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Models of twin to twin transfusion syndrome
van den Wijngaard, J.P.H.M.
Publication date 2007
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van den Wijngaard, J. P. H. M. (2007). Models of twin to twin transfusion syndrome.
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Models of Twin to Twin Transfusion Syndrome
Models of Twin to Twin Transfusion Syndrome
PhD Thesis, University of Amsterdam, the Netherlands
© 2006 Jeroen PHM van den Wijngaard Cover by Jeroen PHM van den Wijngaard
Models of Twin to Twin Transfusion Syndrome
Academisch Proefschrift
ter verkrijging van de graad van doctor aan de Universiteit van Amsterdam op gezag van de Rector Magnificus
prof. mr. P.F. van der Heijden
ten overstaan van een door het college voor promoties ingestelde commissie, in het openbaar te verdedigen in de Aula der Universiteit
op vrijdag 9 maart 2007, te 12.00 uur
door
Jeroen Petrus Herman Maria van den Wijngaard
Promotiecomissie:
Promotores: Prof Dr Ir MJC van Gemert Prof Dr MG Ross
Overige Leden: Prof Dr ET van Bavel Dr HM Gardiner Dr JM Karemaker
Prof Dr JAM van der Post Prof Dr Y Ville
Prof Dr N Westerhof
De vishaak van de logische deductie treft zijn doel in de pathologische gevallen.
TABLE OF CONTENTS
Chapter 1 Introduction 9
Chapter 2 Background 11
PART 1
Models
Chapter 3 Modeling a hydropic recipient twin in twin-twin transfusion
syndrome Am J Physiol 288:R799-R814,2005. 35
Chapter 4 Abnormal arterial flows by a distributed model of the fetal
circulation Am J Physiol 291:R1222-R1233,2006. 65
Chapter 5 A mathematical model of twin-twin transfusion syndrome with pulsatile arterial circulations Am J Physiol R in Press 87
PART 2
Model simulations
Chapter 6 Modelling the influence of amnionicity on the severity of twin- twin transfusion syndrome in monochorionic twin pregnancies
Phys Med Biol 49:N57-N64,2004. 111
Letter to the Editor Am J Obstet Gyn 195:881-882,2006. 118 Reply Am J Obstet Gynecol 195:882,2006. 119
Chapter 7 Simulation of therapy in a model of a nonhydropic and hydropic recipient in twin-twin transfusion syndrome
Am J Obstet Gynecol 193:1972-1980,2005. 121
Chapter 8 Modeling severely discordant hematocrits and normal amniotic fluids after incomplete laser therapy in twin-twin transfusion
syndrome Placenta in Press 133
PART 3
Anastomoses & observations in TTTS
Chapter 9 Assessment of feto-fetal transfusion through placental arterio-venous anastomoses in a unique case of twin-to-twin
transfusion syndrome Placenta 28:209-211,2007. 143
Chapter 10 Significance of donor anuria differs between monoamniotic and diamniotic twin-twin transfusion syndrome Placenta in Press 147
Chapter 11 Deep-hidden anastomoses in monochorionic twin placentae
are harmless Prenat Diagn in Press 155
Chapter 12 Arterial stenosis and growth of a collateral artery as a possible
cause of severe twin-twin transfusion syndrome Submitted 165
Chapter 13 Discussion 169
Chapter 14 Summary 173
Chapter 15 Nederlandse Samenvatting 177
Authors affiliations 179
Curriculum Vitae 181
List of Publications 182
Dankwoord 183
CHAPTER 1 INTRODUCTION
INTRODUCTION
For ages mankind has felt the urge to understand its surroundings and subsequently to influence them for the sake of its advantage. Whether this is in the form of the early rock paintings, depicting a successful hunting session [1], or today’s climate models, predicting the weather forecast. All models serve to gain insight into the matter which is subject of study, allowing model developers to influence the course of events or respond to the model predictions.
Medical computational models have played a prominent role in the field of medical engineering for the past decades. Their applications range from a computation of the flows that develop around artificial heart valves, blood pressure in the aortic arch, computation of the stress and strain in the human pelvic bone, simulating laser therapy of port wine stains [11], or simulating different therapeutic interventions in the Twin to Twin Transfusion Syndrome (TTTS) [6,7].
Here, TTTS will be introduced as the subject of model development. TTTS is notorious for its high rates of mortality and morbidity [2,3,9]. The advantage of the use of models to gain insight into TTTS will be indicated, as well as essential aspects on fetal physiology and pathophysiology that are implicated in TTTS. Important for the study of TTTS is a general insight into the placenta and the fetal circulation, where both are affected by and implicated in the development of TTTS [4-10].
Several models of TTTS will be described in detail, together with the advantages and the use of these models, but also their shortcomings. Finally, directions for future modelling will be discussed.
AIM AND OUTLINE OF THIS THESIS
The aim of this thesis is to present models of TTTS which advance the previously existing models [5,10]. These earlier models described TTTS developing as discordant blood and amniotic fluid volumes. A short description of fetal and placental physiology, and an introduction to our models, basically without mathematical equations, will be given in chapter 2.
Part 1 of this thesis includes the models. In chapter 3, a hydropic recipient twin in TTTS will be described. In chapter 4, a model will be described that allows calculation of blood flow waves in the umbilical artery and middle cerebral artery of the fetus, and in chapter 5, a model is described that relates fetal parameters to onset and development of TTTS with abnormal developing flow wave pulsations in donor and recipient twins.
Part 2 includes simulations with the various models. In chapter 6, the influence of amnionicity on the onset and development of TTTS is investigated. In chapter 7, the outcomes of therapy are simulated in a model of TTTS which includes a hydropic recipient twin. Additionally, in chapter 8, two clinical cases are simulated of incomplete laser obliteration of all placental anastomoses, causing continued fetofetal transfusion.
Part 3 includes chapter 9, a clinical case which permitted the assessment of the fetofetal transfusion following incomplete lasering of all placental anastomoses. In chapter 10, the model with a hydropic recipient (described in Chepter 3) [11] is used to simulate multiple amnioreductions in a rare case of monoamniotic-monochorionic TTTS. In chapter 11, the influence of deep anastomoses on the development of a hematocrit discordance is investigated, and in chapter 12, a case is described which presented with overt TTTS, however, in the absence of an arteriovenous anastomosis.
REFERENCES
1 Balter M. What made humans modern? Science 295:1219-1225,2002.
2 Lewi L, Van Schoubroeck D, Gratacós E, Witters I, Timmerman D and Deprest J. Monochorionic diamniotic twins: complications and management options. Curr Opin Obstet Gynecol 15:177-194,2003. 3 Lopriore E, Nagel HTC, Vandenbussche FPHA, Walther FJ. Long-term neurodevelopmental outcome in
twin-to-twin transfusion syndrome. Am J Obstet Gynecol 189:1314-1319,2003.
4 Nikkels PGJ, van den Wijngaard JPHM, van Gemert MJC. Monochorionic twin placentas: clinical outcome and computer modelling of a high-risk pregnancy. Multiple pregnancy. Eds. Kilby M, Baker P, Critchley H, Field D. Royal College of Obstetrics and Gynaecology Press, 2006; Chapter 3, pp 45-59.
5 Umur A, van Gemert MJC, Ross MG. Amniotic fluid and hemodynamic model in monochorionic twin pregnancies and twin-twin transfusion syndrome. Am J Physiol 280:R1499-R1509,2001.
6 Umur A, van Gemert MJC, Ross MG. Fetal urine and amniotic fluid in monochorionic twins with twin-twin transfusion syndrome: simulations of therapy. Am J Obstet Gynecol 185:996-1003,2001.
