Model study of placental water transfer and causes
of fetal water disease in sheep
J. J. Faber and D. F. Anderson
Am J Physiol Regulatory Integrative Comp Physiol 258:1257-1270, 1990.
You might find this additional information useful...
This article has been cited by 3 other HighWire hosted articles:
Angiotensin II in cardiac pressure-overload hypertrophy in fetal sheep
J. L. Segar, G. B. Dalshaug, K. A. Bedell, O. M. Smith and T. D. Scholz
Am J Physiol Regulatory Integrative Comp Physiol, December 1, 2001; 281 (6):
R2037-R2047.
[Abstract] [Full Text] [PDF]
Fetal diuretic responses to maternal hyponatremia: contribution of placental sodium
gradient
T. J. Roberts, M. J. M. Nijland, L. Williams and M. G. Ross
J Appl Physiol, October 1, 1999; 87 (4): 1440-1447.
[Abstract] [Full Text] [PDF]
Medline items on this article's topics can be found at
http://highwire.stanford.edu/lists/artbytopic.dtl
on the following topics:
Biochemistry .. Active Transport
Biochemistry .. Fructose
Medicine .. Polyhydramnios
Physiology .. Blood Circulation
Physiology .. Pregnancy
Chemistry .. Osmosis
Additional material and information about American Journal of Physiology - Regulatory,
Integrative and Comparative Physiology can be found at:
http://www.the-aps.org/publications/ajpregu
This information is current as of January 21, 2007 .
The American Journal of Physiology - Regulatory, Integrative and Comparative Physiology publishes original
investigations that illuminate normal or abnormal regulation and integration of physiological mechanisms at all levels of
biological organization, ranging from molecules to humans, including clinical investigations. It is published 12 times a year
(monthly) by the American Physiological Society, 9650 Rockville Pike, Bethesda MD 20814-3991. Copyright © 2005 by
the American Physiological Society. ISSN: 0363-6119, ESSN: 1522-1490. Visit our website at http://www.the-aps.org/.
Downloaded from ajpregu.physiology.org on January 21, 2007
Amniotic fluid and hemodynamic model in monochorionic twin pregnancies and
twin-twin transfusion syndrome
A. Umur, M. J. C. Van Gemert and M. G. Ross
Am J Physiol Regulatory Integrative Comp Physiol, May 1, 2001; 280 (5): R1499-R1509.
[Abstract] [Full Text] [PDF]
Model study of placental water transfer
of fetal water disease in sheep
and causes
J. JOB FABER
AND DEBRA
F. ANDERSON
Department of Physiology, School of Medicine, Oregon Health Sciences University,
Portland, Oregon 97201
filtration; diffusion;
hydrops fetalis
osmotic pressure;
solute; polyhydramnios;
PLACENTALTRANSFEROF
WATER haslongbeenbelieved
to be a simple process, driven by the combined forces of
hydrostatic and osmotic pressures acting on a semipermeable membrane (5). It is also a process that frequently derails. Prenatal “water diseases” may take the
form of too little or too much extrafetal fluid (oligohydramnios, polyhydramnios) or of generalized fetal edema
(hydrops fetalis). Despite the apparent simplicity of the
basic process, the pathophysiology of these diseaseshas
not been resolved. This is in part because so many solutes
affect the osmotic pressures of fetal and maternal plasmas that the total osmotic pressures are not easily determined.
In the computer model to be presented we attempt to
incorporate all consequential hydrostatic and osmotic
forces. It has been developed in the expectation that a
model that uses realistic values for these variables and
for the relevant placental membrane properties will reveal the components that are of primary importance.
The model concerns the regulation of total conceptual
0363-6119/90
$1.50 Copyright
water content alone. The partitioning of this water into
intrafetal and extrafetal fluids depends on regulatory
mechanisms (41, 43) that have not been completely elucidated. Partitioning, therefore, is not addressed as such.
The simulation concerns the sheep, which is the only
species for which adequate experimental data are available. It covers a gestational period of 99-145 days (term
=I47 days).
METHODS
Outline of Model
The sheep conceptus consists of a fetus, a placenta,
and two extrafetal fluids, the allantoic and amniotic
fluids. The model separately treats 1) fetal dry matter
(to be thought of as dried tissues without solvent), 2) the
electrolyte and other solute complements of fetal and
external fluids, and 3) the water contents of the fetus
and the extrafetal fluids.
Concentrations in the maternal compartment are presumed constant. Maternal major electrolyte concentration (NaCl) in plasma is 250 meq/l (4), glucose concentration is 3.46 mM (37), arterial CO2 concentration is 24
mM, HCO; concentration is 22.8 meq/l, and arterial O2
content is 6.7 mM, or ~15 ~01% (4, 42).
Placental weight is essentially constant during the
period of interest, at 400 g (11). It is, therefore, assumed
that placental glucose consumption is constant also, at
3.266 pmol/s (37). However, other placental functions
are known to increase in magnitude in proportion to fetal
weight, i.e., at 3-4%/day. The placental carbon monoxide
diffusion capacity (25) and the placental urea permeability (24) are typical examples. One interpretation of
their increases is that the placental surface area increases
(16). Because fetal weight normally increases at -3.5%/
day (36), the model applies an increase of 3.5%/day to
maternal placental blood flow, Q”, which is normally
240 ml min-l kg fetal wt-’ (16), to the placental filtration coefficient S L, (4) and to the placental permeabilities for Na+ and Cl- (S PN& (39), all of which are
known to increase in proportion to fetal weight in the
last third of gestation in the sheep. The model does this
by augmenting the surface area of the placenta by 3.5%/
day and calculating each of the other variables (SL,,,
S *&cl, and Ql M ) as the product of surface area and an
appropriate constant multiplier of surface area for that
variable.
0 1990 the American
l
l
Physiological
Society
R1257
Downloaded from ajpregu.physiology.org on January 21, 2007
FABER, J. JOB, AND DEBRA F. ANDERSON. 2ModeL study of
placental water transfer and causes of fetal water disease in
sheep. Am. J. Physiol. 258 (Regulatory Integrative Comp. Physiol. 27): R1257-R1270,
1990.-The
purpose of the computer
simulation
was to use experimentally
measured parameters of
placental water transfer to compute conceptual water acquisition during the last third of ovine pregnancy and to evaluate
the possible role of each of these parameters in the pathophysiology of polyhydramnios.
Total conceptual water at birth was
almost insensitive to the value of the placental filtration
coefficient. It was more sensitive to fetal and maternal placental
blood flows, the concentrations
of actively transported
or metabolically produced solutes in fetal plasma (bicarbonate,
fructose, a-amino acids, urea, lactate), and the hydrostatic pressure
difference across the placental barrier. It was quite sensitive to
the NaCl reflection coefficient and permeability.
We conclude
that the actively transported or produced solutes in fetal plasma
constitute
a primary
driving force. The opposing diffusion
gradient of NaCl, and to a much lesser extent that of glucose,
are essential to restrain the process. The causes of polyhydramnios in this species are, in order of probability,
an increase in
the placental diffusion permeability
of NaCl, a decrease in the
placental reflection coefficient for NaCl, or an increase in the
concentration
of an osmotically effective solute in fetal plasma,
by active transport or metabolic production.
Rl258
REGULATION
OF
PLACENTAL
Glossary
Greek
7r
f;C
AP
C
Kw
K5
J
J NaCl
J Pidc
V
LP
l
102 1
P
/
Pe
l
P NaCl
.
Q
R
RQ
wt
2
W1
W2
Subscripts and superscripts
Fetal placental capillary
Cap
Cryst
Plasma crystalloids
F
Fetal
Fa
Fetal umbilical artery
M
Maternal
Ma
Maternal placental artery
uv
Fetal umbilical vein
Detailed Approach
Oxygen consumption. Oxygen consumption of a fetus
is determined not only by its oxygen needs but also by
the availability of oxygen (3, 13, 20, 42). Oxygen consumption and placental oxygen exchange must be considered together.
We assume that the sheep placenta allows end-venous
fetomaternal equilibration. This is an optimistic assumption in the sheep (see Fig. 4 in Ref. 15), and a correction
factor K5 is introduced to take into account inefficiencies
of exchange due to shunts, etc. Given this assumption,
placental oxygen transfer is determined by the fetal and
maternal placental blood flows, Q” and Q”, and the fetal
and maternal arterial oxygen concentrations. We derived
the relation
.
vo
Osmotic pressure, dyn/cm2
Reflection coefficient, dimensionless
Concentration
difference, mmol/ml,
Pressure difference, dyn/cm2
Concentration,
mmol/ml, meq/ml
e to the power . . . , dimensionless
Glucose concentration,
mmol/ml
Correction factor in &. 1, O-1, dimensionless
Volume flow across placenta, ml/s
Electrolyte
flow, meq/s
Placental
glucose consumption,
3.266 X lo-”
mmol/s
Filtration
coefficient, 1.2 x lo-l2 cm” s-l. dyn-’
Blood oxygen content, mmol/ml
Hydrostatic pressure, dyn/cm2
P&let’s number, equal to Jv (1 - a) . (P- S)-I,
dimensionless
Placental Na+ and Cl- permeability, 3.0 x 10e7
cm/s
Placental blood flow, ml/s
Gas constant, 8.31 x lo7 erg- C-l .rnol-l
Respiratory exchange ratio, dimensionless
Placental surface area, cm2
Absolute temperature, “K
Fetal oxygen consumption, mmol/s
Weight, g
Constant in Widdas equation, 1.933 x low2
mmol/s
Constant in Widdas equation, 3.885 x lo-:’
mmol/ml
-P
s
T.
vo
EXCHANGE
2
=
K5
l
[(Q”*
&“)I(&”
+
&“>I
(I)
. ([021Ma - [021Fa), mmol/s
meq/ml
Roman
a
Asymptotic
value of fetal wet wt, dimensionless
b
Total water/fetal
dry wt, dimensionless
where K5 is the correction factor, whose normal value is
set at 90%. Equation 1 assumes that oxygen is linearly
soluble, which is only approximately true. See Glossary
for symbols and abbreviations.
