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1 Graduate School and Center for Biomedical Engineering, The City College of The City University of New York, New York 10031; and 2 Department of Human Physiology, School of Medicine, University of California at Davis, California 95616
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ABSTRACT |
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 TOP
 ABSTRACT
 INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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We tested the hypothesis that the effective oncotic force that opposes fluid filtration across the microvessel wall is the local oncotic pressure difference across the endothelial surface glycocalyx and not the global difference between the plasma and tissue. In single frog mesenteric microvessels perfused and superfused with solutions containing 50 mg/ml albumin, the effective oncotic pressure exerted across the microvessel wall was not significantly different from that measured when the perfusate alone contained albumin at 50 mg/ml. Measurements were made during transient and steady-state filtration at capillary pressures between 10 and 35 cmH2O. A cellular-level model of coupled water and solute flows in the interendothelial cleft showed water flux through small breaks in the junctional strand limited back diffusion of albumin into the protected space on the tissue side of the glycocalyx. Thus oncotic forces opposing filtration are larger than those estimated from blood-to-tissue protein concentration differences, and transcapillary fluid flux is smaller than estimated from global differences in oncotic and hydrostatic pressures.
surface glycocalyx; interendothelial cleft
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INTRODUCTION |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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1996
MARKED THE 100TH ANNIVERSARY of Starling's
(20) pioneering paper outlining his hypothesis for the
filtration and reabsorption of water in capillaries and the formation
of lymph. He hypothesized that the difference in concentration of
plasma proteins between the plasma and tissue was responsible for an
oncotic pressure, which opposed the hydrostatic filtration. Thus the
driving force for fluid filtration rate across the vessel wall is
determined by four pressures: the hydraulic and colloid osmotic
pressures in the vessel and in the tissue space, respectively, i.e.,
![J<SUB>v</SUB><IT>/A=L</IT><SUB>p</SUB>[P<SUB>c</SUB><IT>−</IT>P<SUB>i</SUB><IT>−&sfgr;</IT>(<IT>&pgr;</IT><SUB>c</SUB><IT>−&pgr;</IT><SUB>i</SUB>)]](/content/vol279/issue4/fulltext/H1724/img001.gif)
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(1) |
is the oncotic reflection coefficient; and Pc,
c, Pi, and i are global
values for the hydrostatic and colloid osmotic pressures in the
capillary and interstitial compartments, respectively. The term
(c 
i), which opposes the fluid
filtration across the endothelial wall, is called the Starling oncotic force.
Starling's equation has been applied across the entire
transendothelial barrier, and the Starling forces have been evaluated by global measurements of P and in the plasma and the tissue space.
However, there is growing recognition that the application of the
Starling equation is much subtler than has previously been realized.
There exists a discrepancy between the measured Starling forces in the
plasma and tissue and the forces that actually appear to determine
filtration (11, 21). Furthermore, Levick and McDonald
(13) have demonstrated that in the synovium, the effect of
extravascular albumin on fluid exchange is much less than the effect of
intravascular albumin.
In Michel (16) and Weinbaum (24), a new
hypothesis is proposed for the effective oncotic barrier that acts
across capillary endothelium. Hu and Weinbaum (8) present
a detailed cellular-level microstructural model to quantitatively
examine this hypothesis. In this spatially heterogeneous
microstructural model, the endothelial surface glycocalyx, which covers
the entire capillary endothelium, serves as the primary molecular
filter for plasma proteins and thus the principal barrier that
determines the effective oncotic force for water flow across the
interendothelial cleft. Therefore, the effective oncotic force across
the capillary is determined by the local difference in protein
concentration across the surface-matrix layer rather than the global
difference in concentration between the plasma and the interstitial
fluid in the tissue. Consequently, the pressures Pi and
i that appear in Eq. 1 will be the local hydrostatic and oncotic pressures behind the surface glycocalyx, where
the effective oncotic pressure is felt, and not Pi and
i in the tissue space at the cleft exit.
In the present studies, the relation between the filtration rates across the capillary wall and the hydrostatic and oncotic pressure difference has been investigated by use of a combined experimental and theoretical approach in single perfused microvessels of frog mesentery. The idea for these experiments arose from the quantitative predictions by Hu and Weinbaum (8) that the protein concentration in the tissue space may differ significantly from that just behind the glycocalyx if there are other parallel nonconvective transcellular pathways for protein flux in addition to the convective pathway through the interendothelial cleft of continuous capillaries. This model shows that the presence of a junction strand with small breaks and pores greatly inhibits back diffusion from the tissue into the shielded region on the lumen side of the junction strand. This leads to a significant reduction in the fluid flux filtered by the capillaries compared with the magnitude predicted by the classical Starling equation.
