Nephrology Unit, Department of Medicine, University of Rochester
School of Medicine and Dentistry, Rochester, New York 14642
Previously, we demonstrated that
immunoglobulin G (IgG), dissolved in an isotonic solution in the
peritoneal cavity, transported rapidly into the abdominal wall when the
intraperitoneal (ip) pressure was >2
cmH2O. We hypothesized that this
was chiefly caused by convection and that diffusion of IgG was
negligible. To investigate the role of diffusion, we dialyzed rats with
no pressure gradient across the abdominal wall muscle for 2 or 6 h with
an ip isotonic solution containing
125I-labeled IgG. At the end of
the experiment, the animal was euthanized and frozen and abdominal wall
tissue was processed to produce cross-sectional autoradiograms.
Quantitative densitometric analysis resulted in IgG concentration
profiles with far lower magnitude than profiles from experiments in
which convection dominated. In other in vivo experiments, we determined
the lymph flow rate to be 0.8 × 10
4
ml · min1 · g1
and the fraction of extravascular tissue
(
s) available to the IgG to
be 0.041 ± 0.001. An in vitro binding assay was used to determine
the time-dependent, nonsaturable binding constant: 0.0065 min1 × duration of
exposure. A non-steady-state diffusion model that included effects of
s, time-dependent binding, and
lymph flow was fitted to the diffusion profile data, and the IgG
diffusivity within the tissue void was estimated to be 2 × 107
cm2/s, a value much higher than
that published by other groups. We also demonstrate from our previous
data that convection of IgG through tissue dominates over diffusion at
ip pressures >2 cmH2O, but
diffusion may not be negligible. Furthermore, nonsaturable binding must
be accounted for in the interpretation of tissue protein concentration
profiles.
 |
INTRODUCTION |
THE TRANSPORT of high-molecular-weight proteins to and
from the peritoneal cavity is important in clinical physiology and pathophysiology. During peritoneal dialysis (a dialysis technique that
relies on solute and water exchange between a solution in the cavity
and blood circulating in surrounding tissues), 5-15 g of protein
are lost per day (13). Massive quantities of protein can be lost to the
peritoneal cavity in conditions of severe hepatic failure or
intra-abdominal malignancy. In recent years, researchers have attempted
to combat the spread of metastatic colorectal or ovarian carcinoma with
the use of intraperitoneal (ip) monoclonal antibodies, to which are
bound high-energy radionuclides or cellular toxins (10). Understanding
the mechanisms of protein transport through tissue could prove
important in improving therapy, particularly in the case of regional
immunotherapy for malignancy.
In previous work (18), we demonstrated that immunoglobulin G (IgG),
dissolved in solution in the peritoneal cavity, transports into all
surrounding tissues. We measured the concentration profiles in all
tissues and attempted to fit a diffusive model to the data in the
abdominal wall; this effort failed to produce realistic parameters. The
presence of the solution resulted in an ip pressure of 3-4
cmH2O, and we have subsequently
shown that pressures above a threshold of 2 cmH2O produce convection of the
protein into the abdominal wall (19). In another set of experiments, we
showed that there was considerable nonspecific binding of the IgG to muscle (17). All of these results implied that our protein
concentration profiles resulted from a combination of diffusion and
convection with possible effects of binding to tissue.
In this paper, our goal is to study in vivo diffusion of IgG through a
defined tissue system. Because we already have data in the abdominal
wall from presumably convection-dominated transport, we have employed
the anterior abdominal wall muscle as a model tissue for this study to
carry out a comparison between our previous results and diffusive
transport. Our method minimizes convection of the protein from the
cavity into the tissue by maintaining a zero pressure gradient across
the abdominal wall. We use quantitative autoradiography (QAR) to
determine tissue concentration profiles and the binding characteristics
of the IgG to muscle. In addition, we have estimated the space within
the tissue available to the protein (protein void space) and the
lymphatic removal rate of IgG from the abdominal wall. We combine these
measurements with a mathematical model to estimate the effective
diffusivity of IgG in abdominal wall muscle.
| |
THEORY |
The concept used to model the tissue transport process is diffusion
through a porous bed, which has a fixed void fraction (s, the fraction of the tissue
from which protein is not excluded, see Fig.
1). Protein enters from the peritoneal side
of the abdominal wall and diffuses in the free state through the
tissue. Free protein can be "removed" from the tissue void by
either localized binding or lymphatics. If it is assumed that there is
no convective movement of the protein across the abdominal wall
(pressure gradient across wall = 0, see Fig. 1) and no metabolism of
the protein during the experiment, the mass balance for unidirectional
transport of unbound protein with binding and lymphatic removal is
|
(1)
|
s
is the solute or protein void fraction (fraction of total volume
available to the protein within the tissue space).
Deff is the
effective tissue diffusivity
(cm2/s) = Dvs,
where Dv = diffusivity within the protein void fraction of tissue.
Cv is the free protein
concentration within the void fraction, normalized to
CPC(t = 0), where CPC is protein
concentration in solution in the peritoneal cavity and
t is time (s).
FL is the lymphatic removal rate
from tissue (mol
protein · cm3
tissue1 · s1);
transendothelial transfer directly to blood is assumed negligible. FB is the rate of protein removal
from the pool of unbound or free protein, and
x is the distance from the peritoneum
(cm). Values for FL,
FB, and
s are found experimentally as
discussed in METHODS.
s and
Deff are assumed
constant for a given experiment. A mass balance of the total protein in
the tissue is
|
(2)
|
where
Cfree = sCv = unbound protein in tissue,
Cbound = concentration of bound
protein in tissue = g(Cfree),
a function that is defined by experiment, and
Ctissue = total protein
concentration in tissue. Boundary conditions are
where
x1 is the
subcutaneous side of the abdominal wall muscle. In the second boundary
condition, we assume that there is no boundary layer at the peritoneum
and that the concentration measured from the solution in the cavity
matches that at the peritoneal surface. In the third boundary
condition, we assume that the slope of the tissue concentration profile
approaches zero; this is demonstrated in the experiments. The set of
equations was solved with an implicit finite-difference computational
technique (8) programmed in Fortran and computed with an Intel
486-based computer.
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Fig. 1.
Tissue model concept used to formulate mathematical approach to
diffusion across abdominal wall. Tissue is a porous media with a tissue
void (s) through which
macromolecule diffuses. Blood and lymph capillaries are distributed
uniformly throughout tissue. Macromolecule does not penetrate cells or
blood capillaries but can be transported from tissue by lymph flow.
