856
The Interaction of Convection and Diffusion in the
Transport of 131I-Albumin within the Media of the
Rabbit Thoracic Aorta
Alain Tedgui and M. John Lever
From the Physiological Flow Studies Unit, Imperial College, London, Great Britain
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SUMMARY. The interaction of convection and diffusion in the transport of 131I-labeled albumin
within the wall of rabbit thoracic aorta was studied in vessels excised at in vivo length. They were
pressurized with a solution containing no tracer and immersed in a solution containing labeled
albumin. The label then entered the wall tissue via the adventitia and had to diffuse against the
convective flux which occurred from the lumen to the adventitia. Experiments were performed
on intact and deendothelialized vessels pressurized to 70 and 180 mm Hg. At the end of each
experiment the vessels were subjected to sequential frozen sectioning parallel to the lumenal
surface. The radioactivity of the 20-/im-thick sections was determined and expressed as a
tissue:labeled solution concentration ratio. Transmural profiles of these ratios were thus obtained.
The steady state was found to be achieved by about 90 minutes. When the convection was
enhanced by removal of the endothelium, the average ratios were lower than when the endothelium was intact, and the profile was much flatter. The results suggest that convection influenced
macromolecular transport within the arterial wall, even in vessels with intact endothelium. (Circ
Res 57: 856-863, 1985)
MATERIALS are transported through artery walls
by both diffusive and convective mechanisms, but
the relative roles of these processes in protein transport are still unclear (Swabb et al., 1974; Auvert et
al., 1980; Caro et al., 1980a; Truskey et al., 1981).
Uptake of 131I-albumin by the wall is enhanced
by raising the transmural pressure (Duncan and
Buck, 1961; Duncan et al., 1962; Auvert et al., 1980).
Mechanisms proposed to account for this include
increased fluid filtration and distension of the tissue.
In an attempt to resolve these problems, studies
were undertaken (Duncan et al., 1965; Fry, 1973) in
which strips of artery were pressurized while being
prevented from distending. The results of these experiments must now be considered inconclusive,
because it has since been shown that compaction of
the tissue can occur under such experimental conditions (Yamartino et al., 1974; Kenyon, 1979).
To reexamine the question of the interaction of
convection and diffusion, we have filled excised,
pressurized arteries with tracer-free physiological
solution and incubated them in baths containing
131
I-albumin. The tracer could thus diffuse into the
tissue from the external surface while pressuredriven convection occurred in the opposite direction.
The convective flow was varied by using intact and
deendothelialized arteries, and the degree of distension was changed by studying arteries with normal
cylindrical geometry at either 70 or 180 mm Hg
transmural pressure. We have shown in a previous
study that the filtration flow rate through the wall
was enhanced by removing the endothelium and
increasing the transmural pressure (Tedgui and Lever, 1984).
Information about the transport mechanisms was
obtained by examining the spatial distribution of
tracer within the wall after a steady state had been
established.
Methods
Animal Preparation
Male New Zealand white rabbits (2-2.5 kg) were anesthetized by intravenous injection of 30 mg/kg sodium
pentobarbital through the marginal ear vein. Each animal
was artificially ventilated after tracheal intubation, and
the sternum was split lengthwise. Heparin (1000 IU) was
then administered intravenously, and the intercostal arteries were ligated on both sides of the aorta, 1-2 mm
from their origins. The pleural membrane and surrounding
fat were then carefully dissected away from the aorta.
During the whole operation, the surface of the vessel was
kept moist by application of Tyrode's solution containing
2% albumin.
The aorta was ligated above the diaphragm. A 16-gauge
needle pointing toward the heart was inserted just above
this and was tied into the vessel. The needle was connected to a reservoir which was about 80 cm above the
animal, and filled with Tyrode's solution containing 4%
albumin. The reservoir prevented depressurization of the
aorta when a second ligature was placed on the aorta
about 3 cm upstream of the first needle. A second needle
pointing caudally and connected to a tap was then tied in
the upstream end of the ligated segment. Both needles
Tedgui and Leper/Influence of Diffusion and Convection on Macromolecular Transport
then were clamped onto a rig which prevented the artery
from shortening as it was excised. The vessel was finally
immersed, while pressurized and held at in vivo length,
in a bath containing Tyrode's solution incorporating 2%
albumin and 131I-albumin and maintained at 40°C. The
vessel was flushed with Tyrode's solution containing 4%
albumin and Evans blue dye which served to indicate
leaks and to test the integrity of the endothelium (Packham et al., 1967; Bell et al., 1974). The pressure within
the vessel was controlled with a manometer connected to
the upstream tap. Endothelial damage was minimized
during the whole procedure by maintaining physiological
pressure within the vessel and avoiding shortening. hi
about half the vessels, however, the endothelium was
intentionally removed by inserting a snugly fitting silicone
rubber tube into the aorta and rotating it during withdrawal. These vessels were then cannulated and excised
in the same way.