We also present new experimental results on individually perfused microvessels to demonstrate that the effective oncotic pressure across the capillary endothelium is not the global difference in oncotic pressure between blood and tissue. The novel aspect of the present experiments is that tissue albumin concentration was maintained at levels equal to that in the perfusate by the continued presence of albumin in the superfusate, ensuring the back diffusion of albumin from the superfusate into the tissue surrounding the microvessel. The effective filtration rates with albumin in the tissue were compared with the results on the same microvessel when albumin was present only in the perfusate. We show that loading the tissue with albumin from the tissue side produces only small changes in the effective oncotic pressure. These results have been interpreted by use of a detailed three-dimensional model of the surface glycocalyx, the endothelial cleft, and mixing in the tissue space surrounding the cleft exit. We also investigate the effect of the location of the junction strand and the spacing of junction breaks on the Starling forces.
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METHODS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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Experimental Methods
Methods to prepare frog mesentery microvessels for microperfusion and measurement of transcapillary water flows and hydraulic conductivity during transient and steady-state filtration have been described in detail (4, 9). Mesentery is exposed through a lateral abdominal incision, and the gut is draped over a quartz pillar. The tissue is transilluminated and viewed through an inverted microscope equipped for simultaneous observation and recording. Glass micropipettes with tip diameters of 8-10 µm are held in position with micromanipulators and filled with Ringer solution containing albumin.A key requirement of the experimental design when albumin is added to
the superfusate experiments is to set the albumin concentration in the
tissue equal to the albumin concentration in the perfusate. To
establish the time required for albumin in the superfusate to diffuse
into the tissue surrounding the test microvessel, a scanning confocal
microscope (Bio-Rad MRC600) was used to record images such as those in
Fig. 1. Figure 1 shows the distribution of tracer in the tissue space as a function of time after initiation of
superfusion with albumin. The frog mesentery preparation was as above.
Figure 1A is a fluorescent confocal microscope image taken
transverse to the longitudinal axis of a venular capillary in frog
mesentery. The superfusate contains FITC-albumin (2 mg/ml), and
fluorescence intensity is directly proportional to the local concentration of FITC-albumin. The lumen of the venular capillary in
this image is perfused with the frog's own plasma and is not fluorescent. To reduce the resistance of the mesothelium to albumin diffusion, the mesothelium ~100 µm from either side of the venular microvessel was gently stroked with a fine glass rod to irritate the
mesothelial cells and facilitate solute diffusion between the tissue
fluid space and superfusate. Figure 1B shows profiles of
relative tissue concentration of albumin measured close to the
centerline of the tissue over a period of 1-13 min. On this scale,
the superfusate concentration was 160 units. Therefore, after 13 min,
the albumin concentration had reached 75% of the superfusate
concentration. We found that there was no difference between tissue and
superfusate concentrations after 15-20 min. In our experiments, we
allowed up to 45 min for albumin to diffuse into the tissue.
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Figure 1B shows that even though the tissue was stroked at a distance up to 100 µm from the vessel, there are no significant gradients in the tissue at distances >10 µm from the vessel wall. Furthermore, the shapes of the gradients close to the wall reflect the geometry of the vessel wall, which is not a perfect cylinder and is surrounded by pericytes. The nonuniformities in the concentration gradient in the tissue indicate sites where isolated cells or clusters of collagen fibrils that exclude albumin are located.
Two different types of experiments were designed. In the first set, paired measurements were made of the effective oncotic pressure of albumin in the perfusate, first when there was no albumin in the tissue (control) and then when albumin was added to the superfusate at the same concentration as the perfusate. These are called transient experiments because the effective oncotic pressures were measured by rapid reduction of pressures in the vessel, as explained below. In the second series of experiments, we measured the steady-state filtration rates at a series of pressures in each microvessel, with the same albumin in both perfusate and the superfusate, and compared these to the filtration rates expected at each pressure if no oncotic forces oppose filtration. To calculate the latter, we also measured the Lp for each vessel by use of the transient protocol. In each group of experiments, only one microvessel in each animal was studied. The albumin concentration in all experiments was 50 mg/ml.
During control measurements in the first series of experiments, the
upper surface of the tissue was continuously bathed with protein-free
Ringer superfusate. The fluid flux per unit area (Jv/A) was estimated from the motion
of marker erythrocytes by use of the modified Landis technique. Before
each measurement, the pressure in the vessel was held at 35 cmH2O for 2 min by partial occlusion. This established a
high-filtration steady state in which the BSA concentration on the
downstream side of the selectivity barrier was washed down to a minimal
level, thus maximizing the effective oncotic pressure difference. This
is another way of saying that the downstream BSA concentration
approaches the convective limit, (1-)Cc, where
Cc is the concentration in the capillary lumen (15,
17). The steady filtration rate was measured by occluding the
vessel briefly (5-7 s) and then releasing the occlusion. The
measurements of Jv/A at a pressure of
10 cmH2O were made after setting up steady filtration at 35 cmH2O and then rapidly (0.5 s) switching the capillary
pressure from 35 to 10 cmH2O after occluding the
microvessel. Reabsorption was marked by the movement of flow marker
erythrocytes away from the site of cannulation as fluid moved into the
capillary. Three to five measurements of transcapillary water flow per
unit area of vessel wall (Jv/A) were
made at each pressure. Thus the control relationship between Jv/A and pressure is determined by
the oncotic effects of the BSA gradients established at high-filtration
pressure and having no added protein in the superfusate. The slope of
the relation measures Lp, and the effective
oncotic pressure exerted across the filtration barrier in the
microvessel wall was measured from the intercept on the pressure axis.
