An Interface-enriched Level Set Topology Optimization for designing mandibular reconstruction plates made from a functionally graded material

Abstract

Increased capabilities of additive manufacturing technologies have opened up numerous possibilities in mandibular reconstruction surgery. For example, 3D scans can be used to design patient-specific reconstruction plates, resulting in designs that are tailored to prevent plate fracture, wound dehiscence, and malocclusion. However, screw loosening as a result of stress shielding is still an issue. This phenomenon is caused by the mismatch in stiffness between the bone and implant material. The stiff- ness of the titanium in these reconstruction plates can be reduced by using porous microstructures in the proximity of the remaining mandible. However, this makes intuition-based design impossible. This work applies computational tools to optimize the design of a mandibular reconstruction plate with varying microstructure porosity. To achieve this, Topology Optimization (TO) is used that accurately re- solves boundaries utilizing the Interface-enriched Generalized Finite Element Method (IGFEM), which results in a smooth representation of the design. In this work, this methodology is enhanced to result in an even smoother and more accurate boundary. Moreover, additions are made to account for varying material properties in the analytical sensitivities of the compliance objective. The functionally graded designs exhibit significantly higher compliance that should reduce stress shielding. Also, they feature a more porous microstructure near the bone, providing a basis for bone ingrowth. Thus, it is established that enriched TO can be used to optimize the design of mandibular reconstruction plates made out of functionally graded materials that could reduce the risk of screw loosening.