A lumped parameter mathematical model of a hollow fiber membrane device for the controlled insulin release

Abstract

The purpose of this paper is to analyze the performances of a hollow fiber 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 theoretical analysis of the bioreactor has been carried out, leading to the development of a lumped parameter mathematical model for the description of glucose and insulin transport. Actually a number of more sophisticated transport models have been proposed in the literature for similar devices. The purpose of this paper was, however, the presentation of a simpler approach, aiming at a quick description of the system behavior. The model is based on the mass transfer equations, accounting for the radial diffusion of species, their axial and radial convection—the latter due to Starling fluxes—and insulin generation. The kinetics of insulin secretion has been modelled in terms of a linear two-parameter 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 of glucose and insulin concentration distributions, under different operating conditions, with reference to a range of values for the characteristic dimensionless parameters of the model.