Accounting for oxygen in the renal cortex: a computational study of factors that predispose the cortex to hypoxia

Abstract

We develop a pseudo-three-dimensional model of oxygen transport for the renal cortex of the rat, incorporating both the axial and radial geometry of the preglomerular circulation and quantitative information regarding the surface areas and transport from the vasculature and renal corpuscles. The computational model was validated by simulating four sets of published experimental studies of renal oxygenation in rats. Under the control conditions, the predicted cortical tissue oxygen tension ([Formula: see text]) or microvascular oxygen tension (µPo) were within ±1 SE of the mean value observed experimentally. The predicted [Formula: see text] or µPo in response to ischemia-reperfusion injury, acute hemodilution, blockade of nitric oxide synthase, or uncoupling mitochondrial respiration, were within ±2 SE observed experimentally. We performed a sensitivity analysis of the key model parameters to assess their individual or combined impact on the predicted [Formula: see text] and µPo The model parameters analyzed were as follows: ) the major determinants of renal oxygen delivery ([Formula: see text]) (arterial blood Po, hemoglobin concentration, and renal blood flow); ) the major determinants of renal oxygen consumption (V̇o) [glomerular filtration rate (GFR) and the efficiency of oxygen utilization for sodium reabsorption (β)]; and 3) peritubular capillary surface area (PCSA). Reductions in PCSA by 50% were found to profoundly increase the sensitivity of [Formula: see text] and µPo to the major the determinants of [Formula: see text] and V̇o The increasing likelihood of hypoxia with decreasing PCSA provides a potential explanation for the increased risk of acute kidney injury in some experimental animals and for patients with chronic kidney disease.

Renal oxygenation: From data to insight

“…If AV oxygen shunting is not as important as initially postulated, what other mechanisms could account for the susceptibility of the renal cortex to hypoxia? Lee and colleagues addressed this question through “an accounting exercise”, using a pseudo‐three‐dimensional model of the renal cortex to determine the fate of oxygen at various levels of the renal cortical circulation . They concluded that the major factor limiting oxygen delivery to renal cortical tissue is the surface area ( ie density) of peritubular capillaries.…”

“…84,85 It now seems that the quantity of AV oxygen shunting is normally small (<1% of renal oxygen delivery) although it can become more significant under adverse conditions such as ischaemia (up to ~ 4% of renal oxygen delivery). 86 Of course the corollary of this conclusion is that the original experimental data, 78 upon which the initial one-dimensional model was based, may over-estimate the difference in PO 2 between blood in the efferent arteriole and renal vein. Thus, here we have a great example of computational models providing information about the probability of experimental observations.…”

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

“…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 .…”

“…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.…”

“…7,13 To avoid this limitation, we recently quantified the degree of shrinkage of Microfil that would be expected from the protocols followed by Garcia-Sanz et al (~22%) and used these to correct vascular dimensions in a pseudo-three dimensional model of oxygen transport in the kidney of the rat. 14,15 However, development of computational models that can be applied to other species will ideally require methods for quantifying vascular geometry that avoid shrinkage artefacts.…”