Role of structural organization in the urine concentrating mechanism of an avian kidney

The organization of tubules and blood vessels in the quail medullary cone is highly structured. This structural organization may result in preferential interactions among tubules and vessels, interactions that may enhance urine concentrating capability. In this study, we formulate a model framework for the urine concentrating mechanism of the quail kidney. The model simulates preferential interactions among renal tubules by representing two concentric cores and by specifying the fractions of tubules assigned to each of the concentric cores. The model equations are based on standard expressions for transmural transport and on solute and water conservation. Model results suggest that the preferential interactions among tubules enhance the urine concentration capacity of short medullary cones by reducing the diluting effect of the descending limbs on the region of the interstitium where the collecting ducts are located; however, the effects on longer cones are unclear.     

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.     

A numerical method for renal models that represent tubules with abrupt changes in membrane properties

 The urine concentrating mechanism of mammals and birds depends on a counterflow configuration of thousands of nearly parallel tubules in the medulla of the kidney. Along the course of a renal tubule, cell type may change abruptly, resulting in abrupt changes in the physical characteristics and transmural transport properties of the tubule. A mathematical model that faithfully represents these abrupt changes will have jump discontinuities in model parameters. Without proper treatment, such discontinuities may cause unrealistic transmural fluxes and introduce suboptimal spatial convergence in the numerical solution to the model equations. In this study, we show how to treat discontinuous parameters in the context of a previously developed numerical method that is based on the semi-Lagrangian semi-implicit method and Newton's method. The numerical solutions have physically plausible fluxes at the discontinuities and the solutions converge at second order, as is appropriate for the method. Received: 13 November 2001 / Revised version: 28 June 2002 / Published online: 26 September 2002 This work was supported in part by the National Institutes of Health (National Institute of Diabetes and Digestive and Kidney Diseases, grant DK-42091.) Mathematics Subject Classification (2000): 65-04, 65M12, 65M25, 92-04, 92C35, 35-04, 35L45 Keywords or phrases: Mathematical models – Differential equations – Mathematical biology – Kidney – Renal medulla – Semi-Lagrangian semi-implicit     

Concentrating engines and the kidney. III. Canonical mass balance equation for multinephron models of the renal medulla.

The canonical mass balance relation derived for the central core model of the renal medulla is extended to medullary models in which an arbitrary assemblage of renal tubules and vascular capillaries exchange with each other both directly and via the medullary interstitium and in which not all of the vascular loops or loops of Henle extend to the papilla. It is shown that if descending limbs of Henle and descending vasa recta enter the medulla at approximately plasma osmolality, the concentration ratio is given by: r = 1/[1 - ft(1 - fu)(1 - fw)], where ft is fractional solute transport out of ascending Henle's limb, fu is fractional urine flow, and fw is fractional dissipation; fw is a measure of the solute returned to the systemic circulation without its isotonic complement of water. A modified equation that applies to the diluting as well as the concentrating kidney is also derived. By allowing concentrations in interstitium and vascular capillaries to become identical at a given medullary level, conservation relations are derived for a multinephron central core model of the renal medulla.     

Externally driven countercurrent multiplication in a mathematical model of the urinary concentrating mechanism of the renal inner medulla

Substitution of measured permeabilities into mathematical models of the concentrating mechanism of the renal inner medulla yields less than the known urine osmolalities. To gain a better understanding of the mechanism we analyse a model in which a force of unspecified origin [expressed as fraction, ɛ, of entering descending thin limb (DTL) concentration] drives fluid from DTL to interstitial vascular space (CORE), thus concentrating the solution in DTL. When flow in the DTL reverses at the hairpin bend of the loop of Henle, the high solute permeability of ascending thin limb (ATL) permits solute to diffuse into the CORE thus permitting ɛ to be multiplied many-fold. Behavior of the model is described by two non-linear differential equations. In the limit for infinite salt permeability of ATL the two equations reduce to a single equation that is formally identical with that for the Hargitay and Kuhn multiplier, which assumes fluid transport directly from DTL to ATL (Z. Electrochem. Angew. Phys. Chem. 55, 539, 1951). Solutions of the equations describing the model with parameters taken from perfused thin limbs show that urine osmolalities of the order of 5000 mosm L⁻¹ can be generated by forces of the order of 20 mosm L⁻¹. It seems probable that mammals including desert rodents use some variant of this basic mechanism for inner medullary concentration.     

