[Hydrodynamic finite element analysis of biological scaffolds with different pore sizes for cell growth and osteogenic differentiation].

Abstract

Objective: The triply periodic minimal surface (TPMS) Gyroid porous scaffolds were built with identical porosity while varying pore sizes were used by fluid mechanics finite element analysis (FEA) to simulate the in vivo microenvironment. The effects of scaffolds with different pore sizes on cell adhesion, proliferation, and osteogenic differentiation were evaluated through calculating fluid velocity, wall shear stress, and permeability in the scaffolds.

Methods: Three types of gyroid porous scaffolds, with pore sizes of 400, 600 and 800 μm, were established by nTopology software. Each scaffold had dimensions of 10 mm × 10 mm × 10 mm and isotropic internal structures. The models were imported to the ANSYS 2022R1 software, and meshed into over 3 million unstructured tetrahedral elements. Boun- dary conditions were set with inlet flow velocities of 0.01, 0.1, and 1 mm/s, and outlet pressure of 0 Pa. Pressure, velocity, and wall shear stress were calculated as fluid flowed through the scaffolds using the Navier-Stokes equations. At the same time, permeability was determined based on Darcy' s law. The compressive strength of scaffolds with different pore sizes was evaluated by ANSYS 2022R1 Static structural analysis.

Results: A linear relationship was observed between the wall shear stress and fluid velocity at inlet flow rates of 0.01, 0.1 and 1 mm/s, with increasing velocity leading to higher wall shear stress. At the flow velocity of 0.1 mm/s, the initial pressures of scaffolds with pore sizes of 400, 600 and 800 μm were 0.272, 0.083 and 0.079 Pa, respectively. The fluid pressures were gradually decreased across the scaffolds. The average flow velocities were 0.093, 0.078 and 0.070 mm/s, the average wall shear stresses 2.955, 1.343 and 1.706 mPa, permeabilities values 0.54×10^-8 1.80×10^-8 and 1.89×10^-8 m² in the scaffolds with pore sizes of 400, 600 and 800 μm. The scaffold surface area proportions according with optimal wall shear stress range for cell growth and osteogenic differentiation were calcula-ted, which was highest in the 600 μm scaffold (27.65%), followed by the 800 μm scaffold (17.30%) and the 400 μm scaffold (1.95%). The compressive strengths of the scaffolds were 23, 26 and 34 MPa for the 400, 600 and 800 μm pore sizes.

Conclusion: The uniform stress distributions appeared in all gyroid scaffold types under compressive stress. The permeabilities of scaffolds with pore sizes of 600 and 800 μm were significantly higher than the 400 μm. The average wall shear stress in the scaffold of 600 μm was the lowest, and the scaffold surface area proportion for cell growth and osteogenic differentiation the largest, indicating that it might be the most favorable design for supporting these cellular activities.