Transport asymmetry in peritoneal dialysis: application of a
serial heteroporous peritoneal membrane model
Daniele
Venturoli1,2 and
Bengt
Rippe1
1 Department of Nephrology, University Hospital of Lund,
S-22185 Lund, Sweden; and 2 Istituto di Fisiologia Umana,
Università degli Studi di Milano, I-20133 Milan, Italy
 |
ABSTRACT |
The transport of
macromolecules during peritoneal dialysis is highly selective when they
move from blood to dialysate but nearly completely unselective in the
opposite direction. Aiming at describing this asymmetry, we modeled the
peritoneal barrier as a series arrangement of two heteroporous
membranes. First a three-pore membrane was considered, crossed by small
[radius of the small pore (rs)
45 Å], large [radius of the large pore (rL)
250 Å], and transcellular pores accounting for 90, 8, and 2% to
the hydraulic conductance, respectively, and with a corresponding pore
area over diffusion distance
(A0/
x) set to 50,000 cm. We calculated the second membrane parameters by fitting simultaneously the
bidirectional clearance of molecules ranging from sucrose [molecular
weight = 360, permeating solute radius (ae)
5 Å] to
2-macroglobulin (molecular weight = 820,000, ae
90 Å). The results describe a
second two-pore membrane with very large pores (rL
2,300 Å) accounting for 95% of the
hydraulic conductance, minor populations of small
(rs
67 Å) and transcellular pores (3 and
2%, respectively), and an A0/
x
65,000 cm. The estimated peritoneal lymph flow is
0.3 ml/min. The
two membranes can be identified as the capillary endothelium and an
extracellular interstitium lumped with the peritoneal mesothelium.
extracellular interstitium; concentration hyperpolarization; composite membranes; pore theory; mathematical model
 |
INTRODUCTION |
AFTER THE INTRODUCTION
OF peritoneal dialysis (PD) as a tool to replace impaired renal
function, much work has been devoted to the mathematical modeling of
the exchanges of fluid and solutes through the peritoneum (for a review
see, e.g., Ref. 18 or more recently Ref. 29).
The proposed models usually describe the peritoneal exchanges as fluid
flow and solute fluxes between two well-mixed compartments (namely, the
patient's blood and the peritoneal cavity content) through a
"peritoneal membrane." This equivalent peritoneal membrane is in
fact "a complex and complicated system of membranes and pores, which
may be described as a distributed, multilayer, heteroporous, and
topographically nonuniform structure with intramembrane compartments
and possible specific biological transport properties"
(31). The concept of the peritoneal membrane has evolved
from a black box simply described by some kinetic constants
(18) to a heteroporous membrane with precise anatomical correlates to the structures allowing fluid and solute fluxes (23, 24). However, the only way to deal to some extent
with the anisotropy and inhomogeneity of its composition has been so far to refer to a distributed model of peritoneum (8, 17, 25). At variance with the approach above, the distributed models of peritoneal exchanges consider the blood-peritoneal cavity barrier as
a hydrogel matrix (representing the peritoneal tissue), with an
embedded uniform distribution of blood vessels, lined on one side by a
membrane (representing the peritoneal mesothelium). However, this
distributed approach, although very powerful in its description of
peritoneal exchanges, leads to a dramatic increase in the complexity of
the governing equations and in the number of parameters needed to
describe the system. Furthermore, the real values of some of these
parameters are very difficult, if at all possible, to assess
experimentally. Far simpler but as well powerful is the adaptation of
the distributed model of Waniewski et al. (30) to describe
the bidirectional solute transport. However, this approach does not
provide any insights about the structures responsible for the
exchanges. Here we follow an intermediate way between the different
approaches, considering the presently most advanced "planar"
membrane model, the three-pore model (23, 24), and
extending it to the description of a membrane composed of two
heteroporous membrane in series.
