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1 Department of Mathematics, University of North Carolina, Chapel Hill, NC, USA
2 Department of Physiology, University of Arizona, College of Medicine, Tuscon, AZ, USA
3 Department of Mathematics, Duke University, Durham, NC, USA
* To whom correspondence should be addressed. E-mail: layton{at}math.duke.edu.
We used a mathematical model of the urine concentrating mechanism of rat inner medulla (IM) to investigate the implications of experimental studies in which immunohistochemical methods were combined with three-dimensional computerized reconstruction of renal tubules. The mathematical model represents a distribution of loops of Henle with loop bends at all levels of the IM, and the vasculature is represented by means of the central core assumption. Based on immunohistochemical evidence, descending limb portions that reach into the papilla are assumed to be only moderately water permeable or to be water impermeable, and only prebend segments and ascending thin limbs are assumed to be NaCl permeable. Model studies indicate that this configuration favors the targeted delivery of NaCl to loop bends, where a favorable gradient, sustained by urea absorption from collecting ducts, promotes NaCl absorption. We identified two model modes that produce a significant axial osmolality gradient. One mode, suggested by preliminary immunohistochemical findings, assumes that AQP1-null portions of loops of Henle that reach into the papilla have very low urea permeability. The other mode, suggested by perfused tubule experiments from the literature, assumes that these same portions of loops of Henle have very high urea permeabilities. Model studies were conducted to determine the sensitivity of these modes to parameter choices. Model results are compared with extant tissue-slice and micropuncture studies.
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