Vol. 91, Issue 4, 1730-1740, October 2001
Transport properties of alveolar epithelium
measured by molecular hetastarch absorption in isolated rat
lungs
Robert L.
Conhaim1,
Kal E.
Watson1,
Stephen J.
Lai-Fook2, and
Bruce A.
Harms1
1 Department of Surgery, University of Wisconsin-Madison,
The William S. Middleton Memorial Veterans Hospital, Madison,
Wisconsin 53792-7375; and 2 Center for Biomedical
Engineering, University of Kentucky, Lexington,
Kentucky
 |
ABSTRACT |
To evaluate the
transport properties of the alveolar epithelium, we instilled
hetastarch (Het; 6%, 10 ml, 1 
1 × 104
kDa) into the trachea of isolated rat lungs and then measured the molecular distribution of Het that entered the lung perfusate from
the air space over 6 h. Het transport was driven by either diffusion or an oncotic gradient. Perfusate Het had a unique, bimodal
molecular weight distribution, consisting of a narrow low-molecular-weight peak at 10-15 kDa (range, 5-46 kDa) and
a broad high-molecular-weight band (range 46-2,000 kDa; highest at
288 kDa). We modeled the low-molecular-weight transport as (passive)
restricted diffusion or osmotic flow through a small-pore system and
the high-molecular-weight transport as passive transport through a
large-pore system. The equivalent small-pore radius was 5.0 nm, with a
distribution of 150 pores per alveolus. The equivalent large-pore
radius was 17.0 nm, with a distribution of one pore per seven alveoli.
The small-pore fluid conductivity (2 × 10
5
ml · h1 · cm2 · mmHg1)
was 10-fold larger than that of the large-pore conductivity.
pulmonary edema; lung fluid balance; epithelial transport; epithelial permeability
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INTRODUCTION |
REMOVAL OF EDEMA
LIQUID from the air space of the lung is a life-threatening
problem that affects thousands of hospital patients annually. It is
generally agreed that the difficulty in removing edema fluid is due to
the relative impermeability of the air space epithelium to the plasma
macromolecules that enter into the air space during the alveolar
flooding stage of edema formation (6). These
macromolecules exert an osmotic pressure that inhibits the removal of
the edema fluid. This conclusion is based mainly on studies of rates of
edema solute removal from the lungs of experimental animals. For
example, Berthiaume and colleagues (3) measured albumin
removal rates of 0.9-1.4%/h from the lungs of unanesthetized sheep that had had 100 ml of autologous serum instilled into their lungs.
Our understanding of the resolution of edema could be improved by more
quantitative information about the permeability characteristics of the
alveolar epithelium to macromolecules. To address this, Matsukawa and
colleagues (13) measured rates of dextran flux across
cultured lung epithelial cell monolayers. Their results suggested that
the monolayers were perforated by pores with radii of 56 Å. Such pores
would be relatively impermeable to albumin molecules, which have a
radius of 35 Å and which are the main macromolecular component of
edema liquid. The data of Matsukawa et al. additionally suggested that
the epithelial cells also transferred dextran across the monolayers
by endocytosis, a process that would allow the transport of molecules
the size of albumin and larger (7).
Our approach was similar to that of Matsukawa and colleagues
(13), except that we used hetastarch (Het) as a tracer
instead of dextran. Furthermore, we measured Het flux across the
alveolar epithelium of intact lungs that were partially inflated with
Het, rather than across cell monolayers. The advantage of using Het is
that it consists of a continuous spectrum of molecular masses that
range from 103 to 107 Da. Inflating the lung
with Het exposed the air space epithelium to the entire Het molecular
spectrum. To evaluate alveolar epithelial permeability, we measured the
masses of the Het molecules that entered the lung perfusate from the
air space.
The Het molecules detected in the perfusate had a unique, bimodal mass
distribution. We found a narrow peak, consisting of molecules with
masses ranging from 5 to 46 kDa and a lower but much broader band
consisting of molecules with masses up to 2,000 kDa. Our hypothesis was
that each of these components represented a different route of
molecular transfer across the epithelium. We hypothesized that the
narrow peak represented Het flux through small pores in the epithelium,
whereas the broad band represented Het flux through a large-diameter
pore. We applied pore-modeling techniques to both the narrow peak and
the broad band to determine the porosity and conductivity of the
alveolar epithelium on the basis of a two-pore population. Our results
suggest that macromolecules are cleared from the alveolar air space by
diffusion through pores of two different radii.
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MATERIALS AND METHODS |
We anesthetized retired male breeder rats (442 ± 25 g; n = 9) with intraperitoneal ketamine (40 mg/kg),
xylazine (6 mg/kg), and acepromazine (1 mg/kg), and tied them supine.
We infused heparin (750 U/kg) through a cannula (PE-190) that was tied
into a femoral vein. After 10 min, to allow the heparin to circulate,
we cut the femoral artery and allowed the animals to die from
exsanguination. We infused Ringer lactate into the venous cannula
during exsanguination (1 ml/ml of shed blood; total 20 ml) to
facilitate the removal of residual red blood cells from the pulmonary
circulation. Once breathing ceased, we tied a cannula into the trachea,
set the tracheal pressure to 5 cmH2O with air, and opened
the chest using a sternum-splitting incision. After tying cannulas
(PE-190) into the pulmonary artery and left atrium, we removed the
lungs from the chest and placed them into a styrofoam perfusion chamber.