To investigate the effect of the addition of albumin to the tissue on the effective oncotic pressure exerted across the capillary wall in this first series of experiments, measurements were repeated on each of the vessels, with the same protocol as that described above (perfusate albumin concentration 50 mg/ml), except that the superfusate also contained albumin at a concentration of 50 mg/ml, applied for 45 min before the start of measurements of Jv/A (compare Fig. 1). Thus paired measurements of Jv/A at pressures of 35 and 10 cmH2O with and without albumin in the superfusate were made on each microvessel. If a significant oncotic pressure was exerted across the glycocalyx, even when the albumin concentration was equal in the tissue and the perfusate, we expected to measure net reabsorption of water across the vessel wall at the low pressure.
The second series of experiments were designed to test whether oncotic gradients could be established across the surface matrix when albumin was added to the tissue at filtration rates that were lower than those set up at 35 cmH2O. We thus measured filtration rates after steady-state filtration was set up not only at 35 cmH2O but also at 10 and 20 cmH2O on the same capillary. The same protocol used to set up steady-state filtration at 35 cmH2O was also used at the lower pressures. The pressure in the microvessel was set by partially occluding the microvessel to increase resistance and raise the capillary pressure to that in the water manometer connected to the pipette. Two minutes were allowed for the new steady state to be achieved in the tissue at the cleft exit. This method to set up steady-state filtration at a series of pressures in the same microvessels is the same as that used by Michel and Phillips (18) and Huxley et al. (9).
Theoretical Methods
Model description.
Figure 2 shows the idealized mathematical model that
was used to interpret our experimental data. This model is similar to the one introduced in Hu and Weinbaum (8) except for the
boundary conditions applied in the tissue space and the location of the junction strand. The essential physics of the model is contained in
four regions. The first region is a surface glycocalyx of thickness Lf, which covers the entire endothelial surface
including the entrance region to the interendothelial cleft. The second
region is the cleft itself showing the idealized junction strand with periodically distributed orifice breaks, the gap height of which is the
same as the wide part of the cleft. In Hu and Weinbaum (8), the junction strand was located at the midpoint,
x = 200 nm, of the cleft depth for simplicity. However,
experimental measurements (see Ref. 2) show that the junction
strand is frequently close to the cleft entrance, with an effective
average distance of the junction strand from the cleft entrance
(L1) of only 25 nm. In the present
paper, we investigated the effect of the location of the junction
strand on the Starling forces. We also explored two possible approaches
in matching the measured value of Lp. In one we
changed the spacing of the junction-strand breaks (2D), and in the
other we changed the width of the junction orifice (2d). The other
dimensions shown in Fig. 2 are based on the measurements by Adamson and
Michel (2) of cleft ultrastructure in frog mesentery.
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Mathematical formulation. The model consists of an ordered matrix at the endothelial surface, which forms the primary molecular filter to macromolecules, in series with pathways for water and solute through infrequent breaks in the junctional strand. The geometry of these breaks in frog mesenteric microvessels has been quantified by use of serial-section electron microscopy (2). Thus the model is an extension of the fiber-matrix model of Curry and Michel (5), which is modified to take into account the three-dimensional geometry of the cleft between adjacent endothelial cells and the breaks in strand and a more rigorous description of the hydraulic resistance due to the surface-matrix layer. The development and evaluation of the three-dimensional model with the use of permeability data from frog mesenteric microvessels (including permeability coefficients for small and intermediate-sized solutes) have been described in a series of papers over the past decade from our laboratories (6, 7) and have been reviewed in detail recently (17, 24).
In its present form, the surface matrix-junction break model uses rigorous hydrodynamic theory, for 1) the resistance to water flows through an ordered array of surface fibers, 2) the additional resistance arising from the walls of the cleft, and 3) the resistance to water flows through orifice-type openings in the junction strand. A comparison of the original fiber-matrix theory, as described by Curry and Michel (5), and the revised theory is given in Michel and Curry (17). The new model combines the properties of a sieving matrix and the important role of series barriers in the cleft introduced by Perl (19). The detailed description of the basic theoretical model that was used to describe the concentration profiles and analyze the experimental results is provided in Hu and Weinbaum (8). Here, we summarize only its most important features. The present model and that in Hu and Weinbaum (8) differ from all previous studies in that a new form of the Starling equation is proposed in place of Eq. 1. Both the hydrostatic and oncotic pressures are evaluated locally across the surface-matrix layer. The new equation is
![J<SUB>v</SUB><IT>/A=L</IT><SUB>p</SUB>{P<SUB>c</SUB><IT>−</IT>P(<IT>0, y</IT>)<IT>−&sfgr;</IT><SUB>f</SUB>[<IT>&pgr;</IT><SUB>c</SUB><IT>−&pgr;</IT>(<IT>0, y</IT>)]}](/content/vol279/issue4/fulltext/H1724/img002.gif)
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(2) |
(0,y)
represent the local hydraulic pressure and oncotic pressure just behind
the fiber matrix at x = 0, respectively (see Fig. 2),
and f is the reflection coefficient for albumin
in the surface matrix. Equation 2 differs fundamentally from
Eq. 1 in that it is applied just across the sieving matrix rather than in a global sense across the capillary wall, and it is
spatially heterogeneous at the cellular level. Both
P(0,y) and (0,y) vary along the
length of the cleft because of the orifice openings in the junction
strand. The colloid osmotic pressure (cmH2O) of albumin
is related to the concentration C (mg/ml) by the empirical relation
(10) for human albumin
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(3) |
was calculated by use of the
relation of Levick and McDonald (13). The two relations
are nearly equivalent.
