Vol. 85, Issue 2, 575-583, August 1998
Effect of concentration on albumin diffusion in lung
interstitium
Xiao L.
Qiu,
Laura V.
Brown,
Sandhya
Parameswaran,
Geoffrey S.
Ibbott, and
Stephen J.
Lai-Fook
Center for Biomedical Engineering and Department of Radiation
Medicine, University of Kentucky, Lexington, Kentucky
40506-0070
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ABSTRACT |
The transport of macromolecules through the lung interstitium
depends on both bulk transport of fluid and diffusion. In the present
study, we studied the diffusion of albumin. Isolated rabbit lungs were
inflated with silicon rubber via airways and blood vessels, and two
chambers were bonded to the sides of a 0.5-cm-thick slab that enclosed
a vessel with an intersititial cuff. One chamber was filled with either
albumin solution (2 or 5 g/dl) containing tracer
125I-albumin or with tracer
125I-albumin alone; the other was
filled with Ringer solution. Unbound 125I was removed from the tracer
by dialysis before use. The chamber with Ringer solution was placed in
the well of a NaI(Tl) scintillation detector. Diffusion of
tracer through the interstitium was measured continuously for 60 h.
Tracer mass (M) showed a time
(t) delay followed by an increase to
a steady-state flow
(dM/dt
constant). Albumin diffusion coefficient
(D) was given by
L2/(6T),
where T was the time intercept of the
steady-state
M-t line at zero M, and
L was interstitial length.
Interstitial cuff thickness-to-vessel radius ratio
(Th0/R)
was estimated by using Fick's law for steady-state diffusion. Both
D and
Th0/R
were independent of albumin concentration.
D averaged 6.6 × 10
7
cm2/s, similar to the free
D for albumin. Values of
Th0/R
averaged 0.047 ± 0.024 (SD), near the values measured
histologically. Thus pulmonary interstitial constituents offered no
restriction to the diffusion of albumin.
rabbit; fluid balance; permeability
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INTRODUCTION |
THE INTERSTITIUM surrounding the lung microvasculature
contributes to the plasma-to-lymph barrier resistance to water and solute (24, 27), whereas the perivascular interstitium surrounding extra-alveolar blood vessels and conducting airways serves as a
reservoir for excess fluid during the formation of pulmonary edema
(25). The transport of fluid and protein through lung interstitium
occurs partly by bulk flow caused by gradients in interstitial pressure
and partly by diffusion caused by gradients in protein concentration
(24, 27).
Previous studies have focused on measurements of bulk flow through a
1-cm length of perivascular interstitium surrounding a large
pulmonary artery segment (1- to 3-mm diameter) cut from an isolated
rabbit lung filled with silicon rubber. We assumed that flow was
proportional to the driving pressure (Darcy's law) and ignored the
effects of diffusion. These studies showed that hydraulic conductivity
depended on many factors, including the albumin concentration
(Ca) of the solution (12),
electrical charge of the solute (10, 20), interstitial hydration
(26), and the presence of the glycosaminoglycan hyaluronan (10, 26). Interstitial hydraulic conductivity response to albumin and
hyaluronidase relative to that of Ringer solution increased with
interstitial hydration (26). Under nonedematous conditions, this
response was absent, with the flow of albumin solution
(
a) being
viscosity dependent. In subsequent studies, the bulk
a through a
0.5-cm length of interstitium occurred in conjunction with measurable gradients in Ca (22). Gradients in
Ca during bulk flow violated Darcy's law that the flow is inversely proportional to fluid viscosity and are at odds with the viscosity-dependent values of hydraulic conductivity measured under nonedematous conditions. We wondered to
what extent the measured hydraulic conductivity of albumin solution
depended on the diffusive restriction of albumin molecules by
interstitial pores.
Accordingly, we developed a radioactive tracer
(125I-albumin) technique to study
the diffusion of albumin through isolated segments of lung
interstitium. The technique provided estimates for albumin-diffusion coefficient (D) and cross-sectional
area (A) for diffusion. We used the
technique to measure the effect of an increasing concentration gradient
on the diffusion of albumin through lung interstitium. We found that
the D was similar to the free
diffusion for albumin and independent of
Ca.
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METHODS |
The procedure used to fill isolated rabbit lungs with silicon rubber
and to isolate a length of blood vessel with surrounding interstitial
cuff has been described (26). New Zealand White rabbits (3- to 4-kg
body weight, n = 7) were tranquilized
with 130 mg ketamine and 4 mg xylazine injected intramuscularly. After heparinization (3,000 U), each animal was anesthetized and killed by an
overdose of pentobarbital sodium injected through an ear vein. After
the chest was opened, cannulas were tied into the trachea, pulmonary
artery, and left atrial appendage. A tie was secured around the heart.
The lung and heart were left within the thorax, which was separated
from the body by transection across the neck and below the diaphragm.