7 van den Wijngaard JPHM, Ross MG, van der Sloot JAP, Ville Y, van Gemert MJC. Simulation of therapy in a model of a nonhydropic and hydropic recipient in twin-twin transfusion syndrome. Am J Obstet Gynecol 193:1972-1980,2005.
8 van den Wijngaard JPHM, Umur A, Krediet RT, Ross MG, van Gemert MJC. Modeling a hydropic recipient twin in twin-twin transfusion syndrome. Am J Physiol 288:R799-R814,2005.
9 van Gemert MJC, Umur A, Tijssen JGP and Ross MG. Twin-twin transfusion syndrome: etiology, severity and rational management. Curr Opin Obstet Gynecol 13:193-206,2001.
10 van Gemert MJC, Sterenborg HJCM. Haemodynamic model of twin-twin transfusion syndrome in monochorionic twin pregnancies. Placenta 19:195-208,1998.
11 van Gemert MJC, Welch AJ, Pickering JW, Tan OT, Gijsbers GHM. Wavelength for laser treatment of port wine stains and telangiectasia. Lasers in Surg Med 16:147-155,1995.
CHAPTER 2 BACKGROUND
THE TWIN TO TWIN TRANSFUSION SYNDROME
Introduction
Monozygotic (identical) twin fetuses have two separate placentas and 2 amniotic sacs (dichorionic-diamniotic) in about 25% of cases. This is a consequence of embryonic splitting within 3 days following fertilization of the ovum. The remaining 75% share one monochorionic placenta due to splitting after 3 days, where splitting between 3 and 8 days gives 2 amniotic sacs (monochorionic-diamniotic). Splitting beyond 8 days, which occurs in approximately 1% of cases, gives 1 sac (monochorionic-monoamniotic) [9]. Splitting beyond 12 days gives conjoint twins, which is a rare event, occurring approximately only four times per year in the Netherlands. In the USA, based on the 2002 data of the National Center for Health Statistics, the number of twin births was 125,134. Estimating that one fourth of these pregnancies are monozygotic twins, and using that TTTS occurs in 15% of these cases, suggests approximately 3,520 TTTS cases per year in the USA alone, which translates to about 90 cases in the Netherlands.
Monochorionic placentas virtually always contain blood vessels (anastomoses) linking the fetoplacental circulations of the two twins (figure 1). These anastomoses can be arteriovenous (AV), opposite arteriovenous (denoted by VA), which both occur deep within the placental parenchyma, i.e. the placental cotyledon, or superficial on the surface of the chorionic plate, arterioarterial (AA), or venovenous (VV). Whereas the deep anastomoses have a high resistance due to the cotyledon which connects the feeding artery of one twin with the draining vein of the other twin, the superficial anastomoses normally have low resistance.
Figure 1. Taken from Wijngaard et al. 2006 [99] A dye injected monochorionic non-TTTS placenta showing AA, AV and VA anastomoses.
As early as in the late 19th century the German obstetrician Friedrich Schatz observed placental anastomoses in monochorionic twin placentas [72,73] (figure2), and described findings of the various anastomoses in dye injected placentas. In addition, he described his clinical observations [73] of both twins, and suggested that the role of these anastomoses was
the transfusion of blood from one twin to the other, then called the 3rd circulation. It is now confirmed that the anastomoses create an intertwin transfusion of blood volume [47,61,82], which depends on the anastomotic pattern, and allows a net fetofetal transfusion to develop, from donor to recipient.
Since the direction of the anastomotic flow is determined by the pressure gradient between both sides of the anastomosis, the direction of flow of the AV anastomosis is from the arterial to the venous side and by definition unidirectional. In contrast, in the AA and VV anastomoses, the pressure gradient between the twins can change due to various circumstances, including additional anastomoses, and flow can be bidirectional. When the net transfusion is chronic and beyond compensation by the two twins, TTTS may develop with varying severity, affecting both twins in opposite ways [58].
As a direct consequence of the proposition that TTTS is the result of uncompensated fetofetal transfusion, it follows that at least one AV anastomosis is a prerequisite for development of TTTS [102]. The protective role of AA anastomoses follows from their incidence in non-TTTS, i.e. 80-90%, against their incidence in TTTS placentas, i.e. only 20-30% [24], from computer modelling [89], and from a report where AA thrombosis subsequently caused TTTS [82].
Recently, four stages of TTTS of increasing severity have been identified by Doppler insonation [23,63], which increases standard of care and facilitates comparison between studies. Stage I TTTS, i.e. the first diagnostic marker of TTTS, only includes the oligo-polyhydramnios (donor-recipient) sequence of amniotic fluid discordance without further sequelae (figure 3). Stage II also includes lack of donor bladder filling. Stage III includes abnormal umbilical flow patterns in either twin, which can also includes venous pulsations in the recipient twin [69]. Stage IV includes a hydropic recipient due to forward heart failure. Stage V includes intrauterine fetal demise of either or both twins. Untreated TTTS may present with a survival rate of only up to 37% [102].
In addition to the intertwin transfusion of blood, additional large discordances develop between the twins. In the donor kidneys, increased levels of renin gene expression have been identified, which were virtually absent in the recipient twin [43,49]. In addition, discordances were found for plasma levels of angiotensin I, natriuretic peptide and arginine vasopressine [5,59,112]. The finding of a high cord blood renin level in a recipient with renin down regulated production in severe TTTS confirms the anastomotic transfer from the donor towards the recipient [50]. In addition, endothelin levels, where the recipient had a 2- to 3- fold higher concentration than the donor, were found discordant in monochorionc twins with severe TTTS [4]. Given a transfer time in the range of 1 minute from donor to recipient, as was measured using the Doppler contrast agent Levovist in monochorionic twins [20], it is likely that the mentioned mediators are transferred through the placental vascular shunts towards the recipient twin.
Figure 2. Taken from Schatz 1884 [72]. Placentas are drawn showing arteries and veins. Placental anastomoses are encircled. For full color version, see Selected Color figures page 185.
Figure 3. Taken from Fisk and Galea 2004 [27]. The twin–twin transfusion syndrome results in midtrimester discordance in amniotic fluid levels and growth, with signs of hypovolemia and uteroplacental insufficiency in the donor twin and hypervolemia and cardiac dysfunction in the recipient twin. For full color version, see Selected Color figures page 185.
TTTS sequelae
TTTS is a unique but serious disease in medicine, associated with significant intrauterine and neonatal mortality, and serious persistent cardiovascular-neurodevelopmental abnormalities in survivors [29,45,46,48,75,102,114]. In the donor, clear markers of uncompensated fetofetal transfusion are hypovolemia, oligohydramnios or even anhydramnios and the occurrence of a stuck donor twin, i.e. the absence of amniotic fluid, which causes the donor to be covered by the amniotic fluid membranes. Often, though not always, the donor twin suffers from anemia and growth retardation. In the recipient, signs of uncompensated fetofetal transfusion are hypervolemia, polyuria and polyhydramnios, which may develop into congestive heart failure due to volume loading, resulting in fetal edema, i.e. hydrops. In addition, in the placenta, large differences may occur between vascularisation and maturation of the placental villi [71,106].
