Two modes for concentrating urine in rat inner medulla

Sex differences in solute transport along the nephrons: effects of Na+ transport inhibition

Each day, ~1.7 kg of NaCl and 180 liters of water are reabsorbed by nephron segments in humans, with urinary excretion fine tuned to meet homeostatic requirements. These tasks are coordinated by a spectrum of renal Na⁺ transporters and channels. The goal of the present study was to investigate the extent to which inhibitors of transepithelial Na⁺ transport (T_Na) along the nephron alter urinary solute excretion and how those effects may vary between male and female subjects. To accomplish that goal, we developed sex-specific multinephron models that represent detailed transcellular and paracellular transport processes along the nephrons of male and female rat kidneys. We simulated inhibition of Na⁺/H⁺ exchanger 3 (NHE3), bumetanide-sensitive Na⁺-K⁺-2Cl^- cotransporter (NKCC2), Na⁺-Cl^- cotransporter (NCC), and amiloride-sensitive epithelial Na⁺ channel (ENaC). NHE3 inhibition simulations predicted a substantially reduced proximal tubule T_Na, and NKCC2 inhibition substantially reduced thick ascending limb T_Na. Both gave rise to diuresis, natriuresis, and kaliuresis, with those effects stronger in female rats. While NCC inhibition was predicted to have only minor impact on renal T_Na, it nonetheless had a notable effect of enhancing excretion of Na⁺, K⁺, and Cl^-, particularly in female rats. Inhibition of ENaC was predicted to have opposite effects on the excretion of Na⁺ (increased) and K⁺ (decreased) and to have only a minor impact on whole kidney T_Na. Unlike inhibition of other transporters, ENaC inhibition induced stronger natriuresis and diuresis in male rats than female rats. Overall, model predictions agreed well with measured changes in Na⁺ and K⁺ excretion in response to diuretics and Na⁺ transporter mutations.

Solute and water transport along an inner medullary collecting duct undergoing peristaltic contractions

The mechanism by which solutes accumulate in the inner medulla of the mammalian kidney has remained incompletely understood. That persistent mystery has led to hypotheses based on the peristaltic contractions of the pelvic wall smooth muscles. It has been demonstrated the peristaltic contractions propel fluid down the collecting duct in boluses. In antidiuresis, boluses are sufficiently short that collecting ducts may be collapsed most of the time. In this study, we investigated the mechanism by which about half of the bolus volume is reabsorbed into the collecting duct cells despite the short contact time. To accomplish this, we developed a dynamic mathematical model of solute and water transport along a collecting duct of a rat papilla undergoing peristaltic contractions. The model predicts that, given preexisting axial concentration gradients along the loops of Henle, ∼40% of the bolus volume is reabsorbed as the bolus flows down the inner medullary collecting duct. Additionally, simulation results suggest that while the contraction-induced luminal hydrostatic pressure facilitates water extraction from the bolus, that pressure is not necessary to concentrate the bolus. Also, neither the negative interstitial pressure generated during the relaxation phase nor the concentrating effect of hyaluronic acid has a significant effect on bolus concentration. Taken together, these findings indicate that the high collecting duct apical water permeability allows a substantial amount of water to be extracted from the bolus, despite its short transit time. However, the potential role of the peristaltic waves in the urine-concentrating mechanism remains to be revealed.

3D simulation of solutes concentration in urinary concentration mechanism in rat renal medulla

In this work, a mathematical model was developed to simulate the urinary concentration mechanism. A 3-D geometry was derived based on the detail physiological pictures of rat kidney. The approximate region of each tubule was obtained from the volume distribution of structures based on Walter Pfaller's monograph and Layton's region-based model. Mass and momentum balances were applied to solve for the change in solutes concentration and osmolality. The osmolality of short and long descending nephrons at the end of the outer medulla was obtained to be 530 mOsmol/kgH2O and 802 mOsmol/kgH2O, respectively, which were in acceptable agreement with experimental data. The fluid osmolality of the short and long ascending nephrons was also compatible with experimental data. The osmolality of CD fluid at the end of the inner medulla was determined to be 1198 mOsmol/kgH2O which was close the experimental data (1216 ± 118). Finally, the impact of the position of each tubule on the fluid osmolality and solutes concentration were obvious in the results; for example, short descending limb a1, which is the closest tubule to the collecting duct, had the highest urea concentration in all tubules. This reflects the important effect of the 3D modeling on the precise analysis of urinary concentration mechanism.

Mammalian urine concentration: a review of renal medullary architecture and membrane transporters

Mammalian kidneys play an essential role in balancing internal water and salt concentrations. When water needs to be conserved, the renal medulla produces concentrated urine. Central to this process of urine concentration is an osmotic gradient that increases from the corticomedullary boundary to the inner medullary tip. How this gradient is generated and maintained has been the subject of study since the 1940s. While it is generally accepted that the outer medulla contributes to the gradient by means of an active process involving countercurrent multiplication, the source of the gradient in the inner medulla is unclear. The last two decades have witnessed advances in our understanding of the urine-concentrating mechanism. Details of medullary architecture and permeability properties of the tubules and vessels suggest that the functional and anatomic relationships of these structures may contribute to the osmotic gradient necessary to concentrate urine. Additionally, we are learning more about the membrane transporters involved and their regulatory mechanisms. The role of medullary architecture and membrane transporters in the mammalian urine-concentrating mechanism are the focus of this review.

Architecture-Guided Fluid Flow Directs Renal Biomineralization

Nephrocalcinosis often begins on a calcium phosphate deposit, at the tip of the medullo-papillary complex (MPC) known as Randall’s plaque (RP). Contextualizing proximally observed biominerals within the MPC has led us to postulate a mechanobiological switch that can trigger interstitial biomineralization at the MPC tip, remote from the intratubular biominerals. Micro X-ray computed tomography scans of human MPCs correlated with transmission and scanning electron micrographs, and X-ray energy dispersive spectrometry demonstrated novel findings about anatomically-specific biominerals. An abundance of proximal intratubular biominerals were associated with emergence of distal interstitial RP. The fundamental architecture of the MPC and mineral densities at the proximal and distal locations of the MPC differed markedly. A predominance of plate-like minerals or radially oriented plate-like crystallites within spheroidal minerals in the proximal intratubular locations, and core-shell type crystallites within spheroidal minerals in distal interstitial locations were observed. Based on the MPC anatomic location of structure-specific biominerals, a biological switch within the mineral-free zone occurring between the proximal and distal locations is postulated. The “on” and “off” switch is dependent on changes in the pressure differential resulting from changes in tubule diameters; the “Venturi effect” changes the “circumferential strain” and culminates in interstitial crystal deposits in the distal tubule wall in response to proximal tubular obstruction. These distal interstitial mineralizations can emerge into the collecting system of the kidney linking nephrocalcinosis with nephrolithiasis.