A locally one-dimensional convection-diffusion equation across the
surface matrix was solved to obtain the velocity and concentration distribution across the surface matrix. The local coupling equation at
the interface between the backside of the surface matrix and the cleft
requires that the combined convective and diffusive flux of solute
entering the cleft be equal to the total flux of solute leaving at the
backside of the matrix. However, in this coupling condition, the
concentration, velocity, and pressure at the backside of the matrix are
all unknown, and these parameters are nonlinearly related to each
other. This nonlinear coupling requires that all regions be treated
simultaneously by use of iterative convergence techniques.
Within the cleft itself, region A, the height of the cleft,
2h (see Fig. 2B), is small compared with both the
average distance between the pores and the depth of the cleft, so that
the water flow in the wide part of the cleft can be approximated by
Hele-Shaw flow, as first proposed in Tsay et al. (22). The
local velocity profile is parabolic and satisfies Laplace's equation
for the pressure. Similarly, the concentration field satisfies a
two-dimensional convection-diffusion equation, which is averaged across
the cleft height. The treatment of regions B and
C, the cleft exit region and larger tissue space, was
simplified in Hu and Weinbaum (8) to provide for
closed-form analytic solutions. These same simplifications are applied
herein except that the concentration at the edge of region C
is required to equal the concentration in the superfusate, where the
mesothelium is damaged.
Parameters.
The geometry of the junction strand and surface matrix is shown in Fig.
2, A and B. We shall also present results for
other junction-strand geometry to show the effect of orifice spacing, orifice width, and junction-strand location on the filtration flow and
effective oncotic pressure. Small solutes have only a minor influence
on the oncotic force across the surface matrix, because the fiber
matrix offers only a minor resistance to the small solutes. In a
previous study by our laboratory (7), we showed that the
primary resistance for small solutes was determined by the
two-dimensional diffusion through the breaks in the junction strand of
the interendothelial cleft. The selection of the diffusion coefficient
(Df) for albumin in the surface glycocalyx is
determined by the requirement that our current model provides an
optimum fit to the measured steady-state filtration profile in the
absence of tissue loading. The model predicts a dense matrix, the
effective value of which for Df for albumin is
three orders of magnitude smaller than its value in solution. This is
discussed at length in Hu and Weinbaum (8).
f for albumin in the surface matrix is determined by our
experimental measurements of the effective oncotic pressure in the
high-filtration limit (f2c) in Tables
1 and 2. The values of f fall in the range of 0.8-0.94.
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RESULTS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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Experimental Results
Figure 3 shows an example of an experiment from the first series of experiments on a single venular microvessel, where multiple measurements of the transcapillary water flows (Jv/A) were made first with albumin solution (50 mg/ml) in the perfusate and no albumin in the superfusate and then with albumin (50 mg/ml) in both the perfusate and the superfusate. When the pressure was quickly dropped to 10 cmH2O, there was significant absorption. In fact, the effective oncotic pressure exerted across the filtration barrier in the vessel wall was 17 cmH2O. After albumin was allowed to distribute throughout the tissue, the striking result was that the transcapillary fluid fluxes at pressures of 35 and 10 cmH2O were the same as those when albumin was absent from the tissue. In particular, absorption was still measured at a pressure of 10 cmH2O, showing that the presence of albumin in the superfusate at the same concentration as in the perfusate did not reduce the effective oncotic pressure to close to zero, as expected if diffusion of albumin in the tissue raised the concentration of albumin on the tissue side of the filtration barrier. The results from four experiments in the first series of experiments with a mean Lp of 3.8 ± 1.5 × 10
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cm/(cmH2O · s) showed no significant difference
between filtration rates and effective oncotic pressures exerted by
albumin, measured before albumin was added to the superfusate and
measured after albumin was added to the superfusate, as summarized in
Table 1. The mean oncotic pressure with no albumin in the tissue was
18.2 ± 1.7 (SE) cmH2O and with albumin in the tissue
was 18.2 ± 3.1 cmH2O. Thus, after filtration at high
capillary pressures, the oncotic difference was established across the
primary oncotic barrier within the capillary wall even though there was
no effective concentration difference between lumen and tissue.