Long-term unbalanced fetofetal transfusion causes serious abnormal fetal alterations, which may cause diseases in childhood or even in adult life: TTTS survivors develop cerebral palsy much more frequently than singletons [45]. Recipients may develop right ventricular
outflow tract obstruction [48], cardiomegaly and impaired diastolic function [7]. Donors may increase their cardiac afterload from a decreased vascular distensibility (increased arterial stiffness) [15], extending into childhood, consistent with the concept of fetal programming [29]. These factors may extend into adulthood, and may predispose to onset of hypertension, diabetes, and atherosclerosis [6,14,69,105]. Recently, Chescheir [14] stated that the increased rate of functional heart diseases among TTTS recipient twins is a model for the theory of the fetal origins of adult health. She mentioned potential mechanisms for future heart diseases that include alterations in the hormonal environment within the fetal bodies (i.e. renin-angiotensin-system, erythropoietin, aldosteron), and blood pressure-driven alterations in blood flow (i.e. hypotensive donor, hypertensive recipient) and blood vessel distensibility (i.e. increased donor arterial wall stiffness).
Management of TTTS
Management options nowadays widely used in the clinic encompass amnioreduction and laser ablation of placental anastomoses, see figure 4, with subsequent normalisation of the amniotic fluid volume [19, 35,76]. In addition, and to a lesser extent, septostomy [56,70] and feticide (intentional fetal demise) are offered as therapy.
Therapeutic amnioreduction is the most widely used procedure and is the removal of excess amniotic fluid volume from the recipient’s amniotic sac. This process can be done rapidly or slowly (on minutes to hours scale) and even serially, removing up to several litres until the recipient amniotic fluid volume is normalised, or even reduced below normal [39]. Although this therapy does not resolve the cause of TTTS, premature rupture of membranes and preterm labour can be prevented, with a procedure related risk of immediate delivery of 4% per procedure [45,102]. Total survival may be up to 60% [79] however with high incidences of severe neurological sequelae of up to 16% [46,102].
Laser ablation of placental anastomoses along the vascular equator, first introduced by DeLia [19], actually removes the cause of the syndrome by functionally creating bichorionic twin placentas. This therapy however carries the limitation that unless all intertwin anastomoses are coagulated, fetofetal transfusion may remain and cause additional complications [66,93]. In addition, this therapy normally is not performed after 26 weeks of gestation, in part but not solely, due to the size of the anastomoses, the decreased manoeuvrability inside the uterus and the possibility that the placenta may be partly covered by one fetus. In addition, the procedure related risk of immediate delivery, e.g. due to premature rupture of membranes, may be about 11% [102]. Total survival with this therapy may be up to 56%, with at least one survivor in 76% of cases [76], and is even reported as 68% of total fetal survival with 81% of at least one survivor by Hecher et al. [35], where the risk for severe neurological sequelae is 5% [45], significantly lower than following amnioreduction.
Septostomy, i.e. puncturing the intertwin membrane and functionally creating a monoamniotic twin pregnancy [56,70], probably has no additional benefit when compared with normal amnioreduction [41,56,97], albeit at the significant risk of cord entanglement [67]. The mechanism here is that the donor twin gains access to the amniotic fluid volume,
hence, septostomy was introduced in view of the significantly lower incidence of TTTS in monoamniotic twins. Recently however, Umur et al. [88] indicated the anastomotic pattern in monoamniotics always to contain a large AA anastomosis (observed in 25/25 of monochorionic monoamniotic cases). The latter observation is now observed in 35/36 cases, where the case without a superficial anastomosis contained the rare type of a jump anastomosis [104], connecting the umbilical arteries of both twins. In this case however, severe TTTS developed [71], chapter 10. Computer modelling [97] suggests only minimal use for septostomy since the underlying cause, i.e. the anatomotic pattern, remains unchanged. Selective feticide, often performed by bipolar cord coagulation, may be used to sacrifice one of the twins, i.e. the one which is in exceedingly poor condition, in order to prevent untoward clinical outcomes in the other cotwin after demise of the former. This therapy however, is not widely used and implies fetal survival cannot exceed 50%. In general, amnioreduction is used for TTTS presenting in stages I and II [53], whereas laser ablation of placental anastomoses with subsequent normalisation of the amniotic fluid volume is the preferred therapy for severe TTTS presenting prior to 26 weeks [35,76,91].
Figure 4. Taken from Lewi et al. 2003 [45] (a) Schematic drawing of fetoscope laser coagulation by the percutaneous approach using a flexible cannula and curved fetoscope. (b) Curved fetoscope of 2.0 mm in sheath with operative channel for the laser fiber.
Development of TTTS models
Research on TTTS is hampered by the absence of a suitable animal model, the fact that it is unethical to perform invasive fetal measurements and that many of the parameters involved in onset and development of TTTS and its sequelae; e.g. the fetal and amniotic fluid osmolalities, the fetal blood pressures, and the net flow through the placental anastomoses cannot be studied by insonation techniques alone. Although models of TTTS inevitably may be a considerable simplification of the clinical circumstances in which the two twins develop, models of TTTS can function to elucidate the underlying (patho)-physiology. In addition, models can demonstrate general trends after simulated interventions [91, 89, 93, 95,98], illustrate the influence of varying clinical parameters [97, 98], and identify possible mechanisms that are the basis of clinical observations [89-93,99]. An introduction to the basics of our models will be given in the paragraph on Models of Twin to Twin Transfusion Syndrome below.
PLACENTAL PHYSIOLOGY
The placenta can be regarded as one of the most important and yet short-lived organs in mammals. Except for the physical protection that the placenta and the uterus offer the developing fetus, the placenta is the connecting organ between the fetus and its mother in terms of transfer of nutrients and respiratory gas. In total, the placenta allows approximately 5.6 liter of water to pass either into the fetus, its placenta or its amniotic fluid [8]. Furthermore the placenta provides hormones regulating maternal metabolism and inhibiting uterine contractions [78], and provides matching between the maternal and fetal genes, so that a response of the maternal immune system is absent. The human placenta is of the hemochorial type; the maternal blood is in direct contact with a syncytial trophoblast layer which covers the fetal endothelium. In general, the hemochorial placenta is more permeable than the other placentas in the animal kingdom for molecules depending on diffusion transport through pores [8]. A schematic picture of the human placenta is provided in figure 5.
Five major routes of placental transfer can be distinguished, a) simple diffusion of lipophilic substances, b) restricted diffusion of hydrophilic substances through transmembrane channels, c) facilitated diffusion, d) active transport and e) receptor mediated endocytosis [8,74]. The blood flows of the maternal and fetal circulations can either be considered as concurrent, counter current, crosscurrent or combinations of these flows [74]. It is assumed that the human placenta exhibits characteristics of both flow and membrane limited diffusion. At term, the human placenta may weigh up to 0.5 kg, whereas the fetus may weigh more than 3.5 kg. The fetal umbilical cord contains two arteries and one draining vein, and may be up to 60 cm [9]. In total, the human placenta may contain 10 to 40 cotyledons, comprised of several villous trees. The exchange area at term is estimated to be 11 to 25 m2 [74].
After the blastocyst has implanted into the endometrium, syncytiotrophoblasts start to develop from the cytotrophoblast and invade the maternal tissue, where the syncytium is a layer of multinucleated fetal tissue with only few intercellular boundaries. Before two weeks, maternal capillaries are opened and maternal erythrocytes come into contact with the syncytiotrophoblast. The first villi then develop, which continue to grow consisting of a layer of cytotrophoblasts, which grow into branches forming a secondary chorionic villus. After about three weeks, tertiary chorionic villi are formed, containing connective tissue and the fetal capillaries, the cytotrophoblasts are in some parts in contact with the maternal circulation [57]. Maturation of the placenta subsequently involves ongoing branching and proliferation of terminal villi, enlarging exchange area, increasing vascularisation and reducing the distance between fetal and maternal circulations, thus optimizing placental exchange [3, 42, 106]. Maternal blood is supplied to the intervillous space via the spiral arteries ending at the basal plate and is drained via the venous openings in the basal plate.
