Institut Nationale de la Santé et de la Recherche
Médicale, Unité 467 Necker Faculty of Medicine, 75730 Paris Cedex 15, France
This study gives the first
quantitative analysis of net steady-state transmural fluxes of water,
urea, and NaCl in a numerical model of the rat renal medulla in
antidiuresis, revealing the model's predictions of water, urea, and
NaCl cycling patterns. These predictions are compared both to in vivo
micropuncture data from the literature and to earlier qualitative
proposals (e.g., K. V. Lemley and W. Kriz. Kidney Int. 31:
538-548, 1987) of cycling and exchange patterns based on medullary
anatomy and available permeability and transport parameter
measurements. The analysis is based on our most recent
three-dimensional model [X. Wang, S. R. Thomas, and A. S. Wexler.
Am. J. Physiol. 274 (Renal Physiol. 43):
F413-F424, 1998]. In general agreement with earlier proposed patterns, this analysis predicts the following: 1) important
water short-circuiting from descending structures to ascending vasa recta in most medullary regions, 2) massive urea recycling
in the upper inner medulla, 3) a progressive increase of the
ratio of urea to total osmoles along the corticopapillary axis,
4) urea dumped from the collecting ducts (CD) into the deep
papilla is returned to the cortex essentially via outer medullary short
vasa recta, bearing witness to a shift from the long descending limbs and vasa recta of the inner medulla (IM) to short structures in the
outer medulla (OM). The analysis also shows that the known radial
heterogeneity of the inner stripe (IS) implies unequal osmolalities in
long descending limbs, vasa recta, and CDs entering the IM across the
OM/IM border and explains the model's unorthodox osmolality profile
along the CD. In conflict with micropuncture evidence of a doubling of
urea flow in superficial Henle's loops (SHL) between the end proximal
and early distal tubule (T. Armsen and H. W. Reinhardt.
Pflügers Arch. 326: 270-280, 1971), the model
predicts net urea loss from SHL due to the model's inclusion of
nonneglible measured urea permeability of medullary thick ascending limbs [M. A. Knepper, Am. J. Physiol. 245 (Renal
Fluid Electrolyte Physiol. 14): F634-F639, 1983]. We present a
suite of adjusted model permeabilities that improves agreement with the
micropuncture data on this point. In conclusion, this modeling analysis
of solute and water recycling serves as a quantitative check on
qualitative propositions in the literature and allows closer critical
comparison of model behavior with published experimental results than
was heretofore possible.
 |
INTRODUCTION |
THE URINARY CONCENTRATING MECHANISM remains a mystery
despite a long history of both experiment and modeling efforts. The basic enigma centers on our inability to explain the origin of the
corticopapillary gradient of osmolality in the passive inner medulla,
i.e., in the absence of evidence for active transepithelial salt
transport. The earliest explanation, the "passive hypothesis" (PH), was set down in 1972 by Stephenson (35) and by Kokko and Rector
(17). Modeling studies based on this hypothesis predicted the
permeabilities in various nephron segments in order for the PH to
explain the inner medullary gradient. When it became possible to
measure these permeabilities in in vitro microdissected tubules, they
were found not to agree with the model's requirements. In particular,
salt and urea permeabilities in the inner medullary (IM) portion of the
long descending limbs (LDL) were found to be higher in species that
concentrate well than in those, such as the rabbit, that cannot
elaborate a concentrated urine, whereas the PH requires exactly the
opposite. In the context of the PH, solute entry (especially urea
entry) into the LDL compromises the inner medullary osmotic gradient
(21, 36, 43). Although it is tempting to question the validity of the
permeability measurements, it is also clear from micropuncture studies
at the papillary tip (9) that there is considerable urea entry into
long Henle's limbs somewhere between the end of the proximal tubule
and the tip of the medulla, i.e., either in the outer or inner medulla or both. Therefore, we are brought to the conclusion that the PH misses
some essential feature of the concentrating process.
Up to now, virtually all modeling studies testing new hypotheses or the
effects of new permeability measurements or anatomical juxtapositions
have judged the degree of success of new model features based on a
single criterion, namely, the predicted osmolality of fluid leaving the
collecting duct (CD). There have been no studies that employ model
predictions of the cycling of water and solutes among the various
nephron and vascular pathways and compare them with the several
thoughtful discussions in the literature based on anatomy and
permeability data. In particular, Lemley and Kriz (22), Bankir and de
Rouffignac (3), Jamison and Robertson (13), de Rouffignac (30), and
others have made detailed suggestions about probable recycling paths
for water, urea, and salt founded in the general framework of the PH
but enhanced by additional knowledge of the system. A recent model (44)
(hereafter called the WKM model, for Wexler-Kalaba-Marsh) incorporated
as much detail as possible, and it seems to be an improvement over earlier models, since it "concentrates better" (however, WKM is not without its critics, see Ref. 37). However, it remains the case
that increasing salt and/or urea permeabilities along the inner
medullary descending limb in these models leads to worse, not better,
inner medullary osmotic concentration; so there remains a fundamental problem.
In hopes of suggesting some new directions for research, the present
study explores the detailed recycling patterns predicted by our most
recent incarnation of the WKM model (41), compares these patterns with
those predicted by the authors mentioned above, and also compares model
predictions of fractional deliveries to structures in the papillary tip
and in accessible surface loops with available experimental data. Since
this model is currently our best attempt to represent present
hypotheses, this study is a gauge of the extent to which the suggested
recycling patterns are in fact consistent with known anatomy and
permeability measurements. We find that on most points the suggested
patterns match those observed in the simulation, but the exceptions are
interesting and may be important for improving our understanding of
this system.
