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Arterio-venous flow between monochorionic twins determined during intra-uterine transfusion
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2008 Phys. Med. Biol. 53 N109 (http://iopscience.iop.org/0031-9155/53/7/N02) View the table of contents for this issue, or go to the journal homepage for more
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IOP PUBLISHING
PHYSICS IN MEDICINE AND BIOLOGY
Phys. Med. Biol. 53 (2008) N109–N117
doi:10.1088/0031-9155/53/7/N02
NOTE
Arterio-venous flow between monochorionic twins determined during intra-uterine transfusion Martin J C van Gemert1, Jeroen P H M van den Wijngaard1,2, Enrico Lopriore3, Suzanne A Pasman4 and Frank P H A Vandenbussche4 1 Laser Centre and Department of Obstetrics, Laser Center, Academic Medical Center, Meibergdreef 9, 1105 AZ Amsterdam, The Netherlands 2 Department of Medical Physics, Academic Medical Centre, University of Amsterdam, Amsterdam, The Netherlands 3 Division of Neonatology, Department of Pediatrics, Leiden University Medical Centre, Leiden, The Netherlands 4 Division of Fetal Medicine, Department of Obstetrics, Leiden University Medical Centre, Leiden, The Netherlands
E-mail:
[email protected]
Received 1 October 2007, in final form 27 February 2008 Published 18 March 2008 Online at stacks.iop.org/PMB/53/N109 Abstract Twin–twin transfusion syndrome (TTTS) is a severe complication of monozygotic (identical) twin fetuses sharing one single (monochorionic) placenta. TTTS is caused by a net inter-twin transfusion of blood through placental anastomoses, from one twin (the donor) to the other (the recipient), which link the two feto-placental circulations. Currently, the only reliable method to measure the net inter-twin transfusion clinically is when incomplete laser therapy of TTTS occurs and one of the twins becomes anemic and requires an intra-uterine transfusion of adult red blood cells. Then, differences between adult hemoglobin concentrations measured during the transfusion and at birth relate not only to the net inter-twin transfusion but also to the finite lifetime of the adult red blood cells. We have analyzed this situation, derived the differential equations of adult hemoglobin in the donor and recipient twins, given the solutions and given expressions relating the net inter-twin flow with clinically measured parameters. We have included single and multiple intrauterine transfusions. In conclusion, because incomplete laser therapy occurs frequently, and some cases require an intra-uterine transfusion, this method may allow collecting a wealth of net inter-twin flow data from clinicians involved in laser therapy of TTTS. To aid to the widespread use of this method, we have presented the equations as clearly as possible in tables for easy use by others.
0031-9155/08/070109+09$30.00
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1. Introduction About 75% of monozygotic (identical) twin fetuses share one single (monochorionic) placenta. Virtually all monochorionic twin pairs are hemodynamically linked by placental vascular anastomoses, which can be of three types: arterio-venous (AV), where a placental cotyledon receives its arterial blood from one twin but drains its venous blood to the other, causing a unidirectional inter-twin transfusion, arterio-arterial (AA) and less frequently veno-venous (VV) anastomoses, which directly link the two arterial or venous circulations. The latter two types of anastomoses cause an inter-twin transfusion only when one twin has a higher arterial or venous pressure than the other. About 10% of monochorionic twins develop twin–twin transfusion syndrome (TTTS) which is associated with considerable intra-uterine mortality and serious post-natal morbidity (Lopriore et al 2003). TTTS is caused by a significant net inter-twin transfusion from one twin (the donor) to the other (the recipient), causing various stages of complications in both twins (Quintero et al 1999). The donor becomes hypotensive and hypovolemic and virtually without amniotic fluid, and the recipient becomes hypervolemic, with excess amniotic fluid, and often but not always suffering from cardiac dysfunction (van Gemert et al 2001, Lewi et al 2003, Galea et al 2005). It is now generally accepted that laser obliteration of anastomoses during fetoscopy is the preferred therapy for severe TTTS (Senat et al 2004). The actual volume of net inter-twin transfusion causing TTTS was unknown for a long time. This was due to the lack of an animal model as well as insufficient accuracy of Doppler ultrasonography to assess the net flow from measured individual anastomotic transfusions (Denbow et al 2004, Nakata et al 2004, Wee et al 2007). Computational modeling (van den Wijngaard et al 2007) suggested that it is small, limited to tens of ml per 24 h (van den Wijngaard et al 2008). Recently, our group determined the first accurate value of net inter-twin transfusion. We utilized a case of incomplete laser therapy of TTTS where five AV