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A region-based mathematical model of the urine concentrating mechanism in the rat outer medulla. I. Formulation and base-case results

Department of Mathematics, Duke University, Durham, North Carolina

Submitted 29 September 2003 ; accepted in final form 17 May 2005

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 physiological literature, resulted in model osmolality profiles along the OM that are consistent with tissue slice experiments. TAL luminal NaCl concentrations at the corticomedullary 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 physiological literature, including significant urea addition from long ascending vasa recta to inner-stripe short descending limbs. In a companion study (Layton AT and Layton HE. Am J Physiol Renal Physiol 289: F1367–F1381, 2005), the impact of model assumptions, medullary anatomy, and tubular segmentation on the UCM was investigated by means of extensive parameter studies.

kidney; countercurrent multiplication; countercurrent exchange; NaCl transport; urea transport

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