In an extravascular bioartificial pancreas (BAP), islet functions are probably limited by diffusive mass transfer and local consumption, leading to low oxygenation. A mathematical model based on finite elements and focusing on local oxygen transport in both the alginate core and the islets of Langerhans has been proposed to help design an efficient pancreas supply. It was possible to randomly localize islets in a hollow fiber at different densities, and the effects of hypoxia and necrosis were included in the mass transfer simulations. Thorough study of the numerical results first led to the analysis of several relevant parameters, such as necrosis factor and efficacy in terms of insulin secretion, as a way to optimize fiber geometry. The approach was then to calculate the number of islets that needed to be implanted in order to obtain a correct response in terms of insulin secretion. In most configurations, it was found to be much higher than that of ultimately functional islets, because of hypoxia and necrosis. Fiber length should thus be adjusted accordingly. Finally, we demonstrated that the compromise to be found between the reduction of the number of implanted islets and fiber length and diameter did not correspond to realistic hollow fiber systems. The alternative of using flat geometry was also envisaged with more optimistic feasibility assessments.

Interaction, in real time, between a designer and a virtual prototype is a promising way to optimize the parts design in mechanical industries. These interactions can induce deformation of some flexible parts of the prototype. The analysis in real time of nonlinear mechanical model by finite element method (FEM) is impossible. Our approach is based on two phases: 1-some load cases, characteristic of possible handlings, are precalculated; 2-results of this campaign are interpolated during the real-time immersion. This paper compares 4 approaches to calculate a reduced result of the campaign as fast as possible: an a posteriori reduction, an a priori enrichment method, an a priori enrichment-reduction and the hyperreduction.

A sphere within a cylinder representing the islet encapsulated in a hollow fiber can model an implantable bioartificial pancreas. Based on a finite element model for insulin response to a glucose load in the presence of various oxygen supplies, the present study aimed at pointing out the major parameters influencing this secretion. The computational results treated with the Taguchi method clearly demonstrated that geometrical parameters (fiber length and islet density) should be precisely optimized for an enhanced insulin response. This requires the collection of more relevant experimental data concerning the islet oxygen consumption. Moreover, the relative errors on glucose consumption or insulin secretion by the islets do not seem to affect the whole optimization process, which should focus on the oxygen supply to islets.