Glossary
| OM |
Outer medulla
|
| IM |
Inner medulla
|
| OS |
Outer stripe
|
| IS |
Inner stripe
|
| UIM |
Upper inner medulla
|
| TZ |
Transition zone
|
| LIM |
Lower inner medulla
|
| LDL |
Long descending limb
|
| LAL |
Long ascending limb
|
| LHL |
Long Henle's loop
|
| SDL |
Short descending limb
|
| SAL |
Short ascending limb
|
| SHL |
Short Henle's loop
|
| LDV |
Long descending vasa recta
|
| LAVn |
Long ascending vasa recta
|
| LVR |
Long vasa recta
|
| SVR |
Short vasa recta
|
| SDV |
Short descending vasa recta
|
| SAVn |
Short ascending vasa recta
|
| CD |
Collecting duct
|
| OMCD |
Outer medullary collecting duct
|
| IMCD |
Inner medullary collecting duct
|
| GFR |
glomerular filtration rate
|
| SNGFR |
Single-nephron glomerular filtration rate
|
| FLi |
Filtered load of substance i
|
| SNFLi |
Single-nephron filtered load of substance i
|
| Fi,
Fij
(x) |
Tubular flow of i, tubular flow of i in
tubule j at point x, where x = 0 is
corticomedullary border, and x = L = 0.6 cm is papillary tip
|
| %FDi |
Fractional delivery of i at a given point x
as a percent of total filtered load, 100 × Fi(x)/FLi
|
| %SNFDi |
Fractional delivery of i per tubule at a given point
x as a percent of single-nephron filtered load, 100 × (Fi(x)/n(x))/SNFLi, also equal to (TF/P)i/(TF/P)inulin
|
| FEi |
Fractional excretion of i, = FCDi(L)/FLi
|
| (TF/P)i |
Ratio of tubular fluid to plasma concentrations of i
|
| (U/P)i |
Ratio of urinary to plasma concentrations of i
|
| Uosm |
Urine osmolality (mosmol/l)
|
 |
METHODS |
Model Description
The present study treats only the case of the antidiuretic rat kidney.
The mathematical description of tubular flow and transport and the
numerical solver are described in previous work (38, 42, 44). These
steady-state models were based on existing qualitative and quantitative
descriptions of rat renal medullary anatomy [see especially Lemley and
Kriz (22)].
The present analysis uses our most recent model (41), which, compared
with the original WKM model, more faithfully represents the anatomy of
the IM and OM and measured permeabilities in all segments. The
architectural organization of the renal medulla is shown in Fig.
1. Figure 1, left, shows
transverse cuts at each medullary level, indicating the relative
positions of each tubular structure and giving the "connection
strengths" used to calculate solute and volume exchanges between
structures. In each medullary zone, transmural and convective
connections between structures are represented by straight lines and
curved arrows, respectively. Each circle represents a collection of a
given type of tubules or vessels, the numbers of which used in the
model are listed in Table 1. The distances
between structures in the diagram are not to scale; relative anatomic
distances between the respective tubes in the model are accounted for
by the values of the connections strengths. Figure 1, right,
gives a view of these relationships along the corticomedullary axis to
illustrate the continuity from one medullary zone to the next, but
since it is flattened to two dimensions, it does not faithfully
represent the spatial distribution of the structures.

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Fig. 1.
Model illustration. Left: placement of each structure in
cross section through each medullary region. Right: tubes in
a flattened 2-dimensional projection, approximately in their correct
positions. Values in left (e.g., 0.33, 0.25) indicate
connection strengths from Henle's loops and from descending vasa recta
to ascending vasa recta, reflecting their relative proximities in each
region. Distances are not to scale. Arrows indicate convective
connections.
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In accordance with the assumed tubular distribution (Table 1), the
ratio of SDL population to LDL population is two to one in outer
medulla (3, 22); the ratio of the Henle's loop population to the
collecting duct population is six to one in outer medulla (~5 to 1 in
Ref. 16). At the outer-inner medullary border, the ratio of the number
of long loops to collecting ducts is two to one, and the ratio becomes
one to one as they approach the tip of the papilla (16). The
model structure thus explicitly represents the six nephrons
associated with a single OMCD, but it is scaled according to total
numbers of nephrons at each medullary level in rat kidney. Thus
"total GFR" (as given, e.g., in Table 3) is not here numerically
equal to whole kidney GFR but rather equals a value six times greater
than the SNGFR.
Boundary conditions and parameters.
The model treats the renal medulla from the corticomedullary border
down to the papillary tip. The boundary conditions (flow rates and
concentrations) are specified for all the descending limbs and vasas
recta at the corticomedullary border, for mass conservation in the
descending and ascending structures at the loop bends, and for solute
and fluid reabsorption at the end of the late distal tubule (entry to
the CD). Proximal tubules are assumed to reabsorb two-thirds of
filtered NaCl and volume flow and one-third of filtered urea, so at the
corticomedullary border, single-tubule flow rates in LDL and SDL are 10 nl/min and NaCl and urea concentrations are 140 and 18 mM. The cortical
portions of the distal tubules and cortical collecting ducts are not
treated explicitly. Instead, fluid and solute entry into the medullary collecting ducts are calculated from values at the top of the ascending
limbs, using three assumptions: 1) fluid entering the medullary CD is isosmotic to blood; 2) NaCl concentration is
35 mM; and 3) urea delivery to the CD is 85% of its
delivery to the beginning of the distal tubules, i.e., the distal
tubules reabsorb 15% of the urea delivered to them by the ascending
limbs. The detailed formulation is given in previous work (38, 42, 44).
Model parameters (see Table 3 of Ref. 41) assume values of tubular and
vascular transport properties based on available experimental
measurements in rat and hamster in antidiuresis. We assumed that the
length of the medulla is 6 mm divided as: outer stripe, 0.7 mm; inner
stripe, 1.3 mm; upper portion of the inner medulla, 1.3 mm; transition
zone, 0.2 mm; and lower portion of the inner medulla, 2.5 mm.
Numerical method.
The numerical package based on collocation, COLNEW (available in the
netlib archives on the internet at
http://netlib.bell-labs.com/netlib/ode/), was used to solve the models.
Detailed descriptions of the system equations and numerical scheme have
been given previously (38, 42, 44). The computations were performed in
double precision on an IBM RS/6000-590 or RS/6000-320H running AIX. The
predictions converged after calculating over two meshes and one or two
iterations for each mesh, using the initial set of estimations saved
from previous runs to reduce numerical instability. On an IBM
RS/6000-590, one iteration takes about 1 to 2 CPU seconds, and a run
from a previous solution to convergence is completed in less than 10 s.