The lungs were perfused with albumin in phosphate-buffered saline (see
concentration below) and ventilated with air using a piston pump (25 breaths/min). Inflation and deflation pressures were set to 15 and 5 cmH2O, respectively. We used a recirculating perfusion
system. The perfusate that dripped from the left atrial cannula was
pumped to a perfusion chamber set 10 cm above the base of the lung.
These airway and vascular pressures were chosen to obtain an air
space-vascular pressure gradient near zero in a ventilated lung. Thus
the transport of Het from the air space to the vasculature was mainly
due to concentration gradients. Perfusate flow was measured by using a
drop counter placed beneath the left atrial cannula, and vascular and
inflation pressures were measured via transducers (Statham) connected
to an oscillograph (Grass). After 10 min, to allow the pulmonary
circulation to clear of any remaining red blood cells, we stopped the
perfusion and introduced 10 ml of Het (6%; oncotic pressure, 40.0 ± 0.6 mmHg) into the tracheal cannula, using a reservoir placed 10 cm
above the lung.
We prepared two sets of lungs. In the first (n = 5),
the perfusion solution contained 10% albumin in phosphate-buffered
saline (oncotic pressure, 57.3 ± 1.7 mmHg) (oncotic gradient).
The second (n = 4) contained 7.2% albumin (measured
oncotic pressure, 39.7 ± 1.0 mmHg), to match the oncotic pressure
of Het filling the air space (oncotically balanced). Oncotic pressures
were measured by use of an oncometer (Wescor) equipped with a 10-kDa
membrane (Fig. 1). Before reestablishing
perfusion, we filled the perfusion system with fresh solution using a
minimal volume (27 ml) to minimize dilution of Het entering the
perfusate from the air space. Perfusion and ventilation with air were
reestablished by using the baseline (pre-Het inflation) pressures
(above).
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Fig. 1.
Oncotic pressures ( , in mmHg) measured in hetastarch
(Het; solid symbols) and albumin (Alb; open symbols) solutions. The
regression equation fit to the Het data has a value of = 0.542 + 1.499 Het + 0.75 Het2
(R2 = 0.98). The regression equation fit to
the Alb data has a value of = 0.683 + 3.27 Alb + 0.27 Alb2 (R2 = 0.99).
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Once each hour during perfusion, 2 ml of the perfusion solution were
withdrawn for Het analysis and replaced with 2 ml of fresh solution.
After the last perfusate sample was collected (hour 6), the
lung was homogenized and a sample of the lung supernatant was collected
after centrifugation.
Het concentrations and molecular distributions in the homogenate and in
the hourly perfusate samples were measured by use of high-performance
size-exclusion chromatography (HPSEC). Details of our HPSEC system have
been published elsewhere (10). Briefly, the perfusate Het
samples were pumped through three columns, arranged in series, each of
which was packed with inert particles of specific size. The rate at
which Het polymers flowed through the spaces between the particles was
inversely proportional to the polymer molecular weight. Polymer
emergence from the columns was measured by use of a refractance
detector, the output of which was proportional to polymer
concentration. Het consists of polymers ranging from 103 to
107 kDa, and refractance detector output for a Het
stock solution produces a peak in which retention time is shown on the
horizontal axis and concentration on the vertical axis. The retention
times were converted to molecular mass on the basis of the results of a
calibration plot consisting of the retention times of dextran samples
of known molecular mass (2,000, 580, 71, and 11 kDa). The peak produced
by a 6% Het sample consists of ~600 individual retention times (1 s
apart), each of which represents a unique Het polymer weight. The area
enclosed by such a peak is proportional to the Het sample
concentration. Peak areas were converted to concentration by using a
calibration plot composed of peak areas produced by Het samples of
known concentration. Before lung perfusate samples were introduced into
the HPSEC, trichloroacetic acid was added to each sample to precipitate
all proteins and prevent protein contamination of the size-exclusion
columns. After centrifugation to remove the precipitate, the pH of the
supernatant was restored to neutral by using 5 N KOH before analysis of
the supernatant by HPSEC (10).
Electron Microscopy
Analysis of our Het data suggested that some
large-molecular-weight Het entered the perfusate by way of a nonpore
mechanism. We speculated that epithelial cell vesicles might have been
responsible for this transport (see DISCUSSION). To
investigate the potential for vesicular transport, we used electron
microscopy to examine the lungs of two anesthetized rats into which a
colloidal gold solution had been instilled. The gold instillate was
prepared by centrifugation of 100 ml of a commercial gold solution
(Aurion, 3-nm radius, Electron Microscopy Sciences) at 105
g for 1 h. The pellet was resuspended in 0.2 ml of 5%
bovine serum albumin labeled with Evans blue (albumin-to-Evans blue
molar ratio of 4:1). The resulting solution (0.25 ml) was instilled into the trachea of each spontaneously breathing rat, which had been
anesthetized by the methods described above (n = 2).
The rats were returned to their cages and allowed to recover from anesthesia. Six hours later, each rat was anesthetized again and killed
by exsanguination, and its lungs were removed. The pulmonary circulation was flushed briefly with saline to remove residual blood,
and the lungs were then perfused with 30-40 ml of 2.5% glutaraldehyde in Sorenson's phosphate buffer. Tissue blocks were harvested from Evans blue-stained areas and postfixed in Caulfield's fixative. The blocks were dehydrated through increasing concentrations of ethanol, embedded in EM bed-812 (Electron Microscopy Sciences), and thin sections were cut by using a diamond knife (100 nm) on a
Reichert-Jung microtome. The sections were stained with uranyl acetate
and lead citrate and were examined by use of a Hitachi H600
transmission electron microscope. Epithelia in six to eight alveoli of
each rat were examined.