 |
THEORY |
Pore Theory of Peritoneal Exchanges
In the pore model of peritoneal exchanges (23, 24)
the equivalent peritoneal membrane is considered to be crossed by
straight cylindrical channels, then applying the pore theory heretofore used in the description of the movement of fluid and solute through the
capillary walls (6, 27). In this framework, the parameters defining a membrane are the number of pores of different radii and
their relative weight and unrestricted (and "restricted") surface
area available for exchange over the diffusion path length (A0/
x). The corresponding fluid
and solute permeability parameters are summarized in Table
1. The equivalent peritoneal membrane has
been characterized (23) as a three-pore membrane crossed by small pores, large pores, and transcellular pores. The small pores,
radius (r) ~45 Å, approximately account for 90% of the hydraulic conductance and represent the main route of passage for small
solutes, whereas 8% of the hydraulic conductance is accounted for by
large pores (r
250 Å), allowing the passage of
macromolecules. Transcellular pores representing a water-only conductive pathway account for the remaining 2% of the hydraulic conductance. This was introduced to explain the paradox of an apparently "open" peritoneal membrane effectively sieving small solutes. These pores have been recently identified as the plasmalemmal "aquaporins" (5). The three-pore model has been
successfully applied in the interpretation of a large set of
experimental data obtained in studies of fluid and solute exchanges in
PD (21). However, some problems arise when the three-pore
model is applied to explain the observation that the peritoneal
transport of molecules across the peritoneum is not symmetric. In fact,
if a solute is moving from the blood to the peritoneal cavity, it has
to permeate the capillary endothelium, the interstitium, and the
mesothelial layer, whereas in the opposite direction, an additional
pathway exists provided by the lymphatic drainage. Also, the addition of a peritoneal lymphatic drainage to one side of the "peritoneal" membrane described by the three-pore model does not account completely for the possibly different permeability properties of the different layers. Therefore, we try to address the problem of estimating the
relative weight of the two different fluxes from the peritoneal cavity
by considering an equivalent peritoneal membrane structured as two
three-pore membranes arranged in series.
Theory of Composite Membranes
A system model for a series array of membranes can be considered
as composed by two membranes that we name a and
b. In Table 2 are the
definitions of hydraulic conductivity, diffusional permeability, and
reflection coefficient for two membranes arranged in series as obtained
by Kedem and Katchalsky (15). It is readily apparent that
the usual Kirchoff's law, which states that the reciprocal of the
resulting resistance of a series arrangement of resistances corresponds
to the sum of the reciprocal of each single resistance, still holds
only for the overall diffusional permeability. On the other hand, the
total reflection coefficient for the series array results from a
crossed-weighted sum of the reflection coefficient and the diffusional
permeability of both membranes. The hydraulic conductivity of the
series array (Lp) as obtained by Kedem and
Katchalsky (15) is
|
(1)
|
where Lp,a and
Lp,b are the hydraulic conductivies
of the two membranes, R is the gas constant, T is
the absolute temperature, JV is the fluid flow,
Cus is the upstream concentration,
a and
b are the
reflection coefficients for the two membranes, and
=(
a
b)/(PSa + PSb), where PSa and
PSb are the permeability surface area products
for each membrane. The last term in Eq. 1 takes into account
the appearance of an intermediate layer at the interface in between the
two layers. The fluid flow for a series arrangement is then defined by
the implicit equation (15)
|
(2)
|
where
is the total reflection coefficient for a
membrane series as reported in Table 2 and
P and 
are the
hydraulic and colloid-osmotic pressure gradients across the series
arrangement. A similar implicit equation has been obtained by Patlak et
al. (20) by considering a system in which two membranes in
series are delimiting an inner compartment with finite volume. With the same assumptions, it is possible also to obtain the general solute flux
(Js) equation for a membrane series arrangement
(20) as
|
(3)
|
where Cds is the downstream concentration and
Pea and Peb
are the Peclet number {JV[(1
)/PS]} for each membrane (2).
