Impact of renal medullary three-dimensional architecture on oxygen transport

Abstract

We have developed a highly detailed mathematical model of solute transport in the renal medulla of the rat kidney to study the impact of the structured organization of nephrons and vessels revealed in anatomic studies. The model represents the arrangement of tubules around a vascular bundle in the outer medulla and around a collecting duct cluster in the upper inner medulla. Model simulations yield marked gradients in intrabundle and interbundle interstitial fluid oxygen tension (PO2), NaCl concentration, and osmolality in the outer medulla, owing to the vigorous active reabsorption of NaCl by the thick ascending limbs. In the inner medulla, where the thin ascending limbs do not mediate significant active NaCl transport, interstitial fluid composition becomes much more homogeneous with respect to NaCl, urea, and osmolality. Nonetheless, a substantial PO2 gradient remains, owing to the relatively high oxygen demand of the inner medullary collecting ducts. Perhaps more importantly, the model predicts that in the absence of the three-dimensional medullary architecture, oxygen delivery to the inner medulla would drastically decrease, with the terminal inner medulla nearly completely deprived of oxygen. Thus model results suggest that the functional role of the three-dimensional medullary architecture may be to preserve oxygen delivery to the papilla. Additionally, a simulation that represents low medullary blood flow suggests that the separation of thick limbs from the vascular bundles substantially increases the risk of the segments to hypoxic injury. When nephrons and vessels are more homogeneously distributed, luminal PO2 in the thick ascending limb of superficial nephrons increases by 66% in the inner stripe. Furthermore, simulations predict that owing to the Bohr effect, the presumed greater acidity of blood in the interbundle regions, where thick ascending limbs are located, relative to that in the vascular bundles, facilitates the delivery of O2 to support the high metabolic requirements of the thick limbs and raises NaCl reabsorption.

Keywords: hypoxia; mathematical model; metabolism; thick ascending limb transport.

Fig. 1.

Schematic diagram of a cross section through the outer stripe, inner stripe, upper inner medulla (IM), mid-IM, and deep IM, showing interstitial regions (R1, R2, R3, and R4) and relative positions of tubules and vessels. Decimal numbers indicate relative interaction weightings with regions. SDL/SAL, descending/ascending limbs of short loops of Henle; LDL/LAL, descending/ascending limbs of long loops of Henle; CD, collecting duct; SDV, short descending vasa recta; LDV, long descending vas rectum; AVRs, populations of ascending vasa recta. Subscripts S, M, and L associated with a LAL denote limbs that turn with the first millimeters of the IM (S), within the mid-IM (M), or reach into the deep IM (L). Dotted-line box in deep IM indicates that LDV, LDL, LAL_L, and CD are weighted evenly among the 4 regions.

Fig. 2.

Concentration and osmolality profiles. A: interstitial region Po₂. B: short loop, longest loop, and CD tubular fluid Po₂. C: CD tubular fluid Na⁺ concentration, urea concentration, and osmolality.

Fig. 3.

Region Po₂ as a function of medullary depth, for varying degrees of regionalization, obtained by multiplying the region boundary solute permeabilities (P_R,R′) by 0.1, 1 (base case), 10, and 100. When regionalization decreases, the separation between region Po₂ decreases, and oxygen delivery to the deep IM decreases.

Fig. 4.

CD tubular fluid osmolality as a function of medullary depth, for varying degrees of regionalization, obtained by multiplying the region boundary solute permeabilities by 0.1, 1 (base case), 10, and 100. When regionalization decreases, CD tubular fluid osmolality attains a larger increase in the IM, resulting in a higher urine osmolality.

Fig. 5.

Simulated renal tissue oxygenation representing baseline and two hypoxic conditions. Vascular inflow and hematocrit are reduced under hypoxic conditions. “Hypoxic” assumes baseline medullary three-dimensional (3D) architecture; “Hypoxic homogeneous” assumes reduced regionalization. Results show average Po₂ in the SAL lumen, LAL lumen, and interstitial fluid in the 4 regions, in the outer stripe (A) and inner stripe (B). Results suggest that the medullary 3D architecture renders the SAL particularly vulnerable to hypoxic injury under low medullary blood flow conditions.

Fig. 6.

R4 Po₂ as a function of medullary depth for critical Po₂ P_c = 1, 5, 10 (base case), 20 mmHg.

Fig. 7.

Region Po₂ as a function of medullary depth, taking into account the shift in the oxygen dissociation curve due to the Bohr effect.

Fig. A1.

Schematic diagram of a capillary red blood cell (RBC) compartment B (denoted “cap RBC”) and its associated solute fluxes, from Eq. 7. The J_R,B term corresponds to the first term of Eq. 7, representing diffusive flux between the RBC compartment B and its surrounding region R.