Solution containing antibody is kept in contact with peritoneal side on
the left and the peritoneum defines the
x = 0 boundary for the concentration
curve [total protein concentration in tissue
(Ctissue)]. Pressure
across the abdominal wall is maintained at zero.
CPC, protein concentration in
peritoneal cavity; QAR, quantitative autoradiography;
Pip, intraperitoneal pressure;
Pskin, pressure in skin;
 x, change in distance from
peritoneum.
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METHODS |
Animals and surgical preparation.
Sprague-Dawley female rats, 220-270 g, were used in all
experiments. Anesthesia was induced with intramuscular injections of
pentobarbital sodium. When the animal had lost its blink reflex, catheters were placed in the femoral artery (for blood pressure monitoring and sampling) and the femoral vein (for infusion of fluid or
anesthetic). Blood pressure was monitored with a Micromed blood
pressure analyzer and Cobe CDX III transducer. The systolic blood
pressure was noted to be >100 mmHg during all experiments. A
tracheostomy was performed. The animals were kept warm by a servo-controlled heating blanket and overhead heating lamp (36 ± 1°C). Euthanasia was carried out by an overdose (10 × anesthetic induction dose) of pentobarbital sodium or an overdose
followed immediately by decapitation to halt blood flow (used in QAR
experiments). These techniques are documented in previous publications
(14-19).
Isotopic tracers and solutions.
125I-labeled IgG (Amersham
anti-rabbit IgG, no. IM-134, immunoabsorbed against rat antigens;
5-20 µCi/µg protein) was used as the test molecule in the
diffusion and binding experiments and in the estimation of the void
fraction of IgG (s). This IgG
was used as a marker of IgG transport because we have established a
large body of data with it and have found that there is no specific binding to rat tissue, that the label is stable in the rat, and that
its half-life is appropriately long (460 ± 8 min) for its molecular
weight (19).
In the estimation of s, a
second label was required to mark the vascular space. We utilized a
second IgG (G-6638, Sigma Chemical) and labeled it with
131I (purchased from Amersham)
using Iodobeads (Pearce Chemical) and purified it by passing the
solution over an ion-exchange column (Bio-Rad 1-XP). The plasma
half-life of this IgG was approximately the same as that of IM-134.
All isotopic tracers before each experiment were checked for
degradation and free isotope by trichloroacetic acid (TCA). If free
isotope was >1%, the solution was purified further by mixing it with
saline and concentrating the mixture with a Centricon 30 microconcentrator (Amicon) by centrifugation (IEC Centra CL2). Dilution
and concentration of the isotopic solutions were repeated until the
free isotope was <1% by TCA precipitation. At the conclusion of the
experiment, samples of blood, urine, and peritoneal fluid were
processed with TCA to ensure isotopic integrity. The tracer concentration of body fluids and tissue samples was determined by
dividing the total counts per minute (measured with Beckmann 8000 gamma
counter) by the sample volume. Details can be found in our previous
publications (17-19).
In addition to the above procedures, we performed additional
experiments to check for label separation from the protein. Two animals
underwent 3 h of dialysis to load the tissue with
125I-IgG. Tissue samples of the
abdominal wall were collected and macerated and subjected to a
procedure similar to that used by Bratzler et al. (6) to extract the
labeled protein from the tissue. The extracted, labeled material
displayed the same TCA-precipitable fraction of >99% as the dialysis
solution or plasma samples. We therefore concluded that the abdominal
wall muscle lacks the capability to rapidly break down the labeled
protein during short-term experiments.
The experimental dialysis solution
(solution
A) consisted of an isotonic salt
solution [Krebs-Ringer bicarbonate, which contains (in mol/l)
0.12 NaCl, 0.01 KCl, 0.0021 CaCl2 · 2H2O,
0.025 NaHCO3, and 0.00028 KH2PO4
and 1.18 ml of 1 M
MgSO4 · 7H2O]
to which 5% bovine serum albumin (BSA, no. A3912, Sigma Chemical) and
0.01% Evans blue dye (no. E2129, Sigma Chemical; the dye marks the
peritoneum that makes contact with the fluid) were added. The 5% BSA
solution has been used in our experiments to prevent a significant loss of total protein from the serum in this species of rats. Fluid in the
cavity containing no protein has resulted in a 50% reduction in the
total serum protein over 6 h (14). The pH of the solution was adjusted
to 7.4, and osmolality was determined to be 290 ± 5 mosmol/kg.
Effect of albumin in solution on transport.
Despite the fact that the peritoneal solution is isotonic, the 5% BSA
solution may set up an oncotic difference between the bulk solution in
the peritoneal cavity and the interstitial space of the rat (typically
2%; Ref. 24). Prior experiments in our lab (19) demonstrated that
fluid absorption from the cavity for 3 h at 4 cmH2O of pressure was not affected
by altering the BSA concentration between 0 and 5%. However,
short-term (30 min) experiments in another rat species demonstrated a
significant slowing of the rate of absorption by a solution containing
5% BSA (34). Although the experimental methods used in each of these
studies were very different, neither study can truly resolve the
question of the effect of a 2-3% difference in albumin on transport of the labeled IgG for two reasons. First, transport across
the peritoneum is dependent on the total surface area exposed to the
solution, and evidence exists (16) that only 25-30% of the
dissected area of the peritoneum is touched by the fluid, even with use
of a large volume dwell. If the presence of the protein altered the
surface tension of the fluid between surfaces in the cavity, there is
the possibility that the peritoneal area of contact with the solution
was changed as well. Secondly, the rate of uptake may vary from tissue
to tissue, and changes in the contact area of specific tissues might
change the total absorption rates. Experiments in intact animals cannot
distinguish the specific surface areas that are touched by the
peritoneal solution.
Because the assumption of no convection in the abdominal wall is
important to the analysis of the data, we designed a specific set of
experiments to address the hypothesis that a protein difference of
2-3% BSA between the solution in the cavity and the interstitial fluid does not cause a significant flow from the tissue to the cavity.