From the relationships in Table 2 and Eq. 3 we obtained the
Peclet number, the sieving coefficient, the unidirectional clearance, and the intermediate layer concentration for a membrane series array.
In Table 3, the definitions of each
parameter are compared for a single membrane and a series of two
membranes.
Peclet number.
We obtained the Peclet number for a series arrangement of membranes by
substituting the expressions for total P and
in Table 1 in the Peclet number definition. The resulting overall
Peclet number is the sum of the Peclet number of each membrane.
Sieving coefficient.
The sieving coefficient is defined as the ratio between the downstream
and the upstream concentrations of the filtrate crossing a membrane. We
obtained the sieving coefficient for the series arrangement by
considering that the equilibrium concentration in ultrafiltration
conditions (no changes in filtrate concentration with time) is given by
Cds = JS/JV. The equation
reported in Table 3 follows by substituting Eq. 3 for
JS and rearranging the resulting expression.
Interestingly, the equation is identical to that obtained by
integrating the flow equations on a path crossing the two membranes (4).
Clearance.
The unidirectional clearance of a solute through a membrane is defined
as the ratio between the solute flux and the upstream solute
concentration, considering the downstream concentration equal to zero.
The extension of the unidirectional clearance to a series of two
membranes reported in Table 3 is straightforward, applying the
definition to Eq. 3.
Intermediate layer concentration.
For the sake of simplicity, we assumed in our model that fluid flow and
solute fluxes are completely developed after crossing the membrane.
This allowed us to describe the basic permeability coefficients of each
membrane according to the three-pore theory but considering only one
overall fluid flow or solute flux across the membrane. This assumption
lead us to consider that an intermediate region (or layer) has to be
present delimited by the two membranes. On the other hand, the concept
of "intermediate layer" follows by the consideration that two
membranes in series should always include an intermediate region at the
interface between the contacting sides. This region may be
infinitesimally thin, as in the theoretical approach in Ref.
15, or may have a definite volume
(20). However, it is interesting to observe that both
approaches lead to similar equations, as stated above, e.g., for the
sieving coefficient. We address the search for the equation defining
the intermediate layer concentration by considering that the Patlak
form of the solute flux equation for a single membrane should apply
simultaneously to both membranes, so that
|
(4)
|
This equation follows immediately considering that for two
membranes arranged in series the solute flux crossing the overall system is equal to the solute flux crossing each membrane.
Equation 4 can be solved for Cil by obtaining
the corresponding equation in Table 3.
Characterization of the Double-Layered Equivalent Peritoneal
Membrane
We extend the pore theory of peritoneal exchanges by considering
the equivalent peritoneal membrane as composed by two heteroporous membranes arranged in series. Therefore, to characterize the equivalent membrane, we have to determine the number of pores of different radii
and their relative weight and the unrestricted (and restricted) surface
area available for exchange over the diffusion path length (A0/
x) for each membrane. As
experimental reference points, we took the unidirectional clearances
measured simultaneously for both flow directions, namely from blood to
dialysate and from dialysate to blood (see below). Furthermore, if we
simulate the lymphatic drainage of biological tissues by adding a
nonsieving purely convective flow as a possible egress route from the
peritoneum, the clearance to blood simply becomes
|
(5)
|
where Clm represents the clearance through the
membrane system and JL is the lymph flow
contribution to the total clearance ClTOT. In equilibrium,
steady-state ClTOT equals JL.
We described the dependence of the permeability coefficients on
membrane structure parameters and solute size by applying the pore
theory. We calculated the unidirectional clearance by applying the
composite membranes theory (see the equation reported in Table 3) for
the different solute sizes and flow direction. We searched for the
membrane structure parameters and the peritoneal lymph flow using a
best-fit procedure, iteratively minimizing the function
2 defined as
|
(6)
|
where ClTOT,th is the total theoretical clearance
from the peritoneal cavity and Clexp is the corresponding
experimental clearance for a given solute. The sum is extended over all
of the considered solutes.
