Hypoxia in vascular networks: a complex system approach to unravel the diabetic paradox

Abstract

In this work we model the extent of hypoxia in the diabetic retina as a function of the area affected by vessel disruption. We find two regimes that differ on the ratio between the area of disrupted vasculature and the area of tissue in hypoxia. In the first regime the hypoxia is localized in the vicinity of the vascular disruption, while in the second regime there is a generalized hypoxia in the affected tissue. The transition between these two regimes occurs when the tissue area affected by individual sites of vessel damage is on the order of the square of the characteristic irrigation length in the tissue (the maximum distance that an irrigated point in the tissue is from an existing vessel). We observe that very high levels of hypoxia are correlated with the rupture of larger vessels in the retina, and with smaller radii of individual sites of vessel damage. Based on this property of vascular networks, we propose a novel mechanism for the transition between the nonproliferative and the proliferative stages in diabetic retinopathy.