scholarly journals A mathematical model of the rat kidney. II. Antidiuresis

2020 ◽  
Vol 318 (4) ◽  
pp. F936-F955
Author(s):  
Alan M. Weinstein
Keyword(s):  
Mathematical Model ◽  
Water Conservation ◽  
Rat Kidney ◽  
Model Parameters ◽  
Reflection Coefficients ◽  
Model Computation ◽  
Outer Medulla ◽  
Nacl Transport ◽  
Solute Flow ◽  
Vasa Recta

Kidney water conservation requires a hypertonic medullary interstitium, NaCl in the outer medulla and NaCl and urea in the inner medulla, plus a vascular configuration that protects against washout. In this work, a multisolute model of the rat kidney is revisited to examine its capacity to simulate antidiuresis. The first step was to streamline model computation by parallelizing its Jacobian calculation, thus allowing finer medullary spatial resolution and more extensive examination of model parameters. It is found that outer medullary NaCl is modestly increased when transporter density in ascending Henle limbs from juxtamedullary nephrons is scaled to match the greater juxtamedullary solute flow. However, higher NaCl transport produces greater CO2 generation and, by virtue of countercurrent vascular flows, establishment of high medullary Pco2. This CO2 gradient can be mitigated by assuming that a fraction of medullary transport is powered anaerobically. Reducing vascular flows or increasing vessel permeabilities does little to further increase outer medullary solute gradients. In contrast to medullary models of others, vessels in this model have solute reflection coefficients close to zero; increasing these coefficients provides little enhancement of solute profiles but does generate high interstitial pressures, which distort tubule architecture. Increasing medullary urea delivery via entering vasa recta increases inner medullary urea, although not nearly to levels found in rats. In summary, 1) medullary Na+ and urea gradients are not captured by the model and 2) the countercurrent architecture that provides antidiuresis also produces exaggerated Pco2 profiles and is an unappreciated constraint on models of medullary function.

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.

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.

Localization of angiotensin II type 1 receptor subtype mRNA in rat kidney

1995 ◽  
Vol 268 (2) ◽  
pp. F220-F226 ◽  
Author(s):  
D. P. Healy ◽  
M. Q. Ye ◽  
M. Troyanovskaya
Keyword(s):  
In Situ Hybridization ◽  
Rat Kidney ◽  
At1 Receptor ◽  
Receptor Subtypes ◽  
Mrna Levels ◽  
Ang Ii ◽  
Outer Medulla ◽  
Vasa Recta

The physiological effects of angiotensin II (ANG II) on the kidney are mediated primarily by the ANG II type 1 (AT1) receptor. Two highly similar AT1 receptor subtypes have been identified in the rat by molecular cloning techniques, namely AT1A and AT1B. The intrarenal localization of the AT1A and AT1B receptor subtypes has not been studied by hybridization methods with subtype-specific receptor probes. Using radiolabeled probes from the 3' noncoding region of the AT1A and AT1B cDNAs, we localized AT1 mRNA in rat kidney by in situ hybridization. Specificity of the 3' noncoding region probes was tested by Northern blot and solution hybridization methods. AT1A mRNA levels were highest in the liver, kidney, and adrenal. In contrast, AT1B mRNA levels were highest in the adrenal and pituitary and low in kidney. Autoradiographic localization of 125I-[Sar1,Ile8]ANG II binding indicated that the highest levels of AT1 receptors were found in glomeruli and vascular elements. In situ hybridization with a nonselective AT1 receptor riboprobe indicated that the highest levels of AT1 mRNA were in the outer medullary vasa recta and cortical glomeruli with additional diffuse labeling of the cortex and outer medulla, consistent with labeling of tubular elements. In contrast, in situ hybridization with the AT1 subtype selective probes revealed that AT1A receptor mRNA was primarily localized to the vasa recta and diffusely to the outer stripe of the outer medulla and the renal cortex.(ABSTRACT TRUNCATED AT 250 WORDS)

scholarly journals Impact of nitric oxide-mediated vasodilation on outer medullary NaCl transport and oxygenation

2012 ◽  
Vol 303 (7) ◽  
pp. F907-F917 ◽  
Author(s):  
Aurélie Edwards ◽  
Anita T. Layton
Keyword(s):  
Nitric Oxide ◽  
Blood Flow ◽  
Supply And Demand ◽  
Vascular Bundles ◽  
Concentration Gradients ◽  
Outer Medulla ◽  
Nacl Transport ◽  
Reciprocal Interactions ◽  
Medullary Blood Flow ◽  
Vasa Recta

