INVITED REVIEWConcentration of solutes in the renal inner medulla:interstitial h - 《American Journal of Physiology》美国生理学杂志干细胞之家



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发表于 2009-4-21 13:34 |只看该作者 |倒序浏览 |打印

作者：Mark A.Knepper, Gerald M.Saidel, Vincent C.Hascall,  TerryDwyer作者单位：1 Laboratory of Kidney and Electrolyte Metabolism,National Heart, Lung, and Blood Institute, National Institutes ofHealth, Bethesda, Maryland 20892; Department ofBiomedical Engineering, Case Western Reserve University, Cleveland43560; Department of Biomedical Engineering, TheCleveland Clinic Foundat

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      【摘要】
   Although the concentrating process in therenal outer medulla is well understood, the concentrating mechanism inthe renal inner medulla remains an enigma. The purposes of this revieware fourfold. 1 ) We summarize a theoretical basis forclassifying all possible steady-state inner medullary countercurrentconcentrating mechanisms based on mass balance principles. 2 ) We review the major hypotheses that have been proposed toexplain the axial osmolality gradient in the interstitium of the renalinner medulla. 3 ) We summarize and expand on theSchmidt-Nielsen hypothesis that the contractions of the renalpelvocalyceal wall may provide an important energy source forconcentration in the inner medulla. 4 ) We discuss thespecial properties of hyaluronan, a glycosaminoglycan that is the chiefcomponent of a gel-like renal inner medullary interstitial matrix,which may allow it to function as a mechano-osmotic transducer,converting energy from the contractions of the pelvic wall to an axialosmolality gradient in the medulla. These considerations set the stagefor renewed experimental investigation of the urinary concentratingprocess and a new generation of mathematical models of the renalconcentrating mechanism, which treat the inner medullary interstitiumas a viscoelastic system rather than a purely hydraulic system. 2 Y+ Y. x. X* w& j% b
      【关键词】 glycosaminoglycans renal pelvis vasopressin hyaluronan
   INTRODUCTION

IN STATES OF FLUID DEPRIVATION ornonrenal water loss, the kidney can conserve water while maintainingexcretion of solutes. It does this by concentrating the solutes in theurine to osmolalities that markedly exceed the osmolality of plasma. Alarge number of studies, exemplified by the data shown in Fig. 1, have demonstrated that the urinaryconcentrating process is associated with the generation of acorticomedullary osmolality gradient in the medullary tissue, orientedwith the maximum osmolality in the deepest part of the inner medulla,i.e., at the papillary tip. The classic micropuncture studies ofGottschalk and Mylle ( 17 ) have established that themedullary hypertonicity is due to solute accumulation in all structuresin the medulla, including loops of Henle, vasculature, and collectingducts. The high medullary interstitial osmolality provides a drivingforce for osmotic water flow across the collecting ducts, which arerendered permeable to water through the action of vasopressin( 33 ). The high water permeability allows osmotic equilibration of urine with the medullary interstitial fluid.0 t: X" T3 i' w5 z4 P  k
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Fig. 1. Osmolality gradient in renal medullary tissue ofantidiuretic rabbit. Measurements were made by vapor pressure osmometryof slices from different levels of rabbit kidney after quick freezing.The figure is drawn from data from Ref. 32.; Q: N* L: E. A& ?

In 1959, Kuhn and Ramel ( 43 ) proposed a model to explainconcentration of solutes in the renal medulla based on countercurrent amplification of a small osmotic difference between the ascending limband the descending limb of Henle's loop, resulting from active solutetransport out of the ascending limb. Their version of Hargitay andKuhn's ( 22 ) countercurrent multiplier hypothesis hasbecome generally accepted as the mode of solute accumulation in therenal outer medulla and is now supported by extensive experimentalevidence (reviewed in Ref. 55 ). The key evidence was thedemonstration that the thick ascending limb of Henle's loop is capableof a high rate of active NaCl transport out of the lumen, which results in luminal dilution owing to the low osmotic water permeability of thissegment ( 3, 67 ).5 @% H8 \) J' F. Z' u! D
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Thus renal physiologists have developed a good understanding of theprocess that concentrates solutes in the renal outer medulla. The samecannot be said for the renal inner medulla, however. The ascendingportion of Henle's loop (the thin ascending limb) has been shown tohave extremely limited, if any, capacity for active transport in theinner medulla ( 25, 26, 53, 54, 59, 80 ). Therefore, in theinner medulla there is no energy source for a classic Kuhn-Ramelcountercurrent multiplier, and other explanations must be sought forthe medullary osmolality gradient in the renal inner medulla.+ a5 Y6 n2 _0 w) d

The objectives of this paper are 1 ) to summarize a simpletheoretical scheme for classification of all possible steady-state countercurrent concentrating models in the inner medulla; 2 )to review proposed steady-state models for concentration of solutes inthe inner medullary interstitium; 3 ) to readdress theSchmidt-Nielsen hypothesis that energy from smooth muscle contractionsof the pelvocalyceal wall is responsible for concentration of solutes in the inner medulla; and 4 ) to discuss the possible role ofinner medullary interstitial hyaluronan as a mechano-osmotic energy transducer converting mechanical energy of renal pelvic contractions toaxial osmolality gradients in the inner medulla.: i7 q+ B% r: S- H/ n& S
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MASS BALANCE REQUIREMENTS FOR URINARY CONCENTRATION
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Knepper and Stephenson ( 37 ) and Knepper et al.( 34 ) developed a mathematical analysis of concentratingprocesses in the renal inner medulla that allows classification of allpossible steady-state countercurrent concentrating models based on mass balance requirements. The full mathematical analysis will not berepeated here but is summarized concisely in APPENDIX A. This analysis assumes that solutions exhibit ideal behavior and thatchemical reactions have negligible effects. Possible repercussions ofthese assumptions will be considered in later sections. We discuss theapproach and the principles that derive from the analysis in thefollowing paragraphs.! x# J, H; N! h- R- k# m
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Figure 2 A is a diagram of aunipapillate kidney typical of a rat, rabbit, or mouse. It illustratesthe relative positions of the three major regions of the kidney: thecortex, the outer medulla, and the inner medulla. The deepest portionof the inner medulla is a tapering structure, the papilla, whose tip isthe site of exit of urine formed by the kidney. After exiting the kidney at the papillary tip, this urine is carried downward to theurinary bladder via the ureter. To analyze the processes responsible for generation of the osmotic gradient in the inner medulla, we apply a"control volume" for mass balance (Fig. 2 B ), whichcreates a boundary to allow us to account for flows into and out of a portion of the inner medulla. The lower end of this control volume isdefined to be at or just beyond the papillary tip. The upper end of thecontrol volume is arbitrary; it can be drawn at any level of the innermedulla, for example, as defined by the solid line shown in Fig. 2 B or by the horizontal dashed line just below it. Theanalysis that we present applies to all such control volumes. Figure 2 C shows the same control volume identifying all of the relevant flows into and out of it. Entering flows include those in thedescending vasa recta, the descending limb of Henle's loop, and thecollecting ducts. Exiting flows include those in the ascending vasarecta, the ascending limbs of Henle's loop, and the final urinary flowexiting the papillary tip. At steady state, the flow of water, NaCl,and urea into the control volume must exactly equal the flows out ofthe control volume.
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Fig. 2. Structural basis of steady-state mass balance analysis ofrenal inner medulla of a unipapillate kidney. A :diagrammatic representation of kidney structure. See text fordescription. B : cutaway view showing a "control volume"for analysis of mass balance defined by the heavy solid rectangle. Aseries of such control volumes can be defined by moving the upperborder of the control volume upward or downward. An alternative choicefor the upper border is illustrated by the horizontal dashed line. Forsteady-state operation of the inner medulla, mass balance must bemaintained for all such control volumes. C : enumeration ofthe individual flows into and out of an inner medullary control volumerepresented by the rectangle. Each flow stream is the aggregate offlows in all individual structures of a given type. For example, if theupper border of the control volume is assumed to be at the inner-outermedullary junction, the descending limb stream is the aggregate of11,000 individual descending limbs ( 35 ). Asc., ascending;Desc., descending.