anastomoses from the ex-recipient to the ex-donor remained patent. The ex-recipient became anemic and required an intra-uterine blood transfusion. We measured the total Hb concentration before and after transfusion, and after emergency delivery 2 days later, related the decrease in total Hb to the AV flow and determined it as 28 ml/24 h (Lopriore et al 2007). Incomplete laser therapy occurs in about 27% of treatments (Robyr et al 2006) and one of the twins may become anemic requiring an intra-uterine blood transfusion. In such cases, it is easy to collect the Hb concentrations before and after the transfusion and after birth from which the net inter-twin transfusion can be calculated. Thus, it may now become practicable to collect Hb data from incomplete laser cases, which will accumulate a wealth of net inter-twin transfusions, covering a range of gestational ages and TTTS stages. For a long time, such an achievement was considered exceedingly important but technically impossible. Intra-uterine blood transfusions are given with processed adult red blood cells. The advantage of their use to assess the net inter-twin transfusion is that native adult Hb has a significantly smaller, virtually negligible production in newly formed fetal red blood cells than fetal Hb. Thus, utilizing the time behavior of adult Hb concentrations gives more accurate values of inter-twin transfusions than total, i.e. adult plus fetal Hb concentrations. However, two complicating factors not addressed previously (Lopriore et al 2007) need to be dealt with: first, the finite lifetime of adult red blood cells, which is on the order of tens of days (Brace et al 2000) and, second, multiple intra-uterine transfusions. Therefore, we sought to derive the equations relating net inter-twin transfusions with adult Hb concentrations, neglecting the small production in fetal red blood cells, but accounting for their finite lifetime. We include single and multiple transfusions, and present the equations in tables 2 and 3 for easy use by colleagues involved in laser therapy of TTTS.
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Table 1. List of symbols. IUT: intra-uterine transfusion. Symbol
Description
AA AV AVflow D dt HbA HbA(0) HbAk (0) HbAk (tk ) HbT HbT(0) HbTk (0) HbTk (tk ) [Hb(t)] LT R t t1 t2 tk Volblk VV
Arterio-arterial anastomosis Arterio-venous anastomosis Arterio-venous inter-twin transfusion (ml 24 h−1) Donor (as superscript) Infinitesimal time period (days) Adult Hb concentration (g dl−1) Adult Hb, just after a single IUT (g dl−1) Adult Hb, just after the kth IUT (g dl−1) Adult Hb, tk days after the kth IUT, just before the (k + 1)th IUT or just after birth (g dl−1) Total hemoglobin concentration (g dl−1) Total Hb, just after a single IUT (g dl−1) Total Hb, just after the kth IUT (g dl−1) Total Hb, tk days after the kth IUT, just before the (k + 1)th IUT or just after birth (g dl−1) Weight of Hb, t days after IUT (g) Life time of adult red blood cells (days) Recipient (as superscript) Time (days) Time between the first IUT and the second IUT or birth (days) Time between the second IUT and the third IUT or birth (days) Time between the kth IUT and the (k + 1)th IUT or birth (days) Blood volume during and after the kth IUT (ml) Veno-venous anastomosis
2. Theory Table 1 summarizes the symbols used in this note. We assume for convenience that incomplete laser therapy leaves one patent AV anastomosis, connecting the arterial side of one twin, the donor, with the venous side of the other, the recipient. One AV anastomosis also covers the effects of multiple unidirectional AV anastomoses. For the analysis to follow, it is irrelevant whether the new donor (further expressed as the donor) was the donor or the recipient before the laser procedure. If more types of anastomoses remain patent, e.g. also including anastomoses oppositely directed than AV, the analysis below determines the sum of all inter-twin transfusions, i.e. the net inter-twin transfusion from donor to recipient. We also assume that the blood volume of the donor at the moment of intra-uterine transfusion is known from standard dilution methodology (Hoogeveen et al 2002). Further, the recipient’s blood volume is also included in the equations and we suggest that it follows from the ratio of the birth weights to the donor’s measured pre-natal blood volume. Previously (Lopriore et al 2007), we presented the expression for the AV flow related to measured total Hb concentrations, neglecting the production and decay of fetal red blood cells. Although not addressed further in this note, these results will also be summarized in tables 2 and 3. 2.1. One transfusion Table 2 summarizes the outcomes of the analysis. The donor’s decrease in adult Hb concentration is the result of two main mechanisms. The first is the AVflow . The second is the natural decay of adult red blood cells due to their finite lifetime (LT) (days). We recall that we neglected the small production term of natural adult red blood cells in the fetal blood.