We fixed the parameters of the blood-facing membrane to the values
determined in Refs. 22 and 23 and calculated
the parameters for the dialysate-facing membrane and the peritoneal
lymph flow. We set the fluid flow from plasma to the peritoneal cavity
at 1.5 ml/min and the reverse fluid flow at 1 ml/min.
The best-fitting procedure was performed using a Mathcad program
(Mathsoft, Cambridge, MA) on a personal computer (Compaq Deskpro;
Compaq Computer, Houston, TX).
The bidirectional clearance data.
The clearance data used as experimental points to direct the
best-fitting procedure are represented in Fig.
1. We considered molecules with a
molecular weight ranging from 360 (sucrose) to 820,000 (
2-macroglobulin), corresponding to molecular sizes
between 5 and 90 Å. We obtained the values for the small solutes
(sucrose and vitamin B12) from Babb et al. (2)
and the inulin value from Struijk et al. (26). We used
macromolecule data using the clearances measured in Ref.
16 that compared dextran and protein bidirectional
transport. For the intermediate molecular weight range, the dextran
clearance data of Hirszel et al. (13) obtained in rabbit
were rescaled for a 70-kg man using body surface area as the scaling
factor (i.e., by body weight0.67).

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Fig. 1.
Experimental (symbols) and theoretical (lines)
unidirectional clearances. Open symbols and continuous line correspond
to transport from blood to peritoneal cavity (B P). Filled symbols
and dashed line represent the opposite flow direction (P B).
Squares, data from Ref. 2; diamonds, data from Ref.
26; circles, data from Ref. 13; triangles,
data from Ref. 16. The theoretical lines correspond to the
average parameter values resulting from the best-fit procedure in Table
4. The fluid flow from plasma to peritoneal cavity and the reverse
fluid flow have been set to 1.5 and 1 ml/min, respectively.
|
|
Sensitivity analysis.
To assess the sensitivity of the results upon the parameter values
guessed to start the iterations, we selected a set of three out of a
broad interval of possible parameter values (reported in the last
column of Table 4). We repeated the
best-fit procedure for each allowable combination of these values,
e.g., we discarded combinations with the small pore radius larger than
the large pore radius, resulting in 216 of 243 total combinations. By
selecting only the resulting values with
2 < 0.5, we obtained 85 different estimations that we used to calculate the
means and the SD of the resulting parameter values.
 |
RESULTS |
The parameter values resulting from the best-fitting program are
reported in Table 4 while the corresponding curves are plotted in Fig.
1. The resulting parameters show that the measured clearance data are
compatible with a second membrane containing mostly very large pores
with radius ~2,300 Å and a small number of transcellular pores
(~2%). The small pores account in average for 4% of the overall
hydraulic conductance and have an average radius of ~70 Å. The
calculated lymph flow is ~0.3 ml/min.
In Fig. 2, the relationships between the
basic permeability parameters are a function of molecular size of the
molecules. Figure 2, top, represents one minus the osmotic
reflection coefficient, (1
), which corresponds to the
sieving coefficient when JV
. Figure 2,
middle, shows the PS, and Fig. 2,
bottom, shows the Peclet number
[JV · (1-
)/PS] as
calculated for a fluid flow of 1 ml/min. The curves for the two single
membranes and their series arrangements are compared in the same graph.

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Fig. 2.
Basic permeability properties of the single membranes
(dotted and dashed lines) and their series arrangement (solid lines) as
functions of the molecular size of the permeating molecule.
Top: one minus the sieving osmotic coefficient (1 ); middle: permeability surface area product
(PS); bottom: Peclet number
[JV · (1 )/PS]
calculated for a fluid flow, JV, of 1 ml/min.
|
|
In Fig. 3, we determined the flow
dependence of the sieving coefficient (A) and unidirectional
albumin clearance (B) for this membrane series arrangement.