Downloaded from ajpregu.physiology.org on January 21, 2007
The simulation begins with a conceptus of 99 days.
The 99-day-old fetus is assumed to weigh 800 g and to
consist of 20% (160 g) dry matter and 640 ml of water
and to have a total of 300 ml extrafetal
(allantoic and
amniotic) fluid. The initial fetal major electrolyte (Na+
plus Cl-) concentration
is 250 meq/l, i.e., equal to maternal NaCl concentration
([NaCl]).
The details of the
following steps are given below but, in short, the model
computes for each time interval of 1,200 s:
Fetal oxygen consumption
and carbon dioxide production
Fetal glucose consumption
and glucose concentration
Total fetal plasma osmotic pressure exerted by its
crystalloid components of glucose, NaCl, bicarbonate, and “other” solutes, which comprise a-amino
acids, Ca2+, Mg2+, lactate, phosphate, fructose, urea,
etc.
Transplacental
difference in crystalloid osmotic pressure
Hydrostatic
and colloid osmotic (oncotic)
pressure
differences across the placenta
Transplacental
volume flow
Transplacental
NaCl flux
Increase in fetal dry weight
Increase in placental surface area
The model then updates the values of:
Fetal NaCl pool (= total NaCl content)
Water pools (total, intrafetal, and extrafetal)
Fetal dry weight
Fetal wet weight
Fetal NaCl distribution
volume
Fetal NaCl concentrations
Fetal placental blood flow
Fetal placental capillary blood pressure
Placental surface area
Maternal placental blood flow
Placental permeability
and filtration constant
Fetal arterial oxygen content
Fetal plasma HCO; concentration
The cycle then resumes, until sufficient iterations
have
been performed to reach a gestational age of 145 days.
At the end of each “day,” the values of the various
variables are stored for later presentation
in graphic
form.
Units used in the simulation are millimole, milliequivalent, milliosmole, centimeter, milliliter, dyne ( =10m5 N),
gram, and second. To enable the reader to compare text
and figure numbers with published data, some of the
units are converted into more conventional
units before
being entered into the text or legends that follow.
WATER
REGULATION
OF
PLACENTAL
WATER
Equation 1 contains the fetal arterial oxygen content
as one of its variables. This quantity cannot be considered constant, because variations
in it constitute
the
major means by which the fetus adapts its placental
oxygen uptake to its systemic
oxygen consumption.
There is however, a well-documented
relation between
oxygen uptake per gram of fetal body weight and fetal
umbilical arterial oxygen content (3, 13, 20, 42). Figure
1 shows the ratio of voZ/Wt
as a function of fetal arterial
oxygen content over a large range of values for acute and
chronic conditions in fetal lambs. This function is well
approximated
by the empirical relation
Vo,/Wt” = 0.000487(
[Oa]Fa)‘=5,
mmol*g-‘4
20, 23, 42).
Carbon dioxide and bicarbonate. Fetal carbon dioxide
production is equal to the product of its oxygen consumption and RQ, which is set to 0.8. RESULTS show to
what extent this choice of RQ affects water transfer. To
c-u
>”
3
5
Fetal
Arterial
vol
0,
pmol/ml
%
10
Content
Experimental
values of VO2 as a function
of fetal arterial
0,
([ OZIFa). Weights
are fetal wet weights. Fitted curve represents
Eq. 2. Data- from
Itskovitz
et al. (20, +), Edelstone
et al.-(13,
x),
Anderson
et al. (3, 0), and Wilkening
et al. (42, 0).
FIG.
content
1.
placental
100
Haternal
placental
blood
flollr
ml/(kg*nin)
1
200
blood
flow
ml/(kg*min)
FIG. 2. Relation
between
fetal and maternal
placental
blood flows
and fetal O2 consumption
as represented
by Eqs. 1 and 2. Fetal weight
(kg) is wet weight.
compute fetal arterial [CO& the model uses Eq. 1, with
carbon dioxide substituted for oxygen, and solves for
[COzlFa. This means that the model sets fetal arterial
carbon dioxide concentration equal to the value needed
to elim inate carbon dioxide at the same rate at which it
1s produced, given the prevailin ,g Pl .acental blood flows.
B icarbonate concentrations are set equal to 95% of the
carbon dioxide concentrations (10).
It would have been possible to use much more detailed
models for oxygen and carbon dioxide exchange (19, 26,
34). However, those theoretically refined models may be
based on placental vascular geometries that are not applicable to the sheep (15, 35). There is the further problem that the available experimental data are much too
imprecise to justify the computational complexity demanded by such models, see, for instance, Fig. 1. Last,
but not least, RESULTS show that the outcome of the
model is only moderately sensitive to fetal oxygen consumption or carbon dioxide production.
Dry weight growth. It is well established that the rate
of fetal weight increase is diminished when oxygen supply is inadequate (1, 32). Normal fetal growth is -3-4%/
day, depending somewhat on gestational age (5, 36). We
measured fetal growth during long-term reduction of
fetal placental blood flows and found a growth of -2%/
day (1) under conditions where fetal oxygen consumption
should have been about half of the normal value of -8
ml. min-’ . kg fetal body wt-’ (6.0 ,umol . s-l. kg-‘) according to Fig. 3 in Ref. 3. In the model, .therefore, fetal
growth is made proportional to fetal To2 per gram of dry
fetal weight; the proportionality factor is chosen to give
a growth of 3.8%/day at a vo2 of 8 ml/min per 200 g dry
wt, which would, in a normally hydrated fetus, correspond to 8 ml min-lo kg wet wt-‘. The simulation uses
this growth factor to compute the increment in only dry
weight. The total weight of the fetus is always equal to
dry weight plus fetal water weight.
Fetal glucose concentration. Fetal growth is due to the
deposition of lipids, carbohydrates, and protein, and
these same metabolites fuel oxygen consumption (17).
As indicated below, the model assumes that there is a
constant transplacental concentration difference of ac-
Downloaded from ajpregu.physiology.org on January 21, 2007
l
2
Fetal
(2)
where oxygen consumption
is in millimoles per second,
fetal dry weight is in grams, and fetal arterial oxygen
content is in millimoles per milliliter. Equations 1 and 2
permit the calculation
of both VOW and [02]“” when
placental blood flows and fetal dry weight are known.
Maternal placental blood flow is tied to the maturation
of the fetus via the increase in the surface area of the
placenta, as described above. The fetal placental blood
flow is set equal to 180 ml. min. kg fetal wet wt-‘;
weight will be calculated below.
Figure 2 shows the resulting ~oZ for a fetus of 200 g
dry body wt (or ~1.0 kg wet wt) at various maternal and
fetal placental blood flows. We consider flows of -240
and 180 ml kg-‘. min-‘, respectively, to be normal (see
Tables 2.2 and 2.1 in Ref. 16). The relative insensitivity
of Voz to changes in placental blood flows is in part due
to the nature of the exchanger (end-venous equilibration
system) and in part to the adaptive decrease in fetal
arterial [02] when flows decrease. The basis of this
relative insensitivity of fetal iTo2 to placental blood flows
has been discussed by Meschia (29), and experimental
support for it is found in numerous publications (3, 13,
Rl259
EXCHANGE
R1260
REGULATION
OF PLACENTAL
tively transported
solutes, such as a-amino acids, and of
metabolites produced by the fetus, such as fructose, urea,
and lactic acid. The fetus uses these fuels to defray part
of its oxygen consumption.
A constant transplacental
difference in concentration
cannot be assumed for glucose, however, since it crosses the placenta by carriermediated diffusion (37).
To simulate the process that supplies glucose, we use
the Widdas equation, as modified by Meschia in the
paper by Simmons et al. (37). It takes the form
JFglc
=
W,
l
([Glcl”/(
[GlclM
- [Glc]“/([Gl~]~
+ I&)
+ wZ))
- Jzc,
mmol/s
(3)
flNaC1)
l
[
c&aCl
l
[exp(-Pk)
- 11, meq/s
(4)
where P& is a form of P&let’s number (9), given by
Pi = J,*(l - aNaCl)/(S
’ PNaCl)
P&let’s number, in this case, is a dimensionless ratio of
the effective ultrafiltration
flow in the absence of diffusion, JVo(1 - ONacl),and the diffusion permeability 5’g
PNacl,in the absence of filtration. Equation 4 gives results
that are similar to those given by Eq. 33 of Kedem and
Katchalsky (22), in which ultrafiltration
and diffusion
are represented by two separate terms, but it is more
accurate when applied to conditions that are not close to
equilibrium (8).
