Computational Design of Additively Manufactured Curvilinear Scaffolds for Bone Repair With Analytical Sensitivities

This work introduces a computational method for designing ceramic scaffolds fabricated via direct ink writing (DIW) for maximum bone growth, whereby the deposited rods are curvilinear. A mechanobiological model of bone adaptation is used to compute bone growth into the scaffold, taking into account the shape of the defect, the applied loading, and the density distribution of bone in which the scaffold is implanted. The method ensures that smooth, continuously varying rod contours are produced, which are ideal for the DIW process. The method uses level sets of radial basis functions to fully define the scaffold geometry with a small number of design variables, minimizing the optimization's computational cost. Effective elastic properties of the scaffold as a function of the scaffold design and the bone density are obtained from previously constructed surrogates. These property surrogates are in turn used to perform bone adaptation simulations of the scaffold-bone system. Design sensitivities of the bone growth within the scaffold are computed using the direct sensitivity method. A demonstration of the methodology on a scaffold implanted in a pig mandible is presented. The scaffold is optimized to maximize bone ingrowth with geometric constraints to conform to the manufacturing process.