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Measurement of Filtration through the Wall
This procedure has been described in detail elsewhere
(Tedgui and Lever, 1984). Filtration was measured by
following the movement of a meniscus along a capillary
tube interposed between the artery segment and the manometer which was used to maintain transmural pressure.
The integrity of the smooth muscle cells of the vessel
wall at the conclusion of some experiments was assessed
by applying a solution containing angiotensin II (3 X 10"9
M) to the vessel. Marked vasoconstriction occurred, causing considerable reverse movement of the meniscus along
the capillary.
Estimation of Radioactivity within the Wall
After incubation in the labeled solution, the artery was
removed from the bath and then rapidly cut from the
needles, opened axially, and divided into four segments
of roughly equal area: two each from the dorsal and
ventral regions. The segments were rinsed for 10 seconds
in cold Tyrode's solution, laid on a lightly greased microscope slide and rapidly frozen in a cryostat at —20°C. In
view of the relatively long time constants found for protein
uptake, it was assumed that a negligible quantity of label
was lost from the tissue during washing.
A layer of mounting on the chuck of a freezing microtome (Brights or SLEE-HR) was cut so its exposed face
was parallel to the cutting planes. A small quantity of
mounting medium was spread on the uppermost adventitial surface of the frozen artery slab, which was brought
up to and frozen onto the chuck. A ring placed around
the tissue on the microscope slide ensured that the lumenal
surface was parallel to the previously cut face on the
chuck. The edges of the segments wwe trimmed to remove
overhanging material, and their surface area (about 0.4
cm2) was measured. En face serial sections 20 fim thick
then were cut through the whole thickness of the wall
from the lumenal surface (Adams, 1973; Bratzler et al.,
1977; Caro et al., 1980a). The boundary between the
media and the adventitia was noted by an alteration in
the appearance of the sections. The distance of the boundary from the lumenal surface varied between 160 and 200
fim. The sections were dried and weighed to check the
accuracy of sectioning and to allow estimation of the
thickness of the first lumenal section (its weight relative
to that of the subsequent sections was assumed to indicate
its thickness). The dried weights of the medial sections
(except the first one) were constant to within 10%, indi-
857
cating that the sections were uniform and that sectioning
had been performed in planes parallel to the intimal
surface. The average thickness of the first sections was
half of that of the subsequent medial sections. The volume
of each tissue section was calculated from its thickness
and surface area, and the quantity of label within it was
measured in a 7-counter. Counts ranged from 10-1000
counts/min (after subtraction of background which was
approximately 40 counts/min) and were measured for at
least 4 minutes and usually 10 minutes. At the same time,
the concentration of the label in the external bath was
measured by counting 0.04-cm3 aliquots which were sampled at the beginning and end of the period of incubation.
The concentration was found to be constant during the
incubation period. Tissue concentration ratios Ct/Cb were
calculated for each section, i.e, the counts per minute per
unit volume of wet tissue (G) divided by the counts per
minute per unit volume of external labeled solution (Q,).
The CyCb values for the various sections cut from a single
segment were plotted as a function of their distance x,
from the lumenal surface to the external surface. Distances
for each segment were normalized by dividing by the
medial thickness, L.
Average profiles were constructed by averaging Ct/Cb
values at equal intervals across the wall.
Tracer
I31
I-labeled human serum albumin (Amersham International) was purified by serial 4-fold filtration through
an ultrafilter with nominal cut-off at 50,000 daltons
(Chem Lab Ltd.). The tracer was added to the external
bath to give a concentration of approximately 10 /iCi/cm3.