The diffusion of water into the fetus is probably far greater than that of any other compound [8,36]. It was shown by Hutchinson et al. [38] that unidirectional flow of water across the placenta is approximately 60 ml/minute for the entire placenta, exceeding the net flux approximately 10.000 fold. Osmotic gradients therefore probably do not persist long. Given the large bidirectional flow, it is conceivable that the net transfer is influenced by
hydrostatic and colloid osmotic pressure differences between the maternal and fetal circulations [2]. However, the exact magnitude of hydrostatic and osmotic pressure differences during gestation remains elusive.
Recently, it was reported that at least part of the transcellular water flux may be mediated by water channel membrane proteins referred to as aquaporins (AQPs) [17]. AQPs are generaly assumed to be capable to increase the rates of diffusion of water and other small hydrophilic solutes across membranes by raising osmotic and hydraulic permeability [8]. A more extensive discussion of placenta types, function and development can be found in the literature [8,9,26,42,77].
Figure 5. Diagram of the nearly mature human placenta in situ, taken from Kaufmann [42]. Loose centers of the villous trees arranged around the maternal arterial inflow area are a frequent feature. These placentome centers usually exhibit immature patterns of villous branching and differentiation. P = perimetrium; M = myometrium; CL = chorion laeve; A = amnion; MZ = marginal zone between placenta and fetal membranes, with obliterated intervillous space and ghost villi; CI = cell island, connected to the villous tree; S = placental septum; J = junctional zone; BP = basal plate; CP = chorionic plate; IVS = intervillous space; UC = umbilical cord; UV = umbilical vein; UA = umbilical artery.
PHYSIOLOGY OF THE FETAL CIRCULATION
The fetal heart and circulation differ significantly from that of the adult. Important differences include the presence of three ducts, i.e; the ductus venosus, the foramen ovale and the ductus arteriosus [18], allowing a large proportion of the cardiac output to be directed to the placenta and a small proportion through the pulmonary circulation [65] (figure 6). The fetal blood volume is approximately 10% of the fetal weight [33,90,100], which is approximately 2 to 3 percent more than in the adult circulation. The fetal blood pressures are assumed to increase linearly during gestation [64,90,100]. Several models have been developed of the fetal circulation [37] and of the neonatal circulation [30]. Clinically, the
human fetal circulation is assumed to respond similar as in experimental studies on fetal sheep; redistributing blood flow in favour of the fetal brain and placenta when compromised [40].
Both fetal ventricles, which operate in parallel, have only a very small capacity to increase the cardiac output upon increased preload. Therefore, cardiac reserve as determined by the Frank-Starling mechanism in the fetus is extremely limited compared to adult physiology [85,86]. Fetal biventricular cardiac output equals approximately 425 ml/min/kg [54], and is directed for a large part into the fetal systemic circulation, including flow from the right ventricle with only a small fraction entering the pulmonary arteries [65]. Additional details on the fetal circulation can be found in the literature [33,69,34,44].
Figure 6. Taken from Kiserud et al. [44]. Pathways of the fetal heart. The via sinistra (red) directs well-oxygenated blood from the umbilical vein (UV) through the ductus venosus (DV) (or left half of the liver) across the inferior vena cava (IVC), through the foramen ovale (FO), left atrium (LA) and ventricle (LV) and up the ascending aorta (AO) to reach the descending AO through the isthmus aortae. De-oxygenated blood from the superior vena cava (SVC) and IVC forms the via dextra (blue) through the right atrium (RA) and ventricle (RV), pulmonary trunk (PA) and ductus arteriosus (DA). CCA, common carotid arteries; FOV, foramen ovale valve; LHV, left hepatic vein; LP, left portal branch; MHV, medial hepatic vein; MP, portal main stem; PV, pulmonary vein, RHV, right hepatic vein; RP, right portal branch. For full color version, see Selected Color figures page 185.
MODELS OF TWIN TO TWIN TRANSFUSION SYNDROME
Introduction
The first TTTS computer model, published in 1996, developed by the British medical physicist David G Talbert [81], included two identical pulsating fetoplacental units at about 28 weeks gestation, which were abruptly connected by unidirectional or AA anastomoses [82]. The subsequent progression of the two fetoplacental circulations and amniotic fluid volumes towards a new steady state was then computed. This model identified for the first time a sequence of events that related AV fetofetal transfusion with onset of the TTTS stages I and II. Although the arterial circulations were pulsatile, pathologic mechanisms that influence the propagation of the cardiac output pulse along the arterial tree were not included, implying that stage III pathophysiology could not be simulated. Chorionic circulations however were included [21,84].
Since Talbert’s initial TTTS model, four additional models of TTTS have been developed by our group [90,96,100,99]. The first three models developed, all used non-pulsating circulations, but included fetoplacental and anastomotic growth and varying placental sharing and amnionicity. The recently developed fourth model [99], chapter 5,
included the propagation, attenuation and reflection of the arterial pulse waves in the arterial part of the fetal circulation. In all our models, anastomoses were modelled as tubes directly connecting the arterial and venous compartments of the two umbilical circulations, hence chorionic placental circulations were neglected.
Although some of the details of these models may appear complex, the underlying concepts are simple, based on well-known (patho)physiology mechanisms. Therefore, we present here a brief overview of the TTTS pathophysiology modelling, with only those equations expressed in words that are essential for understanding.
Transplacental flow
In all our models, we assume that the growing fetus acquires its growth of total body fluids (GrowthTotalBodyFluidVol) as well as growth of its amniotic fluid volume (GrowthAmniotVol) from the maternal circulation. This growth is related to the (net) transplacental flow (TransPlacentFlow) as
GrowthTotalBodyFluidVol = TransPlacentFlow – GrowthAmniotVol (1) which are all expressed in ml/week.
The transplacental fluid flow is assumed proportional to the difference between the maternofetal hydrostatic and colloid osmotic pressure gradients, i.e. expressed as Starling’s equation [81,90]. The proportionality factor is the transplacental filtration coefficient;
TrPlaFiltCoeff (ml·week-1·mmHg-1).
TransPlacentFlow = TrPlaFiltCoeff· (MatFetPressGrad – MatFetCOPGrad) (2) Since the normal values for total body fluid and amniotic fluid, depending on gestational age, are known, the normal growth of these volumes is also known, which, from equation 1 gives the normal transplacental flow. Subsequently, using the normal transplacental flow and the normal fetal and maternal blood hydrostatic and colloid osmotic pressures, the transplacental filtration coefficient can be obtained for all gestational ages. The transplacental filtration coefficient is subsequently used for donor and recipient. Although the Starling equation is an accepted choice here [25], we acknowledge that transplacental fluid transfer is a complex and still incompletely understood mechanism. Recently, new pathways have been identified which are known to be capable of somehow regulating this fluid transfer [8].
Our series of consecutive models basically refers to differences in the relation of fetal total body fluid and blood volume, i.e. the first model only considered fetal blood volumes [100], the second model included the total fetal body fluid [90], where 10% consisted of blood, and the third and fourth models consist of arterial and venous blood, and the intracellular and interstitial fluid volumes [96,99]. Growth of amniotic fluid volume has been described in the same way in the various models, except for differences in the control functions of urine production.
