Water and electrolyte acquisition
the placenta of the sheep
EDWARD
E. CONRAD,
Department
of Physiology,
Portland,
Oregon 97201
JR., AND J. JOB FABER
School of Medicine, University
CONRAD, EDWARD E., JR., AND J. JOB FABER. Water and
electrolyte acquisition
across the placenta
of the sheep. Am. J.
Physiol.
233(4): H475-H487,
1977 or Am. J. Physiol.:
Heart
Circ. Physiol.
2(4): H475-H487,
1977. -Fetal
plasma is known
to be hyperosmotic
with respect to maternal
plasma. Although
some solutes are actively transported
across the placenta
and
occur in higher
concentrations
in fetal than in maternal
plasma,
the total concentration
difference
is reversed by an
opposite difference in the concentrations
of electrolytes.
Calculations on the basis of the Kedem and Katchalsky
equations
for a homogeneous
membrane
demonstrate
that active solute
transfer and a physiologically
plausible
hydrostatic
pressure
difference
account for the known rates at which water and
electrolytes
are accumulated
in the fetus. Best estimates
of the
membrane
parameters
(per kilogram
fetal weight) are P&, c1
= 0.23 ml min+
kg-l, bS = 5.10V6 cm5 min-l
kg-’ dyne’l,
and cNaCI = 0.5. (where PS is the permeability-surface
area
product, L,S is the filtration
coefficient,
and u is the Staverman reflection
coefficient).
The driving
forces for water and
electrolyte
transfer
(active transfer and hydrostatic
pressure)
are not used as regulators.
Rather,
electrolyte
permeability,
which is the major constraint
on fetal growth,
and which
continuously
increases during
gestation,
makes possible the
exponential
increase in fetal weight during gestation
l
water metabolism;
growth; filtration
permeability
l
l
electrolyte
coefficient;
metabolism;
reflection
across
l
l
plasma osmolality;
coefficient;
diffusion
IN THE PREGNANT
SHEEP, the osmolality
of the maternal
plasma is normally somewhat higher than the osmolality of the fetal plasma (3, 39). It has been shown that
measurable
flows of water occur through the placental
barrier under the influence
of experimentally
created
osmotic gradients
(3, 15). These findings mean that, if
prenatal
water acquisition
by the fetus is an osmotic
process, the reflection coefficients of the various plasma
solutes must be ordered so that the net osmotic pressure
is directed from mother to fetus. There may also be a
hydrostatic
pressure difference.
Kedem and Katchalsky
(24-28) proved, on the basis of
thermodynamic
considerations,
that a minimum
of
three coefficients
are necessary to fully describe the
passage of solute and water through
a homogeneous
membrane.
In this paper, the values of these three
coefficients are calculated from the Kedem and Katchalsky equations on the assumption
that one must be able
to account for the normal rates at which water and
H475
of Oregon Health
Sciences Center,
electrolytes
are accumulated
in the fetus during gestation.
The conditions under which the equations are valid
are sufficiently
general to justify their use as a first
approximation
to a description
of water and solute
transfer across the placenta of the sheep. The analysis
(25, 26) holds true for electrolyte
and mixed solutions.
An electrical potential across the membrane
is permitted and no constraints are placed on the charge selectivity of the membrane
(25). However,
no net electric
current through the membrane
is allowed, but in view
of the capacitance
that one may ascribe to fetus and
placenta, the net transplacental
current is infinitesimal. There is the further condition that the system must
be isothermal.
The fetus is about 0.5” Celsius warmer
than its mother (1, 19), but the mean temperature
difference across the placental barrier is much less than a
I). A polycomponent
sysmillidegree
Celsius (APPENDIX
tem of solutes is permitted,
the osmotic pressure exerted
by the impermeable
solutes may be incorporated
in the
hydrostatic pressure term with very little error (25), and
the actual osmotic pressures exerted by other solute
species are additive
(23).
It appears, therefore,
that solute and water transfer
through
the sheep placenta may be approximated
according to the equations given by Kedem and Katchalsky. The strength of this approach is that no assumptions are made regarding
the nature of the physical
processes that determine
the permeability
properties of
the membrane.
It seemed worthwhile,
therefore,
to attempt such an analysis with the new data available
for
the placenta of the sheep.
METHODS
Adaptation
of Basic Equations
The equations
with which Kedem and Katchalsky
(24) described solute and water flow were presented in a
variety of forms. Most useful for the present purpose are
J, = L, @P - &U’AC),
cm/min
J S = oRTAC
+ (1 - cr)C J,, mmol/(cm2.min)
(1)
(2)
Symbols are listed in Table 1. The first equation states
that the volume flow J, (in ml/min per cm2 of membrane) is determined
by a filtration
coefficient
L, and
the sum of the hydrostatic
pressure difference
(Ap) and
H476
TABLE
E. E. CONRAD,
1. List of symbols
Molecular
defined
defined
defined
by equation
by equation
by equation
16
16
16
c
Mean concentration,
D
Coefficient
of free diffusion,
cm2. mix+
Subscripts:
0, and th identify coefficients
mmol/g
water,
Water
flow
Solute
flow per cm2 of membrane,
Amount
of solute,
for oxygen
and thermal
mmol
ml min-l
l
l
x, solute
coefficient
in
w, in water
dyne-l
Table 2
Calculated
transplacental
water
Transplacental
flow
of an inert
Transplacental
flow
of a marker
Transplacental
I;
of all solutes;
l
permeability
of 1 cm2 of membrane,
cm/min
a, actively transported
solutes; i, inert solutes;
oxygen; th, thermal conductivity
water
APPENDIX
T, total
cmm2 min+
Diffusional
+bscripts:
identifies
Real transplacental
solute;
cm/min
of 1 cm2 of membrane,
mmol/liter,
n, every
cm/min
per cm2 of membrane,
coefficient
solute;
+ V2CFa
V2CMa
flow per cm2 of membrane,
Filtration
J. J. FABER
and meanings
Concentration,
mmol/g water
Superscripts:
F, fetal; M, maternal;
a, arterial; v, venous (placental)
Subscripts:
a, actively transported
solutes; i, inert solutes; m, marker
experimentally
used to make plasma hypertonic
Volume
AND
A = lo-* cm
radius,
Coefficient
Coefficient
Coefficient
JR.,
flow,
solute,
Placental blood flow, ml min+
Superscripts:
as for C
l
mmol
solute,
flow,
flow of solute
ml. min-l
mmol
ml min-l
l
l
(unspecified),
l
l
n, general,
unspecified
solutes;
m, marker
solute.
