Study of the Relationship Between Plasma Volume and
Transcapillary Protein Exchange Using I131-Labeled
Albumin and I125-Labeled Globulin
By W. GORDON WALKER, M.D., RICHARD S. ROSS, M.D., AND
JOHN D. S. HAMMOND, M.B.,
to protein varies directly with plasma volume
and with total vascular albumin (or globulin)
mass. At low values for total vascular albumin, transcapi'.lary exchange of this protein
appears to cease.1--1S In several subjects an
effort has been made to eliminate some of the
uncertainties of the method through the use
of 2 labeled proteins injected simultaneously,
permitting comparison of the behavior of 2
proteins in the same subject under identical
conditions. For this purpose I1-3 (half-life
60 ± 0.5 d.)ir'"17 has been used in conjunction
with I m (half-life 8 d.) to label gamma globulin and albumin respectively.
CONSIDERABLE quantity of extravascular albumin and globulin is in
pqiu ibrium with plasma albumin and globulin.1"4 Tracer studies in man using plasma
proteins labeled either in vivo or in vitro have
shown concentration-time curves of plasma
radioactivity that fall rapidly and at a changing rate during the first 3 to 4 days and at
a constant rate thereafter/""8 Disappearance
of the labeled material from the plasma during the early phase has been interpreted as
representing equilibrium with the extravascular mass of the protein under study. Analysis of edema fluid has confirmed that this
equilibrium occurs.0"11
In the present study, transcapillary protein
exchange was estimated by measuring the rate
of equilibrium of labeled plasma proteins with
their respective extravascular protein pools.
The relations between the transcapillary exchange rate so measured and such variables
as the plasma protein concentrations, total
circulating protein mass and plasma volume
have been appraised by testing for correlation among these variables.12"14 Since it was
not feasible to study these interrelationships
in man by altering deliberately one or more
of these variables in a single individual, correlations among these variables have been studied in the group of individuals. It appears
from these data that capillary permeability
A
Downloaded from http://circres.ahajournals.org/ by guest on June 16, 2017
Methods
Iodinated Proteins
I1:!1-labeled albumin with an initial specific activity of about 75 JXC. per nig. of albumin was obtained from Abbott Laboratories (Risa, Abbott).
It was always used within approximately 2 weeks
following shipment. Twenty-four hour dialysis
yielded no more than 2 to 3 per cent unbound or
dialyzable iodine. Countercurrent electrophoretic
separation of the albumin fraction of sera from 2
patients following injection of the above material
revealed that the radioactivity migrated with the
albumin fraction.0 As has been pointed out
previously,8 this separation is crude and the albumin fraction contains variable amounts of
alpha-1 and alpha-2 globulins, and hence would
not pick up the "tailing" demonstrated by paper
electrophoresis. Armstrong8 has subjected samples
of Abbott's I 131 albumin, as currently prepared,
to paper electrophoresis and reports that with this
preparation there is no more "tailing" than is
found with S3r'-lnbeled albumins in vivo.
I1-"' has a half-life of 60 days and emits a
27 kev x-ray and a 35.4 kev gamma ray.1"'"17
The I1-'"' used in the present studies was prepared
in the cyclotron at the Oak Ridge National Laboratory. Significant quantities (10-12 per cent)
of I 1 - 0 were also produced by this method. However, this isotope has a half-life of 13 days and
analyses of the protein data were not begun until
approximately 100 days had elapsed after produc-
Prom the Department of Medicine, Johns Hopkins
University and Hospital, Baltimore, Md.
Supported by a grant from the Life Insurance
Medical Research Fund. A grant from the Heart
Association of Maryland was used to meet the hospital expenses of some patients admitted for investigation.
Dr. Walker is an Established Investigator of the
American Heart Association, formerly Fellow of the
American Heart Association.
Received for publication May 6, 1960.
Circulation Research, Volume VIII, September 1900
M.D.
1028
PERMEABILITY OF CAPILLARIES TO PROTEIN
Downloaded from http://circres.ahajournals.org/ by guest on June 16, 2017
tion of the material, allowing the interfering radioactivity from I 1 -" to decay to a point where it constituted less than 0.05 per cent of the total measured radioactivity.
Processing of the cyclotron target and separation of the iodine was carried out by the chemical
division of the Oak Ridge National Laboratory and
the processed carrier free I'- r ' was forwarded to
Abbott Laboratories, where subsequent handling
was identical to that of I 131 except that the material was used to label human gamma globulins.
Dialysis and electrophoretic separation gave results similar to those described above for I 131
labeled albumins.
Because of the reports of low concentration of
dialyzable radioiodide in the Abbott preparations8' 18 and our own findings, the iodinated protein was not dialyzed routinely before use. Urine
radioactivity in our subjects during the first few
days was no higher than that reported by others
who have used only dialyzed material.6
Measurement of Radioactivity
In the earliest experiments using only I131-labeled albumin, radioactivity was measured with an
end-window G-M tube. Samples were prepared
by drying the plasma and urine (1.0 ml. aliquots
of each) in nickel planchets. Appropriate corrections were employed for self-absorption due to
dried proteins and other solids. The coefficient of
variation (C.V.) for a single sample was ± 4
per cent.