The total amount of NaCl acquired in each iteration
interval is the product of the influx rate and the duration
of the interval. This amount is then added to the total
NaCl pool of the conceptus before the next iteration.
Crystalloid osmotic gradients across the placenta. The
plasma crystalloids are grouped as glucose, major electrolytes (Na+ and Cl-), bicarbonate, and “other” solutes.
Maternal plasma values are maintained constant. For
the “other” solutes, the combined transplacental concentration difference is set at a fixed value, normally -5
mM (4); the minus sign signifies that the fetal value is
greater than the maternal value. This lumping of all
other solutes under one heading is permitted by the fact
that their reflection coefficients must all be close to 1.0
because of the small equivalent pore radius of the placenta of the sheep (6). RESULTS show to what extent the
net transplacental concentration difference of the other
solutes affects the outcome of the model. Fetal NaCl,
glucose, and bicarbonate concentrations are allowed to
vary, as described above, and the transplacental differences are the differences between the varying fetal and
the constant maternal plasma concentrations.
The net transplacental osmotic pressure exerted by
each group of crystalloids is calculated from Staverman’s
modification of van’t Hoff s law (38)
7r = aoACRoT,
dyn/cm”
(5)
where 0 is the osmotic reflection coefficient (22). The
reflection coefficients of glucose and the “other” solutes
are set at 1.0 (12). For NaCl, the mean reflection coefficient measured in sheep (39) for Na+ and Cl- is used,
i.e., 0.8. There is no directly measured value of 0 for
bicarbonate. In fairness to the “bicarbonate hypothesis”
(see below), a value of gnco, = 1 is used for bicarbonate.
The importance of the magnitude of the NaCl reflection
coefficient will be taken up in RESULTS.
Transplacental hydrostatic and colloid osmotic pressures. Plasma protein contents of fetal sheep are less
than those of maternal sheep (4). The difference corresponds to an osmotic force of -4.5 mmHg (6,000 dyn/
cm”), favoring water transfer from fetus to mother; the
slight gestational variation in this value is ignored. Maternal placental capillary blood pressure is arbitrarily set
at 40 mmHg (53,000 dyn/cm2); this pressure is between
the measured arterial and venous pressures in the maternal placenta of the sheep (31). RESULTS report the
effects of deviations from this pressure. Fetal capillary
blood pressure depends on fetal arterial blood pressure,
which, in turn, depends on fetal weight. The simulation
assumesthat
Pcap = Puv + (l/3) . (PFa - Puv),
dyn/cm2
(6)
Fetal arterial blood pressure is empirically related to
fetal weight by the relation log,,(PFa - Puv) = 1.39 +
0.27 sloglo(WtF), where fetal (wet) weight is in kilograms
and pressures are in millimeters Hg, and where umbilical
Downloaded from ajpregu.physiology.org on January 21, 2007
where the values of the constants
I& (=1.933 x IO-’
mmol/s) and I& (=3.885 x lo-” mmol/ml)
and Jzo the
placental glucose consumption
(=3.266 X lo-” mmol/s)
are also taken from Simmons et al. (37). The maternal
plasma glucose concentration
is set constant at 3.46 X
lo-3 mmol/ml, based on the same source. As pointed out
by Simmons et al. (37), placental glucose consumption,
the last term in Eq. 3, is considerably
greater than fetal
glucose consumption.
The model sets fetal glucose consumption (Jr!,) at 0.06 times CO2 consumption
(VCO~),
a value that makes glucose consumption
account for 36%
of the carbon excreted as COZ. Thus, since VCO~ is related
to VO,, glucose consumption
is related to fetal weight.
The simulation uses an algebraically
rewritten
form of
Eq. 3 to solve for fetal glucose concentration,
which is
calculated from the values supplied above.
Fetal plasma NaCl concentration.
The fetal plasma
NaCl concentration
is calculated at each iteration by
dividing the total NaCl content (see below) of the conceptus by the distribution
volume for NaCl, which is set
at 654 ml/kg fetal wet wt (39) plus the volume of the
extrafetal fluids.
Na+ and Cl- are lumped as NaCl. This can be done,
because the placental permeabilities
of Na+ and Cl- in
the sheep are similar (39) and because plasma bicarbonate largely compensates the charge difference due to the
difference in plasma Na+ and Cl- concentrations.
Furthermore, there is good experimental
evidence that even
if there would be a potential difference of more than 1
or 2 mV across the placenta (which we doubt), it does
not affect the transplacental
distribution
of electrolytes
(40)
Transplacental
flux of NaCl. The net transplacental
influx rate of NaCl (meq/s) consists of the combined
contributions of ultrafiltration
and diffusion. It was calculated from the modified Hertzian equation of Patlak
and co-workers (33), as presented by Bresler and Groome
(8)
J NaCl = Jv*(l
exp
(-pe)
CfaCl]
/
WATER EXCHANGE
REGULATION
OF
PLACENTAL
vein pressure is constant at 7.5 mmHg, or 10,000 dyn/
cm2 (1). Hence fetal capillary blood pressure can be
recalculated at the end of each iteration, when fetal
weight is known; RESULTS show it varies only a little.
Because capillary hydrostatic pressures and plasma colloid osmotic pressures are of similar magnitude, the four
pressures (fetal and maternal hydrostatic and oncotic)
are added (represented by AP) and AP is displayed
separately in RESULTS. Thus the magnitude of the combined capillary and colloid osmotic pressures can be
compared with the magnitude of the combined crystalloid
osmotic pressures.
Transplacental water flux. Transplacental volume flow
is calculated by means of the equation of Kedem and
Katchalsky (22)
J = L,S[AP
V
+ Z(~oRoT~AC,,,,,)],
ml/s
(7)
l
l
RI261
EXCHANGE
extrafetal fluid. (In practice, of course, one must assume
that a fetus that contains much less than its normal
complement of 80% water would not survive, see RESULTS). When the total water is between four and five
times the fetal dry weight, the intrafetal water is four
times the dry weight, and the remainder is allocated to
the extrafetal compartment. When the total water in the
conceptus is greater still, we chose to calculate intrafetal
water from the formula
wet weight = 5 (dry weight)
l
l ae[l
- (1 - l/a)“],
ml
(‘)
where a is an asymptotic value (a factor of 1.5) and where
b is equal to the ratio of (total water)/(fetal dry weight).
The effect of this formula is to make total fetal weight
up to 50% greater than it would normally be when the
water supply is ample. Figure 3 shows the allocation of
conceptual water as a function of the ratio (total water)/
(fetal dry weight). The reasoning behind Eq. 8 and Fig.
3 is that if the total water volume is less than the normal
water volume, the fetal kidneys first reserve water for
intrafetal use, whereas when conceptual water is excessive, fetal wet weight will be greater than the normal five
times dry body weight, to a maximum of 7.5 times dry
body weight.
Computations
The programs were written in Hewlett-Packard Basic
2.0. All computations were performed on a HewlettPackard 9826 computer with a Motorola 68000 microprocessor. The entire program takes only a few hours of
computer time when the duration of the iteration intervals is set at 1,200 s. The program has been deposited
with the National Auxiliary Publication Service c/o MiF (kd
fetus
dry
of 2009
weightextrafetal
water
/
/
normal
I
I
"I
/
/
/
. asymptote
of
fetal
-----
wet
weight
/
fetal
weight
(we
t)
I
-_------
---intrafetal
---.
water
TOTAL WATER (kg>
FIG. 3. Allocation
of intrauterine
water to intrafetal
and extrafetal
compartments
in case of a fetus of 200 g dry wt (corresponding
to
normally
hydrated
fetus of 1 kg wet wt). Arrow shows normal values.
Asymptote
shows maximal
fetal weight at infinite
intrauterine
water
volume. Except for calculation
of fetal placental
flow, which is proportional
to fetal wet weight,
allocation
of water is without
effect on
operation
of model.
Downloaded from ajpregu.physiology.org on January 21, 2007
where L, is the filtration coefficient (normally 1.2 x lo-l2
cm’. dyn-’ . s-l, see Table 7.1 in Ref. 16) and S (cm2) is
the surface area of the placenta, calculated for each
iteration as described above. The last factor, in the
square brackets on the right, is the sum of the combined
net transplacental hydrostatic and colloid osmotic pressures, AP, and the combined net transplacental crystalloid osmotic pressures, 2 (0. R T AC&J.
The reason for using concentrations instead of activities is that the available experimental values for placental filtration coefficient L, and for Na+ and Cl- permeabilities, & and Pcl, are based on measured concentrations rather than measured chemical activities (4, 39).