Descending thin limb of the intermediate loop expresses both aquaporin 1 and urea transporter A2 in the mouse kidney

A new intermediate type of Henle's loop has been reported that it extends into the inner medulla and turns within the first millimeter beyond the outer medulla. This study aimed to identify the descending thin limb (DTL) of the intermediate loop in the adult C57Bl/6 mouse kidney using aquaporin 1 (AQP1) and urea transporter A2 (UT-A2) antibodies. In the upper part of the inner stripe of the outer medulla (ISOM), AQP1 was expressed strongly in the DTL with type II epithelium of the long loop, but not in type I epithelium of the short loop. The DTL of the intermediate loop exhibited weak AQP1 immunoreactivity. UT-A2 immunoreactivity was not observed in the upper part of any DTL type. AQP1 expression was similar in the upper and middle parts of the ISOM. UT-A2 expression was variable, being expressed strongly in the DTL with type I epithelium of the short loop, but not in type II epithelium of the long loop. In the innermost part of the ISOM, AQP1 was expressed only in type III epithelium of the long loop. UT-A2-positive and UT-A2-negative cells were intermingled in type I epithelium of the intermediate loop, but were not observed in type III epithelium of the long loop. UT-A2-positive DTLs of the intermediate loop extended into the UT-A2/AQP1-negative type I epithelium in the initial part of the inner medulla. These results demonstrate that the DTL of the intermediate loop is composed of type I epithelium and expresses both AQP1 and UT-A2. The functional role of the DTL of the intermediate loop may be distinct from the short or long loops.

Aquaporins in desert rodent physiology

Desert rodents face a sizeable challenge in maintaining salt and water homeostasis due to their life in an arid environment. A number of their organ systems exhibit functional characteristics that limit water loss above that which occurs in non-desert species under similar conditions. These systems include renal, pulmonary, gastrointestinal, nasal, and skin epithelia. The desert rodent kidney preserves body water by producing a highly concentrated urine that reaches a maximum osmolality nearly three times that of the common laboratory rat. The precise mechanism by which urine is concentrated in any mammal is unknown. Insights into the process may be more apparent in species that produce highly concentrated urine. Aquaporin water channels play a fundamental role in water transport in several desert rodent organ systems. The role of aquaporins in facilitating highly effective water preservation in desert rodents is only beginning to be explored. The organ systems of desert rodents and their associated AQPs are described.

Urine-concentrating mechanism in the inner medulla: function of the thin limbs of the loops of Henle

The ability of mammals to produce urine hyperosmotic to plasma requires the generation of a gradient of increasing osmolality along the medulla from the corticomedullary junction to the papilla tip. Countercurrent multiplication apparently establishes this gradient in the outer medulla, where there is substantial transepithelial reabsorption of NaCl from the water-impermeable thick ascending limbs of the loops of Henle. However, this process does not establish the much steeper osmotic gradient in the inner medulla, where there are no thick ascending limbs of the loops of Henle and the water-impermeable ascending thin limbs lack active transepithelial transport of NaCl or any other solute. The mechanism generating the osmotic gradient in the inner medulla remains an unsolved mystery, although it is generally considered to involve countercurrent flows in the tubules and vessels. A possible role for the three-dimensional interactions between these inner medullary tubules and vessels in the concentrating process is suggested by creation of physiologic models that depict the three-dimensional relationships of tubules and vessels and their solute and water permeabilities in rat kidneys and by creation of mathematical models based on biologic phenomena. The current mathematical model, which incorporates experimentally determined or estimated solute and water flows through clearly defined tubular and interstitial compartments, predicts a urine osmolality in good agreement with that observed in moderately antidiuretic rats. The current model provides substantially better predictions than previous models; however, the current model still fails to predict urine osmolalities of maximally concentrating rats.

Oxygen transport in a cross section of the rat inner medulla: impact of heterogeneous distribution of nephrons and vessels

We have developed a highly detailed mathematical model of oxygen transport in a cross section of the upper inner medulla of the rat kidney. The model is used to study the impact of the structured organization of nephrons and vessels revealed in anatomic studies, in which descending vasa recta are found to lie distant from clusters of collecting ducts. Specifically, we formulated a two-dimensional oxygen transport model, in which the positions and physical dimensions of renal tubules and vessels are based on an image obtained by immunochemical techniques (T. Pannabecker and W. Dantzler, Three-dimensional architecture of inner medullary vasa recta, Am. J. Physiol. Renal Physiol. 290 (2006) F1355-F1366). The model represents oxygen diffusion through interstitium and other renal structures, oxygen consumption by the Na(+)/K(+)-ATPase activities of the collecting ducts, and basal metabolic consumption. Model simulations yield marked variations in interstitial PO2, which can be attributed, in large part, to the heterogeneities in the position and physical dimensions of the collecting ducts. Further, results of a sensitivity study suggest that medullary oxygenation is highly sensitive to medullary blood flow, and that, at high active consumption rates, localized patches of tissue may be vulnerable to hypoxic injury.

Advances in Understanding the Urine-Concentrating Mechanism

The renal medulla produces concentrated urine through the generation of an osmotic gradient that progressively increases from the cortico-medullary boundary to the inner medullary tip. In the outer medulla, the osmolality gradient arises principally from vigorous active transport of NaCl, without accompanying water, from the thick ascending limbs of short- and long-looped nephrons. In the inner medulla, the source of the osmotic gradient has not been identified. Recently, there have been important advances in our understanding of key components of the urine-concentrating mechanism, including (a) better understanding of the regulation of water, urea, and sodium transport proteins; (b) better resolution of the anatomical relationships in the medulla; and (c) improvements in mathematical modeling of the urine-concentrating mechanism. Continued experimental investigation of signaling pathways regulating transepithelial transport, both in normal animals and in knockout mice, and incorporation of the resulting information into mathematical simulations may help to more fully elucidate the mechanism for concentrating urine in the inner medulla.