For experiments with 2 isotopes and all subsequent experiments, a sodium iodide crystal well
scintillation counter was used. For iodine-131 this
had an efficiency of 43 per cent. For I 123 the
efficiency was 19 per cent, and showed some variation but by keeping' all counting conditions as nearly constant as possible the C.V. for a total of
10,000 counts was 2.5 per cent.*
In experiments involving simultaneous use of
2 labeled proteins, radioactivities due to the constituent isotopes were separated by counting each
sample on 2 occasions at an interval of 2 to 3
weeks. The fraction of the total measured radioactivity due to I1"5 or to I 131 respectively was
obtained by solution of a pair of simultaneous
linear equations. The interval between counting
was sufficiently long to allow I 131 to decay to 30
per cent of its original value or less. The number
of counts recorded at eact counting was sufficiently
large to reduce the coefficient of variation to 0.7
•Under these conditions the value we obtained for
the half-life of I lsl was 62 days, a value in good
agreement with Friccllander and Orr's reported value.17
This may also bo construed as evidence that there
was no contaminating radioactivity from other sources
in the I 13 at the time the material was analyzed.
Circulation Research, Volume VIII, September I960
1029
per cent. For a mixture with a ratio of unity,
this should have given a coefficient of variation
of 1 per cent for the constituent radioactivities.
Measurement of Protein
Total serum nitrogen was measured by the
Kjeldahl method and converted to protein by
multiplication by 6.25 after correction for nonprotein nitrogen (NPN). Constituents of the
serum proteins were measured by free electrophoresis with the Tiselius instrument using a barbiturate buffer with pH at 8.6. The proportion of
the various constituents in the serum was obtained
from the area under the appropriate portion of
the schlierin diagram. The accuracy of this method
has been reported by others.19 In the first 10
subjects, electrophoretic patterns were not usually
done more than once, but total serum nitrogen was
measured repeatedly and the coefficient of variation of these repeated measurements during the
course of an experiment was never more than 4.5
per cent. In subsequent experiments, each serum
sample was subjected to electrophoresis using the
paper strip technic described by Mackay.20 Proportions of the constituents of the plasma, proteins
were measured by the scanner and automatic integrator. Total protein was determined on each
sample. The coefficient of variation of replicate measurements of albumin by this technic was
2.5 per cent.
Experimental Procedure and Subjects
Studies were carried out on patients from the
wards of the Johns Hopkins Hospital. The patients studied had a variety of illnesses and were
chosen as a control group for projected studies on
patients with heart failure. Availability, absence
of heart failure and duration of hospitalization
were the primary factors influencing selection of
patients. Thus, these were not normal subjects,
but represented a variety of illnesses, as shown in
table 1. None had any signs or symptoms of congestive heart failure.
Forty to 50 /xo. of I'-^'-labeled globulin and/or
12 to 20 (U.c. of I131-lnbeled albumin were injected
intravenously and blood samples were collected
30 minutes after injection, then at hourly intervals for the next 4 hours and finally with progressively decreasing frequency over the next 14 to IS
days. A total of 24 to 28 blood samples were
usually collected during the entire observation period. In most cases, complete urine collections were
obtained during the first few days of the experiment in order to make certain that there was no
rapid initial loss of radioactivity in the urine,
which would have suggested the presence of excessive unbound iodine. Patients were kept in bed
until extravascular equilibration had occurred to
avoid changes in protein concentration associated
Downloaded from http://circres.ahajournals.org/ by guest on June 16, 2017
39.4
12.4
25.7
.564}
.129
•Key to abbreviations: HASCVD ^hypertensive and arteriosclerotic cardiovascular disease;
CVA=cerebral vascular accident; AS=arteriosclerosis; HCVD=hypertensive cardiovascular
disease; DM=diabetes mellitus; kp<,=fraction of plasma protein exchanged with extravaseular
protein per unit time.
tData incomplete.
{Comparable values for globulin.
16.0
2.38
Globulin data
Mean
Standard deviation
70
WM
35.26
8.16
1.14
44.2
25.9
42.0
35
46
1.01
0.42
0.52
0.98
0.36
0.81
1.36
39.6
56.7
24.3
33.0
58.4
21.1
17.7
15.0
28.6
23.3
48.5
54.0
75.5
64.4
57.6
73
65
WM
WM
CF
CF
WM
5.0
Thrombophlebitis
Schizophrenia,
Scurvy
Convalescent
Pneumonia
CVA
Morphine Addict.