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M J C van Gemert et al Table 2. One transfusion, summarizing the equations, the known parameters and the parameters to be determined. Equations AVflow =
AVflow =
VolD bl t1
VolD bl t1
ln
HbTD (0)
HbTD (t1 )
VolR HbAR (t1 )−HbAR (0) bl · · ln 1 + D D HbA (t1 )
Volbl
Known
To determine
HbTD (0),
AVflow
HbTD (t1 ), VolD bl HbAD (0),
AVflow , LT
D
LT =
VolD bl VolR bl VolD bl VolR bl
−HbAR (t1 )+
HbA (t1 ), HbAR (t1 ), ·t1 ·HbAD (0)
· HbAD (0)−HbAD (t1 )
R VolD bl , Volbl ,
Table 3. Two transfusions, summarizing the equations, the known parameters and the parameters to be determined. Equations AVflow1 = AVflow2 =
VolD bl1 t1 VolD bl2 t2
ln
HbT1 D (0) HbT1 D (t1 )
HbT2 D (0) HbT2 D (t2 )
ln
Known
To determine
HbT1 D (0),
AVflow1 ,
HbT1 D (t1 ),
AVflow2
HbT2 D (0),
LT =
−HbA2 R (t2 )+
AVflow1 = AVflow2 =
VolD bl1 t1 VolD bl2 t2
HbA1 R (t1 ) =
VolD bl1 VolR bl1
· ln · ln
VolD bl1 VolR bl1
·t1 ·HbA1 D (0)+
·[HbA1 D (0)−HbA1 D (t1 )]+
D (0)
HbA1 HbA1 D (t1 ) HbA2 D (0) HbA2 D (t2 )
· 1−
· 1−
t1 LT
·t2 ·HbA2 D (0) VolD bl2 VolR bl2
·[HbA2 D (0)−HbA2 D (t2 )]
t2 LT
VolD
bl1 · HbA1 D (0) · 1 − R Volbl1
VolD bl2 VolR bl2
HbT2 D (t2 ), D VolD bl1 , Volbl2
t1 D LT − HbA1 (t1 )
HbA1 D (0),
LT,
HbA1 D (t1 ),
AVflow1 ,
HbA2
D (0),
HbA2 D (t2 ),
AVflow2 , HbA1 R (t1 )
HbA2 R (t2 ), R VolD bl1 , Volbl1 , R VolD bl2 , Volbl2
The second mechanism obviously applies to the total weight (or total number) of adult Hb in the blood volumes of the donor and recipient together, a consequence of net intertwin transfusion through the anastomoses. Therefore, we will first derive equations for the weight of adult Hb, denoted here with brackets, i.e. [HbA]. Subsequently, we will transform the outcomes back to equations describing the concentration of adult Hb in both twins, the parameters measured during blood sampling. The AV flow reduces the donor’s weight of adult Hb by a small amount, d[HbAD (t)], transfused to the recipient within infinitesimal time period dt, according to AVflow · [HbAD (t)] dt AV transfusion. (1) d[HbAD (t)] = − VolD bl The product AVflow · dt is the donor’s loss of blood volume (ml) during dt due to AV transfusion and (AVflow · dt) VolD bl is the fraction of donor blood volume transfused during
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dt to the recipient. Thus, the total right-hand side term, the transfused donor’s blood volume fraction times the weight of adult Hb, gives the loss of adult Hb weight in the donor’s blood by AVflow . AVflow and VolD bl are assumed to remain constant during the time period between transfusion and delivery. In the recipient, the simultaneous increase of adult Hb weight by the AV flow within dt is AVflow · [HbAD (t)] · dt AV transfusion, (2) d[HbAR (t)] = VolD bl identical but opposite to equation (1) The finite lifetime of adult red blood cells causes an assumed linear decaying weight of HbA, starting with [HbAD (0)], at t = 0, just after the intra-uterine transfusion to the donor and ending with no adult Hb in either twin at t = LT days. Thus, t Natural decay. (3) [HbAD (t)] + [HbAR (t)] = [HbAD (0)] · 1 − LT