Structure and function of the thin limbs of the loop of Henle

The thin limbs of the loop of Henle, which comprise the intermediate segment, connect the proximal tubule to the distal tubule and lie entirely within the renal medulla. The descending thin limb consists of at least two or three morphologically and functionally distinct subsegments and participates in transepithelial transport of NaCl, urea, and water. Only one functionally distinct segment is recognized for the ascending thin limb, which carries out transepithelial transport of NaCl and urea in the reabsorptive and/or secretory directions. Membrane transporters involved with passive transcellular Cl, urea, and water fluxes have been characterized for thin limbs; however, these pathways do not account for all transepithelial fluid and solute fluxes that have been measured in vivo. The paracellular pathway has been proposed to play an important role in transepithelial Na and urea fluxes in defined thin-limb subsegments. As the transport pathways become clearer, the overall function of the thin limbs is becoming better understood. Primary and secondary signaling pathways and protein-protein interactions are increasingly recognized as important modulators of thin-limb cell function and cell metabolism. These functions must be investigated under diverse extracellular conditions, particularly for those cells of the deep inner medulla that function in an environment of wide variation in hyperosmolality. Transgenic mouse models of several key water and solute transport proteins have provided significant insights into thin-limb function. An understanding of the overall architecture of the medulla, including juxtapositions of thin limbs with collecting ducts, thick ascending limbs, and vasa recta, is essential for understanding the role of the kidney in maintaining Na and water homeostasis, and for understanding the urine concentrating mechanism.

Transepithelial water and urea permeabilities of isolated perfused Munich-Wistar rat inner medullary thin limbs of Henle's loop

To better understand the role that water and urea fluxes play in the urine concentrating mechanism, we determined transepithelial osmotic water permeability (Pf) and urea permeability (Purea) in isolated perfused Munich-Wistar rat long-loop descending thin limbs (DTLs) and ascending thin limbs (ATLs). Thin limbs were isolated either from 0.5 to 2.5 mm below the outer medulla (upper inner medulla) or from the terminal 2.5 mm of the inner medulla. Segment types were characterized on the basis of structural features and gene expression levels of the water channel aquaporin 1, which was high in the upper DTL (DTLupper), absent in the lower DTL (DTLlower), and absent in ATLs, and the Cl-(1) channel ClCK1, which was absent in DTLs and high in ATLs. DTLupper Pf was high (3,204.5 ± 450.3 μm/s), whereas DTLlower showed very little or no osmotic Pf (207.8 ± 241.3 μm/s). Munich-Wistar rat ATLs have previously been shown to exhibit no Pf. DTLupper Purea was 40.0 ± 7.3 × 10(-5) cm/s and much higher in DTLlower (203.8 ± 30.3 × 10(-5) cm/s), upper ATL (203.8 ± 35.7 × 10(-5) cm/s), and lower ATL (265.1 ± 49.8 × 10(-5) cm/s). Phloretin (0.25 mM) did not reduce DTLupper Purea, suggesting that Purea is not due to urea transporter UT-A2, which is expressed in short-loop DTLs and short portions of some inner medullary DTLs close to the outer medulla. In summary, Purea is similar in all segments having no osmotic Pf but is significantly lower in DTLupper, a segment having high osmotic Pf. These data are inconsistent with the passive mechanism as originally proposed.

Hormonal regulation of salt and water excretion: a mathematical model of whole kidney function and pressure natriuresis

We present a lumped-nephron model that explicitly represents the main features of the underlying physiology, incorporating the major hormonal regulatory effects on both tubular and vascular function, and that accurately simulates hormonal regulation of renal salt and water excretion. This is the first model to explicitly couple glomerulovascular and medullary dynamics, and it is much more detailed in structure than existing whole organ models and renal portions of multiorgan models. In contrast to previous medullary models, which have only considered the antidiuretic state, our model is able to regulate water and sodium excretion over a variety of experimental conditions in good agreement with data from experimental studies of the rat. Since the properties of the vasculature and epithelia are explicitly represented, they can be altered to simulate pathophysiological conditions and pharmacological interventions. The model serves as an appropriate starting point for simulations of physiological, pathophysiological, and pharmacological renal conditions and for exploring the relationship between the extrarenal environment and renal excretory function in physiological and pathophysiological contexts.

Mathematical modeling of kidney transport

In addition to metabolic waste and toxin excretion, the kidney also plays an indispensable role in regulating the balance of water, electrolytes, nitrogen, and acid-base. In this review, we describe representative mathematical models that have been developed to better understand kidney physiology and pathophysiology, including the regulation of glomerular filtration, the regulation of renal blood flow by means of the tubuloglomerular feedback mechanisms and of the myogenic mechanism, the urine concentrating mechanism, epithelial transport, and regulation of renal oxygen transport. We discuss the extent to which these modeling efforts have expanded our understanding of renal function in both health and disease.

Comparative physiology and architecture associated with the mammalian urine concentrating mechanism: role of inner medullary water and urea transport pathways in the rodent medulla

Comparative studies of renal structure and function have potential to provide insights into the urine-concentrating mechanism of the mammalian kidney. This review focuses on the tubular transport pathways for water and urea that play key roles in fluid and solute movements between various compartments of the rodent renal inner medulla. Information on aquaporin water channel and urea transporter expression has increased our understanding of functional segmentation of medullary thin limbs of Henle's loops, collecting ducts, and vasa recta. A more complete understanding of membrane transporters and medullary architecture has identified new and potentially significant interactions between these structures and the interstitium. These interactions are now being introduced into our concept of how the inner medullary urine-concentrating mechanism works. A variety of regulatory pathways lead directly or indirectly to variable patterns of fluid and solute movements among the interstitial and tissue compartments. Animals with the ability to produce highly concentrated urine, such as desert species, are considered to exemplify tubular structure and function that optimize urine concentration. These species may provide unique insights into the urine-concentrating process.(1)

Development of a physiologically based computational kidney model to describe the renal excretion of hydrophilic agents in rats

A physiologically based kidney model was developed to analyze the renal excretion and kidney exposure of hydrophilic agents, in particular contrast media, in rats. In order to study the influence of osmolality and viscosity changes, the model mechanistically represents urine concentration by water reabsorption in different segments of kidney tubules and viscosity dependent tubular fluid flow. The model was established using experimental data on the physiological steady state without administration of any contrast media or drugs. These data included the sodium and urea concentration gradient along the cortico-medullary axis, water reabsorption, urine flow, and sodium as well as urea urine concentrations for a normal hydration state. The model was evaluated by predicting the effects of mannitol and contrast media administration and comparing to experimental data on cortico-medullary concentration gradients, urine flow, urine viscosity, hydrostatic tubular pressures and single nephron glomerular filtration rate. Finally the model was used to analyze and compare typical examples of ionic and non-ionic monomeric as well as non-ionic dimeric contrast media with respect to their osmolality and viscosity. With the computational kidney model, urine flow depended mainly on osmolality, while osmolality and viscosity were important determinants for tubular hydrostatic pressure and kidney exposure. The low diuretic effect of dimeric contrast media in combination with their high intrinsic viscosity resulted in a high viscosity within the tubular fluid. In comparison to monomeric contrast media, this led to a higher increase in tubular pressure, to a reduction in glomerular filtration rate and tubular flow and to an increase in kidney exposure. The presented kidney model can be implemented into whole body physiologically based pharmacokinetic models and extended in order to simulate the renal excretion of lipophilic drugs which may also undergo active secretion and reabsorption.