In
APPENDIX
I,
02
mkg-l
min-l
l
l
min-l
kg-l
l
kg-l
kg-’
mmol
l
min-l
l
kg-’
kg-l
A = 10e8 cm
Pore radius,
Gas constant
Surface
area of placenta
Absolute
temperature,
Volume,
ml
Thickness
of placental
per kg fetal wt,
cm2 kg-l
“K
barrier,
cm
Concentration
of inert solutes in ultrafiltrate
mmol/g water; defined by equation 13
AC
l
of plasma
arriving
at fetal
CM - C*, concentration
difference across placental barrier, mmollg water
Subscripts:
a, actively transported
solutes; i, inert solutes; m, marker
solute;
concentration
difference of all solutes present
AP
Hydrostatic
Subscript:
II
Osmotic
CT
Reflection coefficient (dimensionless)
Subscripts:
a, actively transported
solutes; i, inert solutes; m, marker
Fig. 3; x, solute experimentally
used to make plasma hypertonic
0
side of barrier,
PIRT,
n, general,
as required
by fetal body composition,
unspecified
solute;
T identifies
total
pressure difference across placental barrier,
dyne cme2
o, nominal value of 42 mmHg, Table 3 and Fig. 3
l
pressure,
defined
dyne * crne2
in equation
2 and in Ref. 24
solute; n, every solute; o, nominal
value of ui, Table 3 and
OSMOSIS
AND
PRESSURE
FILTRATION
H477
IN PLACENTA
that fraction
(CT) of the Van’t Hoff osmotic pressure
difference
(RTAC)
that is actually exerted across an
imperfectly
semipermeable
membrane.
The letter (T is
the reflection
coefficient
(47) and AC is the solute concentration
difference
(mmol/g water). The second equation states that the solute flux J, across the membrane is
the sum of a flux driven by the concentration
difference
AC and a flux carried across the membrane by the net
volume flow J,. The product oRT is the diffusional
permeability,
P, measured under conditions of zero volume flow across the membrane
(24), and C is the average solute concentration
on the two sides of the membrane. l Equations 1 and 2 apply to single-solute
systems
only.
It is proper to normalize all flows and the coefficients
(L p and wRT) per kilogram fetal weight, because in the
sheep the functional
area of the placenta appears to be
proportional
to fetal weight in the last trimester
of
gestation.
This is evident
from measurements
of the
electrolyte permeabilities
(3) and the urea permeability
(29, 41). Fetal and maternal
placental blood flows also
appear constant if expressed per kilogram
fetal weight
(15, 48). When placental surface area per kilogram fetal
weight is defined by S (cm2/kg), it follows that J,S = &
is the real transplacental
water flow, per kilogram
fetus, defined in the preceding
companion
paper (3) as
positive from mother to fetus; the value of volume flow,
the product J,S, is so nearly equal to the water flow, JWS
= &, that the two are used interchangeably.
L pS is the
placental
filtration
coefficient,
per kilogram
fetal
weight. wRTS = PS is the diffusional
permeability
of
the placenta per kilogram
fetus, defined in the preceding paper (3), and J,S = & is the solute flux per kilogram fetus, defined as positive from mother to fetus.
Hence, equations 1 and 2 may be rewritten
in the
form
Qr = L,Shp
4s = PSAC
- aL,SRTAC,
ml min-l
l
+ (1 - a)C &, mmol
l
l
kg-l
min-l
l
kg-l
(3 a )
(4a)
The pressure difference,
Ap, and the solute concentration difference,
AC, are defined positive when the pressure or the concentration
in the maternal
plasma exceeds the corresponding
quantity in the fetal plasma.
Since plasma is a polycomponent
system, equation 3a
must be modified to incorporate
the sum of the osmotic
pressures exerted by all the solutes, n
CL=
L,S{Ap
- RT C (u~ACQ},
mlmin-l
l
kg-l
(3b)
Equation
4a applies to each of the n solutes separately; the total solute fl ux is therefore given by the sum
of the individual
fluxes
.
% s = SC (P,AC,>
W)
+ a, w
- un )C,}, mmol
l
min+
l
tions 3 b and 4b is determined
by L,S and the P,S and gn
for each solute. Whereas L,S is a function of the placental membrane
and the solvent (water) only, P,S and or,
are also functions
of the solute under consideration.
These coefficients must be determined
from the available experimental
data.
Membrane
Quantity Determined
with Osmotic Experiments
In the preceding paper (3) the calculated water flow
through the membrane
was obtained from the formula
tic=
QFa(CmFa - CmFV)/C,FV, ml .rnin-l.
of the placenta
expressed
jrp
=
@V
_
@a,
ml.
l An electrical
potential
between
fetal lamb and ewe does not
imply that there must be an electrical potential across the placental
exchange area. It may and probably does arise elsewhere.
The assumption of a transplacental
membrane potential in the sheep would
require a cascade of additional assumptions
of such complexity
that
it must be rejected as implausible
in the absence of compelling
evidence.
kg-1
min-I.
6)
The flow of the marker solutes (qm) across the membrane is the difference
between outflow of the marker
solute in the umbilical
vein and inflow in the umbilical
artery:
CTm= QvCmFV - QYZmFa, mmol
Rearrangement
of equations
am=
Combination
the marker
&C,FV
l
min+
l
kg+
- &CmFv, mmolmir+
l
m
4a applied
to
(9)
- Cm + Cmcm), ml min+
Fv
(8)
kg-l
al- = (&C,FV + P,SAC,)
IW
(7)
5-7 yields
of equation 8 with equation
solute (m) yields
l
l
kg-’
The data reported
in the preceding
paper show that
equation
9 may be simplified:
CmFV and Cm are not
grossly different after the infusion of hypertonic mannito1 or sucrose, typical differences would be t 10%. It will
be shown later than mm is of the order of 0.5-0.8. Hence,
the denominator
is approximately
equal to C,“‘*gm.
Figures 2 and 3 of the preceding paper (3) show that at a
total concentration
difference
across the placenta of 40
mM, the calculated
water flow is of the order of 3
ml min-l
kg-l, and the permeabilities
(Pm S) of the
marker solutes Na+ and Cl- were found to be of the
order of 0.2-0.3 ml min+ kg-l. Since CmFVis also much
greater than AC,, equation 9 can be simplified
to the
form
l
l
l
kg-l
bY equa-
(5)
where QFa is the umbilical
blood flow and CmFa and CmFV
are the concentrations
of a marker solute m (Na+, or
Cl-, or K+) in the fetal arterial
and venous plasmas.
This formula gives the real water flow, &., only if the
marker
solute is completely
impermeable
((T, = 1).
Since this is generally not the case, we derive an expression relating
real water flow to calculated water flow.
The real water flow is the difference between fetal placental outflow and inflow
l
ql* = cTc/om, ml min-l
l
The passive behavior
kg-l
In order to apply
osmotic experiments
tlr =
L,S[Ap
l
kg-’
equation 3b to the results
(3), it is rewritten
of the
- RT n$ @,A&)
L
-ORTV~AC~], ml- min+
(3d
kg-l
H478
E. E. CONRAD,
where x is the solute (mannitol
or sucrose) that was
used to make one of the two plasmas hypertonic.
Differentiation of equation 3c yields
d&/dAC,
= - (T,L* SRT,
and combining
equations
m12*min-1~kg-1~mmol-1(11)
11 and10
d&/dAC,
=
- cmcX I+, SR T, ml2 min-l
l
=
- vi L, S R T , ml2 min-l
l
(12d
kg+ . mmol+
Wb)
l
kg-l
l
mmol-l
to descri .be the qua ntity (slopes of regression
lines in
figures 2 and 3, Ref. 3) tha .t was m .easured in the osmotic
experiments.
