A Multiphysics-Deep Learning Model for Optimizing Printable Triply Periodic Minimal Surface Bone Scaffolds

Bone tissue engineering requires scaffolds that simultaneously provide mechanical stability, enable nutrient transport, and maintain physiologically safe wall shear stresses to support osteogenesis. Triply periodic minimal surface (TPMS) architectures, including Gyroid, Schwarz-P, and Diamond, offer continuous curvature and tunable porosity, but optimizing these geometries under competing mechanical, transport, and manufacturability constraints remains challenging. This study develops a unified multiphysics-constrained optimization framework for TPMS scaffold design, integrating surrogate deep learning models, geometric analysis, and constraint-aware search across large parametric spaces. A dataset of 1000 high-resolution TPMS scaffold volumes (porosity 0.55–0.80; unit-cell sizes 0.8-1.2 mm) was used to train a 3D convolutional neural network capable of predicting apparent elastic modulus, effective diffusivity, and permeability directly from voxelized geometry. The model achieved MAE = 3.89 GPa for stiffness and 4.07×10⁻¹¹ m²/s for diffusivity, enabling rapid evaluation of more than 3,000 candidate designs without performing full FEM or CFD simulations. Multiphysics screening revealed strong trade-offs: diffusivity increased by up to 4× as stiffness decreased, while manufacturability constraints excluded over 99% of high-porosity configurations. Pareto analysis identified a top-performing Schwarz-P scaffold (ϕ = 0.86, a = 2.6 mm) with E_app= 115 GPa, D_eff = 3.54×10⁻¹¹ m²/s, k = 2.63×10⁻¹⁰ m², and a manufacturable minimum wall thickness of t_min = 0.257 mm. In conclusion, the proposed framework provides a reproducible, computationally efficient pathway for identifying bone scaffolds that balance stiffness, transport performance, and fabrication feasibility. These results demonstrate the potential of constraint-aware, deep-learning-enabled optimization to accelerate the development of clinically viable bone tissue engineering scaffolds.