Solute and Water Cycles: Flux Calculations
In a model where a single loop-structure represents not one but a
collection of tubes that turns back at various depths, also called
"n-nephron shunt models" or "lumped
n-nephron models" in the literature, one cannot calculate
the amount of, say, urea secreted into or absorbed from the inner
medullary interstitium by all LDL simply by subtracting the amount
delivered to LDL at the tip from the amount entering the inner medulla
at the OM/IM border, since most of the transport is due not to
transmural flux but to shunts reducing the number of LDL, i.e., in our
model, the ratio of the number of long Henle's loops traversing the OM to the number arriving at the papillary tip is 128, reflecting the fact
that, in the rat, for 10,000 LDL only about 75 arrive at the tip (10,
16, 18). Because of these shunts, it is necessary in descending
structures to subtract (and in ascending structures to add) the shunt
flows to obtain the transmural flux into the interstitium. Although
these shunt transfers from descending to ascending limbs of Henle and
vasa recta are simple convective flows, they are not readily separable
from the transmural fluxes, since solute concentrations at each level
depend on cumulative transfers up to the given point.
A program was written to calculate net transmural flux from each tube
within an arbitrary medullary slice, i.e., between any two medullary
depths, from the output data.
To illustrate the description of the new cycles' calculations, Fig.
2 schematically depicts a portion of the
shunted tubular structure that represents the long Henle's limbs,
illustrating the early returning loops in the inner medulla. The
diagram applies equally to flows of volume, urea, or NaCl. The model
(for more detail, see Ref. 44) uses the following differential
equations for conservation of mass within a section of lumped
tubule
|
(1)
|
and
|
(2)
|
where
Fd and Fa are tubular (i.e., luminal) flow
rates within the descending and ascending lumped structures,
respectively (flows toward the papilla are positive, and those away
from papilla are negative), Jd and
Ja are the fluxes across the descending and
ascending tubular walls at depth x (i.e., loss from the
tubular lumen; secretion into lumen if the value is negative), and
Fshunt is the shunt flow at depth x, which is
given
by
|
(3)
|
where
n (x) is the number of individual tubes
represented by the lumped structure at depth x, so
Fd (x)/n (x) is the
single-nephron flow at x.
The number of long limbs and vasa recta decreases exponentially within
the inner medulla, falling at the papillary tip (x = 0.6 cm) to
th of their value at the OM/IM border
(x0 = 0.2 cm), according
to
|
(4)
|
which
has the
derivative
|
(5)
|
We know the values of the tubule flows Fd and
Fa at every point (from the simulation output) and are
interested in calculating the integral fluxes from descending
tubules
|
(6)
|
and
from ascending
tubules
|
(7)
|
within
any given slice, i.e., within a region from arbitrary depth
x1 to x2. Illustrating
the calculation first for Jd, we substitute in
Eq. 6 from Eq. 1
|
(8)
|
Substitution for Fshunt (x) from
Eq. 3
gives
|
(9)
|
Since
n (x) and
dn (x)/dx are available
analytically (Eqs. 4 and 5), and
Fd (x) is available at every point from the
simulation output, we can approximate the integral on the
right-hand-side as the
sum
|
(10)
|
where N = (x2
x1)/
x,
x 1i = x1 + (i
1)
x, and
x 2i = x1 + i
x.
Similarly, for flux from the ascending tubule, we
have
|
(11)
|
with
the same approximation for the integral of Fshunt.
As a check on the accuracy of these calculations, we took advantage of
the fact that water permeability along the LAL is zero in the model, so
LAL volume flux calculated using this method must give values
arbitrarily near zero. By this criterion, it was necessary to chop each
medullary region of interest into at least 30 slices.
The same method was used for LVR, but since each LDV gives rise in the
model to two LAV, we have, instead of Eq. 2
|
(12)
|
Likewise,
for the SVR in the inner stripe, each SDV gives rise to four SAV, so we
have
|
(13)
|
 |
RESULTS |
Since the following discussion is rather detailed, we first present the
basic model results in three different ways, to make things more accessible.
Basic results
Standard output: Volume flows and concentrations.
Table 2 presents the basic model output,
namely, volume flows and solute concentrations and osmolality, plus
TF/P inulin values, in each tube structure at key medullary levels (the
actual simulation output table gives the results over a much finer mesh and to greater precision). Slight differences from the numbers in table
4 of Wang et al. (41) are due to stricter error tolerance here
(attested by the smaller % imbalances). These numbers are used for
construction of Tables 3 and 4. Figure
3A shows the profiles of urea and salt concentration and of osmolality in each structure along the corticopapillary axis.

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Fig. 3.
Corticopapillary profiles along each tube predicted by the model
simulation. Top graphs in each of A-C
show profiles for short nephrons and short vasa recta (and for OMCD in
some). Bottom graphs in each of A-C show
profiles for long nephrons, long vasa recta, and CD. A:
profiles of urea and NaCl concentrations and osmolality (from Table 2).
B: profiles of fractional deliveries (FD) as percents of
total (tot) filtered loads, i.e., 100 × Fi(x)/FLi(x),
where i is urea, salt, or osmoles (from Table 3).
C: profiles of single-nephron fractional deliveries (SNFD)
as percents of single-nephron filtered loads, i.e., 100 × (Fi(x)/ni(x))/SNFLi(x),
where i is urea, salt, or osmoles (from Table 4).
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We reiterate that in a lumped model such as this one, these values
represent the lumped averages over the population of each tube type at
a given level. In the actual kidney, it must be the case that fluid in
LALs that turn back in the upper inner medulla does not have the same
composition as fluid at the same depth in LALs of longer loops. It is
thus legitimate to ask whether such models give accurate results. Wang
et al. (40) demonstrated that lumped, shunted n-nephron
models are an excellent approximation to discrete n-tube
models, if all tubes of a given type are assumed to have similar
permeability and transport properties at each level.
Two points are especially revealing about the behavior of this model
and will be discussed further below: 1) fluid composition and osmolality are predicted by the model to be widely different in
LDV, LDL, and CD as they descend into the IM across the OM/IM border, a
reflection of the inclusion in this model of the lateral inhomogeneity
of the inner stripe; and 2) the predicted profiles along the
CD are unlike those for the other tubes or for the IM as a whole:
osmolality, for example, reaches its maximum before the OM/IM border
instead of steadily increasing through the IM as is usually thought to
occur (more on this below).
Total tubular flows as a percent of total filtered loads.