The net transplacental water flux is equal to the net
transplacental volume flux minus the part of that volume
flux that is due to the volume of the dissolved major
electrolytes. For NaCl this volume is 0.0174 ml/mmol.
This almost negligible correction is made in the simulation. However, volume corrections for all other solutes,
which are vanishingly small, are neglected.
At the end of each iteration, the total conceptual water
content is recalculated by adding the product of water
flux and duration of the iteration to the water already
present.
Allocation of water in the conceptus to intrafetal and
extrafetal compartments. The bicarbonate hypothesis of
Longo and Power (27) has a bearing on some of the
results of this simulation. Their hypothesis requires that
conceptual water is in part incorporated into the fetal
soma and thus affects fetal cardiac output and fetal
placental blood flow. In the present model, fetal placental
blood flow is made proportional to fetal wet body weight.
The allocation formula that follows has no other purpose
then to ensure that this vital link of the bicarbonate
hypothesis between conceptual water content and fetal
placental blood flow is in place. It has no other effect on
the behavior of the model. Although the allocation appears realistic (18), it is not completely based on quantitative knowledge.
The normal fetal water content is -80% of body
weight. The model assumesthat if there is less water in
the conceptus than needed (e.g., less than four times the
dry weight of the fetus) all of that water will be conserved
by the fetus and none of it will be excreted in the
WATER
R1262
REGULATION
OF
crofiche Publications,
PO Box 3513, Grand Central
tion, New York, NY 10017.
PLACENTAL
Sta-
Data Presentation
After sufficient iterations have been performed to attain a gestational age of 145 days, the program stops.
The computer prints out selected final data and it graphs
several variables of interest as functions of gestational
age from 100 to 145 days.
WATER
EXCHANGE
plasma [HCO;] was 25.5 meq/l (maternal 22.8), fetal
[NaCl] was 242.7 meq/l (maternal 250) and fetal [glc]
was 23.0 mg/dl, or 1.27 mM (maternal 62.6 mg/dl, 3.46
mM). Although the “other” solutes were set 5 mM higher
in fetal than in maternal plasma, the total crystalloid
water
contant
RESULTS
To determine whether the iteration interval of 1,200 s
was short enough, the standard model was run with a 10
times shorter interval also. The greatest discrepancy
noticed in any of the calculated values was in the fourth
significant
decimal, being less than one part in 1,000,
which, for the present purpose, is negligible.
All data are presented in mutually corresponding
order
to avoid the repetitive use of the word “respectively”.
Differences
are always the maternal
minus the fetal
values, except as noted.
.-’
7//’
e-0
,-
,,-----
---
---wo
110
e-’
e--
/-
1: ght
120
130
GESTATIONAL
AGE (days)
GESTHTIONAL
AGE (days>
140
Downloaded from ajpregu.physiology.org on January 21, 2007
Standard
growth
---A-----
10 r
Model
The results for the normal case are shown in Fig. 4.
Fetal growth rate (dry weight) slightly diminished during
gestation and was 356%/day
at day 145. Fetal water
content (as percent of body weight) rose immediately to
the model value, from its (arbitrary)
starting value of
80% at 99 days, but then slowly diminished to 80.3% at
the end of gestation. Fetal birth weight was 4.14 kg. The
extrafetal water volume near birth was 872 ml (combined
amniotic and allantoic fluids), and total conceptual water
was 4,195 ml. All of these values are well within
the
normal range for sheep.
Tables 1 and 2 summarize the normal values obtained
at day 145 for several variables of interest and also their
values at the extremes of the ranges over which some of
the parameters of the model were varied, see below.
On day 145, oxygen consumption
was 29.9 ml/min (22
pmol/s), or 7.24 ml. mine1 kg (wet) wt-’ (5.4 ,umol . s-l.
kg-‘), maternal placental blood flow was 229, and fetal
placental blood flow was 180 ml. min-’ . kg-‘.
At this time, fetal (femoral or umbilical)
arterial
0
15
mM
2
L
-
1
1
A
.--------------------------.
l
FIG. 4. Results
obtained
with standard
model as function
of fetal
age between
100 and 145 days. First panel, fetal water content
(%wet
body wt), fetal growth rate (%dry wt/day),
and fetal (wet) body weight;
2nd panel, total water and extrafetal
water; 3rd panel, transplacental
concentration
differences
(in meq/l)
for HCO;,
glucose,
and NaCl.
Values above abscissa represents
differences
where fetal concentration
is higher than maternal
concentration
and vice versa. Lines above 0,
therefore,
represent
concentration
differences
that promote
water
transfer
into the conceptus.
Concentration
difference
of NaCl must be
multiplied
by reflection
coefficient
cNac1 (and by R. 7’) to obtain osmotic
pressure;
other reflection
coefficients
are equal to 1. Panel does not
show constant
concentration
difference
(-5 mM) of “other”
solutes,
which, like HCO:
concentration
difference,
promotes
water entry into
the conceptus.
Fourth
panel, pressure
difference
of combined
hydrostatic and oncotic pressures
(AP) and pressure difference
due to combined crystalloid
osmotic pressures
(Ax); lines above 0 represent
pressures that promote
water transfer
into the conceptus
and lines below 0
represent
pressure differences
that promote
transfer
out of the conceptus.
CHCO;l
A
Cglucosel
-
v-_----m-
-
A
-15
CNaC13
mM
GESTATIONAL
50
AGE (days)
mmHg
AP
El
go,:
: : : : : : : :
--w--m-
”I
50
110
120
-w----
130
ATT
r
mmHg
L
GESTATIONAL
AGE (days)
140
150
REGULATION
OF
PLACENTAL
WATER
R1263
EXCHANGE
1. Model values on day 145, normal and at extremes of ranges tested
TABLE
Fetal
VO2,
ml/min
29.9
29.6
I$, =
QF =
'F
. M=
Q
Q =
'M =
Q
30.2
16.3
35.5
19.0
34.4
30.3
29.7
24.9
31.4
29.6
31.0
29.3
34.2
17.4
33.6
3.2x
0.33x
1.67x
0.33x
1.67x
RQ = 1.0
RQ = 0.6
“Other”
solutes
“Other”
solutes
PM = 0 mmHg
PM = 80 mmHg
~NaCl
oN,Cl
PS
= 1.0
= 0.2
NaCl
=
P&&Cl
X, times
= 0
= -8
OX
= 5.3x
normal
value.
See Glossary
for units
Fetal Water
Content,
%
4.1
4.0
4.2
3.5
4.5
3.7
4.4
4.3
4.0
2.4
4.9
4.0
4.7
3.9
6.6
1.1
6.3
80.3
80.0
80.7
84.3
80.0
83.7
80.0
81.0
80.0
67.9
82.9
80.0
82.2
79.3
86.7
38.9
86.1
and definitions
4,195
3,797
4,368
4,720
4,086
4,631
4,102
4'501
3'915
1,603
5,718
3,308
5,243
3,081
27,285
434
12,780
Capillary
Pressures,
mmHg
Placental
Flows,
ml/min
Total
Water,
ml
M
960
960
960
960
960
320
1,600
960
960
960
960
960
960
960
960
960
960
F
M
F
745
726
762
211
1,361
662
798
775
728
425
876
724
840
699
1,189
201
1,127
40
40
40
40
40
40
40
40
40
40
40
0
80
40
40
40
40
20
19
20
19
20
19
20
20
19
18
20
19
20
19
21
16
21
Downloaded from ajpregu.physiology.org on January 21, 2007
Normal
L, = 0.32x
Fetal
Wet Wt,
kg
of symbols.
2. Plasma values of day 145, normal and at extremes of ranges tested
TABLE
Fetal
Plasma
[HCO,],
mm
Normal
L, = 0.32x
i$
= 3.2x
QF = 0.33x
&" = 1.67x
= 0.33x
= 1.67x
lM
Q
' M
Q
RQ = 1.0
RQ = 0.6
“Other”
solutes
“Other”
solutes
PM = 0 mmHg
PM = 80 mmHg
ONaCl
=
1.0
ONaCl
=
o-2
PS
PS
NaCl
=
OX
NaC!l
=
5.3x
= 0
= -8
25.5
25.5
25.5
26.4
25.2
26.1
25.2
26.1
24.8
26.0
25.4
25.5
25.4
25.5
25.2
26.7
25.2
All differences
are maternal-fetal
(M-F).
Driving
See GZossary for units and abbreviations
of symbols.
[Na+]
Concentrations
+ [Cl-],
me41
Transplacental
[glucose],
mM
AR
mmHg
AT Crysty
mmHg
1.27
1.28
1.27
1.45
1.20
1.42
1.22
1.17
1.37
1.34
1.25
1.28
1.26
1.28
1.22
1.44
1.23
16.0
16.1
15.9
16.5
15.7
16.4
15.8
15.9
16.1
17.7
15.5
- *23.9
55.6
16.2
14.4
19.6
14.6
+7.3
-8.6
+13.0
+6.4
+7.1
+6.6
+7.1
+6.4
+7.9
+16.0
+2.5
-30.0
+44.0
+10.8
-55.4
+21.1
-17.1
242.7
243.7
242.3
241.4
243.1
241.7
243.1
242.0
243.3
247.7
239.4
245.1
240.4
243.9
238.3
240.0
244.6
pressure
gets “+”
in direction
osmolality of fetal plasma was 1.8 mosmol/l lower than
that of maternal plasma, in accord with the constant
findings reported in the literature for the maternofetal
difference in freezing-point depressions (4, 18, 28, 30).