Blood volumetric growth
In the current models, growth of fetal blood volume cannot be calculated directly. Blood is considered to be either in the arterial or venous compartment and to constitute part of the fetal total body fluid, together with the interstitial and the intracellular fluid. We use the
term AnticipatedBloodVol to denote the blood volume which is the result of the physiological parameters of that fetus, excluding fetofetal transfusion. The first step is to determine the growth of the anticipated blood volume (GrowthAnticipatedBloodVol) of a fetus. This follows from growth of the fetal total body fluid minus growth of the interstitial fluid volume (GrowthInterstVol) and growth of the intracellular volume (GrowthIntracelVol).
GrowthAnticipatedBloodVol=GrowthTotalBodyFluidVol –(GrowthInterstVol+GrowthIntracelVol) (3)
Here, growth of the fetal total body fluid follows from equation 1.
The second step is calculating blood volume of donor and recipient twins. We assessed that overall growth of the blood volume of each twin is a linear combination of (1) (GrowthAnticipatedBloodVol) and (2) the “net fetofetal transfusion” through the placental anastomoses (NetFetofetalTransf). Both parameters are expressed in ml/week.
GrowthBloodVolRecipient = GrowthAnticipatedBloodVol + NetFetofetalTransf (4a)
GrowthBloodVolDonor = GrowthAnticipatedBloodVol – NetFetofetalTransf (4b) Determination of the net fetofetal transfusion will be given in the paragraph Anastomoses below.
In our model, we assume that growth of the interstitial and intracellular fluid volumes, and the lymph flow, all are caused by the transvascular flow as
GrowthInterstVol + GrowthIntracellVol = TransVascularFlow - LymphFlow (5) Lymph flow is governed by the hydrostatic pressure difference between the interstitial space and the venous blood [12,96]. Growth of the interstitial fluid volume is governed by Starling forces [12,83], comparable to equation (2), which determine magnitude and direction of the transvascular flow from the fetal circulation to the interstitial compartment as
TransVascularFlow =VasFiltCoeff· (VascInterstPressGrad – VascInterstCOPGrad) (6) The proportionality factor is the vascular filtration coefficient, VasFiltCoeff (ml·week-1 ·mmHg-1), which is determined from the normal transvascular flow and the normal interstitial hydrostatic and colloid osmotic pressure gradients with the fetal blood. Actually, this is similar to how the transplacental filtration coefficient is determined. Here, the interstitial hydrostatic pressure follows from the interstitial fluid volume and the compliance of the interstitial compartment. Growth of the fetal intracellular space was modeled proportional to the fetal blood volume. Since transvascular flow can be determined for donor and recipient from equation 6 and the lymph flow follows from the hydrostatic pressure difference between the interstitial space and venous blood, subsequently from equations 5 and 3, growth of the anticipated blood volume of donor and recipient can be determined.
Growth of arterial and venous blood
To obtain the arterial and venous parts of the blood volume, we separately calculated the cardiac output and venous return for donor and recipient. This allows the arterial and venous blood volumes and pressures to become severely discordant, needed to describe nonimmune hydrops due to congestive heart failure [25,62]. In the fetus, the heart operates near the maximal cardiac output plateau in the Frank-Starling curve [85,86]. In comparison to the adult circulation, this implies that fetal cardiac reserve is limited. We used pre- and afterload dependence of the cardiac output as measured by Thornburg and Morton [85,86].
From the cardiac output, and the flow from the arterial to the venous part of the circulation, the arterial and venous blood volumes can be obtained. Following forward heart failure in the recipient, excess blood volume is removed from the arterial circulation and accumulates in the venous circulation, ExcVenVol. An excess blood volume in the venous circulation, increases the VascInterstPressGrad (see equation 6) and reduces the lymph flow returning from the interstitial space. Together, this causes an abnormal increasing interstitial fluid volume resulting in hydrops. We defined hydrops as an increase in the interstitial fluid volume of at least 18% [32].
The equations describing arterial and venous blood volumetric growth follow as a linear combination of (a) the RemovedExcVenVol, and (b) volumetric growth of arterial and venous blood volumes, expressed as blood volumetric growth (arterial plus venous), multiplied by the ratio of arterial or venous volume to total blood volume, (VbArt/Vb or
b bVen V V / ). Thus, b bArt V V odVol cipatedBlo GrowthAnti ExcVenVol Removed th ArtVolGrow =− +( )⋅ (7a) b bVen V V odVol cipatedBlo GrowthAnti ExcVenVol Removed th VenVolGrow =+ +( )⋅ (7b)
Here, the GrowthAnticipatedBloodVol denotes either the donor or recipient blood volume, so that for each twin the arterial and venous blood volumetric growth is obtained. In the growth of the anticipated blood volume, the decrease by urine production and lung secretion and the increase by swallowing and intramembranous flow is included. These flows will be described below.
Growth of amniotic fluid volume
Growth of the amniotic fluid volume (ml/week) is governed by the fetal urine production plus lung secretion minus fetal swallowing and the transmembranous flow,
GrowthAmniotVol=UrineProd+LungSecr-Swallowing-IntramemFlow (8)
Here, all these mechanisms have control functions to impose a boundary of their output. Fetal urine production, the main contributor to growth of the amniotic fluid volume, was first modelled to be controlled by a pressure diuresis curve only [90]. Urine production was zero when the arterial pressure was half or less than the normal pressure at the gestational age considered, normal at normal arterial pressure, and increased to eightfold when arterial pressure was doubled compared to normal. In the recent model [96], urine production is also influenced by the colloid osmotic pressure of the blood [51] and the blood concentration of renin angiotensin system (RAS) mediators [32]. In the donor twin, hypovolemia stimulates the production of RAS mediators [43,49,50], leading to a rapidly decreasing urine production. Part of these RAS mediators are transfused to the recipient twin through the AV anastomosis, contributing to recipient hypertension [50]. Details on the synthesis, transfusion and influence of colloids and RAS on the diuresis curve can be found in our model paper [96], chapter 3.
The lung fluid secretion is the second albeit smaller contribution to growth of the amniotic fluid volume. To date, no control mechanism for lung secretion has been identified and normal values computed for the ovine fetus were used [16,90].
Swallowing, the most important pathway for removal of amniotic fluid, is controlled by the fetal blood osmolality [60] and the size of the fetus [90]. We included that a decrease in osmolality of 4% leads to a cessation of swallowing, according to experiments in rats [80].
The intramembranous flow, the flow from the amniotic fluid into the circulation of the fetus, depends on the fetal blood and amniotic osmotic pressures. Using estimated normal values for the intramembranous parameters, the filtration coefficient of the intramembranous pathway was determined [90]. An overview of the flows that are included in the model is given in figure 7.
The amniotic fluid pressure of the donor and recipient twins was obtained from the combined amniotic fluid volumes and the uterus compliance. Here we use that the normal amniotic fluid hydrostatic pressure is 10 mmHg, which, divided by the normal amniotic fluid volume, yields the inverse of the compliance of the uterus. Since a twin pregnancy is modeled here, the compliance of the uterus was doubled [90]. Polyhydramnios was defined as an increase of amniotic fluid volume of at least two times the normal amniotic fluid volume [90].
Figure 7. Adapted from Brace RA 1997 [11]. Overview of flows that are believed to be present in a human fetus. Note, 1 = urine production, 2 = fetal swallowing, 3 = intramembranous flow, 3a = intramembranous flow via the umbilical cord surface, 3b = intramembranous flow via the fetal skin surface, 4 = lung secretion, 5 = oral and nasal secretion, 6 = transmembranous flow (not considered in the numerical model).
