Bioartificial livers (BALs) are a potentially effective countermeasure against liver failure, particularly in cases of acute or fulminant liver failure. It is hoped these devices can sustain a patient's liver function until recovery or transplant. However, no large-scale clinical trial has yet proven that BALs are particularly effective and evidently design issues remain to be addressed. One aspect of BAL design that must be considered is the mass transfer of adequate oxygen to the hepatocytes within the device. We present here a mathematical modeling approach to oxygen mass transport in a BAL. A mathematical model based upon Krogh cylinders is outlined to describe a diffusion-limited hollow fiber bioreactor. In addition, operating constraints are defined on the system cells should not experience hypoxia and the cell population should be of adequate size. By combining modeling results with these operating constraints and presenting the results graphically, "operating region" charts can be constructed for the hollow fiber BAL (HF-BAL). The effects of varying various operating parameters on the BAL are then established. It is found that smaller radii and short, thin walled fibers are generally advantageous while cell populations in excess of 10 billion could be supported in the BAL with a plasma flow rate of 200 mL/min. For fibers of intermediate length and lumen radius, the minimum number of fibers required to produce a viable design ranges approximately from 7,000-10,000. In theory, this may be enough to support patients with failing livers. Biotechnol. Bioeng. 2010;106: 980-988. (C) 2010 Wiley Periodicals, Inc.