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1 Bioinformatics, Xenometrix, Boulder, Colorado 80301; 2 Institut National de la Santé et de la Recherche Médicale Unité 467, Necker Faculty of Medicine, 75730 Paris Cedex 15 France; and 3 Department of Mechanical Engineering, University of Delaware, Newark, Delaware 19716-3140
In earlier work, mathematical models of the urine concentration mechanism were developed incorporating the features of renal anatomy. However, several anatomic observations showed inconsistencies in the modeling representation of the outer stripe (OS) anatomy. In this study, based on observations from comparative anatomy and morphometric studies, we propose a new structural model of outer medullary anatomy, different from that previously presented [A. S. Wexler, R. E. Kalaba, and D. J. Marsh. Am. J. Physiol. 260 (Renal Fluid Electrolyte Physiol. 29): F368-F383, 1991]. The modifications include the following features of rat outer medullary anatomy, for example, 1) in the OS, the limbs of long loops of Henle surround the descending and ascending vasa recta that develop into the vascular bundles in the inner stripe (IS), whereas the limbs of short loops are close to the collecting ducts; and 2) the descending limbs of short loops shift from the tubular region in the OS to near the vascular bundle in the IS, whereas the limbs of long loops are situated away from the vascular bundles in the tubular region. The sensitivity of the concentrating process to the relative position of loops and vessels was investigated in the different medullary regions. With these modifications, the model predicts a more physiological, axial osmolarity gradient in both outer and inner medulla with membrane parameters that are all in the range of measured physiological values, including the urea permeabilities of descending vasa recta reported by Pallone and co-workers (T. L. Pallone, J. Work, R. L. Myers, and R. L. Jamison. J. Clin.Invest. 93: 212-222, 1994).
mathematical model; sensitivity analysis
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