Positive values on the abscissa correspond to a flow directed from the
blood to the peritoneal cavity, whereas negative values represent flow
in the opposite direction.

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Fig. 3.
Sieving coefficient (A) and unidirectional
clearance (B) for albumin through the resulting peritoneal
equivalent membrane as function of fluid flow. Positive fluid flows
represent transport between blood and peritoneal cavity, whereas
negative fluid flows correspond to the reverse transport direction. The
asymmetry of both curves is readily evident.
|
|
Figure 4 is another way to represent the
asymmetry in the intermediate layer concentration between the different
flow directions as a function of molecular size. The three curves
represent the ratio between the two directional intermediate layer
concentrations for a fluid flow of 0.5 ml/min in each direction and a
ratio between the downstream and the upstream concentrations equal to
0.1, 1, or 10. The vertical lines correspond to the molecular radii of sodium (2.3 Å), urea (2.6 Å), glucose (3.7 Å), and albumin (35.5 Å).

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Fig. 4.
Concentration hyperpolarization phenomenon. Intermediate
layer concentration, expressed as relative to the upstream
concentration, as function of molecular size for different combinations
of upstream and downstream concentrations. The curves refer to equal
upstream and downstream concentrations (solid line) or to a downstream
concentration equal to 10 times or [1/10] of the upstream
concentration (dashed and dotted curves, respectively). The vertical
lines indicate, from left to right, the size of
sodium (2.3 Å), urea (2.6 Å), glucose (3.7 Å), and albumin (35.5 Å). The accumulation of solute molecules in the intermediate layer is
particularly evident for the larger solutes. C, concentration;
Cus, upstream concentration.
|
|
By considering the simultaneous membrane transport of the four solutes
of interest with the concentrations reported in Table 5, we calculated the overall hydraulic
conductance, compared with a constant resulting from the Kirchoff's
summation rule, in Fig. 5.

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Fig. 5.
Hydraulic conductance for the concentrations reported in
Table 5. Horizontal dotted line represents the hydraulic conductance
obtained by the usual Kirchoff's summation rule. As in Fig. 3,
positive fluid flows represent transport between blood and peritoneal
cavity, whereas negative fluid flows correspond to the reverse
transport direction. The flow direction-dependent asymmetry is a
consequence of the concentration hyperpolarization phenomenon.
LpS, hydraulic conductance.
|
|
It is readily apparent from Fig. 4 that the molecules most affected by
the introduction of this membrane series arrangement are the
macromolecules. To apply our model to a real case, we selected one
measurement of the albumin kinetics during PD, as reported in Ref.
14, and applied our model to predict the
albumin concentration in the intermediate layer during the dwell. In
Fig. 6A, a representative
volume vs. dwell time curve for a 1.36% PD is shown together with the
calculated net flow in and out of the peritoneal cavity. Figure
6B represents the blood and dialysate concentrations of an
intravenously or intraperitoneally injected tracer albumin expressed
relative to the blood concentration at time 0. Also
represented is the intermediate layer concentration calculated by the
measured upstream and downstream concentrations and the fluid flow
reported in Fig. 6A.

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Fig. 6.
Model prediction for the calculation of the intermediate
layer albumin concentration from the data reported in Ref.
14. A: representative volume (V;
and ordinate on left) and flow
( and ordinate on right) kinetics during a
1.36% dwell. B: experimental blood ( ) and
peritoneal ( ) and theoretical (*) intermediate layer
albumin concentrations. The albumin concentrations (C) are expressed
relative to the blood concentration at the start of the dwell
[C(0)]. It is possible to observe that the concentration
hyperpolarization phenomenon takes place when the fluid flows from the
peritoneal cavity to the blood.
|
|
 |
DISCUSSION |
According to the theoretical model fit of the experimental
data, two different membranes compose the peritoneal membrane. A
three-pore membrane as proposed by Rippe and coworkers
(22-24) represents the endothelial (capillary)
barrier, whereas a second membrane traversed by a great amount of very
large pores (~94% of the total pore area) and few small and
transcellular pores lines the peritoneal cavity. A unidirectional
lymphatic channel directly connects the peritoneal cavity by the blood.