Although ultrafiltration removed virtually all the low molecular weight impurities, previous studies using the same
preparation and following the same purification procedure
had shown that after 90 minutes at 40°C, the concentration of free iodide rose to an average of 0.26% of that of
the labeled albumin (Caro et al., 1980a). In four gel
fractionation assays, the mean free iodide:labeled albumin
ratio averaged 0.28% (range 0.14-0.35) after an incubation
of 90 minutes.
The presence of this contaminant could have led to
overestimates of 13II-albumin uptake. The error might be
a non-uniform proportion of the total label at a given
x/L, since Ct/Cb values were always lower at the lumenal
surface than at the external surface. In order to correct the
Q/Cb profiles across the wall for this contamination, in a
small series of experiments, the labeled albumin was replaced by Na131I. The distribution of labeled iodide values,
(Ct/Cb)i, across the wall, permitted calculation of the correct Q/Cb values for albumin uptake (Ct/Q,)c at each x/L,
from those measured (Q/Cb)m as:
= (Q/CbUx/L) x
/
0.0026 x
where 0.0026 is taken as the proportion of free iodide
present in the labeled solution after 90 minutes of incubation.
As the Q/Cb values of the first sections were already
corrected for the difference in thickness from the subsequent sections, the actual correction for free iodide in
these becomes:
(Q/Cb)c =
-
2X
0.0026 x
858
Circulation Research/VoJ. 57, No. 6, December 1985
since the average thickness of the section was found to be
half of that of the subsequent sections.
To confirm this correction, a further series of four
experiments was performed on deendothelialized arteries;
because of their low Ct/Cb values, the correction had been
relatively larger in this group. At the end of incubation of
these vessels, they were removed from the bath, and after
brief rinsing they were immersed in 4% glutaraldehyde
for 30 minutes before freezing and sectioning. In some
unpublished studies on the uptake of iodinated albumin
by the rabbit aorta in vivo, the distribution of label in the
tissue after glutaraldehyde fixation in situ was comparable
with that found in unfixed tissue. When labeled iodide
was injected into rabbits and the arteries were fixed in the
same way, the label was completely washed out of the
wall. The concentration profiles across the fixed arteries
in the present series were very similar to the corrected
profiles found in the other experiments. Comparisons of
the corrected Ct/Cb values at each interval across the
media with the corresponding values obtained after this
fixation procedure gave no statistical differences.
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Results
Artery Structure
The results of scanning electron microscopic and
transmission electron microscopic studies of intact
and deendothelialized aortas, fixed under 70 and
180 mm Hg, are presented in detail elsewhere (Tedgui and Lever, 1984). A completely intact layer of
normal endothelial cells has been found on the
vessels not subjected to silicone catheterization. In
these arteries subjected to endothelial removal, the
endothelial cells were damaged or absent. In both
intact and deendothelialized arteries, the internal
elastic lamella was intact and the underlying tissue
appeared undamaged.
On some of the deendothelialized arteries in this
study, we performed histoenzymic studies using
Takeuchi's method (Takeuchi and Kiriaki, 1955).
Phosphorylase activity in the smooth muscle cells
of the inner, mid, and outer media, after 90 minutes
10 i -
» 1$ min
« 30mln
SO min
90 min
• USmin
0.1
0J2 0.3
Normalized
(5)
(3)
(5)
(7)
()
(2)
0.4
0.S
Distance
0.6
from
0.7 0.8
Lumen
0.9
1
FIGURE 1. Relative "lI-albumin tissue concentration across the walls
of intact arteries, pressurized to 70 mm Hg, as a function of normalized
distance from lumen for different incubation times. Numbers of
arteries are given in brackets. Bars represent SEM.
of incubation at 70 and 180 mm Hg was similar to
that found in control arteries freshly taken from an
animal. Phosphorylase activity has been shown to
be an early and significant index of arterial damage
(Numano et al., 1973). These results suggest thus
that the viability of the smooth muscle cells was
maintained in the aortic preparation.
Label Uptake Studies
Twenty two arteries with intact endothelium and
pressurized to 70 mm Hg weTe incubated in labeled
solution for periods ranging from 15-180 minutes.
The average C,/Cb profiles for each incubation time
are shown in Figure 1. The increase in Ct/Cb from
zero with time at the lumenal boundary was possibly
due to the accumulation of tracer in the lumenal
solution, which increased with time.