To determine the effects of the dialysis solution on the fluid flux
across the peritoneum of the abdominal wall, we carefully glued small
plastic chambers to the serosal side of the anterior abdominal wall
(without touching the peritoneum within the chamber) of anesthetized
rats (n = 3). Details of the chamber
construction and testing can be found in a previous publication (16). A
predetermined volume of one of two solutions (Krebs-Ringer bicarbonate
or Krebs-Ringer bicarbonate with 5% BSA, as specified in
Isotopic tracers and solutions) was
initially placed into the chamber, with the height of the fluid at
1.4-1.5 cm. A small quantity of
[14C]mannitol
(0.2-0.3 µCi) was dissolved in each solution to provide a means
to calculate the residual volume in the chamber at the end of an
experimental period of 60 min. Volumes were determined by weight on a
digital scale accurate to ±1 mg; the density of the solutions was
assumed to be 1 mg/µl. After 60 min, the solution in the chamber was
carefully drawn up into the original syringe and needle, and the total
volume (weight) was redetermined. The chamber was then washed with the
Krebs solution containing no labeled mannitol to determine the residual
volume in the chamber and to prepare for the next 60-min dwell with the
other solution [residual volume = (wash volume × wash fluid
concn)/(chamber concn at t = 60 min)]. Solutions were alternated several times in each animal,
and data was taken from the second dwell period and thereafter (the
initial dwell with either solution was used as a period of stabilization of the tissue after the tissue preparation). The resulting fluxes [calculated as (final volume 
initial
volume)/(60 min × exposed surface area),
µl · min1 · cm2,
mean ± SE] were, for the Krebs-Ringer solution, 0.30 ± 0.08 (n = 6) and, for the solution
with 5% BSA, 0.37 ± 0.07 (n = 6). A one-way analysis of variance revealed no significant dependency on
the solution type (P > 0.5). These
results confirm our hypothesis that the 5% BSA solution does not
significantly alter the flux of fluid from the tissue across the
parietal peritoneum into the cavity because of a potential protein
gradient between the tissue and the fluid in the cavity. Although no
difference in fluid flux is noted in this model system with small
changes in the oncotic pressure of the bulk fluid, the result may not
apply to other serosal tissues. For the relative significance of the
observed volume flux to diffusive transport of IgG, see
DISCUSSION.
Protein binding assay.
Because the IgG protein had been selected for its lack of specificity
for rat antigens, our goal in these experiments was to determine the
nonspecific binding. We used the technique of Del Vecchio et al. (11)
to determine these characteristics in the abdominal wall of
Sprague-Dawley rats for the
125I-IgG used in the diffusion
experiments. Briefly, the abdominal wall of normal rats was rapidly
frozen, and 8-µm sections were cut with a cryomicrotome and fixed to
microscopic slides. All sections were preincubated for 30 min in a
solution containing 2% BSA and 10% chicken serum (no. 6773, Sigma
Chemical) to decrease binding of the labeled IgG to the glass slide.
Separate fixed sections were then incubated in solutions (made up of
the Krebs-Ringer bicarbonate solution containing 5% BSA) of increasing
concentration of the labeled protein for 1, 10, 60, or 240 min to test
the effect of time of exposure of the protein to the tissue (see Ref.
12). The solution was made up from the experimental dialysis solution containing 5% BSA. Each slide was then washed three times and incubated in a fourth tank of buffered saline for 30 min; on the basis
of the characteristic diffusion time across the 8-µm section [tchar = L2/4D = (8 × 104
cm)2/(4 × 108
cm2/s) = 16 s;
L = length,
D = diffusivity], the 30-min
incubation is more than sufficient for free IgG to diffuse from the
tissue. Slides were then dehydrated with ethanol and air-dried. The
amount of deposition was determined with QAR (see
QAR). The measurements of the total
binding of the protein were then correlated with the free concentration
in the incubation tank and with the time of incubation of the tissue
slice in a given concentration of tracer protein. These data permit the
calculation of an apparent binding constant. Forward binding or
association constants are typically found by using the technique
outlined with minimal time in a saline bath. Dissociation constants are
determined by carrying out the forward binding experiment, but the
final incubation medium (saline) is replaced by a solution containing
an overabundance of unlabeled IgG; the displacement of labeled IgG is
measured versus time. Unfortunately, the unlabeled form of the test IgG was not commercially available, and therefore this portion of the
binding assay could not be determined. Because the reverse constants
for specific binding are typically two orders of magnitude less than
the forward rate constants (12), we assumed that the determination of
the apparent association constant would permit us to adequately
describe the short-term (2-6 h) nonspecific binding of this
immunoglobulin.
QAR.
We have performed extensive studies with this technique, including
dual-label QAR (17-18). QAR was used to determine the local concentration of each tracer in the tissue at the time of animal death.
Briefly, at the end of an experiment in which tissue profiles were to
be measured, the following steps were taken in rapid succession: the
animal was euthanized with an overdose of anesthetic and decapitation,
the fluid was drained from the cavity, and the animal was rapidly
frozen to prevent further transport of the tracer material. The
anterior abdominal wall was cut from the carcass with an autopsy saw.
Sections (20 µm) were obtained horizontally through this tissue with
a Hacker-Bright cryomicrotome and were heat-dried. The sections were
placed with standards (tissues with known isotope concentration)
against X-ray film (Kodak Biomax MR) to produce autoradiograms. After
development, the films were analyzed with a computerized densitometer
(MCID) that measures optical density (OD) versus position in the
tissue. The isotopic standards are used to construct a calibration
curve (concentration vs. OD) to convert the unknown ODs from the tissue
samples to concentration. After exposure, the tissue slides were
stained with hematoxylin and eosin. By superimposing the autoradiogram over the tissue histology, we carefully determined the location of the
reading, and a concentration vs. position curve (diffusion experiments)
or mean concentration was obtained in a large area of the tissue
(binding experiments). For the diffusion experiments, the serosal
surface was used as the reference point, and concentration was plotted
versus distance into the abdominal wall.
Experimental protocol: IgG diffusion through abdominal wall muscle.
The diffusion of labeled IgG from the peritoneal cavity into
surrounding muscle must be studied when the solvent drag or convection is near zero. This condition can be obtained by eliminating the forces
for convection through use of isotonic solutions and by maintaining
zero hydrostatic pressure difference across the abdominal wall (see
Fig. 1 for conceptual model). We have previously shown that with the
cavity at zero ip pressure, the tissue pressures in abdominal wall
muscle of animals have been approximately zero (15). However, because
the standard deviation of the micropipette-servo null technique is
±1 mmHg (15), we cannot rule out a small gradient of 1 mmHg into
the tissue [0 (1 mmHg)]. Previous studies
have demonstrated no significant convective flow from the cavity at these low pressures (19). In addition, the 5% BSA solution, used to
maintain the total serum protein at a normal level, results in a
gradient of albumin from 5% in the cavity to approximately one-half
that value within the tissue. In none of our previous studies
(17-19) have we observed the protein added to peritoneal fluid to
result in fluid flow into the cavity or to diminish the flow of an
isotonic solution from the cavity into tissue. Our chamber experiments
(described in Effect of albumin in solution on
transport) have confirmed these observations and
determined that the addition of BSA to the dialysis fluid does not
alter fluid movement significantly across the abdominal wall
peritoneum. If we used a solution containing a lower albumin content,
the serum protein concentration would continuously decrease, resulting in decreased oncotic pressure in the microcirculatory system. During
the diffusion experiment with the 5% BSA solution, the BSA profile
would likely be similar to the IgG profiles with the exception that the
value for s would likely
increase. With these caveats, we assume that movement of protein into
the wall in the direction perpendicular to the peritoneum under these
conditions is caused by diffusion alone. The experiments were carefully
conducted with an attempt at measurement of all factors that could
influence the transport. However, the characteristics of this in vivo
model system should be taken into account when the data are compared with the results of other studies.
