Diffusive oxygen shunting between vessels in the preglomerular renal vasculature: anatomic observations and computational modeling

Abstract

To understand how geometric factors affect arterial-to-venous (AV) oxygen shunting, a mathematical model of diffusive oxygen transport in the renal cortex was developed. Preglomerular vascular geometry was investigated using light microscopy (providing vein shape, AV separation, and capillary density near arteries) and published micro-computed tomography (CT) data (providing vessel size and AV separation; Nordsletten DA, Blackett S, Bentley MD, Ritman EL, Smith NP. IUPS Physiome Project. http://www.physiome.org.nz/publications/nordsletten_blackett_ritman_bentley_smith_2005/folder_contents ). A “U-shaped” relationship was observed between the arterial radius and the distance between the arterial and venous lumens. Veins were found to partially wrap around the artery more consistently for larger rather than smaller arteries. Intrarenal arteries were surrounded by an area of fibrous tissue, lacking capillaries, the thickness of which increased from ∼5 μm for the smallest arteries (<16-μm diameter) to ∼20 μm for the largest arteries (>200-μm diameter). Capillary density was greater near smaller arteries than larger arteries. No capillaries were observed between wrapped AV vessel pairs. The computational model comprised a single AV pair in cross section. Geometric parameters critical in renal oxygen transport were altered according to variations observed by CT and light microscopy. Lumen separation and wrapping of the vein around the artery were found to be the critical geometric factors determining the amount of oxygen shunted between AV pairs. AV oxygen shunting increases both as lumen separation decreases and as the degree of wrapping increases. The model also predicts that capillaries not only deliver oxygen, but can also remove oxygen from the cortical parenchyma close to an AV pair. Thus the presence of oxygen sinks (capillaries or tubules) near arteries would reduce the effectiveness of AV oxygen shunting. Collectively, these data suggest that AV oxygen shunting would be favored in larger vessels common to the cortical and medullary circulations (i.e., arcuate and proximal interlobular arteries) rather than the smaller vessels specific to the cortical circulation (distal interlobular arteries and afferent arterioles).