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

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Abstract

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.

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Abbreviations

OM:

outer medulla

IM:

inner medulla

DHL:

descending Henle’s limbs (generic term for all SDL and LDL)

SDL:

short descending loop of Henle

LDL:

long descending loop of Henle

ATL:

ascending thin limb

TAL:

thick ascending limb

SDT:

distal tubule of short nephrons

LDT:

distal tubule of long nephrons

CD:

collecting duct (tube 4)

DVR:

descending vasa recta (tube 5)

AVR:

ascending vasa recta (tube 6), also assumes the role of Interstitium

i :

tube number (i=1, ..., 21)

j :

solute number (j=1 for salt,j=2 for urea)

x :

distance along the cortico-medullary axis (mm)

F iv :

axial volume flow along tubei (mm3 s−1)

F ij :

axial flow of solutej along tubei (nmol s−1), =F iv ·c ij

J iv :

transmural volume flux out of tubei per unit tube length (mm2 sec−1)

J ij :

transmural solute flux out of tubei per unit tube length (nmol mm−1sec−1)

c ij :

concentration of solutej in tubei (mmol l−1=nmol mm−3)

Lp i :

hydraulic permeability of tubei (mm sec−1 (mosm/l)−1)

P ij :

permeability of tubei to solutej (mm sec−1)

N i :

number of tubesi at a given depth,x, in the medulla

r i :

radius of tubei (mm)

A i :

total circumference of tubesi(=2πr i N i ) (mm)

σ ij :

reflection coefficient of tubei to solutej

a ij :

maximum rate of active transport (nmol mm−2 sec−1)

b ij :

Michaelis constant (mmol l−1)

RT :

universal gas constant times temperature (0.02545 atm (mmol/l)−1 at 37°C)

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  1. Faculté de Mèdecine Necker, INSERM U. 323, 156, rue de Vaugirard, 75015, Paris, France

    S. R. Thomas

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Thomas, S.R. Effect of varying salt and urea permeabilities along descending limbs of Henle in a model of the renal medullary urine concentrating mechanism. Bltn Mathcal Biology 53, 825–843 (1991). https://doi.org/10.1007/BF02461486

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  • DOI: https://doi.org/10.1007/BF02461486

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