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To further test our hypothesis, we extended this approach to set up
initial steady states not only at 35 cmH2O but also at lower capillary pressures, as outlined in the methods for the second
series of experiments (see METHODS). Figure 4 compares the
transient reabsorption rates measured at 10 cmH2O with
additional filtration measurements made after setting up steady-state
filtration at a pressure of 10 cmH2O. Albumin was in the
superfusate throughout the experiment. If albumin was able to diffuse
into the water pathway at lower filtration rates, then we expected that
the effective oncotic pressure difference would be close to zero and
the filtration rate would be determined mainly by the difference in
capillary pressure across the wall, in this case, 10 cmH2O.
The dotted line is the expected filtration rate if there were no
effective oncotic difference. The line has the same slope as the
initial transient experiments [dashed-dotted line,
Lp = 2.44 × 107
cm/(cmH2O · s)]. The results of the experiment
show that, after establishing steady-state filtration at 10 cmH2O, the filtration rate was 0.0054 × 104 cm/s, which is 20% of the filtration rate expected
in this microvessel if no oncotic force were opposed to the applied
pressure of 10 cmH2O. This result indicates that there was
a significant oncotic pressure due to an albumin concentration
difference even under low-filtration-rate conditions. The results
suggest that some mechanism protects a region on the downstream side of
the filtration barrier from back diffusion. The same result was
obtained in four microvessels. Three additional experiments were
carried out in which steady-state filtration was set up at pressures of
10, 20, and 35 cmH2O. The results of all four experiments
are shown in Fig. 5, A-D, where each experiment has
been specifically modeled by use of the approach explained below. The
transient measurements for these four experiments are not plotted in
Fig. 5, A-D, for simplification. The
Lp values and the oncotic pressure intercepts (
) for these four experiments are shown in Table 2. The
mechanisms leading to the maintenance of the concentration difference
of albumin across the endothelial glycocalyx under our experimental conditions are illustrated by use of the following theoretical results,
which model the experimental conditions described above.
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Theoretical Results
Detailed concentration distribution.
The key predictions of the theoretical model corresponding to the
experimental results shown in Figs. 3-5 are presented in Figs. 6-8, where the concentration
profiles for albumin from the lumen to
the tissue are plotted at three positions
within the cleft: along the centerline (y = 0) of the
orifice break in the junctional strand; along the edge of the orifice
(y = 75 nm); and at y = 2,160 nm,
corresponding to y = D, the one-half spacing of the neighboring orifices. The junction strand lies at the midpoint of the
cleft depth (x = 200 nm), and the other parameters are shown in Fig. 2, which are the typical values based on the
microstructural measurements of frog mesentery capillaries
(2). Thus the Lp of the
wall is evaluated to be 2.43 × 107
cm/(cmH2O · s), which is similar to the mean value
of Lp in Tables 1 and 2. The effect of
junction-strand geometry and location will be examined later. The
concentration profiles in the surface glycocalyx, the cleft, and tissue
space when the albumin is in the perfusate alone are shown in Fig. 6
for the high-filtration flow, Pc = 35 cmH2O. The protein concentration just behind the surface
glycocalyx at y = 0 and within the break is 0.066 for f = 0.94. The values approach the high-filtration
limit, (1 f)Cc, as expected when the
concentration leaving the tissue is determined by the steady-state flux
of albumin and water through the vessel wall. The tissue concentration
is set at zero at a distance of 100 µm from the vessel wall, because
the resistance of the mesothelium was deliberately reduced by placing a
glass rod on the tissue to damage the mesothelial barrier. As a result, the albumin concentration falls toward zero in the tissue side of the
cleft and in the tissue. It is important to note that, because of the
wide spread of the water flow in the tissue space, the Peclet number Pe
in the tissue, region C in the model, is 
1, and this
region is diffusion dominated. Thus the concentration decreases almost
linearly with distance in the tissue, as shown in Fig. 6,
inset.
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Filtration-pressure curves.
The comparison of the experimental results with the predictions of the
theoretical model are shown in Fig. 5, A-D, for four microvessels with hydraulic conductivity (Lp)
ranging from 0.67 to 3.0 × 107
cm/(cmH2O · s). Also shown are the theoretical
predictions of the classical Starling theory with tissue loading and
the steady-state predictions of the present model and the earlier
one-dimensional model of Michel and Phillips (18) without
tissue loading. Because Adamson and Michel (2) found that
the length of the breaks in the junction strand in frog vessel was
relatively constant, Lp was varied by changing
break frequency. The filled circles in Fig. 5 are our experimental
measurements for tissue loading. The value of f in our
experiment ranged from 0.8 to 0.94. To show the effect of the variation
of f, we show results for the two extreme values,
f = 0.8 and f = 0.94. The solid
curves in Fig. 5 are the steady-state relations between the fluid
filtration and capillary pressure when the tissue has been loaded to
the same protein concentration as the plasma. The dotted and dashed curves show the steady-state relation without tissue loading, where the
tissue concentration achieves the equilibrium value Ci = Js/Jv. The dotted
curves are the predictions of the present spatially heterogeneous
model, and the dashed curves are the predictions of the homogeneous
one-dimensional model (18) with an adjusted Lp. The dashed-dotted line is the result
calculated by use of the classical Starling equation, where P and are evaluated with the use of the global values for the concentration
in the lumen and tissue. When the interstitial protein concentration is
the same as the plasma (Ci = Cc),
Eq. 1 reduces to Jv/A = Lp(Pc Pi).