After the lungs were degassed by vacuum, the airways and vessels were
filled with silicon rubber compound (Microfil, Flow-Tek) through
reservoirs connected to the artery, vein, and trachea. The artery was
filled first, followed by the vein and airways. White rubber was used
to fill the airways; pink and yellow rubber was used to fill the
arteries and veins, respectively. The reservoirs were set to 15-20
cmH2O relative to the lung base to
ensure a fully inflated lung. With the use of a catalyst (5%), the
rubber solution hardened within 2 h. After the rubber had set, each
caudal lobe was cut into 0.5-cm-thick slabs transverse to the main
dimension of the vessel tree, starting from the hilum. Each rabbit
provided at least six slabs; four slabs were chosen for each
experiment.
Figure 1 is a diagram of the experimental
assembly used to measure the diffusion of the radiolabeled tracer
125I-albumin through the lung
interstitium. Two chambers were bonded to the opposite faces of each
slab with cyanoacrylate adhesive to enclose the largest arterial
segment. The (outside) chamber containing the test albumin solution
with radioactive tracer was constructed of a plastic tube (0.7-cm
length, 13-mm outer diameter, and 3-mm wall thickness) bonded to one
side of a plastic plate (6 × 8 × 0.3 cm) adjacent to a
0.7-cm-diameter hole in the plate. The plate was oriented to the lung
slab so that the hole enclosed the arterial segment. The other (inner)
chamber was constructed of a plastic tube (4.7-cm length, 7.3-mm outer
diameter, and 0.22-mm wall thickness) bonded to a plate similar to that
used for the outer chamber. The inner chamber was designed so that a
4-cm length of the 4.7-cm-long tube would fit into a well-type NaI(Tl)
scintillation detector (model no. TB-2L, Oxford Instruments, Oak Ridge,
TN). The tube passed through a 0.9-cm-diameter entry hole made in a lead cap that covered the opening of the detector. The inner chamber was bonded to the face of the arterial segment with the smaller diameter, consistent with the procedure used to measure hydraulic conductivity (26). After the two chambers were bonded to the lung slab,
the entire assembly was stabilized by bolts and nuts located at the
corners of the plates. The interstitium surrounding the artery was
prevented from drying by applying Ringer solution to both ends of the
arterial segment during the setting-up procedure.
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Fig. 1.
Schematic diagram of experimental setup used to measure diffusion of
radioactive tracer 125I-albumin
through an isolated segment of lung interstitium. Alb., albumin. See
text for details.
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The inner chamber was filled with 1.8 ml Ringer solution, and its end
was sealed with a plastic cap. The cap had a tiny hole that prevented
compression of the liquid within the chamber when the end of the
chamber was covered with the cap. The hole was subsequently sealed with
vacuum grease. A small magnetic bar (6.5 mm in length), used to mix the
chamber liquid during the diffusion experiment, was located ~1 cm
from the end of the arterial segment via a string attached to the cap.
The inner chamber was then placed inside the scintillation counter. The
background radioactivity from the chamber was measured for 1 min. The
outer chamber was filled with 0.2 ml of a test solution of albumin that
contained tracer 125I-albumin, and
the chamber was sealed with a rubber cap. The rubber cap had a tiny
hole which prevented compression of the liquid within the chamber
during insertion. The hole was subsequently sealed with vacuum grease.
To prevent radiation from the outer chamber from reaching the
scintillation detector, the outer surface of the detector was covered
with a 2-mm-thick lead sheet. In addition, the bottom surface of the
detector well was lined with lead to prevent the radiation emitted in
an axial direction by the outer chamber from reaching the detector. The
detector was oriented with its cylindrical axis horizontal. A
thin-walled plastic tube (3-cm length, 1-cm inner diameter) was bonded
to the inner surface of the lead cap to maintain the chamber axis in a
horizontal position and at a fixed orientation relative to the
detector. The plastic material used to construct the two chambers and
supporting plate was tested to ensure that it did not absorb the
radioactive tracer.
The diffusion of the radioactive tracer through the interstitium was
measured continuously in the chamber located in the counter. The
solution was stirred continuously by slowly rotating the magnetic bar
placed within the chamber by using an external electromagnetic source
(Thermix stirrer, model 120S; Fisher Scientific, Pittsburgh, PA). The
emitted radiation was measured during consecutive 30-min periods
for 60 h.
We measured the diffusion of albumin through lung interstitium at
different Ca. Stock solutions (4 ml) were made with albumin (bovine serum albumin, batch no. A9647;
Sigma Chemical, St. Louis, MO) of the test concentration in lactated
Ringer solution and ~10 µCi
125I-albumin (~0.5 µCi/0.5
µl; cat no. NEX-076, New England Nuclear, Boston, MA).