From equation (3), the rate of change of [HbAD (t)] + [HbAR (t)] follows from the time derivative as [HbAD (0)] · dt Natural decay. (4) LT For the donor, the rate of change of its weight of adult Hb follows from the rate of change of total weight times the donor’s weight fraction, or as [HbAD (t)] D D R Natural decay. d[HbA (t)] = d([HbA (t)] + [HbA (t)]) · [HbAD (t)] + [HbAR (t)] (5a) d([HbAD (t)] + [HbAR (t)]) = −
From equations (3) and (4), this becomes [HbAD (t)] D · dt d[HbA (t)] = − LT − t
Natural decay.
(5b)
A similar result holds for the recipient. Thus, combining both mechanisms gives [HbAD (t)] AVflow · [HbAD (t)] d[HbA (t)] = − · dt − · dt LT − t VolD bl [HbAR (t)] AVflow · [HbAD (t)] d[HbAR (t)] = · dt − · dt. LT − t VolD bl
D
(6) (7)
Note that the donor’s [HbAD (t)] is included in the recipient’s equation (7), expressing that the donor received the intra-uterine transfused adult red blood cells. Our aim is to derive equations for the adult Hb concentrations in the donor and D recipient, the parameters measured during
actual
Rblood sampling. Using that HbA (t) = D D R R [HbA (t)] Volbl and HbA (t) = [HbA (t)] Volbl , equations (6) and (7) become HbAD (t) AVflow · HbAD (t) · dt − · dt LT − t VolD bl HbAR (t) AVflow · HbAD (t) R dHbA (t) = · dt − · dt. LT − t VolRbl
dHbAD (t) = −
(8) (9)
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Equations (8) and (9) can be solved easily using that donor and recipient HbA are the product of an unknown time function, say F(t) and G(t), and (1 − t/LT). Both F(t) and G(t) follow by inserting the product of functions in equation (8) or (9) and solving the resulting differential equation for F(t) and G(t). Subsequently, the solution of equation (8) has to be substituted in (9) and integrated over time. The solutions are AVflow HbAD (t1 ) · 1− · = exp −t 1 HbAD (0) VolD bl D HbAR (t1 ) Volbl · 1 − exp −t1 · = HbAD (0) VolRbl
t1 LT
AVflow VolD bl
(10) t1 · 1− . LT
(11)
In both equations we neglected the small adult Hb concentration that can naturally be present in fetal blood, expressed as HbAR (0) = 0. It is straightforward to check that equations (10) and (11) satisfy equations (3) and (4), respectively, by using that [HbA(t)] = HbA(t) · Volbl for both twins. AVflow and LT follow straightforwardly from equations (10) and (11), respectively: first, by substituting the right-hand side of equation (10) in (11) and solving for LT and, subsequently, by taking the ratio of both equations and solving for AVflow . The result is
VolDbl
LT =
· t1 · HbAD (0)
VolD −HbAR (t1 ) + VolblR · (HbAD (0) − HbAD (t1 )) VolRbl
(12)
bl
AVflow =
VolD bl t1
R HbAR (t1 ) Volbl . · · ln 1 + VolD HbAD (t1 ) bl
(13)
