Abstract
During water deprivation, the kidney of a mammal can conserve water by producing a urine that is more concentrated than blood plasma. That hypertonic urine is produced when water is reabsorbed, in excess of solutes, from the collecting ducts and into the renal vasculature, thereby concentrating the collecting duct fluid, which eventually emerges as urine. In this chapter, we introduce mathematical models that simulate the urine concentrating process. To learn how to build those models, we first derive equations that represent tubular flow, transmural water flux, and transmural solute fluxes along a renal tubule. We then develop models that simulate countercurrent multiplication in a loop, and we study factors that affect the efficiency of the concentrating mechanism.
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Layton, H.E.: Mathematical models of the mammalian urine concentrating mechanism. In: Layton, H.E., Weinstein, A.M. (eds.) Membrane Transport and Renal Physiology. The IMA Volumes in Mathematics and Its Applications, vol. 129, pp. 233–272. Springer, New York (2002)
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Pannabecker, T.L., Dantzler, W.H., Layton, H.E., Layton, A.T.: Role of three-dimensional architecture in the urine concentrating mechanism of the rat renal inner medulla. Am. J. Physiol. Ren. Physiol. 295, F1217–F1285 (2008)
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Layton, A.T., Edwards, A. (2014). Urine Concentration. In: Mathematical Modeling in Renal Physiology. Lecture Notes on Mathematical Modelling in the Life Sciences. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27367-4_3
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DOI: https://doi.org/10.1007/978-3-642-27367-4_3
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