Measurements of exponential gradients of sodium and chlorine in the rat kidney medulla using the electron microprobe

Koepsell, Hermann; Nicholson, W. A. P.; Kriz, Wilhelm; Höhling, H. J.

doi:10.1007/bf00586235

Cited by 66 publications

(46 citation statements)

References 17 publications

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“…2, A1 and A3). These increases are consistent with tissue slice experiments in rats (12,70), rabbits (20), and dogs (62), and with electron microprobe experiments in rats (25). However, it is noteworthy that in the IM, the model's osmolality increases are attributable almost entirely to axial urea concentration increases.…”

Section: Model Formulation and Implicationssupporting

confidence: 81%

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

Layton

2011

American Journal of Physiology-Renal Physiology

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Layton AT. A mathematical model of the urine concentrating mechanism in the rat renal medulla. I. Formulation and base-case results. Am J Physiol Renal Physiol 300: F356 -F371, 2011. First published November 10, 2010 doi:10.1152/ajprenal.00203.2010.-A new, region-based mathematical model of the urine concentrating mechanism of the rat renal medulla was used to investigate the significance of transport and structural properties revealed in anatomic studies. The model simulates preferential interactions among tubules and vessels by representing concentric regions that are centered on a vascular bundle in the outer medulla (OM) and on a collecting duct cluster in the inner medulla (IM). Particularly noteworthy features of this model include highly urea-permeable and water-impermeable segments of the long descending limbs and highly urea-permeable ascending thin limbs. Indeed, this is the first detailed mathematical model of the rat urine concentrating mechanism that represents high long-loop urea permeabilities and that produces a substantial axial osmolality gradient in the IM. That axial osmolality gradient is attributable to the increasing urea concentration gradient. 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 that the interstitial NaCl and urea concentrations in adjoining regions differ substantially in the OM but not in the IM. In the OM, active NaCl transport from thick ascending limbs, at rates inferred from the physiological literature, resulted in a concentrating effect such that the intratubular fluid osmolality of the collecting duct increases ϳ2.5 times along the OM. As a result of the separation of urea from NaCl and the subsequent mixing of that urea and NaCl in the interstitium and vasculature of the IM, collecting duct fluid osmolality further increases by a factor of ϳ1.55 along the IM. countercurrent system; NaCl transport; urea transport; kidney DURING PERIODS OF WATER DEPRIVATION, the mammalian urine concentrating mechanism, which is localized in the renal medulla, stabilizes the osmolality of blood plasma by producing a urine that has an osmolality that substantially exceeds that of blood plasma. However, despite decades of sustained experimental and theoretical investigation (24,37,54,58), the nature of the urine concentrating mechanism in the inner medulla (IM) of the mammalian kidney remains controversial.Anatomic studies have revealed a highly structured organization of tubules and vasa recta in the outer medulla (OM) of some mammalian kidneys (2, 29), with tubules and vessels organized concentrically around vascular bundles, tightly packed clusters of parallel vessels, and tubules containing mostly vasa recta. Recent studies of the three-dimensional architecture of the rat IM and expression of membrane proteins associated with fluid and solute transport in nephrons and vasculature have revealed transport and structural properties that likely impact th...

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Section: Model Formulation and Implicationssupporting

confidence: 81%

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

Layton

2011

American Journal of Physiology-Renal Physiology

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“…In the following, the above parameter set will be referred to as the base case. The bounds of Table 3 define the vectors l and u of the inequalities (37). The objective funetion (38) and the constraints (40)- (43) complete the definition of the inverse problem.…”

Section: Simulationsand Resultsmentioning

confidence: 99%

“…In addition to (37), further constraints are imposed on the parameters: First, experimental results [35] demonstrate that the osmolarity of the collecting duet fluid at the papillary tip is nearly the same as that of the fluid in the adjacent central core at the same level. This fact is modeled by the constraint 0.9Osm 4 (10.5;p)<Osm 6 (10.5;p)<l.lOsm 4 (10.5;p).…”

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confidence: 99%

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The kidney model as an inverse problem

Breinbauer¹,

Lory

1991

Applied Mathematics and Computation

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The mammalian kidney is modeled by a multipoint boundary-value problem for a System of nonlinear ordinary differential equations. A corresponding inverse problem is presented, which allows the rigorous judgement of the potential of the given modeling technique. For its numerical Solution a discretization is proposed, which is tailor-made for kidney models. It leads to a nonlinear-programming problem with nonlinear equality and inequality constraints. The suggested methods are applied to current research problems in renal physiology.

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“…This would be followed by similar principles throughout much of Kriz's later work. Probing the medulla for local ion concentrations in those days was another major step in understanding the concentration gradients of the renal medulla [33,60]. Measuring functional oxygen deficiency together with Joachim Schurek, another long-term collaborator with a physiological and clinical background, was another step towards understanding major questions in medullary function [91].…”

Section: The Renal Medulla and Urinary Concentrating Mechanismmentioning

confidence: 99%

From tubular sublimate nephropathy via urinary concentrating mechanism to glomerular disease—Wilhelm Kriz’s contribution to modern nephrology

Bachmann

2017

Pflugers Arch - Eur J Physiol

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Measurements of exponential gradients of sodium and chlorine in the rat kidney medulla using the electron microprobe

Cited by 66 publications

References 17 publications

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

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

The kidney model as an inverse problem

From tubular sublimate nephropathy via urinary concentrating mechanism to glomerular disease—Wilhelm Kriz’s contribution to modern nephrology

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