Low-salt diet and cyclosporine nephrotoxicity: changes in kidney cell metabolism

Cyclosporine (CsA) is a highly effective immunosuppressant used in patients after transplantation; however, its use is limited by nephrotoxicity. Salt depletion is known to enhance CsA-induced nephrotoxicity in the rat, but the underlying molecular mechanisms are not completely understood. The goal of our study was to identify the molecular effects of salt depletion alone and in combination with CsA on the kidney using a proteo-metabolomic strategy. Rats (n = 6) were assigned to four study groups: (1) normal controls, (2) low-salt fed controls, (3) 10 mg/kg/d CsA for 28 days on a normal diet, (4) 10 mg/kg/d CsA for 28 days on low-salt diet. Low-salt diet redirected kidney energy metabolism toward mitochondria as indicated by a higher energy charge than in normal-fed controls. Low-salt diet alone reduced phospho-AKT and phospho-STAT3 levels and changed the expression of ion transporters PDZK1 and CLIC1. CsA induced macro- and microvesicular tubular epithelial vacuolization and reduced energy charge, changes that were more significant in low-salt fed animals, probably because of their more pronounced dependence on mitochondria. Here, CsA increased phospho-JAK2 and phospho-STAT3 levels and reduced the phospho-IKKγ and p65 proteins, thus activating NF-κB signaling. Decreased expression of lactate transport regulator CD147 and phospho-AKT was also observed after CsA exposure in low-salt rats, indicating a decrease in glycolysis. In summary, our study suggests a key role for PDZK1, CD147, JAK/STAT, and AKT signaling in CsA-induced nephrotoxicity and proposes mechanistic explanations on why rats fed a low-salt diet have higher sensitivity to CsA.

Architecture of vasa recta in the renal inner medulla of the desert rodent Dipodomys merriami: potential impact on the urine concentrating mechanism

We hypothesize that the inner medulla of the kangaroo rat Dipodomys merriami, a desert rodent that concentrates its urine to over 6,000 mosmol/kg H(2)O, provides unique examples of architectural features necessary for production of highly concentrated urine. To investigate this architecture, inner medullary vascular segments in the outer inner medulla were assessed with immunofluorescence and digital reconstructions from tissue sections. Descending vasa recta (DVR) expressing the urea transporter UT-B and the water channel aquaporin 1 lie at the periphery of groups of collecting ducts (CDs) that coalesce in their descent through the inner medulla. Ascending vasa recta (AVR) lie inside and outside groups of CDs. DVR peel away from vascular bundles at a uniform rate as they descend the inner medulla, and feed into networks of AVR that are associated with organized clusters of CDs. These AVR form interstitial nodal spaces, with each space composed of a single CD, two AVR, and one or more ascending thin limbs or prebend segments, an architecture that may lead to solute compartmentation and fluid fluxes essential to the urine concentrating mechanism. Although we have identified several apparent differences, the tubulovascular architecture of the kangaroo rat inner medulla is remarkably similar to that of the Munich Wistar rat at the level of our analyses. More detailed studies are required for identifying interspecies functional differences.

Modeling Transport and Flow Regulatory Mechanisms of the Kidney

The kidney plays an indispensable role in the regulation of whole-organism water balance, electrolyte balance, and acid-base balance, and in the excretion of metabolic wastes and toxins. In this paper, we review representative mathematical models that have been developed to better understand kidney physiology and pathophysiology, including the regulation of glomerular filtration, the regulation of renal blood flow by means of the tubuloglomerular feedback mechanisms and of the myogenic mechanism, the urine concentrating mechanism, and regulation of renal oxygen transport. We discuss how such modeling efforts have significantly expanded our understanding of renal function in both health and disease.

Effects of sodium diclofenac on the concentration function in animals with different neurohypophyseal status

The characteristics of the osmotic concentration system under conditions of sodium diclofenac treatment were studied in Wistar rats with normally functioning vasopressin gene and homozygotic Brattleboro rats completely lacking endogenous vasopressin. Blockade of prostaglandin synthesis in rats with different neurohypophyseal status stimulated urinary osmolality to a different degree. Different contribution of sodium cations and urea to osmotic concentration was revealed.

Mechanisms of pressure-diuresis and pressure-natriuresis in Dahl salt-resistant and Dahl salt-sensitive rats

Background

Data on blood flow regulation, renal filtration, and urine output in salt-sensitive Dahl S rats fed on high-salt (hypertensive) and low-salt (prehypertensive) diets and salt-resistant Dahl R rats fed on high-salt diets were analyzed using a mathematical model of renal blood flow regulation, glomerular filtration, and solute transport in a nephron.

Results

The mechanism of pressure-diuresis and pressure-natriuresis that emerges from simulation of the integrated systems is that relatively small increases in glomerular filtration that follow from increases in renal arterial pressure cause relatively large increases in urine and sodium output. Furthermore, analysis reveals the minimal differences between the experimental cases necessary to explain the observed data. It is determined that differences in renal afferent and efferent arterial resistances are able to explain all of the qualitative differences in observed flows, filtration rates, and glomerular pressure as well as the differences in the pressure-natriuresis and pressure-diuresis relationships in the three groups. The model is able to satisfactorily explain data from all three groups without varying parameters associated with glomerular filtration or solute transport in the nephron component of the model.

Conclusions

Thus the differences between the experimental groups are explained solely in terms of difference in blood flow regulation. This finding is consistent with the hypothesis that, if a shift in the pressure-natriuresis relationship is the primary cause of elevated arterial pressure in the Dahl S rat, then alternation in how renal afferent and efferent arterial resistances are regulated represents the primary cause of chronic hypertension in the Dahl S rat.

