Gaussian curvature-mechanical environment-tissue regeneration relationships at the bone-implant interface of porous implants: a simulation study

Curvature-driven structural design is emerging as a promising paradigm for bone repair materials. Experimental evidence from animal studies suggests that negative curvature facilitates orchestrate cell proliferation and tissue growth, but the underlying mechanical mechanisms remain unclear. This study aimed to explore the relationships between curvature design, mechanical environment, and tissue regeneration in porous implants using computational methods. Four samples with Gaussian curvature ranging from -1 to -6 were designed (referred to as K1 to K6), and their effects on tissue differentiation and mass transport were evaluated through computational models. The results showed that greater curvature (K6) effectively inhibited the formation of fibrous tissue, thereby leaving more space for bone tissue, which is consistent with the results of animal experiments, where tissue differentiation was primarily influenced by strain levels. In addition, curvature design was accompanied by changes in pore diameter. This study revealed that smaller pores inherently created micro-mechanical environments that improved tissue differentiation, while larger pore diameters enhanced mass transport, promoting long-term bone regeneration. The above contradiction implies that optimal Gaussian curvature can be achieved by balancing mechanical stimulation with mass transport capacity, offering a new paradigm for the design of bone implants.