Page 63 - Development of Functional Scaffolds for Bone Tissue Engineering Using 3D-Bioprinting of Cells and Biomaterials - Yasaman Zamani

Figure 2. Schematic illustration of a 3D-printed cubic scaffold measuring 1×1×2 cm (length×width×height; 700 m diameter strands, total scaffold volume 2 cm3) with homogeneous void sizes (0.3 mm, 0.6 mm, and 0.9 mm) and gradient void sizes (0.3-0.6 mm and 0.3-0.6-0.9 mm) used to simulate fluid shear stress and fluid pressure on the strands surface. (a) Structure of the scaffold showing the outer surface of the strands inside the 3D-printed scaffold as well as front, back, top, and bottom side of the scaffold. (b) Simulation volume, mesh, and boundary conditions (inlet fluid flow and outlet zero static pressure) applied in the finite element model.
Mathematical equations
To simulate the fluid flow inside the scaffolds, the following assumptions and boundary conditions were made. The fluid flow approaches the scaffolds from the top and front surfaces of the scaffolds (Fig. 2a). The fluid flow inside the scaffolds was considered as incompressible and homogeneous Newtonian fluid, with a dynamic viscosity of μ= 0.89 mPa.s and a density of ρ= 990 kg/m. The culture medium specifications, such as viscosity and temperature, were assumed to be constant during the modeling. The average pressure at the outlet surfaces (bottom and back) of the scaffolds was set to zero, and no-slip boundary condition was applied to the inner surface of the scaffolds (Fig. 2b). The scaffolds were assumed solid, which is incompressible and impermeable to the fluid, and the strands topography was considered constant during the FE modeling.
Laminar fluid flow equations
The governing equations applied for FE modeling of the fluid flow inside the scaffolds were the momentum (equation 1) and continuity (equation 2) equations, which considered momentum and
mass, respectively [29]:
∇.𝑢𝑢𝑢𝑢 =0 (2)
𝜌𝜌𝜌𝜌𝜌𝜌𝜌𝜌𝑢𝑢𝑢𝑢𝑖𝑖𝑖𝑖=−∇𝑝𝑝𝑝𝑝+𝜇𝜇𝜇𝜇∇ 𝑢𝑢𝑢𝑢𝑖𝑖𝑖𝑖 (1) 𝜌𝜌𝜌𝜌𝐷𝐷𝐷𝐷 𝑖𝑖𝑖𝑖 2
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