A comparative 2D study of topology optimization strategies for promoting bone ingrowth

Topology optimization (TO) has increasingly been used in the orthopedic field to design bone implants with enhanced mechanical performance. The optimized final structure depends on the choice of objective and constraint functions. Typically, a volume-constrained optimization with stiffness maximization strategy, equivalent to strain energy (SE) minimization, is adopted. However, highly stiff constructs may hinder bone formation due to stiffness mismatch with surrounding bone. In contrast, bone formation is stimulated by specific deformation fields experienced by osteogenic cells. These considerations suggest that alternative optimization strategies may better support bone regeneration. Therefore, this 2D finite element study compares five TO strategies: (1) SE minimization with a volume constraint; volume minimization with (2) a global SE constraint, (3) a local SE constraint or (4) a local strain constraint; volume minimization with a strain target and total SE constraint (5). Two 2D structures are analyzed: a rectangle under distributed compressive load, and an L-bracket, fixed at the upper edge and loaded at its tip. Each strategy produces distinct topologies. For the rectangle, local SE constraint yields a more uniform SE distribution, while local strain control results in a strain variability reduction with higher average values. For the L-bracket, local SE and strain-constrained approaches produce high but heterogeneous distributions of SE and strain. Strategy 5 provides the most consistent control of the strain: for the rectangle, it reduces the strain IQR by 41.3 % compared with Strategy 1 while maintaining a comparable median strain. For the L-bracket, despite an increased IQR of 30.7 %, it enables direct control of the median strain with a variation of only 6 %. This comparison shows that a volume minimization with strain or SE control may be effective for obtaining structures that stimulate bone formation with potential applications in implant design.