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1 Department of Mathematics, Duke University, Durham, NC, USA
* To whom correspondence should be addressed. E-mail: layton{at}math.duke.edu.
We have developed a highly-detailed mathematical model for the urine concentrating mechanism (UCM) of the rat kidney outer medulla (OM). The model simulates preferential interactions among tubules and vessels by representing four concentric regions that are centered on a vascular bundle; tubules and vessels, or fractions thereof, are assigned to anatomically appropriate regions. Model parameters, which are based on the experimental literature, include transepithelial transport properties of short descending limbs inferred from immunohistochemical localization studies. The model equations, which are based on conservation of solutes and water and on standard expressions for transmural transport, were solved to steady state. Model simulations predict significantly differing interstitial NaCl and urea concentrations in adjoining regions. Active NaCl transport from thick ascending limbs (TALs), at rates inferred from the physiologic literature, resulted in model osmolality profiles along the OM that are consistent with tissue slice experiments. TAL luminal NaCl concentrations at the cortico-medullary boundary are consistent with tubuloglomerular feedback function. The model exhibited solute exchange, cycling, and sequestration patterns (in tubules, vessels, and regions) that are generally consistent with predictions in the physiologic literature, including significant urea addition from long ascending vasa recta to inner-stripe short descending limbs. In a companion study (AT Layton and HE Layton. Am. J. Physiol. - Renal Physiol., submitted.), the impact of model assumptions, medullary anatomy, and tubular segmentation on the UCM were investigated by means of extensive parameter studies.
This article has been cited by other articles:
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  A. T. Layton, H. E. Layton, W. H. Dantzler, and T. L. Pannabecker The Mammalian Urine Concentrating Mechanism: Hypotheses and Uncertainties Physiology, August 1, 2009; 24(4): 250 - 256. [Abstract] [Full Text] [PDF]
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 J. Chen, A. T. Layton, and A. Edwards A mathematical model of O2 transport in the rat outer medulla. I. Model formulation and baseline results Am J Physiol Renal Physiol, August 1, 2009; 297(2): F517 - F536. [Abstract] [Full Text] [PDF]
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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. [Abstract] [Full Text] [PDF]
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T. L. Pannabecker, W. H. Dantzler, H. E. Layton, and A. T. Layton Role of three-dimensional architecture in the urine concentrating mechanism of the rat renal inner medulla Am J Physiol Renal Physiol, November 1, 2008; 295(5): F1271 - F1285. [Abstract] [Full Text] [PDF]
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 T. L. Pallone Aquaporin 1, Urea Transporters, and Renal Vascular Bundles J. Am. Soc. Nephrol., November 1, 2007; 18(11): 2798 - 2800. [Full Text] [PDF]
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W. Zhang and A. Edwards A model of nitric oxide tubulovascular cross talk in a renal outer medullary cross section Am J Physiol Renal Physiol, February 1, 2007; 292(2): F711 - F722. [Abstract] [Full Text] [PDF]
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A. T. Layton and H. E. Layton A region-based mathematical model of the urine concentrating mechanism in the rat outer medulla. II. Parameter sensitivity and tubular inhomogeneity Am J Physiol Renal Physiol, December 1, 2005; 289(6): F1367 - F1381. [Abstract] [Full Text] [PDF]
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