Table 3 and Fig. 3B present the
same results as Table 2 and Fig. 3A but in a different form,
namely, as the tubular flow rates not only of water but also of urea
(Fv × cu ), salt (Fv × cs ), and total osmoles [Fv × (cu + 1.82 × cs )] all scaled as a
percent of their respective total filtered loads. These flows represent
the sums of flows in, say, all LDL, represented in the model by the
lumped LDL structure. These values make clear the reduction of flows
toward the papillary tip due to the reduced numbers of nephrons and
vasa recta, and permit evaluation of the contribution of each structure
to global balance. For instance, if we look at just the flows entering
and leaving the IM via the whole population of long loops of Henle (LDL
and LAL), we see that 1) the LDL enter the IM carrying
3.14% of GFR and leave in LAL carrying 3.65%, showing a small net
gain of water, which occurs in the LDL, since LAL are impermeable to
water; 2) the LDL carry 21.9% of FLu, the
filtered load of urea, into the IM and LAL carry 45.8% back out to the
OM, more than doubling the urea flow within the long loops within the
IM; 3) the LDL enter the IM carrying 11.3% of
FLs, the filtered load of salt, but LAL carry only 9.63% back up to the OM, for a net loss of 1.67% of the filtered salt load;
4) the net osmole contribution of Henle's loops to the IM is 1% of the filtered load of osmoles (11.7-10.8%).
One point worth noticing, given the extent of urea exchange and
recycling between Henle's loops and the vascular vessels (discussed below), is that total urea delivery to the medulla is 116% of the
total urea load filtered into the nephrons, since Henle's loops
deliver 66.6% of FLu to the medulla (22.2% in LDL and
44.4% in SDL) and the vasa recta deliver the equivalent of another
50% of FLu (16.6% in LDV and 33.3% in SDV).
Tubular fractional deliveries.
From the values in Table 3 alone it is not possible to know whether
individual long nephrons gain or lose solutes or water along their
course in the IM. Table 4 and Fig.
3C give average flows per tube as a percent of
single-nephron filtered loads, which is often called the fractional
delivery (given here as percentages) and is the same as reporting 100 × (TF/P)i/(TF/P)inulin from
micropuncture data. These values are best for evaluation of net gain or
loss of solutes or water along individual nephrons of a given type and
can be directly compared with micropuncture data (see below). From
Table 4 and Fig. 3C, one can see that luminal water and salt
flows change very little in the IM along the longest LDLs, whereas
luminal urea flow increases 10-fold, attaining 658% of the
single-nephron filtered load of urea at the hairpin turn, though we see
in Table 3 that total urea flow at the tip in the whole (small)
population of longest LDLs amounts to only 1.71% of the total filtered
load of urea.
Table 5 presents some results from
micropuncture experiments in the literature for comparison with the
simulation results. The experimental data given here are meant only to
indicate physiological ranges for the nondiuretic rat kidney, not to
give a consistent set of data for a given kidney, since no study
has measured all the relevant parameters under identical
conditions.
Exchange and Recycling of Urea, Salt, and Water
Tables 6 and
7 give the results of the flux
calculations explained previously. Table 6 gives the amounts of volume,
urea, salt, and total osmols transported into (positive values) or out of (negative values) each medullary region from each tubule population by transmural flux, expressed as a percentage of total GFR or total
filtered loads of solutes. Table 7 presents the same results but scaled
as a fraction of the respective flows at the tip of LDL. Figure 4,
A-C, illustrates the
main cycling patterns for water, urea, and salt deduced from
these numbers, which we explain here and discuss below in relation to
the literature.
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Table 6.
Net fluxes across tubule walls within each medullary region, expressed
as percent of total filtered load
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Table 7.
Net fluxes across tubule walls within each medullary region, expressed
as fraction of LDL flows at the papillary tip
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Fig. 4.
Fluxes in each medullary region. Arrow bars represent fluxes out
of/into each structure, and the relative thickness of the arrows
roughly indicates the relative flux values in a given region (actual
values given in Table 6). Note that the algebraic sum of fluxes at any
given level is zero, by mass conservation. A: water fluxes.
Note that OS water fluxes are about 100-fold greater than those in the
papilla (LIM), so arrow thicknesses cannot be exactly to scale.
B: urea fluxes. C: salt fluxes.
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Let us define some terminology: we will use the word "recycling"
to describe transfers from ascending to neighboring descending tubes,
which tend to keep a substance from escaping into higher regions of the
medulla; the word "short-circuit" will be applied especially to
water flows effectively shunted from descending to neighboring
ascending tubes, thereby reducing total volume flow in the next deeper
slice; instead of referring to (re)absorption and secretion, we will
use the terms "dumping" (for transport out of a tubule) and
"uptake" (for transport into a tubule).
Water cycles (as percent of total GFR to all model nephrons).
Starting our description in the deepest region, LIM, we see (Fig.
4A; Tables 6 and 7) that the CD and to a lesser extent the
LDV dump volume, all of which is recovered by the ascending vasa recta.
In the narrow transition zone, not only LDV and CD but also LDL dump a
bit of volume on their way down, all of which is carried back up by the
LAVs. We thus see that total volume flow at the tip is reduced due not
only to the smaller number of tubes but also to a water
"short-circuit" which transfers water from the downward-flowing
tubes to the upward-flowing vasa recta. This behavior matches the usual
notions of water cycling in the deep inner medulla, except perhaps for
the lack of water loss from LDL in the deepest part of the papilla.
In the upper inner medulla, this simulation's water recycling picture
is less classic. We see that in the descending structures that there is
only a very slight water loss from the CD, and there is massive loss
from the LDV, but that not all of this water is carried back up in the
LAVs; a considerable amount is taken into the neighboring descending
limbs of Henle! This is because the LDL fluid is relatively hypertonic
as it enters the IM from the inner stripe, a point to which we come
back, below.
In the OM, water movements in this simulation conform to the usual
expectations; namely, there is massive osmotic water loss from
descending structures, especially in the outer stripe, and this lost
water is carried up to the cortex by the ascending vasa recta. We
nonetheless note that the model predicts no water loss from SDL in the
inner stripe (it predicts in fact a slight gain of water), despite the
high water permeability of SDL. Instead, the rise in osmolality along
this part of the SDL is entirely due to urea entry. This is interesting
in light of recent reports that only the early part of inner stripe SDL
expresses the aquaporin channel AQP-1 (24), whereas only the terminal
portion of SDL expresses the urea transporter UT2 (short transcript)
(25).