Figure 3 is a detailed view of thecontrol volume for a portion of the inner medulla defining theterminology used. Here, the subscripts have been modified to indicateexplicitly the structure being considered [e.g., descending vasa recta(DV); ascending vasa recta (AV); descending limb (DL); ascending limbof Henle's loop (AL); collecting duct (CD); final urine (U),peritubular interstitium (P)]. Total solute concentrations arerepresented by C j, where the subscript j designates the structure. Volume flow rates arerepresented by Q j. The products C j · Q j represent the total solute flow rates into and out of the controlvolume. The total solute concentrations in the interstitium are givenby the C j terms. Using this terminology, themass-blance equation ( APPENDIX A, Eq. A7 ) can bewritten in terms of the individual structures involved. This equationcan be arranged so that the left-hand side expresses the interstitialtotal solute gradient from a given point (point x ) along theinner medulla to the papillary tip L as follows C P ( L ) − C P ( x ) =          [Q DV ( x )/Q u ] [C DV ( x ) − C P ( x )] + [Q AV ( x )/Q u ] [C AV ( x ) − C P ( x )] + [Q DL ( x )/Q u ] [C DL ( x ) − C P ( x )] + [Q AL ( x )/Q u ] [C AL ( x ) − C P ( x )] + [Q CD ( x )/Q u ] [C CD ( x ) − C P ( x )]
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To have a positive osmotic gradient between point x andthe papillary tip [C P ( L ) C P ( x 0], at least one of the terms onthe right-hand side must be positive. Each of these terms consists of anormalized flow multiplied by a total solute concentration difference("osmolality difference") across a given structure. Such atransverse osmolality difference has been referred to in thephysiological literature as a "single effect," a literaltranslation of the German term "Einzeleffekt" ( 22, 43 ). The normalized flow is the absolute flow divided by thefinal urinary flow. The flow represents an aggregate of all flows for agiven structure; e.g., Q AL ( x ) is the sum offlows in all individual ascending limbs at level x. Eachtotal solute concentration difference in the equation is a potentialsingle effect, which could account for the positive gradient in themedulla.
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Fig. 3. Control volume for analysis of mass balance requirementfor steady-state countercurrent multiplier mechanisms in the renalmedulla. See text for definiton of terms.
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The direction of the concentration difference (single effect) that isnecessary for medullary interstitial concentration is dependent on thedirection of flow in the structure. The flows oriented in the directionof the papillary tip (DV, DL, and CD) are positive and thereforerequire a positive value ofC i ( x ) C P ( x ). The flows oriented away from thepapillary tip (AV and AL) are negative and therefore require a negativevalue of C i ( x ) C P ( x ) to obtain a positive axial gradient. Forthe ascending limb, the requirement for a single effect is[C AL ( x ) C P ( x )] out of the thick ascending limb. Table 1 summarizes all possible single effects that could account for apositive axial interstitial gradient in the inner medulla forsteady-state operation. Potential concentrating models can therefore beanalyzed on the basis of their ability to generate one or more of therequired single effects indicated in Table 1. In summary, steady-stateconcentrating models must dilute the ascending limb of Henle or theascending vasa recta relative to the surrounding interstitium or,alternatively, must concentrate the descending limb of Henle, thedescending vasa recta, or the collecting duct relative to thesurrounding interstitium. In the next section, we discuss some of themodels that have been proposed in the context of the mass balancerequirements summarized in Table 1.( W( L; g/ x7 c' r6 m4 V3 ]
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Table 1. Classification of steady-state inner medullary concentrating modelsbased on structure responsible for concentrating "singleeffect": b/ P; m- F. }/ T$ z3 q: j; H
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PROPOSED STEADY-STATE MODELS
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Single Effect in the Thin Ascending Limb of Henle
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As noted in Table 1, a positive axial osmolality gradient in theinner medulla could be generated as a result of any process thatdilutes the lumen of the thin ascending limb relative to theinterstitium. The possibility that the thin ascending limb functionslike the thick ascending limb to dilute its lumen relative to theinterstitium by active NaCl transport has been ruled out, as discussedabove. It has been proposed that urea may be actively reabsorbed fromthe thin ascending limb ( 45 ), although this hypothesislacks experimental verification.

