A 3D Convolutional Neural Network for Design Optimization of Minimal Surface Scaffolds in Bone Tissue Engineering

Triply periodic minimal surfaces (TPMS) have emerged as promising scaffold architectures for bone tissue engineering due to their ability to balance mechanical stiffness with fluid transport. However, evaluating these trade-offs typically requires separate finite element (FEA) and computational fluid dynamics (CFD) analyses, which are computationally expensive and hinder large-scale design exploration. In this study, we propose a multitask 3D convolutional neural network (3D-CNN) surrogate that jointly predicts apparent elastic modulus (\(\:{E}_{app}\)), permeability (\(\:k\)), effective diffusivity (\(\:{D}_{eff}\)), and a wall shear stress (WSS)-exposure metric from voxelized TPMS geometries. The model was trained on 30 scaffold designs spanning Gyroid, Schwarz-P, and Diamond families, with iso-threshold and unit-cell variations covering porosities of 0.55–0.80. Results demonstrate high predictive performance (\(\:{R}^{2}>0.90\) across targets), with up to 35% error reduction compared to analytical baselines such as Kozeny–Carman and Bruggeman formulations. Pareto analysis revealed distinct family-specific trade-offs, with Gyroid scaffolds achieving the most stable shear metrics, while Schwarz-P and Diamond offered higher transport efficiency at moderate stiffness levels. This model provides a reproducible, physics-aware surrogate for rapid scaffold evaluation and optimization, offering significant potential to accelerate scaffold design for bone tissue engineering.