the components of the overall homogenized stiffness tensor expressed in (2). The studied structures were therefore numerically subject to various macro-strain (denoted 𝐸 𝑖𝑗 ), limited to loading cases in the current work, and the total SE stored in the structure under the prescribed Boundary Conditions (BC) was computed using the Abaqus solver (Dassault Systèmes Simulia, United States) after discretization of the structure into C3D4H first-order tetrahedral elements.…”

“…These mechanical effective properties strongly depended on the UC used in the generation of the 3D scaffold. In our last work (Cheikho et al, 2022), we compared 6 unit cells to illustrate the large range of reachable crosssectional properties, in order to generate scaffolds that can mimic as close as possible the original mechanical physiological functions of the bone tissue it aims to replace. As stated above, HC and SC cells were used in the present work for illustrative purpose, since they were associated with the maximal and minimal computed transverse cross-sectional compressibility in our former study.…”

“…In opposition to these perfectly periodic structures, it has been reported that scaffolds with pore size gradients offer better seeding efficiency than homogeneous scaffolds (Sobral et al, 2011) and enhance the diffusion of nutrients from the core to the periphery of scaffolds (Ahn et al, 2010). As a result of these observations, various heterogeneous geometries with pore size gradients have been proposed in order to counter the limited proliferation and vascularization of 3D scaffolds observed for large bone defects (Afshar et al, 2016;Cheikho et al, 2022;Liu et al, 2018;Melchels et al, 2010;Poh et al, 2019;Yook et al, 2012).…”

“…In a recent study (Cheikho et al, 2022), an original framework has been proposed to design graded circular porous architectures based on different mappings of a UC, as well as an efficient energy-based method to compute the effective mechanical properties of the resulting structures. However, this preliminary study suffers from several limitations: firstly, it is limited to the design of two-dimensional (2D) scaffold cross-sections, while 3D porous structures are needed for bone regeneration.…”