2.2. Two transfusions Table 3 summarizes the equations for two intra-uterine transfusions. As notation, also summarized in table 1, we use that the first intra-uterine transfusion occurs at t = 0, the second transfusion t1 days later, and birth t2 days following the second transfusion. Also, the donor’s Hb concentration just after the first transfusion is Hb1 D (0), just before the second transfusion is Hb1 D (t1 ), just after the second transfusion is Hb2 D (0), and just after birth is Hb2 D (t2 ). For the recipient, we have that HbA1 R (t1 ) = HbA2 R (0). We first assume that the adult red blood cells have the same LT during both transfusions. Then, equations (10) and (11) become t1 AVflow1 HbA1 D (t1 ) · 1 − = exp − · t 1 HbA1 D (0) LT VolD bl1 HbA2 D (t2 ) t2 AVflow2 · t2 · 1 − = exp − HbA2 D (0) LT VolD bl2 D HbA1 R (t1 ) t1 AVflow1 Volbl1 · 1 − exp −t · 1 − · = 1 HbA1 D (0) LT VolRbl1 VolD bl1 HbA2 R (t2 ) − HbA2 R (0) t2 VolD AVflow2 bl2 · 1 − exp −t2 · · 1− = . HbA2 D (0) LT VolRbl2 VolD bl2
(14) (15) (16) (17)
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HbA1 R (0) = 0 and HbA1 D (t1 ) = HbA2 D (0). The four unknown parameters AVflow1 , AVflow2 , LT, HbA1 R (t1 ) can be solved in a closed form from the four equations (14)–(17) as
VolDbl1
· t1 · HbA1 D (0) +
VolDbl2
· t2 · HbA2 D (0) LT =
VolD
VolD · [HbA1 D (0) − HbA1 D (t1 )] + Volbl2 · [HbA2 D (0) − HbA2 D (t2 )] −HbA2 R (t2 ) + Volbl1 R R VolRbl1
VolRbl2
bl1
bl2
VolD HbAk D (0) tk blk , k = 1, 2, AVflowk = · ln · 1 − tk HbAk D (tk ) LT D Volbl1 t1 D D HbA1 R (t1 ) = · HbA − HbA (0) · 1 − (t ) . 1 1 1 LT VolRbl1
(18) (19) (20)
LT was solved in a similar way as in equation (12), as follows: first, by eliminating both AV flows in equations (16) and (17) by using equations (14) and (15) respectively; second, by eliminating HbA1 R (t1 ) by combining (16) and (17) and solving for LT in the remaining equation; third, although a solution for the AV flows and HbA1 R (t1 ) with only measured HbA values is easily possible, by substituting equation (18) in (19) and (20), the results cannot be reduced to reasonable size equations. Therefore, we preferred retaining LT in equations (19) and (20). 2.3. Multiple transfusions The use of adult Hb concentrations in the donor as well as in the recipient after birth, to determine the N individual AV flows, the LT value, assumed identical in all transfusions, and the (N − 1) values of recipient adult Hb concentrations before delivery, thus 2N parameters, requires extending equations (14)–(17) to N equations. The solutions can again be expressed in closed form relations, as
VolDbl1
LT =
bl1
· t1 · HbA1 D (0) +
VolDbl2
· t2 · HbA2 D (0)
VolD VolD · HbA1 D (0) − HbA1 D (t1 ) + Volbl2 · HbA2 D (0) − HbA2 D (t2 ) −HbA2 R (t2 ) + Volbl1 R R VolRbl1
VolRbl2
bl2
HbAk (0) tk · ln · 1 − AVflowk = tk HbAk D (tk ) LT D Volblk tk D D HbAk R (tk ) = HbAk R (0) + · HbA − HbA (0) · 1 − (t ) , k k k LT VolRblk VolD blk
(21)
D
(22) (23)
where k = 1 through N. We emphasize that HbA1 R (0) = 0 and HbAk R (tk ) = HbA(k+1) R (0). 3. A simulated example To demonstrate the outcome of the equations, we used the HbA data summarized in table 4. Although these values are made up, they are based on our experience of measuring the AV flow (Lopriore et al 2007). Thus, we simulated a theoretical case of incomplete laser therapy of TTTS that left one patent AV from the ex-recipient (new donor) to the ex-donor (the new recipient), requiring two intra-uterine transfusions, at t = 0 and 11 days, and emergency delivery 7 days later. The resulting HbA-time sequence is shown in figure 1.