With respect to the crucial question of the concentration of urine on
its final path, that is, along the CD, the CDs lose only 1.55% and
0.6% of GFR in the OS and IS, respectively, and then 0.2% in the LIM,
but due to the low volume flow entering the CD (only 2.55% of GFR, see
Table 3), this volume reabsorption suffices to raise
(TF/P)inulin (Table 2) from 39 at the top of the OM to 730 at the exit from the papilla. Note, however, that the maximum
osmolality in CDs is reached here within the inner stripe, which is
contrary not only to the usual notions of the system's behavior but
also apparently to the scant direct experimental data on the question
(23, 24), a point to which we will come back, below.
We also point out (Table 2) that the (TF/P)inulin only
doubles along LDV and SDV in the OM and reaches a value of only 3.8 at
the papillary tip. In SDL, (TF/P)inulin reaches 8.4 at the bottom of the OS and then actually falls slightly to 7.9 at the bottom
of IS. Along the LDL, (TF/P)inulin rises from 3 to 10.5 within the OM and is only 10.8 at the papillary tip, so net water flux
is negligible along the LDL in the IM. Nonetheless, the value of
(TF/P)inulin attained in LDL at the papillary tip closely
matches the reported value of 11 found in the literature (9, 20).
Urea cycles.
UREA CYCLES IN THE IM.
As with the above account of water cycles, we begin in the deep papilla
and work upward (Fig. 4B). The discussion of inner medullary
urea exchanges centers naturally around the destiny of the urea dumped
there from the CDs. The CDs in this simulation dump into the LIM an
amount of urea equivalent to nearly one-third of the total filtered
load of urea (Table 6) (also equivalent to 7.7 times the total osmoles
delivered to the papillary tip in LDLs, Table 7). This urea load is
picked up by all the other structures in the region, descending as well
as ascending (except for LAV1).
In the TZ, the CDs dump 8.3% of FLu. A third of this urea
is picked up by the LDV, and the rest enters Henle's loops, both LDL
and LAL. In this region, the ascending vasa rectae already start losing
urea back to their surroundings, i.e., it is recycled back toward the
papilla via the LDV.
In the UIM, the small urea loss from the CD (3.4% of FLu)
is picked up entirely and carried deeper into the papilla by the LDL.
Much more important in this region is the massive urea recycling from
ascending to descending tubes: i.e., 20.5% of FLu from LAL to LDL and 104.6% of FLu from LAV1 and LAV2 to LDV and
LDL. This recycling can be revealed in the model only by the present
new flux calculations and cannot be measured in vivo.
To summarize the net steady-state urea transfers within the IM among
the three tube systems (see Table 6, columns CD, LHLtot, and LVRtot) in this simulation (quantities as
%FLu): in LIM, of the 31.7% of FLu lost from
IMCD, somewhat more is picked up by the vasa recta (17.8%) than by
Henle's loops (13.8%); in zone TZ, of the 8.3% of FLu
dumped by IMCD, more goes to Henle's loops (5.3%) than to the vasa
recta (3%); in the UIM zone, the amounts of urea transferred from IMCD
(3.4%) and vasa recta (1.4%) to Henle's loops are dwarfed by the
amounts of urea recycled from ascending to descending limbs of vasa
recta and Henle's loops.
UREA CYCLES IN THE OM.
The lateral inhomogeneity of especially the inner stripe, typified by
the grouping of all descending vasa recta and of the long (but not the
short) ascending vasa recta into vascular bundles (VB), are crucial to
understanding urea movements. It is also worth recalling that the urea
permeability of OMCD is very low even in antidiuresis, so urea
transfers occur only among the non-CD sturctures. Within the vascular
bundles, fluid in the LAV1 and LAV2 arrives carrying the equivialent of
80% of FLu from their trip into the urea-rich IM; they
dump a total of 49% of FLu as they pass through the IS and
another 9.9% in the OS and carry the remaining equivalent of 21% of
FLu back to the cortex. Within the IS, about half of the
urea dumped in the VB by LAVs is recycled to the inner medulla via the
LDV; of the other half, most is picked up by the SDV, which are
situated in the perimeter of the VB (before splitting off into the
interbundle region to form capillary beds and thence SAVs), and the
rest (5.8% of FLu) is picked up by the SDL, as is usually
supposed, since they run close to the VB in the IS in rats and have
high urea permeability.
Within the interbundle region of the IS in this simulation, the LAL
dump about one-fourth of their urea (10.8% of FLu), all of
which is returned to the blood via SAVs. Urea fluxes are virtually absent along LDL and SAL of the inner stripe.
In the OS, the LAL and SAL each dump 7.7% of FLu, and the
SDL also dumps 3.3% of FLu. The equivalent of 7.6% of
FLu is recycled deeper into the medulla via the LDV, and
the rest is picked up by the SDV. There is also considerable urea
recycling in the OS by transfer from ascending to descending short vasa recta.
In summary, for urea balance in the OM (see the "tot" columns of
Tables 6 and 7), the long vasa recta dump 15% of FLu and Henle's long loops (essentially the LAL) dump 18.8% of
FLu. The short limbs of Henle are also net urea
contributors (5.2% of FLu), since the SAL dump more in the
OS than is picked up by the SDL during their inner stripe excursion
near the vascular bundles. This whole urea load is of course picked up
by the short vasa recta system, since net inflow equals net outflow in
the steady state.
Salt cycles.
Along the CD, although salt reabsorption is quantitatively very small,
it is crucial for the organism's salt balance; absolute NaCl
reabsorption along the IMCD in antidiuresis has been reported as high
as 3% of FLs (34), about 10 times the rate of fractional salt
excretion. Moreover, sodium concentration along the CD may rise in the
OM before falling again in the IM (5). However, models of the medullary
countercurrent system, the present one included, do not yet do justice
to the role of the CD in salt regulation; they lump all salt into one
pool labeled "NaCl," whereas renal handling of sodium and
potassium (to say nothing of ammonium, phosphate, etc.) are in fact
quite different, especially in the distal nephron and CD. For instance,
by free-flow micropuncture at both the base and tip of IMCD, Diezi et
al. (5) showed clearly that Na+ concentration
([Na+]) falls and [K+] rises along the
IMCD. The minimal salt reabsorption included in the present model
(~0.1% of FLs) avoids some problems of
earlier models, but proper treatment of this question must await more complete models.