Statistics
Data are expressed as means ± SE. Data between treatment
groups (oncotic gradient, oncotically balanced) were compared by using
Student's unpaired t-test. Comparisons within treatment groups were completed by using paired t-tests. The
comparisons were made by commercially available software (StatView
v.5.0.1, SAS Institute). This software was also used for regression
analysis of the data. Differences were considered significant at
P 
0.05.
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RESULTS |
Baseline perfusate flows before Het inflation averaged 2.4 ± 0.9 ml/min in both groups. One hour after Het inflation, flows were
2.2 ± 1.1 ml/min in the oncotically balanced group and 2.9 ± 0.9 in the oncotic gradient group (not significant). After 6 h,
flows in the two groups were, respectively, 1.7 ± 0.5 and
2.2 ± 0.9 ml/min (P = 0.03).
Examples of the molecular distribution in Het tracheal instillation
solution and lung homogenate are shown in Fig.
2. Molecular masses in the instillation
solutions for both groups ranged from 4.2 ± 2.9 to 14,095 ± 5,410 kDa with a peak at 228 ± 38 kDa that had an average height
of 13,224 ± 230 (HPSEC refractance detector units) (Fig. 2). The
lung homogenates, which did not differ significantly between the two
groups, ranged from 5.0 ± 3.2 to 10,408 ± 2,120 kDa, with a
peak at 304 ± 46 kDa that had an average height of 6,811 ± 3,301.
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Fig. 2.
Het molecular distributions in a 6% Het lung instillate
solution and in lung homogenate after perfusion for 6 h (oncotic
gradient study). The height of the homogenate peak is lower than that
of the instillate because of dilution of the instillate concentration
by the lung tissue. That is, the Het concentration in a mixture of
Het + lung is lower than in the Het solution alone. There is some
loss of the smallest Het fractions in the homogenate (<104
Da), perhaps due to tissue amylase activity.
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An example of HPSEC analysis from a lung inflated with 6% Het and
perfused with 10% albumin (oncotic gradient) is shown in Fig.
3. The most striking finding is the
bimodal shape of the Het molecular distribution in the hourly perfused
samples. Each sample is composed of a narrow, low-molecular-weight peak
followed by a broader but lower high-molecular-weight band. This
profile is distinctly different from that of the Het infusate or the
Het remaining within the lung at the end of the perfusion period
(homogenate), both of which have single peaks. These were the source of
the Het entering the perfusate. Note too that the heights of the peaks in the perfusate samples increased with time, as a result of increasing Het concentration within the perfusate. The low peaks ranged from 6.3 ± 3.3 to 46.0 ± 6.9 kDa, with a maximum at 16.0 ± 1.5 kDa that had an average height of 448 ± 395 (Table
1). The high-molecular-weight band had a
maximum mass of 2,120 ± 522 kDa with an average height of 63 ± 4.1 at 288 ± 85 kDa.
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Fig. 3.
High-performance size-exclusion chromatography (HPSEC)
Het peaks from a lung inflated with 6% Het ( = 35.7 mmHg) and
perfused with 10% Alb ( = 59.6 mmHg) for 6 h. Het
measured in each of the hourly perfusate samples had a bimodal
distribution, consisting of a low-molecular-weight peak and a
high-molecular-weight band. These shapes are distinctly different from
those of the infusate and the homogenate (peak tops not shown),
suggesting possible mechanisms by which Het crossed the alveolar
epithelium to enter the perfusate (see DISCUSSION). Values
used to characterize the perfusate Het molecular distributions are
noted (Table 1). The vertical axis is expressed in units of HPSEC
detector output, which is proportional to concentration. m.w.,
Molecular weight; max., maximum; min., minimum; Homog.,
homogenate.
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HPSEC analysis from a lung perfused with 7.2% albumin (oncotically
balanced) is shown in Fig. 4. The
molecular weight ranges of the low-molecular-weight peaks and
high-molecular-weight bands in these lungs were not significantly
different from those of the 10% albumin group, with one exception. The
low-molecular-weight peak occurred at 10.4 ± 1.0 kDa, which was
significantly less than that for the oncotic gradient group (16.0 ± 1.5 kDa; P = 0.0001) (Table 1). The heights of the
peaks for the 7.2% albumin group were also significantly lower than
those of 10% albumin-perfused lungs (Table 1). The maximum height of
the low-molecular-weight peak was only 15% of that in the oncotic
gradient group, whereas the maximum height of the high-molecular-weight
band was 38% of the gradient group (Table 1).
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Fig. 4.
HPSEC peaks from a lung inflated with 6% Het ( = 35.7 mmHg) and perfused with an Alb solution of equal osmotic pressure
(7.2%). The bimodal Het mass perfusate distributions seen in Fig. 3
are evident, although the peak heights are only ~[1/5] as
great.