10r
X/L
1.0
<Vcb
10-2
o.e
0.5
0.2
10
30
50
180
90
Incubation
Time
(min)
FIGURE 2. Relative "ll-albumin tissue concentration, CtfCt, across the walls of intact arteries,
pressurized to 70 mm Hg, as a function of incubation time for each interval across the wall, x/L L
= the distance between the intimal surface and the
medial-adventitial border. Solid lines are the best
fits to the data of an exponential equation: C'(t) =
C ' f l - cxp(-t-Log 2/tin)]. C - CJCt. C =
the steady state relative concentration, fi/j «= the
time when C = 0.5CJ. The calculated values of
Un for eacfl fit are given ' " Table 1. Curves for x/
L •= 0.3 and 0.4 are not drawn, to simplify the
graph.
Tedgui and Lever/Influence of Diffusion and Convection on Macromolecular Transport
TABLE 1
Values of i^ C'(90)/C_', and C'(180)/C Calculated for x/L
from 02 to 1*
x/L
ty,(min)
C'(90)/C-
C'(180)/C
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
32
31
27
28
26
32
31
27
28
0.87
0.89
0.89
0.89
0.91
0.87
0.89
0.91
0.89
0.98
0.96
1.0
1.0
0.99
0.93
0.94
0.97
0.95
• C'(90) and C'(180) represent the C,/Cb values at 90 and 180
minutes, respectively, ty, and CV are the values obtained as the
best-fit parameters of the equation C'(t) = C ' [ l — exp{—t-Log
2/ti/i)] to the experimental data.
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In order to estimate the time required to achieve
the steady state, the mean Ct/Cb values, obtained at
each location across the wall, were plotted against
time (Fig. 2). By the least-squares fitting of an exponential regression curve to the data, the times
(ti/2) when half the steady state concentration, G»,
was attained, were determined for each curve. The
ti/2 values at different locations ranged from 26-32
minutes. Thus, the Ct/Cb values obtained after 90
minutes represented 87-91% of G», and those obtained after 180 minutes represented 93-100% of
C« (Table 1). Since the Ci/Cb values for arteries
incubated for 90 minutes were within 10% of C , it
was assumed that 90 minutes was an adequate
period to achieve a steady state.
To verify that 90 minutes were sufficient to
achieve a steady state in deendothelialized arteries,
experiments were run for 90 minutes on three of
those arteries pressurized to 70 mm Hg and for 180
minutes on three additional deendothelialized ves-
859
sels. At 90 minutes, the average Ct/Cb values at each
interval across the wall were found to be within
10% of the corresponding values for arteries incubated for 180 minutes.
Of the five deendothelialized vessels pressurized
to 180 mm Hg, three were incubated for 90 minutes
and two for 180 minutes. In this series too, the
average 90-minute Ct/Cb value at each interval
across the wall was found to be within 10% of those
at 180 minutes.
No complete time-course study was performed on
arteries with intact endothelium and pressurized to
180 mm Hg. Four arteries were used under this
experimental condition, and they were incubated for
90 minutes.
Figure 3 shows the profiles after 90 minutes of
incubation of the relative Na131I tissue concentration
(Ct/Cb)i in one aorta with and without endothelium
at 70 and 180 mm Hg. Maximum values were found
in the mid-media. At the end of the incubation
period, the lumenal concentration in labeled iodide
was found to be 25-35% of that in the external bath.
This could account partly for the lumenal concentration gradient. The fall in concentration toward
both the external and lumenal surfaces might also
be due to some loss of the low molecular weight
molecules from both sides of tissue when it was
rinsed in cold Tyrode's solution for 10 seconds. In
each experimental condition, the (Ci/Cb)i values obtained at each location were used to correct the
corresponding measured I31I-albumin Ct/Cb values,
as described above.
For each experimental condition, average steady
/Cb profiles were obtained by pooling data from
90- and 180-minute experiments. The profiles for
both intact and deendothelialized arteries incubated
at 70 and 180 mm Hg before and after correction
for free iodide contamination are shown in Figure
.55 _
.50
.45
FIGURE 3. Relative No131/ tissue concentration as
a function of normalized distance from lumen obtained in one intact and deendothelialized aorta,
pressurized to 70 and 180 mm Hg.
.40
70 mm Hg
• Intact Endo.
i. Damaged Endo.
IBOmmHg
• Intact Endo.
>-. Damaged Endo.