All solutions were filtered (0.45-µm pore diameter) and adjusted to
pH of 7.35-7.45. The outer chamber was filled with 0.2 ml of a
test solution (0, 2, or 5 g/dl albumin solution) containing the
radioactive tracer (~4 × 107 g/dl). Before the
solution was used for the diffusion experiment, any unbound
125I was separated from the stock
solution by dialyzing the 4 ml of stock solution for 24 h with the use
of an SS-030 wet-pack membrane (Wescor model 4000 series, Colloid
Osmometers). The pore size (20,000 Da) of the membrane allowed the
passage through the membrane of
125I but not
125I-albumin (66,000 Da). The 4 ml
of stock solution containing the 125I-albumin were placed on one
side of the membrane, with 200 ml of solution of the same
Ca as the stock solution on the
other side. The similar Ca on both
sides of the membrane prevented osmotic flow through the membrane. The
radiation emitted by the unbound 125I that passed through the
membrane was measured and compared with the radiation emitted by the
stock solution. For these and other calibration measurements, we used a
chamber identical in volume (1.8 ml) and dimensions to the inner
chamber used for the diffusion of albumin through lung interstitium.
Unbound 125I was <2% of the
stock solution, thus verifying the manufacturer's specification. After
dialysis for 24 h, the unbound
125I was reduced to ~0.04% of
that from the stock solution. Any stock solution not used in one
experiment was used in the next experiment after being dialyzed again
for 24 h to remove any unbound
125I. Consequently, the unbound
125I in the diffused sample at the
end of the diffusion experiment was often immeasurably small.
After the diffusion experiment, the solution in the inner chamber was
collected and dialyzed for 6 h to measure the amount of unbound
125I present in the tracer that
diffused through the interstitium. We accepted the results of an
experiment only if the radioactivity of the unbound
125I was <10% of the
radioactivity of the tracer that diffused through the interstitium. In
occasional experiments, the steady-state rate of tracer diffusion was
considerably greater than that from the rest of the experiments,
resulting in a considerably greater value of
A. This was attributed to a leak from
outer to inner chamber via spaces between the vessel wall and the
silicon rubber used to filled the vessel. Also, on occasion, a leak
occurred from a chamber because of improper bonding of the lung slab to the chamber. The results of those experiments were not reported. At the
end of the diffusion measurements, we measured the diameter of each end
of the arterial segment through a macroscope (×18). Segment
length was measured by calipers. The entire experiment, including the
dialysis of the test solutions, was conducted at room temperature
(22-24°C).
Calibration of the scintillation counter.
The system consisted of four NaI(Tl) scintillators, each connected to a
photomultiplier tube (used to detect the light emitted from the
scintillator when subjected to radiation), and a preamplifier and
amplifier with a single high-voltage power supply (model 5040, Oxford
Instruments). The output of the amplifier was connected to a computer
(PC-AT 386, AT&T) via a pulse-height selector and a count-rate meter
for automatic data collection. The four single-channel analyzers were
calibrated in turn by measuring the spectrum of X- and gamma-rays from
a 1-µCi 125I-albumin sample. The
voltage applied to the photomultiplier tubes and the amplifier gain
were adjusted so that the threshold voltage of 0.2-10 V
corresponded approximately to gamma-ray energies of 2-100 KeV.
Figure 2 shows a representative energy
spectrum obtained by moving a 0.04-V window incrementally through the
range from 0 to 10 V. The principal gamma-ray peak at 35 KeV was
observed, as well as a coincidence peak at 70 KeV. Measurements of
125I-albumin in the experiments
were made with the lower discriminator set at 0.2 V to eliminate
detector noise and low-energy background radiation, and the upper
discriminator was set at 10.2 V to accept pulses from both the 35- and
the 70-KeV peaks.
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Fig. 2.
Representative energy spectrum, count rate (counts/s) vs. energy level
(in V), of a 1-µCi 125I-albumin
sample measured in a well-type NaI(Tl) scintillation detector. Bottom
curve, background spectrum.
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We determined the mass of tracer that diffused through the interstitium
by comparing the radioactivity detected in the inner chamber to that
measured from the stock solution used in the outer chamber. Before its
use in the diffusion experiment, the stock solution that was dialyzed
for 24 h (as previously described) was diluted with a solution of
similar Ca until the radioactivity measured in the calibration chamber was ~60,000 counts/s. This amount
of radioactive tracer was the minimum needed to give an accurate
measurement of the diffused tracer, as determined from preliminary
studies. However, a count rate of 60,000 counts/s fell in
the nonlinear range of the detector, as indicated by the calibration
curve of radiation count rate vs. relative concentration (Fig.
3). Therefore, in every experiment, the
stock solution was diluted 20-fold to reduce the count rate to a level
that fell on the linear part of the calibration curve of the detector.
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Fig. 3.
Calibration curve of radioactivity (counts/s) vs. relative
concentration of a 25-µCi
125I-albumin sample. Note
linearity of curve below ~3 × 104 counts/s.
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The calibration curve was developed by measuring the radiation from a
1.8-ml sample of a stock solution containing 25 µCi 125I-albumin, after dilution of
the stock solution with lactated Ringer solution by a factor of 2, followed by 10-fold increments in dilutions up to a dilution of 2 × 106. To ensure accuracy at
the greater dilutions, it was necessary to increase the counting time.