The various simplifications
made in the
derivation
of equation 12b could cause it to be in error
by no more than 20%. This value may seem high, but
the subsequent calculations
will be shown to be quite
insensitive
to errors in equation l2b even if as large as
50% (Figs. 3 and 4 below).
Equations
3b and 4b in a Form
to Placenta of Sheep
J. J. FABER
other processes still gives rise to concentration
differences across the placenta that must be taken into account in the description of the filtration
of water. Hence
equation 3b becomes
- RTC
where d&/dAC, is the slope of the regression lines relating transplacental
water flow to transplacental
concentration gradient
(Figs. 2 and 3, Ref. 3).
The preceding PaPer further
showed that any of the
marker solutes Na+, K+, and Cl- could be used to calculate transplacental
water flow with no significant
difference in the results. Equation 12a shows that this is only
possible if there are no significant
differences
between
the reflection
coefficients (T, of these solutes. Since the
marker solutes belong to the cla ss of “inert”
solutes
(defined below)
we wi .ll write vi for urn. APPENDIX
II
demonstrates
that the reflection
coefficients for the solutes used to make the plasmas hypertonic
(mannitol
and sucrose) are essentially
1.0. We therefore
rewrite
equation 12a as
d&/da&
AND
11r = LpS{Ap - RTC (CiACi)
we find
l
JR.,
Applicable
The preceding paper provides two experimental
measurements
for the evaluation
of the membrane
coefficients L,S, PiS, and ci: one to be used with equation 12b
and the other the direct measurement
of the diffusional
permeability
of the inert solutes Na+ and Cl-, (PiS). It is
therefore,
to derive
a third independent
necessary,
expression to evaluate
all three constants empirically.
Under conditions of normal fetal growth, the acquisition of certain solutes is independent
of the pressure
filtration
and diffusion process. This may be so because
of active transport or because the materials
are derived
from fetal metabolism
(e.g., urea and bicarbonate).
The
transplacental
concentration
difference
of the “active”
solutes, represented by AC,, is relatively
constant under
normal conditions. All remaining
solutes are defined as
“inert” solutes. Normal fetal growth requires an influx
of these inert solutes also, which is represented
by xqi.
The molality
of the transplacental
ultrafiltrate
of maternal plasma is defined by the variable
p as
(13)
P = CC&)I& 7 mmol/g water.
Although
filtration
ma ,y be assumed not to affect the
transfer of active solutes, the transfer of these solutes by
(14)
(caACa)},
ml min-l
l
l
kg-l
where the subscripts a and i identify the active and the
inert solutes, whose osmotic forces are additive (23). The
small difference
in colloid osmotic pressures between
maternal
and fetal plasmas (15, 38) is legitimately
incorporated into the hydrostatic
pressure difference
(24).
Equation
4b is rewritten
in terms of the inert solutes
only and since Ci = (CiM - l/2 ACi), equation 4b becomes
a.
= SC (PiACi)
i
(15)
+ &I: { (1 - ci) (CiM - ‘/2ACi)}
mmol
l
min-l
l
kg-’
The variable sqi can be eliminated
by combining equations 15 and 13.
The Na+ and Cl- concentrations
constitute 98% of the
total concentrations
of the inert solutes (Na+, K+, Mg++,
and Cl-) in the plasmas of fetal and maternal sheep, and
as explained above, there is good reason to believe that
the reflection
coefficients for the inert solutes Na+ and
Cl- are not very different.
Equation 14 can therefore be
simplified
with little error by substitution
of UiACi for
x(uiACi),
where Ci is the total concentration
of inert
solutes and gi is a weighted average inert solute reflection coefficient. Similarly,
equation 15 can be simplified
since PNa+S = Pcl-S = PiS (3). Hence, the system of the
two equations 14 and 15 can be solved for ACi and qr.
The result is a quadratic
expression of the form
a(ACi)2
where
a=
the variables
-l/2cTi
b = {-PiS
(1
-
+ b(ACi)
+
C
= 0
a, b, and c are defined
gi)
l
(16)
by
(L,SRT)
(16d
+ l/2 (1 - CJLpSAP
- [p - (1 - Cri) Ci”] (riI$mT
C
l/2
(1
U6b)
- ui) a,AC,L,SRn
= (p - (1 - ci) Ci”)* (I&Sap
- caAC,L,SRT)
(16~)
and where a,AC, stands for X(cr,AC,). The single physically possible solution of this equation can be shown to
be
ACi = [- b - (b2 - 4ac)1/2]/2a
(17)
With this solution in hand qr can be solved from equation 14.
Since fetal water inflow (&) and electrolyte
concentration (p) are known from normal gestational
growth
data of the sheep fetus and its fluids, there are three
equations
(no. 12b, 14, and 17) with three unknowns
(L,S, ci, and Ap).
RESULTS
Estimation
of Parameters
for Placenta of Sheep
L,S, PiS, and ui
The PS product for Na+ was found to be 0.20 ml/
(min. kg) and for Cl- it was found to be 0.27 ml/
OSMOSIS
AND
PRESSURE
FILTRATION
H479
IN PLACENTA
(min. kg) (3). We will assign the average value of 0.233
ml/(min
kg) to the salt NaCl. According
to equation
12b, the value of(ribSRT
is 61 m12*min-1*kg-1*mmol-1
(3) and at 39”C, the value of the product RT is 2.595. lo7
erg/mmol,
hence CibS
is equal to 2.35 10V6 (cm5
dyne-l min-l
kg-l). The most direct approach
to solv-ing all three variables
would be the determination
of
vi by the application
of pore theory (10,44,46) as applied
to the sheep placenta by Boyd and co-workers
6), but
this is not valid for ions.
The theoretic relation between the ratio of pore diameter and solute diameter
and the resulting steric and
frictional
hindrance to diffusion is visualized by a plot of
the ratio of placental permeability
and coefficient of free
diffusion
(PS/D) against molecular
radius on logarithmic scales. The details of this application
of Renkin’s
formula
can be found elsewhere
(16). Figure 1 shows
such a plot for permeability
data on the sheep placenta
from a variety of sources, which are listed in APPENDIX
II. Our new results (3) with Na+ and Cl- are divergent
to
a degree that cannot be explained by errors of measurement. It would be hazardous,
therefore,
to use pore
theory to predict reflection coefficients of electrolytes.
A more reliable method for estimating
the reflection
coefficient is the use of equation 1 7 and the normal rates
of water and solute acquisition
during gestation.
Acit is
cording to the reasoning
developed
in METHODS,
necessary to make estimates of: a) the osmotic pressure
exerted by the con .centration
di .fference (AC,) between
maternal
and fetal plasma of solutes that are transferred independently
of water flux, and b) the ratio p of
inert solute and water flow across the placenta.
Ad. a: APPEN DIX II lists those solutes whose influx
into the fetal lamb does not significantly
depend on the
rate of water filtration
for either of two reasons: they
may be actively transported
( e. g ., glucose, lactate, frucl
l
l
l
5.0
3H20
Urea
\
\I,Ethylene
\
I
glycol
\
\
Erythri
\
\
d-glucose
\
tol I\\
\
\
Nat (goat
-glucose
Nat
2.0
-
I
t
-I-
-4.0i
1
0.2
1
1
04
I
0.6
0.8
Log a (x IO-'cm)
FIG.