The 3rd panel in Fig. 4 shows the transplacental concentration differences of bicarbonate, NaCl, and glucose
during the period of interest, and the 4th panel shows
the net hydrostatic and oncotic pressure difference (16
mmHg, 21,000 dyn/cm2, at day 145) and the net crystalloid osmotic pressure difference (7 mmHg, 9,300 dyn/
cm2, at day 145). (+7 mmHg signifies that the osmotic
pressure of maternal plasma was 7 mmHg higher than
the osmotic pressure of the fetal plasma). Because of the
large value of the placental filtration coefficient I&, the
net pressure difference that drives the transplacental
water flux is an infinitesimal fraction of the total chem-
of fetus
and “-”
in direction
Differences
(M-F)
Net driving
pressure,
mmHg
AOsmol,
mosmol/l
8.7
24.7
2.9
10.1
8.6
9.8
8.7
9.5
8.2
1.7
13.0
6.4
11.6
5.4
69.8
-1.5
31.7
of mother.
1.8
0.8
2.2
2.1
1.7
2.0
1.8
1.9
1.7
1.3
2.3
-0.6
4.2
0.6
6.5
3.1
0.2
X, times
normal
value.
ical potentials of maternal or fetal plasma (Tables 1 and
2).
Effect of Filtration
Coefficient
The simulation was performed with five different values of the filtration coefficient (I,,), which was changed
over a lo-fold range from 3.8 X lo-l3 to 3.8 X lo-l2
(normal is 1.2 X lo-l2 cm3. dyn-’ . s-l). Figure 5 shows
the comparatively very small changes in total conceptual
water contents (from a low of 3.8 to high of 4.4 liters,
respectively) at day 145. Fetal wet weights varied by
~200 g, and no other variables showed much change,
with the exception of fetal plasma NaCl concentrations,
which were 243.7 and 242.3 mM. The lower panel of Fig.
5 shows that because of this change in fetal plasma NaCl
R1264
REGULATION
total
110
PLACENTAL
water
aas---
---
m-e-
OF
extrafetal
-6=
130
120
140
water
h
I
I
150
GESTATIONAL AGE (days)
mM
k?
A
CHCO$
EXCHANGE
1.5 to 1.2 mM. The result, therefore, was that a decrease
in fetal placental blood flow lead to an increase of the
transplacental bicarbonate gradient, but this increase
was matched by a corresponding increase in the transplacental NaCl gradient and, thus, no large water effect
ensued. This was true through the entire period of 99145 days. The relatively mild effect on fetal growth is
explained by the relative insensitivity of fetal oxygen
consumption to placental flow until flow is greatly reduced, as was shown in Fig. 2 and discussed in METHODS.
The results are compatible with the wide variation in
fetal placental flows reported in the literature (Tables
2.1 and 2.2 in Ref. 16) in otherwise apparently normal
fetal lambs and with the long-term survivability of the
drastic experimental reductions in fetal placental blood
flow reported by Anderson and Faber (1).
Maternal placental blood flow was changed in five
simulations, also from 0.33 to 1.67 times its normal value.
The results were essentially similar to those obtained
when fetal flows were changed. The reason for this is
that the main effect of flow concerns the transfer of flowlimited materials (e.g., oxygen and carbon dioxide) and
that those effects are very similar for changes in fetal
and maternal blood flows (Fig. 2). Tables 1 and 2 summarize some of the results.
-_-__-----_----------------------_.
Effect of Fetal Bicarbonate
A
z
8
Cglucosel
A
-15
t
CNaCll
mM
GESTATIONAL AGE (days)
FIG. 5. Changes
in total and extrafetal
water and in transplacental
concentration
differences
when value of filtration
coefficient
(L,) is
changed over a IO-fold range. Note that as L, is made larger (direction
of arrow),
opposing
NaCl gradient
increases
also, while HCO;
and
glucose concentration
gradients
change too little to show. Plotting
conventions
as in Fig. 4.
concentration, the transplacental concentration difference in plasma NaCl concentration increased in magnitude as L, increased and, thus, negated the increase in
water flow that would otherwise have occurred. A corollary of the finding that the effect of LP on water transfer
is not great is that extreme experimental accuracy of LP
(4) is not required for correct predictive power of the
model.
Fetal and Maternal Placental Blood Flows
Fetal placental blood flow was varied in five simulations from 0.33 to 1.67 times its normal value, i.e., a
range from 60 to 300 ml. rnirPo kg wet wt-‘). On day 145
(and all through gestation), the results of these drastic
changes were benign. Fetal wet weight varied from 3.5
kg (84% water) to 4.5 kg (80% water) and total conceptual water content varied from 4,720 to 4,086 ml. Fetal
plasma [HCO:] decreased from 26.4 to 25.2 mM, fetal
plasma [NaCl] increased by about the same amount from
241.4 to 243.1 mM, and fetal nlasma Lglcl changed from
To investigate the effect of fetal bicarbonate, five
simulations were performed in which the respiratory
exchange ratio was varied from 1.0 to 0.6. Fetal oxygen
consumption near birth (145 days) changed from 7.0 to
7.3 ml. min-lo kg-’ (5.2 to 5.4 prnol. s-l. kg-‘), and fetal
carbon dioxide production, therefore, varied from 7.0 to
4.4 ml min. kg-’ (5.2-3.3 pmol . s-l. kg-‘). The effect
on fetal growth was quite small: at 145 days, fetal wet
weights were 4.31 kg (81% water) and 4.04 kg (80%
water). Figure 6 shows that there is an effect on total
conceptual water; at 145 days it was 4,501 and 3,915 ml.
As in the case of changes in placental blood flow, the
transplacental osmotic pressure changes due to the
changes in fetal plasma [HCO,] were partly offset by
changes in fetal plasma [NaCl] (Fig. 6, bottom). Thus a
1.60-fold difference in carbon dioxide production per
kilogram fetal weight was associated with a IX&fold
difference in conceptual water; the effect would have
been still less, if the reflection coefficient for bicarbonate
= 1.0) had been set to the same value of 0.8 that
(OHCO,
applied to NaCl.
l
Transplacental Concentration Difference
of “Other” Solutes
The driving forces that attract fetal water across the
placenta are due to the hydrostatic pressure difference
between the plasmas in maternal and fetal microvessels,
the fetal production of bicarbonate, and the presence in
fetal plasma of a number of solutes that are either
actively produced (urea, fructose, bicarbonate) or are
actively transported across the placenta (a-amino acids,
Ca2+). The group (except for bicarbonate) was taken
together. and its net transplacental concentration differ-
Downloaded from ajpregu.physiology.org on January 21, 2007
15r
WATER
REGULATION
OF
PLACENTAL
total
water
extrafetal
water
0
’
100
h
I
Electrolyte Reflection Coefficient (a~&
I
I
1
I
I
110
120
130
140
150
AGE (days)
The flow of ultrafiltrate
across the placental membrane into the fetus carries with it a fraction of the
maternal plasma NaCl. In the absence of diffusion, this
fraction is exactly equal to (1 - (TN~c~). Thus, under
normal circumstances, only -20% of the maternal NaCl
is carried into the conceptus with the ultrafiltrate,
and
the remaining 80% requires a diffusion gradient. This
W
v
10
5
c)i
A
CHCOSI
r
h
t
E
5
l-4
O
1I
1
I
1
I
1
1
I
I
I
I
1
I
1
I
I
I
I
----~~-~~-~--I--~---r-rr-rr-rr-r.-.,
A
Cglucosel
h
i
total
GESTATIONAL
water
/
cc
AGE (days)
FIG. 6. Top: changes
in total water
and extrafetal
water
when
respiratory
exchange
ratio RQ is changed from 0.6 to 1.0 (direction
of
arrows).
Bottom: as HCO, concentration
gradient
increases, opposing
NaCl gradient
increases also. Plotting
conventions
as in Fig. 4.
ence was normally set at -5 mM, i.e., in favor of the
fetus.
In five simulations, the net transplacental
concentration difference of these “other” solutes was varied from
0 to -8 mM. The value of 0 was not compatible with
fetal life much beyond 115 days, since the simulation
predicted a fetal birth weight of only 2.36 kg, only 68%
of which was water, and no extrafetal fluid at all. With
values of -2 to -8 mM, fetal weight at 145 days varied
from 3.54 kg (77% water, no extrafetal water) to 4.87 kg
(82.9% water and 1,683 ml extrafetal water).
Although substantial changes in conceptual water content ensued, they were still in large part restrained by
the generation of increases in the opposing NaCl gradient
(see fetal Na+ and Cl- concentration in Table 2).