In the situation where the sample radioactivity was a small fraction of
background, it was necessary to accumulate sufficient background counts
so that the SD of the background measurement was negligibly small
compared with the sample count rate. Thus, for the highest dilution of
2 × 106, the
sample count rate was reduced to ~3 counts/s (Fig. 3); with a background of ~100 counts/s, the count-rate period was increased to
30 min to accumulate 105 counts of
background radioactivity with a SD for the measurement of 0.3% of
background or 10% of the diluted sample. For the same reason, we used
a period of 30 min for the accumulation of the radiation counts because
of diffusion (1-5
counts · s1 · h1) to ensure that the
error in measurement of the background radioactivity was small compared
with the diffused radioactivity.
Effect of time on interstitial hydraulic conductivity.
To determine the effects of tissue deterioration, in separate
experiments, we measured the flow of lactated Ringer solution (r) followed
by the a (5 g/dl, bovine serum; Sigma Chemical) under conditions of 5 cmH2O driving pressure and 7.5 cmH2O mean interstitial pressure.
We followed the method used previously (26). Each flow
measurement required 1 h. The
r and
a measurements were repeated after 24 and 48 h. Finally, the flow of 0.02%
hyaluronidase (h;
hyaluronidase from bovine testes; Sigma Chemical) was measured. Between
the periods when flows were measured, the driving and mean pressures
were reduced to 0 cmH2O (ambient)
to approximate the conditions of the diffusion experiment. The pressure
conditions were chosen because they previously produced a positive
hydraulic-conductivity response to albumin and hyaluronidase (26).
Statistics.
Results were reported as mean values ± SD. We used a
linear-regression analysis to test the correlation between two
parameters and an analysis of variance to test the correlation among
more than two parameters. We used an unpaired
t-test or paired
t-test, where appropriate, to evaluate
statistical differences between two groups of measurements.
Significance was accepted at the P < 0.05 level.
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THEORY |
We analyzed the experimental results within the framework of
unidirectional diffusion of a solute across a membrane of uniform length (L) and uniform surface area
(A) after a constant solute concentration (C1) is applied at
time 0 to one side of the membrane (x = 0). The membrane concentration
(C0) is initially zero, and the
solute concentration (C2) on the
other side of the membrane (x = L) is maintained at zero. The
solution C(x, t) of the one-dimension diffusion equation at any distance x
within the membrane and at time t is
given by (3)
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(1)
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The mass of solute
(M2) that
diffuses through the membrane (at x = L) is given by
![<LIM><OP>∑</OP><LL><IT>n</IT> = 1</LL><UL>∞</UL></LIM> [(−1)<SUP><IT>n</IT></SUP>/<IT>n</IT><SUP>2</SUP>]<IT>e</IT><SUP>−<IT>Dn</IT><SUP>2</SUP>&pgr;<SUP>2</SUP><IT>t</IT>/<IT>L</IT><SUP>2</SUP></SUP>](/content/vol85/issue2/fulltext/575/img004.gif)
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(2)
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As t 
,
Eq. 2 approaches the straight line
![<IT>M</IT><SUB>2</SUB> = (<IT>DA</IT>C<SUB>1</SUB>/<IT>L</IT>)[<IT>t</IT> − <IT>L</IT><SUP>2</SUP>/(6<IT>D</IT>)]](/content/vol85/issue2/fulltext/575/img005.gif)
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(3)
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which
has an intercept (T) on the
t-axis given by
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(4)
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The
steady-state mass flow
(dM2/dt)
of solute from Eq. 3 is then
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(5)
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The
latter is Fick's law for steady-state diffusion. Figure
4 shows a plot of the dimensionless solute
mass
M2/(ALC1)
vs. dimensionless time
Dt/L2
of Eq. 2 (3). The intercept
DT/L2
on the
Dt/L2-axis
of the straight line given by Eq. 3 is
1/6. D is then equal to
L2/(6T).
A good approximation to within 5% of the actual value of T is attained by using the straight
line through the solution from a time of
~3T to
~4T. Following the work of previous
investigators (3, 4), we used Eqs.
3-5 to determine the
D for albumin through lung
interstitium and cross-sectional A of
the interstitial cuff. From experimental measurements of
M2 vs.
t, the intercept
T is measured, and
D follows from Eq. 4. With the steady-state value of
dM2/dt
and the value of D,
A follows from Eq. 5.
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Fig. 4.
Theoretical solution of 1-dimensional diffusion of solute mass
(M2) through a
membrane of length (L) and surface
area (A) vs. time
(t). Membrane is subjected to solute
concentration C1 on 1 side, with 0 concentration on other side. Solute concentration within membrane is
initially 0. Dimensionless solute mass
(M2/ALC1)
is plotted vs. dimensionless time
(Dt/L2;
solid line). Dashed line, steady-state solution extrapolated to zero
mass, intersects
Dt/L2-axis
at intercept given by
DT/L2 = 1/6. Diffusion coefficient (D) is
L2/(6T).