1. Restricted
diffusion across sheep placenta . Ratio of permeability and diffusion coefficient in water PS/D declines with increasing size of diffusing
particle,
indicative
of a geometric constraint.
Line is the best fit of Renkin equation (44) for diffusion
through
cylindrical
pores. The term D’/D,
is ratio of diffusion
coefficient
through porous membrane and coefficient of free diffusion in water,
a is molecular
radius and r, pore radius.
Data from Table 4 in
APPENDIX
II. Best fit is obtained
at r = 4.55- 10vs cm. Note logarithmic scales.
tose, amino acids, calcium, and inorganic phosphate), or
they are produced by the fetus and their diffusional
permeability
is so high that the second term on the
right-hand
side of equation 4a is insignificant
in comparison to the first, the diffusional
term. Urea and
bicarbonate
(COZ) fall in this latter category. APPENDIX
III discusses the evidence
for active transport
and for
predominantly
diffusional
transfer.
Ad. b: Table 2 identifies “inert” solutes (whose transfer is significantly
affected by filtration).
The quantities
transferred
to the fetus per unit time near the end of
gestation were computed from fetal composition
at various gestational
ages (17) and fetal growth (4). Amniotic
and allantoic fluid accumulation
was also accounted for
(37, 51). Total water required
for fetal growth and the
growth of the extrafetal
fluid volumes was found to be
2.1 10e2 ml/(min
kg), and total inert solute flux was
kg). Metabolic
water
found to be 5.054 pmol/(min
accounted for 3.9. 10d3 ml/(min
kg), the ratio p was
therefore
0.295 mmol/ml.
The relation between qr, ACT (= CACi + XAC,), Ap,
and ci as specified by equations 14 and 17 is shown in
Fig. 2. In the sheep, the normal
gestational
rate of
water accumulation
is 1.71 10e2 ml/(min
kg), and there
is a total concentration
difference
between maternal
and fetal plasma of 7.2 mmol/kg water (the average of
the osmolalities
determined
by freezing-point
depression osmometry
(3, 39) and vapor-pressure
osmometry
(3) and the total difference in solute concentration
(3) after correction
for plasma water content).
Figure 2
shows that the reflection
coeficient
vi = 0.52 and the
hydrostatic
pressure difference
between maternal
and
fetal plasma in the placental capillaries
Ap is about 42
mmHg (not corrected for a difference in colloid osmotic
pressures (15, 38) which is included in Ap). We conclude
that these values are the normal ones for the placenta of
the fetal sheep in the last trimester
of gestation (Table
3)
The inert solutes exert an osmotic pressure of about
-124 mmHg and the active solutes exert an osmotic
pressure of about +84 mmHg. The hydrostatic
pressure
difference
is 42 mmHg. Of these 42 mmHg, about 40
mmHg balance the osmotic pressure associated with the
difference
in inert and active solute concentrations.
Thus, a net filtration
pressure of only 2 mmHg suffices
to supply the growing sheep fetus with water.
The concentration
difference
in inert solutes (major
electrolytes)
is generated by the sieving of these solutes
when maternal
plasma is filtered through the placental
barrier. Fetal (major) electrolyte
requirements
are met
in two ways. Part of it is met by electrolytes that diffuse
across the barrier under the influence of the generated
solute concentration
difference
(about 57%) and the remainder is the amount that is carried across the barrier
with the filtrate
(about 43%); these two contributions
correspond
to the first and the second terms, respectively, on the right-hand
sides of equations 4 and 15.
l
l
l
l
Sensitivity
of Derived Parameters
ui and Ap
to Experimental
Error in Experimentally
Determined
Variables
Equations 14 and I7 can be solved for the value of the
reflection
coefficient
ci and the hydrostatic
pressure
H480
E. E. CONRAD,
TABLE
2. Fluxes
of water
and inert solutes during
last trimester
of gestation
Fetus
Amniotic
o.7501
AND
Fluid
Allantoic
Fluid
.17g2
concentrations,
o.1433
0.06tS3
J. J. FABER
in sheep
.2472
Solute
Na+
K+
Mg2+
Cl-
JR.,
mmollg
water
.1034
.0564
. oog4
.0504
0.0163
.09!j4
o.0775
Fetus6
Amniotic
flui@
.0514
Allantoic
97
fluis,
7
Total
C (dV/dt)
V(dC/dt)
C (dV/dt)
V(dC/dt)
Water
1.2
l
1o-2
+o
+4.4*
Metabolic
water
1o-3
1,720
+o
816
+o
192
+o
924
+o
solute concn is 5,050 nmoUl.17
mllmin
lO-3
+4.6.
l
flux,
V(dC/dt)
-kg
3.9 10d3; net water
production*
+453
+40
l
flux,
+o
Solute
Na+
K+
Mg2+
Cl(Average
C (dV/dt)
nmollmin
-104
+30
influx:
+o
l
1.71. 10v2
-kg
+258
+230
+418
-126
10m2 ml = .295 mmol/g H,O
(= 2.1 10-2)
+235
-230
2,097
+ 194
1,310
192
+o
1,451
= p.)
Total
5,050
l From Refs. 8 and 54.
2 From Ref. 51.
3 From Ref. 17 (fetuses of 120 days’ gestation or older only, data converted from per kilogram
weight to per kilogram
water).
4 From Ref. 37.
5 Based on assumption
that 76% of fetal sodium content is extracellular
(Ref. 54, p. 2l),
in a sodium-to-chloride
ratio of 140/100.
6 Fetal growth estimated from Barcroft’s
data (4) at 1.62 10m2 g/(kg min), suitably adjusted for
water content and electrolyte
contents which are constant from 120 days’ gestational
age onward (17).
7 If total content N is given by the
product of volume and concentration,
N = V C, the time derivative
(rate of inflow) is given by dN/dt = C(dV/dt)
+ V(dC/dt);
data from Ref.
8 Fetal oxygen consumption
is approximately
6 ml min+ . kg-l (21). Since water production
and carbon dioxide production
are com37.
parable for most metabolic fuels, we will assume a ratio of 0.8 mol of water produced for every molecule of oxygen used. This metabolic water
production
of 3.9 10m3 ml/(min
kg) must be subtracted
from the total fetal water requirements
to obtain net transplacental
water flow.
l
l
l
l
l
TABLE 3. Normal
values for sheep placenta
in last trimester of gestation
Parameter
/
Normal
GM
0.272
PNa+S
0.20
ed
0.27
Values
Units
Source
mmol/g
water
Ref.
3
+ 0.036*
ml/ (min
. kg)
Ref.
3
+ 0.036*
ml/ (min
. kg)
Ref.
3
Ref.
3
/
a*L,SR
T
ekg-1 s
m12. mine1
61
mmol-1
-5.1.10-3
AC,
mmol/g
water
Table
5
Table
5
(+a
0.845
Dimensionless
P
0.295
mmol/g
water
Table
2
ilr
1.71.
ml/(min
. kg)
Table
2
mmol/g
water
Text
1o-2
-I
-2
0
0.02
Transplacental
0.04
0.06
Water Flow 4, (ml mid kg?