0.99
0.79
0.46
32.1
33.9
22.0
31.0
23.0
21.0
70.0
53.5
66.8
60
65
73
.328}
.144
.889}
.201
2.78
1.31
3.05
1.91
1.77
0.94
1.19
2.94
1.06
2.15
3.61
3.51
2.02
0.72
5.30
3.60
2.12
2.42
3.18 •
5.50
2.10
0.67
1.96
0.69
1.34
2.25
2.52
1.26
0.26
—
3.34
—
1.96
31.0
CM
CF
CF
2.27
1.21
1.33
0.91
53.2
32.0
30.0
63.0
28.0
29.0
52.5
63.6
60.1
49.0
54
65
36
42
CM
WM
CF
CM
—
1.43
1.75
4.00
1.54
0.99
1.43
1.54
0.56
31.2
45.0
46.0
22.4
32.0
32.0
27.0
25.0
47.5
47.5
39.5
62.0
kpp*
.355}
.062
.078
.62
.63
.0049}
.0017
.0033
.0011
.053
.014
.064}
.029
.0035
.064
.0171}
.0077
.026
.0083
.033
.023
.041
.022
.026
.037
.0057
.0031
.0041
.0025
.0022
.056
.073
.047
.052
.068
.56
.66
.66
.63
.62
.026
.021
.018
.0025
.0043
.0052
.046
.038
.062
.017
.034
.014
.042
.020
.023
.027
.017
(HR-1)
.72
.61
.36
.0022
.0030
.0028
.0026
.0028
.0024
.0028
.0043
X:
.033
.069
.030
.075
.043
.050
.048
.039
X,
.63
.57
.66
.63
.59
.54
.72
.73
ExtraTotal
Extravascular exchangeable vascular
albumin
albumin
albumin
Gm./Kg.
fraction
Gm./Kg.
53
54
56
58
Age
Vascular
albumin
Gm./Kg.
Plasma
volume
ml./Kg.
Plasma
protein
albumin
mg./ml.
Weight
(Kg.)
CM
CM
CF
CF
Kace,
sex
Mean
Standard deviation
JM
GP
CL
IP
TD
JH
WB
NH
SD
HC
HMcLf
CVA
HASCVD, CVA
AS, CVA
CVA, DM, HCVD
ASCVD, DM
Mult. CVA
CVA, (L), HASCVD
Neurosyphilis
Myocarditis
Epilepsy
Idiopathic
CVA (R), HASCVD
CVA (L), HCVD
HCVD, Subarach.
Hemorrage
PT
PT
LM
RT
TW
JE
Diagnosis*
Patient
Albumin
Table 1
d
O
M
Ul
Ul
r1
o
CO
o
PERMEABILITY OF CAPILLARIES TO PROTEIN
with water shifts during postural changes.21' 22 A
representative plasma concentration curve of radioactivity for a 15-day period is shown in figure 1.
Plasma volume was taken as the initial distribution
volume of the labeled proteins. In the simultaneous
albumin and globulin experiments a duplicate measure of this volume was afforded. The mean difference in these duplicate measurements was 8 per
cent with no consistent discrepancy between the 2.
Model Used for Analysis of Disappearance Curves
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Rates of transcapillary exchange and degradation of the plasma proteins were estimated from
data obtained from the concentration-time plots of
plasma radioactivity by use of methods similar to
those used previously by other investigators in
the study of rate phenomena.11' 23 Mathematical
treatment of tracer data has been presented in
detail by Sheppard and Householder.24 The model
presented below follows the treatments outlined
by Sheppard and Householder and others with
certain simplifying assumptions. The limitations
which the assumptions place upon the method will
be discussed later.
Consider a model such as that schematically
represented in figure 2, consisting of 3 regions in
series. One region, by synthesis and catabolism
of proteins, maintains the plasma protein pool.
Between the plasma protein pool and an extravascular-extracellular protein pool there is a steady
state of protein exchange. It is assumed that:
(a) the steady state exists unchanged throughout the period of the observations; (b) the behavior and metabolism of the labeled protein is in
no way different from the native protein of the
individual; (c) metabolic degradation occurs at
some site that is in direct equilibrium with the
plasma (e.g., liver) ; 25 (d) no reutilization of the
radioiodine occurs following metabolic degradation; (e) mixing within the plasma and within the
extracellular pool is rapid and complete; and (f)
transeapillary protein exchange can be represented by a single rate. This is clearly an oversimplification and the limitation of this assumption will be discussed further subsequently.
The derivation to be employed is similar to previous presentations.6' 23> 24
Let: P=total quantity of protein under consideration in the vascular bed.
E=total quantity of that protein that is
extravaseular.
fcj,e=fraction of plasma protein exchanged
with extravaseular protein per unit
time.
7cej,=fraetion of extravascular protein exchanged per unit time with vascular
protein.
&pm=fraction of vascular protein metabolized per unit time.
Circulation Research, Volume VIII, September 1960
1031
Xj Xs=exponential constants appearing in
solution (and experimental data).
If now a small quantity P* of a protein species
is labeled and introduced into the plasma at time
t = 0 and rapid mixing occurs, then the rate of
change of the labeled protein is given by:
dP"
(la)
= -kpP' + kepE*
dE*
(lb)
— J,
dt
~
V
where P* is the quantity of labeled protein in vascular volume at time t and E* is the quantity of
labeled protein in extravascular protein pool at the
same time.
