Cellular porous structures are increasingly used for biomedical applications. Triply Periodic Minimal Surfaces (TPMS) are mathematically defined cellular structures whose geometry can be quickly adjusted to achieve the desired mechanical response (structural and fluid). This has made them desirable as bioinspired materials for bone replacement. Scaffolds for bone replacements should be designed to respond to the mechanical environment:​ they should provide enough structural support during bone regeneration, while also enabling nutrient diffusion through its pores to allow cell proliferation and differentiation. Mechanobiology plays an important role in bone regeneration and understanding the interaction between the scaffold's geometry, its material, and the mechanobiological environment is required to improve tissue regeneration. The main purpose of this dissertation is to improve the understanding of the mechanical behavior and mechanobiological properties of TPMS structures to design bone replacements that can accurately mimic bone properties.

The design of TPMS scaffolds was parametrized and automated to target bone porosity and pore size while maintaining a good manufacturability. Then, the structural and fluid flow properties of the scaffolds were assessed using Finite Element (FE) and Computational Fluid Dynamics (CFD) models respectively. The results were introduced into an uncoupled tissue differentiation model to predict the TPMS architectures that could be most promising to induce bone differentiation. Finally, a previously validated mechanobiological computational model (FE) was enhanced to evaluate the bone regeneration potential of complex porous structures and integrate the influence of patient-specific properties and clinical strategies to maximize bone regeneration.

The obtained results showed that the permeability of the studied TPMS architectures was affected by pore distribution and architecture. In addition, a novel analytical model that enables the prediction of the permeability values of TPMS structures based on geometrical parameters was developed. The results also indicated that the TPMS Gyroid architecture was the most suitable for promoting tissue differentiation when considering both the structural and fluid flow properties.

Furthermore, the computational mechanobiological model successfully assessed the ability of various scaffolds to promote bone regeneration, emphasizing the importance of scaffold’s geometry and material. The bone ingrowth within the scaffold pores demonstrated that the scaffold's geometrical properties influence cellular diffusion and strain distribution, resulting in differences in regenerated bone volume and distribution. Furthermore, bone ingrowth was found to be material-dependent, implying that the material can be used to fine-tune strain distribution and improve bone growth. Similarly, the use of clinical strategies and consideration of the host's physiological characteristics resulted in variations in bone regeneration, emphasizing the importance of incorporating such parameters into the design process of bone substitutes.

In conclusion, this dissertation provides a framework for designing optimal patientspecific strategies to promote bone regeneration, thereby improving the conceptualization and design of bone replacements.