FIG.
2. Total transplacental
solute concentration
difference AC,
(=C AC, + X ACi) in mosmol/kg
water, plotted against fetal water
acquisition
rate, qr, in ml/(min
kg). A positive value of AC, indicates maternal
solute concentration
exceeds fetal solute concentration. Total concentration
difference and fetal water acquisition
rate
are a function of reflection coefficient of barrier for inert solutes, ci,
and hydrostatic
pressure
across barrier,
Ap, (defined positive
if
maternal
pressure exceeds fetal pressure
in the placental capillaries). Conversely,
if AC, and qr are known, values of reflection coeficient and hydrostatic
pressure
difference
can be read off graph.
Normal point is indicated
(+). Values from Table 3 were used to
solve equations 14 and 17.
+7.2.
ACT
RT
2.595
ui
0.52
1O-3
* 10’
ergs
* mmol-’
At 39°C
Dimensionless
Fig.
2
Fig.
2
l
difference
Ap, once
best estimates for
Table 3. In order to
the derived values
all other variables
are known. The
these other variables
are listed in
investigate
the sensitivity
to error of
for AD and (7;. we computed AD and
42
AP
5.10-e
Lls
mmHg
cm5. min-1
dyne-’
* Mean
mkg-1 a
From above
data
+ SE.
ci> while all other variables were held constant at their
best estimate (Table 3), except for one which was varied
from 0.5 to 1.5 times its best estimate. Figure 3 and 4
show how ui and Ap vary when each of the other variables in turn deviates from its best estimate.
The derived value for the average inert solute reflection coefficient ai (Fig. 3) is almost comnletelv
insensi-
OSMOSIS
AND
PRESSURE
FILTRATION
H481
IN PLACENTA
difference in the concentrations
of inert solutes, ACi, or
in the inert solute permeability
PiS.
One cannot express much confidence in the derived
value for the transplacental
difference
in hydrostatic
pressure, Ap. Figure 4 shows that the derived value of
the hydrostatic
pressure difference is inordinately
sensitive to errors in the best estimates of all other variables,
with exception only of the filtration
coefficient complex,
(TiL,SRT.
A Different
05
1.0
Value of Pa
FIG.
3. Inert solute reflection coefficient, (Ti 7 relative to its nominal value of 0.52, plotted as a function of each of placental permeability parameters
as they are varied individually
from 50% to 150% of
their best estimates
(Table 3). Slopes of these relations are measures
of sensitivity
of derived value oi to errors in empirical
values of
placental permeability
parameters.
a,AC, stands for C ((T,AC,).
Experiment
to Estimate
ci
Equations
14 and 15 show that mi and Ap can be
solved if water flux & and solute flux I]Qi are known. In
addition
to values derived
from normal
gestational
growth,
experiments
in which transplacental
fluxes
were actually measured can be used also.
In an experiment
on the renal clearances
of fetal
sheep (18), fetal urine was collected externally
over long
periods of time, causing a significant
increase in transplacental water flow. One protocol was published in toto
(Table 4 of Ref. 18). Over a period of 18 days, 9,250 ml of
fetal urine was drained. It contained 281 mM of inert
solutes (Na+, K+, Cl-). Fetal weight at birth was 4.9 kg,
a value so high that one must assume that growth was
not affected by the experiment.
Water flow, &, therefore, was 7.3 10V2 ml/(kg*min)
plus the water flow
necessary for normal growth,
1.7 10e2 ml/(kg min), a
total of 9 low2 ml/(kg min). Similarly,
solute flow qi
was 2.21 10m3 + 5.054 10m3 = 7.27 10m3mmol/(kg
min).
Although the results could have been presented in the
form of a graph like Fig. 2, it is more instructive
to plot
the transplacental
hydrostatic
pressure and the transplacental total concentration
difference
AC, as a function of the unknown inert solute reflection coefficient ci*
This has been done in Fig. 5. It is seen that the
pressure difference
Ap is very sensitive to the assumed
value of gi and that only values of ui in the range of
about 0.76-o. 78 are compatible with physiologically
reasonable pressure differences.
The center value of ci of
0.77 agrees only moderately
well with the value of 0.52
suggested by the analysis presented in Fig. 2 and presented again in Fig. 5. The drainage
experiment
analyzed in Fig. 5 is potentially
capable of a much more
precise estimation
of mi than the analysis of normal
gestational
values, but with only one experiment
available, there is no basis for judging whether the difference
in reflection
coefficients is individual
or systematic.
l
l
l
l
1.0
1.5
Relative Value of Parameters
FIG.
4. Difference
in hydrostatic
pressure between maternal and
fetal placental capillaries,
Ap, relative to its nominal value of 42
mmHg, plotted as a function of each of placental permeability
variables as they are varied individually
from 50% to 150% of their best
estimates (Table 3).
tive to errors in the estimates of the variable
aiL,SRT,
which contains the hydraulic
conductivity
L,S, or to
errors in the estimate of the osmotic pressure exerted
by the “actively
transported”
solutes,
the sum
Z((T,AC~T).
The reflection coefficient would be in error
approximately
in proportion
to errors in the best estimates of normal gestational
transplacental
water flow,
qr, or in the ratio p, or in the normal transplacental
Constraints
l
l
l
on Fetal
l
l
Growth
Figure 2 shows that for a reflection coefficient of 0.52,
the rate of fetal water acquisition
is accelerated by an
increase in the hydrostatic
pressure difference between
maternal
and fetal capillaries
in the placenta.
It is
evident, however, that this mechanism is a weak one. A
large increase in pressure is required
for a modest increase in transplacental
water flow.
Nevertheless,
it is known that fetal growth is continuously accelerating
during gestation
(4, 17, 51). Fetal
water content being about 75% of fetal body weight (54),
an accelerated growth rate directly reflects an acceler-
E. E. CONRAD,
H482
JR.,
AND
J. J. FABER
FIG. 5. Transplacental
hydrostatic
pressure difference,
Ap, (mmHg)
and solute
concentration
difference, ACT, (mmol/kg)
as functions
of inert solute reflection
coefficient,
(Tip of the placental barrier. Data from experiment
published
by Gresham
et al. (18) are represented
by broken lines and data
from normal gestational
growth
(Table 2) are represented by solid lines.
Inert Solute Reflection Coefficient,
ci
ated water acquisition
rate. It is of interest, therefore, to
investigate
which of the placental
permeability
variables has most control over the rates at which water and
electrolytes
can pass from mother to fetus. Figure 6
shows the effects of variations
in the parameters
of
equations 14 -17 on the rates of fetal water and electrolyte acquisition.
Both qr, the water flow, and zqi, the
electrolyte flow are insensitive
to changes in the filtration coefficient, L,S, and progressively
more sensitive to
changes in transplacental
pressure difference,
Ap, the
osmotic pressure exerted by the active solutes represented by the sum C ((T,AC,) the electrolyte permeability
P,S, the required electrolyte
concentration
of the ultrafiltrate p, and the reflection
coefficient of the placental
barrier for electrolytes,
pi.
