Deep artificial neural network-powered optimization approach for ideally nonlinearly functionally graded titanium trabecular and cortical bone scaffolds with TPMSs

The trabecular and cortical bones are essential components of the skeletal system, occupying the majority of our skeleton and playing critical and complementary roles in maintaining bone function and overall health. This work introduces a novel deep artificial neural network (DANN)-powered optimization approach to determine the gradient index for producing ideal nonlinearly functionally graded (NFG) titanium trabecular and cortical bone scaffolds with triply periodic minimal surface (TPMS) structures. These scaffolds are designed to achieve target densities, elastic stiffnesses and yield strengths. The novel DANN model is integrated within a loop with multiple conditions (LMCs) to significantly improve its accuracy. The optimization’s accuracy are validated through a numerical model, a force reaction method, and an experiment, with an agreement found. To ensure fair assessment, the mechanical properties from the numerical model used for comparison are not part of the DANN model’s training dataset. Remarkably, the trained DANN model demonstrates accurate prediction at various gradient indices, achieving results thousands of times faster and at a significantly reduced cost compared to numerical and experimental methods. It also intelligently identifies the gradient index for optimal NFG trabecular and cortical bone scaffold, surpassing the capabilities of numerical models or experimental methods. More interestingly, the results reveal that all identified scaffolds exhibit a higher yield strength than the host bone, while maintaining Young’s modulus values within the reported range for biological bone. This is crucial in preventing bone loss and permanent deformation, thereby increasing the lifespan of the composite of bone tissue and scaffold. Additionally, the NFG scaffolds with a Gyroid structure exhibit a Young’s modulus in the direction perpendicular to the thickness gradation that is approximately 1.5 times higher than in the graded direction. A nearly similar ratio is observed in biological bone, further supporting the potential of these scaffolds as ideal candidates for bone replacement. Importantly, the anisotropy of the multidirectional yield surfaces of predicted scaffolds is extreme, reflecting through a distribution of yield strength data on a narrowed ellipsoidal shape, which is well captured by the extended Hill’s criterion, providing a less-expensive approach to determine the surface. Lastly, the DANN approach is employed to generate 2D maps illustrating energy absorption and buckling resistance of scaffolds as the gradient indices vary, providing an efficient and rapid means of evaluating these properties before practical application.