Pulsating arterial circulations and/or other parameters
To simulate the fetal arterial tree, we use a distributed network of 13 arterial segments, which represent the main conduit arteries (figure 8). To represent the various peripheral organ beds, three-element Windkessels [98,99,110,111] were used, nine in total. A three-element Windkessel mimics the resistance against the pulsatile blood flow of a vascular organ bed. In addition, in the mathematical description of a Windkessel, the resistance and the compliance of the organ are included. The term Windkessel is derived from the old fire-engine construction, where manual force provided pulsatile waterflow, which was damped by using a partly air and water-filled capacitance so that the firefighters actually obtained a steady waterstream without pulsations [111]. Similarly, the pulsating arterial blood flow enters the organ and perfuses it, and is drained with non pulsatile venous flow. For the fetal model, details of the major arteries, i.e. length, radius, wall thickness, wall stiffness and viscoelastic properties, as well as organ resistance and compliance, and blood viscosity were, as far as possible, all taken from the literature.
Since calculations of blood flow wave propagation through the vascular tree are done in the frequency domain, we use Fourier transformation to convert the cardiac output flow from the time domain to the frequency spectrum. For each separate frequency that constitutes
the cardiac output, propagation along the vascular tree, i.e. attenuation and phase shifting, can be calculated. Then, at each arterial segment, all attenuated and phase shifted frequency components are recombined using inverse Fourier transformation, yielding the time domain flow at the segment considered.
Using this approach, parameters were identified, which are implicated in the development of abnormal umbilical artery flows [98]. Abnormalities in these parameters leading to abnormal umbilical arterial flow are; increased placental resistance, decreased brain resistance, increased vascular wall stiffness, increased wall thickness and changes in blood viscosity. Simulations however indicate an increased placental resistance is the most important contributor to abnormal flow in the umbilical artery [98], Chapter 4. Placental resistance is modelled to depend on the blood concentration of vasoconstrictive RAS mediators [2,25], blood viscosity, and placental compression resulting from increased amniotic fluid pressure in polyhydramnios [28].
To compute changes in blood viscosity we included the dynamics of fetal blood hematocrit, using its known relation with viscosity [109]. This was done by assessing the production, fetofetal transfusion to the other twin, and decay of red blood cells [13,99], chapter 5.
A decrease in brain resistance following fetal compromise, as in reduced placental perfusion [1,87] or maternal hypoxia [31], is a common compensatory mechanism to supply the fetal brain with sufficient oxygen [40]. In the model, we included that brain resistance decreases in response to a decreased placental perfusion [99].
In the donor, growth restriction may reduce the synthesis and deposition of elastin in the large arteries [52]. As a consequence, the arteries develop a stiffer wall. In the model, this behaviour was simulated by including elastin deposition in the donor arteries proportional to the blood volume so that stiffer arteries develop in growth retardation [99], Chapter 5.
In the recipient twin, however, the wall content of elastin and collagen and therefore the wall stiffness normalised to its thickness, is assumed to remain normal [10,113]. Instead, hypertension [50] likely increases the recipient’s vascular wall tension which results in thickening of the vascular wall as found e.g. by Naeye [58]. In the model, the increase in wall thickness was included as a consequence of increased arterial pressure, Chapter 5.
We acknowledge that this simplified representation of the fetal arterial tree (figure 8) has several important limitations. First, the distribution of the cardiac output with gestational age over the various organs in this model [99] remains fixed. The distribution of blood flow as measured in the clinic may change, however, during gestation [65], but will certainly change during fetal compromise [31,40,68]. In addition, compromise such as hypoxia may have different hemodynamic sequelae, depending on the mechanism that causes the hypoxia, e.g. placental insufficiency, cord occlusion, or maternal hypoxia.
In spite of these limitations, this model has enabled us to investigate the separate consequences of abnormalities in e.g. blood viscosity, vascular wall stiffness, increased placental resistance. Obviously, finding these influences is impossible in the human fetus, and in an animal model it would be costly, technically challenging, and impossible for prolonged periods of gestation.
Figure 8. Taken from Wijngaard et al. 2006 [98] Schematic overview of the fetal arterial circulation, consisting of 22 segments. The 13 conduit arteries are: 1 Ascending aorta, 2 (left and right) carotid arteries, 3 (left and right) middle cerebral arteries (MCAs), 4 (left and right) anterior cerebral arteries, 5 thoracic aorta, 6 abdominal aorta, 7 (left and right) iliac arteries, 8 two umbilical arteries. The 9 Windkessels represent the fetal brain (B, 4 Windkessels), kidneys (K, 2 Windkessels), lower body (L, 2 Windkessels) and the placenta (1 Windkessel).
Anastomoses
An AV anastomosis connects the umbilical artery of the donor with the umbilical vein of the recipient. The AV connections occur at the capillary level within a cotyledon that receives its blood from a donor chorionic artery and drains it by a recipient chorionic vein. VA anastomoses, i.e. AVs from recipient to donor, often exist next to primary AVs, where the VAs are defined as having the smaller diameter (higher resistance) compared to the primary AV with the largest diameter. Further, AA or VV anastomoses directly connect chorionic arteries or veins of the two twins [61].
Recently, a third type of anastomosis has been described, which we will refer to here as deep-hidden anastomoses since these occur deep within the placenta between the cotyledons [108]. These anastomoses are small however and on the basis of a hemodynamic analysis and an analysis of the Hb discordance in monochorionic twins at birth with placentas without superficial anastomoses, it is suggested these deep-hidden anastomoses likely are without clinical consequences [94], chapter 11.
In our models, the AV, VA, AA and VV anastomoses are represented by tubes, which directly connect with the arterial and venous compartments of the two umbilical circulations, without branches to the normal placental chorionic vessels. This is obviously a simplification because most, if not all, anastomoses have branches to the normal chorionic circulation of the placenta. All anastomotic tubes are assumed to grow in volume proportional to the placental volume. Based on Fig. 19 of Dawes [18], showing that fetal weight of animals and humans behave proportional to gestational age to the third power, and assuming for convenience that fetal and placental weight are proportional to each other, we assumed that the placental volume increases proportional to the 3rd power of gestational age until about 31 weeks (∝ denotes proportional to)
1 5 6 8 7 2 3 K L K B L Placenta Hyrtl’s anastomosis 4 B 4 B B 2 3 8 7
PlacentalVolume ∝ (t)3 t<31 weeks (9) where t denotes gestational age (weeks). Thus, at least until 31 weeks, and using that the blood volume of a tube equals (π·radius2·length), gives that both radius and length of anastomoses behave proportional to gestational age, or
AnastLength ∝ t t<31 weeks (10a)
AnastRadius ∝ t t<31 weeks (10b)
From serial ultrasonographic measurements, this behaviour has very recently been shown to apply for diameters of AA as well as draining veins of AV anastomoses [22,107].Beyond 31 weeks we assumed a smaller growth rate. In our modelling, one of the necessary input parameters needed to run the model is the radius at 40 weeks; the length at 40 weeks has been taken as 15 cm (the other input parameter is the degree of placental sharing).