DISCUSSION
Applicability
Permeability
of Theory to
of Sheep Placenta
This study required some simplifications
that are only
approximately
correct. The sheep placenta is not a homogenous single-layer
membrane
as required
by the
theory in the form used here (26-28). Figure 7 shows the
ultrastructure
of this barrier
in which the presence of
several histological
layers is evident. The ultrastructure
of the sheep pl acenta differs signi ficantly from those of
the ra bbit (49) or gui .nea pig ’ (11) placentas. The dense
extracellular
material
between maternal
and fetal canillaries (arrows in Fig. 7) of the sheep placenta is absent
in these other species. One may speculate, therefore,
that the presence of this dense extracellular
material in
the sheep placenta is related to the very high diffusion
resistance compared to the diffusion resistance found for
the placentas of the rabbit and the guinea pig (13). It is
known that, in the rabbit placenta, the diffusional
resistance for small molecules is lower across the endothe-
lial layer than across the center of the placental barrier
(13). If this is also true for the sheep placenta,
the
behavior of the membrane
as a diffusional
barrier may
be approximated
with a single-layer
model.
Although
the osmotic pressures exerted by a variety
of solutes are additive
(23), it is not correct to assign a
single reflection
coefficient, ci, to all electrolytes.
However, the major electrolytes
are Na+ and Cl- whose
diffusional
permeabilities
in the placenta of the sheep
are at least comparable
(3). The error was therefore
accepted in the analysis.
It is clear that these approximations
restrain
the
interpretation
of the results. Quantitatively,
the results
are reliable for the estimation
of the average inert solute reflection
coefficient vi, which is not unduly sensitive to errors in the empirically
determined
parameters.
The hydrostatic
pressure difference,
Ap, however,
is so
sensitive
to errors of measurement
in the empirical
parameters
that no certain value can be given for it.
This uncertainty
is compounded
by the approximations
that went into the analysis.
Mechanism
ElectroJyte
of Fetal Water and
Acquisition
The presence of a hydrostatic
pressure
difference
across the placental
barrier
helps to explain that the
maternal
plasma osmolality
exceeds the fetal plasma
osmolality, in spite of a net inflow of water into the fetus
during
the entire gestational
period.
Although
the
quantitative
value of this pressure difference is not yet
known with acceptable accuracy, the values suggested
by the present calculations
are well within the range of
physiologically
reasonable
pressure differences.
Moll
and Kunzel (42) measured maternal
arterial pressures
in the smallest placental
arteries that were accessible
to direct puncture. In cotyledonary
arteries of the sheep
which were from 0.5 to 1 mm in outside diameter,
they
OSMOSIS
AND
PRESSURE
FILTRATION
H483
IN PLACENTA
0.06
3
70AC,,
4)
LPS
over placental transfer
of water
FIG. 6. Control
and electrolytes.
Top : rate of transplacental
water
flow, &, when each v .ariabl e that controls it is varied in turn from 50% to 150% of its normal values in
Table 3. Slopes of these lines are measures of degree
of control exercised by each of these variables.
Bottom: rate of fetal inert solute acquisition,
4, when
each variable that controls it is varied in turn as
above (rr,A C, = C (G~AC,); PS = PiS).
Relative Value of Parameter
PS
q&l
AP
LPS
B
I
I
I
I
I
I
I
I
I
1.0
Relative Value of Parameter
recorded a mean arterial pressure of 84 mmHg (42). This
value was in sharp contrast to the corresponding
values
recorded in the guinea pig (12 mmHg),
the rat (14
mmHg), and the rabbit (8 mmHg) (42). Fetal arterial
blood pressure in the sheep is about 39 mmHg, umbilical vein pressure is about 7 mmHg, and uterine vein
pressure is about 3 mmHg (48). The available
evidence
is compatible with hydrostatic
pressure differences of 20
to 60 mmHg between the maternal
and fetal capillaries
in the placenta of the sheep. The existence of such a
large pressure difference
is also compatible
with the
finding that large increases in maternal
placental vein
pressure do not affect the pressures or the flow in the
fetal placental circulation
(48).
The mechanism of fetal water and electrolyte acquisition in the sheep appears to be a combination
of hydrostatic pressure and the active transfer of some metabolically important
substrates. The present best estimate
of the hydrostatic
pressure difference is of the order of 40
mmHg and the osmotic pressure exerted by the actively
transported
PENDIX
solutes is about
80 mmHg
(Table
5 in
AP-
III).
Regulation
Electrolyte
of Fetal Water and
Acquisition
Placental parameters.
Figure 6 shows that the magnitude of the hydraulic conductivity
of the sheep placenta,
L,S, is almost without
influence
on the rate of fetal
water uptake. Placental
hydraulic
conductivity
would
be a significant
factor in transplacental
water flow only
if the conductivity
was less than l/lOth of the observed
value. This is because of the total hydrostatic
pressure
difference
across the placenta of 42 mmHg, 40 mmHg
are required to balance the osmotic disequilibrium
due
to the concentration
differences
across the barrier
of
inert and actively
transported
solutes. This finding
means that the prime constraint
on fetal growth is not
water acquisition
but electrolyte
acquisition.
It follows
that the magnitude
of the diffusional
H484
E. E. CONRAD,
JR.,
AND
J. J. FABER
FIG. 7. Electronmicrograph
of nearterm sheep placenta.
Abbreviations:
FC, fetal - capillary;
E, endothelial
laver: TE. tronhoblast
enithelium
(fetai origin); CL: crypt lining (a modified
uterine endometrial
layer); J, junction
between
fetal and maternal
tissues;
dark intercellular
material
in this
junction is absent in placentas of rabbit, guinea pig, and man; MBS, maternal blood space. Bar is 2 pm. Perfusion fixation through fetal circulation
with glutaraldehyde/Formalin,
embedded in VCD; JEOL JEM 100s electronmicroscope.
Courtesy
of Dr. Kent L.
Thornburg
of Dept.
of Physiology,
School of Medicine.
permeability
of the placenta for inert electrolytes
(PiS)
must have a major effect on the rate of water transfer.
Figure 6 confirms this by showing that transplacental
water flow and the diffusional
permeability
of the placenta are for practical
purposes proportional
to each
other.
For the same reason, the magnitude
of the inert solute reflection coefficient oi must affect the rate of water
transfer. Figure 6 shows that this reflection
coefficient
is indeed one of the most powerful controllers
of the rate
of fetal water acquisition.
A decrease in the reflection
coefficient decreases the counter osmotic pressure of the
inert solute concentration
difference
generated by sieving. A greater fraction of the driving pressure difference
remains available
for pressure filtration.
The osmotic pressure difference
exerted by the actively transported
solutes is represented
by the product
cr,AC!, in Fig. 6. Its control over fetal water acquisition
is a relatively
weak one.
Nonplacental
parameters.
The parameter
/3, the ratio
of inert solute and water flows, has a significant
influence on fetal water acquisition.
This emphasizes again
that the main constraint
is on electrolyte
uptake. This
influence
of p explains
why, in the experiments
in
which fetal urine was drained over a period of several
weeks (18), transplacental
water flow could be more
than 5 times greater than the normal rate of fetal water
acquisition.
The value of /3 in these experiments
was
only 87 mosmol/kg
as opposed to 295 mosmol/kg during
normal
gestation.
