Mathematical model of an avian urine concentrating mechanism

2000 ◽  
Vol 279 (6) ◽  
pp. F1139-F1160 ◽  
Author(s):  
H. E. Layton ◽  
John M. Davies ◽  
Giovanni Casotti ◽  
Eldon J. Braun
Keyword(s):  
Mathematical Model ◽  
Flow Parameter ◽  
Urine Osmolality ◽  
Energetic Cost ◽  
Loop Of Henle ◽  
Nacl Transport ◽  
A Value ◽  
Concentrating Mechanism ◽  
Collecting Ducts ◽  
Urine Concentrating Mechanism

A mathematical model was used to investigate how concentrated urine is produced within the medullary cones of the quail kidney. Model simulations were consistent with a concentrating mechanism based on single-solute countercurrent multiplication and on NaCl cycling from ascending to descending limbs of loops of Henle. The model predicted a urine-to-plasma (U/P) osmolality ratio of ∼2.26, a value consistent with maximum avian U/P osmolality ratios. Active NaCl transport from descending limb prebend thick segments contributed 70% of concentrating capability. NaCl entry and water extraction provided 80 and 20%, respectively, of the concentrating effect in descending limb flow. Parameter studies indicated that urine osmolality is sensitive to the rate of fluid entry into descending limbs and collecting ducts at the cone base. Parameter studies also indicated that the energetic cost of concentrating urine is sensitive to loop of Henle population as a function of medullary depth: as the fraction of loops reaching the cone tip increased above anatomic values, urine osmolality increased only marginally, and, ultimately, urine osmolality decreased.

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

2011 ◽  
Vol 300 (2) ◽  
pp. F356-F371 ◽  
Author(s):  
Anita T. Layton
Keyword(s):  
Mathematical Model ◽  
Collecting Duct ◽  
Renal Medulla ◽  
Base Case ◽  
Nacl Transport ◽  
Rat Urine ◽  
Concentrating Mechanism ◽  
Steady State Model ◽  
Model Equations ◽  
Urine Concentrating Mechanism

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 ∼2.5 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 ∼1.55 along the IM.

Urea gradient-associated fluid absorption with sigma urea = 1 in rat terminal collecting duct

1990 ◽  
Vol 258 (5) ◽  
pp. F1173-F1180 ◽  
Author(s):  
C. L. Chou ◽  
J. M. Sands ◽  
H. Nonoguchi ◽  
M. A. Knepper
Keyword(s):  
Mathematical Model ◽  
Absorption Rate ◽  
Collecting Duct ◽  
Null Point ◽  
Absorption Measurement ◽  
Urea Transport ◽  
Fluid Absorption ◽  
A Value ◽  
Collecting Ducts ◽  
Isolated Rat

It has been proposed that inner medullary collecting ducts (IMCDs) can absorb fluid in the absence of a transepithelial osmolality gradient if a perfusate-to-bath urea gradient is present. Such a process has been suggested to be caused by a nonunity reflection coefficient for urea (sigma urea less than 1). However, our recent measurements of sigma urea yielded values not significantly different from 1.0. The present study was done to readdress the possibility of direct coupling of water and urea transport in the rat IMCD. Isolated rat terminal IMCD segments were studied in the presence of 10(-10) M vasopressin with the osmolality of the perfusate equal to that of the peritubular bath but with a perfusate-to-bath urea gradient (bath osmolality balanced with NaCl). We measured both fluid absorption rate and urea concentration in collected fluid and calculated the osmolality of the collected fluid. We observed rapid fluid absorption associated with substantial urea absorption. The urea absorption caused a large fall in the osmolality of the collected fluid with respect to the bath. Simulations with a mathematical model of an isolated perfused tubule revealed that the transepithelial osmolality gradient generated along the length of tubule (caused by urea absorption) was large enough to account for the fluid absorption. Measurement of sigma urea with the "zero-flux" (or null point) method revealed a value of 1.00 +/- 0.02. Thus we conclude that the observed fluid absorption is the result of a transepithelial osmolality gradient generated by rapid urea absorption and does not require sigma urea less than one.

