title: 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.
authors.affiliation: Department of Mathematics, Duke University, Durham, North Carolina; and.
authors.forename: Brendan C
authors.initials: BC
authors.lastname: Fry
authors.affiliation: Centre National de la Recherche Scientifique ERL 8228, Centre de Recherche des Cordeliers, Paris, France.
authors.forename: Aurélie
authors.initials: A
authors.lastname: Edwards
authors.affiliation: Department of Mathematics, Duke University, Durham, North Carolina; and.
authors.forename: Ioannis
authors.initials: I
authors.lastname: Sgouralis
authors.affiliation: Department of Mathematics, Duke University, Durham, North Carolina; and alayton@math.duke.edu.
authors.forename: Anita T
authors.initials: AT
authors.lastname: Layton
mesh_terms: D000818:Animals; D001692:Biological Transport / Q000502:physiology; D006863:Hydrogen-Ion Concentration; D007679:Kidney Medulla / Q000033:anatomy & histology* / Q000378:metabolism*; D023421:Models, Animal; D008962:Models, Theoretical; D009994:Osmolar Concentration; D010100:Oxygen / Q000378:metabolism*; D010101:Oxygen Consumption / Q000502:physiology; D051381:Rats; D012965:Sodium Chloride / Q000378:metabolism
chemical_list: D012965:Sodium Chloride; D010100:Oxygen
keywords: hypoxia; mathematical model; metabolism; thick ascending limb transport