Converting to concentrations and solving equations (1) yields the second order equation:
d*Cp*(t) + (kp+kep) dCp*(t) +
dt'
dt
(kpkep — kpekep) Cp* (t) = 0
(2)
which has for its solution:
Cp*(t) = C1e~X't+
(3)
where Ct and C2 are constants of integration evaluated for the condition Gp*(0) — Ct +Cs and
dCp*(0)
—
= \,Cj + \2CS; and \ u X2 are exponential constants determined from the auxiliary
equation:
X* + (kp + kep) X + (kpkep — kpeK,,) = 0. (4)
Thus, equation (3) is a description of the plasma
concentration of radioactivity as a function of
time. By evaluating the constants from the experimental data as described in figure 2, the fractional exchange rates can be determined by the
following relations obtained from (4) :
i. — ~^'C,-X2C2
Cp»(0)
(5b)
r»i
K,
(5c)
7,
— 7.
(5d)
"'pm — '"p
While these relations permit calculations of the
rates, it should be reemphasized that they are
based on the assumptions listed above and, hence,
failure of the system to meet these assumptions
will result in false estimates of the rates.
Results
Table 1 contains data obtained from 17 subjects chosen from the hospital population to
represent a "control" group as described
above. Complete studies were obtained on all
except one subject. In the figures to follow,
each point represents one subject.
Diffusion rather than filtration must be
WALKER, ROSS, HAMMOND
1032
PLASMA
l"
DISAPPEARANCE
LABELED
CURVE
ALBUMIN
Figure 1
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Plasma disappearance curve of ItJ'-labeled
albumin. Xj> (see text) is taken as the slope of the
linear second phase. Extrapolation of this second
function (C2e ~^'1 as described in the text) and
subtraction of this function from each of the observed points yields the points from ivhich the
first slope, X,, is obtained.
invoked to explain transeapillary exchange of
substances of small molecular weight.-*1 -7 If
this is the mechanism for transcapillary protein exchange, then it is expected that the
quantity of protein exchanged per unit time
will vary linearly with its concentration in
the plasma, providing that the permeability
characteristics of the capillaries are constant,
or nearly so.
Figure 3 is a scattergram showing the relation between serum albumin concentration
and the "mean transcapillary exchange rate"
for each subject (kpe times plasma albumin
concentration gives a value for this rate in
grams exchanged per 100 ml. of plasma per
hour). The scatter is great and affords no
significant support for a linear relation.
Hence, if diffusion is to be retained as the
mechanism of transcapillary albumin exchange, it is necessary to postulate considerable variation in capillary permeability to
albumin. The permeability constant of a
membrane with regard to any given solute is
defined as the quantity of solute passing
across the membrane per unit surface area of
membrane, per unit thickness of membrane,
per unit concentration difference across the
membrane per unit time. In the intact individual, it is impossible to obtain information
about size and thickness of the capillary membrane and consequently a precise measure of
the permeability of the capillary membrane
to protein is not possible under these circumstances. However, k1M! is a rate constant for
transcapillary albumin and in a given individual the value of this constant is determined
by the variables above. In trying to evaluate
the factors involved in the regulation of kpe,
this rate constant Avas tested for correlation
Avith serum albumin contraction and plasma
volume. These results are shown in figure 4,
left and right. There is evidently no correlation between plasma albumin concentration
and k,,e in the subjects studied; hoAvever, a
close correlation exists between the plasma
volume and kpe (r = .75, p < .001). Indeed,
partial correlations between the 3 variables,
plasma albumin concentration, plasma volume
and k|)e, reA'eal that the correlation between
plasma A'olnme and kpe is the only one of significance and it is not altered appreciably by
eliminating any possible correlation between
plasma albumin concentration and kpe. Thus,
the larger the plasma volume, the greater kpi.
for albumin, and coiwersely, Avith small plasma volumes the permeability to albumin becomes quite low.
The Starling hypothesis assigns to the
plasma proteins (primarily albumin) the
principal role in maintenance of the volume
of plasma. Since the resultant of the opposing
hydrostatic and osmotic forces on either side
of the capillary membrane determines the
equilibrium distribution of Avater across this
membrane, the total circulating vascular protein mass is the principal determinant of the
plasma A'olume. One factor regulating the size
of this vascu'ar mass is the leakage rate of
the protein across the capillaries. Figure 5 is
a graph of vascular albumin mass (albumin
concentration X plasma A'olume H- body
Aveight) against albumin exchange rate (k,M,
X vascular albumin mass). The dashed lines
and heavy dots show the relation expected between plasma A'olume and kpe shown in figure
4 right (A'ascular albumin mass calculated for
plasma volumes between 10 and 70 ml./Kg. at
10 ml. intervals assuming no change from the
main albumin concentration of 2.6 found in
these studies; corresponding values for kpe
Circulation Research, Volume VIII, September 19C>0
1033
PERMEABILITY OF CAPILLARIES TO PROTEIN
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for these plasma volumes obtained from the
relation given in figure 4 right). The open
circles represent the data obtained from the
subjects studied. The agreement is good and
shows that as the vascular albumin mass
diminishes the quantity of albumin exchanged
approaches zero. Thus, at values below 0.3
Gin. albumin/Kg, body weight, the albumin
exchange becomes quite small. From this and
observations on animals,1' 3 it is to be expected
that the quantity of albumin in the extravascular pool should diminish quite rapidly as
the quantity of vascular albumin approaches
0.3 Gin. per Kg. body weight. Figure 6 confirms this relation (the line of best fit for regression of Y on X has an intercept at y =
0.35 when X = 0). It is also evident that
there is considerably greater variation in the
quantity of extravascular albumin than in
the vascular albumin.