Placental Capillary Blood Pressures
Only the difference between maternal and fetal hydrostatic pressures is of consequence. It suffices to change
extrafet
*water
al
0
-1 00
110
120
130
140
150
GESTATIONALAGE (days)
15
mM
=ET
LV
1
t
---e--e-----
A
v---
z
4:
-IS
Cglucosel
-----------
-----_I--w----
----
e-m-
----
----
1
E
?-fNaFl
I-
I mfl
GESTATIONAL AGE (days)
FIG. 7. Effect of increasing
capillary
blood pressure
from
in Fig. 4.
(direction
of arrows)
maternal
placental
0 to 80 mmHg.
Plotting
conventions
as
Downloaded from ajpregu.physiology.org on January 21, 2007
GESTATIONAL
R1265
EXCHANGE
one of the two pressures to investigate the importance of
hydrostatic pressure for water exchange. Maternal placental capillary blood pressure, normally 40 mmHg (5.3
x lo4 dyn/cm’),
was varied from 0 to 80 mmHg in steps
of 20 mmHg. This large range was used, because there
are experimental uncertainties in both the maternal and
the fetal placental capillary blood pressures.
Table 1 shows that the hydrostatic pressure difference
had a noticeable effect on water transfer; the total water
volumes on day 145 were 3,308 and 5,243 ml at maternal
pressures of 0 and 80 mmHg. Figure 7 demonstrates that
an increase in the pressure difference doubled the opposing NaCl gradient, with little change during the period
of gestation from 100 to 145 days.
r
1u
WATER
R1266
REGULATION
OF
PLACENTAL
WATER
EXCHANGE
r
100
diffusion gradient exerts an opposing osmotic force. We
anticipated, therefore, that values of ~&cl CO.8 would
facilitate water transfer and this proved to be the case.
The value of the NaCl reflection coefficient was varied
from 1.0 (its theoretic maximum)
to 0.2 (normal value
0.8). The model showed that a reflection coefficient of
1.0 (zero ultrafiltration
of NaCl) noticeably reduced the
water content of the conceptus, but, probably, was not
lethal, although the extrafetal
water volume was zero
(Fig. 8 and Tables I and 2). In this case, all influx of
NaCl was due to diffusion.
At a value of the reflection coefficient equal to 0.2, the
total conceptual water content at day 145 was in excess
of 27 liters. A value of 0.2 is extreme. But even when
ON&l was reduced from its nominal value of 0.8 to 0.6,
total water volume at day 145 increased from 4,195 to
6,713 ml, and a reflection coefficient of 0.4 produced an
extreme polyhydramnios
with a total water volume of
more than 12 liters. Figure 8 shows that at reduced values
of g&cl the concentration
difference of NaCl across the
placenta is increased. But because of the decrease in the
reflection coefficient, the osmotic pressure exerted by the
NaCl gradient decreased to such an extent that at values
of ar\r&lof 0.6 and less the net crystalloid osmotic pressure
difference reversed polarity and was acting in favor of
water transfer to the fetus (see Fig. 8).
s
V
water
content
(
L
-I
110
100
120
130
GESTATIONAL
total
140
AGE Idays)
water
1
110
of NaCl
15
This hypothetical self-steering mechanism for the regulation of fetal cardiac output and placental blood flow
is based on the assumption that if placental flow is
suddenly decreasedbelow normal, fetal plasma bicarbonate concentration rises and that, therefore, fetal plasma
osmolality rises also. This rise in fetal plasma osmotic
pressure should attract extra water across the placenta,
increase blood volume and cardiac output until, at a new
steady state, flows are normalized. Equation 1 of Longo
and Power (27) explicitly states that fetal plasma osmolality is constant (at 270.5 mM) except for a variable
addition due to bicarbonate.
To specifically test the proposed regulatory value of
HCO:, the program was modified. Until day 120, it
proceeded normally. At day 120, the proportionality factor between fetal wet weight and fetal placental blood
flow was reduced to one-half of its standard value, thus
150
AGE (days)
mM
2
L
v
[
e
El
E!5
r
k
E
O
A
1
I
------------m-e----
1I
25
A
r
-
1
-\-----il~a~llk
---
E8
-15 -
1I
1I
1I
I1
---me_
_,_________.
80
,1
Cglucosd
__---SC---_____-L----
E
!5
CHCO;l
I
?
!
I
--Cc
-- -
--------,
-
-
mM
GESTATIONAL
Test for Bicarbonate Hypothesis
140
130
120
GESTATIONAL
A NaCl permeability of zero was not compatible with
life. Total water at day 145 was less than at day 100, and
fetal water content was 39%. When PNaClwas increased
from its normal value of 3 X 10e7to 16 X 10M7cm/s (a
5.3 times increase), total conceptual water increased to
more than 12 liters, and gross polyhydramnios resulted.
The net crystalloid osmotic pressure gradient across the
placenta actually reversed (Tables 1 and 2). It should be
noted that normally the Na and Cl permeabilities of the
sheep placenta are only -1% of the permeability of a
similarly sized noncharged molecule (6,39) and that even
at the increased value of 16 X 10m7they are still more
than 10 times smaller.
water
AGE (days)
mmHg
AlT
--v--
v-
AP
--------------------
I,:
:
,:
i
:---!
:
I
Iyzo
:
-I
1
ATT
50
mmHg
c
GESTATIONAL
AGE (days)
FIG. 8. Second panel,
large changes in intrauterine
water volumes
as reflection
coefficient
of NaCl is increased
(direction
of arrows)
from
0.2 to 1.0. At low values of reflection
coefficient,
crystalloid
osmotic
pressure
difference
across placenta
reverses polarity
(4th panel: note
ordinate
differs from those in other figures).
Plotting
conventions
as
in Fig. 4.
Downloaded from ajpregu.physiology.org on January 21, 2007
1
1 00
Permeability
v
I
-4
0
Diffusion
I
-
REGULATION
OF
PLACENTAL
reducing fetal placental flow from 180 to 90 ml min.
kg-‘). To determine to what extent the induced changes
in fetal plasma HCO, concentration
play a role in the
subsequent
events, two cases were considered.
In the
first, the model was allowed to proceed according to the
WATER
3. Selected values at 145 dclys of gestation
after fetal placental blood flow reduction on day 120
------TABLE
IfVtF, wet,
1
water
content
]
growth
--m--
7
---
,-
,,-----
---
&5
c
/..--
,--@ l -M
--A
-*-we
‘O
L
120
-7
1
I
130
GESTATIONRL
0
140
150
AGE (days)
10
l(-!s
signiffas
held
that
fetal
constant
after
CHCOil
day
120
;Lyeee::
,
110
100
140
130
120
GESTATIONAL
Fetal [ HCO,]
Held Constant
From duy 120
_
q
Onward
4.0
22.8
4,488
361
26.1
241.9
1.36
3.9
22.5
4,227
350
25.4
242.6
1.37
150
AGE (days>
rules established for it. In the second case, fetal plasma
bicarbonate concentration
was not allowed to change in
response to the reduction in fetal placental flow. It was
held constant at the value it had at 120 days, thereby
eliminating any further regulatory role of fetal bicarbonate.
The results of the experiment are shown in Fig. 9. On
day 120, fetal growth rate suddenly decreased, because
placental blood flow was halved. The 3rd panel of Fig. 9
shows that when the model was otherwise
left unchanged, there was an immediate increase in fetal plasma
bicarbonate
concentration,
as predicted by the Longo
and Power (27) model. This panel also shows, however,
that there was also an immediate increase in the opposing
NaCl gradient. This gradient did not quite compensate
for the osmotic effect of the bicarbonate, at least in part
because the reflection coefficient of bicarbonate was set
at 1.0, whereas that of NaCl was only 0.8. Nevertheless,
the increase in the NaCl gradient greatly diminished the
effect bicarbonate
might otherwise
have had. Table 3
lists some critical values on day 145. Comparison
with
the second case, in which fetal plasma bicarbonate concentration
was not allowed to increase, shows that the
regulatory
effect of the rise in bicarbonate
is modest.
The discrepancy
between the present model and the
Longo and Power model stems primarily
from the assumption in the latter model that all fetal plasma constituents except bicarbonate are constant.
.--------mm-
A
glucose
-t
-y
A
L
mmHg
=
--
<--
NaCl
GESTATIONAL
50
DISCUSSION
--
AGE (days)
-
5
ii
A
I
E
AP
.
110
g
O
I
1I
---
120
1I
II
--
130
II
1I
LX===
I,
--
=
AlT
SO
mmHg
L
GESTATIONAL
flGE (days)
150
140
1I
II
c
II
E
<--
A viable model should be based on sound experimental
data. Given these data, it must reproduce all known
aspects of placental water exchange in the sheep, as
measured in healthy animals under near-normal and
steady-state conditions.
The development of the model in METHODS gives the
values and the sources of the parameters that determine
it. With a few exceptions, they are all based on the
results of direct experimentation on chronically instruFIG. 9. Same simulation
as presented
in Fig. 4, except that factor
of’ proportionality
between
fetal wet weight and fetal placental
blood
flow is abruptly
reduced by 50% on day 120. When fetal HCO; concentration
is clamped to the value it has on day 120 (marked
by arrows),
no further
changes in fetal HCO, concentration
can occur (3rd panel),
but this elimination
of HCO:I regulation
has only a modest effect on
intrauterine
water acquisition
(2nd panel) or fetal weight (1st panel).