After surgical preparation, a laparotomy was carried out and the
viscera were retracted medially from both sides of the abdominal wall
(see Fig. 2). This, in effect, formed a
space between the viscera and the abdominal wall to ensure that the
isotonic solution, containing the labeled protein, would be in
continuous contact with the abdominal wall peritoneum. The cavity was
left open to ensure that ip hydrostatic pressure was 0 cmH2O at the abdominal opening.
Peritoneal and blood samples were collected every 30 min for 2 or 6 h
(minimum of 3 animals per time period) to allow for measurable
deposition of protein (17-19). The two experimental durations were
performed to determine the diffusivity by matching concentration
profiles at two different times; we assumed that tissue properties
[void space diffusivity
(Dv),
s] were constant over the
entire 6 h. At the end of each experiment the animal was euthanized,
and the final dialysate concentration of the labeled protein was
determined. The carcass was frozen and processed for QAR to obtain
concentration profiles within this tissue. The concentrations determined were total protein concentration (bound + free tracer), based on the total volume of the tissue (cells, interstitium, and
intravascular space).
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Fig. 2.
Cross section through peritoneal cavity demonstrating experimental
model. Cavity is opened with a midline laparotomy incision and left
open so that there is no pressure difference between solution in cavity
and skin. Hollow viscera are retracted (retractors not shown) so that
solution containing labeled immunoglobulin G (IgG) in cavity bathes
peritoneal side of abdominal wall. Tissues are collected in upper part
of abdominal wall to ensure that there are no convective effects of
hydrostatic pressure, which might be present in lower regions of
cavity.
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Experimental protocol: Lymphatic flow from abdominal wall.
Proteins are removed from the interstitial space of tissue by
lymphatics. Although the lymphatics of the abdominal wall are located
in the tissue planes and in the subcutaneous space (27), we assume in
our model that lymph flow is uniformly distributed in the tissue.
Despite data showing that the protein turnover rate is quite slow in
skeletal muscle (28), protein diffusion is also a slow process and
resulting tissue profiles may be affected by tracer removal via the
lymphatics. Therefore, the rate of lymph flow in the abdominal wall was
estimated by using a technique similar to that of Reed et al. (28),
which determines the rate of disappearance of a radiolabeled protein
infused or injected into the extracellular space of the
tissue. This experiment measures the outflow rate of
protein, which is contained within a localized region of the abdominal
wall interstitium.
Six animals were anesthetized and surgically prepared as described in
Animals and surgical preparation. During initial
experiments, it was found that the interstitial space of the abdominal
wall could be loaded with radioactive tracer
(125I-IgG) equally well from the
subcutaneous side or the peritoneal side. Because the animal is more
stable with a closed abdomen, in five of six experiments, loading of
the tissue was performed as depicted in Fig.
3A. As
shown, a plastic chamber (inner diameter 1 cm, with a flange, outer
diameter 2 cm; height 4-6 cm) was affixed with cyanoacrylate glue
to the subcutaneous side of the anterior abdominal wall muscle (16).
Solution
A containing 5% BSA, Evans blue dye,
and isotope (125I-IgG) was added
to the chamber until the height of solution was at least 3 cm above the
surface to cause a convection of the protein into the tissue. The
chamber fluid was sampled hourly and mixed every 30 min. After 1-2
h, the solution was removed from the chamber, and it was washed out by
rinsing with Krebs-Ringer solution. The chamber was carefully removed
from the tissue, and residual counts on the surface were removed by
washing with saline and making light contact with a gauze pad.
Typically, the Evans blue dye, which is tightly bound to the BSA,
showed staining in an area equal to the chamber base and through the
tissue thickness. If gross edema had formed in the tissue, the
preparation was not used. As noted above, urine was collected to check
on excretion of low-molecular-weight labeled protein fragments and free
iodine; in all experiments there was negligible excretion of the
isotope. Plasma concentrations of the isotopic protein were very low in all experiments, with a TCA-precipitable fraction of
125I of >99%.
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Fig. 3.
Experimental procedure to estimate protein clearance from the abdominal
wall muscle. A: chamber is attached to
subcutaneous side of abdominal wall muscle and a radioactive solution
is placed in chamber to load tissue immediately under chamber with a
flow rate Q induced by hydrostatic pressure P, which corresponds to
height of liquid in chamber. B: later,
chamber is removed and disappearance rate of labeled protein is
determined with a shielded scintillation probe and meter. It is assumed
that protein is removed from tissue by lymphatic capillaries only. cpm,
Counts per minute.
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To determine the turnover rate of the protein in the interstitium, a
directional scintillation probe (Dosimeter Model 41) was mounted as
illustrated in Fig. 3B, as close as
possible to the tissue that was previously under the chamber. The
localized labeled protein had a diameter approximately two-thirds of
the shielded probe detection area. Significant localized transport beyond the area of detection of the probe was not observed. Great care
was taken not to change the position of the probe with respect to the
tissue surface. The shielded scintillation probe was connected to a
digital ratemeter (Ludlum model 2241-2), and readings were taken
every 15 min for 5-6 h. The raw counts per minute (cpm) were then
corrected for background cpm, divided by the cpm at time
0, and plotted on semilog paper. The
half-life of the labeled IgG
(t1/2) was then
determined. The turnover rate or fractional removal rate was then
calculated as
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(3)
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The
local rate of lymphatic removal of the protein is
FL = klymphCtissue
[(cpmtissue/cpmperitoneal
cavity at
t=0)/(time × cm3 tissue), see
Eq.
1].
Ctissue is used in this expression
because Eq. 3 is based on the turnover
of all counts in the tissue, which includes both bound and free
protein. An estimate of the tissue lymph flow rate can be derived from
lymph flow = klymphif,
where if = the interstitial
void fraction (ml/cm3 tissue, see
Experimental protocol: Solute void
fraction). Because these experiments are carried out
under anesthesia, rates will likely be lower than if they were carried
out in awake animals (28).