Effect of junction-strand structure and location.
We also investigated the effect of changes in the length and frequency
of the breaks in the junction strand by determining combinations of
length and frequency that give the same Lp as measured. For example, for Lp = 4.6 × 107 cm/(cmH2O · s), we can either
maintain a 2d of 150 nm but decrease the spacing of the junction-strand
orifices to 2D = 1,478 nm or double the break length to 2d = 300 nm and have a 2D = 2,010 nm. Although break length has been
doubled from 150 to 300 nm, the change in the fluid filtration curve is
negligible, as shown in Fig. 9. Similar
results are presented for Lp = 0.67 × 107 cm/(cmH2O · s), a low-filtration
rate that approaches mammalian muscle capillaries, where results are
shown for 2d = 40 and 150 nm and 2D = 6,696 and 10,160 nm,
respectively. For both high and low Lp, one
observes that the detailed structure of the strand has only a minimal
effect on the curves for the steady-state water flux.
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cm/(cmH2O · s)] and the same junction orifice
length (2d = 150 nm). To achieve the same
Lp, the spacing of the junction strand (2D) was
reduced to 2,940 nm for the junction strand close to the matrix. The
filtration-pressure curve for the junction strand at
L1 = 200 nm lies beneath the curve for the
junction strand, close to the entrance. The velocity and concentration
profiles (not shown) show that as the junction strand moves closer to
the entrance, the velocity profile behind the surface glycocalyx is a
more highly convergent flow with a higher maximum velocity on the
centerline (y = 0). In the region removed from the
junction orifice, the velocity is close to zero, and in the
concentration field, diffusion dominated. Thus the concentration in the
region removed from the junction orifice is increased because of
diffusion from the lumen. The Starling force is therefore reduced, and
the fluid filtration is increased.
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Diffusion distance in tissue.
The length of region C is determined by the location at
which the mesothelium is opened to facilitate diffusion from the
superfusate to the tissue. The exact location is difficult to control
and thus we have explored different values of the radius of
region C (LC). For a short
distance (LC = 15 µm), the boundary condition Ci = Cc is applied much closer to the
microvessel at a distance that is the sum of LB
and LC (20 µm) by use of our present model. The results shown in Fig. 11 indicate
that even if the albumin concentration near the cleft exit is increased
by reduction of the diffusion distance in the tissue, the increased
tendency for back diffusion remains small and would account for at most
a 15 percent increase in filtration above that predicted for a
diffusion distance of 100 µm.
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DISCUSSION |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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Both the current experiments with loading of albumin in the tissue and their theoretical interpretation conform to the hypothesis that for the continuous capillaries of frog mesentery, the oncotic and hydrostatic pressures that determine transcapillary fluid flux apply across the endothelial cell glycocalyx. Furthermore, the results demonstrate that the local protein concentration and pressure behind the surface-matrix layer can differ greatly from the tissue concentration and pressure, with the result that the Starling forces across the surface-matrix layer will depart significantly from the global Starling forces across the entire endothelial layer, as shown in Figs. 3, 4, 7, and 8. The novel aspect of our experimental design and calculations is the focus on the gradients in the cleft and tissue and the precise link between gradients of albumin in the tissue and the albumin concentrations and hydrostatic pressures in the cleft. In the following discussion, we first review the ultrastructural basis for the model in frog mesenteric capillaries and evaluate new aspects of our experimental design and then consider the application of this conclusion to mammalian microvessels. We note in particular that Levick (12) demonstrated that high-velocity water flows downstream from localized fenestrae resulted in a larger oncotic pressure difference across the fenestral diaphragm than expected from the blood-to-tissue concentration difference after loading of the tissue with elevated albumin concentrations.
Mechanism of the Junction-Strand Shielding
The crucial insight into the detailed mechanism as to when the junction strand will serve to create a protected region on the lumen side of the junction strand that prevents back diffusion through the junction-strand pores is obtained by examining the Peclet number Pe at the orifice openings in the strand. The Peclet number represents the ratio of convection to diffusion, and when Pe > 1.0 at the orifice break, solutes on the tissue side of the cleft will have difficulty diffusing upstream against the convective flux of solutes that is being funneled through the orifice openings by the filtration flow. In this sense, the junction-strand pores act much like a sonic throat in a Laval nozzle, where pressure disturbances cannot travel upstream when the Mach number is >1.0. The calculated values of Pe at the breaks in the junction strand in Figs. 6-8 are 2.34, 2.51, and 0.32, respectively. These values of Pe explain why the oncotic pressure on the backside of the surface glycocalyx is nearly the same in Figs. 6 and 7, where Pe > 1, even though the tissue concentration of albumin is equal to that in the perfusate in Fig. 7. It also explains why there is significant back diffusion in Fig. 8, where the steady-state filtration is low and Pe = 0.32.The concentration behind the surface glycocalyx is raised because of the back diffusion when Pe at the junction orifice is <1, but is still washed down to a value lower than the tissue space, as shown in Fig. 8. In fact, the value of the albumin concentration at the back of the glycocalyx (0.75 Cc) predicts that the oncotic pressure difference across the glycocalyx is 8.6 cmH2O. This value is comparable with the predicted value of 9.9 cmH2O from the steady-state formula of Michel and Phillips (18), which does not take into account back diffusion. Note that under the same conditions, the concentration of albumin at the cleft exit approaches 90% of the concentration in the tissue, and the maximum oncotic pressure across the entire capillary wall is <3 cmH2O. These results clearly demonstrate that oncotic gradients across the entire capillary wall are not the determinants of the fluid balance. Rather, the fluid balance is determined by the albumin concentration differences across the surface glycocalyx, maintained by a protected region between the downstream side of the surface glycocalyx and the break in the junctional strand. The principal mechanism acting to prevent albumin accumulation on the tissue side of the glycocalyx is the throat effect of the break in the strand, which increases the local fluid velocity sufficiently to reduce the tendency of albumin to back diffuse from the tissue and thereby abolish the concentration difference across the glycocalyx.