Fetal placental
blood flow is not shown, as it is proportional
to fetal
weight,.
Downloaded from ajpregu.physiology.org on January 21, 2007
I
kg
V02, ml/min
Total water, ml
Fetal placental
flow, ml/min
[ HCOJ F, mey/l
[Na’]’
+ [Cl-]‘,
meq/l
[ Glc] F, mm01
Standard
Model
With HCO;
“Defense”
Intact
<--
i ght
110
R1267
EXCHANGE
R1268
REGULATION
OF
PLACENTAL
EXCHANGE
osmotic force. The model shows that this electrolyte
(NaCl) gradient constitutes
the major restraining
force
on intrauterine
water acquisition.
This is most evident in the results obtained by changing the filtration coefficient &,. Although Lp is a proportionality factor in the equation that rules volume flow
(Eq. 7), when L, is changed over a IO-fold range, there
is little change in conceptual
water acquisition.
The
reason for this is that as soon as filtration
slightly
increases, the opposing NaCl gradient increases also (Fig.
5 and Table 2) and stops any further increase in transplacental water flow.
Very much the same mechanism is at work when we
attempt to increase or decrease the rate of intrauterine
water acquisition by changing fetal RQ from 1.0 to 0.6
or by changing fetal or maternal placental blood flows
from one-third
to five-thirds
of their normal values.
These interventions
cause a primary
change in fetal
plasma [HCO;],
but also a secondary
change in the
opposing electrolyte gradient.
Setting the concentration
difference of the “other”
solutes to zero was not compatible with fetal survival;
clearly, the osmotic force of the actively transported
or
produced solutes is essential (unless maternal placental
capillary blood pressure is much higher than the 40
mmHg we assumed). However, increasing the concentration difference of the “other” solutes from -5 to -8 mM
had only a modest effect, for the same reasons that
applied to increases in fetal bicarbonate concentrations.
The results obtained by changing maternal capillary
blood pressure from 0 to 80 mmHg further support this
reasoning.
Quite different results were obtained, however, when
the brakes were released. This can be done either by
setting the NaCl reflection coefficient to a lower value
than 0.8 or by increasing the value of the NaCl diffusion
permeability.
In these cases, vast amounts of water accumulate by day 145 (Fig. 8 and Tables 1 and 2), because
the restraining
force of the electrolyte gradient is eliminated.
The model predicts, therefore, that polyhydramnios
induced in sheep, e.g., by the long-term infusion into the
fetus of angiotensin I (2), must be due to a change in the
NaCl reflection coefficient or the permeabilities
of Na’
and Cl-. There is a remote possibility
that the primary
change will be found to be an increase in the transplacental concentration
difference in the “other”
solutes,
attributable
to one or more of these solutes being increased in concentration
in fetal plasma. The model
predicts, however, that such an increase would have to
be substantial
(e.g., >5 mM) and should be easily detectable by chemical analysis of plasma.
It should again be emphasized that the partition
of
total water into an intrafetal and an extrafetal compartment was made only to test the bicarbonate hypothesis.
The model, therefore, was not intended to come to grips
with the distinction
between polyhydramnios
and hydrops fetalis. Both are water diseases of pregnancy and
both depend on a defect that increases intrauterine
water
content above its normal value. The differential
pathophysiology of these two diseases probably depends only
on the mechanisms
that regulate intraconceptual
parti-
Downloaded from ajpregu.physiology.org on January 21, 2007
mented fetal lambs and ewes. These parameters fall into
two groups. In the case of the permeability
parameters,
such as Pa S, 0 (except onCo:J, and &-,. S, the parameter
values are determined by means of the application
of
physicochemical
laws (8, 9, 12, 33, 38) to experimental
data (4, 24, 25, 39). Placental glucose transfer
also is
solidly footed on theory (37). In other cases, e.g., oxygen
consumption,
the physicochemical
basis is refractory
to
analysis in elementary terms, and empirical relations are
used. In the case of capillary blood pressures, however,
there is a range of uncertainty.
Capillary blood pressures
cannot be outside the limits set by its corresponding
arterial and venous pressures. Moll and Kiinzel(31)
have
shown that in pregnant ewes the pressure in small maternal placental arteries is still fairly close to central
arterial pressure; therefore, no narrow limits can be set
on maternal placental capillary blood pressure. The limits on fetal placental capillary blood pressure are only
slightly narrower. However, the model shows that despite
the multitude of osmotic pressures that are involved,
hydrostatic
pressures
need not be negligible and are,
therefore, well worth further experimentation
in vivo.
This is one example where the model yields results that
are counterintuitive,
see, e.g., the discussion
after Ref.
14.
Tables 1 and 2 show that the data produced by the
standard model at day 145 (term is 147 days) are compatible with generally accepted values in the sheep near
birth. Under normal circumstances,
there is a net crystalloid osmotic pressure difference of -7 mmHg (9,300
dyn/cm’) in favor of maternal plasma and a summed net
hydrostatic
and oncotic pressure
difference
of -16
mmHg (21,300 dyn/cm2) in favor of the fetus, resulting
in a net filtration
pressure of -9 mmHg (12,000 dyn/
cm”).
Historically,
the most puzzling in vivo finding concerning steady-state
placental water transfer
has been
that the total plasma osmolalities in a (healthy) ewe and
fetus are always higher in the maternal plasma than in
the fetal plasma (4, 18, 28, 30), usually by an amount
that makes compensation by hydrostatic
pressure a priori
unlikely. Table 2 shows that also in this respect the
model accurately mimics reality. The transplacental
difference in plasma osmolality is in favor of the maternal
plasma, as it is in vivo, in the standard case and also in
all cases in which modified parameters were used, except
in the one extreme case of a maternal placental capillary
hydrostatic
pressure of zero (Table 2).
The results of the simulation
lead to the following
general view of placental water transfer
in the sheep.
The primary forces that attract water into the conceptus
are the osmotic pressures exerted by the actively transported solutes (e.g., a-amino acids, Ca2+, lactate) and
solutes produced by the fetus (bicarbonate,
urea, fructose). Possibly, there is also a contribution
by a hydrostatic pressure difference. The plasma ultrafiltrate
attracted by these forces into the conceptus is, however,
80% denuded of its Na+ and Cl- complements.
As a
result, the fetal plasma NaCl concentrations
are always
lower than those of the maternal plasma (Table 2), and
this also is in accord with experimental
findings in vivo
(4, 21, 28). This electrolyte gradient exerts an opposing
WATER
REGULATION
OF
PLACENTAL
tioning of water (18, 41), such as fetal swallowing,
renal
excretion (43), and amniotic and allantoic fluid exchange
with the blood in the capillaries in these membranes.
This reasoning is supported by the finding that if our
angiotensin-infusion
method (2) is used to create fetal
water disease in nephrectomized
fetal lambs, the result
is hydrops fetalis instead of polyhydramnios
(unpublished observations).
Intraconceptual
water partitioning
deserves to be modeled in its own right as soon as the
relevant physiological mechanisms have been elucidated.
Finally, the results, including those of the test of the
bicarbonate
hypothesis,
should not be extrapolated
to
the human hemochorial
placenta. Quite possibly,
the
barrier in the hemochorial
placenta cannot be represented by a population of pores of only one equivalent
pore radius. In any case, too few of the required parameters are available for successful modeling.
Received
6 November
1989; accepted
in final
form
28 December
1989.
REFERENCES
1. ANDERSON,
D. F., AND J. J. FABER. Regulation
of fetal placental
blood flow in the lamb. Am. J. Physiol. 247 (Regulatory
Integrative
Comp. Physiol.
16): R567-R574,
1984.
2. ANDERSON,
D. F., AND J. J. FABER. Animal
model for polyhydramnios. Am. J. Obstet. GynecoZ. 160: 389-390,
1989.
3. ANDERSON,
D. F., C. M. PARKS, AND J. J. FABER. Fetal O2
consumption
in sheep during
controlled
long-term
reductions
in
umbilical
blood flow. Am. J. Physiol. 250 (Heart
Circ. Physiol.
19):
H1037-H1042,
1986.
T., S. KATZ, K. L. THORNBURG,
AND J. J. FABER.
4. ARMENTROUT,
Osmotic flow through
the placental
barrier
of chronically
prepared
sheep. Am. J. Physiol. 233 (Heart
Circ. Physiol.
12): H466-H474,
1977.
5. BARCROFT, J. Researches on Pre-Natal
Life. Oxford,
UK: Blackwell
Scientific,
1946.
6. BOYD, R. D. H., C. HAWORTH,
T. E. STACEY, AND R. H. T. WARD.
Permeability
of the sheep placenta
to unmetabolized
polar nonelectrolytes.
J. Physiol. Lond. 256: 617-634,
1976.
7. BRACE, R. A., L. K. MINER, A. D. SIDEROWF,
AND C. Y. CHEUNG.
Fetal and adult urine flow and ANF responses to vascular
volume
expansion.