Architecture of kangaroo rat inner medulla: segmentation of descending thin limb of Henle's loop

We hypothesize that the inner medulla of the kangaroo rat Dipodomys merriami, a desert rodent that concentrates its urine to more than 6,000 mosmol/kgH(2)O water, provides unique examples of architectural features necessary for production of highly concentrated urine. To investigate this architecture, inner medullary nephron segments in the initial 3,000 μm below the outer medulla were assessed with digital reconstructions from physical tissue sections. Descending thin limbs of Henle (DTLs), ascending thin limbs of Henle (ATLs), and collecting ducts (CDs) were identified by immunofluorescence using antibodies that label segment-specific proteins associated with transepithelial water flux (aquaporin 1 and 2, AQP1 and AQP2) and chloride flux (the chloride channel ClC-K1); all tubules and vessels were labeled with wheat germ agglutinin. In the outer 3,000 μm of the inner medulla, AQP1-positive DTLs lie at the periphery of groups of CDs. ATLs lie inside and outside the groups of CDs. Immunohistochemistry and reconstructions of loops that form their bends in the outer 3,000 μm of the inner medulla show that, relative to loop length, the AQP1-positive segment of the kangaroo rat is significantly longer than that of the Munich-Wistar rat. The length of ClC-K1 expression in the prebend region at the terminal end of the descending side of the loop in kangaroo rat is about 50% shorter than that of the Munich-Wistar rat. Tubular fluid of the kangaroo rat DTL may approach osmotic equilibrium with interstitial fluid by water reabsorption along a relatively longer tubule length, compared with Munich-Wistar rat. A relatively shorter-length prebend segment may promote a steeper reabsorptive driving force at the loop bend. These structural features predict functionality that is potentially significant in the production of a high urine osmolality in the kangaroo rat.

A METHODOLOGY FOR TRACKING SOLUTE DISTRIBUTION IN A MATHEMATICAL MODEL OF THE KIDNEY

The goal of this study is to develop a methodology for tracking the distribution of filtered solute in mathematical models of the urine concentrating mechanism. Investigation of intrarenal solute distribution, and its cycling by way of countercurrent exchange and preferential tubular interactions, may yield new insights into fundamental principles of concentrating mechanism function. Our method is implemented in a dynamic formulation of a central core model that represents renal tubules in both the cortex and the medulla. Axial solute diffusion is represented in intratubular flows and in the central core. By representing the fate of solute originally belonging to a marked bolus, we obtain the distribution of that solute as a function of time. In addition, we characterize the residence time of that solute by computing the portion of that solute remaining in the model system as a function of time. Because precise mass conservation is of particular importance in solute tracking, our numerical approach is based on the second-order Godunov method, which, by construction, is mass-conserving and accurately represents steep gradients and discontinuities in solute concentrations and tubular properties.

Urine concentrating mechanism in the inner medulla of the mammalian kidney: role of three-dimensional architecture

The urine concentrating mechanism in the mammalian renal inner medulla (IM) is not understood, although it is generally considered to involve countercurrent flows in tubules and blood vessels. A possible role for the three-dimensional relationships of these tubules and vessels in the concentrating process is suggested by recent reconstructions from serial sections labelled with antibodies to tubular and vascular proteins and mathematical models based on these studies. The reconstructions revealed that the lower 60% of each descending thin limb (DTL) of Henle's loops lacks water channels (aquaporin-1) and osmotic water permeability and ascending thin limbs (ATLs) begin with a prebend segment of constant length. In the outer zone of the IM (i) clusters of coalescing collecting ducts (CDs) form organizing motif for loops of Henle and vasa recta; (ii) DTLs and descending vasa recta (DVR) are arrayed outside CD clusters, whereas ATLs and ascending vasa recta (AVR) are uniformly distributed inside and outside clusters; (iii) within CD clusters, interstitial nodal spaces are formed by a CD on one side, AVR on two sides, and an ATL on the fourth side. These spaces may function as mixing chambers for urea from CDs and NaCl from ATLs. In the inner zone of the IM, cluster organization disappears and half of Henle's loops have broad lateral bends wrapped around terminal CDs. Mathematical models based on these findings and involving solute mixing in the interstitial spaces can produce urine slightly more concentrated than that of a moderately antidiuretic rat but no higher.

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

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

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.

Maximum urine concentrating capability in a mathematical model of the inner medulla of the rat kidney

In a mathematical model of the urine concentrating mechanism of the inner medulla of the rat kidney, a nonlinear optimization technique was used to estimate parameter sets that maximize the urine-to-plasma osmolality ratio (U/P) while maintaining the urine flow rate within a plausible physiologic range. The model, which used a central core formulation, represented loops of Henle turning at all levels of the inner medulla and a composite collecting duct (CD). The parameters varied were: water flow and urea concentration in tubular fluid entering the descending thin limbs and the composite CD at the outer-inner medullary boundary; scaling factors for the number of loops of Henle and CDs as a function of medullary depth; location and increase rate of the urea permeability profile along the CD; and a scaling factor for the maximum rate of NaCl transport from the CD. The optimization algorithm sought to maximize a quantity E that equaled U/P minus a penalty function for insufficient urine flow. Maxima of E were sought by changing parameter values in the direction in parameter space in which E increased. The algorithm attained a maximum E that increased urine osmolality and inner medullary concentrating capability by 37.5% and 80.2%, respectively, above base-case values; the corresponding urine flow rate and the concentrations of NaCl and urea were all within or near reported experimental ranges. Our results predict that urine osmolality is particularly sensitive to three parameters: the urea concentration in tubular fluid entering the CD at the outer-inner medullary boundary, the location and increase rate of the urea permeability profile along the CD, and the rate of decrease of the CD population (and thus of CD surface area) along the cortico-medullary axis.

Architecture of inner medullary descending and ascending vasa recta: pathways for countercurrent exchange

Pathways and densities of descending vasa recta (DVR) and ascending vasa recta (AVR) in the outer zone of the inner medulla (IM) were evaluated to better understand medullary countercurrent exchange. Nearly all urea transporter B (UT-B)-positive DVR, those vessels exhibiting a continuous endothelium, descend with little or no branching exclusively through the intercluster region. All DVR have a terminal fenestrated (PV-1-positive) segment that partially overlaps with the UT-B-positive segment. This fenestrated segment descends a distance equal to approximately 15% of the length of the connecting UT-B-positive segment before formation of the first branch. The onset of branching is indicative of vessel entry into the intracluster region. The number density of UT-B-positive DVR at 3,000 mum below the OM-IM boundary is approximately 60% lower than the density at 400 mum below the OM-IM boundary, a result of DVR joining to fenestrated interconnecting vessels and an overall decline in UT-B expression. AVR that lie in the intercluster region (designated AVR(2)) lie distant from CDs and ascend to the OM-IM boundary with little or no branching. AVR(2a) represent a subcategory of AVR(2) that abut DVR. The mean DVR length (combined UT-B- and PV-1-positive segments) nearly equals the mean AVR(2a) length, implying a degree of overall equivalence in fluid and solute countercurrent exchange may exist. The AVR(2)/DVR ratio is approximately 2:1, and the AVR(2a)/DVR ratio is approximately 1:1; however, the AVR/DVR ratio determined for the full complement of fenestrated vessels is approximately 4:1. The excess fenestrated vessels include vessels of the intracluster region (designated AVR(1)). Countercurrent exchange between vasa recta occurs predominantly in the intercluster region. This architecture supports previous functional estimates of capillary fluid uptake in the renal IM.

