A theoretical study of oxygen transfer including cell necrosis for the design of a bioartificial pancreas.

In an extravascular bioartificial pancreas (BAP), islet functions are probably limited by diffusive mass transfer and local consumption, leading to low oxygenation. A mathematical model based on finite elements and focusing on local oxygen transport in both the alginate core and the islets of Langerhans has been proposed to help design an efficient pancreas supply. It was possible to randomly localize islets in a hollow fiber at different densities, and the effects of hypoxia and necrosis were included in the mass transfer simulations. Thorough study of the numerical results first led to the analysis of several relevant parameters, such as necrosis factor and efficacy in terms of insulin secretion, as a way to optimize fiber geometry. The approach was then to calculate the number of islets that needed to be implanted in order to obtain a correct response in terms of insulin secretion. In most configurations, it was found to be much higher than that of ultimately functional islets, because of hypoxia and necrosis. Fiber length should thus be adjusted accordingly. Finally, we demonstrated that the compromise to be found between the reduction of the number of implanted islets and fiber length and diameter did not correspond to realistic hollow fiber systems. The alternative of using flat geometry was also envisaged with more optimistic feasibility assessments.