Am. J. Physiol. 255 (Regulatory
Integrative
Comp. PhysioZ. 24): R846-R850,
1988.
8. BRESLER, H., AND L. J. GROOME.
On equations
for convective
and
diffusive transport
of neutral solute across porous membranes.
Am.
J. Physiol.
241 (Renal Fluid Electrolyte
Physiol.
10): F469-F476,
1981.
9. CURRY, F. E. Mechanics
and thermodynamics
of transcapillary
exchange.
In: Handbook
of Physiology.
The Cardiovascular
System.
Microcirculation.
Bethesda,
MD: Am. Physiol.
Sot., 1984, sect. 2,
vol. IV, pt. 1, chapt. 8, p. 309-374.
10. DAVENPORT,
H. W. The ABC of Acid-Base
Chemistry
(4th ed.).
Chicago, IL: Univ. of Chicago Press, 1958.
11. DAWES, G. S. Foetal and Neonatal
Physiology.
Chicago,
IL: Year
Book, 1968.
R. P. Osmotic
flow of water across permeable
cellulose
12. DURBIN,
membranes.
J. Gen. Physiol. 44: 315-326,
1960.
D. I., B. B. PETICCA, AND L. J. GOLDBLUM.
Effects
13. EDELSTONE,
of maternal
oxygen
administration
on fetal oxygenation
during
reductions
in umbilical
blood flow in fetal lambs. Am. J. Obstet.
Gynecol. 152: 351-358,
1985.
14. FABER, J. J. Regulation
of placental
blood flow. In: Respiratory
Gas
EXCHANGE
R1269
Exchange
and Blood Flow in the Placenta,
edited by L. D. Longo
and H. Bartels. Bethesda,
MD: Dept. of Health, Educ. and Welfare,
1972, p. 157-177.
I5 FABER,
J. J. Steady-state
methods
for the study of placental
ex” change. Federation
Proc. 36: 2640-2646,
1977.
E. FABER, J. J., AND K. L. THORNBURG.
Placental
Physiology.
New
York: Raven, 1983.
17* FABER, J. J., AND L. L. WOODS. The use of chemical analyses of
umbilical
cord blood for the computation
of instantaneous
fetal
growth.
J. Theor. Biol. 89: 433-448,
1981.
18. GILBERT,
W. M., AND R. A. BRACE. Increase
in fetal hydration
during
long-term
intraamniotic
isotonic
saline infusion.
Am. J.
Obstet. Gynecol. 159: 1413-1417,
1988.
HILL, E. P., G. G. POWER, AND L. D. LONGO.
A mathematical
I’* model of placental 0, transfer with consideration
of hemoglobin
reaction
rates. Am. J. Physiol. 222: 721-729,
1972.
J., E. F. LAGAMMA,
AND A. M. RUDOLPH.
The effect
20. ITSKOVITZ,
of reducing
umbilical
blood flow on fetal oxygenation.
Am. J.
Obstet. Gynecol. 145: 813-818,
1983.
21. KAISER, I. H., AND J. N. CUMMINGS.
Plasma electrolytes
of the
pregnant
ewe and the fetal lamb. Am. J. Physiol,
193: 627-633,
1958.
Thermodynamic
analysis of the
22. KEDEM, O., AND A. KATCHALSKY.
permeability
of biological
membranes
to non-electrolytes.
Biochim.
Biophys. Acta 27: 229-246,
1958.
23. KITANAKA,
T., J. G. ALONSO,
R. D. GILBERT,
B. L. SIU, G. K.
CLEMONS,
AND L. D. LONGO. Fetal responses to long-term
hypoxemia in sheep. Am. J. Physiol.
256 (Regulatory
Integrative
Comp.
Physiol. 25): R1348-R1354,
1989.
24. KULHANEK,
J. F., G. MESCHIA,
E. L. MAKOWSKI,
AND F. C.
BATTAGLIA.
Changes in DNA content and urea permeability
of the
sheep placenta. Am. J. Physiol. 226: 1257-1263,1974.
diffusing
capacity
for
25. LONGO, L. ID., AND K. S. CHING. Placental
carbon monoxide
and oxygen
in unanesthetized
sheep. J. Appl.
Physiol. 43: 885-893,
1977.
26. LONGO, L. D., E. P. HILL, AND G. G. POWER. Theoretical
analysis
of factors affecting
placental
0, transfer.
Am. J. Physiol. 222: 730739,1972.
27. LONGO, L. D., AND G. G. POWER. Long-term
regulation
of fetal
cardiac output. Gynecol. Invest. 4: 277-287,
1973.
28. MELLOR,
D. J. Distribution
of ions and electrical
potential
differences between
mother
and foetus at different
gestational
ages in
goats and sheep. J. Physiol. Lond. 207: 133-150,
1970.
29. MESCHIA,
G. Safety margin of fetal oxygenation.
J. Reprod. Med.
30: 308-311,
1985.
30. MESCHIA,
G., F. C. BATTAGLIA,
AND D. H. BARRON. A comparison
of the freezing
points of fetal and maternal
plasmas of sheep and
goat. Q. J. Exp. Physiol. Cogn. Med. Sci. 42: 163-170,
1957.
31. MOLL, W., AND W. KUNZEL.
The blood pressure in arteries entering the placenta
of guinea pigs, rats, rabbits and sheep. Pfluegers
Arch. 338: 125-131,1973.
32. OWENS, J. A., J. FALCONER,
AND J. R. ROBINSON.
Effect
of
restriction
of placental
growth on oxygen delivery
to and consumption by the pregnant
uterus and fetus. J. Dev. Physiol. Oxf. 9: 137150, 1987.
33. PATLAK, C. S., D. A. GOLDSTEIN,
AND J. F. HOFFMAN.
The flow
of solute and solvent
across a two-membrane
system. J. Theor.
BioZ. 5: 426-442,
1963.
34. POWER, G. G., E. P. HILL, AND L. D. LONGO. Analysis
of uneven
distribution
of diffusing
capacity
and blood flow in the placenta.
Am. J. Physiol. 222: 740-746,
1972.
35. RANKIN,
J. H. G. The effects of shunted and unevenly
distributed
blood flows on cross-current
exchange
in the sheep placenta.
In:
Respiratory
Gas Exchange
and Blood Flow in the Placenta,
edited
by L. D. Longo and H. Bartels.
Bethesda,
MD: Dept. of Health,
Educ. and Welfare,
1972, p. 207-224.
36. RATTRAY, R. V., W. N. GARRETT, N. E. EAST, AND N. HINMAN.
Growth,
development
and composition
of the ovine conceptus
and
mammary
gland during pregnancy.
J. Anim. Sci. 38: 613-626,1974.
37. SIMMONS,
M. A., F. C. BATTAGLIA,
AND G. MESCHIA.
Placental
transfer
of glucose. J. Dev. Physiol. Oxf. 1: 227-243,
1979.
38. STAVERMAN,
A. J. The theory of measurement
of osmotic pressure.
Reel. Trav. Chim. 70: 344-352,
1951.
39. THORNBURG,
K. L., N. D. BINDER,
AND J. J, FABER. Diffusion
Downloaded from ajpregu.physiology.org on January 21, 2007
We thank Thomas
Green, Jackie Niemi, and Dr. Nancy Binder for
their help.
These studies were supported
by the National
Institute
of Child
Health and Human
Development
through
Grants
HD-21387
and HD10034 and by a grant from the Medical
Research Foundation
of Oregon.
Address for reprint
requests: J. J. Faber, Dept. of Physiology,
School
of Medicine,
L334, Oregon Health
Sciences University,
Portland,
OR
97201-3098.
WATER
RI270
REGULATION
OF
PLACENTAL
permeability
and ultrafiltration
reflection
coefficients
of Na’ and
Cl- in the near term placenta
of the sheep. J. Deu. Physiol.
Oxf. 1:
47-60, 1979.
40. THORNBURG,
K. L., N. D. BINDER,
AND J. J. FABER.
Distribution
of ionic sulfate, lithium,
and bromide
across the sheep placenta.
Am. J. Physiol. 236 (Cell Physiol. 5): C58-C65,
1979.
41. TOMODA,
S., Ri A. BRACE,
AND L. D. LONGO.
Amniotic
fluid
volume regulation:
basal volumes
and responses
to fluid infusion
WATER
EXCHANGE
or withdrawal
Comp. Physid.
42. WKKENING,
genation,
and
Am. J. Physiol.
43. WLODEK,
M.
urachal
urine
sheep. J. Dev.
in sheep. Am. J. Physiol. 252 (Regulatory
Integrative
21): R380-R387,
1987.
R. B., AND G. MESCHIA.
Fetal oxygen
uptake,
OXYacid-base balance as a function
of uterine blood flow.
244 (Heart Circ. Physiol.
13): H749-H755,
1983.
E., J. R. G. CHALLIS,
AND J. PATRICK.
Urethral
and
output
to the amniotic
and allantoic
sacs in fetal
Physiol. Oxf. 10: 309-319,
1988.
Downloaded from ajpregu.physiology.org on January 21, 2007