Vol. 280, Issue 5, R1499-R1509, May 2001
Amniotic fluid and hemodynamic model in monochorionic twin
pregnancies and twin-twin transfusion syndrome
Asli
Umur1,
Martin J. C.
Van Gemert1, and
Michael G.
Ross2
1 Laser Center and Department of Obstetrics and Gynecology,
Academical Medical Center, University of Amsterdam, 1105 Amsterdam,
The Netherlands, 2 Department of Obstetrics and
Gynecology, Harbor University of California-Los Angeles Medical Center,
Torrance, California 90502
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ABSTRACT |
We developed a mathematical
model of monochorionic twin pregnancies and twin-twin transfusion
syndrome (TTTS), combining both fetal fluid dynamics and fetoplacental
growth and circulation alterations and assuming that transplacental
fluid flow from mother to fetus accounts for normal fetal and amniotic
fluid volumes. Ten coupled differential equations, describing fetal
total body and amniotic fluid volumes, their osmolalities, and fetal
blood colloid osmotic pressure, for both donor and recipient twins, were solved numerically. Amniotic flows are controlled by fetal plasma
osmolality and hydrostatic and colloid osmotic pressures. We included
varying placental anastomoses and placental sharing of the
circulations. Consistent with clinical experience, model predictions
are: fetofetal transfusion from unidirectional arteriovenous anastomoses cause oligo-polyhydramnios, a normal size recipient but
hypovolemic donor; compensating oppositely directed deep and superficial anastomoses moderate discordant development; and
anhydramnios results from mild and severe TTTS, where milder forms may
even present earlier in gestation than severe TTTS. Unequal placental circulatory sharing may exacerbate discordant development. In conclusion, our model simulates a wide variety of realistic
manifestations of amniotic fluid volume and fetal growth in TTTS
related to placental angioarchitecture. The model may allow an
assessment of the efficacy of current therapeutic interventions for TTTS.
fetoplacental growth; placental anastomoses; circulatory and
amniotic fluid imbalance; mathematical model
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INTRODUCTION |
MONOCHORIONIC TWINS
COMPLICATED by the twin-twin transfusion syndrome (TTTS) commonly
develop discordant amniotic fluid volume and often but not always
discordant fetal weight, with presentation between 16 and 34 wk of
gestation. As a result of imbalanced fetofetal transfusion along
vascular anastomoses, the donor twin becomes oliguric and hypotensive
and develops oligohydramnios, while the polyuric, hypertensive
recipient develops polyhydramnios (13, 20). Despite these
accepted concepts, predictive abilities, early diagnosis, and treatment
options remain markedly limited.
Because there is no appropriate animal model of TTTS, computer models
have been developed to aid in understanding the pathophysiology (31, 34). Talbert et al. (31) developed a
mathematical model of monochorionic twin fetoplacental units utilizing
numerous interrelated hemodynamic, osmotic, and metabolic physiological
variables. This model of the acute onset of uni- and bidirectional
arteriovenous (AV) anastomotic blood flow identified a sequence of
events resulting in oligo- and polyhydramnios. However, the model was
limited to a 27-wk twin gestation of previously concordant twins
occupying an equally shared placenta and only including AV anastomoses. In view of the enormous variability in clinical presentation of TTTS
and the significant influence of superficial anastomoses and unequal
placental sharing (2, 9, 34), it is unlikely that the
acute introduction of uni- or bidirectional AV anastomoses in an
otherwise normal 27-wk concordant twin pregnancy is a realistic picture
of clinical TTTS.
Our laboratory subsequently derived a computer model (34)
of TTTS that predicted twin fetal growth discordance resulting from
placental angioarchitecture and fetoplacental circulation alterations.
Physiological realities including gestational growth of anastomoses and
unequal placental sharing of the circulations were incorporated in
model equations. Model simulation indicated that fetofetal transfusion
from unidirectional (donor to recipient) AV anastomoses causes
progressive and irreversible fetal discordance with advancing gestation
and fetoplacental growth, because AV transfusion occurs at a rate in
excess of fetal growth. Steady-state discordant growth may develop if
AV anastomotic transfusion is compensated by oppositely directed
transfusion, either from other deep oppositely directed AV or
superficial arterioarterial (AA) or, less frequently, venovenous (VV)
anastomoses. Although the fetal growth predictions of this model are
highly consistent with clinical observations (23, 35, 37,
39), the model did not include an assessment of amniotic fluid dynamics.
In the present study, we sought to combine mathematical models of both
fetal fluid dynamics (8, 31) and fetoplacental growth and
circulation alterations (34) throughout gestation of
monochorionic twin pregnancy to predict the clinical manifestations of
amniotic fluid volume disturbances in TTTS.
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METHODS |
Outline of the model.
Model development consisted of two phases: phase 1 was the
model of normal physiology of fetal and amniotic fluid development; phase 2 incorporated the effects of fetofetal transfusion of
blood along placental anastomoses into the phase 1 model.
