Efficient calculation of fluid-induced wall shear stress within tissue engineering scaffolds by an empirical model

Mechanical stimulation,such as fluid-induced wall shear stress(WSS),is known that can influence the cellular behaviours.Therefore,in some tissue engineering experiments in vitro,mechanical stimulation is applied via bioreactors to the cells in cell culturing to study cell physiology and pathology.In 3D cell culturing,porous scaffolds are used for housing the cells.It is known that the scaffold porous geometries can influence the scaffold permeability and internal WSS in a bioreactor(such as perfusion bioreactor).To calculate the WSS generated on cells within scaffolds,usually computational fluid dynamics(CFD)simulation is needed.However,the limitations of the computational method for WSS calculation are:(i)the high time cost of the CFD simulation(in particular for the highly irregular geometries);(ii)accessibility to the CFD model for some cell culturing experimentalists due to the knowledge gap.To address these limitations,this study aims to develop an empirical model for calculating the WSS based on scaffold permeability.This model can allow the tissue engineers to efficiently calculate the WSS generated within the scaffold and/or determine the bioreactor loading without performing the computational simulations.