scholarly journals The urea transporter UT-A1 plays a predominant role in a urea-dependent urine-concentrating mechanism

2020 ◽  
Vol 295 (29) ◽  
pp. 9893-9900 ◽  
Author(s):  
Xiaoqiang Geng ◽  
Shun Zhang ◽  
Jinzhao He ◽  
Ang Ma ◽  
Yingjie Li ◽  
...  
Keyword(s):  
Knockout Mice ◽  
Urine Output ◽  
Urine Osmolality ◽  
Urine Concentration ◽  
Urea Transporter ◽  
Predominant Role ◽  
Concentrating Mechanism ◽  
Daily Urine ◽  
Urine Concentrating Mechanism ◽  
Daily Urine Output

Urea transporters are a family of urea-selective channel proteins expressed in multiple tissues that play an important role in the urine-concentrating mechanism of the mammalian kidney. Previous studies have shown that knockout of urea transporter (UT)-B, UT-A1/A3, or all UTs leads to urea-selective diuresis, indicating that urea transporters have important roles in urine concentration. Here, we sought to determine the role of UT-A1 in the urine-concentrating mechanism in a newly developed UT-A1–knockout mouse model. Phenotypically, daily urine output in UT-A1–knockout mice was nearly 3-fold that of WT mice and 82% of all-UT–knockout mice, and the UT-A1–knockout mice had significantly lower urine osmolality than WT mice. After 24-h water restriction, acute urea loading, or high-protein (40%) intake, UT-A1–knockout mice were unable to increase urine-concentrating ability. Compared with all-UT–knockout mice, the UT-A1–knockout mice exhibited similarly elevated daily urine output and decreased urine osmolality, indicating impaired urea-selective urine concentration. Our experimental findings reveal that UT-A1 has a predominant role in urea-dependent urine-concentrating mechanisms, suggesting that UT-A1 represents a promising diuretic target.

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

2005 ◽  
Vol 289 (6) ◽  
pp. F1346-F1366 ◽  
Author(s):  
Anita T. Layton ◽  
Harold E. Layton
Keyword(s):  
Mathematical Model ◽  
Rat Kidney ◽  
Tubuloglomerular Feedback ◽  
Transepithelial Transport ◽  
Base Case ◽  
Model Parameters ◽  
Outer Medulla ◽  
Concentrating Mechanism ◽  
The Impact ◽  
Urine Concentrating Mechanism

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.

scholarly journals A mathematical model of the urine concentrating mechanism in the rat renal medulla. II. Functional implications of three-dimensional architecture

2011 ◽  
Vol 300 (2) ◽  
pp. F372-F384 ◽  
Author(s):  
Anita T. Layton
Keyword(s):  
Mathematical Model ◽  
Collecting Duct ◽  
Rat Kidney ◽  
Renal Medulla ◽  
Base Case ◽  
Unexpected Finding ◽  
Thick Ascending Limb ◽  
Model Calculations ◽  
Concentrating Mechanism ◽  
Urine Concentrating Mechanism

In a companion study [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. (First published November 10, 2010). 10.1152/ajprenal.00203.2010] a region-based mathematical model was formulated for the urine concentrating mechanism in the renal medulla of the rat kidney. In the present study, we investigated model sensitivity to some of the fundamental structural assumptions. An unexpected finding is that the concentrating capability of this region-based model falls short of the capability of models that have radially homogeneous interstitial fluid at each level of only the inner medulla (IM) or of both the outer medulla and IM, but are otherwise analogous to the region-based model. Nonetheless, model results reveal the functional significance of several aspects of tubular segmentation and heterogeneity: 1) the exclusion of ascending thin limbs that reach into the deep IM from the collecting duct clusters in the upper IM promotes urea cycling within the IM; 2) the high urea permeability of the lower IM thin limb segments allows their tubular fluid urea content to equilibrate with the surrounding interstitium; 3) the aquaporin-1-null terminal descending limb segments prevent water entry and maintain the transepithelial NaCl concentration gradient; 4) a higher thick ascending limb Na+ active transport rate in the inner stripe augments concentrating capability without a corresponding increase in energy expenditure for transport; 5) active Na+ reabsorption from the collecting duct elevates its tubular fluid urea concentration. Model calculations predict that these aspects of tubular segmentation and heterogeneity promote effective urine concentrating functions.

