Optimization of construct perfusion in radial-flow packed-bed bioreactors for tissue engineering with a 2D stationary fluid dynamic model

Cell culture in three-dimensional hollow cylindrical porous scaffolds in radial-flow packed-bed bioreactors (rPBBs) has advantages over static culture and axial perfusion bioreactors. Transport models of rPBBs for tissue engineering proposed thus far neglect the effect of the fluid dynamics of the bioreactor void spaces on radial flux maldistribution, although such an effect was proven important for industrial reactors. In this paper, a two-dimensional axisymmetric model is proposed for steady-state momentum transport in the three compartments of rPBBs under conditions and for construct permeability typical of tissue engineering applications. Transport in the inner hollow cavity and outer peripheral annulus is described according to Navier-Stokes equations, while Darcy-Brinkman equation is used for transport across the annular construct. Model predictions were qualitatively validated against literature data. Effects of the performance-determining dimensionless groups on radial flux distribution along the bioreactor length were investigated, and a criterion was proposed to design and operate rPBBs in which radial fluxes are uniformly distributed along the bioreactor length under conditions typical of tissue engineering. Bioreactor designs and operation meeting the criterion will avoid non-uniform development of tissue structure and functional properties.