See text for details.
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RESULTS |
Calculation of albumin D.
Figure 5A
shows a representative example of the radioactivity (counts/30 min)
measured in the inner chamber by the scintillation counter over the
period of 60 h. In this example, the test solution in the outer chamber
consisted of lactated Ringer solution with ~10 µCi of
125I-albumin. The inner chamber
was filled with lactated Ringer solution. Note that the measured
behavior was similar to the theoretical curve of unidirectional
diffusion through a membrane (Fig. 4). The measured curve showed a
characteristic delay before any radioactivity above baseline
(background) was detected, followed by a continuous monotonic rise to a
steady-state increase after ~40 h. To determine the steady-state line
needed to obtain the intercept on the time axis passing through the
background-count rate (R), we used a linear regression of the data
(dashed line) between 40 and 60 h: R = 7,368 t + 29,694;
r2 = 0.999, n = 40. R is in counts/30 min;
t is in h. The dashed line was
extrapolated to intercept the t-axis
through the background-count rate (1.35 × 105 counts/30 min). This resulted
in an intercept T of 14.3 h on the
t-axis, passing through the background
radioactivity (solid horizontal line). This value of
T and
L of 0.45 cm, when substituted in
Eq. 4, resulted in a value of
D of 6.6 × 107
cm2/s. The pooled values for
L averaged 0.48 ± 0.056 cm.
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Fig. 5.
A: example of diffusion of
radioactive tracer 125I-albumin
through 0.45-cm-long lung interstitial segment. Test solution consisted
of lactated Ringer solution with radioactive tracer. Radioactive count
rate (R, counts/30 min) is plotted at 30-min intervals for 60 h. Dashed
line, linear regression equation of steady-state response of R between
40 and 60 h, extrapolated to an intercept value
(T = 14.3 h) on time axis passing
through background-count rate (1.35 × 105 counts/30 min).
Linear-regression equation was R = 7,368 t + 29,695 (r2 = 0.999;
n = 40). R is in counts/30 min; time
(t) is in h. Steady-state rate of
diffusion through interstitium is the slope (7,368 counts · 30 min1 · h1).
See text for details. B: pooled values
of R  background radiation (means ± SE) are plotted at 2-h
time intervals from 15 experiments given in Fig. 6. Dashed line,
linear-regression equation of steady-state response between 40 and 60 h: R = 4,700 t 77,100 (r2 = 0.102, n = 165, P < 0.0001). Intercept
T on time axis was 16.4 h.
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Table 1 summarizes mean values (± SD)
of T obtained by using the above
method at test Ca of ~0, 2, and
5 g/dl in the outer chamber. The values of
D (Table 1 and Fig.
6) were independent of
Ca (in g/dl) by linear-regression
analysis: D = 6.58 × 107 6.24 × 1010
Ca
(n = 15, r2 = 0.0002, P = 0.96). The pooled data provided a
mean value of D of 6.6 ± 0.97 × 107 (SD)
cm2/s
(n = 15), within 10% of the value for
free diffusion of albumin (6 ×107
cm2/s; Ref. 28).
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Table 1.
Summary of time intercept, albumin-diffusion coefficient, and
thickness-to-vessel radius ratio at various albumin concentrations
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Fig. 6.
Albumin D (means ± SD) vs. albumin
concentration (g/dl) in test solution. Nos. in parentheses, nos. of
experiments. Values at 0 g/dl represent test solution with
125I-albumin tracer alone (~4 × 107 g/dl). Dotted
line, value (6 × 107
cm2/s) for free diffusion of
albumin.
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The pooled values of count rate minus the background radiation
(mean ± SE) vs. time for the 15 experiments of Table 1 are shown as
Fig. 5B. The linear-regression
equation of the steady-state response between 40 and 60 h was as
follows: R = 4,700 t 77,100; r2 = 0.102, n = 165, P < 0.0001. The time intercept
(T) for R = 0 was 16.4 h. Based on
this value of T and the mean value of
L (0.48 cm), the value of
D from the pooled
R-t data was 6.5 × 107
cm2/s, consistent with the mean
value calculated from individual experiments.
Calculation of interstitial area and thickness.
An estimate of interstitial surface (cross-sectional)
A for diffusion was obtained from
Fick's law (Eq. 5). The mass flow of albumin
(dM2/dt)
through the interstitium into the inner chamber was calculated by using
the following equation
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(6)
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Here
M1 was the mass
of albumin present in the 1.8 ml of test solution, from which 0.2 ml
were used to fill the outer chamber. R1 was the radioactivity measured
in the calibration chamber containing 1.8 ml of test solution diluted
20-fold to reduce the count rate to the linear part of the calibration
curve. K is the dilution factor (= 20)
that corrected for the nonlinearity of the calibration curve.