In the inner medulla (Fig. 4C; Tables 6 and 7), salt flux
along the LDL is outward but is very slight due to their relatively low
permeability, but the LAL dump salt along their whole length, as
posited by the familiar passive hypothesis (17, 35). However, this salt
is not recycled back down into the papilla. Somewhat surprisingly, the
LDV also dump salt along their whole length within the IM (even more
than by the LAL), because water is drawn out faster than salt,
maintaining a favorable gradient for salt exit even as the LDV fluid
descends into a region of increasing salt concentration. The salt
dumped from these structures and from the CD (by the active pumps) is
carried up to the OM by the LAVs; thus vasa recta salt balance is
negative at every level in the IM, i.e., the vasa recta carry salt
upward out of every successive IM "slice."
In the outer medulla, SAL and LAL actively dump 20.6% and 8.9% of
FLs, respectively, with most of it being
pumped out in the IS (see Tables 6 and 7). Though a very small part of
this salt is recycled to the IM in the LDL, the great majority is
carried back to the general circulation in the short vasa recta. In
accord with established facts, given the water impermeability of the LAL and SAL, this salt dumping also dilutes the LAL and SAL and renders
the OM hyperosmotic with respect to the fluid in entering descending
tubes. In addition, as the WKM models in general and the present model
in particular reflect, the inner stripe has not only an axial (i.e.,
corticopapillary) but also a radial (i.e., from vascular bundles to
CDs) osmolality gradient.
Total osmoles.
One of the basic tenets of the classic view of the concentrating
mechanism is that at the OM/IM border the descending structures, LDV,
LDL, and CD, enter the IM with nearly equivalent osmolalities and that
the rising LAL fluid is dilute relative to the other structures at the
same level as it leaves the IM (not all workers insist that LAL fluid
must be dilute as it leaves the IM; see Refs. 4, 21, 30). The present
model contradicts both of these tenets, namely, we see (Table 2) that
at the OM/IM border c LDVosm < c LDLosm < c CDosm , reflecting the respective positions of LDV, LDL, and CD along the
radial osmolality gradient in the IS. Furthermore, despite the
considerable loss of "water-free" osmoles along the LAL within the IM, LAL is here an osmotically equilibrating rather than a diluting
segment in the IM. Although these two points both seem quite
straightforward consequences of the anatomic and permeability characteristics represented by the model, the matter of the profiles along the CD remains troublesome. This will be discussed below.
As we saw above, the LDL lose salt and gain urea as they descend within
the IM. Since LDL osmolality increases from 984 to 1,525 mosmol/kgH2O within the IM in this simulation, the LDL
clearly gain more urea osmoles than the salt osmoles they lose,
recalling that (TF/P)inulin (Table 2) in the LDL that reach
the tip is virtually identical to mean (TF/P)inulin of LDL
at the OM/IM border, so their increased osmolality is due here not to
water loss but virtually exclusively to solute (i.e., urea) entry.
 |
DISCUSSION |
For the discussion that follows, we remind the reader that our purpose
is not to justify the present model (41) but rather to explore its
predictions in detail, since to date it is the most accurate
representation of the available experimental measurements and anatomic
data. As such, this model analysis serves two purposes: 1)
it serves as a quantitative check on qualitative extrapolations that
have been based on these same data; and 2) by our detailed analysis, we hope to clarify directions for future improvements and new measurements.
To facilitate the discussion in comparison with the experimental
literature, Fig. 4, A-C, illustrates the results
given in Tables 6 and 7, showing the basic patterns of intertubular
exchanges and recycling of water, urea, and salt, respectively, for the present model.
Summary of Water Cycles
This model's water exchanges basically conform to the accepted idea of
water "short-circuiting" in each medullary region; that is, with
few exceptions, the descending structures lose water and ascending vasa
recta take up water. In combination with the greatly reduced number of
loops and capillaries toward the papilla, this results in a progressive
reduction of total volume toward the papilla, thus reducing the amount
of osmotic work needed to render the deep papilla hyperosmotic.
The model predicts exceptions to this water short-circuiting pattern in
descending Henle's loops where water uptake accompanies high urea
influx, namely, in the LDL of the deep papilla (uptake of urea dumped
form the terminal IMCD), in LDL of the UIM (massive recycling of urea
dumped from parallel ascending LAL and LAV), and in SDL running close
to vascular bundles in the inner stripe (uptake of urea dumped from LAV
in the vascular bundles and also form nearby LAL). A close look at
Tables 6 and 7 reveals (see columns LVRtot and
LHLtot, row IMtot) that in the IM, the net volume receivers are in fact LDL due to their considerable (for the
region) water uptake in the UIM, not the LVR, which despite their
considerable water short-circuiting from LDV to LAV actually have a
small net water loss within the IM of this model.
Summary of Salt Cycles
Salt is actively transported out of thick ascending limbs (LAL and SAL)
in the outer medulla, diluting the tubule lumen due to the negligible
water permeability of these segments. This is recognized as the basic
motor for the concentrating mechanism. It is also known that there is
salt transport (not only of sodium but also of potassium, to say
nothing here of ammonium and bicarbonate) along the CD throughout the
medulla, but it has generally been assumed in modeling studies that
these transport systems transfer no net osmoles, being based on
one-for-one ion exchangers, and should thus have minimal effect on the
concentrating mechanism, a view which may merit revision. The present
model follows tradition and neglects this CD transport except within
the UIM, where we now include slight net active salt transport (41,
42), which is too small to affect overall medullary salt balance
significantly but is crucial for the organism's salt balance.
Improving the CD solute transport is desirable but must be
done by accomodating other solutes, including at least KCl.
Within the IM, according to the passive hypothesis, passive salt loss
from LAL, made possible by high interstitial urea thanks to urea dumped
from the CD (17, 35), is taken to be the single effect for buildup of
the IM osmotic gradient. In the present model, the LAL does in fact
dump salt along its whole IM ascent; this salt is not here recycled
into the parallel descending Henle's limbs but is instead carried up
and out of the IM by the ascending vasa recta, which corresponds to
Stephenson's analysis of the passive mechanism (36). It is sometimes
suggested (2, 3, 22, 30) that some or most of the salt transported out
of the ascending limbs in the OM is recycled down into the IM in the LDL, which have a moderately high measured salt permeability, but in
this model osmotic equilibration along the LDL in the OM by water loss
occurs fast enough to keep the salt gradient small across the LDL wall;
consequently, the amount of salt diffusing into the LDL within the OM
(0.3% of FLs, see Table 6) is only a negligible fraction
of that dumped into the OM by the SAL and LAL (20.6% and 8.9% of
Fls, respectively). We thus see that in this simulation
virtually all of the salt actively transported out of ascending limbs
in the OM is returned directly to the general circulation via the vasa
recta. The role of this active salt transport in the concentrating
mechanism is thus to dilute the ascending limb fluid and concentrate
the descending fluid not by adding salt but by drawing water out of the
LDL and CD (but not from SDL in the inner stripe, which is concentrated
by urea uptake as mentioned above).