Experimental protocol: Solute void fraction.
To calculate the role of diffusion with the mathematical model
(Eqs. 1-2),
s must be determined. The
solute void fraction, s, is
equivalent to the interstitial fraction,
if, for small solutes such as
mannitol, EDTA, or inulin. To determine
if, we injected a bolus of
[14C]mannitol
intravenously into rats with either no fluid in the peritoneal cavity
or a volume of the isotonic Krebs-Ringer with 5% BSA (after dwell time = 3 h). The
[14C]mannitol was
continuously infused to maintain a constant plasma concentration over 1 h. Ten minutes before the end of the experiment, 131I-IgG was administered to mark
the vascular space. At the conclusion of the experiment, the animal was
given an overdose of pentobarbital sodium and rapidly decapitated and
frozen. The abdominal wall tissue was collected, sliced, and processed
for QAR as described in QAR.
if was calculated as follows
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(4)
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We
have found that the abdominal wall muscle at zero ip pressure with
either fluid or no fluid in the cavity
(n = 3 each, means ± SE) has a
vascular space fraction of 0.01 ± 0.00 and an extravascular space
fraction of 0.19 ± 0.00 (no fluid in cavity) and 0.18 ± 0.02 (with fluid in the cavity), which by subtraction gives an interstitial
void fraction of 0.17-0.18. The fact that the
mannitol distribution space stays essentially the same after 3-4 h
of exposure to fluid at zero pressure indicates that the interstitial
hydration is relatively constant during these procedures.
Because of their size and molecular charges, proteins are excluded from
more of the tissue than small solutes, and
s for proteins is not
necessarily equal to if. One
method that is used to estimate the protein void fraction includes the
injection of one labeled protein intravenously (iv) 24 h before an
injection of a second marker of the vascular space. To calculate the
solute void space, it is necessary to assume that during the 24 h, the protein equilibrates with its void space in the extravascular compartment (2, 3). Labeled albumin is considered to come to steady
state in skeletal muscle within 24 h and to reflect the distribution of
native albumin (25). For IgG, this may not actually occur (23), and
therefore our technique could possibly underestimate the true quantity.
After the second injection, the plasma is sampled to determine the
concentration of both isotopes. The animal is euthanized, and the
tissues are collected, weighed, and counted to determine the
concentration of each isotopic label. The protein void fraction can be
calculated from
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(5)
|
where
the first term on the right side of Eq. 5 equals the extracellular fraction of the
"equilibrated" protein and the second term equals the
intravascular fraction of the tissue.
On the first day, the rat was restrained in the prone position, and
with sterile technique the dorsal side of its tail was surgically
prepared, draped, and locally anesthetized with 1% lidocaine. One of
the two veins in the tail was dissected out and catheterized with
sterile PE-10 tubing. Approximately 50 µCi of the test protein
(125I label) were injected iv via
the tail vein catheter. The catheter was then withdrawn, the vein was
tied off, and the wound was sutured closed. The animal was placed back
into the cage with ad libitum access to water and food. On the second
day, the animal was surgically prepared with iv and intra-arterial
catheters, as noted above. The second labeled protein
(131I-IgG) was injected iv, and
plasma samples at 5 and 10 min were obtained. The animal was then
euthanized by pentobarbital overdose and decapitation, and triplicate
tissue samples (100-500 mg) were collected from each side of the
abdominal wall muscle. The tissue samples and plasma samples were then
counted in a gamma counter with settings to exclude the lower-energy
isotope. The samples were stored for 10 half-lives of
131I (2.5 mo) and then recounted
for 125I.
Calculations and statistics.
All calculations were performed on a 486 Intel-based computer.
Microsoft Excel (5.0) and NCSS (Provo, Utah) were used for calculations
or estimation of statistical parameters. Tissue concentrations in the
diffusion experiments were normalized by the concentration in the
peritoneal cavity, which remained relatively constant throughout the
experiment. Mean profiles were calculated for each experimental duration by pooling all normalized data from all animals. With values
for FB,
FL, and
s, fitting of the model was
performed by varying
Dv. The upper
limit of Dv was
the value for IgG diffusivity in water.
Dv was varied
until good fits to the data were obtained by visual inspection. The
sums of the squares of the differences between model output and data
point for the full distance range and both experimental times
were then calculated to ensure that they were at a
minimum.
| |
RESULTS |
Lymph drainage from abdominal wall muscle.
Six experiments were carried out, and the half-life of the protein in
the tissue was ~1,610 min. Figure 4
illustrates the data and the mean values for 5 h. The mean turnover
rate (klymph) or fractional
removal rate was 0.43 ± 0.12 × 103
µl · min1 · g
tissue1. A
rough estimate of the actual lymph flow rate can be obtained by
multiplying the turnover number by the fraction of interstitial space
(if = 0.18 ml/cm3 tissue). This results in an
estimated lymph flow rate of 0.8 × 104
ml · min1 · g
tissue1. The mean
klymph is used directly in the
equation for the mass removal rate due to lymphatics
(FL = klymphCtissue).
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Fig. 4.
Data from experiment in Fig. 3. Natural logarithm of normalized mass of
IgG in tissue
[cpm(t)/cpm(t = 0)] versus time. Open symbols are individual experiments
(n = 6), and filled circles and line
represent means of readings.
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Estimation of protein solute fraction.
Six separate sections of the abdominal wall were used in each of six
animals to determine an estimate of the average of the nonexcluded
space in the tissue available to IgG. The overall mean (±SD) for
the interstitial space available to the protein was 0.041 ± 0.001. The total extracellular space available to the IgG
(125I-IgG) was 0.050 ± 0.014, with the estimated intravascular space (131I-IgG) of 0.009 ± 0.003.
Protein binding to abdominal wall muscle.
Figure 5 shows that the apparent binding,
as determined in the in vitro assay, has a linear dependence on the
free concentration, which is typical of nonspecific tissue binding. In
addition, the slope of the binding curve increases with time of
exposure of the tissue to the protein. A least-squares correlation of
the slopes of these four lines produces the following result
|
(6)
|
where
kB (binding
constant) = 0.0065 min1
(R2 = 0.99).
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Fig. 5.
Bound (Cbound) vs. free
(Cfree) IgG: in vitro binding of
labeled IgG to abdominal wall muscle for different times of incubation
(texposure).
See text for details.
|
|
From Eq. 6, an expression can be
derived for FB (see
Eq. 1)
|
(7)
|
Protein concentration profiles.