Effect of varying salt and urea permeabilities along descending limbs of Henle in a model of the renal medullary urine concentrating mechanism

Modelling studies have played an important role in research on the mechanism of urine concentration and dilution by the medulla of the kidney ever since Hargitay and Kuhn (1951,Z. Elektrochem. 55, 539–558) first proposed that the parallel tubular structures in the kidney medulla must function as a “countercurrent multiplication” system. Present-day models, in keeping with our considerably improved understanding of most aspects of medullary structure-function relationships, have evolved into rather sophisticated systems of parallel tubes. In spite of this increasing complexity, it has remained the case that “model medullas” do not concentrate as well as the real kidney, especially in the inner medulla where only passive, diffusional transport occurs. Inasmuch as these models take into account the majority of contemporary ideas making up our global hypothesis about the functioning of this system, their failure to behave physiologically indicates that our understanding remains incomplete. The purpose of the present modelling study was to evaluate the implications of some recent measurements showing that permeabilities of NaCl (P _s ) and urea (P _u ) vary along the length of the descending thin limbs of Henle (Imaiet al., 1988,Am. J. Physiol. 254, F323–F328), rather than being constant throughout this segment as had been assumed earlier. It was hoped that these newly measured values might explain, by a passive, diffusional process, the net solute addition at the bend of Henle’s loop observed under some circumstances and heretofore attributed (though without any supporting experimental evidence) to active transport into the descending limb. The results of the present study show that whereas incorporation of the new values forP _s andP _u in the descending limbs of short nephrons does indeed improve the concentrating power of the model, these new values are nonetheless not sufficient to allow the model to build an osmolarity gradient that increases all the way through the inner medulla. This failing, which is common to virtually all modelling studies to date using measured values from rat kidneys, probably points to a key role for preferential exchange supposed by some to exist among certain tubule segments within vascular bundles in species whose kidneys have the highest concentrating power.     

Ultrastructural localization of Na+,K+-ATPase in rat and rabbit kidney medulla

Na+,K+-ATPase was localized at the ultrastructural level in rat and rabbit kidney medulla. The cytochemical method for the K+-dependent phosphatase component of the enzyme, using p-nitrophenylphosphate (NPP) as substrate, was employed to demonstrate the distribution of Na+, K+- ATPase in tissue-chopped sections from kidneys perfusion-fixed with 1% paraformaldehyde-0.25% glutaraldehyde. In other outer medulla of rat kidney, ascending thick limbs (MATL) were sites of intense K+-dependent NPPase (K+-NPPase) activity, whereas descending thick limbs and collecting tubules were barely reactive. Although descending thin limbs (DTL) of short loop nephrons were unstained, DTL from long loop nephrons in outer medulla were sites of moderate K+-NPPase activity. In rat inner medulla, DTL and ascending thin limbs (ATL) were unreactive for K+-NPPase. In rabbit medulla, only MATL were sites of significant K+-NPPase activity. The specificity of the cytochemical localization of Na+,K+-ATPase at reactive sites in rat and rabbit kidney medulla was demonstrated by K+-dependence of reaction product deposition, localization of reaction product (precipitated phosphate hydrolyzed from NPP) to the cytoplasmic side of basolateral plasma membranes, insensitivity of the reaction to inhibitors of nonspecific alkaline phosphatase, and, in the glycoside-sensitive rabbit kidney, substantial inhibition of staining by ouabain. The observed pattern of distribution of the sodium transport enzyme in kidney medulla is particularly relevant to current models for urine concentration. The presence of substantial Na+,K+-ATPase in MATL is consistent with the putative role of this segment as the driving force for the countercurrent multiplication system in the outer medulla. The absence of significant activity in inner medullary ATL and DTL, however, implies that interstitial solute accumulation in this region probably occurs by passive processes. The localization of significant Na+,K+-ATPase in outer medullary DTL of long loop nephrons in the rat suggests that solute addition in this segment may occur in part by an active salt secretory mechanism that could ultimately contribute to the generation of inner medullary interstitial hypertonicity and urine concentration.     

Modulation of outer medullary NaCl transport and oxygenation by nitric oxide and superoxide

We expanded our region-based model of water and solute exchanges in the rat outer medulla to incorporate the transport of nitric oxide (NO) and superoxide (O(2)(-)) and to examine the impact of NO-O(2)(-) interactions on medullary thick ascending limb (mTAL) NaCl reabsorption and oxygen (O(2)) consumption, under both physiological and pathological conditions. Our results suggest that NaCl transport and the concentrating capacity of the outer medulla are substantially modulated by basal levels of NO and O(2)(-). Moreover, the effect of each solute on NaCl reabsorption cannot be considered in isolation, given the feedback loops resulting from three-way interactions between O(2), NO, and O(2)(-). Notwithstanding vasoactive effects, our model predicts that in the absence of O(2)(-)-mediated stimulation of NaCl active transport, the outer medullary concentrating capacity (evaluated as the collecting duct fluid osmolality at the outer-inner medullary junction) would be ～40% lower. Conversely, without NO-induced inhibition of NaCl active transport, the outer medullary concentrating capacity would increase by ～70%, but only if that anaerobic metabolism can provide up to half the maximal energy requirements of the outer medulla. The model suggests that in addition to scavenging NO, O(2)(-) modulates NO levels indirectly via its stimulation of mTAL metabolism, leading to reduction of O(2) as a substrate for NO. When O(2)(-) levels are raised 10-fold, as in hypertensive animals, mTAL NaCl reabsorption is significantly enhanced, even as the inefficient use of O(2) exacerbates hypoxia in the outer medulla. Conversely, an increase in tubular and vascular flows is predicted to substantially reduce mTAL NaCl reabsorption. In conclusion, our model suggests that the complex interactions between NO, O(2)(-), and O(2) significantly impact the O(2) balance and NaCl reabsorption in the outer medulla.     

