A novel deep artificial neural network-powered optimization approach for functionally graded titanium cranial bone implant with triply periodic minimal surfaces

This work presents a novel and efficient optimization framework powered by an enhanced deep artificial neural network (DANN) model to intelligently identify the optimal gradient index for designing nonlinearly functionally graded (NFG) titanium cranial bone implants with triply periodic minimal surfaces (TPMSs). The DANN model is improved by incorporating loops containing multiple conditions (LMCs) to achieve high prediction accuracy. The proposed optimization determines the optimal implant design according to the mechanical requirements of natural cranial bone, including elastic stiffness and yield strength. The reliability of the approach is experimentally validated, showing only a 9.5% deviation in the effective Young's modulus between experimental measurements and DANN predictions. Importantly, neither the experimental nor numerical results were included in the training dataset. Remarkably, the model can be trained and generate accurate predictions within only 3 to 5 min for nearly any gradient index between 1 and 50, making it thousands of times faster than conventional numerical or experimental approaches while maintaining minimal prediction error. The optimization results reveal a strong influence of the gradient index on the implant's elastic stiffness anisotropy and energy absorption capability, with higher gradient indices producing stiffness anisotropy patterns that more closely resemble those of natural cranial bone.