The model of normal physiology of fetal and amniotic fluid development
is based on the assumption that the growing fetus acquires water and
nutrient molecules from the maternal circulation to maintain its volume
of total body fluid (TBF in ml) as well as its amniotic fluid volume
(Vamn in ml), which may be viewed as an extension of the
fetal extracellular volume. It follows that growth of fetal TBF [i.e.,
its rate of change, d(TBF)/dt, where t is
gestational age in wk] can be assumed to be the difference between the
total net flux of fluid across the placenta from mother to fetus
(Trans in ml/wk) and growth of amniotic fluid volume, d(Vamn)/dt (Eq. 1).
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(1)
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We tacitly assumed that the fetoplacental circulation can
incorporate all maternal fluids transferred across the placenta; hence,
Trans is the rate-limiting step of fetal growth.
The second model phase incorporates the effects of net fetofetal
transfusion of blood (34) (Inet in ml/wk),
from donor to recipient along the placental anastomoses. As addressed
previously (34), this blood exchange augments the normal
rate of increase of the fetal blood volume (Vb in ml) for
the recipient twin and reduces the normal rate of blood volume increase
for the donor twin.
We have assumed that 10% of the TBF constitutes the blood volume of
the fetus (3). Thus comparable to our previous
model (34)
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(2A)
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(2B)
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Further, Inet also changes the blood (hydrostatic)
pressure and colloid osmotic pressures of both twins, influencing
Trans (Eq.1) and, subsequently, all other
parameters that control the development of fetal and amniotic fluid
volumes. Hence, through these mechanisms, Inet additionally
affects fetal growth of both twins.
Detailed description.
Table 1 summarizes the main relations
used for the physiological parameters for normal fetal and amniotic
fluid development.
Transplacental fluid flow.
Trans (Eq.1) is assumed to depend on a dynamic
balance between the hydrostatic pressures and colloid osmotic pressures
across the placenta (31)
![Trans=L<SUB>pl</SUB>{[P<SUB>mat</SUB><IT>−</IT>(P<SUB>amn</SUB><IT>+</IT>P<SUB>fet</SUB>)]<IT>−</IT>(COP<SUB>mat</SUB><IT>−</IT>COP<SUB>fet</SUB>)}](/content/vol280/issue5/fulltext/R1499/img004.gif)
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(3)
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where Lpl
(ml · wk
1 · mmHg1) is the
net transplacental filtration coefficient, Pmat is the
maternal mean arterial blood pressure in the intervillous space,
Pamn is the transmitted amniotic fluid pressure, and
Pfet is the fetal capillary blood pressure (Eq. 11, below) assumed equal to the fetal capillary pressure in the placental villi. Within the fetal body, the transmitted amniotic pressure adds equally to arterial and venous pressures, so it is added
to the fetal capillary pressure. COPmat and
COPfet are the colloid osmotic pressures of the maternal
blood and fetal blood, respectively (see Blood pressures, COPs,
and osmolality of fetus).
For practical reasons, we empirically assumed that nutrients are
transported via fluid flow from mother to fetus and we set the
osmolality of the transplacental flow (Trans) to 280 mosmol/kgH20, the value for normal plasma osmolality in humans.
Placental filtration coefficient.
For a hemodynamically unconnected twin (i.e., an uncomplicated
pregnancy), Lpl can be determined as a function of
gestation. First, all parameters within the brackets on the right-hand
side of Eq. 3, as well as Vamn and TBF
(Eq. 1), are known from literature data (4, 8, 34,
38). Consequently, Trans and, therefore, Lpl follow from Eq. 1. Because Lpl
is a placental parameter, we assumed that hemodynamically connected
twins have the same Lpl.
Amniotic fluid.
The two primary sources of amniotic fluid production are fetal urine
production [U(t)] and lung liquid secretion [L(t)]. Amniotic fluid
removal is by fetal swallowing [S(t)] and intramembranous flow
[IM(t)], which is the absorption of water into fetal blood perfusing
the fetal surface of the placenta (4, 8). The latter route
has been generalized to include all exchanges between amniotic fluid
and fetal blood that may occur across other surfaces such as fetal skin
and the umbilical cord (4). All these flows are expressed
in milliliters per week. So, the rate of change (growth) of
Vamn can be expressed as
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(4)
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The amniotic fluid osmolality is also calculated for each time
interval. The rate of change in the total number of osmoles contained
in the amniotic fluid is equal to the number of osmoles entering the
amniotic fluid minus the number of osmoles disappearing out of the
amniotic fluid. Because the product of osmolality
(mosmol/kgH2O) and volume constitutes the total number of
osmoles in the amniotic fluid, its rate of change can be expressed as
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(5)
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where Osm(X) is the osmolality of the corresponding flow X.