.35
.30
.25
0.1
1
0.2
I
I
I
I
I
0.3
0.4
0.5
0.6
0.7
0.8
Normalized Distance
from Lumen
I
09
Circulation Research/Vo/. 57, No. 6, December 1985
860
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4. The presence of free iodide led to overestimates
of 131I-albumin uptake varying from 2% for the
highest measured values of Ct/Cb to about 30% for
the lowest.
The Ct/Cb values decreased nonlinearly from the
external to the lumenal surfaces. The average C^Cb
values were lower in deendothelialized arteries than
in intact vessels. Furthermore, the Ct/Cb profile was
much flatter in deendothelialized arteries pressurized to 180 mm Hg than in the other vessels.
In nine experiments, aliquots of the intralumenal
solution were sampled at the end of the incubation.
The activity of these depended on the incubation
time, and averaged 0.23 ± 0.24% (varying between
0.03% and 0.6%) of that of the external solution. In
six experiments, trichloroacetic acid (TCA) was used
to precipitate protein-bound label from the lumenal
solution. The average TCA-precipitable radioactivity
was only 29 ± 6% of the total radioactivity, indicating that much of the intralumenal radioactivity was
due to free iodide diffusing through the wall from
the external bath.
Discussion
During the in situ preparation of the artery, some
of the adventitia was removed with the pleural
membrane and surrounding fat. The adventitial
layer does not appear to contribute directly to the
mechanical properties of the vascular wall (Wolinsky and Glagov, 1964) and the histological appearance of the media is unchanged when the adventitia
is removed (Wolinsky and Daly, 1970; Tedgui and
Lever, 1984). The transport properties of the media
are therefore assumed to be unchanged when part
of the adventitia is removed.
By assuming that the steady tracer concentration
_
70 mm Hg
• Intact Endo.
a Damaged Endo.
180mmHg
• Intact Endo.
o Damaged Endo.
8
C
'/c
7 ~~
(7)
(6)
•
1
/
3
(4)
(5)
9
4
3
J
2
1 V
7~ i
"T
Cm = C b - e x p l J
l" "
1
0.1
0.2
0.3
0.4
0.5
0.6
Normalized Distance
from
1
1
0.7
0.8
Lumen
09
1
FIGURE 4. Relative l3lI-albumin tissue concentration as a function of
normalized distance from lumen for intact and deendothelialized
arteries, pressurized to 70 and 180 mm Hg. Dashed lines represent
measured CJQ, values. Solid lines represent corrected C,/Ct values.
Numbers of arteries are given in brackets. Bars represent SEM.
-d
where d is the thickness of the unstirred layer (assumed to be 100 /un). The largest average value of
the filtration was 9.5 X 10~* cm/sec (Tedgui and
Lever, 1984) and the free diffusion coefficient of
albumin is 6.8 X 10~7 cm2/sec (Wakeham et al.,
1977) so the wall concentration is at least 87% of
the bath concentration. The effects of the unstirred
layer are therefore probably not responsible for the
much lower concentration of tracer found in deendothelialized vessels at high pressure.
After the beginning of the experiment, when the
tracer has started to enter the wall from the adventitial surface, the tracer flux within the wall 0s) can
be described as a combination of convection (Jc) due
to bulk flow and permeation (JD) due to diffusion
(Kedem and Katchalsky, 1958). If the media is assumed to be a homogeneous membrane extending
from x = 0 (the lumenal surface) to x = L (the
adventitial surface), the diffusional and convective
fluxes of tracer within the wall can be expressed at
any point in the media in a differential form (Patlak
et al., 1963; Brace et al., 1978) as:
/}
6
\
at the adventitial surface is the bath concentration,
there may be some eTror because of the unstirred
layer in the solution next to the outer surface
(Dainty, 1963; Pedley and Fischbarg, 1978). The
bath was not mechanically agitated, but because the
upper surface was open to the atmosphere there
would be appreciable convection within the solution. This factor, together with the convex curvature
of the outer surface of the wall, suggests that the
thickness of this unstirred layer is unlikely to exceed
100 fim (Wright et al., 1972).