We can identify the second membrane with the extracellular interstitium
lumped with the mesothelial cell layer lining the peritoneal cavity. The predominant presence of very large pores is consistent with some of
the morphological changes of the peritoneal barrier occurring in
conjunction with PD, such as widening of the mesothelial intercellular junctions (7). This will impart to the solutes a nearly
free access to the underlying interstitium. As in a number of other organs, the interstitium in the rat mesentery has been shown to be
organized as a heterogeneous matrix of collagen fibers crossed by wide
channels (3). Furthermore, the presence of
"interstitial" pores as large as 1,000 Å was also found by Granger
et al. (11) in their study of the liver blood-lymph
barrier. During a PD session with two liters of fluid with a hydraulic
pressure in the peritoneal cavity averaging ~9 mmHg
(28), we can assume that the same conditions apply for
transport from the peritoneal cavity to blood. A similar explanation
has been proposed by Flessner et al. (9) to explain data
on exchange of macromolecules between the peritoneal cavity and plasma.
Furthermore, the presence of few transcellular pores is not at all
unexpected since aquaporins are common to a wide variety of cells
(1) and have been found in the mesothelium using immune
histochemical and immunogold labeling techniques (5).
It is interesting to note that, although there are great differences in
structure of the two membranes, the resulting basic permeability
coefficients are not much different from those of the least permeable
membrane (Fig. 2). However, the difference between the structures of
the two membranes accounts for the striking feature of this system,
which is the transport asymmetry between the two flow directions, and
the importance of this phenomenon increases with increasing solute
molecular size. The asymmetry is not important for small solutes (up to
~10 Å) but is an important component of the sieving and clearance
curves for albumin (r
35 Å) presented in Fig 3. The
sieving coefficient for albumin from blood to the peritoneal cavity is
~0.11 for all of the (hydraulic) fluid flows, but in the reverse
direction it increases to 0.92 at ~1 ml/min flow and remains actually
constant for higher flows. The peak of the sieving curve for zero flow
is due to the fact that at very low fluxes, solute diffusion tends to
equalize solute concentrations at the two sides of the membrane. One of
the most important consequences of the asymmetry in the sieving
coefficient is its effect on the concentration of solutes in the
intermediate layer. In Fig. 4, this effect is expressed as a ratio
between the intermediate layer concentrations developing for an equal fluid flow but in the opposite direction.
Let us now consider the intermediate curve, obtained for equal
downstream and upstream concentrations. The intermediate layer concentration in this case is equal for flow in both directions (ratio = 1) for a molecular size
15 Å. As the molecular size increases, a steep increase in concentration occurs to about
r = 42 Å, and the curve continues to increase, but
with a lesser slope. This effect is due to the fact that, when the
solute first crosses the most permeable membrane, the barrier
represented by the second membrane is not at all important for small
solutes but becomes more and more difficult for macromolecules to
cross. In turn, this leads to an accumulation of molecules in the
intermediate layer and a "concentration hyperpolarization"
phenomenon. The lower curve represents an upstream concentration 10 times greater than the downstream concentration. We can observe that
the intermediate layer concentration ratio in this case slowly
decreases up to a molecular size of 23 Å, but then the same phenomenon
begins to appear and the ratio increases to 15 for a molecular size of 45 Å. The last portion of the curve is almost parallel to the other
curve. Finally, considering the upper curve, we can see that a huge
hyperpolarization phenomenon is present for small solutes. However, we
should consider that this curve represents an extreme situation in
which the solutes are flowing against a concentration gradient in which
the upstream concentration is 10 times greater than the downstream one.
It is then conceivable that a great quantity of molecules remains in
the intermediate layer because of their difficulty to move both against
the asymmetry of the sieving properties of the series arrangement and
the opposing concentration gradient.