If this phenomenon really represents a
change in the permeability characteristics of
the capillaries, then these relationships should
hold for other plasma proteins. As described
under Methods above, information on this
point has been obtained using I131-labeled
albumin and Iiar>-labeled globulin in experiments designed to obtain simultaneous measures of transeapillary exchange rate of albumin and globulin. A summary of the globulin
data is included in table 1.* Because of the
difficulty in obtaining I125, it has only been
possible to obtain data in 11 individuals; however, in genera], the behavior of the globulin
appears to be qualitatively the same as the
albumin. Figures 7 and 8 are plots of vascular
mass versus exchange rate, and vascular versus
extravascular globulin (r = +76, p < .01).
Globulin exchange rate is plotted against vascular globulin mass in figure 7, while in figure
*Tablc 2, -which contains details of the globulin
data, liiis been deposited as Document number 6312
with the ADI Auxiliary Publications Project, Photoduplication Service, Library of Congress, Washington
25, D. C. A copy may be obtained by citing the
Document number and by remitting $1.25 for photoprints, or $1.25 for 35 nun. microfilm. Advance payment is required. Make checks or money orders payable
to: Chief, Photoduplication Service, Library of
Congress.
Circulation Research, Volume VIII, September 1900
Extravascular
protein space
Plosmo
Site of
protein
metobolism
'Labeled protein p*
introduced here
dP°
dt
Kpei
Kpmr
• Kept.
O E _ _\.
p-o , i, n o
• K pe r
Figure 2
Model for interpreting disappearance curves. P"
and E" denote total quantity of labeled protein in
plasma and extracellular space respectively. The
other symbols are defined in text. The 2 simultaneous equations describe the rate of change of
radioaetively labeled material in the plasma and
extravascular space respectively.
~J"7
-
l\ep
L.
8 the extravascular globulin mass is plotted
against the vascular mass. These plots are
comparable to figures 5 and 6, in which the
same relationships were shown for albumin.
The analysis used in figure 5 for albumin
could not be applied to the small number of
globulin observations. However, comparison
of figures 5 and 7 reveals similar behavior
for the 2 proteins. The relationship between
the vascular and extravascular globulin
masses is shown in figure 8 and is seen to be
similar to that for the albumin masses as in
figure 6.
Additional information regarding the relationship between albumin and globulin transcapillary exchange may be obtained by comparing the simultaneously measured rates directly. As indicated by equations 5a—d, the
data from each individual yield 2 fractional
rates for the transcapillary exchange, one being the fraction of the plasma protein moving
into the extravascular spaces (kpe) and the
other fraction moving from extravascular to
vascular space (ke,,) per unit time. Both of
these fractional rates have been converted to
WALKER, ROSS, HAMMOND
1034
SO
4.0
70
_i
z
o e
_i
o
§3.0
o
o
S
o
.BUI
I 2.0
|
30
3
20
§1.0
o
10
o
<
I 40
o
o
0
o
so
o
o
o
o
0
.01
.02
03
.04
RATE CONSTANT (kp«)
y 11273ft 9.9
.01
02
.03 .04 .05
RATE CONSTANT I kp«l
A comparison of the albumin exchange rate, Gm./
100 ml/hour, ivith the serum albumin concentration in 16 control subjects. The correlation is low
and of doubtful significance. At normal concentrations the exchange rate appears to vary independently of the albumin concentration.
Figure 4
Left. Comparison of the plasma albumin concentration with the fractional exchange rate (kpe)
shows no correlation between these 2 over the
ranges found. Thus, this rate constant which is a
measure of capillary permeability to albumin appears to be uninfluenced by albumin concentration
in the plasma at these ranges.
Right. The correlation between plasma volume and
the rate constant is highly significant in these subjects. Those individuals with the largest plasma
volumes also had the largest fraction of vascular
albumin exchanging loith the extravascular albumin
per unit time. Thus, capillary permeability to
protein appears to be determined by the size of
the plasma volume.
Gm./Kg./hour and the data from these simultaneous studies are shown in figure 9. The
correlation coefficient for the group is .78
(p < .01). Thus, the relation between albumin
transcapillary exchange and simultaneously
measured globulin exchange appears to be a
linear one over the ranges found (regression
equation: albumin exchange rate = 1.20 globulin exchange rate + .013) and the globulin
data appear to support the inferences concerning capillary permeability to protein drawn
from the albumin data. It is interesting that
after correcting the differences in concentration of albumin and globulin, the ratio of
the exchange rates (i.e., the ratio of the fractional exchange rates, kpe albumin/kpe globulin) of albumin to globulin is 1.6, a value very
close to the ratio of their diffusion coefficients
(D alb./D glob. = 1.61 at 20 C. in aqueous
solution).28 This relation is to be expected if
the exchange process is primarily one of diffusion.