Pathways for Water and Solutes
The basic hypothesis in our mathematical model is that the surface glycocalyx provides both the primary molecular sieve and diffusive barrier for plasma proteins crossing via porous pathways and that this sieving matrix does not fill the entire interendothelial cleft. If the sieving matrix were to fill the entire endothelial cleft, the shielding effect of the junction structure would be lost, and the model would reduce to the single-layer model first presented in Michel and Phillips (18). In this limit, the throat effect of the orifice will be lost, and the difference in the concentration between the cleft exit and tissue would be greatly reduced. The pores in the junction strand would behave in a manner similar to the fenestra pores studied by Levick (12). In this case, the convective effect of the flow in washing away the protein in the vicinity of the pores in the junction strand would be greatly reduced.At present, the evidence for the structure of glycocalyx is only indirect, because the matrix under most conditions is difficult to stain and preserve intact for electron microscopy. The most convincing evidence that the sieving structure is confined to a surface layer is the detailed calculations for Lp for frog mesentery in Fu et al. (7), the measurements of the surface-matrix layer thickness for frog mesenteric microvessels in Adamson and Clough (1), and the recent theory and experiments for the labeling of the cleft with the use of high-molecular-weight tracers (6). Furthermore, serial-section electron micrographs (2) clearly reveal that the gap height of the breaks in the junction strand (20 nm) is essentially the same as the wide part of the cleft. Thus the junction strand itself is unlikely to provide the molecular sieve for plasma proteins. This combined evidence has led Michel (16), Weinbaum (24), and Hu and Weinbaum (8) to hypothesize that the surface glycocalyx is the molecular filter, at least for frog mesentery capillaries.
Detailed evaluations of the model parameters and the methods to solve the coupled nonlinear equations to describe the flows of water and albumin through the matrix, cleft, and tissue spaces have been described (8). The new variations of the model described in the present work include a modification of size and frequency of the breaks in the junctional strand to describe the actual range of experimental Lp values measured in our test vessels (Fig. 5, A-D) and to demonstrate that such variation in the junction geometry does not significantly modify the predictions of the model (Fig. 9). There is a tendency for the experimental data to fall slightly higher than the predicted values. One source of this discrepancy may be experimental, reflecting the difficulty of maintaining a uniform pressure in the vessel during partial occlusion while steady-state filtration was set up at a pressure of 10 cmH2O. For example, if the capillary pressure were close to 7 cmH2O during partial occlusion instead of 10 cmH2O, the increase in pressure after occluding the vessel to measure filtration, combined with a smaller transcapillary albumin concentration difference, would impose a small transient filtration on the steady-state flux. This small transient would cause an overestimate of steady-state water flux, but the extent of the error is ~20%.
The other model parameter that we evaluated, both experimentally and theoretically, was the diffusion distance from the vessel wall to the region where the mesothelium was disrupted. In control experiments, we found that placing a glass rod at four to five positions along the length of a vessel at a distance of ~100 µm from the vessel disrupted the mesothelium sufficiently to allow albumin to diffuse into the tissue but did not damage the microvessel wall as demonstrated by a constant microvessel Lp before and after the procedure. The glass rod had a diameter of at least 15 µm and disrupted mesothelial cells with a mean diameter of at least 30 µm. Thus albumin was likely to cross the barrier at distances closer than 100 µm from the vessel. Our calculation shows that there is no significant change in the fluid filtration for a low Lp, and degree of increase in fluid filtration depends on the frequency of the junction orifice.