Summary of Urea Cycles
Although urea is apparently transported passively everywhere in the
kidney under normal conditions, it has long been recognized that it
plays a central role in the concentrating mechanism, though the exact
nature of that role remains one of the central questions about how the
concentrating mechanism works. We are thus particularly interested to
see just what the present model predicts about urea handling, given its
close conformity to measured permeabilities and anatomical arrangements.
Before summarizing the details of the urea exchanges within each
region, it is useful to look at the big picture, starting with the
primary event of interest, namely, the dumping of 43.4% of the
filtered load of urea into the IM by the IMCD. What is the ultimate
fate of this dumped urea in this simulation? From Table 3 we can
calculate the net dumping or uptake of urea in each tube type over the
whole medulla by subtracting urea outflow in the ascending tubes at the
corticomedullary border from urea inflow in the descending tubes. Thus
for
LVR
|
(14)
|
remembering
that upward flows are negative. Similar equations apply for SVR, LHL,
and SHL. Results of these calculations are given in Table
8. From this table, we see that in this
simulation 1) nearly all of the urea dumped from IMCD in the
inner medulla actually ends up returning to the cortex via the SVR, and
2) Henle's loops make no net contribution of urea to the
medulla, since the net amount picked up by the long loops is identical
to the net amount dumped by the short loops. Since the SVR do not
extend into the IM, there is clearly massive urea exchange within the outer medulla from the LAV and LAL, which carry the urea up from the
IM, to other tubes.
Figure 4B shows the urea paths in this simulation. Within
the IM, the two main features are urea dumping by the IMCD and massive urea recycling between descending and ascending branches of both Henle's loops and the vasa recta. To better appreciate the extent of
inner medullary urea recycling, we can point out (Table 6) that the LDL
take up an amount of urea equal to 36% of FLu on their way
down within the IM and the LAL take up another 8% of FLu
in the LIM and TZ before they start dumping urea further up in the IM,
for a total of 44% taken up by Henle's loops. LDV take up an amount
of urea equal to 122% of FLu and LAV2 take up another 14%
in the deepest medulla, for a total of 136% of FLu taken
up by vasa recta. This amounts to a grand total of 180% of
FLu taken up by vasa recta and Henle's loops, whereas
"only" 43.4% of FLu is dumped by the IMCD. The
difference, or the equivalent of 137% of FLu, is recycled
within the IM, where total volume flow is only a small fraction of GFR.
Within the OM, in accord with classic predictions, urea from LAV is
recycled to LDV and SDV within the vascular bundles of the IS and also
within the OS. More surprising, however, is the role of the short Henle
loops in this model; they pick up considerable urea as they pass near
the VB in the IS, as is generally supposed, but then they dump an even
greater quantity of urea in the OS before returning to the cortex (urea
dumping from MTAL has in fact been suggested by some authors; see,
e.g., Ref. 30); that is, the model predicts that the fate of the urea
they pick up is not to be carried up and around to contribute to the
urea load delivered to the collecting ducts, but rather just to be
transferred from the IS to the OS, where part of it is recycled via the
SDV and the rest is lost to the cortex in the SAV. This OS urea loss from the SAL is of course made possible by their relatively low but
certainly not negligible measured urea permeability (15). Although
recently cloned urea transporters have led to localization of their
expression along the nephron (25, 27, 28, 33), none has been found in
the medullary thick assending limb (MTAL), which, assuming the measured
permeability value is correct, suggests either that some as yet
unidentified urea transporter operates in this segment or that urea may
pass between the cells across the tight junctions. A more recent report
confirms this tendency using purified vesicles from apical and
basolateral membranes of MTAL (29), since it suggests that urea
permeability of both cell membranes is very low.
Whatever the eventual outcome of this question of the effective in vivo
urea permeability of the outer stripe MTAL, the handling of urea by
this model's short loops is clearly in disagreement with micropuncture
data from surface convolutions. Armsen and Reinhardt (1) measured end
proximal and early distal tubule fractional delivery of urea in Wistar
rats by micropuncture under antidiuresis and varying degrees of water
diuresis. They found that in accessible short loops of nondiuretic
rats, FDu increased from ~60% of FLu at the
end of the accessible proximal convoluted tubule (PCT) to 100% at the
beginning of the distal convoluted tubule (DCT), a near doubling of
tubular urea flow in superficial nephrons despite a halving of volume
flow [(TF/P)inulin increased from 3 to 6]. This is clear
evidence of considerable net urea uptake in the superficial loops of
Henle during antidiuresis, contrary to the model's prediction of a
small net urea loss.
This suggests, of course, that the model might "work better,"
i.e., might produce a higher urinary osmolality and steeper IM
gradient, if Pu of SAL were reduced to lessen or
prevent urea dumping in the OS and thus increase urea delivery to the
CD. The results of testing this idea with the present model bear
witness to the difficulty of second-guessing this complicated system. In a series of simulations (partial results given in Table
9), Pu(SAL) was
gradually reduced to
th of its control value. The result
was a modest decrease rather than the expected increase of
Uosm, from 1,434 down to 1,396 mosmol/kgH2O, which is explained as osmotic diuresis, i.e., the short loops did in
fact deliver slightly more urea to the CD, but instead of resulting in
greater urea recycling, the CD dumped the same amount of urea into the
IM as before, so FEurea increased from 13.1% to 18.5% of
FLu, resulting in greater urine flow
[(TF/P)inulin decreased from 729 to 535]. These results
suggested that the model's IMCD urea permeability is too low to permit
effective recycling of the higher urea load. Subsequently increasing
Pu(CD) in TZ and LIM to higher measured
values (7, 32) did in fact lead to increased Uosm, but only
if Lp(CD) was also increased to higher measured values (19, 31), permitting water to follow the urea dumping
at the higher rate. This set of parameter changes (indicated by an
asterisk in Table 9) effectively increased the model's urea recycling
(IMCD dumps 57.4% of FLu instead of 43.4%) and increased
Uosm to 1,630 mosmol/kgH2O. It is not our
purpose here to develop this idea systematically, but Table 9 shows
some of the interesting functional parameters in comparison with the
basic simulation results from the earlier tables, and Fig.