Figure 6 displays the 2- and 6-h diffusion
profiles of IgG concentration in the abdominal wall muscle (mean ± SD) normalized by dividing by the IgG concentration in the cavity at
time
0. The values represent total tracer
concentration in the tissue (Ctissue, bound + free). The
protein concentration in the peritoneal cavity was essentially constant
after injection into the cavity. Although the thickness of the
abdominal wall muscle is ~1.5-1.9 mm, only the first millimeter
of tissue adjacent to the peritoneum was used in the analysis because
of artifacts in the tissue caused by inadvertent removal of the skin
from the subcutaneous side of the abdominal wall.
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Fig. 6.
Normalized tissue concentration
[Ctissue /CPC(t=0)]
vs. distance from peritoneum of IgG for 2 ( ,
n = 336)- and 6 ( ,
n = 254)-h periods of diffusion. Data
are reported as means ± SD.
|
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The relatively large variability is typical of these local measurements
and mimics our previous results with QAR (17-18). The intercept of
the curve at the y-axis nearly doubles
over 6 h. If all the protein were unbound and if the transport were
purely diffusion, the intercept at x = 0 (the peritoneum) would be the same. The large difference indicates
that binding is likely a major factor in the observed transport of the
protein.
Mathematical simulations of IgG diffusion.
After substituting the expressions for
s,
FL, and
FB into Eq. 1, we numerically solved the equation for the boundary
conditions presented in THEORY.
Diffusivity was varied until a good fit was observed for both 2- and
6-h data. Because our technique may underestimate the actual fractional
tissue space available to the protein (see DISCUSSION), we increased the value
of s to 0.050 and recalculated the concentration profiles. Figure 7
displays the data with the model calculations for both values of
s and a
Dv of 2.0 × 107
cm2/s. The sums of squares
analysis showed nearly equal minima at either value of
s. The value for
Dv corresponds to
a Deff
(=Dvs) of 8-10 × 109
cm2/s.
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Fig. 7.
Model fits for 2- and 6-h data of Fig. 6.
Dv = 2 × 107
cm2/s with
s varied from 0.041 (dashed
lines) to 0.050 (solid lines).
|
|
To illustrate the effect of binding on the concentration profiles at 2 and 6 h, Fig. 8 displays the mean
concentrations and the calculated profiles of the free, bound, and
total tissue concentrations for the case of
s = 0.05 and
Dv = 2.0 × 107
cm2/s. As shown in the figure, the
profile for Cfree (dotted curves) changes slightly from 2 to 6 h, and the two profiles are nearly superimposed near the peritoneal surface. The profile for
Cbound (dashed profiles in Fig. 8)
is below the Cfree profile at 2 h, but it increases considerably over the next 4 h. The upward
displacement of the tissue concentration curve from 2 to 6 h is
therefore caused by binding of free protein that continues to diffuse
into the tissue.
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Fig. 8.
Model results for
Dv = 2 × 107
cm2/s,
s = 0.05, illustrating
predicted concentration profiles for
Cfree,
Cbound, and
Ctissue IgG at 2 and 6 h of
diffusion. Data are plotted without error bars ( , 2 h;  , 6 h).
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| |
DISCUSSION |
We have carried out a series of in vivo experiments designed to obtain
data necessary for the quantitative description of diffusion of IgG in
muscle. Our animal model permits the control of the major convective
force in transport of protein through the tissue, the hydrostatic
pressure difference across the abdominal wall. To minimize convection,
we maintained the overall pressure gradient at zero. We then kept the
peritoneal side of the abdominal wall in continuous contact with a
solution containing labeled IgG. By rapidly freezing the tissue at 2 or
6 h, we preserved the concentration profiles resulting from diffusion
of IgG into the tissue. Quantitative autoradiography was used to
determine the concentration profiles of Fig. 6. However, to use the
diffusive mathematical model to describe the transport, we were
required to determine the binding characteristics of the IgG, the rate of its removal from the abdominal wall, and an estimate of the actual
fraction of tissue space that is available to the protein (s). Our study provides a
unique set of data from a single in vivo tissue model. The assumptions
and limitations in our methods are discussed below.
Protein binding.
That binding is a significant factor in the diffusive transport of IgG
through the abdominal wall is apparent from Fig. 6. Diffusion is a
passive process in which molecules move from areas of high
concentration to areas of low concentration. The free concentration of
protein at the edge of the tissue can be no greater than the product of
the concentration in the peritoneal cavity (CPC) times the fraction of
tissue available to the protein
(s). Therefore, the intercept
of the concentration data at the peritoneal surface should not be
greater than 0.04-0.05, nor should it change with time if
s (protein void fraction)
within the tissue remains constant. In previous experiments we
demonstrated that the ip pressure was required to surpass 2 cmH2O before significant
convection from the cavity into the abdominal wall (19). We have
therefore assumed that with the hydrostatic pressure gradient across
the abdominal wall equal to zero, there will be no significant influx of fluid into the muscle and no change in the protein void space. In
addition, our determinations of the interstitial fluid fraction (if) have demonstrated that
exposure of the abdominal wall tissue to fluid in the peritoneal cavity
at zero pressure does not change if from the value obtained with
no fluid in the cavity.
A change in apparent protein space could result from binding, and we
therefore determined the binding characteristics of the test IgG with a
published in vitro assay (11), with modifications based on data from
Dower et al. (12). The apparent binding curves (Fig. 5) suggested a
nonsaturable, nonspecific binding of the IgG to the tissue.
However, the slope of the binding curves was directly dependent on the
time of exposure of the tissue to the labeled protein. Could this be
caused by continued diffusion into the tissue from the bulk solution? A
characteristic diffusion time for the 8-µm-thick sections can be
derived from T = (thickness)2/4Deff = (8 × 104
cm)2/(0.8 × 108
cm2/s) = 20 s. Therefore,
diffusional transport would likely not explain the continued binding of
the immunoglobulin. Unfortunately, the investigators who developed the
antibody-tissue binding assay did not check for this effect of time of
incubation, and therefore only data from a single incubation time
are available for comparison. Dower et al. (12) studied specific
binding of monoclonal antibodies (MAb) to antigens on cells grown in
vitro in monolayers.
The apparent nonspecific binding of different antibodies varies
considerably, depending on the conditions of the assay. Although the
true nature of nonspecific binding is unknown in most tissues, it is
thought to involve IgG interaction with Fc receptors on normal cells
(11) or to be caused by electrostatic effects in the tissue matrix
(22). Nonspecific binding is observed under low-salt conditions similar
to those used in our assay; it can be eliminated by solutions with high
salt concentrations (22). However, to increase the salt concentration
to 0.4-0.6 M would produce a very nonphysiological environment in
the tissue sections and would not reflect what occurs in vivo. Although
the test IgG has been processed with immunoadsorption to eliminate
specific binding to a panel of rat antigens, there is the possibility
that this polyclonal antibody has retained the ability to bind to
elements in the muscle of the rat abdominal wall.