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To estimate the fraction of the air space Het that entered the
perfusate, we compared areas enclosed by the highest (hour 6) perfusate sample with those enclosed by the homogenate. These areas are proportional to the total amount of Het found in the perfusate and air space, respectively, after 6 h of perfusion. We
summed these two areas, on the basis of the assumption that this
represented the total amount of Het in the air space at the start of
perfusion. We then divided the area enclosed by the hour 6 perfusate sample by this sum to obtain the percentage of Het initially
in the air space that entered the perfusate after 6 h. The results
(Table 2) show that 0.53 ± 0.57%
of the air space Het entered the perfusate in lungs in which there was
no oncotic gradient. The low-molecular-weight peak and
high-molecular-weight band each accounted for about half of this total
(Table 2). When the perfusate oncotic pressure exceeded that in air
space by 17 mmHg, the percentage of air space Het that appeared in the
perfusate after 6 h increased to 3.9 ± 2.9%
(P = 0.04). The low-molecular-weight peak accounted for
about three-fourths of the total.
Modeling the Small Pore System
We hypothesized that the small-molecular-weight Het peaks in the
perfusate samples of the oncotically balanced studies were due to
passive restricted diffusion of Het out of the alveolar space through
liquid-filled cylindrical pores. We assumed that the diffusive flux was
proportional to the increase in the peak heights over the 6-h perfusion
period. We determined diffusion coefficients (D) for
specific Het fractions (15-40 kDa) from the slopes of linear
regression lines plotted through peak heights of each of these
fractions over hours 3-6 (Fig.
5). Diffusion was immeasurable before
hour 3. The reason for this is speculative, but it might
have been due to the growth of perivascular fluid cuffs that offset
diffusive flux into the perfusate (12). To determine the
mass of each fraction diffusing, we multiplied each slope by the
perfusate volume (27 ml) and divided by the height of each fraction in
a 6% Het sample to obtain the diffusive mass flow (
) per unit
of Het concentration difference (
C), /C (Fig.
6). We assumed that the perfusate Het
concentration was negligible compared with that of the instillate.
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Fig. 5.
Change in peak height vs. time for specific Het fractions
in perfusate samples of oncotically balanced studies (means ± SE). The equation for the 15-kDa regression line is peak height = 23.3 + 9.0 h , n = 4, R2 = 0.88. The equation for the 20-kDa
regression line is peak height = 19.2 + 7.8 h,
n = 4, R2 = 0.86.
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Fig. 6.
Diffusive Het mass flow () per unit of Het
concentration difference (C) for specific Het fractions. The squares
represent measured values (means ± SE). The curve, which
represents a pore with a radius of 5 nm and a total diffusive
area-to-diffusion distance ratio
(Ad/L) of 71, provides a good fit to
the data.
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We attributed the monotonic decrease in /C with increasing
molecular mass (M) to the diffusion of Het molecules of
different size through cylindrical pores of constant radius
(r). The diffusion of a spherical solute molecule through a
cylindrical pore is given by (18)
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(1)
|
Here Dfree is the free diffusion
coefficient of the solute in an unbounded solution; 
is the solute
distribution function, a measure of the steric exclusion of the solute
from a region within one solute radius of the pore wall. is
equal to (1 a/r)2 where
a is the solute radius. The parameter k is the
hydrodynamic drag coefficient of a sphere moving along the pore
centerline, obtained as a function of a/r from
tables (17). Application of the Starling equation to the
excluded region near the wall and the remaining pore region results in
the reflection coefficient (
) of the solute (1)
![&sfgr;=[1−(1−a/r)<SUP>2</SUP>]<SUP>2</SUP>](/content/vol91/issue4/fulltext/1730/img002.gif)
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(2)
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where a is the is the solute radius and r is
the pore radius.
We obtained the pore radius and pore number required to fit the
/C-vs.-M data (Fig. 6) as follows. We used
Eq. 1 to compute D vs. M for a single
pore using a chosen value of r. We assumed that the solute
radius (a) of each molecular weight fraction was proportional to M1/3, which was scaled to albumin, for
which M is 66 kDa and the radius is 3.5 nm. Molecular radii
for molecular weight fractions of 15, 20, 25, 30, 35, and 40 kDa were
2.14, 2.35, 2.53, 2.69, 2.83, and 2.96 nm, respectively. We assumed
that Dfree was proportional to
M1/2 and that Dfree for
albumin was 6 × 107 cm2/s
(21). We chose the value of r so that the
computed values of D multiplied by a constant provided a
good fit to the /C-vs.-M data. The constant
(Ad/L) is given by Fick's equation
for steady-state diffusion
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(3)
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Here Ad is the total diffusive area and
L is the diffusion distance from the alveolar space to the
capillary lumen. The constant Ad/L
that converts D to /C provides an estimate of pore
number if L is known. A pore radius of 5 nm with an
Ad/L value of 71 provided a good fit
to the data (curve, Fig. 6). Using an L value of 5.0 × 105 cm (22) yielded a value for
Ad of 3.6 × 103 cm. This
resulted in a total of 4.5 × 109 pores per lung.
Assuming 3 × 107 alveoli per rat lung, this
equates to 150 pores per alveolus (20) (Table
3).
The reflection coefficients () for each molecular weight fraction,
calculated using Eq. 2, are shown in Fig.
7. The estimated for albumin is 0.83.
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Fig. 7.
Reflection coefficients () calculated for specific Het
fractions ( ) and for Alb ( ) using
Eq. 2. Pore radius is assumed to be 5 nm.
