Kinetic modelling as a tool for the design of a vascular bioartificial pancreas: feedback between modelling and experimental validation

Abstract

A bioartificial pancreas is a system which contains isolated islets of Langerhans protected against immune rejection by an artificial membrane, permeable to glucose and insulin, but not to lymphocytes and immunoglobulins. However, it is necessary to design a device which performs as a closed-loop insulin delivery system, more specifically which rapidly responds to a change in the recipient's blood glucose concentration by an appropriate change in insulin release. We have designed a system intended to be connected as an arteriovenous shunt of the recipient; islets are placed between two flat ultrafiltration membranes, and blood circulates successively above the upper and below the lower, membrane in reverse direction. A complete kinetic model of glucose transfer from blood to the islet compartment, of insulin generation by the islets displaying a biphasic insulin pattern, and of insulin transfer into the bloodstream was described, and parameters were calculated on the basis of experimental data obtained when islets of Langerhans were perfused in vitro with a synthetic buffer. The resulting calculations indicated that both diffusional and convective transfers were involved in glucose and insulin mass transfer across the membrane, the contribution of diffusion being the most important. The geometry of the system was therefore modified in order to decrease the resistance to flow inside the blood channel. This should increase, at a given hydrostatic pressure, the blood flow rate, and thereby improve the diffusional transfer of insulin. This should also decrease the thrombogenicity of the device. This hypothesis was confirmed by in vitro experiments comparing, at a given inlet hydrostatic pressure, insulin kinetics in response to glucose from two devices with a high, or a low, resistance to flow. The kinetics were significantly faster in the latter case. Finally, in vivo experiments using a modified chamber, with a low resistance to flow, were carried out in anaesthetised normal dogs, the bioartificial pancreas being connected directly on an arteriovenous shunt of the animal. Glucose was infused over 1 h upstream of the chamber at a rate which increased blood glucose inside the chamber without altering blood glucose of the dog. Insulin production was calculated by multiplying the difference between insulin concentrations, determined simultaneously upstream and downstream of the bioartificial pancreas, by the blood flow rate, which was estimated from the change in the glucose concentration produced by the glucose infusion (Fick's principle). The data indicated that the system responded rapidly to the change in blood glucose concentration by increasing its insulin release. These studies demonstrate therefore the major interest of kinetic modelling for designing a bioartificial pancreas, with a feedback between modelling and experimental validation.