Concurrent two-scale topology optimization of printable bone scaffolds via rectified-flow generation and exact latent-space refinement

Reza T Batley, Sourav Saha

Bone scaffolds must reconcile a macroscale mechanical response with microscale geometric feasibility, yet conventional approaches to their design restrict attainable constitutive properties. This work presents a concurrent two-scale topology optimization framework; a conditional rectified flow generates periodic lattice microstructures, which are then refined in latent space by exact finite-element homogenization sensitivities. The resulting unit-cell geometries and their spatial assignments are jointly optimized under mechanical and feature-size constraints. In a distal rabbit femur benchmark, all eight flow-started refinements produce printable cells with maximum relative errors under 1\% across six prescribed engineering moduli. Constructing the implant from a single tiled cell reproduces intact whole-femur compliance within 0.1\% and regional strain energy within 0.35\% under four loading conditions. In human femoral reconstruction, multiscale concurrent optimization produces a cortical mid-shaft scaffold with porosity 63\% while satisfying the compliance constraint within 2\% under walking and stair-climbing loads. It achieves an 84\% porosity on a proximal cancellous…