R2 was the radioactivity measured
in the inner chamber, and
dR2/dt
was the slope of the measured
R2-t
curve in the linear range (Fig. 4) after correction for the decay of
the background radiation (see Correction for
background radiation). The use of an outer chamber of
relatively small volume was necessary to reduce the background
radiation that emanated from the outer chamber into the well counter
through the hole in the lead cap through which the inner chamber was
located. This significantly reduced the background correction to
dR2/dt
(see Correction for background radiation).
Implicit in Eq. 6 is the
assumption that the radioactivity measured by the counter scales
directly with the dilution of
125I-albumin in the range between
R2 and
R1. Figure 3 (log-log plot) shows
radioactivity (R, in counts/s) measured in the calibration chamber vs.
relative concentration (C). Note that R scales linearly with relative C
below ~30,000 counts/s, but it becomes nonlinear at higher count
rates. Because M1 = C1V1,
where V1 is the volume of the
calibration chamber, the use of Eq. 6
with Fick's law (Eq. 5) results in
the following solution for A
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(7)
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Note
that Eq. 7 shows that
C1 does not enter into the
calculation of A. Thus
A can be calculated even if
C1 is not exactly known, as is the
case with the test solution containing only the tracer
125I-albumin (~4 × 107 g/dl).
For the example shown in Fig. 5A,
dR2/dt
evaluated from the slope of the linear regression line in the range of
40-60 h was 4.09 counts · s1 · h1,
after a small correction for background decay (see
Correction for background
radiation). The radioactivity of the test solution used in the outer chamber gave a count rate in the calibration chamber
of 59,141 counts/s. A 20-fold dilution of the test solution resulted in
a value of R1 of 5,145 counts/s,
well within the linear range for the detector (Fig. 3). The value of
A (calculated from Eq. 7 with
K of 20, V1 of 1.8 ml, and
L of 0.45 cm) was 0.014 cm2. We assume that the
interstitium surrounding the blood vessel of uniform radius
R was an annular cuff of uniform
thickness
(Th0). Then
from geometry, the ratio of interstitial cuff thickness-to-vessel radius
(Th0/R)
is as follows
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(8)
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In
this example, R was 0.185 cm, so that
Th0/R
was 0.064. Table 1 summarizes values of
Th0/R.
Values of
Th0/R
did not vary significantly with Ca
by a linear-regression analysis:
Th0/R = 0.054-0.0030 C (n = 15, r2 = 0.069, P = 0.34). The pooled values
(n = 15) of
R and
Th0/R averaged 0.19 ± 0.018 cm and 0.047 ± 0.024, respectively.
Correction for background radiation.
The background radiation measured during the diffusion experiments was
mainly emitted from the outer chamber containing
125I-albumin, and this background
radiation decayed during the experiment. Thus the rate of increase in
radioactivity measured in the inner chamber due to diffusion was
accordingly reduced. The activity of
125I-albumin of initial value
R0 at time
t is
R0e
t,
where the decay constant 
, based on a half-life of 60 days, is 4.81 × 104/h. For a
background-count rate R0 from Fig.
5 of 1.35 × 105 counts/30
min, the rate of decay of background radiation evaluated between 40 and
60 h would be 0.035 counts · s1 · h1,
amounting to 0.85% of the measured steady-state value of
dR2/dt. In the experiments reported, the correction for background
radioactivity averaged 3.8 ± 3.0% of steady-state values of
dR2/dt.
The correction for background radiation to the value of
T and
D is considerably more complex and was
not implemented. However, based on the small background correction to
the steady-state values of
dR2/dt,
the effect of background on T would be
small and in a direction that results in an underestimation of
T and overestimation of
D.
Effect of time on interstitial hydraulic conductivity.
Table 2 summarizes values (means ± SD,
n = 10) of
r , a,
and
a/r,
as measured in response to 5 cmH2O
driving pressure and 7.5 cmH2O
mean interstitial pressure at 0, 24, and 48 h after the setting-up
procedure. Linear-regression analyses and an analysis of variance
showed no significant (P > 0.08)
change in r,
a, or
a/r
with time.
a/r
values measured at 0, 24, and 48 h (1.47 ± 0.53, 1.18 ± 0.19, 1.18 ± 0.22, respectively) were significantly greater than Ringer
solution-to-albumin solution viscosity ratio (0.81), indicating that
the a was
viscosity independent (26). The flow of
h was always
greater than the
r measured at 48 h (Table 2), with
h/r
values (1.86 ± 0.58) significantly >1
(P = 0.001), similar to previous
values measured at 0 h (26). Thus the interstitial
hydraulic-conductivity response to albumin and hyaluronidase was still
present after 48 h, suggesting little tissue deterioration with time.
View this table:
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|
Table 2.