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M J C van Gemert et al 16 14
Adult Hb (gr/dl)
12 10 DONOR 8 6 4 RECIPIENT 2 0 0
3
6
9
12
15
18
Time after 1st IUT (days)
Figure 1. Simulated adult Hb concentrations in the donor and recipient in response to two intrauterine transfusions, at t = 0 and t = 11 days. Birth was 7 days later. The HbA concentrations considered here are not based on clinical measurements. The parameters are summarized in table 4. Table 4. Assumed adult Hb concentrations after two intra-uterine transfusions of blood into the anemic donor twin, the first at about 28 weeks and the second 11 days later. Birth was 7 days after the second transfusion. We stress that these numbers are not from a true clinical case but are made up. Superscript X = D, R. X HbA1 D (0) H bA1 D (11) HbA2 D (0) HbA2 D (7) HbA2 R (7) VolX AV1 AV2 HbA1 R (11) bl1 Volbl2 LT −1 −1 −1 −1 −1 (gr dl ) (gr dl ) (gr dl ) (gr dl ) (gr dl ) (ml) (ml) (days) (ml/24 h) (ml/24 h) (gr dl−1)
14
6
15
8
6
100
120
28.8
3.3
6.0
2.6
4. Discussion Direct measurement of the net inter-twin transfusion in monochorionic twin pregnancies and TTTS would require the presence of a single AV anastomosis, or multiple unidirectional AVs, whose situations occur in 5–10% of the cases only (Diehl et al 2001, Berm´udez et al 2002). When multiple and bi-directional anastomoses are present, the majority of cases, measurement of the net inter-twin transfusion is virtually impossible. Here, the individual AV and opposite AV flows are so large, tens to thousands of ml h−1 (Nakata et al, Wee et al), with a measurement uncertainty that is significantly larger than the values for single or unidirectional AV flows, assumed to represent net anastomotic flows. In addition, such measurements which have to be performed during fetoscopy are currently not standard. Thus, a productive way of assessment of net anastomotic inter-twin transfusions utilizes the cases of incomplete TTTS laser therapy that require an intra-uterine transfusion to correct the severe anemia of one of the twins. For clinicians, measurement of the fetal and adult Hb concentrations before and after transfusions and at birth is not difficult, albeit not a (yet) standard practice. The true complexity of assessment of net inter-twin transfusions is then the inevitable use of equations, simple for physicists but less so for clinicians. Therefore, we derived these equations in the present note, but, perhaps equally important, we presented them in a form that hopefully contributes to an easy future use. Tables 2 and 3 summarize the equations relating AV flows with total or adult Hb concentrations from single and multiple intra-uterine transfusions to the anemic donor. These
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equations follow straightforwardly from the derived differential equations relating donor and recipient adult Hb concentrations with AV flows, fetal blood volumes and lifetime of adult red blood cells. One of the main additional assumptions that had to be made but cannot be validated by intra-uterine blood sampling in the donor only is a constant lifetime of adult red blood cells during multiple transfusions, also assumed equal in both twins. However, multiple intra-uterine transfusions are not frequently given. The authors anticipate that the methods may find their way to many clinicians involved in TTTS laser therapy, which may produce a wealth of AV or net inter-twin transfusions from collected cases of incomplete laser therapy. Such data likely relate net inter-twin transfusions at various gestational ages to all four stages of TTTS. For a long time, being able to collect this information was the Holy Grail in this field. We believe that this new opportunity will aid achieving an improved understanding of the complex pathophysiology of TTTS presentation. References Berm´udez C, Becerra C H, Bornick P W, Allen M H, Arroyo J and Quintero R A 2002 Placental types and twin-twin transfusion syndrome Am. J. Obstet. Gynecol. 