Amniotic pressure is defined as the ratio of total amniotic fluid
volume and uterine compliance. We have calculated the uterine compliance as a function of gestation using normal amniotic volumes for
both twins (4, 6) and an amniotic pressure of 10 mmHg for
an uncomplicated pregnancy (14).
Urine production.
We related the actual fetal urine production to normal singleton urine
production rates [UN(t)] and assumed that it is
controlled by a pressure diuresis curve
[UCont(Pax)]. Thus
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(6)
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where UN(t) was derived from Rabinowitz et al.
(25) (Eq. m4; Table 1). Pax is the
mean arterial pressure of the hemodynamically connected twin (x = d or r; representing donor or recipient). The function
UCont(Pax) was derived from adult physiology
(16), where urine output is zero at a mean arterial
pressure of 50 mmHg, at 100 mmHg it is normal, and at 200 mmHg it is
about eight times larger than normal (16). We scaled these
data to fetal mean arterial pressures.
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(7A)
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(7B)
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where Pa0 (mmHg) is the mean arterial pressure of
the uncomplicated twin (at the same gestational age).
Urine osmolality decreases as gestation progresses (21)
(Eq. m5; Table 1).
Swallowing.
Because there are no available data for swallowed volumes throughout
gestation, we used the values calculated by Curran et al.
(8) [SN(t); Eq. m6; Table 1].
Swallowed volume is considered to be directly proportional to the size
of the fetus, so we included a factor f, which is the ratio of TBF of a
hemodynamically connected twin over the TBF of a normal uncomplicated
twin. In addition, we assumed that swallowed volumes are controlled by
blood osmolality of the fetus (22, 27), expressed as
control function SCont. Thus
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(8)
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Here, SCont is a second degree control parameter of
fetal osmolality. Assuming that a 4-7% decrease in osmolality is
sufficient to stop drinking in rats (30), the swallowed
volume has been set equal to lung liquid secretion when fetal blood
osmolality (Osmfetx) of fetus x has decreased by 4%,
i.e., when Osmfetx has become 96% of its normal value
(OsmfetN).
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(9A)
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(9B)
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The osmolality of the swallowed volume is equal to amniotic
fluid osmolality.
Intramembranous flow.
Intramembranous flow is defined as the water transfer between the
amniotic cavity and fetal blood. Gilbert et al. (15)
showed that intramembranous absorption of water occurs and plays an
important role in rhesus monkey amniotic fluid volume regulation. We
neglected the potential intramembranous solute exchange (i.e., the
reflection coefficient is assumed to be 1) and assumed that only free
water moves across the intramembranous pathway, driven by osmotic and hydrostatic pressures gradients.
![IM(t)<IT>=</IT>S<SUB>IM</SUB>(t)<IT>·</IT>L<SUB>IM</SUB>(t)<IT>·</IT>[(P<SUB>AF</SUB><IT>−</IT>P<SUB>fet</SUB>)<IT>−</IT>(<IT>&pgr;</IT><SUB>AF</SUB><IT>−&pgr;</IT><SUB>fet</SUB>)]](/content/vol280/issue5/fulltext/R1499/img013.gif)
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(10)
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where 
AF and fet are the osmotic
pressures of the amniotic fluid and fetal blood, respectively (1 mosmol/l = 19.6 mmHg at 37°C; Ref. 16), and
PAF and Pfet are hydrostatic pressures of the
amniotic fluid and fetal blood volume, respectively. SIM(t) (m2) denotes the combined surface of the placenta at the
fetal side, fetal skin, and umbilical cord as a function of gestation.
LIM(t) is the filtration coefficient of the intramembranous pathway.
We have calculated the product of
SIM(t) · LIM(t) for an
uncomplicated pregnancy (Eq. m7; Table 1) from
Eq.10, using intramembranous flow values calculated by
Curran et al. (8), amniotic fluid osmolality determined
for a singleton pregnancy by Brace and Edward (4), and
assuming a fetal plasma osmolality of 280 mosmol/kgH2O.
Lung fluid.
Because no human fetal data are available for lung fluid secretion, we
used values from Curran et al. (8) that were derived from
ovine studies (Eq. m8; Table 1). Because 50% of the lung liquid produced is swallowed before excretion into the amniotic fluid
(4), the values given by Eq. m8 are 50% of
normal lung liquid production. Lung fluid osmolality is assumed to be
isotonic to fetal plasma osmolality throughout gestation
(8).
Blood pressures, COPs, and osmolality of fetus.
Pmat is set to 40 mmHg (12). Fetal capillary
blood pressure (Pfet) is calculated by using fetal mean
arterial (Pa) and venous (Pv) blood pressures
as (12)
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(11)
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Fetal mean arterial and venous blood pressures during gestation
are calculated from fetal blood volumes as described previously (34).