Two-compartment model of inner medullary vasculature supports dual modes of vasopressin-regulated inner medullary blood flow

The outer zone of the renal inner medulla (IM) is spatially partitioned into two distinct interstitial compartments in the transverse dimension. In one compartment (the intercluster region), collecting ducts (CDs) are absent and vascular bundles are present. Ascending vasa recta (AVR) that lie within and ascend through the intercluster region (intercluster AVR are designated AVR(2)) participate with descending vasa recta (DVR) in classic countercurrent exchange. Direct evidence from former studies suggests that vasopressin binds to V1 receptors on smooth muscle-like pericytes that regulate vessel diameter and blood flow rate in DVR in this compartment. In a second transverse compartment (the intracluster region), DVR are absent and CDs and AVR are present. Many AVR of the intracluster compartment exhibit multiple branching, with formation of many short interconnecting segments (intracluster AVR are designated AVR(1)). AVR(1) are linked together and connect intercluster DVR to AVR(2) by way of sparse networks. Vasopressin V2 receptors regulate multiple fluid and solute transport pathways in CDs in the intracluster compartment. Reabsorbate from IMCDs, ascending thin limbs, and prebend segments passes into AVR(1) and is conveyed either upward toward DVR and AVR(2) of the intercluster region, or is retained within the intracluster region and is conveyed toward higher levels of the intracluster region. Thus variable rates of fluid reabsorption by CDs potentially lead to variable blood flow rates in either compartment. Net flow between the two transverse compartments would be dependent on the degree of structural and functional coupling between intracluster vessels and intercluster vessels. In the outermost IM, AVR(1) pass directly from the IM to the outer medulla, bypassing vascular bundles, the primary blood outflow route. Therefore, two defined vascular pathways exist for fluid outflow from the IM. Compartmental partitioning of V1 and V2 receptors may underlie vasopressin-regulated functional compartmentation of IM blood flow.

Functional implications of the three-dimensional architecture of the rat renal inner medulla

A new, region-based mathematical model of the urine concentrating mechanism of the rat renal inner medulla (IM) was used to investigate the significance of transport and structural properties revealed in recent studies that employed immunohistochemical methods combined with three-dimensional computerized reconstruction. The model simulates preferential interactions among tubules and vessels by representing two concentric regions. The inner region, which represents a collecting duct (CD) cluster, contains CDs, some ascending thin limbs (ATLs), and some ascending vasa recta; the outer region, which represents the intercluster region, contains descending thin limbs, descending vasa recta, remaining ATLs, and additional ascending vasa recta. In the upper portion of the IM, the model predicts that interstitial Na(+) and urea concentrations (and osmolality) in the CD clusters differ significantly from those in the intercluster regions: model calculations predict that those CD clusters have higher urea concentrations than the intercluster regions, a finding that is consistent with a concentrating mechanism that depends principally on the mixing of NaCl from ATLs and urea from CDs. In the lower IM, the model predicts that limited or nearly zero water permeability in descending thin limb segments will increase concentrating effectiveness by increasing the rate of solute-free water absorption. The model predicts that high urea permeabilities in the upper portions of ATLs and increased contact areas of longest loop bends with CDs both modestly increase concentrating capability. A surprising finding is that the concentrating capability of this region-based model falls short of the capability of a model IM that has radially homogeneous interstitial fluid at each level but is otherwise analogous to the region-based model.

Hyperfiltration and inner stripe hypertrophy may explain findings by Gamble and coworkers

Simulations conducted in a mathematical model were used to exemplify the hypothesis that elevated solute concentrations and tubular flows at the boundary of the renal outer and inner medullas of rats may contribute to increased urine osmolalities and urine flow rates. Such elevated quantities at that boundary may arise from hyperfiltration and from inner stripe hypertrophy, which are correlated with increased concentrating activity (Bankir L, Kriz W. Kidney Int. 47: 7-24, 1995). The simulations used the region-based model for the rat inner medulla that was presented in the companion study (Layton AT, Pannabecker TL, Dantzler WH, Layton HE. Am J Physiol Renal Physiol 298: F000-F000, 2010). The simulations were suggested by experiments which were conducted in rat by Gamble et al. (Gamble JL, McKhann CF, Butler AM, Tuthill E. Am J Physiol 109: 139-154, 1934) in which the ratio of NaCl to urea in the diet was systematically varied in eight successive 5-day intervals. The simulations predict that changes in boundary conditions at the boundary of the outer and inner medulla, accompanied by plausible modifications in transport properties of the collecting duct system, can significantly increase urine osmolality and flow rate. This hyperfiltration-hypertrophy hypothesis may explain the finding by Gamble et al. that the maximum urine osmolality attained from supplemental feeding of urea and NaCl in the eight intervals depends on NaCl being the initial predominant solute and on urea being the final predominant solute, because urea in sufficient quantity appears to stimulate concentrating activity. More generally, the hypothesis suggests that high osmolalities and urine flow rates may depend, in large part, on adaptive modifications of cortical hemodynamics and on outer medullary structure and not entirely on an extraordinary concentrating capability that is intrinsic to the inner medulla.

Modeling transport in the kidney: investigating function and dysfunction

Mathematical models of water and solute transport in the kidney have significantly expanded our understanding of renal function in both health and disease. This review describes recent theoretical developments and emphasizes the relevance of model findings to major unresolved questions and controversies. These include the fundamental processes by which urine is concentrated in the inner medulla, the ultrastructural basis of proteinuria, irregular flow oscillation patterns in spontaneously hypertensive rats, and the mechanisms underlying the hypotensive effects of thiazides. Macroscopic models of water, NaCl, and urea transport in populations of nephrons have served to test, confirm, or refute a number of hypotheses related to the urine concentrating mechanism. Other macroscopic models focus on the mechanisms, role, and irregularities of renal hemodynamic control and on the regulation of renal oxygenation. At the mesoscale, models of glomerular filtration have yielded significant insight into the ultrastructural basis underlying a number of disorders. At the cellular scale, models of epithelial solute transport and pericyte Ca2+ signaling are being used to elucidate transport pathways and the effects of hormones and drugs. Areas where further theoretical progress is conditional on experimental advances are also identified.