Under
conditions
of normal
fetal
growth, the value of /3 is fixed by the compositions of the
fetal body and the extrafetal
fluids; therefore,
@ cannot
be considered a controlling
variable.
The effect of the hydrostatic
pressure difference,
Ap,
is much too small to explain the continuous
increase in
fetal water demands during the progression
of gestation. It is too small even to account for the day to day
regulation
of fetal water content and cardiac output
(14), in the sheep. Moreover,
fetal arterial
blood pressure rises with gestational
age, which is hard to reconcile with an increase in Ap.
In conclusion,
this analysis shows that the combination of a transplacental
difference in hydrostatic pressure and the active transport
of some metabolites
accounts quantitatively
for fetal water and electrolyte
acquisition
where neither
one can do so alone. The
analysis, however,
does not shed light on the question:
does the fetus control placental
transfer
or does the
placenta control fetal growth?
If fetal control exists in the form of feedback steering,
what is the most powerful
possibility?
Control of the
placental
electrolyte
permeability
(PiS) would be adequate to explain the ever increasing
fetal water and
electrolyte acquisition
rates during the course of gestation. The experimental
results (3) fully agree with the
theoretic prediction
that the permeability
of inert solutes (Na+, Cl-, K+, Mg2+) must increase during the
course of gestation. Urea permeability
is known to increase also (29,41), but fetal control over these increases
has not been demonstrated.
Fetal control of the reflection
coefficient
(+i, for instance by endocrine mechanisms, would powerfully
control fetal water and electrolyte
uptakes. Although
such
a mechanism
need not account for the gestational
increase in the acquisition
rates, its existence would make
available to the fetus an hour to hour control of extracellular water volume. We plan to investigate
the possible
role of antidiuretic
hormone at a later time.
There is no evidence of fetal control of the concentration difference of actively transported
solutes (AC,) and
OSMOSIS
AND
PRESSURE
FILTRATION
H485
IN PLACENTA
there is no evidence of an increase of this difference
during the course of gestation. The effect of AC, on fetal
water acquisition,
moreover,
is not a large one. The
calculations
do not give evidence for a major contribution of bicarbonate
ion, which is only a fraction of the
total concentration
difference
AC,, in the long term
regulation
of fetal water and electrolyte acquisition
(32).
Similarly,
the hydrostatic
pressure difference Ap across
the placental barrier has too little effect on the regulation of fetal water and electrolyte acquisition
rates to be
considered a regulator
(14), at least in the sheep. These
conclusions
must be drawn notwithstanding
the fact
that the hydrostatic
pressure difference
and the difference in concentrations
of actively transported
solutes
together constitute the driving force for water and electrolyte transfer.
Somewhat
contrary
to our expectations, variation
of the driving
forces does not appear to
be used for the regulation
of water and solute flows. It
seems, rather, that another variable,
namely, the electrolyte permeability
PiS (3), is responsible
for the long
term regulation
of these flows, in the face of comparatively constant driving forces.
It should be noted that these conclusions apply only to
the placenta
of the sheep, and perhaps to the very
similar
placenta of the goat. In the placenta of, for
instance, the rabbit and the guinea pig, the diffusional
permeabilities
do not decline as rapidly with increasing
molecular weight (13, 16). Theories of fetal water acquisition that are falacious when applied to the placenta of
the sheep (14) may well be valid in these species. The
human placenta, judged histologically,
is much more
closely related to those of the rabbit and the guinea pig
than to those of the sheep and goat. It is likely that the
regulation
of transplacental
water
and electrolyte
fluxes is fundamentally
different
in these species.
APPENDIX
Transplacental
I
Difference
in Temperature
Placental exchange can be shown to be essentially
isothermal
by
comparing the diffusivities
of oxygen and heat. The carbon monoxide
diffusion capacity of the sheep placenta has been shown to be 0.54 ml/
(min. mmHg. kg body wt), and the oxygen diffusion
capacity has
been estimated
to be 1.2-2
times
higher,
ca. 0.86 ml/
(min. mmHg. kg) (33). With an oxygen solubility
of about 0.021 ml/
(ml. 760 mmHg) (2) the permeability-surface
area product for oxygen
is PO,. S = 3.1. lo4 ml/(min . kg). Since oxygen may be assumed to
have the entire placental area available for its diffusion, the permeability surface area product is given by
Do,. S/w = PO,. S, ml/(min
. kg)
(18)
where w is the average thickness
of the placental barrier and Do, the
coefficient of diffusion of oxygen in placental tissue. The value of DO,
is not exactly known,
but estimates
in plasma (55) and in other
tissues (36) suggest a value about 1.2 10m3 cm2/min. Thus, equation
18 yields a value for S/w of about 2.6.10’ cm/kg fetus.
The thermal conductivity
of tissue is not much different from the
thermal
conductivity
of water
(53) at 4O”C, for which 0.001499
cal . s-l. crnm2 * “C +cm is given. If we approximate
1°C by 1 Cal/ml, and
convert seconds to minutes, the thermal conductivity
is (Dlh) about
9. 10h2 cm2/min. The “thermal
permeability”
of the placenta is therefore given by
Fetal oxygen consumption
is of the order of 6 ml/(minkg)
(21),
and at a caloric equivalent
of 5 Cal/ml, fetal heat production is of the
order of 30 cal/(min
kg). The average temperature
difference across
the placental barrier
is therefore
about 30/(2.3* 106) = 1.3. 10V5 “C.
Exchange is therefore
isothermal
to within
a fraction of a millidegree Celsius.
l
APPENDIX
Estimation
Reflection
II
of Molecular
Coefficients
Radii
and
Molecular radii were calculated with the equation of Gierer and
Wirtz,
as described
by Durbin
(10). We used a water radius of
1.65 lop8 cm (5). Permeability-surface
area products for the nearterm sheep placenta were taken from the literature
and, where
necessary,
corrected for fetal weight (Table 4).
If the placental pathways
are only slightly larger than the diffusing molecules, the ratios of the permeability-surface
area products to
the coefficients of free diffusion (PS/D,) will decline with increasing
molecular diameter. Such appears to be the case for inert nonelectrolytes in the placenta of the sheep (Fig. 1).
An equation derived by Renkin (44) describes the diminution
in
the ratio PS/D, that is to be expected if the passages are cylindrical.