A model by which the luminal fluid in the thin ascending limb could bediluted by purely passive means has been proposed by Kokko and Rector( 39 ) and by Stephenson ( 77 ) (Fig. 4 ). This model assumes that the luminalfluid at the bend of the loop contains NaCl as the predominant soluteand that the inner medullary interstitium contains a fluid in whichurea is the predominant solute. It has been noted that the permeabilityto NaCl is higher than the permeability to urea in the thin ascendinglimb ( 25 ). These permeability characteristics predict thatNaCl would escape the lumen more rapidly than urea would enter,resulting in passive dilution, a prediction that was bourne out byperfused tubule experiments in vitro ( 25 ). Although thismodel appeared promising at first, thorough quantitative analysis didnot support an important contribution of this process to the generationof an inner medullary osmolality gradient ( 5, 6, 46, 81, 83, 92 ). Furthermore, a physiological analysis on the basis of theknown permeability properties, medullary solute concentrations, andflow rates in medullary structures has led to the conclusion that theKokko-Rector-Stephenson passive model could account for only a modestaxial osmolality gradient in the inner medulla ( 55 ). Oneimportant discrepancy between the experimental data and therequirements of the Kokko-Rector-Stephenson model is the ureapermeability of the ascending thin limb epithelium. Measurements inisolated perfused rodent thin ascending limbs yielded extremely highvalues, in the range 38-170 × 10 5 cm/s( 7, 24 ), which is too high to permit sustained net luminaldilution along the length of the thin ascending limb. In addition,measurements of the urea permeability of the descending limb epitheliumin the inner medulla demonstrated values too high to preventsubstantial urea entry into the descending limb ( 46 ). Itis beyond the scope of this article to analyze the full evidence indetail; see Masilamani et al. ( 55 ) for a thorough analysis of the feasibility of the Kokko-Rector-Stephenson model.
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Fig. 4. Proposed function of the thin ascending limb of Henle inthe Kokko-Rector-Stephenson passive model for concentration of theinner medullary interstitium. The entering fluid and peritubular fluidare assumed to have the same osmolality (osm) but to have equal andopposite transepithelial gradients for urea and NaCl. If the thinascending limb has the special properties indicated in the text (highNaCl permeability, low urea permeability, low water permeability),rapid NaCl efflux would occur without a balancing entry of urea, thuslowering luminal osmolality below that of the peritubular fluid.Measurements of urea permeability of the thin ascending limb haveyielded relatively high values, seemingly ruling out the hypothesis(see text).; P9 @' }/ Q. x
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Although the existing literature raises considerable doubt about theview that the single effect for inner medullary concentration residesin the thin ascending limb, recent evidence from studies of geneknockouts of the ClC-K1 chloride channel in mice emphasizes that thethin ascending limb is nonetheless important in the inner medullaryconcentrating mechanism ( 1, 56 ). ClC-K1 is expressed exclusively in the thin ascending limb, where it is responsible forextraordinarily high chloride permeabilities in that segment ( 85, 86 ). The knockout mice exhibited a severe concentrating defectand a failure to substantially concentrate the inner medullary interstitium in association with a low chloride permeability in itsthin ascending limbs. The basis of the defect can be understood from Eq. A1 in APPENDIX A. As can beappreciated, if the transepithelial osmolality gradient across the thinascending interstitium, this wouldprovide a negative term in the equation calculating the axialosmolality gradient (compare with single-effect condition, Table 1 ).This would create essentially a "negative single effect" as fluidflowed upward from the highly concentrated papillary tip to theless-concentrated outer medulla. Thus failure of osmotic equilibrationacross the thin ascending limb would decrease the axial gradient thatcould be generated in the inner medulla by any mechanism. Therefore, high permeabilities to NaCl and urea in the thin ascending limb areextremely important as a means of preventing dissipation of the innermedullary solutes by the upward flow in thin ascending limbs asillustrated by the ClC-K1 knockout studies.
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Single Effect in the Descending Limb of Henle
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As noted in Table 1, a positive axial osmolality gradient in theinner medulla could be generated as a result of any process thatincreases the osmolality of the luminal fluid in the thin descendinglimb relative to the interstitium. If active transport of solute inthis segment were to be implicated in generation of a single effect,the direction of transport would have to be in the secretory direction,i.e., into the lumen. Kriz and colleagues ( 41, 42 ) haveproposed such a solute secretory mechanism as part of a "cascademodel" of inner medullary concentration, but there is thus far noevidence to support the presence of active solute transport into thethin descending limb. Bonventre and Lechene ( 2 ) have alsopresented a similar concept. They suggested that the tubule fluid ofthe long descending limbs in the outer medulla may be hypertonic to theinterstitium of the upper part of the inner medulla because ofselective interaction with the interstitial subregion that surroundsthe thick ascending limbs in the outer medulla. Mathematical modelingstudies by Lory ( 48 ) have predicted that even with asubstantial rate of solute transport into the descending limb, otherconcomitant processes would decrease the axial osmolality gradient inthe renal medulla. Apparently, the extremely high water permeability ofthe descending limb would make it impossible for the thin limb tosustain the required transepithelial osmolality difference. The highwater permeability of this segment owes to the abundant expression ofthe aquaporin-1 water channel in the plasma membranes of the thindescending limb cells ( 8, 50 )., N' g: [# E" X$ X! h6 W1 O( g

Given the high water permeability of the thin descending limb, it hasalso been proposed that a single effect (luminal osmolality interstitial osmolality) could be generated as a result of unequal osmotic reflection coefficients for urea and NaCl ( 34 ).The urea concentration in the interstitium is higher than that in thedescending limb lumen, whereas the NaCl concentration in the lumen ishigher than that in the interstitium ( 15, 29, 52 ). Underthese circumstances, the urea gradient would tend to drive water out ofthe lumen and the NaCl gradient would tend to drive water inward. Ifthe reflection coefficient for NaCl were lower than that for urea,osmotic equilibration would occur with a higher NaCl gradient than theopposing urea gradient, resulting in an osmolality that is higher inthe lumen than the interstitium. That is, a single effect would begenerated (Table 1 ). This hypothesis has not been experimentally testedfor thin descending limbs from the inner medulla. However, thehypothesis seems somewhat questionable based on characterization of theaquaporin-1 water channel, the main pathway for water movement acrossthe thin descending limb. Fundamentally, a reflection coefficient of requires that the water pathway across thebarrier membranes be permeable to that solute ( 30 ).Measurements of solute permeability of aquaporin-1 heterologouslyexpressed in Xenopus laevis oocytes or reconstituted intoartificial lipid vesicles indicate that the urea and NaClpermeabilities are extremely low ( 64, 95 ). However,passive cation fluxes associated with aquaporin-1 have been reported in X. laevis oocyte expression studies, and these fluxes havebeen noted to be increased by cAMP treatment ( 94 ). Nevertheless, the chloride permeability remained very low, seemingly ruling out substantial net penetration of NaCl through aquaporin-1. Because the reservations to this model are based on theoretical considerations only, direct measurements in isolated perfused innermedullary descending limbs will be necessary to rule out the hypothesiswith certainty.

