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

Abstract

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.

Fig. 1.

Schematic representation of the region-based model. Displayed in A and B are the cross sections of the outer stripe (OS) and inner stripe (IS) of rat outer medulla (OM), respectively. In the model formulation, the four regions (R1–R4) have coincident centers; the display in this figure is intended to minimize the figure area. LDV, long descending vas rectum; SDVa and SDVb, 2 populations of short descending vasa recta; LAVa and LVAb, 2 populations of long ascending vasa recta; SAVa and SAVb, 2 populations of short ascending vasa recta; LDL, long descending limb of Henle's loop; SDL, short descending limb; LAL, long ascending limb; SAL, short ascending limb; CD, collecting duct. The numbers represent the relative weight of interaction between a type of vessel or tubule and a given region (i.e., the parameter κ_{i, R} in Eqs. 5, 7a, and 12). As shown in C, we differentiate between the red blood cell (RBC) and plasma compartments within vasa recta. The vascular endothelium and tubular epithelium are not explicitly distinguished in this model, but their thickness is taken into account in calculating cellular O₂ consumption. The arrows show the direction of the O₂ fluxes (see Eqs. 11, 13, and 14).

Fig. 2.

Po₂ in tubules, vasa recta, and concentric regions. A-D: regions R1, R2, R3, and R4; tubules are assigned to the region with which they are in contact for 50% or more of their inner stripe length. E: Po₂ profiles in the interstitium of the 4 regions. Vertical dotted lines mark the boundary between the OS and IS, and x/L denotes the ratio of the axial coordinate to total length of outer medulla.

Fig. 3.

Fluid osmolality profiles in the CD and in the interstitial regions R1, R2, R3, and R4 as a function of medullary depth.

Fig. 4.

Predicted transepithelial electrical potential difference (V_te) across SAL and LAL as a function of medullary depth. The potential difference is calculated based on charge balance across the medullary thick ascending limb of Henle's loop (mTAL) epithelium.

Fig. 5.

Base-case Na⁺ concentration profiles in thick ascending limbs (SAL and LAL) and their surrounding interstitium (R2, R3, and R4) along the corticomedullary axis. Solid lines in B, base-case interstitial-to-lumen Na⁺ concentration ratios for the SAL and LAL as a function of medullary depth. Dashed lines, interstitial-to-lumen Na⁺ concentration ratios at which net paracellular Na⁺ fluxes are zero (see Eq. 16).

Fig. 6.

Interstitial-to-mTAL lumen Na⁺ concentration ratios for 2 different values of α: 0.35 and 0.65. The parameter α represents the absolute value of the total-to-Na⁺ transcellular current ratio. Solid lines, predicted interstitial-to-mTAL lumen Na⁺ concentration ratios; dashed lines, critical ratio values, at which net paracellular Na⁺ fluxes are zero. A: SAL. B: LAL. In these simulations, α is taken to be constant throughout the OM, whereas in the base case, α = 0.65 in the outer stripe and 0.35 in the inner stripe. The lumen-positive V_te across mTAL increases with increasing α.

Fig. 7.

Effects of blood pH on total mTAL Na⁺ reabsorption (A) and CD tubular fluid osmolality at the OM-IM boundary (B). In case 1, variations in blood pH in R3 and R4 are shown; blood pH in R1 and R2 is fixed at 7.4. The concentrating capability of the OM increases as blood in the interbundle region becomes more acidic, thereby facilitating O₂ dissociation from oxyhemoglobin near the mTALs. In case 2, variations in blood pH in R1 and R2 are shown; blood pH in R3 and R4 is fixed at 7.2. The concentrating capability of the OM decreases as blood in the vascular bundle region becomes more acidic, thereby reducing O₂ delivery to the interbundle region.

Fig. 8.

Total mTAL Na⁺ reabsorption (A) and CD tubular fluid osmolality at the OM-IM boundary (B) as a function of blood pH. A uniform pH is assumed throughout the entire OM.

Fig. 9.

Total mTAL Na⁺ reabsorption (A) and CD tubular fluid osmolality at the OM-IM boundary (B) as a function of the critical Po₂ (P_c), below which O₂ consumption becomes limited by O₂ availability (Eq. 8).

Fig. 10.

Total mTAL Na⁺ reabsorption (A) and CD tubular fluid osmolality at the OM-IM boundary (B) as a function of the anaerobic metabolism contribution, given by the coefficient a (Eq. 17). In the base case, which assumes negligible anaerobic metabolism, a = 0; in the idealized case, in which mTAL Na⁺ active transport rate is taken to be independent of O₂ supply, a = 1.

Fig. 11.

Ratio of O₂ consumption to O₂ supply in the OM, as medullary blood flow (MBF) and glomerular filtration rate (GFR) are varied by the same factor. Percent increase or decrease in MBF and GFR is relative to base-case values.

Fig. 12.

Interstitial Po₂ in the 4 regions, assuming a 25% increase in the flow entering descending vasa recta, descending limbs, and CDs. Po₂ is significantly higher in R2–R4 relative to the base case (Fig. 2E).