These results reveal a much more highly
significant correlation between the plasma
volume and the transcapillary exchange rate
of the proteins studied than between this rate
and serum protein concentration. The correlation between this rate and the vascular albumin mass (Gm. albumin/Kg, body weight)
is also greater than the rate-concentration
correlation. These observations, plus the relationship observed between the quantities of
protein in the vascular and extravascular regions and the other data presented above, are
consistent with the interpretation that the
capillary permeabiliy to protein is greatest
with large quantities of protein and large
plasma volumes and diminishes as these 2
quantities diminish. Indeed, extrapolation
suggests that below a value of 0.3 Gm. albumin/Kg, capillary permeability to protein is
insignificant. Such fluctuating permeability
would serve to maintain plasma volume within relatively narrow limits despite wide fluc-
2 i.o
LJ
CO
Downloaded from http://circres.ahajournals.org/ by guest on June 16, 2017
o
.02 0 4 .06 .08 .10 .12 .14
ALBUMIN EXCHANGE GM/IOOML/HR
Figure 3
Discussion
Circulation Research, Volume VIII, September 1960
1035
PEEMEABILITY OP CAPILLARIES TO PROTEIN
© 2.0
5
1.6
2
2
1.2
CD
'o
o
m
<
r>.84
p<.OOI
0.8
cr
_i
y=.38x+.35
0.4
o
3
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.02 .04 .06 .08 .10 .12
ALBUMIN EXCHANGE GM/KG/HR
Figure 5
The relation between the albumin exchange rate
(Gm./Kg./hour) and the total circulating vascular
albumin (Gm./Kg.). The dashed line and closed
circles are calculated from the relation shown in
figure 4 right (plasma volume and kpe) for plasma
volumes between 10 and 70 ml./Kg. body iveight
assuming a constant plasma albumin concentration.
(Coordinates for closed circles were obtained from
the relations: Y in Gm./Kg. body weight = plasma
volume ml/Kg, body iveight X average plasma
albumin concentration; X in Gm./Kg. body weight
= T X hpe expected from figure 4 right.) Open
circles are actual values for these parameters in
the group of subjects studied. It can be seen
that at lower values for vascular albumin the albumin exchange approaches zero, while at higher
values the exchange increases much more rapidly
than does the vascular albumin.
tuations in total exchangeable protein. There
appear to be 2 possible explanations for this
variation in permeability with variation in
plasma volume. The first is that the individuals with the largest plasma volumes have a
greater number of capillaries per unit body
weight, providing a greater surface for exchange ; the second is that there is an actual
change in permeability of the capillary (i.e.,
a change in the fraction of the capillary area
available for diffusion). The results of these
studies do not provide information that permits a choice between these 2 possibilities.
It must be emphasized that the relations
described above are obtained from studies on
a number of subjects and it does not necessarily follow that these relations hold in a
given individual when one or more of the
Circulation Research, Volume VIII, September I960
>u
1
2
EXTRAVASCULAR
3
ALBUMIN
4
GMS/KG
Figure 6
Comparison of vascular albumin and extravascular
albumin. The line of best fit for Y on X intercepts
the Y axis at .35 Gm. vascular albumin per Kg.
This intercept is significantly different from zero
and it is apparent that the variation in extravascular albumin is much greater than the variation in
vascular albumin.
quantities measured above is varied. Evidence from other sources to be considered below suggests that these observations also hold
for the individual.
Other criticisms are to be raised concerning
this type of approach to the study of capillarypermeability, and these are concerned with
the assumptions made in order to analyze these
plasma disappearance curves of labeled protein. The first of these is the assumption of
integrity of the labeled protein. Evidence has
been offered to support the suggestion that
iodination of the protein may alter it sufficiently to change its rate of destruction.0
However, since the present data suggest that
the transcapillary exchange appears to be a
function of the phj^sical characteristics of the
molecule (size, diffusion coefficient), this criticism has less force here than in studies concerned primarily with degradation rates.
A second assumption, much more difficult
to justify, is the assumption that transcapillary exchange can be represented by one rate
(this assumption is inherent in the model described above). This is an obvious oversimplification, since evidence is available in the
literature indicating that there are several
different rates.11' 20 In a more general treatment, Sheppard and Householder have shown
that in a system such as that considered here.
WALKER, ROSS, HAMMOND
1036
1.0
(9
I 0.8
0.6
O
0.4
<
s°
0.2
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.01
.02
.03
EXCHANGE -GM/KG/HR
Figure 7
Correlation between the total vascular gamma
globulin and the transcapillary globulin exchange
rate. Comparison ivith figure 5 reveals that the
behavior of albumin and globulin is very similar,
(r = +.76, p <.O1).