Single Effect in the Collecting Duct
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As summarized in Table 1, a single effect accounting for an axialosmolality gradient in the inner medulla could theoretically begenerated in the collecting duct if the luminal osmolality weremaintained greater than that of the surrounding interstitium throughoutmost of the inner medulla. Wexler et al. ( 93 ) have proposed one means by which this could happen. Specifically, an extremely hyperosmotic fluid may be generated in the outer medullary collecting duct and delivered to the inner medullary collecting duct(IMCD). Based on the prior studies of Lemley and Kriz( 47 ), it has been concluded that the outer medullarycollecting ducts are segregated with the thick ascending limbs in theouter medulla. Theoretically, the rapid active NaCl transport from thethick ascending limbs would concentrate the interstitium adjacent to the collecting ducts to a level that greatly exceeds the average osmolality of the outer medullary tissue. This would raise the osmolality to a high level in the collecting duct lumen, and this highly concentrated fluid would enter the IMCDs, providing a single interstitial osmolality). Amathematical model devised by Wexler and colleagues ( 93 )showed that such a process could result in concentration of the innermedullary interstitium, but this model required a special condition:the osmotic water permeability of the initial portion of the IMCD wasrequired to be very low to prevent the high luminal osmolality frombeing dissipated by the water secretion that would otherwise occur.Experimental studies by Han and colleagues ( 21 ) did not confirm that key assumption and instead found a high osmotic water permeability in the initial IMCD, apparently ruling out the model ( 21 ). Subsequent papers by Wang and colleagues ( 87, 88 ) suggested that the requirement for a low water permeabilityin the initial IMCD could be relaxed somewhat if a high rate of rapid active NaCl transport occurs out of the initial IMCD. However, based onfurther analysis using a detailed three-dimensional model of themedullary concentrating process, Thomas and Wexler ( 83 ) concluded that4 {9 x, }4 S  b3 k  `

if realistic values of urea permeability in the inner medullarydescending limbs and water permeability in the upper inner medullarysection of the collecting ducts are taken into account, even a modelincluding the three-dimensional vascular bundle structures fails toexplain the experimentally observed inner medullary osmolality gradient. interstitial osmolality) in the IMCD, based on a difference in reflection coefficients for urea and NaCl, has been proposed several times ( 2, 5, 6, 20, 27, 65, 68 ). Theprinciple is similar to that proposed for generation of a single effectin the thin descending limb as discussed above, except that thedirections of the transepithelial urea and NaCl gradients in the IMCDare opposite those seen in the descending limb. Therefore, the proposedmodel depends on the assumption that in the IMCD, the reflectioncoefficient for urea is much lower than that for NaCl. Indeed, earlymeasurements of reflection coefficients in the IMCD seemed consistentwith this assumption [see Morgan and Berliner ( 58 ) andImai et al. ( 27 ), for example]. However,subsequently the transport proteins responsible for water transport[aquaporin-2 ( 14 )] and urea transport [UT-A1( 74 )] across the apical plasma membrane of the IMCD havebeen identified by molecular cloning, providing direct evidence forindependent, highly selective transport pathways for water and urea.These results provided no evidence for a shared pathway for water and urea transport as required for a true reflection coefficient of 30 ). Indeed, careful measurements in isolated perfusedtubules demonstrated that the reflection coefficient for urea isvirtually 1 and that the apparent low value of the reflectioncoefficient was due to rapid dissipation of imposed urea gradients byfacilitated urea transport ( 9, 36 ). A mathematicalanalysis of transport of solutes and water across the IMCD indicatesthat the presence of unstirred layers (chiefly in the cytoplasm) cancontribute to the presence of an apparent reflection coefficient forurea of across the plasma membranes ( 19 ).& ?6 f1 _6 N, w/ \$ l- n( ~+ t5 H

In general, models that depend on a single effect in the IMCD are at atheoretical disadvantage relative to models that depend on a singleeffect in the loop of Henle because of the low aggregate tubule fluidflow rate in collecting ducts relative to the loop of Henle. As can beseen in Eq. A1 in APPENDIX A, the degree ofcountercurrent multiplication is directly proportional to both thenormalized tubule fluid flow rate and the magnitude of the single effect.1 m8 K* j5 ?3 [: N
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Proposed Single-Effect Mechanisms in the Vasa Recta7 w4 y3 _% r- z6 s" s& V3 H

The ascending vasa recta are lined by fenestrated endothelialcells ( 57 ), which presumably permit free exchange ofsolutes and water between the interstitium and the ascending vas rectum lumen. Consequently, the composition of the interstitial fluid hasgenerally been assumed to be similar to that of the blood plasma in theascending vas rectum. In contrast, the endothelium of the descendingvasa recta is continuous, and transendothelial gradients are apossibility. Thus it is conceivable that the inner medullaryconcentrating process could be driven by generation of a single effectin the descending vasa recta, i.e., a process that maintains theosmolality of the lumen greater than that of surrounding interstitium(Table 1 ). The water permeability of the thin descending limbs is veryhigh due to the expression of very high levels of the water channelaquaporin-1 in the plasma membranes of the endothelial cells( 61 ). Therefore, steady-state models that depend on activeor passive solute transport are unlikely to generate sustainedosmolality gradients, as discussed above with regard to the descendinglimb of Henle's loop. Nonetheless, it is conceivable that a processbased on a difference in reflection coefficients for NaCl and ureacould contribute to the concentration of solutes in the inner medullaryinterstitium by increasing the luminal osmolality above that of thesurrounding interstitium. The same reservations can be made about thismodel in the descending vasa recta as were made for the descending limbof Henle (see above).3 @2 A0 O# n7 |7 P1 Q
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NONCONVENTIONAL MODELS0 v0 [$ `( N+ H0 x# L" u" C
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Conventional models of the medullary concentrating process haveassumed steady-state conditions, ideal solutions, and negligible soluteproduction by chemical reactions (see APPENDIX A ). However,the appropriateness of these assumptions has been questioned. In theremainder of this review, we examine potential concentrating modelsbased on reconsideration of these assumptions.

Possible Role of Solute Generation Via Chemical Reactions

In 1994, Jen and Stephenson ( 28 ) provided theoreticaljustification for the view that generation of some "externalosmolyte" in the inner medulla could provide the driving force forthe inner medullary concentrating process. In their formulation, anunspecified solute is assumed to be added de novo and continuously tothe inner medullary interstitium. A subsequent mathematical modeling study by Thomas and Wexler ( 83 ) using a complexthree-dimensional model of the renal medulla confirmed that addition ofsuch a solute to the inner medullary interstitium could potentiallyexplain the axial concentration gradient in the inner medulla bydriving water efflux from the thin descending limb. This wouldconcentrate NaCl in the descending limb, setting up a favorablegradient for NaCl efflux from the ascending limb and dilution of theascending limb lumen relative to the interstitium. In effect, thisexternal solute substitutes for urea in the Kokko-Rector-Stephensonpassive model.. k* x3 C( x* h* ^+ N" Y" o) r

What could be the identity of this "external solute"? The modelrequires a chemical reaction that generates more osmotically activeparticles than it consumes. Thomas ( 82 ) has proposed thatthe external solute is lactate, which is generated by anaerobic glycolysis (the predominant means of ATP generation in the inner medulla) in the proportion of 2 lactate ions/glucose molecule consumed: −  + 2 H +

The feasibility of the proposed model depends on the fate of theH ions that are generated. If the H ionstitrate HCO 3 −, they will remove two osmotically activeparticles (HCO 3 − ions), resulting in a netdisappearance of osmotically active particles − 3  → 2 lactate −  + 2 CO 22 X( `( w# M( W" B6 J" [1 O
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Because CO 2 readily permeates lipid bilayers, it isunlikely to be osmotically effective. Alternatively, if theH ions titrate buffers other than HCO 3 −, e.g., NH 3, phosphate, and proteins with relatively neutralisoelectric points, a net generation of osmotically active particlescan be expected.