Colloid osmotic pressures (COP in mmHg) for mother and uncomplicated
fetus are calculated according to Wu (38) (Eqs.
m1 and m2; Table 1). For hemodynamically connected
twins, colloid osmotic pressures are calculated as follows. COP is
given by (24)
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(12)
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Equation 12 was combined with the available curves of
COP vs. gestation (38) and fetal blood volume vs.
gestation (34), determining the total number of colloids
in a singleton as a function of gestation. The time derivative gave us
the net colloid production of a singleton fetus as a function of
gestation. Furthermore, the net colloid production of each twin is
considered to be directly proportional to the twin's size. Thus, for
the twins, the colloid production of a singleton was multiplied by the
function f, as was done for swallowing (Eq. 8).
Total amount of colloids in the blood compartment of each fetus changes
not only with the net colloid production but also with exchange of
blood through anastomoses.
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(13A)
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(13B)
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The number of colloids transfused through the anastomoses was
calculated as
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(14)
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where IXY(t) (ml/wk) is the blood flow through the
corresponding XY anastomosis.
Finally, from Eq. 13, the number of total colloids and,
subsequently from Eq. 12, the COP of both twins were calculated.
The number of osmoles in the fetal total body fluid volume also changes
with 1) transplacental fluid transfer and amniotic flows and
2) anastomotic blood transfusion from donor to recipient.
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(15A)
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(15B)
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The number of osmoles transfused from donor to recipient can be
calculated as in Eq. 14 replacing blood colloid
concentration with blood osmolality.
Unequal placental circulatory sharing
We assumed that the number of available cotyledons for the twins,
representing their placental circulatory fractions, remains constant
throughout pregnancy (34). For IM flow across the fetal skin (prior to keratinization), we have also assumed that fetal skin
surface is proportional to its placental surface [i.e.,
Lpl = X · Lpl for
Trans and
SIM(t) · LIM(t) = X · SIM(t) · LIM(t) for IM, where X is the normalized placental fraction (34)
defined as X1 + X2 = 2, subscripts 1 and 2 denote fetuses 1 and 2].
Model description.
Essential to the model is our previous assumption that each anastomosis
grows in volume proportionately with the placental volume,
approximately proportional to gestational age to the third power
(34). As a consequence, we derived that each anastomotic resistance decreases proportional to (t-4) to the third power, where t
is gestational age (wk) and blood vessels become functional at 4 wk of
gestation (34). Therefore, anastomotic resistance can be
expressed as
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(16)
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where Eq. 16 implies that the resistance value at 40 wk completely determines resistance values throughout pregnancy.
Because the mechanisms of fetal and amniotic fluid dynamics before 11 wk of gestation are significantly different from those of the second
and third trimester, the model is initiated at 11 wk. Fetal blood
volume and pressures before 11 wk were calculated on the basis of our
previous model (34) using as input parameters: 1) degree of placental sharing, 2) types of
anastomoses, and 3) their resistance during gestation
defined by the values chosen at 40 wk (Eq. 16). At 11 wk,
our model starts with the assumption of equal amniotic fluid volumes of
40 ml for both twins and osmolality of amniotic fluid and blood of 280 mosmol/kgH2O.
The model program runs for both uncomplicated and for hemodynamically
connected twins. First, normal twin data are deduced from the run of
the uncomplicated twin. Second, all amniotic fluid flows (U, L, S, IM),
transplacental flow (Trans), and Inet are calculated. From these flows, new blood volumes, pressures,
osmolalities, and COPs for the twins and osmolalities and pressures for
the amniotic fluid result. We solved the 10 coupled differential
equations between 11 and 40 wk gestation by a standard numerical
forward finite difference method with a total time step of 1/10,000
wk (~1 min).
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RESULTS |
Uncomplicated twins (no vascular anastomoses).
The amniotic fluid volume as predicted by our model for an
uncomplicated twin fetus is shown as the curve labeled "Normal" in
Fig. 1. Normal amniotic fluid volume
steadily increases until 35 wk of gestation and decreases
throughout the remainder of the pregnancy, with values well within the
normal range of widely varying volumes (quoted as 39-257% of the
mean volume for any given gestational age; Ref. 4). Normal
amniotic and fetal blood parameters predicted by our model are
summarized in Table 2.
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Fig. 1.
Numerical results of amniotic fluid volumes for a single
arteriovenous (AV) anastomosis and equal placental sharing. Resistances
(R) of the anastomoses at 40 wk are 6.91, 4.05, 2.53, and 1.66 mmHg · ml1 · day1,
respectively, where largest resistance corresponds to smallest
discordance. "Normal" denotes amniotic fluid volume of an
uncomplicated fetus used in the model (Table 2).
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Twins with unidirectional AV anastomoses.
Blood transfusing along the AV anastomosis from donor to recipient,
which occurs at a rate in excess of fetal growth (34), reduces the donor twin's blood volume, blood pressures resulting in
hypotension (20), urine production rate, blood osmolality, and COP. The decrease in fetal COP is greater than the decrease in
total capillary pressure of the donor, so the total net fluid flux
across the placenta will decline (Trans; Eq. 3).
