Analysis of ultrafiltration and mass transfer in a bioartificial pancreas

A bioartificial pancreas is an implantable device which contains insulin secreting cells (Langerhans islets), separated from the circulating blood by a semi-permeable membrane to avoid rejection. This paper describes the operation of such a device and evaluates the respective contributions of diffusion and ultrafiltration to the glucose and insulin mass transfer. It is shown that the pressure drop along the blood channel produces across the first half of the channel an ultrafiltration flux toward the islet compartment followed in the second half by an equal flux in reverse direction from islets to blood. The mass transfer analysis is carried out for an optimal geometry in which a U-shaped blood channel surrounds closely a very thin islet compartment formed by a folded flat membrane. A complete model of insulin release by this device is developed and is compared with in vitro data obtained with rats islets. Satisfactory kinetics is achieved with a polyacrylonitrile membrane used in hemodialysis. But the model shows that the membrane hydraulic permeability should be increased by a factor of 10 to significantly improve the performance.