Title:
Numerical optimization of open-porous bone scaffold structures to match the elastic properties of human cortical bone.

Abstract:
Treatment of large segmental bone defects, especially in load bearing areas, is a complex procedure in orthopedic surgery. The usage of additive manufacturing processes enables the creation of customized bone implants with arbitrary open-porous structure satisfying both the mechanical and the biological requirements for a sufficient bone ingrowth. Aim of the present numerical study was to optimize the geometrical parameters of open-porous titanium scaffolds to match the elastic properties of human cortical bone with respect to an adequate pore size. Three different scaffold designs (cubic, diagonal and pyramidal) were numerically investigated by using an optimization approach. Beam elements were used to create the lattice structures of the scaffolds. The design parameters strut diameter and pore size ranged from 0.2 to 1.5mm and from 0 to 3.0mm, respectively. In a first optimization step, the geometrical parameters were varied under uniaxial compression to obtain a structural modulus of 15GPa (Young׳s modulus of cortical bone) and a pore size of 800µm was aimed to enable cell ingrowth. Furthermore, the mechanical behavior of the optimized structures under bending and torsion was investigated. Results for bending modulus were between 9.0 and 14.5GPa. In contrast, shear modulus was lowest for cubic and pyramidal design of approximately 1GPa. Here, the diagonal design revealed a modulus of nearly 20GPa. In a second step, large-sized bone scaffolds were created and placed in a biomechanical loading situation within a 30mm segmental femoral defect, stabilized with an osteosynthesis plate and loaded with physiological muscle forces. Strut diameter for the 17 sections of each scaffold was optimized independently in order to match the biomechanical stability of intact bone. For each design, highest strut diameter was found at the dorsal/medial site of the defect and smallest strut diameter in the center. In conclusion, we demonstrated the possibility of providing optimized open-porous scaffolds for bone regeneration by considering both mechanical and biological aspects. Furthermore, the results revealed the need of the investigation and comparison of different load scenarios (compression, bending and torsion) as well as complex biomechanical loading for a profound characterization of different scaffold designs. The usage of a numerical optimization process was proven to be a feasible tool to reduce the amount of the required titanium material without influencing the biomechanical performance of the scaffold negatively. By using fully parameterized models, the optimization approach is adaptable to other scaffold designs and bone defect situations.