The physiology of urinary concentration: an update

The renal medulla produces concentrated urine through the generation of an osmotic gradient extending from the cortico-medullary boundary to the inner medullary tip. This gradient is generated in the outer medulla by the countercurrent multiplication of a comparatively small transepithelial difference in osmotic pressure. This small difference, called a single effect, arises from active NaCl reabsorption from thick ascending limbs, which dilutes ascending limb flow relative to flow in vessels and other tubules. In the inner medulla, the gradient may also be generated by the countercurrent multiplication of a single effect, but the single effect has not been definitively identified. There have been important recent advances in our understanding of key components of the urine concentrating mechanism. In particular, the identification and localization of key transport proteins for water, urea, and sodium, the elucidation of the role and regulation of osmoprotective osmolytes, better resolution of the anatomical relationships in the medulla, and improvements in mathematic modeling of the urine concentrating mechanism. Continued experimental investigation of transepithelial transport and its regulation, both in normal animals and in knock-out mice, and incorporation of the resulting information into mathematic simulations, may help to more fully elucidate the inner medullary urine concentrating mechanism.

The Mammalian Urine Concentrating Mechanism: Hypotheses and Uncertainties

The urine concentrating mechanism of the mammalian kidney, which can produce a urine that is substantially more concentrated than blood plasma during periods of water deprivation, is one of the enduring mysteries in traditional physiology. Owing to the complex lateral and axial relationships of tubules and vessels, in both the outer and inner medulla, the urine concentrating mechanism may only be fully understood in terms of the kidney’s three-dimensional functional architecture and its implications for preferential interactions among tubules and vessels.

Role of three-dimensional architecture in the urine concentrating mechanism of the rat renal inner medulla

Recent studies of three-dimensional architecture of rat renal inner medulla (IM) and expression of membrane proteins associated with fluid and solute transport in nephrons and vasculature have revealed structural and transport properties that likely impact the IM urine concentrating mechanism. These studies have shown that 1) IM descending thin limbs (DTLs) have at least two or three functionally distinct subsegments; 2) most ascending thin limbs (ATLs) and about half the ascending vasa recta (AVR) are arranged among clusters of collecting ducts (CDs), which form the organizing motif through the first 3-3.5 mm of the IM, whereas other ATLs and AVR, along with aquaporin-1-positive DTLs and urea transporter B-positive descending vasa recta (DVR), are external to the CD clusters; 3) ATLs, AVR, CDs, and interstitial cells delimit interstitial microdomains within the CD clusters; and 4) many of the longest loops of Henle form bends that include subsegments that run transversely along CDs that lie in the terminal 500 microm of the papilla tip. Based on a more comprehensive understanding of three-dimensional IM architecture, we distinguish two distinct countercurrent systems in the first 3-3.5 mm of the IM (an intra-CD cluster system and an inter-CD cluster system) and a third countercurrent system in the final 1.5-2 mm. Spatial arrangements of loop of Henle subsegments and multiple countercurrent systems throughout four distinct axial IM zones, as well as our initial mathematical model, are consistent with a solute-separation, solute-mixing mechanism for concentrating urine in the IM.

Mechanisms to concentrate the urine: an opinion

PURPOSE OF REVIEW

Our goal is to suggest how the renal concentrating mechanism is regulated in vivo.

RECENT FINDINGS

The majority of descending thin limbs of the loop of Henle lack aquaporin-1 water channels, and loops of Henle in the inner medulla lack urea transporters.

SUMMARY

Lack of water permeability in the descending thin limbs of the loop of Henle offers several advantages. First, since much less water is added to the outer medullary interstitial compartment, inhibitory control mechanisms on sodium and chloride reabsorption from the medullary thick ascending of loop of Henle initiated by water addition from the medullary collecting duct can be effective. Second, recycling of urea is efficient, as little urea will be washed out of the medulla. Third, delivery of a larger volume of filtrate to the medullary thick ascending limb of the loop of Henle permits both an appreciable reabsorption of sodium along with only a small fall in the luminal concentration of sodium in each of these liters. Hence there need be only a small lumen positive voltage in the medullary thick ascending limb of the loop of Henle. The absence of urea transporters in the loop of Henle in the inner medulla is required for a passive mechanism of sodium and chloride reabsorption in the inner medulla. Control of urea reabsorption from the medullary collecting duct is needed to prevent excessive oliguria in electrolyte-poor urine.

Loop of Henle interaction with interstitial nodal spaces in the renal inner medulla

Understanding dynamics of NaCl reabsorption from loops of Henle, and cellular and physiological consequences, requires a clear understanding of the structural relationships of loops with other functional elements of the inner medulla (IM). Pathways taken by ascending thin limbs (ATLs) and prebend segments along the corticopapillary axis were evaluated for the outer zone of the IM of the Munich-Wistar rat. Connectivity between these segments and microdomains of interstitium adjacent to collecting ducts (CDs) and abutting ascending vasa recta (interstitial nodal spaces) was assessed by evaluating their physical contacts. For each secondary CD cluster, the number of contacts made between the total population of ATLs and interstitial nodal spaces declines as a function of depth below the outer medulla (OM)-IM boundary at near the same exponential rate that loop number declines. The proportion of each loop that makes contact with nodal spaces is inversely related to loop length. Prebend and postbend equivalent length ATL segments lie in contact with an interstitial nodal space along nearly their entire lengths. The number of contacts made by the total population of prebend or postbend segments exhibits a marked, periodic increase and decrease as a function of depth below the OM-IM boundary; this number of contacts correlates with equivalent periodic changes in prebend number. Simulations of loop distribution indicate that small discontinuities in loop distribution contribute to periodic changes in prebend number. Convergence of IM loop bends within CD clusters likely plays an essential role in NaCl compartmentalization by promoting NaCl reabsorption near interstitial regions lying adjacent to CDs and ascending vasa recta.

Quantitative analysis of functional reconstructions reveals lateral and axial zonation in the renal inner medulla

Three-dimensional functional reconstructions of descending thin limbs (DTLs) and ascending thin limbs (ATLs) of loops of Henle, descending vasa recta (DVR), ascending vasa recta (AVR), and collecting ducts (CDs) permit quantitative definition of lateral and axial zones of probable functional significance in rat inner medulla (IM). CD clusters form the organizing motif for loops of Henle and vasa recta in the initial 3.0-3.5 mm of the IM. Using Euclidean distance mapping, we defined the lateral boundary of each cluster by pixels lying maximally distant from any CD. DTLs and DVR lie almost precisely on this independently defined boundary, placing them in the intercluster interstitium maximally distant from any CD. ATLs and AVR lie in a nearly uniform pattern throughout intercluster and intracluster regions, which we further differentiated by a polygon around CDs in each cluster. Loops associated with individual CD clusters show a similar axial exponential decrease as all loops together in the IM. Because approximately 3.0-3.5 mm below the IM base CD clusters cease to form the organizing motif, all DTLs lack aquaporin 1 (AQP1), and all vasa recta are fenestrated, we have designated the first 3.0-3.5 mm of the IM the "outer zone" (OZ) and the final 1.5-2.0 mm the "inner zone" (IZ). We further subdivided these into OZ-1, OZ-2, IZ-1, and IZ-2 on the basis of the presence of completely AQP1-null DTLs only in the first 1 mm and on broad transverse loop bends only in the final 0.5 mm. These transverse segments expand surface area for probable NaCl efflux around loop bends from approximately 40% to approximately 140% of CD surface area in the final 100 microm of the papilla.