GLOBULIN
if there is a large number of rates normally
distributed about a single mean, instead of
one transcapillary rate, the error introduced
in measuring this mean rate by assuming that
it is a single rate is quite small.24 However,
if the distribution is not normal, or if the
rates are distributed about 2 or more means,
then the error introduced may be appreciable.
The closeness with which the data can be represented by a function of the form of equation
(3) (i.e., the sum of 2 exponentials) is one
measure of the validity of this assumption.
Although in some subjects considerable scatter was evident in the concentration of radioactivity in the early samples, in only 2 cases
did it appear that the data could be better
represented by the sum of 3 exponentials.
This observation is not consistent with the
experience reported by Berson:0 his report
emphasized the necessity for postulating at
least 2 rates to describe trauscapillary exchange. The difference between his data and
those reported here may have arisen as a result of the difference between the duration
of observation in the 2 groups. His observations usually extended over a period of 30 or
more days and it was impossible to follow the
present group for more than 2 weeks. Because
of this, it is possible that an intermediate
rate (Avith half-life 4 to 6 days) may have
been overlooked. If this is a true discrepancy,
then the estimates of the transcapillary exchange rate will be in error by a variable
amount, depending upon the magnitude of
this second phase. Our average figure for
transcapillary albumin exchange rate (k,,e) of
0.026 per hour agrees reasonably well with the
value of 0.031 per hour reported by Schoenberger and others using a similar method of
estimation of the transcapillary exchange rate
from the plasma disappearance curve of I131labeled albumin.30 The 5 curves obtained by
these authors containing 3 exponential terms
gave values for the total exchange rate (transcapillary plus metabolic) that did not differ
greatly from values obtained from the curves
containing only 2 exponential terms. The values for plasma volume and transcapillary exchange rate obtained by Lewallen and others
on their patients studied in the euthyroid state
fall within one standard deviation of the regression line when compared with our data
presented in figure 4 right.51 Another consequence of overlooking an intermediate rate
in our data would be that we underestimate
the fraction of protein that is extravascular.
The average value for the extravascular fraction of the above data is .61 ± .03 (SEM),
which compares very favorably with Berson's
value of .60 ± .01 (SEM). Although we cannot be certain that we have not overlooked a
very fast component of transcapillary albumin exchange, this should not invalidate the
relation between plasma volume and transcapillary exchange rate described in figure 4
right, since such an error would yield plasma
volumes that are too high and exchange rates
that are too low. Such errors would tend to
obscure the positive correlation between
plasma volume and transcapillary exchange
rate.
Two other assumptions require justification.
The first is that reutilization of the radioiodine
does not occur. Evidence tending to justify
this has been presented by others.6'32 The
second is that metabolism of serum albumin
is not a property of all body cells, i.e., that
Circulation Research, Volume VIII, September 1960
PERMEABILITY OP CAPILLARIES TO PROTEIN
.1037
.05
.04
i
.03
2 02
r- +.78
.01
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v
Si
^02JOS
GLOBULIN EXCHANGE
Figure 9
.04
.05
GMS/KG/HR
Correlation between total vascular and extravascular globulin. The similarity between this and figure
6 can be seen. The intercept of the regression
equation for Y on X is significantly different from
zero (p <.O1).
Correlation between transcapillary albumin and
globulin exchange rates (r = .78, p <.07; y = 1.20
X. + .013). Dots represent albumin and globulin
moving from plasma to extracellular fluid and
circles represent albumin and globulin movement
from extracellular fluid to plasma. See text for
details. Although data on labeled globulin were
obtained in 12 patients, simultaneous studies with
both labeled albumin and globulin were done in
only 11, so that comparison is possible in only
11 subjects.
it occurs at some site supplied by only a
small segment of the total circulation. Evidence to support this assumption has been
obtained by Miller and Bale by perfusion
studies of the rat liver and carcass.25 The
curves published by Bei'son are presumptive
evidence that this is also true of man.11
The assumption that the steady state obtained is likewise an approximation at best
since there is evidence that the relation between vascular and extravascular compartments varies throughout the day.21'22 However, if there are no net trends, no serious
error should arise. While it seems reasonable
that this should be so in normal individuals,
it is much less likely that these conditions
should be met in a variety of diseases associated with disturbances in the vascular and
interstitial fluid volumes; however, some index of the validity of the steady state assumption in such situations should be afforded by
following body weight, plasma protein con-
centration and hematocrit. These were stable
in the above subjects during the period of
study.
There is evidence from several sources suggesting that this relation between total circulating protein, plasma volume and protein
permeability holds in individual subjects.
Chinard33 demonstrated a marked increase in
urinary albumin clearance following intravenous infusion of serum albumin to nephrotics. Moreover, when expressed as the ratio
albumin clearance/creatinine clearance, this
increase persists (i.e., the albumin clearance
increases out of all proportion to increase in
creatinine clearance, with this divergence of
the clearances becoming much more pronounced as the serum albumin concentration
approaches normal values). It is also interesting that this ratio correlated much more
closely with the plasma volume than with the
serum albumin concentration. This was interpreted as evidence that the permeability of
0.1
02.
