A pseudo-three-dimensional model for quantification of oxygen diffusion from preglomerular arteries to renal tissue and renal venous blood

Abstract

To assess the physiological significance of arterial-to-venous (AV) oxygen shunting, we generated a new pseudo-three-dimensional computational model of oxygen diffusion from intrarenal arteries to cortical tissue and veins. The model combines the 11 branching levels (known as "Strahler" orders) of the preglomerular renal vasculature in the rat, with an analysis of an extensive data set obtained using light microscopy to estimate oxygen mass transfer coefficients for each Strahler order. Furthermore, the AV shunting model is now set within a global oxygen transport model that includes transport from arteries, glomeruli, peritubular capillaries, and veins to tissue. While a number of lines of evidence suggest AV shunting is significant, most importantly, our AV oxygen shunting model predicts AV shunting is small under normal physiological conditions (~0.9% of total renal oxygen delivery; range 0.4-1.4%), but increases during renal ischemia, glomerular hyperfiltration (~2.1% of total renal oxygen delivery; range 0.84-3.36%), and some cardiovascular disease states (~3.0% of total renal oxygen delivery; range 1.2-4.8%). Under normal physiological conditions, blood Po is predicted to fall by ~16 mmHg from the root of the renal artery to glomerular entry, with AV oxygen shunting contributing ~40% and oxygen diffusion from arteries to tissue contributing ~60% of this decline. Arterial Po is predicted to fall most rapidly from Strahler , under normal physiological conditions. We conclude that AV oxygen shunting normally has only a small impact on renal oxygenation, but may exacerbate renal hypoxia during renal ischemia, hyperfiltration, and some cardiovascular disease states.

Micro‐computed tomographic analysis of the radial geometry of intrarenal artery‐vein pairs in rats and rabbits: Comparison with light microscopy

“…A major limitation of previous studies in which renal vascular geometry was quantified by micro‐CT 17 was that the tissues were exposed to organic solvents which would promote shrinkage of Microfil. Indeed, by using the same solutions as that used by Garcia‐Sanz and colleagues we have estimated that the processing of the tissues analysed by Nordsletten and colleagues would have led to approximately 22% shrinkage . Therefore, in the current study we avoided use of such solvents.…”

“…There is experimental evidence that diffusive AV oxygen shunting in the renal vasculature may be significant . However, the quantitative significance of this phenomenon remains a matter of controversy . Currently, it is not possible to accurately measure AV oxygen shunting experimentally.…”

“…All available models of oxygen transport in the renal cortex are based on the eleven branching orders, termed “Strahler orders”, of the rat renal circulation defined by Nordsletten et al . using the micro‐CT data of Garcia‐Sanz and colleagues .…”

“…[10][11][12] However, the quantitative significance of this phenomenon remains a matter of controversy. 5,8,9,13,14 Currently, it is not possible to accurately measure AV oxygen shunting experimentally. For this reason, we rely on mathematical modelling to investigate this phenomenon by simulating diffusion and convection of oxygen within the renal cortex.…”

“…All available models of oxygen transport in the renal cortex 4,7,[13][14][15][16] are based on the eleven branching orders, termed "Strahler orders", of the rat renal circulation defined by Nordsletten et al 17 using the micro-CT data of Garcia-Sanz and colleagues. 18 Shrinkage of Microfil likely confounded the observations of Garcia-Sanz and colleagues due to tissue immersion in alcohols.…”