3.12 Fluid Mechanics: Transport and Diffusion Analyses as Applied in Biomaterials Studies

A review of some of the recent mathematical models used for solving transport problems involving porous biomaterial scaffolds is presented. Both direct numerical simulation (DNS) methods and macroscopic averaged equations for porous media have been reviewed in detail. DNS methods provide the most accurate details of the flow, shear stress, and species concentration fields. The state-of-the-art imaging techniques coupled with DNS may serve to be helpful in pore-scale optimization studies of the scaffold geometry. However, the dynamic changes in the geometry of the scaffold architecture due to cell growth and proliferation pose significant research challenges for DNS methods. DNS calculations are also computationally intensive for large scale optimization studies. On the other hand, macroscopic averaged equations are simpler to solve and by the very nature of their construction may be scaled up for the system level (up to the length scale of bioreactors) optimization. However, the averaging procedure smoothes the flow structure at the pore scales and may under predict shear stress variations at the cellular scale. But in most situations, they produce reasonable engineering estimates of the flow and concentrations fields. While each of the described methods has its own advantages and disadvantages, the choice of any particular method depends on the desired level of accuracy sought for a given application. Both DNS and averaged methods will continue to serve as powerful tools for performing quantitative engineering studies of transport involving bioreactors and biomaterials. Combining the best features of both the methods may enable multiscale optimization studies involving both the bioreactor scale (macroscale) and the pore scale (microscale).