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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 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 and diffusive 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 ingrowth within the scaffold are efficiently obtained using a finite difference scheme implemented in parallel. 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. 

Abstract This work introduces a computational method for designing bone scaffolds for maximum bone growth. A mechanobiological model of bone adaptation is used to compute the bone growth, taking into account the shape of the defect, the applied loading, and the existing density distribution of the bone in which the scaffold has been implanted. Numerical homogenization and a geometry projection technique are used to efficiently obtain surrogates of the effective elastic and diffusive properties of the scaffold as a function of the scaffold design and the bone density. These property surrogates are in turn used to perform bone adaptation simulations of the scaffold–bone system for a sampling of scaffold designs. Surrogates of the bone growth in the scaffold at the end of the simulated time and of the strain energy of the scaffold at implantation time are subsequently constructed from these simulations. Using these surrogates, we optimize the design of a scaffold implanted in a rabbit femur to maximize volume bone growth into the scaffold while ensuring a minimum stiffness at implantation. The results of the optimization demonstrate the effectiveness of the proposed method by showing that maximizing bone growth with a constraint on structural compliance renders scaffold designs with better bone growth than what would be obtained by only minimizing compliance.