Three-dimensional architecture of collecting ducts, loops of Henle, and blood vessels in the renal papilla

Three-dimensional architecture of vasculature and nephrons in rat renal papilla was assessed by digital reconstruction. Descending vasa recta (DVR), ascending vasa recta (AVR), descending thin limbs (DTLs), ascending thin limbs (ATLs), and collecting ducts (CDs) were identified with antibodies against segment-specific proteins. DTLs are distributed nonuniformly in transverse sections of papilla, but lateral compartmentation between DTLs and CD clusters that occurs in outer IM makes no contribution to concentrating mechanism in papilla. ATLs are distributed nearly uniformly throughout IM. Vasa recta within approximately 2 mm of the papilla tip are primarily fenestrated vessels; therefore, AVR and DVR can only be determined by blood flow direction. CDs within approximately 500 microm of the papilla tip have nearly 100% greater circumference than CDs within first 1-2 mm below the IM base. Return of water to general circulation from deep papillary CDs appears to be facilitated by a 150% increase in the number of AVR closely abutting these CDs. Consequently, average fractional CD surface area abutting AVR is 0.61, about the same as that (0.54) for smaller CDs that lie near the IM base. Interstitial nodal compartments, bounded by CDs, ATLs, and AVR, surround CDs along the axis of the IM. Fewer ATLs exist in the final 1 mm, as there are fewer loops and the number of these nodal arrangements is therefore reduced. However, tips of many of those loops reaching this area have bends with 50-100% greater transverse lengths than bends of loops near the IM base. This may be significant for solute movement out of loop bends.

Role of UTB urea transporters in the urine concentrating mechanism of the rat kidney

A mathematical model of the renal medulla of the rat kidney was used to investigate urine concentrating mechanism function in animals lacking the UTB urea transporter. The UTB transporter is believed to mediate countercurrent urea exchange between descending vasa recta (DVR) and ascending vasa recta (AVR) by facilitating urea transport across DVR endothelia. The model represents the outer medulla (OM) and inner medulla (IM), with the actions of the cortex incorporated via boundary conditions. Blood flow in the model vasculature is divided into plasma and red blood cell compartments. In the base-case model configuration tubular dimensions and transport parameters are based on, or estimated from, experimental measurements or immunohistochemical evidence in wild-type rats. The base-case model configuration generated an osmolality gradient along the cortico-medullary axis that is consistent with measurements from rats in a moderately antidiuretic state. When expression of UTB was eliminated in the model, model results indicated that, relative to wild-type, the OM cortico-medullary osmolality gradient and the net urea flow through the OM were little affected by absence of UTB transporter. However, because urea transfer from AVR to DVR was much reduced, urea trapping by countercurrent exchange was significantly compromised. Consequently, urine urea concentration and osmolality were decreased by 12% and 8.9% from base case, respectively, with most of the reduction attributable to the impaired IM concentrating mechanism. These results indicate that the in vivo urine concentrating defect in knockout mouse, reported by Yang et al. (J Biol Chem 277(12), 10633-10637, 2002), is not attributable to an OM concentrating mechanism defect, but that reduced urea trapping by long vasa recta plays a significant role in compromising the concentrating mechanism of the IM. Moreover, model results are in general agreement with the explanation of knockout renal function proposed by Yang et al.

Mathematical model of nitric oxide convection and diffusion in a renal medullary vas rectum

In this study, the generation, convection, diffusion, and consumption of nitric oxide (NO) in and around a single renal medullary descending or ascending vas rectum in rat were modeled using CFD. The vascular lumen (with a core RBC-rich layer and a parietal layer), the endothelium, the pericytes and the interstitium were represented as concentric cylinders. We accounted for the generation of NO by vascular endothelial cells, and that by the epithelial cells of medullary thick ascending limbs (mTALs) and inner medullary collecting ducts (IMCDs), the latter via interstitial boundary conditions. Luminal velocity profiles were obtained by modeling blood flow dynamics. Our results suggest that convection (i.e., blood flow per se) does not significantly affect NO concentrations along the cortico-medullary axis, because the latter are mostly determined by the rate of NO production and that of NO consumption by hemoglobin. However, the shear stress-mediated effects of blood flow on NO generation rates, and therefore NO concentrations, were predicted to be important. Finally, we found that unless epithelial NO generation rates (per unit tubular surface area) are at least 10 times lower than endothelium NO generation rates, NO production by mTALs and IMCDs affects vascular NO concentrations, with possible consequences for medullary blood flow distribution.

An optimization algorithm for a distributed-loop model of an avian urine concentrating mechanism

To better understand how the avian kidney's morphological and transepithelial transport properties affect the urine concentrating mechanism (UCM), an inverse problem was solved for a mathematical model of the quail UCM. In this model, a continuous, monotonically decreasing population distribution of tubes, as a function of medullary length, was used to represent the loops of Henle, which reach to varying levels along the avian medullary cones. A measure of concentrating mechanism efficiency - the ratio of the free-water absorption rate (FWA) to the total NaCl active transport rate (TAT) - was optimized by varying a set of parameters within bounds suggested by physiological experiments. Those parameters include transepithelial transport properties of renal tubules, length of the prebend enlargement of the descending limb (DL), DL and collecting duct (CD) inflows, plasma Na(+) concentration, length of the cortical thick ascending limbs, central core solute diffusivity, and population distribution of loops of Henle and of CDs along the medullary cone. By selecting parameter values that increase urine flow rate (while maintaining a sufficiently high urine-to-plasma osmolality ratio (U/P)) and that reduce TAT, the optimization algorithm identified a set of parameter values that increased efficiency by approximately 60% above base-case efficiency. Thus, higher efficiency can be achieved by increasing urine flow rather than increasing U/P. The algorithm also identified a set of parameters that reduced efficiency by approximately 70% via the production of a urine having near-plasma osmolality at near-base-case TAT. In separate studies, maximum efficiency was evaluated as selected parameters were varied over large ranges. Shorter cones were found to be more efficient than longer ones, and an optimal loop of Henle distribution was found that is consistent with experimental findings.