Effect of time on interstitial hydraulic conductivity response to
albumin (5 g/dl) and hyaluronidase (0.02%)
|
|
| |
DISCUSSION |
The major result of this study is that the diffusion of albumin caused
by concentration differences up to 5 g/dl through pulmonary interstitium was similar to values reported for the free
D of albumin. This indicated that the
pores through which albumin molecules diffused through pulmonary
interstitium were essentially filled with free liquid, were much larger
in dimension than the size of an albumin molecule, and offered no
restriction to albumin. The estimate of the interstitial
cross-sectional A available for diffusion was of the same order of magnitude as the total
cross-sectional A measured
histologically in other studies (9, 13), indicating that the volume of
pulmonary interstitium that excludes albumin was immeasurably small by
this technique.
Potential errors in the method.
The method for determining the D for
albumin and cross-sectional A for
diffusion entailed several assumptions and details that would affect
accuracy. First, we assumed that the unbound 125I present in the
125I-albumin tracer was negligibly
small at the start of the experiment and did not increase during the
course of the experiment. The former was ensured by removing 98% of
the unbound 125I from the
125I-albumin tracer by dialysis
before the experiment. In preliminary experiments in which the unbound
125I was not removed (11), the
estimate of the D was overestimated due to the 23-fold faster diffusion rate of
125I compared with albumin,
because D is proportional to
M1/2, and
the molecular weights (M) of albumin
and 125I are 66,000 and 125, respectively. In other preliminary experiments, we found that the
unbound 125I suddenly increased in
every experiment after ~60 h. Hence we limited the experimental time
to 60 h. Nevertheless, in ~50% of the experiments conducted for 60 h, the unbound 125I accounted for
>10% of the total radioactivity measured from the diffused tracer.
We rejected the results of these experiments on this basis. In the
experiments reported, the unbound
125I averaged 1.6 ± 2.9%
(range, 0-8.5%) of the total radioactivity measured. Thus the
errors in the estimate of D due to
unbound 125I were deemed to be
small.
Second, bulk flow caused by Ca
gradients (osmotic flow) that would occur because of the spatial
differences in Ca was eliminated by using a closed system with a constant liquid volume.
Third, the solution of the diffusion equation used to evaluate the
experimental results assumed an initial
Ca of zero in the interstitium.
However, the Ca in the
interstitium was not initially zero, so that an additional diffusion
process must occur in conjunction with the response to the
Ca in the outside chamber. We
assumed that the interaction between these two diffusion processes did not substantially contribute to the diffusion of the tracer. This assumption was supported by the fact that the change in
Ca in the outside chamber from
nearly 0 to 5 g/dl did not change the diffusion response of the tracer.
Fourth, the method of continuous measurement by using a well counter
ensured that the diffusion process was not disturbed during the course
of the experiment. This was evident from the smoothness of the measured
R-t curve (Fig. 5). Because the
diffusion rate of radioactivity through the interstitium was extremely
small, amounting to only 1-5
counts · s1 · h1,
the alternative approach of sampling and subsequent remote measurement was deemed to be too disruptive. However, in the present
method, only part of the inner chamber (~80%) was
within the well counter, so that only part of the tracer that diffused
was actually counted. A correction for the reduced volume within the
well counter was effectively eliminated by ensuring a uniformly mixed
solution in the inner chamber. This was achieved by continuous stirring and by measuring the radiation from the test solution in a chamber of a
volume and dimensions identical to the inner chamber used to measure
the diffused tracer.
Fifth, the application of Fick's law for steady-state diffusion to
calculate interstitial cross-sectional
A assumed that the Ca and tracer concentrations
acting across the interstitium were similar to those acting in the two
chambers. The presence of an unstirred layer adjacent to the membrane
would reduce the actual concentration difference acting across the
interstitium (19) and result in an underestimation of
A (Eq. 5). Furthermore, any concentration gradient in the
inner chamber would result in an underestimation of the diffused tracer
measured in the part of the chamber within the well counter. To
minimize errors due to the thickness of the unstirred layer and to any
nonuniformity in tracer concentrations and
Ca, the liquid in the inner
chamber was stirred continuously. The outer chamber with the test
solution was not stirred because of its small volume, and this would
result in an underestimation of A.
However, our measurements of interstitial area were somewhat higher
than values measured histologically (9, 13), so unstirred layer effects
could not account for these differences.
Sixth, the experiments were conducted at room temperature
(22-24°C) that was below body temperature. Thus, the measured
D was most likely less than that
existing in vivo. In vitro measurements in mesentery indicated that
values of D measured at 25°C were ~20% less than values measured at 37°C (21).
Seventh, changes in interstitial diffusional properties due to
ischemia might occur during the 60-h time period of the
experiment. Because the D was measured
from a dynamic response that required ~40 h to reach a steady state,
it was not possible to determine whether the diffusion properties
changed over the course of the experiment. Instead, we showed that the
interstitial hydraulic conductivity measured in response to albumin and
hyaluronidase was constant over 48 h (Table 2). However, the
absence of a change in hydraulic conductivity might not rule out a
change in diffusion. This issue warrants further study.