187 489–94 Brace R A, Langendorfer C, Song T B and Mock D M 2000 Red blood cell life span in the ovine fetus Am. J. Physiol. Regul. Integr. Comp. Physiol. 279 R1196–1204 Denbow M L, Taylor M, Cox P and Fisk N M 2004 Derivation of rate of arterio-arterial anastomotic transfusion between monochorionic twin fetuses by Doppler waveform analysis Placenta 25 664–70 Diehl W, Hecher K, Zikulnig L, Vetter M and Hackel¨oer B-J 2001 Placental vascular anastomoses visualised during fetoscopic laser surgery in severe mid-trimester twin-twin transfusion syndrome Placenta 22 876–81 Galea P, Jain V and Fisk N M 2005 Insights into the pathophysiology of twin-twin transfusion syndrome Prenat. Diagn. 25 777–85 Hoogeveen M, Meerman R H, Pasman S and Egberts J 2002 A new method to determine the feto-placental volume based on dilution of fetal haemoglobin and an estimation of plasma fluid loss after intrauterine intravascular transfusion Br. J. Obstet. Gynaecol. 109 1132–6 Lewi L, van Schoubroeck D, Gratacos E, Witters I, Timmerman D and Deprest J 2003 Monochorionic diamniotic twins: complications and management options Curr. Opin. Obstet. Gynecol. 15 177–94 Lopriore E, Nagel H T, Vandenbussche F P H A and Walther F J 2003 Long-term neurodevelopmental outcome in twin-to-twin transfusion syndrome Am. J. Obstet. Gynecol. 189 1314–9 Lopriore E, van den Wijngaard J P H M, Middeldorp J M, Oepkes D, Walther F J, van Gemert M J C and Vandenbussche F P H A 2007 Assessment of feto-fetal transfusion flow through placental arterio-venous anastomoses in a unique case of twin-to-twin transfusion syndrome Placenta 28 209–11 Nakata M, Martinez J M, Diaz C, Chmait R and Quintero R A 2004 Intra-amniotic Doppler measurement of blood flow in placental vascular anastomoses in twin-twin transfusion syndrome Ultrasound Obstet. Gynecol. 24 102–3 Quintero R A, Morales W J, Allen M H, Bornick P W, Johnson P K and Kruger M 1999 Staging of twin-twin transfusion syndrome J. Perinatol. 19 550–5 Robyr R, Lewi L, Salomon L J, Yamamoto M, Bernard J P, Deprest J and Ville Y 2006 Prevalence and management of late fetal complications following successful selective laser coagulation of chorionic plate anastomoses in twin-to-twin transfusion syndrome Am. J. Obstet. Gynecol. 194 796–803 Senat M V, Deprest J, Boulvain M, Paupe A, Winer N and Ville Y 2004 Endoscopic laser surgery versus serial amnioreduction for severe twin-to-twin transfusion syndrome N. Engl. J. Med. 351 136–44 van den Wijngaard J P H M, Umur A, Ross M G and van Gemert M J C 2008 Twin–twin transfusion syndrome: mathematical modelling Prenat. Diagn. doi:10.1002/pd.1944 van den Wijngaard J P H M, Westerhof B E, Ross M G and van Gemert M J C 2007 A mathematical model of twin–twin transfusion syndrome with pulsatile arterial circulations Am. J. Physiol. Regul. Integr. Comp. Physiol. 292 R1519–31 van Gemert M J C, Umur A, Tijssen J G P and Ross M G 2001 Twin-twin transfusion syndrome: etiology, severity and rational management Curr. Opin. Obstet. Gynecol. 13 193–206 Wee L Y, Sullivan M, Humphries K and Fisk N M 2007 Longitudinal blood flow in shared (arteriovenous anastomoses) and non-shared cotyledons in monochorionic placentae Placenta 28 516–22