Anastomotic resistance
Blood flow velocities in fetal arteries and veins are relatively small, with Reynolds numbers (i.e. (diameter·velocity)/(viscosity/density)) well below 2000, implying that blood flow is laminar [55]). This implicates that Poiseuille’s law can be used to define the resistance of each vessel tube (anastomosis), related to blood viscosity, vessel length and diameter, as
4 8 Radius Length Viscosity t AnastResis π = (11)
The unit of resistance is pressure gradient (mmHg) divided by flow (ml·week-1), i.e. Ohm’s law, thus mmHg·ml-1·week. Here, the radius is included to the fourth power, implying radius has an exceedingly strong influence on resistance, e.g. a radius increase by a factor of two decreases the resistance by a factor of 24 = 16, at constant viscosity and length. Equations 10a and 10b can then be substituted in equation 11, yielding that anastomotic resistances behave approximately as the following proportionality relation
3 4 1 t t t t AnastResis ∝ = t<31 weeks (12)
In addition, measurements in humans [64] show that arterial and venous pressures of normal pregnancies increase linearly with gestation. Hence, an arteriovenous pressure gradient develops proportional to gestational age, thus
AV-PressGrad∝ GestationalAge (13)
It is straightforward from Ohm’s law and equations 13 and 12 that
4 3 / 1 t t t Resist -AV Grad Press -AV Flow -AV = ∝ = t<31 weeks (14)
Recently, Wee et al. [107] made serial measurements of the AV flow in 10 monochorionic twin pregnancies, as well as the normal cotyledonic flow (CotFlow), and derived that the median fetofetal transfusion measurements fit the following equations
AV-Flow = exp[0.13·t – 0.92] CotFlow = exp[0.13·t – 0.42] (15) figure 9 compares these fit curves with our estimate of equation 14. The correspondence between measurement fit and our estimate is striking, implying that our method of incorporating growth of length and diameter of anastomoses gives results quite close to reality.
0 20 40 60 80 100 120 15 20 25 30 35 40 Gestation (weeks) A V F lo w ( m l/ m in ) AV Flow Cotyledon Flow
Cotyledon Flow Wee et al. Cotyledon Flow 4th degree fit AV Flow Wee et al. AV Flow 4th degree fit
Figure 9. Plot of AV flow as a function of gestation, taken from Wee et al. [107], with fourth degree function, equation 14, (4th power curve), fitted at 40 weeks.
Placental anastomoses cause a fetofetal transfusion of blood between various combinations of arterial and venous blood compartments of the twins. Obviously, AV transfusion is the designated principle flow here and the combined VA, AA and VV transfusions return part of the AV flow back to the donor. The resulting net fetofetal transfusion is from donor to recipient and defined as
NetFetofetalTransf = AV-Flow – (VA-Flow + AA-Flow + VV-Flow) (16) The net amount of anastomotic fetofetal transfusion then results from the driving pressure gradients of the AV versus the VA, AA and VV, divided by the respective anastomotic resistances to blood flow.
Although a joint cotyledon (AV and VA anastomoses) is anatomically not a tube, the resistance nevertheless is treated equivalent in our model, because of the assumed identical growth behaviour and, therefore, the identical resistance decrease proportional to gestational age to the 3rd power. In a cotyledon, the radius of the capillaries does not vary with gestational age. Instead, the number of capillaries grows commensurate with the placental volume, assumed proportional to gestational age to the third power. Thus, approximating the vascular resistance of a cotyledon by the parallel circuit of identical capillary resistances, overall cotyledonic resistance is inversely proportional to the number of capillaries, hence, inversely proportional to the 3rd power of gestation, identical to AV and VA tube resistances. Several unidirectional AV anastomoses are equivalent to a circuit of parallel AV tube resistances, hence, equivalent to one overall AV tube resistance using the law of parallel resistances, i.e. (RAVoverall)-1 = (RAV1)-1 + (RAV2)-1 + (RAV3)-1 + ---. This holds for VA, AA and VV resistances too. So, multiple AV, VA, AA, and VV anastomoses are equivalent to a set of overall single AV, VA, AA, and VV resistances. An important result is that the resulting net fetofetal transfusion is not so much related to the total number of anastomoses, or the difference between the number of AV and the number of VA anastomoses [21], but rather to the capacity of all AV compared to the overall capacity of all VA, AA, and VV.
TTTS etiology
The etiology of TTTS was proposed to be a consequence of the natural development of the placental anastomoses as compared to the natural growth of the fetal blood volumes [100]. As discussed above, AV transfusion is proportional to gestational age to the 4th power. In contrast, natural growth of fetuses (and their blood volumes), is approximately proportional
to gestational age to the second power [18], which is a slower increasing function than the AV flow. Thus
AV-Flow ∝ (GestationalAge)4 (17a)
NaturalBloodVolGrowth ∝ (GestationalAge)2 (17b)
These different growth rates cause donor twins to effectively lose blood volume through the AV and recipients effectively to gain this blood volume. Because of this mechanism, the natural fetal growth of each twin loses the competition with this continuous exogenous change in its blood volume. Obviously, if only unidirectional AV anastomoses are present, the well-known deleterious effects of TTTS develop with increasing severity without the possibility of recovery. On the other hand, if other anastomoses (VA, AA, VV) are also present, part of the AV transfusion will be returned back to the donor, equation 16. Under these circumstances, TTTS either will not develop, or it will have a reduced severity compared to TTTS caused by the single AV. Consequently, whether TTTS develops or not, and its severity, is determined by the capacity (length and diameter) of the unidirectional AV anastomoses, i.e. total AV transfusion, compared to the combined capacity of VA, AA, and VV anastomoses (recipient to donor), i.e. the sum of VA, AA and VV transfusions. This mechanism explains why some but not all monochorionic twin placentas with anastomoses develop TTTS [100].
Thus far, quantifying unidirectional AV fetofetal transfusion throughout gestation has been impossible, although assessment of individual unidirectional AV anastomotic flow at one gestational age was published very recently, based on measurement of the decreasing hemoglobin concentrations between the moment of an intrauterine blood transfusion and birth, yielding 27.9 ml/24 hours at 29 weeks from 5 unidirectional small AV connections [47], chapter 9. Very recently, Wee et al. [107] made serial measurements of AV flow from one twin to the other and found at 28 weeks a median value between 15.5 and 21 ml/min, versus 25 - 35 ml/min in normal cotyledons. Obviously, these values cannot represent unidirectional AV flow, as this would not be compatible with fetal survival, and likely represent AV flow in cases of bidirectional AV anastomoses.
Discussion
The development of realistic TTTS mathematical models is a challenging enterprise. The complexity of fetal physiology may at first seem to render modeling to be hopeless. Not only is there a paucity of information available on normal fetoplacental cardiovascular function and amniotic fluid homeostasis, the influence of TTTS on such developments is poorly understood. Therefore, simplified and sometimes empirical description of fetoplacental and amniotic fluid development is unavoidable. In view of the complexity of TTTS pathophysiology, a sequence of models of increasing sophistication, with model testing at each state of development, we believe, represents the optimal practical approach. An overview of the proposed physiological mechanisms causing TTTS sequalae from stage I to IV is given in figure 10. We submit that TTTS modeling thus far has illustrated important mechanisms and leads to simulations of clinically realistic scenarios. Several models and outcomes of their simulations are presented in this thesis.
Figure 10. Mechanisms responsible for development of TTTS stages I through IV.
REFERENCES
1 Adamson SL, Whiteley KJ, Langille BL. Pulsatile pressure-flow relations and pulse-wave propagation in the umbilical circulation of fetal sheep Circ Res 70:761-772,1992.
2 Anderson DF Faber JJ. Water flux due to colloid osmotic pressure across the haemochorial placenta of the guinea-pig. J Physiol 332:521-527,1982.
3 Aron EA, Anthony RV. Angiogenesis. In Polin RA, Fox WW, Abman SH, Editors. Fetal and Neonatal Physiology. 1st Vol., 3rd Ed. Chapter 9 Philadelphia: Saunders; 2004.
4 Bajoria R, Sullivan M, Fisk NM. Endothelin concentrations in monochorionic twins with severe twin-twin transfusion syndrome. Hum Reprod 14:1614-1618,1999.