Once the flow is stopped, the smaller solutes will move mainly by
diffusion (like the three smaller solutes represented by the left
vertical lines in Fig. 4) and can quite easily leave the intermediate
compartment. At variance, macromolecules, like albumin (Fig. 4, line on
right), should remain trapped in this compartment if some
clearing mechanism such as the lymphatic system is not sufficiently
active. One consequence of this concentration hyperpolarization
phenomenon is the asymmetry that is generated in hydraulic conductance.
In fact, if we refer to Fig. 5, we can observe that the hydraulic
conductance increases or decreases after the direction of flow. These
consequences of the series membrane arrangement and hyperpolarization
in PD are in reality somewhat hypothetical, however, since fluid flows
from the peritoneum to the plasma in PD and is not driven by
hydrostatic pressure gradients. Instead, the convective transport of
fluid from peritoneum to plasma under these conditions is driven by the
difference in oncotic pressures between the plasma and the
interstitium, created by the continual removal of bulk proteins from
the peritoneal cavity occurring during chronic PD. In PD, the hydraulic
conductance will actually be unchanged regardless of the direction of
flow, because a "macroscopic" concentration hyperpolarization of
plasma proteins does not occur. However, the present model can be used to understand the behavior of tracer macromolecular clearances between
plasma and the peritoneal cavity or vice versa when the macroscopic
(nontracer) albumin concentrations do not show a hyperpolarization concentration. We can, for example, consider the typical data for
tracer albumin kinetics during a 1.36% glucose dialysis dwell reported
by Joffe and Henriksen (14), and we can calculate from these data a tentative intermediate layer tracer albumin concentration. By considering a representative volume vs. time curve (reported in Fig.
6A), we calculated the net fluid flow by the differences between subsequent points divided by the corresponding time difference (also represented in Fig. 6A). By considering the
intermediate layer albumin concentration (expressed as relative to the
initial serum concentration in Fig. 6B), we see that the
concentration remains in the low and high concentrations when the flow
is directed from blood to the peritoneal cavity. However, when the flow
is reversed, the hyperpolarization phenomenon occurs and at the end of
the dwell the intermediate layer tracer albumin concentration would be
as high as about eight times the initial blood concentration. Also, if
the lymphatic drainage is actively clearing this albumin, a
long-lasting hyperpolarization is predicted due to the volume exclusion
effect that impedes albumin free motion. This accumulation has been
observed experimentally by several different techniques in mice
(19) and in rats (10). Furthermore, the slow
release of this sequestrated albumin to blood could explain the
observation that several days after an intraperitoneal injection of
radioactive albumin the blood tracer activity continues to increase
(12, 14).
The model presented here can be considered as complementary to the
"distributed model" of Flessner et al. (8) and the
simplified version of this model recently presented by Waniewski et al.
(30) in describing the bidirectional peritoneal solute
transport. Although the model may be too simplistic to deal with
membrane permeability in terms of straight cylindrical channels
("pores"), our modeling technique is still sufficiently powerful to
allow a prediction of the bidirectional clearance through a relatively
simple two-membrane system. Furthermore, the application of modern pore
theory allows us to consider the effects of molecular weight (or size)
on transport of the different solutes, since the proposed insights
concerning the structure of an "equivalent peritoneal membrane" are
dependent upon a lesser number of parameters compared with the
distributed model approach.
 |
ACKNOWLEDGEMENTS |
This work was supported by European Union contract
FMRX-CT98-0219 and by Swedish Medical Research Council Grant 8285.
 |
FOOTNOTES |
Address for reprint requests and other correspondence: D
Venturoli, Dept of Nephrology, Univ Hospital of Lund, S-22185 Lund, Sweden.
The costs of publication of this
article were defrayed in part by the
payment of page charges. The article
must therefore be hereby marked
"advertisement"
in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 2 May 2000; accepted in final form 21 November 2000.
 |
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