A LUMPED-PARAMETER MATHEMATICAL-MODEL OF A HOLLOW-FIBER MEMBRANE DEVICE FOR THE CONTROLLED INSULIN RELEASE

The purpose of this paper is to analyze the performances of a hollow f iber membrane bioreactor with Langerhans islets entrapped in the shell . A number of experiments have been performed in order to characterize the device with respect to the fluid dynamics and mass transport. A t heoretical analysis of the bioreactor has been carried out, leading to the development of a lumped parameter mathematical model for the desc ription of glucose and insulin transport. Actually a number of more so phisticated transport models have been proposed in the literature for similar devices. The purpose of this paper was, however, the presentat ion of a simpler approach, aiming at a quick description of the system behavior. The model is based on the mass transfer equations, accounti ng for the radial diffusion of species, their axial and radial convect ion-the latter due to Starling fluxes-and insulin generation. The kine tics of insulin secretion has been modelled in terms of a linear two-p arameter rate equation, accounting for the glucose concentration level and the insulin negative bio-feedback. Diffusive mass transfer across the membrane has been described according to the series resistance's model. The resulting equations have been solved numerically in terms o f glucose and insulin concentration distributions, under different ope rating conditions, with reference to a range of values for the charact eristic dimensionless parameters of the model.