If Jv is the velocity of the pressure driven water
flow through the wall and D is the diffusion coefficient of tracer molecules in the external solution,
then the concentration of tracer next to the wall Cm
can be expressed (Dainty, 1963) as:
dx
(1)
and
(2)
Jc = (1 "
where Ct and dCt/dx are the actual concentrations
of tracer and the concentration gradient at that point
in the media, Dw is an effective diffusoin coefficient
for albumin within the tissue, a is the reflection
coefficient of the wall for albumin. The fluxes are
taken to be positive when they occur in the direction
of increasing x; i.e, toward the adventitial surface.
We have assumed that tracer movement can be
considered to be a one-dimensional flux problem.
In the present study, the convective tracer flux,
Jc, was opposite in direction to the diffusional flux
JD. When a steady state is attained, the net flux
through the wall and at any point within the media
Tedgui and Lever/Influence of Diffusion and Convection on Macromolecular Transport
is constant. Under these circumstances, the net tracer
flux (Js) is given by:
Js = - D w - ^
+ (1 - < T ) J V Q = Const
(3)
This equation can be nondimensionalized by scaling the length and concentration variables: x' =
x/L and C = Ct/Cb, where x' is the fractional
distance through the whole medial thickness L, and
C is the tissue concentration relative to the external
bath concentration of the label.
When introduced into Equation 3, this becomes:
Js' = - — + P e - C = Const,
/C L ,
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JvL
0.1
Js-L
CD
(5)
0.3
0.4
0.5
Ontario
0.»
from
. o.7
as
0.8
Lumen
FIGURE 5. Theoretical C,/Ct profiles across the walls of intact and
deendothelialized arteries, pressurized to 70 and 180 mm Hg. Theoretical curves were obtained by least-squares fitting of nonlinear
regression lines to the experimental corrected data from Figure 4,
using Equation 6.
(6)
Pe is a measure of the relative contribution of convection and diffusion to the overall tracer flux.
Integration of Equation 4 gives an expression for
the concentration profile through the wall:
C = K, + K2-exp(Pe-x')
0.2
Normalized
and
Js' J
70 mm HQ
• Intact Endo.
D D a m i g l d Endo.
180mmHg
• Intact Endo.
O Damaged Endo.
(4)
where Pe is the Pedet number given by:
Pe = (1 - a)-
861
(7)
where Ki = Js'/Pe and K2 is a constant. Ki and K2
can be defined in terms of boundary conditions. At
the lumenal surface, the boundary condition equates
steady tracer flux Js to rates of transport by convection and diffusion through the intima (Truskey et
al., 1981). A similar condition applies for the boundary condition at the medial-adventitial interface.
These appropriate boundary conditions would necessitate the knowledge of the exact tracer concentrations in the solutions at the intimal and adventitial
surfaces, but these are subject to uncertainties, as
discussed above. Moreover, these boundary conditions would introduce other unknown parameters
to define the different mass transport properties of
the intimal and adventitial layers (Truskey et al.,
1981). These parameters would be impossible to
determine from the data obtained in the present
experiments. We have therefore calculated values
for Pe, Ki, and K2 by least-squares fitting of regression lines to the corrected data in Figure 4 using
Equation 7. The best-fit parameters were in turn
used to calculate theoretical Ct/Cb profiles which are
superimposed on the experimental data points in
Figure 5. The best fit Peclet numbers are given in
Table 2. If convection and diffusion contribute
equally to transport, then Pe would be expected to
be approximately one; so it seems that in our experiments the effects of convection are not negligible,
particularly in arteries with damaged endothelium,
in which transmural fluid flow rates are greater than
in intact vessels (Tedgui and Lever, 1984).
Duncan et al. (1965) and Fry (1973) suggested
that the effect of transmural pressure on macromolecular uptake was due to stretching, rather than to
pressure-driven convection. In their experiments,
arteries were pressurized against a supporting screen
which may have caused tissue compaction (Harrison
and Massaro, 1976). Filtration through vessels pressurized in this way may be diminished by a factor
of 10, compared with vessels with normal cylindrical
geometry (Yamartino et al., 1974), and any effects
of convection on label transport would have been
reduced.