When we compared the 60-min curve with our previous result for MAb 96.5 (specifically binds to FEMX-2 cells, a human melanoma cell line), we
found that the nonspecific binding to muscle or other tissues was far
less (bound pmol/g = 0.042 × pmol/ml of antibody; Ref. 17).
However, the nonspecific binding of MAb 96.5 was assayed with a large
amount of unlabeled antibody present in the solution. On reexamination
of our previous data (17), abdominal wall muscle and heart muscle, when
incubated with tracer concentrations of MAb 96.5 for 60 min, produced a
linear relationship with a slope of 0.25, similar to the 60-min line in
Fig. 5, which has a slope of 0.39. Del Vecchio et al. (11) found a
slope similar to ours when they determined the binding of MAb 96.5 to
antigen-negative tumor cells by incubating the cells for 60 min; the
slope of the bound versus free correlation was 0.25-0.5, close in
magnitude to our measurement. Therefore, the method of the binding
assay will greatly influence the quantitative result. We believe that our results reflect the in vivo binding of tracer quantities of IgG in
the model transport system.
Lymph flow from abdominal wall muscle.
An important factor to assess in a model transport tissue is the rate
of protein removal from the tissue. In accordance with pore theory, we
assume that transfer directly to blood across the wall of a blood
capillary does not occur (30). The chief means of removal of protein
from tissue is via lymphatics, which are located at tissue planes of
the abdominal wall (27). Because the rate of protein diffusion will
likely be a slow process, we cannot assume that the relative removal
rate from tissue is insignificant. We have assumed that the removal of
protein from the tissue is governed by a process that is uniformly
distributed in the tissue space. This is necessary because the model
does not contain specific spatially related sinks for protein transport
but distributes them uniformly. In addition, the form of the in vivo
model restricts us from experimentally assessing the function of
individual lymph capillaries.
Our experimental procedure is analogous to that of Reed et al. (28).
Instead of a direct injection of protein-containing solution into the
interstitium (28), we delivered the material into the tissue
interstitium with convection, to a specific area that was slightly
smaller than the diameter of the shielded scintillation probe. We then
determined the elimination rate of IgG from the local tissue space by
monitoring the total radioactivity in the tissue. Our turnover number
or fractional removal rate is similar to that found by Reed et al. (28)
for albumin in the hindleg muscle of an anesthetized rat (0.5 × 103
min1). Our estimate of
the lymph flow is almost the same number as that found by Reed et al.
(0.5 × 104
µl · min1 · g
tissue1; Ref. 28). Bill
(5), who infused radiolabeled protein for 24-48 h to maintain a
constant plasma concentration in awake rabbits, calculated a turnover
rate of 0.0017 min1 for the
triceps muscle, which is nearly four times the rate that we
found. Anesthesia is known to slow lymphatic rates by a
factor of four to five (28); the difference between our value and that of Bill is likely caused by this factor. We therefore conclude that the
IgG fractional removal rate that we have determined in the anterior
abdominal wall of the anesthetized rat is very similar in magnitude to
that found in skeletal muscle by other investigators.
Protein void fraction.
The interstitium can be described as a two-phase system in which a
colloid-rich, water-poor phase is in equilibrium with a water-rich,
colloid-poor phase. The colloid-rich phase consists of several
mucopolysaccharides, which exclude solutes and, in particular, protein.
These excluded solutes transport primarily through a tortuous,
water-rich phase by diffusion and convection. Recent
ultramicrospectrophotometric measurements of protein in the rat
mesentery (23) have demonstrated the heterogeneity of the interstitial
space between blood capillary and lymphatic. These investigators
demonstrated variable concentration profiles of endogenous serum
proteins in the tissue interstitium between blood capillaries and
lymphatics. If these native proteins are not in equilibrium, it is
unlikely that exogenous tracers will be at a uniform concentration in
their void space even after circulating for 24-48 h in the blood.
However, the overall tissue concentration may approach an in vivo
steady-state concentration from which one can estimate the solute void
space.
In vitro estimates of protein s
do approach true equilibrium in the tissue because the transport system
is a closed one: there is no lymph removal of protein. The excised
tissues are typically incubated in a medium containing the labeled
marker until equilibration occurs. Using this method, Schultz and
Armstrong (31) obtained an estimate of
s = 0.08 for albumin. Page and Bernstein (26) performed similar experiments in slices of cat heart
muscle and obtained s of 0.09 for inulin and 0.01-0.06 for dextrans with molecular weight of
150,000-180,000.
All in vivo experimental techniques used to estimate
s are based on the principle of
equilibration between the plasma and the interstitium after sufficient
time has passed after an intravenous injection/infusion of the
substance under study. On the basis of the observations discussed
above, "equilibration" of protein between the plasma and the
interstitium may be unattainable. The lack of equilibration between the
plasma and the solute void space in the tissue may lead to an
underestimation of the true void space. On the other hand, binding of
the protein to the tissue may tend to offset this effect. Although our
technique mimics that of others, all of these data must be interpreted
within the context of these limitations.
Bell and colleagues (3) injected labeled sucrose, albumin, and
fibrinogen intravenously into dogs and determined the plasma equivalent
space in the extracellular compartment after 24 h. In the interosseous
muscle of the leg, the estimated
s was 0.20, 0.05, and 0.002 ml/g of tissue, respectively. Bill (5), on the other hand, infused
labeled albumin and IgG to maintain a constant plasma concentration in
rabbits for 48 h; he determined the tissue concentration versus time
and divided tissue concentration by plasma concentration to obtain an
equivalent plasma space. For albumin, a steady-state concentration was
obtained in the triceps muscle after 24 h and the extravascular space
was estimated as 26 µl/g tissue or a
s of 0.026 ml/g tissue. For
IgG, the corresponding estimate of
s was 0.011 ml/g tissue. Other
investigators have noted significant increases in
s with tissue hydration (2) or
significant decreases with dehydration (29). Variation in species,
tissue, and experimental preparation including degree of hydration may
account for some of the variation in the measurements. A third group
(33) infused labeled serum albumin into rats for several days and found
the s to be 26% of the
interstitial space in the hindlimb muscle. This would correspond to a
s of 0.041 ml/g tissue (0.26 × 0.18 ml/g tissue, where
if = 0.18).
