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

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.