In proposing that lactate generation provides a driving force for theinner medullary concentrating process, Thomas ( 82 ) raisescritical questions about lactate transport in the inner medulla. Forthe model to explain the axial osmolality gradient in the innermedulla, the lactate generated would need to be transported out of theepithelial and endothelial cells in a polarized fashion, so as togenerate osmotic differences across individual renal tubule segments(Table 1 ). Thomas proposes that lactate should be preferentiallytransported across the basolateral plasma membranes of all cell types.3 u2 o4 G+ K$ M! N+ S
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Possible Role of Solution Nonideality in the RenalMedulla% ]; P" Z# T  K) S% P% _8 d
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Most models of the urinary concentrating mechanism have assumedthat the tubule fluid and interstitial fluids in the renal medullabehave as ideal solutions. However, as pointed out by Wang et al.( 89 ), renal medullary fluids may deviate substantially from ideality under antidiuretic conditions. Their preliminary calculations using a complex multinephron model of the renal medulla indicate that compared with ideal solution models, decreased activity coefficients for urea tend to increase predicted urinary osmolalities, while decreased activity coefficients for NaCl tend to decrease predicted urinary osmolalities. Such nonideal effects probably shouldbe taken into consideration in any model of the urinary concentrating process.
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Non-Steady-State, Periodic Models
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The potential role of periodic contractions of the renal pelvicwall as a source of energy for the concentrating process in the innermedulla has been emphasized by Schmidt-Nielsen ( 70 ). Therenal inner medulla is surrounded by the renal pelvocalyceal wall (Fig. 2 A ), a structure comprised chiefly of two thick smooth muscle layers ( 75 ). The pelvocalyceal wall undergoesintermittent contractions, which have been seen to compress the renalmedullary parenchyma ( 71 ) (Fig. 5 ). These compressions, occurring at a frequency of 15-40/min in rodents, have been seen to alter flow rates in tubule and vascular structures of the inner medulla ( 66, 73 ). The frequency of the contractions is regulated via both sympathetic and parasympathetic inputs ( 12, 40 ). Thuspelvocalyceal wall contractions impart a periodic character to thefunction of the inner medulla that has been largely ignored in formalmathematical modeling studies of the urinary concentrating process. Aspointed out by Schmidt-Nielsen ( 70 ), the pelvic wallcontractions could provide an energy input to the concentrating processitself. In support of this view is the longstanding observation thatdisruption of the continuity of the pelvocalyceal wall markedly reducesthe tonicity of the inner medullary tissue and urine ( 10, 16, 60 ). Two studies have directly addressed this possibility with differing conclusions. Oliver et al. ( 60 ) tested theeffects of paralyzing the upper portion of the ureter (which surrounds the papillary tip) in young rats and found no impairment ofconcentrating ability. In contrast, Schmidt-Nielsen et al.( 72 ) found in hamsters that paralysis of the pelvic wall(or mechanical damage to the pelvic wall) significantly decreasedconcentrating ability. In the remainder of this article, we present adiscussion of ways that periodic contractions of the renal pelvic wallcould concentrate the inner medulla, including consideration of therole of hyaluronan in the interstitial matrix as a molecularmechano-osmotic transducer for the concentrating process.
9 E) w- `5 V/ y  w7 {' c! d
Fig. 5. Renal pelvic wall contractions in hamster kidney. A : back-illuminated image of renal papilla. Video clipshowing contractions can be viewed at URL http://ajprenal.physiology.org/cgi/content/full/284/1/F433/DC1 orthrough the WWW at URL http://rover.nhlbi.nih.gov/labs/review/index.htm (login: lkem; password: review). B : optical recordings ofintensity of transmitted light during contractions of renal pelvic wallshowing morphology and frequency of contractions. The contraction phasetypically takes up 1/5 of the cycle and the relaxation phase 4/5 of thecycle. Adapted from Ref. 69 with permission.

Before a consideration of specific models, it is important to note thatthe formulation which defines possible single-effect mechanisms for theinner medulla given in APPENDIX A applies only to thesteady state. Further work will be needed to extend the analysis toperiodic and other non-steady-state conditions. Nevertheless, it isreasonable to assume that in the periodic case, single-effectconditions similar to those presented in Table 1 will apply. Inparticular, we assume that positive axial osmolality gradients will begenerated when the contents of the descending limbs (or descending vasarecta) are concentrated relative to the surrounding interstitium orwhen the contents of the ascending limbs (or ascending vasa recta) arediluted relative to the surrounding interstitium.
1 f4 A) k  _" n* j" M) b* C3 }
CONCENTRATING MODEL DRIVEN BY RENAL PELVIC WALL CONTRACTIONS:HYALURONAN AS A MECHANICO-OSMOTIC TRANSDUCER

Schmidt-Nielsen ( 70 ) was the first to emphasize theremarkable spongelike properties of the renal interstitial hyaluronan matrix and the potential role of hyaluronan in concentration of themedullary interstitium. In this section, we describe a concentrating model based on the view that the inner medullary interstitium consistsof a semisolid, viscoelastic hyaluronan gel rather than being a freelyflowing aqueous compartment. As outlined in detail below, it isproposed that the hyaluronan matrix can store the mechanical energyfrom the pelvic contractions by direct mechanical compression withoutthe need to generate high hydrostatic pressures and can utilize thisenergy to lower interstitial pressure after completion of eachcontraction of the pelvic wall to drive water efflux from thedescending limb of Henle. The latter process would increase the luminalosmolality to above that of the interstitium, thereby generating asingle effect for concentration of urine. Before laying out this model,we summarize the necessary background regarding the biochemistry ofhyaluronan and its physicochemical properties.# ~( F* p8 W% _  x
- K% L5 _' y" L1 p5 u6 v. L5 e2 C
Hyaluronan (hyaluronic acid) is a member of a family of biomoleculescalled glycosaminoglycans (GAGs), which are all unbranched polysaccharide chains composed of repeating disaccharide units. Asidefrom hyaluronan, other mammalian GAGs include chondroitin sulfates,dermatan sulfate, keratan sulfate, heparan sulfate, and heparin.Hyaluronan differs from the other GAGs in that it is not generallycovalently linked to proteins to form proteoglycans and is not sulfated( 23 ). Furthermore, in contrast to the other GAGs that aresynthesized in the Golgi apparatus, hyaluronan is produced at theplasma membrane by an integral membrane protein, hyaluronan synthase(HAS) ( 84, 90 ). Three mammalian HAS genes have beenidentified, namely, HAS1, HAS2, and HAS3. All three produce hyaluronan on the cytoplasmic sideof the plasma membrane and transport it across the plasma membrane tothe extracellular fluid. Thus hyaluronan secretion does not directlyinvolve vesicular trafficking, in contrast to most other types ofsecreted biomolecules. Because of the importance of GAGs in thestructure of connective tissues, such as cartilage, bone, synovialfluid, intervertebral disks, tendon, skin, and cornea, thephysicochemical properties of these substances have been thoroughlycharacterized ( 11 ).6 a, v; p: ~- X- [7 R
  s& b! g; Q2 S
Several studies have demonstrated that hyaluronan is highly abundant inthe interstitium of the renal inner medulla in contrast to the lowamounts seen in other regions of the kidney ( 4, 13, 18 ).Figure 6 illustrates the high level ofhyaluronan accumulation in the rat inner medulla as revealed by Alcianblue staining. Other GAGs are present in the inner medulla in much lower amounts. The hyaluronan in the inner medulla is believed to beproduced by a specialized interstitial cell (the so-called type 1 interstitial cell) that forms characteristic "bridges" between thethin limbs of Henle and vasa recta ( 62 ).