0.3
0.4
0.5
EXTRAVASCULAR GLOBULIN
Figure 8
0.6
0.7
GM/KG
Circulation Research, Volume VIII, September I960
1038
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the glomerular capillaries to protein was
changed following the protein infusions, the
direction of change being consistent with the
data above. Gitlin's observation that the concentration of albumin in edema fluid of
nephrotics was .001 and .002 Gm. per cent on
2 occasions constitutes evidence from still
another source.34 This value for protein concentration is much less than one per cent of
the values reported by Stead and Warren35
for normal individuals.
Weech and others30 in plasmapheresis experiments made serial simultaneous measurements of lymph and plasma protein and noted
" . . . that the fall in lymph protein occurred
at a more rapid rate than the decline in
plasma protein." In an attempt at explanation they comment, " . . . diminished permeability of the capillaries has to us been the
most acceptable explanation . . . . " They did
not, however, have any data on plasma volume
or total circulating protein, and hence it was
not possible to relate this to changes in plasma
volume. Wasserman, Joseph and Mayerson37
have published the half-times and vascular extravascular albumin ratios for dogs before
and after infusion of an amount of albumin
approximately equal to the circulating plasma
albumin. Calculation of exchange rates from
their data using equation (4) above reveals
that, on the average, infusion of this quantity
of albumin resulted in a 3-fold increase of
the transcapillary exchange rate of albumin.
Evidence of a different sort was obtained by
these workers in experiments using infusions
of large quantities of dextrans of varying
molecular weights.38 They noted that when
the plasma volume was markedly expanded
with high molecular weight dextrans the concentration of protein in the plasma and lymph
tended to become equal. Thus, the experimental data available both in man and in animals
following infusion of albumin and plasmapheresis are all consistent with the interpretation of the data presented in the present
report.
Summary
A mean transcapillary exchange rate for
albumin and gamma globulin has been ob-
WALKER, ROSS, HAMMOND
tained from plasma disappearance curves of
I131-labeled albumin and I125-labeled gamma
globulin. A much closer correlation exists between transcapillary exchange rate for albumin and the plasma volume than between the
rate and serum albumin concentrations. Also,
for albumin this rate varies with plasma volume and circulating protein in such a manner
as to suggest that the capillary permeability
changes with changing plasma volume. The
relation between vascular and extravascular
albumin is consistent with this interpretation,
the extravascular mass of albumin appearing
to approach zero as vascular albumin approaches the vicinity of 0.35 Gm./Kg. In experiments in which I131-labeled albumin and
I125-labeled globulin were employed to obtain
simultaneous data on albumin and gamma
globulin, a good correlation has been obtained
between the simultaneously measured albumin
and globulin transcapillary exchange rates.
The ratio of the fractional capillary exchange
rates of these 2 substances is very nearly the
same as the ratio of their diffusion coefficients,
a relation to be expected if diffusion is the
mechanism of transcapillary exchange.
Acknowledgment
It is a privilege to acknowledge the assistance of
Mr. F. Green and the members of the cyclotron staff
at the Oak Ridge National Laboratory, without whose
help the I123 could not have been obtained and
processed.
We are indebted to Dr. D. L. Tabern and Mr. T. N.
Lahr for the preparation of II==-labeled globulin.
Summario in Interlingua
Un valor medie pro le intensitate del excambio
transeapillar de albumina e globulina gamma csseva
obtenite ab curvas de disparition de albumina a I1'11
e de globulina gamma a I121 ab le plasma. TJn multo
plus directe correlation existe inter le excambio transcapillar de albumina c le volumine del plasma quo
inter ille excambio e le concentration de albumina in
le sero. In plus, in le caso de albumina le intensitate
del excambio varia con le volumine del plasma e le
proteina del circulation in un maniera que suggere
que le permeabilitate capillar so altera con alterationcs
del volumine de plasma. Le relation inter albumina
vascular e albumina extravaseular es in congruentia
con iste interpretation, in tanto que le massa extravascular de albumina pare approehar zero quando le
Circulation Research, Volume VIII, September 1960
PERMEABILITY OF CAPILLARIES TO PROTEIN
albumina vascular approcha un nivello de 0,35 g per
kg. In expcriincntos in quo albumina a I m e globulina
a I'"' osscva utilisate pro obtener datos simultanee pro
albumina e globulina gamma, un bon correlation
essova obtenito inter le simultaneomente mesurate intensitates del cxcanibio transcapillar de albumina e
do globulina. Lo proportion del intensitates de exeambio capillar pro le 2 nientionate substantias es plus
o minus identic con le proportion de lor coeffieientes
do diffusion. Un tal relation es a expeetar si diffusion
es do facto lc mochanisnio del excambio transcapillar.
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Circulation Rescai-ch, Volume. Vlll,
Circulation
September
I960
Study of the Relationship Between Plasma Volume and Transcapillary Protein
Exchange Using I 131-Labeled Albumin and I125-Labeled Globulin
W. GORDON WALKER, RICHARD S. ROSS and JOHN D. S. HAMMOND
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Circ Res. 1960;8:1028-1040
doi: 10.1161/01.RES.8.5.1028
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