Deep learning based constraint aware design exploration of triply periodic minimal surface bone scaffolds

Abstract

Bone tissue engineering scaffolds must provide structural support while permitting fluid transport and maintaining safe hydrodynamic conditions for cell activity. Triply Periodic Minimal Surface (TPMS) architectures such as Gyroid, Schwarz-P, and Diamond offer continuous curvature and tunable porosity, yet identifying configurations that simultaneously satisfy mechanical, transport, and manufacturability requirements remains computationally expensive. This study presents a constraint-aware computational framework for rapid exploration of TPMS scaffold design spaces by combining procedural geometry generation, analytical physics-consistent property estimation, and a geometry-aware deep learning surrogate model. A dataset of 1000 voxelized scaffolds (porosity 0.55–0.80; unit-cell size 0.8–1.2 mm) was used to train a multitask 3D convolutional neural network to approximate apparent modulus, permeability, effective diffusivity, and shear-exposure indicators derived from established mechanistic relations. The surrogate achieved a mean absolute error of approximately 3.9 GPa for predicted stiffness and reproduced transport trends on the order of 10−11 m2/s, enabling screening of more than 3000 candidate geometries without performing high-fidelity simulations. Pareto analysis revealed strong stiffness–transport trade-offs across TPMS families. Manufacturability constraints, particularly a minimum printable wall thickness of approximately 0.30 mm, eliminated many high-porosity designs. A near-feasible Schwarz-P configuration (ϕ ≈ 0.86, a ≈ 2.6 mm) exhibited moderate predicted stiffness (~ 2.1–2.5 GPa after thickness adjustment), effective diffusivity ≈3 × 10−11 m2/s, and permeability on the order of 10−10 m2, illustrating the competing requirements of structural support and perfusion. The proposed framework functions as a geometry-aware design-screening and prioritization tool that identifies candidate scaffold configurations prior to detailed finite-element, computational-fluid-dynamics, or experimental validation. The work provides a reproducible approach for accelerating early-stage scaffold design exploration and guiding subsequent biomechanical evaluation.