In this paper, a theoretical framework is presented for the design of hollow fiber membrane bioreactors (HFMIBs) operated in closed shell mode in the presence of high recirculation flows in the cell compartment. Navier-Stokes and Brinkman equations were used to describe fluid transport, and the convection-diffusion-reaction equations to describe transport of dissolved oxygen and glucose to cells. Numerical solutions were sought with the finite element method for the high permeability typical of new medical membranes, and operating conditions typical of therapeutic applications. Generalized charts intended to help the bioreactor designer were obtained giving the non-hypoxic (or well nourished) fractional shell volume as a function of the main dimensionless groups influencing the magnitude of the recirculation flow. Results indicate that designs and operations promoting moderateto-high recirculation flows in the bioreactor shell markedly enhance solute transport and permit much better cell oxygenation and nourishment, and control of the pericellular environment, than diffusion-limited bioreactors. With these charts, bioreactor design may be optimized for a given therapeutic treatment, or operation adjusted to the properties of the cell aggregate as tissue forms in tissue engineering applications, so as to provide cells with a physiological supply of oxygen and nutrients and a physiological pericellular environment. (C) 2014 Elsevier B.V. All rights reserved.