A region-based mathematical model of the urine concentrating mechanism in the rat outer medulla. II. Parameter sensitivity and tubular inhomogeneity

2005 ◽  
Vol 289 (6) ◽  
pp. F1367-F1381 ◽  
Author(s):  
Anita T. Layton ◽  
Harold E. Layton
Keyword(s):  
Mathematical Model ◽  
Boundary Conditions ◽  
Rat Kidney ◽  
Vascular Bundles ◽  
Thick Ascending Limb ◽  
Outer Medulla ◽  
Model Calculations ◽  
Concentrating Mechanism ◽  
Vasa Recta ◽  
Urine Concentrating Mechanism

In a companion study (Layton AT and Layton HE. Am J Physiol Renal Physiol 289: F1346–F1366, 2005), a region-based mathematical model was formulated for the urine concentrating mechanism (UCM) in the outer medulla (OM) of the rat kidney. In the present study, we quantified the sensitivity of that model to several structural assumptions, including the degree of regionalization and the degree of inclusion of short descending limbs (SDLs) in the vascular bundles of the inner stripe (IS). Also, we quantified model sensitivity to several parameters that have not been well characterized in the experimental literature, including boundary conditions, short vasa recta distribution, and ascending vasa recta (AVR) solute permeabilities. These studies indicate that regionalization elevates the osmolality of the fluid delivered into the inner medulla via the collecting ducts; that model predictions are not significantly sensitive to boundary conditions; and that short vasa recta distribution and AVR permeabilities significantly impact concentrating capability. Moreover, we investigated, in the context of the UCM, the functional significance of several aspects of tubular segmentation and heterogeneity: SDL segments in the IS that are likely to be impermeable to water but highly permeable to urea; a prebend segment of SDLs that may be functionally like thick ascending limb (TAL); differing IS and outer stripe Na+ active transport rates in TAL; and potential active urea secretion into the proximal straight tubules. Model calculations predict that these aspects of tubular of segmentation and heterogeneity generally enhance solute cycling or promote effective UCM function.

Genetic restoration of aldose reductase to the collecting tubules restores maturation of the urine concentrating mechanism

2006 ◽  
Vol 291 (1) ◽  
pp. F186-F195 ◽  
Author(s):  
James Y. Yang ◽  
W. Y. Tam ◽  
Sidney Tam ◽  
Hong Guo ◽  
Xiaochun Wu ◽  
...  
Keyword(s):  
Cell Survival ◽  
Aldose Reductase ◽  
Developmental Stages ◽  
Urine Osmolality ◽  
Concentrating Mechanism ◽  
Structural Abnormalities ◽  
Underlying Causes ◽  
Vascular Structures ◽  
Collecting Tubules ◽  
Urine Concentrating Mechanism

To investigate the underlying causes for aldose reductase deficiency-induced diabetes insipidus, we carried out studies with three genotypic groups of mice. These included wild-type mice, knockout mice, and a newly created bitransgenic line that was homozygous for both the aldose reductase null mutation and an aldose reductase knockin transgene driven by the kidney-specific cadherin promoter to direct transgene expression in the collecting tubule epithelial cells. We found that from early renal developmental stages onward, urine osmolality did not exceed 1,000 mosmol/kgH2O in aldose reductase-deficient mice. The functional defects were correlated with significant renal cellular and structural abnormalities that included cell shrinkage, apoptosis, disorganized tubular and vascular structures, and segmental atrophy. In contrast, the transgenic aldose reductase expression in the bitransgenic mice largely but incompletely rescued urine concentrating capacity and significantly improved renal cell survival, cellular morphology, and renal structures. Together, these results suggest that aldose reductase not only plays important roles in osmoregulation and medullary cell survival but may also be essential for the full maturation of the urine concentrating mechanism.

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