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Modeling Small-Pore Membrane Conductivity
We used the data from the oncotic gradient studies to estimate
membrane conductivity (K), on the basis of the Starling
equation, as follows
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(4)
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where b is the bulk (convective) liquid (Het) flux,
K is the membrane conductivity per unit area (total alveolar
surface area, At), dP is the hydrostatic
pressure difference between the circulation and the air space, and
is the albumin-Het oncotic pressure difference, which in our
studies was 17 mmHg. We used a value for equal to the mean value
calculated for the six Het fractions (Fig. 7). We assumed dP to be
zero, on the basis of the airway pressure (5-15 cmH2O)
and vascular (0-10 cmH2O) pressures used. The mean
airway air pressure (10 cmH2O) was higher than the mean
vascular pressure (5 cmH2O). However, alveolar liquid pressure could be 5 cmH2O with an airway air pressure of 10 cmH2O, reducing the airway liquid-to-vascular pressure
gradient to zero (2). In any case dP was small compared
with .
A value for b can be obtained from the solute flux equation
(19)
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(5)
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where s is the solute flux, Cm is the mean solute
concentration in the membrane, and C is the concentration
difference. The first term on the right-hand side of Eq. 5
is the solute flux due to osmotic flow that arises from the bulk flow
due to the osmotic pressure difference in the Starling equation
(4). Rewriting Eq. 5
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(6)
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We assumed that the last term of Eq. 6 was negligibly
small relative to b. That is, the diffusive flux was small
compared with the bulk flow. This assumption is verified after the
calculation for b. With this assumption, b is equal to
either the slope magnitude or the intercept of the linear equation fit
to the s/Cm-vs.- data.
s/Cm was obtained from the oncotic gradient data (Fig. 3) as
follows. First, we calculated the slope of the linear regression fit to
the peak heights of each of the six Het fractions (15-40 kDa) over
hours 1-6 (Fig. 8).
s/Cm for each molecular fraction was equal to the slope divided
by one-half of the height of the corresponding peak in the 6% Het
sample (Cm), then multiplied by the perfusate volume (27 ml).
s/Cm was plotted vs. its reflection coefficient (Fig. 7,
Eq. 2), and a regression equation fit to the data (Fig.
9) was calculated: s/Cm = 0.99 + 0.73, n = 6, R2 = 0.99, P < 0.0001. The
slope magnitude (0.99 ml/h) is equal to b, the bulk flow
(Eq. 6).
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Fig. 8.
Change in peak height vs. time for specific
low-molecular-weight Het fractions in perfusate samples of the oncotic
gradient studies (means ± SE). The equation for the 15-kDa
regression line is y = 108.9 + 23.6 h,
n = 6, R2 = 0.89. The
equation for the 40-kDa regression line is y = 1.22 + 8.06 h, n = 6, R2 = 0.83.
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Fig. 9.
Ratio of s to mean solute concentration (Cm;
s/Cm) for 6 low-molecular-weight Het fractions (15-40 kDa)
(Eq. 6). The slope of the regression line through these data
is equal to the bulk solute flow (b). This value was used to
calculate the membrane conductivity (K; Eq. 4).
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We applied this b value to Eq. 4 to calculate the
membrane conductivity (K). We used the mean value of
0.59 (Fig. 7), of 17 mmHg, and value for
At of 5 × 103 cm2
on the basis of a mean alveolar radius for the rat of 35 µm
(20). The resulting K value was 2.0 × 105 ml · h
1 · cm2 · mmHg1.
This value for membrane conductivity is 103-fold smaller
than the value measured for systemic capillaries (16).
Thus the resistance to flow from the air space to the vasculature is
associated almost entirely with the epithelium.
Errors in the method.
Only the solute flux due to osmotic flow was considered in the
calculation of b; the diffusive flux was neglected. This was
justified because the diffusive term in Eq. 6,
DAdC/(CmL), was much
smaller than b. The estimated value of the diffusive term, based
on a D value of 3.6 × 104
cm2/h (value for 15 kDa fraction),
Ad/L of 71 cm, and a C/Cm value of
2, was 0.05 ml/h, which is 5% of the b value of 0.99 ml/h. From
Eq. 6, b is the y-intercept of the linear
regression fit to the s/Cm-vs.- data (Fig. 9) and was equal
to 0.73 ml/h, which is 26% less than the estimate based on the slope
and within the error on the basis of the scatter in the data.
The foregoing analysis assumed that the oncotic pressure of the Het
instillate remained constant over the 6 h in the oncotic gradient
experiment. However, the osmotic flow calculated (1 ml/h) in
conjunction with the relatively slow rate of Het absorption would
indicate that Het instillate concentration increased over the 6 h,
consistent with the behavior measured in awake sheep (14).
Accordingly, both the oncotic gradient and the absorption rate were
reduced with time. This might be the reason why the linear regression
line plotted through the Het peak-vs.-time data for the lower molecular
fractions did not pass through zero (Fig. 8). The net effect of a
decreasing oncotic gradient with liquid absorption would result in an
underestimate of K. This would be offset by the absorption
of Het from the instillate. Another error in the calculation of
K was the use of an average value for to calculate a
representative value for K in the Starling equation (Eq. 4). A more precise analysis that requires a separate
equation for each molecular fraction with different values for
K and was not justified.