The donor becomes growth retarded. Furthermore, swallowing and
intramembranous flow will decrease because fetal blood osmolality and,
consequently, osmotic pressure decrease. The decrease in urine
production rate is greater than the sum of swallowed volume and
intramembranous flow, causing the donor twin's amniotic fluid volume
to increase slower than normal and even to decrease for sufficiently
large AV anastomotic flow. In the recipient twin, the converse applies. In our model, the donor becomes "stuck" to the uterine wall. Larger AV anastomotic flow (lower AV resistances) increases the severity of
the situation, causing larger fetal and amniotic fluid discordance and
earlier occurrence of a stuck donor twin (Fig. 1).
Figure 2 shows simulations of estimated
fetal weight and amniotic fluid volume (Fig. 2, inset) from
a clinical single AV case (29). Clinically,
ultrasonographic examination at 13 wk identified adequate amniotic
fluid volumes with an impression of decreased fluid surrounding the
smaller fetus and increased fluid surrounding the larger fetus. At 18 wk, the smaller twin was found stuck to the uterine wall and the larger
twin had cardiomegaly and was surrounded by polyhydramnios. At 19 wk,
the patient went into spontaneous labor with the resulting loss of both
fetuses. An AV anastomosis from smaller to larger twin was identified
after placental examination. We fitted the AV resistance (at 40 wk in the model) until the ratio of the simulated fetal blood volumes at
birth agreed best with those of the clinically measured birth weights.
The simulated amniotic fluid volume followed directly from the model,
without any additional fit procedure. Table
3 summarizes other model parameters for
both twins.
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Fig. 2.
Numerical results of estimated fetal weights of a single AV
anastomosis and equal placental sharing, based on clinical data by
Sharma et al. (29).  ,  :
Reported estimated fetal weights (29) (error bars ± 20%);  ,  : birth weights; bold lines:
model prediction using an AV resistance of 1.02 mmHg · ml1 · day1 at 40 wk.
AV resistance resulted from a best fit of ratio between calculated
fetal blood volumes at 19 wk with ratio between birth weights.
Inset: numerical results of amniotic fluid volumes for same
AV resistance; bold lines: model predictions; normal lines: normal
amniotic fluid volume used in the model. We emphasize that our model
predictions are not a best fit to data points of estimated fetal
weights but predicted using only the fitted AV resistance of 1.02 mmHg · ml1 · day1.
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Table 3.
Amniotic and fetal parameters for an AV anastomosis, from Sharma et al.
(29), throughout gestation as predicted by the model
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Twins with AV plus compensating superficial
anastomoses.
Superficial AA and VV anastomoses compensate for the effects of the AV
anastomoses (2, 10, 32, 37), albeit that VV is estimated
to be about eight times less effective at equal resistance, where the
factor eight simulates the ratio between fetal mean arterial and venous
pressures (34). For simplicity, therefore, we only show
results for AV plus AA anastomoses.
Figure 3, A and B,
shows predicted fetal blood volumes and amniotic fluid volumes in
response to various combinations of AV plus compensating AA anastomoses
of increasing significance. Increasing fetal discordance will develop
first, due to AV transfusion, causing the donor twin's mean arterial
pressure to become smaller than the recipient's mean arterial pressure
(20). This allows compensating blood flow to develop from
recipient to donor via the AA anastomosis. If the AA resistance is
sufficiently small, the AA transfusion is of sufficient quantity
compared with the AV transfusion and oppositely directed, which
mitigates the increase in the net donor to recipient transfusion. In
contrast to our previous model (34), this process
continues, allowing the net fetofetal transfusion to decrease until the
oppositely directed AA flow becomes virtually equal to the AV flow.
This is due to increased osmolality and COP of the recipient twin,
resulting in increased transplacental and intramembranous flow followed
by a continuous increase in the fetal blood volume and, particularly,
in the recipient's mean arterial pressure. Therefore, the compensating
AA anastomotic transfusion increases stronger than the AV transfusion,
which decreases the net fetofetal transfusion, mitigating further
decrease of the donor's arterial pressure relative to normal values.
The donor's urine production therefore continues albeit at a smaller rate compared with normal. There is still discordance between the
fetuses (Fig. 3A) and their amniotic fluid volumes (Fig.
3B), but the donor twin is not "stuck" if there are
sufficiently large AA anastomoses (Fig. 3B). Figure
3A suggests that donor twins become growth retarded, but
recipient twin's blood volume remains near normal values, in agreement
with clinical findings (11, 35, 39).
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Fig. 3.
A: numerical results of fetal blood volumes for AV + AA anastomoses and equal placental sharing, with decreasing AA
resistances compared with single AV case (dotted lines).