Our estimate of s of 0.04 ml/g
tissue is in the same order of magnitude as previously determined
values. However, we would caution that all of these data should not be
viewed as absolute determinations of the actual space but as a dynamic
property that likely depends on the specific tissue, the degree of
local tissue binding, and the state of hydration of the animal. We have
previously shown (19) that water transport into the abdominal wall
muscle is minimal at ip pressures <2
cmH2O and that the
if in the abdominal wall muscle
does not change after 4 h of exposure to fluid. Therefore, it is unlikely that a swelling phenomena occurs in the space available to the protein (s) over the
course of the experiment. However, our measurements of
s were carried out in animals
that had no large bulk of fluid in the peritoneal cavity. To obtain
such data would be technically quite difficult in our in vivo model.
Model results: Estimates of IgG diffusivity.
Although the model fits shown in Fig. 7 are quite reasonable given the
uncertainty in the data, the lack of a perfect fit to the data may be
caused by several factors. The model assumes an isotropic tissue bed;
the abdominal wall has at least one tissue plane in its cross section.
Lymphatic flow is averaged over the entire tissue; in reality, the
lymphatics are located in tissue planes and in the subcutaneous
space. Binding has been based on large cross-sectional
analyses of the abdominal wall and has not been studied for variation
with the abdominal wall. In addition, despite careful precautions to
eliminate significant pressure forces external to the tissue, we cannot
completely rule out local convection caused by pressure gradients
within the tissue. These assumptions in the model are necessary because
of limitations in our ability to obtain data that would justify more
complex approaches.
Care must be taken to define the diffusivity of a molecule as it
transports through a tissue. If the model of porous media is assumed,
which has a nonexcluded fraction of the tissue
s, the effective diffusivity
for the whole tissue is
Deff = sDv. Dv equals the
diffusivity within the tissue space available to the substance and
takes into account the tortuousity of the path and any retardation by
charged molecules surrounding the void space. Early estimates of
Dv for IgG in
normal tissue were on the order of 1-2 × 108 (32) to 2-4 × 109 (9)
cm2/s. The estimated diffusivity
in water for IgG is 6 × 107
cm2/s (9). These earlier
techniques did not account for binding of the protein. The effects of
specific binding on the transport of monoclonal antibodies have been
explored by several authors (see Refs. 1, 21). All demonstrate that the
total antibody concentration increases in tissue with increasing
binding effects and that if free protein is not separated from bound in
the analysis, the apparent transport can appear retarded in tumor
tissue. Our findings mirror this effect for nonspecific binding of
tracer quantities of IgG as well.
Recently, Jain's group has reassessed their previous estimate of
Dv with the
technique of fluorescence recovery after photobleaching (see Ref.
4). They have demonstrated in a mouse dorsal skinfold model containing human tumor xenografts that ~30% of the IgG that extravasated from the tumor circulation was rapidly bound in the tissue
and Dv was 35%
of the diffusion coefficient in water or ~2 × 107
cm2/s (4). Fortuitously, this is
the same number which we have obtained in normal muscle. The estimated
tortuousity within the tissue space (equals the actual distance
traveled divided by the shortest distance between two points, 
)
varies between 1.4 and 4.5 (7, 26). The average of all of these
determinations is 2.5 (31) and might account for the difference between
Dv and Dwater, where
Dv = Dwater /.
IgG diffusion vs. convection.
Because our original goal was to investigate the significance of the
diffusive transport of IgG versus the transport under conditions of
both diffusion and convection, we have replotted the results of Fig. 5
with data from an earlier study of IgG transport (18).
Figure 9 displays concentration profile
data from this study and from experiments in which the pressure
gradient across the abdominal wall muscle was 3-4
cmH2O. The profiles at 20 min and
200 min clearly demonstrate the marked effect that convection has on
the transport of large proteins. The IgG in the earlier study was a
monoclonal antibody (MAb 96.5) to a human melanoma cell line (FEMX-2)
and had no specific receptors in normal rat tissue. The binding
characteristics were not determined for different times of incubation,
but for comparable incubation times (60 min), the nonspecific binding
of MAb 96.5 was of the same order of magnitude as that of the IgG of
this study (17).
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Fig. 9.
Comparison of IgG concentration profiles from Fig. 6 with those of
previously published data (Ref. 18) in which convection was dominant
mechanism of transport.
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|
From the model using the parameters that have been estimated from our
data, we have calculated the diffusive flux of IgG across the
peritoneal surface to be on the order of 2-3 × 106
ml · s1 · cm2.
This flux is two orders of magnitude greater than the fluid flux that
was determined in the chamber experiments that were presented in
METHODS [water flux = 0.3 × 106
ml · min1 · cm2
or 0.005 × 106
ml · s1 · cm2];
therefore, the small fluid flux that may be present at very low ip
pressures should not interfere with the diffusion of IgG across the
peritoneum of the abdominal wall. However, higher ip pressures increase
the convection considerably and can have a significant effect on the
transport process. From our previous work (18-19), we estimate the
total IgG flux (convection and diffusion) into the abdominal wall at an
ip pressure of 4 cmH2O as ~2 × 105
ml · s1 · cm2,
which is an order of magnitude larger than the estimated diffusive flux
from our experiments. The actual ratio of convective to diffusive flux
may not be 10, however. This would assume that the tissue space remains
unchanged when under pressure from fluid in the cavity. In unpublished
studies, we have found that increasing the ip pressure to 4 cmH2O results in a doubling of the
extracellular space in the abdominal wall. This would likely increase
s and would therefore increase
Deff
(Deff = Dvs),
which would in turn increase the rate of diffusion. Fox and Wayland
(20) observed significant increases in
Dv of serum
albumin in the case of a hydrated mesentery
(Dv = 6 × 107
cm2/s) versus the nonhydrated
mesentery (0.4 × 107
cm2/s).
We conclude that convection, in general, dominates over diffusion, but
we would caution that diffusion of macromolecules in tissue may not be
negligible. More experimentation will be required to sort out the
complex structural changes of the tissue space under a variety of
stresses, the local flow regime, binding phenomena, and lymph flow.
This work was supported by National Institute of Diabetes and
Digestive and Kidney Diseases Grant R29-DK48479-01 and a grant from the Whitaker Foundation.
Preliminary results of this paper were presented in abstract form at
Experimental Biology 1996, Washington, DC, and at the 1996 annual
meeting of the Biomedical Engineering Society, University Park,
PA.
Address for reprint requests: M. F. Flessner, Box 675, 601 Elmwood
Ave., Univ. of Rochester Medical Center, Rochester, NY 14642.
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Abstract
Introduction