Modeling the Large-Pore System
In the oncotically balanced experiments (Fig. 4), the
high-molecular-weight fractions showed no systematic increase with
time, indicating a nondiffusive transport process. Thus those data
could not provide estimates of a pore radius and pore number by the method used to model the small-pore system (Eqs. 1-3).
By contrast, the transport of the large-molecular-weight fractions
increased linearly with time in the oncotic gradient experiments (Fig.
3), and we applied the solute flux equation (Eq. 6) to those
data to model an equivalent large-pore system.
First, we calculated the slope of the linear regression fit to the peak
heights of each of five Het fractions (100, 200, 400, 800, and 1,600 kDa) over hours 1-6 (Fig.
10). Molecular radii for these
molecular weight fractions were 4.02, 5.06, 6.38, 8.04, and 10.1 nm,
respectively. s/Cm for each molecular fraction was equal to the
slope divided by one-half of the height of the corresponding peak in
the 6% Het sample (Cm), then multiplied by the perfusate volume (27 ml). We used a trial-and-error procedure to fit the s/Cm-
data to obtain the osmotic flow (b). We chose a value for the
large pore (Rl), and from the a/Rl
values for the five molecular weight fractions we computed the values for (Eq. 2). The value Rl was adjusted until
the y-intercept equaled the slope magnitude of the linear
regression equation fit to the s/Cm- data. The resulting
equation satisfied Eq. 6 for solute flux without the
diffusion term: s/Cm = 0.080 0.082 b,
R2 = 0.98. The equivalent large-pore radius
was 17 nm (Table 3). The osmotic flow through the large pores
(bl) was 0.082 ml/h, which is 8% of the total flow
through both sets of pores (Fig. 11).
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Fig. 10.
Change in peak height vs. time for specific
high-molecular-weight Het fractions in perfusate samples of the oncotic
gradient studies (means ± SE). The equation for the 200-kDa
regression line is y = 1.56 + 13.1 h,
n = 6, R2 = 0.83. The
equation for the 1,600-kDa regression line is y = 1.57 + 2.74 h, n = 6, R2 = 0.64.
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Fig. 11.
s/Cm for 6 high-molecular-weight Het fractions
(100-1,600 kDa) (Eq. 6). The slope of the regression
line through these data is equal to large-pore b.
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In the absence of diffusive transport of the large-molecular-weight
fractions in the oncotic balanced data, the diffusion area and number
of the large pores were estimated as follows. The large-to-small pore
number ratio (Nl/Nsm) was obtained by using
Poiseuille's law for osmotic flow through cylindrical pores
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(7)
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Here the subscripts l and sm denote large-pore and small-pore
variables, respectively. We used the molecular mass fractions of 16 and
288 kDa at the peak signals (oncotic gradient data, Table 1) to
represent the transport of low- and high-molecular-weight fractions
through the small (5 nm) and large (17 nm) pores. The large and small
solute radius of 5.7 nm and 2.2 nm produced a value of
sm/l of 0.46/0.31 (Eq. 2).
With bl/bsm of 0.082 and
Rsm/Rl of 5/17, Nl/Nsm
was 1/1,100. For Nsm of 150 pores per alveoli,
Nl was one pore for every seven alveoli (Table 3). The area
ratio (Al/Asm), given by
(Nl/Nsm)(Rl/Rsm)2,
was 1/95. On the basis of the estimated
Asm/L of 71 cm,
Al/L was 0.75 cm.
From the estimates of Rl and
Al/L, we justified omitting the
diffusive term from Eq. 6 to calculate
bl, as follows. The magnitude of the diffusive term
Dl(Al/L)(C/Cm) was
calculated by using the molecular mass fraction of 100 kDa.
Dl was 5.4 × 104 cm2/h,
calculated from values for Dfree, , and
k (Eq. 1), appropriate for the molecular radius
of 4 nm. The diffusive term was 0.0014 ml/h or 2% of the calculated
Qbl.
To determine the contribution of nondiffusive transport mechanisms to
the transport of the large-molecular-weight band, we compared the mass
flux of the large molecular fractions transported through the large
pores by restricted diffusion to that measured in the oncotic balanced
data (Table 2). The large-to-small pore mass flux ratio
(sl/ssm) is related to the
diffusion and area ratios as follows
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(8)
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We used the molecular weight fractions of 10 and 288 kDa at the
peak signals to represent the low- and high-molecular-weight bands
(oncotic balanced data, Table 1). Large- and small-pore diffusion
coefficients Dl and Dsm
were 1.6 × 104 and 7.0 × 104
cm2/h, calculated from values for
Dfree, , and k (Eq. 1)
appropriate for Het molecular radii of 5.7 and 1.9 nm, respectively.
sl/ssm was 1/530. This ratio for
diffusive mass flux through the large pores was considerably smaller
than that measured at 6 h in the oncotically balanced experiments
(Table 2). Thus, in the absence of osmotic flow, the transport of the
large molecular fractions must have occurred via a nondiffusive mechanism.
To determine the contribution of this nondiffusive mechanism, the
mass flux of the large molecular fractions transported by osmotic flow
through the large pores was compared with that from the oncotic
gradient data (Table 2). From the solute flux equation (Eq. 6)
|
(9)
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For high- and low-molecular-weight fractions of 288 and 16 kDa at
the signal peaks, was 0.31 and 0.46, respectively.
Cml/Cmsm was 2.5 ± 0.56 (Fig. 3).