: Result of equal AV + AA anastomoses of our
previous model (34) (resistances are 1.66 mmHg · ml1 · day1 at 40 wk), showing increased recipient's blood volumes. B:
corresponding results of amniotic fluid volumes (bold lines) compared
with single AV case (dotted lines). Resistances at 40 wk are 1.66 mmHg · ml1 · day1 for AV
anastomosis and 1.66, 0.80, 0.43, 0.25, 0.16, and 0.10 mmHg · ml1 · day10 for AA
anastomoses. Largest discordance corresponds to largest AA resistance.
Inset: numerical results of amniotic fluid volumes for an AV
resistance of 0.80 mmHg · ml1 · day1 with AA
resistance of 0.33 mmHg · ml1 · day1. Lowest
solid curve indicates a stuck donor twin at 22 wk and spontaneous
reaccumulation of amniotic fluid at 27 wk.
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Interestingly, larger size AV and AA anastomoses (Fig. 3B,
inset) simulated a "stuck" twin occurring at 22 wk of
gestation. Discordance in blood volumes was ~33%. However, because
net fetofetal transfusion decreases and may ultimately approach zero
(not shown), reaccumulation of amniotic fluid in the donor twin occurs
spontaneously, here at ~27 wk. Comparison with Fig. 3B
(lowest solid curve) suggests that occurrence of a stuck twin is not a
unique indication of the severity of TTTS.
Twins with bidirectional AV anastomoses.
If the AV anastomosis is compensated by an oppositely directed AV
anastomosis, the most common types of vascular anastomoses in TTTS
(9, 10, 32, 36, 37), a steady state of the smallest
possible net fetofetal transfusion develops, quite similar to the case
of AV plus AA anastomoses. Bidirectional AVs therefore differ in their
hemodynamic effects from single or unidirectional AVs
(34). In response to various combinations of AV plus
opposite AV anastomoses, our model predicts similar amniotic fluid and fetal blood volumes as shown in Fig. 3 for AV plus AA anastomoses.
Twins with unequal placental sharing of their circulations.
In our model unequal placental sharing of the two circulations causes
discordant fetal and amniotic fluid development, because the fetus
having the smaller placental circulation receives a smaller
transplacental fluid flow from the mother (see dots in Fig.
4). Our model predicts that unequal
placental sharing, with an AV anastomosis from the larger to the
smaller placental circulations, results in later onset of TTTS than in
the case of equal sharing (see bold lines in Fig. 4A) and a
seemingly paradoxical reversal of the oligo-polyhydramnios sequence in
which the initially larger twin with greater amniotic fluid volume
becomes the smaller twin with oligohydramnios (see bold lines in Fig.
4B). This phenomenon has been described (18)
but, unfortunately, without placental analysis. Recently, late onset of
TTTS has indeed been correlated with unequal circulatory sharing and
two small unidirectional AV anastomoses from larger to smaller
placental parts (23).
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Fig. 4.
A: numerical results of fetal blood volumes
for 0.25:0.75 unequal placental sharing without anastomoses (dots) and
same placental sharing with a single AV anastomosis from larger to
smaller placental parts of resistance 6.91 mmHg · ml1 · day1 at 40 wk
(bold lines). B: corresponding results of amniotic fluid
volumes.
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Severity of TTTS.
In our present and previous (34) models, the etiology of
TTTS is a stronger increase in net fetofetal transfusion
(Inet) than fetal growth of each twin. Consequently, the
ratio of fetal growth of the donor twin's blood volume and
Inet represents a proper model parameter to indicate the
severity of the imbalance that develops between the twins'
circulations. Thus the closer this ratio remains near one when a stuck
twin occurs, the milder is the TTTS. Conversely, the smaller the ratio,
the more severe forms of TTTS develop. Figure
5A shows predicted evolution
of this ratio for two different AV anastomoses (I and II) without compensation (Ia, IIa) and with compensating AA anastomoses (Ib, Ic,
IIb) and for unequal placental circulatory sharing (III) with an AV
anastomosis from larger to smaller placental part, again without
compensation (IIIa) and with compensating AA anastomoses (IIIb, IIIc).
Bold lines indicate cases resulting in a "stuck" donor and severe
discordance between fetuses. Thin lines indicate cases not resulting in
a stuck twin before 30 wk of gestation. Figure 5A also shows
that a "stuck" twin may occur early in pregnancy (Ia, Ib) or late
(IIIa) depending on the placental angioarchitecture. Furthermore, a
stuck twin occurring early, e.g., curves Ib and Ic, representing milder
TTTS cases, does not necessarily indicate increased severity of TTTS
compared with a stuck twin occurring later, e.g., curves IIa, IIb, and
IIIa, representing more severe TTTS. In addition, curve Ic represents a
case (also shown in Fig. 3B, inset) where the donor grows
only slightly less than net fetofetal transfusion, from 14.5 to 23 wk,
sufficient to become stuck at 22 wk of gestation. However, because net
fetofetal transfusion started to decrease at 18 wk, the donor could
accumulate amniotic fluid again at ~27 wk (Fig. 3B,
inset), indicative of mild TTTS.
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Fig. 5.