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.     

Tubuloglomerular Feedback Signal Transduction in a Short Loop of Henle

In previous studies, we used a mathematical model of the thick ascending limb (TAL) to investigate nonlinearities in the tubuloglomerular feedback (TGF) loop. That model does not represent other segments of the nephron, the water, and NaCl transport along which may impact fluid flow rate and NaCl transport along the TAL. To investigate the extent to which those transport processes affect TGF mediation, we have developed a mathematical model for TGF signal transduction in a short loop nephron. The model combines a simple representation of the renal cortex with a highly-detailed representation of the outer medulla (OM). The OM portion of the model is based on an OM urine concentrating mechanism model previously developed by Layton and Layton (Am. J. Renal 289:F1346–F1366, 2005a). When perturbations are applied to intratubular fluid flow at the proximal straight tubule entrance, the present model predicts oscillations in fluid flow and solute concentrations in the cortical TAL and interstitium, and in all tubules, vessels, and interstitium in the OM. Model results suggest that TGF signal transduction by the TAL is a generator of nonlinearities: if a sinusoidal oscillation is added to constant intratubular fluid flow, the time required for an element of tubular fluid to traverse the TAL is oscillatory, but nonsinusoidal; those results are consistent with our previous studies. As a consequence, oscillations in NaCl concentration in tubular fluid alongside the macula densa (MD) will be nonsinusoidal and contain harmonics of the original sinusoidal frequency. Also, the model predicts that the oscillations in NaCl concentration at the loop-bend fluid are smaller in amplitude than those at the MD, a result that further highlights the crucial role of TAL in the nonlinear transduction of TGF signal from SNGFR to MD NaCl concentration.     

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.     

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.     

The effect of solution non-ideality on membrane transport in three-dimensional models of the renal concentrating mechanism

Previous models of the renal concentrating mechanism employ ideal approximations of solution thermodynamics for membrane transport calculation. In three-dimensional models of the renal medulla, predicted urine concentrations reach levels where there idealized approximations begin to break down. In this paper we derive equations that govern membrane transport for non-dilute solutions and use these equations in a three-dimensional model of the concentrating mechanism. New numerical methods were employed that are more stable than those employed previously. Compared to ideal solution models, the urea non-ideality tends to increase predicted osmolarities, whereas NaCl non-ideality decreases predictions.     

An inverse algorithm for a mathematical model of an avian urine concentrating mechanism

A nonlinear optimization technique, in conjunction with a single-nephron, single-solute mathematical model of the quail urine concentrating mechanism, was used to estimate parameter sets that optimize a measure of concentrating mechanism efficiency, viz., the ratio of the free-water absorption rate to the total NaCl active transport rate. The optimization algorithm, which is independent of the numerical method used to solve the model equations, runs in a few minutes on a 1000 MHz desktop computer. The parameters varied were: tubular permeabilities to water and solute; maximum active solute transport rates of the ascending limb of Henle and the collecting duct (CD); length of the prebend enlargement (PBE) of the descending limb; fractional solute delivery to the CD; solute concentration of tubular fluid entering the CD at the cortico-medullary boundary; and rate of exponential CD population decrease along the medullary cone. Using a base-case parameter set and parameter bounds suggested by physiologic experiments, the optimization algorithm identified a maximum-efficiency set of parameter values that increased efficiency by 40% above base-case efficiency; a minimum-efficiency set reduced efficiency by about 41%. When maximum-efficiency parameter values were computed as medullary length varied over the physiologic range, the PBE was found to make up 88% of a short medullary cone but only 8% of a long medullary cone.     

Effect of oxygen and solute on PGE and PGF production by rat kidney slices

Increasing oxygen from 5% to 95% resulted in an increased production of both PGE's and PGF's. The release of prostaglandins from slices of rat kidney cortex and outer and inner medulla was measured. Prostaglandin production was observed predominantly in the inner medulla, was close to the lower limit of detection in the outer medulla, and was undetectable in the cortex. Increasing oxygen concentration resulted in a threefold increase in inner medullary prostaglandin production. Synthesis at 95% O₂ was less at 2100 mOsm than at 300 mOsm, while synthesis at 5% O₂ was not affected by high solute concentration. The implications of these results with respect to kidney function are discussed.     