Fig. 6. Alcian blue staining of normal rat kidney revealing distribution ofhyaluronan in inner medulla. Bar = 2 mm.

Figure 6 illustrates that the hyaluronan-laden inner medulla iscontained within the renal pelvic wall with its thick smooth musclelamina. The compression of hyaluronan in the medullary interstitium bythe peristaltic contractions of the pelvic wall can hypotheticallyserve to generate a single effect for inner medullary concentration intwo ways: 1 ) by lowering the osmolality of the surroundinginterstitial fluid; and 2 ) by storing mechanical energy,which when released can create forces that drive water absorption fromthe descending limb of Henle. We consider these two mechanisms in turn.
/ i3 @& I- R( t' m: x
Hyaluronan Contraction May Lower Local Osmolality/ ^* }) Q0 V- S5 S3 @

Hyaluronan is a large, unbranched polysaccharide molecule composedof repeating glucuronic acid/ N -acetylglucosaminedisaccharide subunits (Fig. 7 A ). 1 It is a polyanion, owing to the carboxylate groups of the glucuronic acid subunits. It is a huge molecule, typically with a molecular massin the range 1,000-10,000 kDa. It is strongly hydrophilic andadopts highly expanded, stiffened random-coil conformations that occupya huge volume relative to their mass. In solutions of physiologicalionic strengths, the domains of individual molecules begin to overlapat low concentrations ( domains are readilycompressed when concentrated under a mechanical load and expand whenthe compressive force is removed. Thus the inner medullary interstitiumcan be visualized as being composed of a compressible, viscoelastichyaluronan matrix. The extended state of hyaluronan owes partly torepulsive electrostatic forces exerted by neighboring COO groups, which maximize the distance between neighboring negative charges (Fig. 7 B ), and partly by the constraints of theglycosidic bonds that prefer somewhat extended conformations. Thiscreates a swelling pressure (turgor) that allows the hyaluronan matrix to generate an elastic-like force (resiliance) that resistscompression. When HA is compressed, as may occur in a meniscus in theknee joint under load-bearing conditions, the repulsive force ofneighboring COO groups is overcome in part byimmobilization (or "condensation") of cations (chieflyNa ), forming a localized crystalloid structure (Fig. 7 C ). Thus compression of a hyaluronan gel results in alowering of the local Na ion activity in the gel. Inaqueous solutions in Donnan equilibrium with the gel, one can predict adecrease in the NaCl concentration secondarily to thecompression-induced reduction in Na activity within thegel. Thus the free fluid that can be expressed from such a gel wouldhave a lower total solute concentration than that of the gel as awhole. Such an effect could be important in the renal inner medullawhen the force of pelvocalyceal contractions compresses the innermedullary interstitial matrix. The slightly hypotonic fluid expressedfrom the interstitial matrix would tend to escape the inner medulla viathe ascending vasa recta, which is the only structure that remains openduring the compressive phase of the contraction cycle( 49 ). Thus an ascending stream (the ascending vasa recta)would have a lower total solute concentration than the interstitium asa whole and therefore this would create a single effect for medullaryconcentration (Table 1 ).; E' s  g) G' n/ f& l0 `: J% U

Fig. 7. Structure of hyaluronan. A : disaccharidesubunit. B : extended polyanion. Hyaluronan is a linearpolymer of the disaccharide shown in A, with a molecularmass in the range 1,000-10,000 kDa. Polymer tends to remain in theextended state because of repulsion of negative charges of carboxylategroups. C : when the hyaluronan polyanion is compressed, freecations are sequestered.