For bl/bsm of 0.082, sl/ssm was 0.26, which is half of
the ratio of the perfusate large molecular mass (0.51 ± 0.37)
measured at 6 h in the oncotic gradient experiments (Table 2).
Thus half of the large molecular mass was transported by osmotic flow
through large pores and half was transported by a nondiffusive
mechanism. Of the half of the nondiffusive transport that occurred with
the osmotic flow, ~10% would have occurred in the absence of osmotic
flow (oncotically balanced data, Table 2), leaving ~40% that was
associated with the oncotic gradient. Thus nondiffusive transport might
have been increased by the presence of an oncotic gradient (Table 3).
The nature of this nondiffusive transport is unknown, but transport by
cytoplasmic vesicles, which are known to be present in alveolar
epithelial cells, is one possibility (5, 22, 23). To
investigate the potential for vesicular transport, we used electron
microscopy to examine alveolar epithelia in the lungs of rats into
which colloidal gold had been instilled. We found gold particles to be
present in epithelial cell vesicles of both type I and type II cells
(Figs. 12 and
13). The number of particles present in
each vesicle ranged from four to six to several dozen. We found no gold
particles in intercellular junctions between alveolar epithelial cells.
These results do not provide direct evidence for Het transport by
epithelial cell vesicles, but they do demonstrate the capability of
these vesicles to engulf particulates that are of approximately the
same size as the largest Het molecules. We will return to this point in
the DISCUSSION.
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Fig. 12.
An alveolar septum in the lung of a rat into which colloidal gold
(3-nm radius) had been instilled. Alveolar air spaces (A) are present
on both sides of the septum, and the gold infusate forms a meniscus on
the upper side. Boxed areas, enlarged at left, show vesicles
that contain gold particles (arrows) within type I cells.
Vesicles such as these may have been responsible for that portion of
the large-molecular-weight Het transport that we could not explain in
terms of pores (Table 3).
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Fig. 13.
Alveolar type II cell from the lung of a rat into which
3-nm-radius colloidal gold solution had been instilled. Gold solution
is present in the alveolar air space (A). Clumps of gold particles are
also present within vesicles inside of the cell (insets,
arrows). Insets are enlargements of the areas enclosed by
rectangles. Vesicular uptake such as this might have accounted for some
of the large-molecular Het transport (Table 3).
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DISCUSSION |
Results of our calculations are summarized in Table 3. The table
shows the radii of the small and large pores, the number of pores of
each type, their fluid conductivity, and the percentage of instilled
Het that passed through each. Also shown is our estimate of the
contribution of nondiffusive mechanisms.
Our results can be compared with those of Matsukawa and colleagues
(13), who measured dextran transport across rat alveolar epithelial type II cell monolayers generated in culture. Using fluorescent dextran fractions ranging from 4 to 150 kDa, these authors
concluded that the smaller fractions crossed the monolayers via
diffusion-limited pores, whereas the larger fractions (>70 kDa)
crossed by means of nondiffusional transcellular mechanisms such as
pinocytosis. They calculated the pore radius to be 56 Å, which is near
to our estimate of 50 Å obtained using Het. On the basis of a pore
area-to-length ratio of 0.05 for their monolayers, Matsukawa and
colleagues estimated the number of equivalent pores to be 2.5 × 106/cm2. From our estimate of the number of
pores per alveolus (150) and the surface area of a
spherical alveolus with a radius 35 µm, the number of pores in the
rat lung should be 1 × 106/cm2. This is
2.5-fold less than the monolayer estimate. However, this difference is
within the expected margin of error, considering the differences
between a type II cell monolayer and the intact lung epithelium, which
consists primarily of type I cells. Furthermore, our estimate for
epithelial fluid conductivity is near that estimated from in vivo sheep
studies (see below).
Our results also support the conclusions of a previous study by Conhaim
and colleagues (4), who inflated lungs with solutes of
various diameters and measured their concentrations in perivascular interstitial liquid-filled cuffs. They concluded that the air space
epithelium could be characterized as if it were perforated by pores
with radii of 10, 400, and 4,000 Å, which accounted for, respectively,
68, 30, and 2% of total liquid flux across the epithelium. Our present
results, obtained using the continuous molecular distribution of Het,
refine this estimate.
The rates of Het disappearance from the air space we measured (Table 2)
can be compared with those of Matthay, Berthiaume, and colleagues
(3, 15), who measured rates of albumin disappearance from
the lungs of unanesthetized sheep into which 100 ml of autologous, radiolabeled serum had been instilled. They measured a protein disappearance rate of 1.6%/h. By comparison, we measured a
disappearance rate of 0.53% after 6 h (0.09%/h) in the absence
of an oncotic gradient and 3.9% after 6 h (0.65%/h) at an
oncotic gradient of 17 mmHg. Oncotic gradients in the sheep experiments
were initially absent because the instillate osmotic pressure (29 mmHg)
was similar to that in the blood plasma (15). Thus the
initial rapid increase in liquid clearance in the first 4 h with
an increasing instillate protein concentration was attributed to active
transport mechanisms. The progressively reduced liquid clearance from
12 to 24 h was attributed to passive osmotic reabsorption (see
below). This is consistent with the results of the oncotic gradient
experiments that modeled macromolecular transport as osmotic flow
through water-filled pores. The higher protein disappearance rate in
the sheep studies might have been due to the larger epithelial surface area in contact with an instillate volume (100 ml) that was larger than
that used in the present studies (10 ml).