A: model results for ratio of fetal growth of donor twin
and net fetofetal transfusion of blood for AV + AA
anastomoses: Ia: single AV with resistance at 40 wk: 0.80 mmHg · ml1 · day1; Ib and
Ic: same AV with AA resistances of 0.58 and 0.33 mmHg · ml1 · day1 at 40 wk,
respectively; IIa: single AV with resistance at 40 wk: 2.31 mmHg · ml1 · day1; IIb:
same AV with identical AA resistance. Furthermore, a 0.25:0.75 unequal
placental sharing (recipient:donor) with IIIa: single AV with
resistance of 6.91 mmHg · ml1 · day1 at 40 wk;
IIIb: same AV with identical AA resistance; IIIc: same AV with an AA
resistance of 4.05 mmHg · ml1 · day1 at 40 wk.
B: corresponding model results of donor twin's urine
production.
|
|
Figure 5B shows the corresponding curves of urine production
(ml/wk) for the donor twins. Our model suggests that fetofetal transfusion from single AV anastomoses (curves Ia, IIa, IIIa) may show
strongly decreasing urine production rates once the donor has become
stuck, suggestive of lack of bladder filling in donor twins, whereas in
cases of compensated AV anastomoses (curves Ib, Ic, IIb) urine
production will not cease, possibly implying that bladder filling
persists in the donor.
| |
DISCUSSION |
Model.
To our knowledge, this mathematical model is the first to incorporate
both hemodynamics and amniotic fluid dynamics in monochorionic twins
throughout pregnancy. The model combines the approaches of Talbert et
al. (31), Curran et al. (8), and van Gemert and Sterenborg's previous hemodynamic model of TTTS
(34). Growth of fetal total body fluid (Eq. 1) is governed by the net transplacental fluid flow
(Trans). Previously (34), fetal growth was
assumed proportional to the fetoplacental circulation. However, in our present model, we tacitly assumed that the fetoplacental circulations can incorporate all fluids transferred across the placenta, and we
adapted the same relationships between fetal blood volume and blood
pressures as before (34). Consequently, although the
mechanisms for fetal growth may seem different in the two models, they
are actually very similar.
Previously (34), we emphasized that incomplete information
is available on the normal cardiovascular development of fetuses, let
alone when the development is complicated by fetofetal transfusion. Equally so, incomplete information is available on the physiology of
amniotic fluid dynamics. We were therefore forced to improvise using a
simplified and sometimes empirical description of fetal and amniotic
fluid physiology. Furthermore, we tried to limit the number of model
variables to those that seemed essential in simulating clinically
realistic TTTS development. Consequently, we did not include
discordantly developing (patho)physiological adaptation processes that
are likely to be secondary to onset of TTTS (e.g., blood viscosity,
oxygenation of fetal organs, and pathological alterations in fetal,
placental, and cardiac development). Including such mechanisms
throughout gestation would not only be a formidable but most likely
impossible task to date in view of the limited information available.
Therefore, like any model, our model is a deliberate oversimplification
that can serve as a point of departure for understanding a much more
complicated reality (5). As a consequence, our model can
only provide trends to illustrate the general concepts. However, these
underlying concepts are likely realistic.
First, in Eq. 3, we assumed the total net flux of water and
nutrient solutes across the placenta (Trans) is governed by
the driving osmotic and hydrostatic pressure gradients. This is a simplification of the placental water and solute transfer. Solutes can
diffuse through the placenta, be actively transported by the placenta,
and be produced by fetal plasma. Water transfer is sensitive to the
fetoplacental and also maternal blood flow, neither of which is
incorporated in the model. Therefore, until these mechanisms have been
fully identified, empirical description is inevitable.
Second, lack of data available for fetuses forced us to adapt empirical
control mechanisms for urine production and fetal swallowing rates
(i.e., control of urine production from scaled adult values for chronic
arterial pressure changes and swallowed volume by fetal osmolality).
Moritz et al. (19) described the association of fetal
arterial blood pressure and urine output in the ovine fetus,
demonstrating that a Pa-to-PaN ratio of
1.35 ± 0.08 gives a U-to-UN ratio of 3.2 ± 0.3, where N denotes normal values. Our control function (16)
gives a quite similar U-to-UN ratio of 2.7 for a
Pa-to-PaN ratio of 1.35. It is also
acknowledged that our regulatory equations for swallowing are in
agreement with data derived from the ovine fetus (22)
where it was reported that a 6% decrease in osmolality causes an
~50% decrease in swallowed volumes. In our model, a 4% decrease in
osmolality causes swallowed volumes to be equal to the lung fluid
produced, which reduces swallowed volume to 53% of its normal value at
30 wk of gestation. Consequently, we believe that the control
mechanisms used generate realistic behavior of these amniotic fluid flows.
TTTS.