Conversion of Mechanical Energy to Chemical Potential Energy Viathe Viscoelastic Properties of Hyaluronan
1 X! @1 I8 S* M; M7 |7 j/ r
During the relaxation phase of the pelvocalycealcontraction-relaxation cycle, two additional processes may contributeto urinary concentration through creation of a single effect (luminal interstitial osmolality) across the thin descending limb epithelium. Both processes result from relaxation of the compressed hyaluronan matrix: 1 ) water would be absorbedfrom the descending limb as a result of a decrease in the hydrostatic pressure in the medullary interstitium; and 2 ) water wouldbe absorbed from the descending limb as a result of elastic forces exerted directly by the expanding medullary interstitial matrix. Therelevant forces have been described by Maroudas ( 51 ) in the analysis of water transport from articular cartilage, aglycosaminoglycan-filled tissue similar in properties to thehyaluronan-filled inner medullary interstitium. Fundamentally, the fluxof water into and out of cartilage (or the inner medullaryinterstitium) may be viewed as being driven by three forces,expressed as pressure differences: P osmotic, P hydrostatic, and P elastic. Inthe context of forces determining water transport between the thindescending limb and the hyaluronan matrix of the inner medulla, P osmotic represents the osmolality difference betweenthe lumen and the interstitial matrix, P hydrostatic represents the hydrostatic pressure difference between the lumen andthe interstitial matrix, and P elastic represents theforce exerted due to the elastic deformation of the interstitial matrix(given here as an equivalent pressure difference). According to thisformulation, during the relaxation phase after passage of the pelvicperistaltic wave, elastic forces from expansion of the compressedhyaluronan would increase water transport in two ways: 1 ) P elastic could directly draw water out of the descending limb (and other water-permeable structures); and 2 ) thetendency to interstitial expansion due to the relaxation of thecompressed hyaluronan may lower the interstitial pressure below ambientpressure levels to produce a hydrostatic pressure difference P hydrostatic, increasing water withdrawal from thedescending limb and other water-permeable structures. The tendency ofthe pressure drop in the interstitium to cause cavitation would becountered by the gel structure. In the inner medulla, the flow of waterdriven by the sum of elastic and hydrostatic pressure forces( P elastic P hydrostatic ) wouldconcentrate the lumen of the descending limb relative to theinterstitium. As water flows out of the descending limb of Henle, thelimiting condition of no water flow is approached where P osmotic = P elastic P hydrostatic. Here, P osmotic represents a limiting single-effect value.
: F7 B; |" C' [# L
It is possible that the sum P elastic P hydrostatic may be much larger than 1 atm, althoughmeasurements of this force are not presently available. It is importantto reemphasize that this represents a very low pressure in theinterstitium rather than a very high pressure in the renal tubulerelative to ambient pressures. The fall in hydrostatic pressure in theinterstitial matrix would be expected to be bounded, if one assumesthat "absolute negative" hydrostatic pressures are animpossibility, so that P hydrostatic would not exceed 1 atm. Nevertheless, negative absolute pressures have been reported, forexample, in the xylem of trees as a result of transpiration( 70 ). These pressures are believed to furnish the drivingforce for the flow of water upward from the roots to the tree tops oflarge deciduous trees, overcoming the weight of a 200-ft column ofwater. Xylem pressures of 5 to 6 atm relative to ambient pressurehave been reported ( 63 ). For values of P elastic P hydrostatic ranging from 1 to 6 atm, the value of the single-effect osmolality differenceacross the thin descending limb would range from 40 to 240 mosmol/kgH 2 O [ C osm = ( P elastic P hydrostatic )/ · RT ].As described in APPENDIX B, this would give a urinary osmolality in the range from 1,416 to 4,000 mosmol/kgH 2 O,spanning the value of maximal urinary osmolality measured in normalrats (2,900 mosmol/kgH 2 O) ( 31 ).; x( G: I. j; x9 l9 I
2 ^& B% S( Z0 Q" `4 g4 V' k! J2 O0 O2 H
In summary, the chief new concept presented in this review is that theinner medullary interstitium might best be modeled as a viscoelasticsystem with stress-strain properties, rather than a purely hydraulicsystem. This necessitates consideration of force terms other thanhydrostatic pressure and osmotic pressure. The main additional forceterm that we add to the analysis is elastic force. During innermedullary compression resulting from the contraction of the pelvicwall, the compression of the hyaluronan matrix stores some of themechanical energy generated from the smooth muscle contraction. Thiscompression would not require an increase in hydrostatic pressure butwould simply require a direct mechanical compression of the hyaluronanmatrix as one would compress a steel spring. After passage of aperistaltic wave, the compressed hyaluronan will tend to spring backfrom its compressed state, exerting an elastic force and loweringinterstitial pressure, thereby driving water from the descending limband other water permeable structures. The water efflux wouldconcentrate solutes in the tubule lumina. This would complete an energyconversion starting with ATP hydrolysis in smooth muscle cells of thepelvic wall, leading to compression of the hyaluronan in the medullary interstitium and then to an increase in electrochemical potential dueto concentration of solutes in the tubule lumina. We have analyzed thisprocess here only with regard to mass balance requirements. Clearly,further theoretical and experimental analysis is required to evaluatethe feasibility of these proposed energy transfers purely on the basisof energy balance, as done previously for steady-state systems( 78, 79, 91 ). The single effect generated from thisprocess could add to single effects from other processes, e.g., lactategeneration in the renal medulla, to concentrate the urine.
; `  G+ z* p5 `; a- D6 R
An important question that must be addressed experimentally is whetherthe rate of energy generation by ATP hydrolysis and contraction of thepelvic wall is sufficient to account for the energy input needed toconcentrate the collecting duct urine as it flows along the innermedullary axis. An additional question concerns the stress-stainproperties of the renal papilla and whether the modulus of elasticityis sufficient to mediate the proposed mechanical energy transduction.Finally, an important experimental question is the degree to which thebasement membrane of the thin limbs of Henle can withstand hypotheticaltransepithelial pressure differences of 1 atm or more withoutundergoing permanent deformation. Perhaps the small radius of thesetubules plays an important role in limiting the wall tension needed tocounter such pressure forces according to the Law of Laplace ( P = T/ r ).  i" {  X1 A2 j: H, Y
7 v! |" A& |9 t% G% e6 J
CONCLUSION& D' _. I, B8 I2 `3 d! T; w; h& Z
: O4 B+ k4 r& W4 l7 Z; a2 ?1 }! t
The identification of the process responsible for concentration ofsolutes in the interstitium of the inner medulla has been elusive. Thelack of definition of these mechanisms undoubtedly owes to thetechnical difficulty of studying processes in the intact renal medullawithout disrupting these processes. In recent years, interest ininvestigation of this problem has flagged as renal physiologists haveturned their attention to individual genes and proteins, focusing onthe molecular aspects of transport regulation and especially onprocesses that are amenable to study in cell culture. Nevertheless, thepurely integrative question of how the inner medullary interstitium isconcentrated remains as important as ever. This review has beenpresented with the idea of stimulating further work on the problem. Byproposing specific hypotheses involving specific genes and geneproducts, e.g., the hyalurononan synthase (HAS) genes and hyaluronan,we hope to stimulate investigators to reexamine this problem with thetools of 21st-century physiology.
. X  G  Z+ E: p  M
For example, it may be possible to use transgenic and gene knockouttechnology to address critical elements of the model such as 1 ) targeted/conditional knockouts of the HAS2 gene in the renal inner medulla; 2 ) targeted deletion ofinterstitial cells of the renal inner medulla, which produce theinterstitial HA; and 3 ) targeted deletion of contractileproteins of the pelvic wall.
) l1 n3 p! u& o% t$ \. j3 C* R" T
APPENDIX A7 r, q9 Y0 k; [& r$ W2 s
8 {0 G/ ~7 S' ^" |! r' H( }
Derivation of General Mass Balance Equation for Renal InnerMedulla for Steady State
9 K+ p- H+ N8 F/ f; _9 n& J
If we view the renal medulla as consisting of parallel tubes(renal tubule segments and vasa recta), oriented in the x direction, we can define the following terms: i ( x ) = net axial volume flow in the  i. P- U' Y. p; u( y( }

C ik ( x ) = concentration ofthe k th solute in the i th tube# k- ^0 v2 [& ]- {1 `
7 D3 w7 K1 g( @9 m3 E/ b! |
at medullarylevel x

Q i ( x ) C ik ( x ) = netaxial flow of the k th solute in the i th tube/ I. r9 V, a0 M( `2 A$ F8 ~
* B$ C3 Y8 a1 T9 V% D5 {: [3 I
at medullary level x1 B5 j. ]4 B/ X: x% F8 p, w. |

The flows are assumed to be positive if oriented towardthe renal papillary tip and negative if oriented toward the cortex (seeFig. 2 for definition of structures and control volumes).6 h, A! M+ i, ?/ n/ R* [

