Hierarchical Topology Optimization for Bone Tissue Scaffold: Preliminary Results on the Design of a Fracture Fixation Plate

A porous material can be designed to promote tissue regeneration as well as satisfy mechanical and biological requirements. The porous microarchitecture can be specifically tailored to locally match the specific properties of the host tissue resulting in a biologically fixed implant. A 2D hierarchical topology optimization scheme is presented here to design a cellular scaffold that optimally reconciles bone resorption and permeability, two antagonist objectives of bone tissue scaffolds. The implant is tailored to reproduce the variable stiffness properties of the surrounding bone while maximizing its permeability for bone ingrowth. The procedure integrates multi-objective optimization with multi-scale topology optimization. In particular, the material layout is sequentially optimized at two length scales: (1) the property distribution varying throughout the implant body, and (2) the topology of each pore of the scaffold. In the first stage, an optimal material distribution is obtained to generate a stiffness match between implant and bone tissue. In the second stage, the optimal relative density distribution is used to interpolate target material properties at each location of the implant domain. Target matching topology optimization is used to obtain unit cells with desired stiffness and maximum permeability throughout the implant. The procedure currently developed in 2D can be extended to produce clinically relevant 3D implant models. As a case study, a 2D bone fracture fixation plate under in-plane load is optimized at both the implant and cellular material level. While the preliminary results presented here need further refinement, such as on the filtering method and the calculation of permeability, the paper contributes to the development of a method to design engineered scaffolds that are both mechanically optimal and conducive to bone tissue regeneration.