• Brendan C Fry and Anita T Layton.
• Department of Mathematics, Duke University, Durham, NC 27708-0320, USA. Electronic address: bfry@math.duke.edu.
• Math Biosci. 2014 Dec 1; 258: 68-76.

AbstractWe have developed a highly detailed mathematical model of oxygen transport in a cross section of the upper inner medulla of the rat kidney. The model is used to study the impact of the structured organization of nephrons and vessels revealed in anatomic studies, in which descending vasa recta are found to lie distant from clusters of collecting ducts. Specifically, we formulated a two-dimensional oxygen transport model, in which the positions and physical dimensions of renal tubules and vessels are based on an image obtained by immunochemical techniques (T. Pannabecker and W. Dantzler, Three-dimensional architecture of inner medullary vasa recta, Am. J. Physiol. Renal Physiol. 290 (2006) F1355-F1366). The model represents oxygen diffusion through interstitium and other renal structures, oxygen consumption by the Na(+)/K(+)-ATPase activities of the collecting ducts, and basal metabolic consumption. Model simulations yield marked variations in interstitial PO2, which can be attributed, in large part, to the heterogeneities in the position and physical dimensions of the collecting ducts. Further, results of a sensitivity study suggest that medullary oxygenation is highly sensitive to medullary blood flow, and that, at high active consumption rates, localized patches of tissue may be vulnerable to hypoxic injury. Copyright © 2014 Elsevier Inc. All rights reserved.

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