Considering a control volume bounded by x 1 atthe top and x 2 at the bottom, mass balance equations can be written for water andindividual solutes. Assuming that there are no chemical reactions inthe system that create or destroy any of the solutes, and that thefluid density is everywhere equal, water balance is given by ∑ i Q i ( x 1 )  = 0 c9 s9 c, ^: m. R) s* v
. ]6 W' R( I+ y3 M
∑ i Q i ( x 22 O& z/ {. Z. W0 V' ]
3 N) |+ }, P5 `( ~4 j
( A1 )
+ V7 f) D* g9 ~
and mass balances for each solute k are given by ∑ i Q i ( x 1 ) C ik ( x 1 )  = 

∑ i Q i ( x 2 ) C ik ( x 2
7 {( s9 F) b2 {1 R
( A2 ). o# H1 ^& G( Y" X, x+ G- P
" o6 Z0 f0 R9 E4 H
Because we are interested specifically in concentration of thefinal urine, we consider the balance where the bottom boundary of the control volume x 2 is at point L, the papillary tip. In this case, there is a single flowstream crossing the bottom boundary, viz., the final urine.Defining Q u as the final urinary volume flow rate andC k u as the concentration of solute k in the final urine, Eqs. A1 and A2 can be rewritten ∑ i Q i ( x 1 )  =  Q u: L) E  Q+ o- ]( e4 n# M( p" H
  m) I, q, v* d: l1 N* W1 R4 E) B
( A3 )  q. S6 v( J& s; t. y4 V% E- S% l$ X

and ∑ i Q i ( x 1 ) C ik ( x 1 ) = Q u  C k u# i" k" f4 {% t5 ~3 @

( A4 )( i- Y0 k# b& z7 D1 C% z
+ q' }0 e/ ?% R2 M3 P) G
For this analysis, we wish to consider the total soluteconcentration rather than the concentrations of the individual solutes. Consequently, we defineC i M ( x ) as the totalsolute concentration in the i th tube at axial level x, which is given by i M ( x ) = 
/ I. g* K1 [$ ]
∑ k C ik ( x0 W. Z, _: e, f; i3 u1 l, C
1 ]. e8 P2 s6 B" y9 o. ^
The total solute concentration in the final urine is defined asC Mu. Using these terms, a mass balance for total solutes can be derived from Eq. A4, yielding ∑ i Q i ( x 1 ) C i M ( x 1 )  =  Q u  C Mu0 o* `5 v. ]- d& Q* L( m4 ?2 e) U
0 a9 q; L- o7 ]+ o0 P. K
( A5 )2 d( I/ Z+ o; H! ^0 q
' n' V2 X9 d+ m& E! |1 p0 n" L
The analysis so far does not take into account the peritubularinterstitial composition. We define C PM ( x ) to bethe peritubular interstitial total solute concentration at level x. In doing so, we assume that the interstitial compositionis not a function of position in a direction perpendicular to the x -axis. We can modify Eq. A5 by arbitrarilysubtracting the term Q u C PM ( x 1 ) from both sides and rearranging (using Eq. A3 to substitute for Q u on the left-handside), giving ∑ i Q i ( x 1 ) [C i M ( x 1 ) − C PM ( x 1 )] = Q u [C Mu  − C PM ( x 17 ~6 u* _7 Z8 Q8 }7 U# p, _: F
8 j6 E+ G) W! I! M) `4 }: }
( A6 ), e. S. o) E. V4 u7 J% T
- \- j6 ?( I7 a# t) q
If we assume that the collecting duct is in osmotic equilibriumwith the medullary peritubular interstitium at the papillary tip( x = L ), i.e., C PM ( L ) = C Mu, then Eq. A6 can be rearranged to give theaxial total solute gradient from point x 1 to thepapillary tip PM ( L ) − C PM ( x 1 ) = 9 {& B3 U. q4 |5 V8 x: Q+ F

∑ i [Q i ( x 1 )/Q u ] [C i M ( x 1 ) − C PM ( x 1
2 i- f- ]9 b$ s' y% ]
( A7 )
" N3 D7 c' G0 {3 d" ]8 N
In other words, the osmotic gradient in the renal medullaryinterstitium (expressed on the left-hand side of the equation) isdetermined by the total solute concentration gradient across eachstructure multiplied by the normalized flow rate in that structure. Theimplications of this equation are described in the text.4 D6 E/ Q- K! S! W

APPENDIX B

Calculation of Maximal Urinary Osmolality That Could be Generatedby Pelvic Contractions Based on Mechano-osmotic Energy Transduction byHyaluronan

If we consider a rat with a mean single nephron GFR in long-loopnephrons of 45 nl/min excreting 0.25% of filtered water, we cancalculate the multiplier factor[Q DL ( x )/Q u ] for text Eq. 1, representing the ratio of total flow in all descending limbs atthe inner-outer medullary junction to the final urinary flow. Of the38,000 nephrons in a rat kidney ( 35 ), 29% have loops ofHenle that extend into the inner medulla ( 76 ), giving atotal of 11,000 long-looped nephrons. If we assume that two-thirds of the filtered water is absorbed in the proximal tubule( 17 ), the aggregate flow out of the proximal tubules canbe calculated to be 15 nl · min 1 · nephron 1 × 11,000 nephrons = 165 µl/min. If we assume that theosmolality in the descending limbs increases from 300 to 900 mosmol/kgH 2 O in the outer medulla solely as a result ofwater abstraction ( 38 ), then the aggregate flow indescending limbs entering the inner medulla would be 165 µl/min × (300/900) = 55 µl/min. The final urinary flow(assuming a mean SNGFR of 45 nl/min) would be 45 nl · min 1 · nephron 1 × 38,000 nephrons × 0.0025 = 4.28 µl/min. The flow ratioor multiplier factor [Q DL ( x )/Q u ]is 55/4.28 = 12.9. This flow ratio would be the mean integratedflow ratio over the entire pelvic contraction cycle. For mean singleeffect values ranging from 40 to 240 mosmol/kgH 2 O, theaxial inner medullary osmolality gradient calculated from text Eq. 1 would range from 516 to 3,096 mosmol/kgH 2 O. This value would be added to the osmolalityat the inner-outer junction (900 mosmol/kgH 2 O) to get arange of values for maximal urinary osmolality from 1,416 to 3,996 mosmol/kgH 2 O.: c( J9 z7 E/ Y

These calculations ignore single effects that might be generated in thedescending vasa recta and collecting ducts by the same mechanism butalso ignores the fact that dissipative terms in text Eq. 1 would tend to reduce the gradient generated.

ACKNOWLEDGEMENTS; g. d' K) |$ u8 d  v$ h6 |) x  K/ R. k

The authors gratefully acknowledge the career and contributions ofBodil Schmidt-Nielsen; many of the concepts presented in this revieworiginated in her work.
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