A mathematical model of O 2 transport in the rat outer medulla. II. Impact of outer medullary architecture

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We used a mathematical model of O(2) transport and the urine concentrating mechanism of the outer medulla of the rat kidney to study the effects of blood pH and medullary blood flow on O(2) availability and Na(+) reabsorption. The model predicts that in vivo paracellular Na(+) fluxes across medullary thick ascending limbs (mTALs) are small relative to transcellular Na(+) fluxes and that paracellular fluxes favor Na(+) reabsorption from the lumen along most of the mTAL segments. In addition, model results suggest that blood pH has a significant impact on O(2) transport and Na(+) reabsorption owing to the Bohr effect, according to which a lower pH reduces the binding affinity of hemoglobin for O(2). Thus our model predicts that the presumed greater acidity of blood in the interbundle regions, where mTALs are located, relative to that in the vascular bundles, facilitates the delivery of O(2) to support the high metabolic requirements of the mTALs and raises the concentrating capability of the outer medulla. Model results also suggest that increases in vascular and tubular flow rates result in disproportional, smaller increases in active O(2) consumption and mTAL active Na(+) transport, despite the higher delivery of O(2) and Na(+). That is, at a sufficiently high medullary O(2) supply, O(2) demand in the outer medulla does not adjust precisely to changes in O(2) delivery.

Section: Anaerobic Metabolismmentioning

confidence: 99%

Section: Model Descriptionmentioning

confidence: 99%

Effects of pH and medullary blood flow on oxygen transport and sodium reabsorption in the rat outer medulla

Chen

Edwards

Layton

2010

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“…Thick ascending limbs at the periphery of vascular bundles escape necrosis, and, at least in the mouse kidney, these are predominantly long-loop thick ascending limbs (58). PO 2 gradients along the corticopapillary axis and projecting radially from the vascular bundles are predicted by a mathematical model of oxygen transport that was based on the complex structural organization of the outer medulla (10,11). The low PO 2 surrounding the thick limbs may be partially alleviated by the Bohr effect, which states that a lower pH reduces the binding affinity of hemoglobin for O 2 .…”

Section: Medullary Metabolic Activity and Oxygenationmentioning

confidence: 99%

Targeted delivery of solutes and oxygen in the renal medulla: role of microvessel architecture

Pannabecker

2014

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Renal medullary function is characterized by corticopapillary concentration gradients of various molecules. One example is the generally decreasing axial gradient in oxygen tension (Po2). Another example, found in animals in the antidiuretic state, is a generally increasing axial solute gradient, consisting mostly of NaCl and urea. This osmolality gradient, which plays a principal role in the urine concentrating mechanism, is generally considered to involve countercurrent multiplication and countercurrent exchange, although the underlying mechanism is not fully understood. Radial oxygen and solute gradients in the transverse dimension of the medullary parenchyma have been hypothesized to occur, although strong experimental evidence in support of these gradients remains lacking. This review considers anatomic features of the renal medulla that may impact the formation and maintenance of oxygen and solute gradients. A better understanding of medullary architecture is essential for more clearly defining the compartment-to-compartment flows taken by fluid and molecules that are important in producing axial and radial gradients. Preferential interactions between nephron and vascular segments provide clues as to how tubular and interstitial oxygen flows contribute to safeguarding active transport pathways in renal function in health and disease.

“…The maximum volumetric rate of O 2 consumption (R max,O 2 basal ) is assumed to be the same in each compartment and taken as 10 M/s, as discussed in the companion study (8) [also known as the T Na -to-Q O 2 ratio (T Na /Q O 2 )] is 18, as suggested by Na ϩ -K ϩ -ATPase stoichiometry. Under favorable thermodynamic conditions, additional moles of Na ϩ are reabsorbed in parallel through the paracellular route, namely, when the driving force imparted by the lumen-negative transepithelial potential is not counterbalanced by too large an interstitium-tolumen Na ϩ concentration gradient.…”

Section: O 2 Consumptionmentioning

confidence: 99%

“…In a companion study (8), we investigate model sensitivity to fundamental structural assumptions and to parameters whose values are uncertain. Osmotic coefficient of solute k SAV / SDV Fraction of SAV/SDV reaching a given medullary level ⌿ i,Na active Rate of Na ϩ active transport in tubule i (in mol ⅐m Ϫ2 ⅐s Ϫ1 ) cell Fraction of solute consumed in epithelial or endothelial cell layer that is taken from the lumen…”

mentioning

confidence: 99%

A mathematical model of O₂transport in the rat outer medulla. I. Model formulation and baseline results

Chen¹,

Layton²,

Edwards³

2009

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The mammalian kidney is particularly vulnerable to hypoperfusion, because the O(2) supply to the renal medulla barely exceeds its O(2) requirements. In this study, we examined the impact of the complex structural organization of the rat outer medulla (OM) on O(2) distribution. We extended the region-based mathematical model of the rat OM developed by Layton and Layton (Am J Physiol Renal Physiol 289: F1346-F1366, 2005) to incorporate the transport of RBCs, Hb, and O(2). We considered basal cellular O(2) consumption and O(2) consumption for active transport of NaCl across medullary thick ascending limb epithelia. Our model predicts that the structural organization of the OM results in significant Po(2) gradients in the axial and radial directions. The segregation of descending vasa recta, the main supply of O(2), at the center and immediate periphery of the vascular bundles gives rise to large radial differences in Po(2) between regions, limits O(2) reabsorption from long descending vasa recta, and helps preserve O(2) delivery to the inner medulla. Under baseline conditions, significantly more O(2) is transferred radially between regions by capillary flow, i.e., advection, than by diffusion. In agreement with experimental observations, our results suggest that 79% of the O(2) supplied to the medulla is consumed in the OM and that medullary thick ascending limbs operate on the brink of hypoxia.