Mammalian Microvessels
One of the key results obtained in the previous section is that the junction-strand structure has only a minor effect on the Starling force if Lp is unchanged. This is important in extending our theoretical model to continuous mammalian vessels. The structure of the interendothelial cleft and the organization of the junction strand observed in rat heart capillaries by Bundgaard (3) are qualitatively similar to frog mesentery capillaries except that the length of the breaks is much shorter, typically the width of a single transmission section: 40-50 nm. However, there was insufficient data to accurately determine break frequency. At present, there are no ultrastructural studies for mammalian capillaries equivalent to that of Adamson and Michel (2) for frog mesentery. In the latter study, measurements of Lp were performed on the same vessels for which serial reconstructions were obtained for both the junction structure and the cleft depth. Figure 9 demonstrates that we could account for the measured filtration rates in one vessel with an Lp of 0.67 × 107
cm/(cmH2O · s) by reducing the break length from
150 to 40 nm (with a corresponding change in break frequency). The
Lp of this vessel overlaps the upper range of
values in mammalian muscle microvessels. Thus the same basic mechanisms
whereby high water velocities at the breaks in the strand reduce the
diffusion of tissue proteins in the cleft between endothelial cells are
expected to apply in mammalian microvessels. Mammalian microvessels
with smaller Lp values or with only a fraction
of the total water flow through a junctional pathway could be described
if the frequency of breaks in the strand was much smaller than in frog
mesenteric vessels or if the pathways for flow were more tortuous than
described above. As suggested by Michel (16), it is likely
that most of these proteins enter the tissue by parallel pathways
formed by large pores or vesicles. The extension of the present theory
to predict the effective Starling force for mammalian capillaries with
continuous endothelium if the surface glycocalyx is the primary sieving
layer for proteins warrants further investigation.
There is still some controversy as to whether the surface glycocalyx or small pores in the junction strand provide the molecular filter for proteins. Bundgaard (3) also observed narrow gaps with a width of 4-6 nm and a height of 10-20 nm between adjacent membranes using ultrathin 10- to 15-nm electron microscopy sections and suggested that these gaps might serve as a molecular sieve. Although such small pores could serve as a molecular filter for albumin, they do not account for the fact that most of the water and solute would pass through the nonselective large breaks (40-50 nm) in the junction strand, the height of which is the same as the wide part of the cleft. Vink and Duling (23) have used fluorescent tracers to measure the thickness of a glycocalyx layer in hamster cremaster muscle capillary in vivo. They found that the thickness of the layer that excludes FITC-dextran is 0.4-0.5 µm. It is not known whether all or a fraction of this layer would serve as a molecular sieve for plasma proteins or what the displacement of the cationized ferritin layer would be if an experiment equivalent to Adamson and Clough (1) could be performed on hamster cremaster microvessels. Experiments are needed to investigate the surface glycocalyx and the size and frequency of junction-strand breaks in mammalian microvessels.
The role of highly localized water flows on the downstream side of fenestrae has been examined both experimentally and theoretically by Levick and co-workers (12, 13) with reference to fluid exchange in the synovium. In experiments in which the tissue concentration of albumin was increased, these investigators also showed that the effects of extravascular albumin on fluid exchange were much less than that of intravascular albumin. The explanation in the fenestrated vessel is that the high water velocity exiting the fenestra decreases the albumin concentration downstream of the fenestra in a region that extends a few micrometers into the tissue. Our calculations show that such tissue gradients also form at the cleft exit in continuous capillaries, although the water velocities are much lower than in fenestrated microvessels. However, for continuous capillaries, the primary interaction of high water velocities and tissue protein occurs within the cleft at the highly localized breaks in the junctional strand. Nevertheless, the elegant studies of Levick and his colleagues (12, 13) in synovium also conform to the hypothesis tested in the present experiments that the Starling forces that determined transcapillary fluid exchange are not the global difference in hydrostatic and oncotic pressure between blood and tissue but the hydrostatic and oncotic pressure across a selective matrix across the glycocalyx or fenestral diaphragm.
Finally, we emphasize that for either frog or mammalian microvessels, it is very difficult, if not impossible, to measure the concentration distribution of the oncotic protein within the cleft itself under experimental conditions. A detailed theoretical model is thus essential to fill in the gaps and provide essential insights as to what is occurring at the cellular microstructural level. The power of the theoretical model is that it has the flexibility to explore in detail the effect of detailed junctional ultrastructure on measured macroscopic behavior.
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ACKNOWLEDGEMENTS |
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This research is supported by National Heart, Lung, and Blood Institute Grant HL-44485.
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FOOTNOTES |
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X. Hu is the recipient of a Whitaker Foundation-sponsored Center for Biomedical Engineering Fellowship.
Address for reprint requests and other correspondence: S. Weinbaum, Dept. of Mechanical Engineering, The City College of New York, Convent Ave. at 138th St., New York, NY 10031 (E-mail: weinbaum{at}me-mail.engr.ccny.cuny.edu).
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 21 October 1999; accepted in final form 11 April 2000.
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REFERENCES |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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,
measured experimental data; solid lines, steady-state curves in the
presence of tissue loading [the albumin concentration at the edge of
region C (Ci) has the same protein concentration
as the superfusate (Cc); Ci = Cc]; dotted lines, steady state without tissue loading
(Ci = Js/Jv, where
Js is total protein flux entering the tissue
space and Jv is total fluid flux into the tissue
space) predicted by the present 3-dimensional heterogeneous model;
dashed lines, based on the 1-dimensional (1-D) theory in work of Michel
and Phillips (
.