Preliminary clinical data suggest that bidirectional AV
anastomoses cause TTTS in ~55%, whereas AV plus AA combinations
cause it only in ~30% (36). Consequently, AA
anastomoses have been touted to play a predictive role in onset and
severity of TTTS (9, 32). The possible differential
effects of polyhydramnios on AV (and opposite AV) vs. AA transfusion
have recently been proposed by the authors (33) as a
possible explanation.
Our model simulated a wide spectrum of TTTS presentations, all of which
have been described clinically. First, the AV anastomotic transfusion
responsible for TTTS causes a continuously increasing fetal discordance
predicted to develop between the twins. Although the donor twin becomes
growth retarded, the recipient twin's blood volumes remain nearly
normal. In our model, this is due to the recipient's increased urine
production in response to increased mean arterial blood pressure that
helps to keep its total blood volume near normal values. In contrast,
compensation of blood loss for the donor twin is insufficient (Fig.
3A). Although this behavior has been observed clinically
(11, 35, 39), it contradicts the predictions of our
previous model (34), which only shows symmetric deviations
from the normal growth curve (see open circles in Fig. 3A).
We emphasize, however, that the size discordance overall in TTTS has an
extremely wide range and not all donors become growth retarded,
depending (at least in part) on gestational age, severity of TTTS, and
circulatory sharing of the placenta. Second, considering uncompensated
as well as compensated anastomotic patterns, we simulated that the
oligo-polyhydramnios sequence can occur early or late during pregnancy
and can represent severe as well as milder forms of TTTS. Notably,
milder TTTS does not necessarily present later in gestation than more
severe TTTS. In addition, we simulated the occurrence of a stuck donor
and a polyhydramniotic recipient with small as well as large fetal discordance in their blood volumes, varying between ~30-55%.
Furthermore, TTTS was simulated to reverse between the donor and
recipient and can even disappear spontaneously, as observed clinically
(1, 7). Components in our model that are responsible for
this wide spectrum of severity of TTTS are 1) size of the AV
anastomoses (donor to recipient), 2) capacity of the
compensating anastomoses with respect to the AV, and 3)
placental circulatory sharing between the twins. This spectrum of
severity included in the stuck twin-polyhydramnios sequence that
defines TTTS has important clinical correlates. Varying therapies,
including septal disruption (28), amnioreduction (17), and laser ablation of placental vessels
(17), may each have specific TTTS anastomotic anatomies
that are amenable to the therapy. However, therapies thought to be
clinically efficacious may be serving only as surgical placebos in
cases that would spontaneously abate. Our model suggests that
measurement of urine production of the donor twin may have a predictive
value in the assessment of severity (26).
In conclusion, our model simulates a wide variety of realistic
manifestations of amniotic fluid and fetal growth behavior in TTTS
during pregnancy related to placental angioarchitecture. We hypothesize
that our model will allow an assessment of the efficacy of current
therapeutic interventions for TTTS, including both hemodynamic and
amniotic fluid volume interventions.
Perspectives
Monozygous twinning has an incidence of ~3.5 in 1,000 pregnancies, with 75% of these cases sharing one monochorionic
placenta in which their fetoplacental circulations are virtually always coupled by one or more placental vascular anastomoses. TTTS complicates monochorionic twin pregnancies in 6-35% of cases by significant net fetofetal transfusion along the anastomoses, from donor to recipient. As a result of net fetofetal transfusion from imbalanced vascular anastomoses, the donor twin may become growth retarded with
oligohydramnios, while polyhydramnios may occur in the normal size
recipient, who often develops circulatory volume overload. If these
sequelae remain untreated, high morbidity and mortality rates ensue.
Despite these consequences, predictive abilities, early diagnosis, and
treatment options remain markedly limited. The mathematical model
developed in the present study may enable an improved understanding of
TTTS pathophysiology and identify the sequence of events that
determines efficacy and outcome of current and potential therapeutic interventions.
| |
ACKNOWLEDGEMENTS |
A. Umur is supported by the The Netherlands Heart Foundation Grant
99.174. M.G. Ross is supported by National Heart, Lung, and Blood
Institute Grant HL-40899.
| |
FOOTNOTES |
Address for reprint requests and other correspondence: M. J. C. van Gemert, Laser Center, Academic Medical Center, Univ. of Amsterdam,
Meibergdreef 9, 1105 AZ Amsterdam, The Netherlands (E-mail:
m.j.vangemert{at}amc.uva.nl).
The costs of publication of this
article were defrayed in part by the
payment of page charges. The article
must therefore be hereby marked
"advertisement"
in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 17 July 2000; accepted in final form 10 January 2001.
| |
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Am J Physiol Regul Integr Comp Physiol 280(5):R1499-R1509
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ABSTRACT
INTRODUCTION
![of donor<IT>−</IT>[I<SUB>AA</SUB>(t)<IT>+</IT>I<SUB>VA</SUB>(t)<IT>+</IT>I<SUB>VV</SUB>(t)]](/content/vol280/issue5/fulltext/R1499/img019.gif)