Solution of a multinephron,multisolute model of the mammalian kidney by Newton and continuation methods

A method of numerically solving the differential equations specifying solute and water flow in a multinephron, multisolute model of the mammalian kidney by a combination of Newton and continuation techniques is described. This method is used to generate a connected component of the steady state solution manifold of the model. A three dimensional section of this manifold is shown to be convoluted, with upper and lower sheets of stable solutions connected by an unstable middle sheet. Two dimensional sections of this surface are followed from a trivial constant profile of concentrations in the nonconcentrating kidney to the profiles of the maximally concentrating kidney. Study of these sections shows that for a given choice of model parameters there may exist no solution, there may be a unique solution, or there may be multiple solutions. A study of the time dependent solutions shows that the dynamic transition from the lower to the upper state and return may be via a hysteresis loop.     

Kidney structure and function of obligate and facultative hibernators: the white-tailed prairie dog (Cynomys leucurus) and the black-tailed prairie dog (Cynomys ludovicianus)

The white-tailed prairie dog is an obligate hibernator that enters a heterothermic phase when maintained in the cold with low intensity light and ad libitum food and water. The black-tailed prairie dog (a facultative hibernator) will not hibernate under similar conditions. It has been suggested that the black tailed prairie dog remains active during the winter because it can conserve water more effectively due to a more efficient kidney. The present study revealed no significant differences between the species in renal morphology: relative medullary thickness, nephron heterogeneity, renal vasculature, or fornix dimensions, all of which are structures associated with the urinary concentrating mechanism. In addition, there was no difference in number of nephrons between the two species. The black-tailed prairie dog does produce a more concentrated urine when food and water deprived. However, this difference was not observed when the animals were salt loaded. The water-deprivation and salt-loading experiments suggest that the higher urine osmolality produced by the back-tailed prairie dog during fasting is a result of a higher urea load due to a greater protein catabolism and not because of a differential capacity to concentrate urine.Abbreviations C cortex - GFR glomerular filtration rate - H height - IS inner stripe - IZ inner zone of medulla - L length - OS outer stripe - PE polythylene - RMT relative medullary thickness - T _a ambient temperature - W width     

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 ∼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 ∼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.     

CFTR structure and function: is there a role in the kidney?

Cystic fibrosis (CF) is a lethal autosomal recessive genetic disease caused by mutations in the CF transmembrane conductance regulator (CFTR). Mutations in the CFTR gene may result in a defective protein processing that leads to changes in function and regulation of this chloride channel. Despite of the expression of CFTR in the kidney, patients with CF do not present major renal dysfunction, but it is known that both the urinary excretion of proteins and renal capacity to concentrate and dilute urine are altered in these patients. CFTR mRNA is expressed in all nephron segments of rat and human, and this abundance is more prominent in renal cortex and outer medulla renal areas. CFTR protein was detected in apical surface of both proximal and distal tubules of rat kidney but not in the outer medullary collecting ducts. Studies have demonstrated that CFTR does not only transport Cl⁻ but also ATP. ATP transport by CFTR could be involved in the control of other ion transporters such as Na⁺ (ENaC) and K⁺ (renal outer medullary potassium) channels, especially in TAL and CCD. In the kidney, CFTR also might be involved in the endocytosis of low-molecular-weight proteins by proximal tubules. This review is focused on the CFTR function and structure, its role in the renal physiology, and its modulation by hormones involved in the control of extracellular fluid volume.     

Isolated interstitial nodal spaces may facilitate preferential solute and fluid mixing in the rat renal inner medulla

Recent anatomic findings indicate that in the upper inner medulla of the rodent kidney, tubules, and vessels are organized around clusters of collecting ducts (CDs). Within CD clusters, CDs and some of the ascending vasa recta (AVR) and ascending thin limbs (ATLs), when viewed in transverse sections, form interstitial nodal spaces, which are arrayed at structured intervals throughout the inner medulla. These spaces, or microdomains, are bordered on one side by a single CD, on the opposite side by one or more ATLs, and on the other two sides by AVR. To study the interactions among these CDs, ATLs, and AVR, we have developed a mathematical compartment model, which simulates steady-state solute exchange through the microdomain at a given inner medullary level. Fluid in all compartments contains Na(+), Cl(-), urea and, in the microdomain, negative fixed charges that represent macromolecules (e.g., hyaluronan) balanced by Na(+). Fluid entry into AVR is assumed to be driven by hydraulic and oncotic pressures. Model results suggest that the isolated microdomains facilitate solute and fluid mixing among the CDs, ATLs, and AVR, promote water withdrawal from CDs, and consequently may play an important role in generating the inner medullary osmotic gradient.