Transport phenomena and kinetics in an extravascular bioartificial pancreas

A bioartificial pancreas, consisting of immobilized islets encapsulated within hollow fibers, is investigated as an alternative treatment for insulin‐dependent diabetes. A mathematical model is developed to determine whether this configuration of the bioartificial pancreas can yield an insulin response to a glucose challenge with the appropriate dynamics in diabetic humans. The model consists of the 2‐D mass‐conservation equations for glucose and insulin within the hollow fiber and capillaries. The equations contain terms for insulin‐production kinetics by porcine islets and glucose‐consumption kinetics. The boundary conditions account for transport resistances of the fiber membrane, the tissue surrounding the implant, and a thin film within the capillaries. The equations are coupled to a pharmacokinetic model of the circulatory system. The calculations show that an optimized design with this configuration will be feasible for human use and requires a total volume of 4.6 mL to reach the target insulin concentration in the bloodstream following a glucose challenge. The parameters and processes controlling the system performance are discussed.