Computational Fluid Dynamics Modeling of Material Transport Through Triply Periodic Minimal Surface Scaffolds for Bone Tissue Engineering
Authors: Coburn Brandon , Salary Roozbeh “Ross” 
Published: January 2025

Abstract
Cell-laden, scaffold-based tissue engineering methods have been successfully utilized for the treatment of bone fractures and diseases, caused by factors such as trauma, tumors, congenital anomalies, and aging. In such methods, the rate of scaffold biodegradation, transport of nutrients and growth factors, as well as removal of cell metabolic wastes at the site of injury are critical fluid-dynamics factors, affecting cell proliferation and ultimately tissue regeneration. Therefore, there is a critical need to identify the underlying material transport mechanisms and factors associated with cell-seeded, scaffold-based bone tissue engineering. The overarching goal of this study is to contribute to patient-specific, clinical treatment of bone pathology. The overall objective of the work is to establish computational fluid dynamics (CFD) models: (i) to identify the consequential mechanisms behind internal and external material transport through/over porous bone scaffolds designed based on the principles of triply periodic minimal surfaces (TPMS) and (ii) to identify TPMS designs with optimal geometry and flow characteristics for the treatment of bone fractures in clinical practice. In this study, advanced CFD models were established based on ten TPMS scaffold designs for (i) single-unit internal flow analysis, (ii) single-unit external flow analysis, and (iii) cubic, full-scaffold external flow analysis, where the geometry of each design was parametrically created. The influence of several design parameters, such as surface representation iteration, wall thickness, and pore size on geometry accuracy as well as computation time, was investigated in order to obtain computationally efficient and accurate CFD models. The fluid properties (such as density and dynamic viscosity) as well as the boundary conditions (such as no-slip condition, inlet flow velocity, and pressure outlet) of the CFD models were set based on clinical/research values reported in the literature, according to the fundamentals of internal and external Newtonian flow modeling. The main fluid characteristics influential in bone regeneration, including flow velocity, flow pressure, and wall shear stress (WSS), were analyzed to observe material transport internally through and externally over the TPMS scaffold designs. Regarding the single-unit internal flow analysis, it was observed that P.W. Hybrid and Neovius designs had the highest level of not only flow pressure but also WSS. This can be attributed to their relatively flat surfaces when compared to the rest of the TPMS designs. Schwarz primitive (P) appeared to have the lowest level of flow pressure and WSS (desirable for development of bone tissues) due to its relatively open channels allowing for more effortless fluid transport. An analysis of streamline velocity exhibited an increase in velocity togther with a depiction of potential turbulent motion along the curved sections of the TPMS designs. Regarding the single-unit external flow analysis, it was observed that Neovius and Diamond yielded the highest level of flow pressure and WSS, respectively, while Schwarz primitive (P) similarly had a relatively low level of flow pressure and WSS suitable for bone regeneration. Besides, pressure buildup was observed within the inner channels of almost all the TPMS designs due to flow resistance and the intrinsic interaction between the fluid flow and the scaffold walls. Regarding the cubic (full-scaffold) external flow analysis, the Diamond and Schwarz gyroid (G) designs appeared to have a relatively high level of both flow pressure and WSS, while Schwarz primitive (P) similarly yielded a low level of flow pressure and WSS. Overall, the outcomes of this study pave the way for optimal design and fabrication of complex, bone-like tissues with desired material transport properties for cell-laden, scaffold-based treatment of bone fractures.