Numerical Accuracy Comparison of Two Boundary Conditions Commonly used to Approximate Shear Stress Distributions in Tissue Engineering Scaffolds Cultured under Flow Perfusion

Abstract: Flow-induced shear stresses have been found to be a stimulatory factor in pre-osteoblastic cells seeded in 3D porous scaffolds and cultured under continuous flow perfusion. However, due to the complex internal structure of the scaffolds, whole scaffold calculations of the local shear forces are computationally-intensive. Instead, representative volume elements (RVEs), which are obtained by extracting smaller portions of the scaffold, are commonly used in literature without a numerical accuracy standard. Hence, the goal of this study is to examine how closely the whole scaffold simulations are approximated by the two types of boundary conditions used to enable the RVEs: "wall boundary condition" (WBC) and "periodic boundary condition" (PBC). To that end, Lattice-Boltzmann Method fluid dynamics simulations were used to model the surface shear stresses in 3D scaffold reconstructions, obtained from high resolution microcomputed tomography images. It was found that despite the RVEs being sufficiently larger than 6 times the scaffold pore size (which is the only accuracy guideline found in literature), the stresses were still significantly under-predicted by both types of boundary conditions: between 20 and 80% average error, depending on the scaffold's porosity. Moreover, it was found that the error grew with higher porosity. This is likely due to the small pores dominating the flow field, and thereby negating the effects of the unrealistic boundary conditions, when the scaffold porosity is small. Finally, it was found that the PBC was always more accurate and computationally efficient than the WBC. Therefore, it is the recommended type of RVE. Overall, this work provides a previously-unavailable guidance to researchers regarding the best choice of boundary conditions for RVE simulations.