Mathematical predictions of oxygen availability in micro- and macro-encapsulated human and porcine pancreatic islets

Optimal function of immunoisolated islets requires adequate supply of oxygen to metabolically active insulin producing beta-cells. Using mathematical modeling, we investigated the influence of the pO₂ on islet insulin secretory capacity and evaluated conditions that could lead to the development of tissue anoxia, modeled for a 300 μm islet in a 500 μm microcapsule or a 500 μm planar, slab-shaped macrocapsule. The pO₂ was used to assess the part of islets that contributed to insulin secretion. Assuming a 500 μm macrocapsule with a 300 μm islet, with oxygen consumption rate (OCR) of 100–300 nmol min⁻¹ mg⁻¹ DNA, islets did not develop any necrotic core. The nonfunctional zone (with no insulin secretion if pO₂ < 0.1 mmHg) was 0.3% for human islets (OCR ~100 nmol/min/mg DNA) and 35% for porcine islets (OCR ~300 nmol/min/mg DNA). The OCR of the islet preparation is profoundly affected by islet size, with optimal size of <250 μm in diameter (human) or <150 μm (porcine). Our data suggest that microcapsules afford superior oxygen delivery to encapsulated islets than macrocapsules, and optimal islet function can be achieved by encapsulating multiple, small (<150 μm) islets with OCR of ~100 nmol min⁻¹ mg⁻¹ DNA (human islets) or ~200 nmol min⁻¹ mg⁻¹ DNA (porcine islets).