The present study aimed to elucidate the reciprocal interactions between oxygen (O2), nitric oxide (NO), and superoxide (O2−) and their effects on vascular and tubular function in the outer medulla. We expanded our region-based model of transport in the rat outer medulla (Edwards A, Layton AT. Am J Physiol Renal Physiol 301: F979–F996, 2011) to incorporate the effects of NO on descending vasa recta (DVR) diameter and blood flow. Our model predicts that the segregation of long DVR in the center of vascular bundles, away from tubular segments, gives rise to large radial NO concentration gradients that in turn result in differential regulation of vasoactivity in short and long DVR. The relative isolation of long DVR shields them from changes in the rate of NaCl reabsorption, and hence from changes in O2 requirements, by medullary thick ascending limbs (mTALs), thereby preserving O2 delivery to the inner medulla. The model also predicts that O2− can sufficiently decrease the bioavailability of NO in the interbundle region to affect the diameter of short DVR, suggesting that the experimentally observed effects of O2− on medullary blood flow may be at least partly mediated by NO. In addition, our results indicate that the tubulovascular cross talk of NO, that is, the diffusion of NO produced by mTAL epithelia toward adjacent DVR, helps to maintain blood flow and O2 supply to the interbundle region even under basal conditions. NO also acts to preserve local O2 availability by inhibiting the rate of active Na+ transport, thereby reducing the O2 requirements of mTALs. The dual regulation by NO of oxygen supply and demand is predicted to significantly attenuate the hypoxic effects of angiotensin II.

scholarly journals A mathematical model of the rat kidney: K+-induced natriuresis

2017 ◽  
Vol 312 (6) ◽  
pp. F925-F950 ◽  
Author(s):  
Alan M. Weinstein
Keyword(s):  
Mathematical Model ◽  
Proximal Tubule ◽  
Blood Vessels ◽  
Collecting Duct ◽  
Rat Kidney ◽  
Reflection Coefficients ◽  
Additional Species ◽  
Connecting Tubule ◽  
Prior Models ◽  
Urine Concentrating Mechanism

A model of the rat nephron (Weinstein. Am J Physiol Renal Physiol 308: F1098–F1118, 2015) has been extended with addition of medullary vasculature. Blood vessels contain solutes from the nephron model, plus additional species from the model of Atherton et al. ( Am J Physiol Renal Fluid Electrolyte Physiol 247: F61–F72, 1984), representing hemoglobin buffering. In contrast to prior models of the urine-concentrating mechanism, reflection coefficients for DVR are near zero. Model unknowns are initial proximal tubule pressures and flows, connecting tubule pressure, and medullary interstitial pressures and concentrations. The model predicts outer medullary (OM) interstitial gradients for Na+, K+, CO2, and [Formula: see text], such that at OM-IM junction, the respective concentrations relative to plasma are 1.2, 3.0, 2.7, and 8.0; within IM, there is high urea and low [Formula: see text], with concentration ratios of 11 and 0.5 near the papillary tip. Quantitative similarities are noted between K+and urea handling (medullary delivery and permeabilities). The model K+gradient is physiologic, and the urea gradient is steeper due to restriction of urea permeability to distal collecting duct. Nevertheless, the predicted urea gradient is less than expected, suggesting reconsideration of proposals of an unrecognized reabsorptive urea flux. When plasma K+is increased from 5.0 to 5.5 mM, Na+and K+excretion increase 2.3- and 1.3-fold, respectively. The natriuresis derives from a 3.3% decrease in proximal Na+reabsorption and occurs despite delivery-driven increases in Na+reabsorption in distal segments; kaliuresis derives from a 30% increase in connecting tubule Na+delivery. Thus this model favors the importance of proximal over distal events in K+-induced diuresis.

AN EFFECT OF ANTIDIURETIC HORMONE ON THE FLOW OF BLOOD THROUGH THE VASA RECTA OF THE RAT KIDNEY

1966 ◽  
Vol 35 (2) ◽  
pp. 173-NP ◽  
Author(s):  
JULIA FOURMAN ◽  
G. C. KENNEDY
Keyword(s):  
Blood Flow ◽  
Diabetes Insipidus ◽  
Antidiuretic Hormone ◽  
Water Conservation ◽  
Rat Kidney ◽  
Renal Medulla ◽  
Countercurrent System ◽  
Vasa Recta ◽  
Collecting Ducts ◽  
Flow Through

SUMMARY The injection of a fluorescent dye which stained the vessel walls showed the pathway taken by the blood in the renal medulla in rats. The vasa recta stained in normal rats given water; they did not stain in dehydrated rats nor did they stain in rats given an antidiuretic dose of vasopressin in addition to water. The vasa recta stained in all rats with diabetes insipidus whether they were given water or dehydrated. These results suggest that antidiuretic hormone increases water conservation in the medulla by reducing blood flow through the countercurrent system as well as by increasing the permeability of the collecting ducts to water.

scholarly journals Countercurrent multiplication may not explain the axial osmolality gradient in the outer medulla of the rat kidney

2011 ◽  
Vol 301 (5) ◽  
pp. F1047-F1056 ◽  
Author(s):  
Anita T. Layton ◽  
Harold E. Layton
Keyword(s):  
Alternative Explanation ◽  
Rat Kidney ◽  
Vascular Bundles ◽  
Outer Medulla ◽  
Anatomic Structure ◽  
Physical Separation ◽  
Nacl Absorption ◽  
Vasa Recta ◽  
Osmotic Water ◽  
Collecting Ducts

