Predicting permeability of regular tissue engineering scaffolds: scaling analysis of pore architecture, scaffold length, and fluid flow rate effects.

The main aim of this research is to numerically obtain the permeability coefficient in the cylindrical scaffolds. For this purpose, a mathematical analysis was performed to derive an equation for desired porosity in terms of morphological parameters. Then, the considered cylindrical geometries were modeled and the permeability coefficient was calculated according to the velocity and pressure drop values based on the Darcy's law. In order to validate the accuracy of the present numerical solution, the obtained permeability coefficient was compared with the published experimental data. It was observed that this model can predict permeability with the utmost accuracy. Then, the effect of geometrical parameters including porosity, scaffold pore structure, unit cell size, and length of the scaffolds as well as entrance mass flow rate on the permeability of porous structures was studied. Furthermore, a parametric study with scaling laws analysis of sample length and mass flow rate effects on the permeability showed good fit to the obtained data. It can be concluded that the sensitivity of permeability is more noticeable at higher porosities. The present approach can be used to characterize and optimize the scaffold microstructure due to the necessity of cell growth and transferring considerations.