The best fit between
experimentally
determined
perrneabilities
of
l
TABLE
4. Summary
of literature data on permeability
of sheep placenta and coefficients of free
diffusion in water at 39°C
Substance
Dw3g, Coef
If Free Diffusion,
l
( lop4 . cm2)/
min
Molecular
wt
3H20
22
Na+
2
Na+
PS,
Permeability,
ml/(min
. kg)
Refl$tion
Coef3
+ 53
(4)
1.80
+ 0.036
(5)
2.61
(0.801)
+ 0.036
(6)
1.99
(0.404)
2255
0.201'
Moltcular
Radius2
1O-8 cm
b>
0.2678
(goats)
Cl-
0.265'
3
K+
39
2.03
(0.443)
Ca2+
40
3.75
(0.979)
Urea
60
2.55
0.778
2.82
(0.886)
2.90
0.885
3.34
0.949
+ 1.6g
(11)
14.9
!I 0.810
(9)
22.3
+ 2.1"
(5)
6.86
2
17.0
HCO,-
61
Ethylene
glycol
62
Glycerol
92
Erythritol
122
o.514g
+
0.044
WI
3.73
0.978
n-Glucose
180
6.5414
I!I
0.83
(10)
4.27
0.998
L-Glucose
180
o.117g
(2)
4.27
0.998
Mannitol
182
0.023g
(2)
4.26
0.998
Sucrose
342
5.23
1.0
o.3gg
(8)
l
Pth . S = Dth . S/w, ml/(min.
kg)
(1%
in analogy to equation 18. Substitution
of the value of S/w of 2.6.10’
cm/kg into this equation yields a thermal
permeability
of about
2.3. lo6 ml/(min
kg), or cal . min-l .OC-’ kg-‘.
l
P * S values
are means
+ SE.
l Corrected
to 39”C, where
necessary,
by adjustment
of
the factors
for absolute
temperature
and the viscosity
of water.
Note units.
2 Computed
from the coefficients
of free diffusion
in water
and the Gierer
and Wirtz
equation
(10) with a
radius
of the water
molecule
of 1.65.10~*
cm (5).
3 Computed
by use of the equation
given
by Renkin
(44) and a best-fit
pore radius
of 4.55.10-*
cm (see Fig. 1). Values
for
electrolytes
are placed
in parentheses
to stress their
questionable
validity.
4 From Ref.
52.
5 Calculated
from data in Ref. 40 with
shunt
corrections
applied
to the maternal
(16%) and fetal
(6%) placental
circulations
according
to the concurrent
exchange
model
g From
Ref.
6 From
Ref. 34.
7 From
Ref. 3.
* From
Fig. 4 of Ref. 43.
6.
lo From Ref. 41, data on fetal lambs
of 2-4 kg.
l1 From Ref. 40, data on fetal lambs
(12).
of 2-4 kg.
l4 From Ref.
l2
50.
From
Ref.
l5 From
9, calculated
Ref. 30.
from
ba+,
A~~+, and
hHcon-.
I3 From
Ref.
35.
H486
E. E. CONRAD,
inert nonelectrolytes
in the sheep placenta and the Renkin equation
was obtained by assuming a pore radius of 4.55 * lo-* cm (Fig. 1); also
see Boyd et al. (6). The value of n-glucose (but not L-glucose) was
anomalous,
plausibly
because of active transport
of this sugar into
the fetal circulation.
The electrolytes
Na+ and Cl- also showed
anomalous permeabilities;
polarity of charge was not discriminated
but the presence of charge was, suggesting
a difference in dielectric
constants
in the membrane and in free solution (5).
Renkin (10, 44, 46) also derived an expression
for the reflection
coefficient as a function of the ratio of molecular and pore radii. The
reflection
coefficients
calculated
from this expression
and an assumed pore diameter
of 4.55 lop8 cm are listed in Table 4. Since
diffusional
permeabilities
for electrolytes
do not fit a model based
only on geometric
and frictional
considerations
(Fig. l), it is not
likely that their reflection
coefficients
can be accurately
predicted
from a similar model.
TABLE
5. Solutes whose
affected by water flux
Plasma
protein
g/100
ml”
Plasma
water
mllliter
transfer
Maternal
Fetal
6.65
3.42
concn,
content,
III
Solutes Whose Transfer
is not Appreciably
Affected by Filtration
of Water
Solutes whose net transfer
is from mother to fetus and which are
present in fetal plasma in a higher concentration
than in maternal
plasma are presumably
transferred
by an energy-dependent
molecular mechanism.
Table 5 shows that the fetal plasma concentration
exceeds the maternal plasma concentration
for fructose, amino acids
(ZO), calcium (17), and phosphate
(17); the references given for each
of these substances
in the above line give evidence that net transfer
is nevertheless
in a direction
from mother to fetus. Glucose is a
special case since the maternal concentration
of glucose in the sheep
is greater than the fetal concentration.
However,
the permeability
of
n-glucose is more than 50 times greater than the permeability
of Lglucose (Table 4 in APPENDIX II), a difference that is presumably
due
to the presence of a carrier mechanism
or an active mechanism.
In
any case, n-glucose
is so permeable
that its rate of transfer
is
independent
of water filtration.
Lactate also is present in the maternal plasma in higher concentration
than in fetal plasma. Recent
evidence (7), however,
shows that the lactate used by the fetus is
produced in the placenta from glucose. The rate of fetal uptake of
this material
is therefore
not dependent on the maternal
plasma
lactate concentration.
Bicarbonate
and urea are products of fetal metabolism
of materials that are mostly actively transported
into the fetal circulation,
glucose (50), amino acids (20), and lactate (45). Bicarbonate
diffuses
across to the maternal
plasma in the form of molecular CO, (31), a
substance
so permeable
in the placental
barrier
that its rate of
transfer is independent
of water filtration.
The permeability
of urea
also is so high (Table 4 in APPENDIX II) that its rate of transfer
by
AND
J. J. FABER
is not appreciably
974
Concn,
mmol/kg2
Solute
3
ua
uaACg;moli
n,
mmHg4
CM
CF
ACa
Lactate5
4.95
3.54
+1.41
0.95
+1.34
+26.1
Fructose6
0
1.75
-1.75
0.998
-1.74
-33.9
2.52
5.46
-2.94
0.858
-2.50
-48.6
-2.11
0.89
-1.87
-36.4
Amino
acids7
HCO,-
APPENDIX
JR.,
Urea’
6.54
7.28
--0.74
0.78
-0.58
-11.3
Calcium’
2.26
3.01
-0.76
0.98
-0.74
-14.5
Phosphate’
0.52
0.76
-0.24
1.00
-0.24
-4.7
n-Glucose*
3.28
1.28
+2.00
0.998
+2.00
+38.9
Total
-5.12
C(uaACa)
2 Corrected
for differences
3.
3 Reflection
coefficient,
estimated
in water
from
=
content
coefficient
-4.33
between
of free
-84.4
maternal
diffusion
and
1 From
Ref.
and
fetal
plasma.
Renkin
equation,
Fig. 1 and APPENDIXII; if not available,
estimate
was made from data on
other
substance
of similar
molecular
weight.
4 Effective
osmotic
pressure.
5 From
Ref. 22, correction
for water
content
added.
6 From Ref. 50, correction
for water
content
added.
R Estimated
average
’ From
Ref.
20, correction
for water
content
added.
reflection
coefficient.
filtration
(second term on the right-hand
side of equation 4a) can be
calculated to be less than 1% of its rate of transfer by diffusion (first
term on the right-hand
side of equation 4a) from the data in Tables 24. Transfer of this solute also can be considered essentially
independent of water filtration
in the placenta of the sheep.
The authors thank Mrs. Alice Fitzgerald
for impeccable secretarial help.
This investigation
was supported by National Institutes
of Health
Grants HD 09428 and HD 10034, and by a grant from the Oregon
Heart Association.
E. E. Conrad was supported by Graduate Traineeship
GM 00538.
Address requests for reprints
to J. J. Faber.
Received
for publication
6 August
1976.
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