Analytical model for the prediction of permeability of triply periodic minimal surfaces

Triply periodic minimal surfaces (TPMS) are mathematically defined cellular structures whose geometry can be quickly adapted to target desired mechanical response (structural and fluid). This has made them desirable for a wide range of bioengineering applications; especially as bioinspired materials for bone replacement. The main objective of this study was to develop a novel analytical framework which would enable calculating permeability of TPMS structures based on the desired architecture, pore size and porosity. To achieve this, computer-aided designs of three TPMS structures (Fisher-Koch S, Gyroid and Schwarz P) were generated with varying cell size and porosity levels. Computational Fluid Dynamics (CFD) was used to calculate permeability for all models under laminar flow conditions. Permeability values were then used to fit an analytical model dependent on geometry parameters only. Results showed that permeability of the three architectures increased with porosity at different rates, highlighting the importance of pore distribution and architecture. The computed values of permeability fitted well with the suggested analytical model (R2>0.99, p<0.001). In conclusion, the novel analytical framework presented in the current study enables predicting permeability values of TPMS structures based on geometrical parameters within a difference <5%. This model, which could be combined with existing structural analytical models, could open new possibilities for the smart optimisation of TPMS structures for biomedical applications where structural and fluid flow properties need to be optimised

In silico assessment of the bone regeneration potential of complex porous scaffolds

Mechanical environment plays a crucial role in regulating bone regeneration in bone defects. Assessing the mechanobiological behavior of patient-specific orthopedic scaffolds in-silico could help guide optimal scaffold designs, as well as intra- and post-operative strategies to enhance bone regeneration and improve implant longevity. Additively manufactured porous scaffolds, and specifically triply periodic minimal surfaces (TPMS), have shown promising structural properties to act as bone substitutes, yet their ability to induce mechanobiologially-driven bone regeneration has not been elucidated. The aim of this study is to i) explore the bone regeneration potential of TPMS scaffolds made of different stiffness biocompatible materials, to ii) analyze the influence of pre-seeding the scaffolds and increasing the post-operative resting period, and to iii) assess the influence of patient-specific parameters, such as age and mechanosensitivity, on outcomes. To perform this study, an in silico model of a goat tibia is used. The bone ingrowth within the scaffold pores was simulated with a mechano-driven model of bone regeneration. Results showed that the scaffold's architectural properties affect cellular diffusion and strain distribution, resulting in variations in the regenerated bone volume and distribution. The softer material improved the bone ingrowth. An initial resting period improved the bone ingrowth but not enough to reach the scaffold's core. However, this was achieved with the implantation of a pre-seeded scaffold. Physiological parameters like age and health of the patient also influence the bone regeneration outcome, though to a lesser extent than the scaffold design. This analysis demonstrates the importance of the scaffold's geometry and its material, and highlights the potential of using mechanobiological patient-specific models in the design process for bone substitutes

Analytical model for the prediction of permeability of triply periodic minimal surfaces

Triply periodic minimal surfaces (TPMS) are mathematically defined cellular structures whose geometry can be quickly adapted to target desired mechanical response (structural and fluid). This has made them desirable for a wide range of bioengineering applications; especially as bioinspired materials for bone replacement. The main objective of this study was to develop a novel analytical framework which would enable calculating permeability of TPMS structures based on the desired architecture, pore size and porosity. To achieve this, computer-aided designs of three TPMS structures (Fisher-Koch S, Gyroid and Schwarz P) were generated with varying cell size and porosity levels. Computational Fluid Dynamics (CFD) was used to calculate permeability for all models under laminar flow conditions. Permeability values were then used to fit an analytical model dependent on geometry parameters only. Results showed that permeability of the three architectures increased with porosity at different rates, highlighting the importance of pore distribution and architecture. The computed values of permeability fitted well with the suggested analytical model (R2>0.99, p<0.001). In conclusion, the novel analytical framework presented in the current study enables predicting permeability values of TPMS structures based on geometrical parameters within a difference <5%. This model, which could be combined with existing structural analytical models, could open new possibilities for the smart optimisation of TPMS structures for biomedical applications where structural and fluid flow properties need to be optimised

In silico assessment of the bone regeneration potential of complex porous scaffolds

Mechanical environment plays a crucial role in regulating bone regeneration in bone defects. Assessing the mechanobiological behavior of patient-specific orthopedic scaffolds in-silico could help guide optimal scaffold designs, as well as intra- and post-operative strategies to enhance bone regeneration and improve implant longevity. Additively manufactured porous scaffolds, and specifically triply periodic minimal surfaces (TPMS), have shown promising structural properties to act as bone substitutes, yet their ability to induce mechanobiologially-driven bone regeneration has not been elucidated. The aim of this study is to i) explore the bone regeneration potential of TPMS scaffolds made of different stiffness biocompatible materials, to ii) analyze the influence of pre-seeding the scaffolds and increasing the post-operative resting period, and to iii) assess the influence of patient-specific parameters, such as age and mechanosensitivity, on outcomes. To perform this study, an in silico model of a goat tibia is used. The bone ingrowth within the scaffold pores was simulated with a mechano-driven model of bone regeneration. Results showed that the scaffold's architectural properties affect cellular diffusion and strain distribution, resulting in variations in the regenerated bone volume and distribution. The softer material improved the bone ingrowth. An initial resting period improved the bone ingrowth but not enough to reach the scaffold's core. However, this was achieved with the implantation of a pre-seeded scaffold. Physiological parameters like age and health of the patient also influence the bone regeneration outcome, though to a lesser extent than the scaffold design. This analysis demonstrates the importance of the scaffold's geometry and its material, and highlights the potential of using mechanobiological patient-specific models in the design process for bone substitutes