5 shows the area-weighted slice profiles of
urea concentration, salt osmoles, and total osmolality, similar to
measurements in whole slices from each medullary depth according
to
|
(15)
|
where
i is urea, NaCl, or osmolality,
ci , j is the concentration of
i in structure j,
nj is the number of structures
j at the given medullary level, and
Aj is the cross-sectional area of the
individual structures (42). The inset to Fig. 5 shows the
ratio of urea to total slice osmolality along the medulla. This
simulation (indicated by an asterisk in Table 9) gives results more
closely in accord with experimental results on several important
points, namely, increased Uosm, steeper and deeper inner
medullary osmolality profile, and better agreement of
SNFDu values with micropuncture results,
especially concerning the significant addition of urea to the short
Henle's loops, which was, after all, the impetus for making these
changes. Table 9 also presents results of simulations in which CD urea
and water permeabilities were changed alone, with or without the
reduction of SAL urea permeability. It nonetheless remains the case
(results not shown) that increasing urea permeability of LDL and/or LAL in the IM in this new scenario still results in poorer performance.

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|
Fig. 5.
Comparison of corticopapillary slice profiles from test simulation
(thick curves) with those of the baseline simulation (thin curves).
Inset: profile of the ratio of urea to total osmoles.
|
|
"Osmole Cycles"
With respect to the literal question of the IM osmolality gradient,
what matters is the net change of osmolality from one slice to the
next, although of course total osmolality is composed both of salt and
urea (as well as other solutes in the kidney itself ). As can be
seen in the inset of Fig. 5, the fraction of this model's
total "slice" osmolality due to urea rises from 12% at the top
of the OM to more than 50% in the TZ of the IM and then remains high
through the remainder of the deep medulla. This increasing ratio of
urea to salt osmoles is accomplished as the result of three features:
urea dumping from the terminal IMCD, efficient urea recycling, and,
last but not least, efficient water short-circuiting, without which the
amount of urea dumped by the CD would be insufficient. It is also
interesting to note that the depth at which total osmolality levels off
(instead of continuing to increase, as observed experimentally)
coincides with the leveling off of the ratio of urea concentration to
total osmolality.
Collecting Duct Profile
As already mentioned, the osmolality and urea concentrations along the
collecting duct in this model (Fig. 3A) reach a maximum in
the inner stripe instead of increasing gradually in tandem with the
rest of the medulla (Fig. 5) as is usually supposed to occur. This
unconventional CD profile results directly from the model's inner
stripe radial heterogeneity, that is, from the fact that each tube in
this region sits in a unique environment along the vascular
bundle-to-CD continuum, rather than all being bathed by a common
interstitial milieu (as in central core models). The immediate
neighbors of the CD in this region of the model are the SAV4, i.e., a
population of short ascending vasa recta that arise from vascular beds
in the region of the thick ascending limbs and the CD, "far" from
the vascular bundles. Due to the vigorous hyperosmotic salt pumping by
the ascending limbs, this neighborhood develops the high osmolality
that draws water out of the CDs, which in this region have high water
permeability but very low salt and urea permeabilities, resulting in
dramatic concentration of the contents of the CD luminal fluid. The
same arguments could be invoked in favor of a mode of operation
proposed by Bonventre and Lechene (4) suggesting that fluid in the LDL is hyperosmotic on exiting the IS into the upper IM and could thus
supply net osmoles to the IM. So, since this is in fact a rather
conventional view of the operation of the outer medullary CD, it seems
reasonable that the CD profile should be different from that of
Henle's loops and the vasa recta; nonetheless, the actual extent of
the difference predicted by the model is surprising. It thus becomes
important to confront the prediction with data.
When it has been mentioned in the literature, it is generally believed
that the CD profile conforms essentially to that observed in medullary
slices, and three studies are most often cited in support of this
belief, namely Wirz (45), Gottschalk and Mylle (8), and Gottschalk et
al. (9). However, a close look at these reports reveals that they do
not in fact provide direct evidence for an inner medullary osmotic
gradient along the CD; the spatial resolution of the cryoscopic slice
technique of Wirz (45), though ingenious, was probably too poor to give
clear evidence of osmotic differences between neighboring structures at
the relatively high temperatures they used (
10°C); Gottschalk and
Mylle (8) made measurements only in structures close to the papillary
tip, not further up the CD near the papillary base; and Gottschalk et
al. (9) did obtain evidence for a considerable osmolality gradient
along the IMCD, but only in Psammomys, a species that cannot
be easily compared to other rodents for both anatomic (100% long
loops) and dietetic reasons (no urea problem because they eat only
succulent plants). So, based only on these reports, it would be
possible to suspect the truth may lie with the model's predictions. There are other data, however, some of which is in favor of and some against an osmotic gradient along the IMCD. These
studies are briefly summarized as follows.
Ullrich (39) measured (TF/P)inulin, [Na], [K], pH, and
[NH+4 ] and total osmolality (but not urea) in fluid samples obtained by retrograde microcatheterization at various levels along the IMCD of golden hamsters in antidiuresis. That study showed clearly that along the IMCD there was considerable water and sodium reabsorption, virtually no potassium reabsorption, and
a decrease of pH (dramatic increase of
[NH4+]), but that the osmolality remained
virtually constant from the OM/IM border to the papilla. This evidence
thus tends to agree with the prediction of the present model, but it
must be pointed out that their animals had urinary osmolality ranging
from 400 to 1,200 mosmol/kgH2O, not frankly antidiuretic.
Jamison (11) used a similar technique in rats with urinary osmolalities
ranging from 800 to 1,450 mosmol/kgH2O and found an average
gradient of 226 mosmol/kgH2O per mm along the final 1.5 mm
of the IMCD.
Sonnenberg (34), also using retrograde microcatheterization in rat
collecting ducts, also found a considerable osmolality gradient within
the IMCD under nondiuretic (Uosm up to 1,400 in the
experimental kidneys, and 1,800 in the control kidney of the<