3-D computational modeling of media flow through scaffolds in a perfusion bioreactor

Media perfusion bioreactor systems have been developed to improve mass transport throughout three-dimensional (3-D) tissue-engineered constructs cultured in vitro. In addition to enhancing the exchange of nutrients and wastes, these systems simultaneously deliver flow-mediated shear stresses to cells seeded within the constructs. Local shear stresses are a function of media flow rate and dynamic viscosity, bioreactor configuration, and porous scaffold microarchitecture. We have used the Lattice-Boltzmann method to simulate the flow conditions within perfused cell-seeded cylindrical scaffolds. Microcomputed tomography imaging was used to define the scaffold microarchitecture for the simulations, which produce a 3-D fluid velocity field throughout the scaffold porosity. Shear stresses were estimated at various media flow rates by multiplying the symmetric part of the gradient of the velocity field by the dynamic viscosity of the cell culture media. The shear stress algorithm was validated by modeling flow between infinite parallel plates and comparing the calculated shear stress distribution to the analytical solution. Relating the simulation results to perfusion experiments, an average surface shear stress of 5×10−5 Pa was found to correspond to increased cell proliferation, while higher shear stresses were associated with upregulation of bone marker genes. This modeling approach can be used to compare results obtained for different perfusion bioreactor systems or different scaffold microarchitectures and may allow specific shear stresses to be determined that optimize the amount, type, or distribution of in vitro tissue growth.