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Am J Physiol Renal Physiol 297: F517-F536, 2009. First published April 29, 2009; doi:10.1152/ajprenal.90496.2008
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A mathematical model of O2 transport in the rat outer medulla. I. Model formulation and baseline results

Jing Chen,1 Anita T. Layton,2 and Aurélie Edwards1

1Department of Chemical and Biological Engineering, Tufts University, Medford, Massachusetts; and 2Department of Mathematics, Duke University, Durham, North Carolina

Submitted 19 August 2008 ; accepted in final form 24 April 2009

The mammalian kidney is particularly vulnerable to hypoperfusion, because the O2 supply to the renal medulla barely exceeds its O2 requirements. In this study, we examined the impact of the complex structural organization of the rat outer medulla (OM) on O2 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 O2. We considered basal cellular O2 consumption and O2 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 PO2 gradients in the axial and radial directions. The segregation of descending vasa recta, the main supply of O2, at the center and immediate periphery of the vascular bundles gives rise to large radial differences in PO2 between regions, limits O2 reabsorption from long descending vasa recta, and helps preserve O2 delivery to the inner medulla. Under baseline conditions, significantly more O2 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 O2 supplied to the medulla is consumed in the OM and that medullary thick ascending limbs operate on the brink of hypoxia.

region-based model; red blood cells; medullary thick ascending limbs; active sodium transport


Address for reprint requests and other correspondence: A. Edwards, Dept. of Chemical and Biological Engineering, Tufts Univ., 4 Colby St., Medford, MA 02155 (e-mail: aurelie.edwards{at}tufts.edu)




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J. Chen, A. Edwards, and A. T. Layton
A mathematical model of O2 transport in the rat outer medulla. II. Impact of outer medullary architecture
Am J Physiol Renal Physiol, August 1, 2009; 297(2): F537 - F548.
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