The sheep studies showed that, by 12 h, liquid clearance
progressively slowed as instillate protein became more concentrated with time. These data are used to estimate epithelial fluid
conductivity as follows. Specifically, the rate of liquid absorption of
the 100 ml of serum albumin instilled into the airways decreased from 3.2 ml/h at 12 h to 1.4 ml/h at 24 h, whereas the instillate
protein concentration increased from 9 g/dl to 12 g/dl. At 12 h,
the instillate volume was reduced to 30 ml (15). We assume
that the reduction in absorption was due to a reduction in osmotic flow
and estimated K from the Starling equation (Eq. 4). At 12 h, when b was 3.2 ml/h and instillate
protein osmotic pressure (i) was 40 mmHg
![−3.2<IT>=KA</IT><SUB>t</SUB>[<IT>&Dgr;</IT>P<IT>−&sfgr;</IT>(<IT>&pgr;</IT>c<IT>−</IT>40)]](/content/vol91/issue4/fulltext/1730/img010.gif)
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(10)
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Here c is capillary protein osmotic pressure, and instillate
i was computed from Landis and Pappenheimer's (11)
relation between protein concentration and osmotic pressure. At 24 h, when b was 1.4 ml/h and i was 60 mmHg
![−1.4<IT>=KA</IT><SUB>t</SUB>[<IT>&Dgr;</IT>P<IT>−&sfgr;</IT>(<IT>&pgr;</IT>c<IT>−</IT>60)]](/content/vol91/issue4/fulltext/1730/img011.gif)
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(11)
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Assuming no change in P and c, subtraction of Eq. 10 from Eq. 11 results in a value of KA
of 0.09. With a value for (albumin) of 0.83 (Fig. 7), the
calculated value for KAt in the sheep lung was
0.11 ml · h1 · mmHg1,
similar to that estimated for the rat lung. On the basis of mean
alveolar diameters of 70 and 100 µm (20) and alveolar
liquid volumes of 10 and 30 ml for the rat and sheep, respectively, the alveolar surface area in contact with alveolar liquid was twofold greater in the sheep than in the rat. Thus K for the sheep
was half that for the rat. The effects of lymphatic drainage and a significant vascular-to-airway hydrostatic pressure gradient may also
contribute to liquid and protein clearance in vivo.
Our electron microscopy studies showed that vesicles of both type I and
type II cells are capable of internalizing colloidal gold particles
present within the airspace. The radius of these particles (3 nm)
corresponds to a protein molecular mass of 40 kDa. However, the
particles were coated with albumin, which means that their effective
radius was larger. The presence of several of these particles within
each vesicle supports our speculation that Het molecules with masses up
to 2,000 kDa (radius 11.5 nm) might have been transported out of the
air space by this mechanism.
In a previous study, 5-nm-radius gold particles were not found to be
present within either type I or type II cell vesicles in the lungs of
rabbits (8). Possible explanations for these discrepant
findings may be differences in the quantity of gold instilled,
differences in the radius of the particles instilled, or differences
between rabbit and rat lungs.
We did not find gold particles to be present in intercellular junctions
between epithelial cells, which supports our estimate for the radius of
the intercellular pores (5 nm radius). The reflection coefficient of a
40-kDa macromolecule by such a pore is 0.7 (Fig. 7). If one albumin
molecule (3.5 nm) were attached to each gold particle (3 nm), its
effective radius would be 6.5 nm and impermeable through a 5-nm radius pore.
Electron microscopic studies have shown that vesicular transport in
rabbit lungs could be inhibited by using the pharmacological agents
monensin and nocodazole (9). However, the authors of those
studies also found that the clearance of albumin and IgG from rabbit
lungs was not significantly decreased by these agents. They concluded
that pathways other than endocytosis were responsible for the air space
clearance of albumin and IgG measured. This is consistent with our
conclusion that the large-molecular-weight Het fractions entered the
perfusate through a combination of large-pore flux plus a nondiffusive
mechanism that might have been vesicular transport.
Our results confirm the conclusions of others that the alveolar
epithelium can be characterized as if it contains both small, diffusion-limited pores as well as larger transcellular pathways (4, 13). However, the continuous distribution of Het that we recorded allows the molecular weight limits of these pathways to be
seen more readily and provides insight into the magnitude of these
processes in intact lungs. The slow rate of Het removal from the air
space that we measured confirms that the alveolar epithelium represents
a significant impediment to the clearance of macromolecules in
pulmonary edema. Our studies allowed us to quantitatively separate the
transport of macromolecules by diffusion (and osmotic flow) through
pores from that due to nondiffusive mechanisms. Vesicular transport may
be such a mechanism.
The methods we have developed will facilitate the study of mechanisms
that promote transcellular diffusion and vesicular transport and
thereby enhance the resolution of this life-threatening condition.
| |
ACKNOWLEDGEMENTS |
We thank Joan Sempf for assistance with electron microscopy.
| |
FOOTNOTES |
This research was supported by a grant from the Department of Veterans Affairs.
Address for reprint requests and other correspondence: R. L. Conhaim, Univ. of Wisconsin Medical School, Dept. of Surgery, H4/710
Clinical Science Center, 600 Highland Ave., Madison, WI 53792-7375 (E-mail: rconhaim{at}facstaff.wisc.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 3 January 2001; accepted in final form 19 June 2001.
| |
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ABSTRACT
INTRODUCTION