Finally, damage to the interstitium at the two ends of the vessel
segment in cutting the lung slab would reduce the effective length of
the interstitial segment and increase the effective interstitial
cross-sectional A. The use of a
reduced effective length would result in a smaller
D from the measured intercept T (Eq. 4). Thus damage to the interstitial segment might
result in an overestimation of both D
and A. These effects could be reduced by using a thicker lung slab, as in previous studies with a 1-cm-thick slab (26). The use of the thinner slab of 0.5 cm was mandated in the
present experiments to reduce the time frame of the experiments. If we
had used a 1-cm-thick slab, the time intercept
T (Fig. 5 and Eq.
4) would have increased fourfold, resulting in a
T value of ~60 h and a prohibitively
long experimental time of ~8 days. Within this longer time frame, the
diffusion of unbound 125I that
became unbound from the tracer
125I-albumin after 2 days would
most likely dominate the diffusion of
125I-albumin, as measured in the
preliminary experiments.
Comparison with other studies.
The D for albumin measured in lung
interstitium in this study was similar to values reported for the free
D for albumin (6 × 107
cm2/s) measured with a variety of
techniques (28). Like the present results, these studies also showed
that the D was independent of
Ca.
Diffusion studies in tissue preparations do not provide an unequivocal
value for tissue D for albumin. Some
studies in isolated subcutaneous tissue (7), human umbilical cord (6),
rat diaphragm (23), and rat mesentery (21) indicated
D values for albumin (30-100%)
near to the free D. By contrast, other
studies in the mesentery produced values that were >10-fold smaller
than those of the free D (5, 14, 16).
The latter study of rabbit mesentery showed that the
D for albumin increased with
Ca and was reduced in the presence
of hyaluronidase, indicating that the diffusion of albumin in mesentery
increased with hyaluronan concentration (16). Both these effects were
attributed to an albumin-hyaluronan osmotic interaction that caused a
reduced excluded volume for albumin as either
Ca or hyaluronan concentration
increased. However, this interaction between albumin and hyaluronan
cannot explain why albumin diffusion in lung interstitium is relatively
high, because lung tissue has a relatively low hyaluronan concentration (~104 g/g; Ref. 8). The
effect of hyaluronidase on the D for
albumin in lung interstitium remains to be evaluated. Preliminary
results with hyaluronidase indicated an apparent greater diffusion of albumin through lung interstitium (11), but this study contained artifacts from the diffusion of unbound
125I that dominated the diffusion
of the tracer 125I-albumin.
The estimate for interstitial cross-sectional
A for diffusion showed a mean
Th0/R
value (0.05) that was of the same order of magnitude as that estimated
for lung perivascular interstitium in rabbit lungs (mean value of 0.02, range 0.004-0.06; Ref. 9). Similar values have been measured in
dog lungs (13). The relatively high diffusion area in conjunction with
the measured albumin D close to the
free D would imply that the volume
excluded from albumin in lung interstitium is negligibly small. This
prediction is in contrast to the relatively high values of excluded
volume fraction measured for albumin in vivo (17, 18). This disparity between the in vitro and in vivo estimates for albumin-excluded volume
might be caused by differences in interstitial constituents (for
example, hyaluronan) between the perivascular interstitial cuffs of the
largest pulmonary vessels in the present study and those of the smaller
exchange vessels associated with the in vivo study. Accordingly, the
differences in the diffusion properties and hyaluronan concentration of
interstitial cuffs as a function of vessel size deserve evaluation, in
particular as they pertain to the inability of a significant fraction
of relatively small vessels (diameter <0.5 mm) to form interstitial
cuffs and the virtual absence of interstitial cuffs around vessels
<0.1 mm diameter in liquid-inflated isolated lungs (1, 2).
In summary, the diffusion of albumin through lung interstitium was
close to the free diffusion for albumin. This implies that the pathways
for the diffusion of albumin in lung interstitium are completely filled
with liquid and have an equivalent pore radius much larger than that of
the albumin molecule. Thus lung interstitial constituents offered no
restriction to the passage of albumin, with a reflection coefficient
virtually equal to zero. This conclusion is at odds with spatial
gradients in Ca measured previously in lung interstitial segments (22). This discrepancy needs
further study. Direct measurements of reflection coefficient close to
zero have been made recently for the rabbit mesentery (15). This
result, in conjunction with the 10-fold smaller
D measured for rabbit mesentery (16),
implies a 10-fold smaller surface area for diffusion and a much larger
volume excluded from albumin in mesentery than in lung interstitium.
| |
ACKNOWLEDGEMENTS |
This research was supported by National Heart, Lung, and Blood
Institute Grant HL-40362.
| |
FOOTNOTES |
Address for reprint requests: S. J. Lai-Fook, Center for Biomedical
Engineering, Wenner-Gren Research Laboratory, Univ. of Kentucky,
Lexington, KY 40506-0070 (E-mail: bme006{at}ukcc.uky.edu).
Received 23 December 1997; accepted in final form 2 April 1998.
| |
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