5 Bajoria R, Ward S, Sooranna SR. Influence of vasopressin in the pathogenesis of oligohydramnios-polyhydramnios in monochorionic twins. Eur J Obstet Gynecol Reprod Biol 113: 49–55, 2004.
6 Barker DJP. Fetal origins of coronary heart disease. BMJ 311:171-174,1995.
7 Barrea C, Alkazaleh F, Ryan G, McCrindle BW, Roberts A, Bigras J, Barrett J, Seaward GP, Smallhorn JF, Hornberger LK. Prenatal cardiovascular manifestations in the twin-to-twin transfusion syndrome recipients and the impact of therapeutic amnioreduction. Am J Obstet Gynecol 192:892-902,2005.
8 Beall MH, van Gemert M, van den Wijngaard JPHM, Ross MG. Water Flux and Amniotic Fluid Volume: Understanding fetal water flow in Questions and Controversies. In Neonatology Series. Oh, Guignard, Baumgart, Eds: Renal/Fluids and Electrolytes Volume.
9 Benirschke K, Kaufmann P. Pathology of the Human Placenta. New York: Springer Verlag, 3rd Edition, 1995.
Net fetofetal transfusion
of blood and colloids Net fetofetal transfusion increases colloids, blood volume and urine production Increased colloids increase the transplacental flow, causing polyuria and polyhydramnios Net fetofetal transfusion decreases
colloids, blood volume and urine production
Increased fetofetal transfusion amplifies the hypotension and ceases donor urination
Increased fetofetal transfusion aggravates hypotension, causing excessive RAS production
Net fetofetal transfusion causes excessive RAS concentration followed by retention of the polyuria, causing aggravation of hypertension, onset of high output cardiac failure followed by hydrops
TTTS Stage I
TTTS Stage II
Recipient Donor
Net fetofetal transfusion of blood, colloids & RAS Decreased urination causes a stuck
twin
Transplacental fluid flow
TTTS Stage IV TTTS Stage III
Increased placental resistance e.g. due to RAS production and placental compression, decreased brain resistance, low blood viscosity, cause abnormal arterial pulsations
Increased placental resistance e.g. due to placenta compression, decreased brain resistance, may cause abnormal arterial pulsations, but increased blood viscosity is a mitigating factor that may prevent abnormal umbilical and brain arterial pulsations.
10 Berry CL, Looker T, Germain J. Nucleic acid and scleroprotein content of the developing human aorta. J Pathol 108:265-275,1972.
11 Brace RA. Physiology of amniotic fluid volume regulation. Clin Obstet Gynecol 40:280-289,1997.
12 Brace RA, Christian JL. Transcapillary starling pressures in the fetus, newborn, adult, and pregnant adult. Am J Physiol 240: H843-H847, 1981.
13 Brace RA, Langendörfer C, Song TB, Mock DM. Red blood cell life span in the ovine fetus. Am J Physiol 279:R1196-R1204,2000.
14 Chescheir NC. Twin-to-twin transfusion syndrome: a model for the fetal origins of adult health. Paediatr Perinat Epidem 19:32-37,2005.
15 Cheung YF, Taylor MJO, Fisk NM, Redington AN, Gardiner HM. Fetal origins of reduced arterial distensibility in the donor twin in twin-twin transfusion syndrome. Lancet 355:1157-1158,2000.
16 Curran MA, Nijland MJM, Mann SE, Ross MG. Human amniotic fluid mathematical model: determination and the effect of intramembranous flow. Am J Obstet Gynecol 178: 484–490,1998.
17 Damiano A, Zotta E, Goldstein J, Reisin I, Ibarra C. Water channel proteins AQP3 and AQP9 are present in syncytiotrophoblast of human term placenta. Placenta 22:776-781,2001.
18 Dawes GS. The foetal circulation. In foetal and neonatal physiology. Year Book Medical Publishers 1973, Chicago.
19 De Lia JE, Cruikshank DP, Keye WR. Fetoscopic Neodymium:YAG laser occlusion of placental vessels in severe twin-twin transfusion syndrome. Obstet Gynecol 75:1046-1053,1990.
20 Denbow ML, Blomley MJK, Cosgrove DO, Fisk NM. Ultrasound microbubble contrast angiography in monochorionic twin fetuses. Lancet 349:773,1997.
21 Denbow ML, Talbert D, Fisk NM. Determinants of flow along arterio-arterial anastomoses in monochorionic placentae by dynamic computer modelling of chorionic plate vasculature. Prenatal Diagn 26, 433-442,2006.
22 Denbow ML, Taylor M, Cox P, Fisk NM. Derivation of rate of arterio-arterial anastomotic transfusion between monochorionic twin fetuses by Doppler waveform analysis. Placenta 25:664-670,2004.
23 Dickinson JE, Evans SF. The progression of disease stage in twin-twin transfusion syndrome. J Matern Fetal Neonatal Med 16:95-101,2004.
24 Diehl W, Hecher K, Zikulnig L, Vetter M, Hackelöer B-J. Placental vascular anastomoses visualised during fetoscopic laser surgery in severe mid-trimester twin-twin transfusion syndrome. Placenta 22:876-881,2001. 25 Faber JJ, Anderson DF. Angiotensin mediated interaction of fetal kidney and placenta in the control of fetal
arterial pressure and its role in hydrops fetalis. Placenta 18:313-326,1997. 26 Faber JJ, Thornburg KL. Placental Physiology. Raven Press, New York, 1983.
27 Fisk NM, Galea P. Twin-twin transfusion as good as it gets? N Engl J Med 351:182-184,2004.
28 Fisk MN, Vaughan J, Talbert D. Impaired fetal blood gas status in polyhydramnios and its relation to raised amniotic pressure. Fetal Diagn Ther 9:7–13, 1994.
29 Gardiner HM, Taylor MJO, Karatza A, Vanderheyden T, Huber A, Greenwald SE, Fisk NM, Hecher K. Twin-twin transfusion syndrome: the influence of intrauterine laser photocoagulation on arterial distensibility in childhood. Circulation 107:1906-1911,2003.
30 Goodwin JA, van Meurs WL, Sa Couto CD, Beneken JEW, Graves SA. A model for educational simulation of infant cardiovascular physiology. Anesth Analg 99:1655-1664,2004.
31 Gunnarsson GO , Gudmundsson S, Hokegard K, Stale H, Kjellmer I, Hafstrom O, Marsal K. Cerebral Doppler blood flow velocimetry and central hemodynamics in the ovine fetus during hypoxemia-acidemia. J Perinat Med 26:107–114,1998.
32 Guyton AC and Hall JE. Textbook of Medical Physiology (9th ed). Philadelphia: Saunders,1996.
33 Harding R and Bocking AD. Eds. Fetal growth and development. Chapt 5 Cambridge Univ Press Cambridge 2001.
34 Hanson MA, Spencer JAD, Rodeck CH. Fetus and neonata physiology and clinical applications. Vol 1 The circulation Cambridge Univ Press Cambridge 1993.
35 Hecher K, Diehl W, Zikulnig L, Vetter M, Hackeloer BJ. Endoscopic laser coagulation of placental anastomoses in 200 pregnancies with severe mid-trimester twin-to-twin transfusion syndrome. Eur J Obstet Gynecol R B 92;135-140,2000.
36 Hellman LM, Flexner LB, Wilde WS, Vosburgh GJ, Proctor NK, Baltimore MS. The permeability of the human placenta to water and the supply of water to the human fetus as determined with deuterium oxide. Am J Obstet Gynecol 56:861-868,1948.