It has become widely accepted that the osmolality gradient along the corticomedullary axis of the mammalian outer medulla is generated and sustained by a process of countercurrent multiplication: active NaCl absorption from thick ascending limbs is coupled with the counterflow configuration of the descending and ascending limbs of the loops of Henle to generate an axial osmolality gradient along the outer medulla. However, aspects of anatomic structure (e.g., the physical separation of the descending limbs of short loops of Henle from contiguous ascending limbs), recent physiologic experiments (e.g., those that suggest that the thin descending limbs of short loops of Henle have a low osmotic water permeability), and mathematical modeling studies (e.g., those that predict that water-permeable descending limbs of short loops are not required for the generation of an axial osmolality gradient) suggest that countercurrent multiplication may be an incomplete, or perhaps even erroneous, explanation. We propose an alternative explanation for the axial osmolality gradient: we regard the thick limbs as NaCl sources for the surrounding interstitium, and we hypothesize that the increasing axial osmolality gradient along the outer medulla is primarily sustained by an increasing ratio, as a function of increasing medullary depth, of NaCl absorption (from thick limbs) to water absorption (from thin descending limbs of long loops of Henle and, in antidiuresis, from collecting ducts). We further hypothesize that ascending vasa recta that are external to vascular bundles will carry, toward the cortex, an absorbate that at each medullary level is hyperosmotic relative to the adjacent interstitium.

scholarly journals A mathematical model of O2 transport in the rat outer medulla. I. Model formulation and baseline results

2009 ◽  
Vol 297 (2) ◽  
pp. F517-F536 ◽  
Author(s):  
Jing Chen ◽  
Anita T. Layton ◽  
Aurélie Edwards
Keyword(s):  
Mathematical Model ◽  
Structural Organization ◽  
Capillary Flow ◽  
Renal Medulla ◽  
Vascular Bundles ◽  
Thick Ascending Limb ◽  
Outer Medulla ◽  
Vasa Recta ◽  
Complex Structural ◽  
The Impact

The mammalian kidney is particularly vulnerable to hypoperfusion, because the O2 supply to the renal medulla barely exceeds its O2 requirements. In this study, we examined the impact of the complex structural organization of the rat outer medulla (OM) on O2 distribution. We extended the region-based mathematical model of the rat OM developed by Layton and Layton ( Am J Physiol Renal Physiol 289: F1346–F1366, 2005) to incorporate the transport of RBCs, Hb, and O2. We considered basal cellular O2 consumption and O2 consumption for active transport of NaCl across medullary thick ascending limb epithelia. Our model predicts that the structural organization of the OM results in significant Po2 gradients in the axial and radial directions. The segregation of descending vasa recta, the main supply of O2, at the center and immediate periphery of the vascular bundles gives rise to large radial differences in Po2 between regions, limits O2 reabsorption from long descending vasa recta, and helps preserve O2 delivery to the inner medulla. Under baseline conditions, significantly more O2 is transferred radially between regions by capillary flow, i.e., advection, than by diffusion. In agreement with experimental observations, our results suggest that 79% of the O2 supplied to the medulla is consumed in the OM and that medullary thick ascending limbs operate on the brink of hypoxia.

scholarly journals A mathematical model of O2 transport in the rat outer medulla. II. Impact of outer medullary architecture

2009 ◽  
Vol 297 (2) ◽  
pp. F537-F548 ◽  
Author(s):  
Jing Chen ◽  
Aurélie Edwards ◽  
Anita T. Layton
Keyword(s):  
Mathematical Model ◽  
Anaerobic Metabolism ◽  
Critical Level ◽  
Vascular Bundles ◽  
Outer Medulla ◽  
O2 Transport ◽  
Vasa Recta ◽  
Parameter Variations ◽  
Complex Structural ◽  
The Impact

we extended the region-based mathematical model of the urine-concentrating mechanism in the rat outer medulla (OM) developed by Layton and Layton ( Am J Physiol Renal Physiol 289: F1346–F1366, 2005) to examine the impact of the complex structural organization of the OM on O2 transport and distribution. In the present study, we investigated the sensitivity of predicted Po2 profiles to several parameters that characterize the degree of OM regionalization, boundary conditions, structural dimensions, transmural transport properties, and relative positions and distributions of tubules and vessels. Our results suggest that the fraction of O2 supplied to descending vasa recta (DVR) that reaches the inner medulla, i.e., a measure of the axial Po2 gradient in the OM, is insensitive to parameter variations as a result of the sequestration of long DVR in the vascular bundles. In contrast, O2 distribution among the regions surrounding the vascular core strongly depends on the radial positions of medullary thick ascending limbs (mTALs) relative to the vascular core, the degree of regionalization, and the distribution of short DVR along the corticomedullary axis. Moreover, if it is assumed that the mTAL active Na+ transport rate decreases when mTAL Po2 falls below a critical level, O2 availability to mTALs has a significant impact on the concentrating capability of the model OM. The model also predicts that when the OM undergoes hypertrophy, its concentrating capability increases significantly only when anaerobic metabolism supports a substantial fraction of the mTAL active Na+ transport and is otherwise critically reduced by low interstitial and mTAL luminal Po2 in a hypertrophied OM.

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