The Peclet numbers determined in this study are
similar to those determined by Truskey et al. (1981)
from a theoretical analysis of the results of in vivo
albumin uptake experiments. They estimated Pedet
TABLE 2
Peclet Numbers, K, and K, (mean ± SD)* for Intact and
Deendothelialized Arteries at Transmural Pressures of 70
and 180 mm Hg
Intact
endothelium
Damaged
endothelium
70 mm Hg
Pe 4.12 ± 1.10
K, 9.53 ± 6.35 X i<r5
K, 1.87 ± 1.64 X io - 3
180 mm Hg
11.25 ±0.29
Pe 4.65 ±0.47
K, 9.52 ± 3.72 X io- 3 3.45 ± 1.84 X io- 3
K, 6.36 ±5.11 X10-1
2.56 ± 3.22 X 10"*
• Calculated using Equation 6.
5.92 ± 0.94
7.21 ± 5.78 X i o - 3
2.08 ± 1.23 X lO"4
862
Downloaded from http://circres.ahajournals.org/ by guest on July 31, 2017
numbers of 3.6 and 13 for intact and deendothelialized vessels, respectively.
It is assumed in the simple theoretical treatment
used above that transport properties are uniform
across the whole thickness of the media. In fact, our
own studies indicate that the distribution volume
for albumin in relaxed (Caro et al., 1980b) and airpressurized arteries [across the walls of which there
is assumed to be no convection (Caro et al., 1981)]
increases toward the outer surface in a manner
dependent on the transmural pressure. In liquidfilled arteries, with the lumenal and external surfaces exposed to the same concentration in labeled
albumin, the steady tracer distribution is found to
be quasi-uniform across the media when the endothelium is removed, whereas a non-uniform distribution is obtained in arteries with an intact endothelium (unpublished data). However, in the latter
case, the steady state uptake of labeled albumin may
not represent the actual distribution volume for the
protein; the distribution volume is an equilibrium
parameter which cannot be determined absolutely
in a dynamic system. The existence of convective
flux, together with a very high resistance to the
passage of tracer through the endothelium, would
be expected to cause deviation of the steady state
concentration values from those which would be
determined by the true distribution volume. The
greatest deviation may be expected in the inner part
of the media, below the endothelium because of the
steep concentration gradient across the intima. In
deendothelialized arteries, the steady uptake of albumin may give a better indication of the distribution volume because a much less steep concentration
gradient occurs at the blood/media interface.
Experiments on the steady state uptake of [14C]sucrose (a standard tracer for indicating the size of
the extracellular space) with the same concentration
inside and outside the artery indicate that the extracellular space is fairly uniform across the wall of
both intact and deendothelialized vessels (Lever and
Tedgui, 1981). Because of the greater diffusion coefficient of sucrose, the convective contribution to its
flux is relatively lower than that for albumin. The
steady state concentration of sucrose is therefore
likely to give a better indication of its distribution
volume.
Both steady state sucrose and albumin levels in
the wall were greater in deendothelialized than intact vessels. Changes in the available space are likely
to affect both the effective diffusion coefficient and
the reflection coefficient; an increase in space would
be expected to raise the former and decrease the
latter. Since these properties are not the same under
all experimental conditions, the Peclet number will
not truly indicate the importance of convection and
of diffusion in a given experimental condition compared to another one. However, it does indicate the
magnitude of the convective flux compared to the
diffusive flux in each experimental condition. In fact,
Circulation Research/Vo/. 57, No. 6, December 1985
convection is likely to be even more important in
affecting transport across deendothelialized arteries
than this analysis would indicate. Although the
available space in deendothelialized arteries is probably much greater than in intact arteries, the amount
of label which could diffuse into the wall from the
outer surface against the convective flux was much
less in the former than in the latter.
We wish to thank Professor CG. Caro for invaluable discussions
during this work, and Dr. ]. Mikol and Miss M.C. Rouch of Laboratoire
d'Anatomo-Pathologie, Hopital Lariboisiere, Paris, for excellent assistance in the histoenzymic studies.
The work was supported by the Medical Research Council (United
Kingdom) and Delegation Generate a la Recherche Scientifique et
Technique (France).
Address for reprints: Alain Tedgui, INSERM U141, 41 Bd. de la
Chapelle, 75010 Paris, France.
Received May 23, 1984; received in revised form Aug Z 1985;
accepted for publication September 12, 1985.
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INDEX TERMS: Diffusion • Convection • Transmural pressure
• Endothelium • Macromolecule transport
The interaction of convection and diffusion in the transport of 131I-albumin within the
media of the rabbit thoracic aorta.
A Tedgui and M J Lever
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Circ Res. 1985;57:856-863
doi: 10.1161/01.RES.57.6.856
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