The Hyrtl anastomosis is a common connection between the umbilical arteries near the cord insertion in most human placentas. It has been speculated that it equalizes the blood pressure between the territories supplied by the umbilical arteries. However, its functional role in the regulation and distribution of fetal blood flow to the placenta has not yet been explored. A computational model has been developed for quantitative analysis of hemodynamic characteristic of the Hyrtl anastomosis in cases of discordant blood flow in the umbilical arteries. Simulations were performed for cases of either increased placental resistance at the downstream end or reduced arterial blood flow due to some pathologies upstream of one of the arteries. The results indicate that when placental territories of one artery impose increased resistance to fetal blood flow, the Hyrtl anastomosis redistributes the blood flow into the second artery to reduce the large pressure gradients that are developed in the affected artery. When one of the arteries conducts a smaller blood flow into the placenta and a relatively smaller pressure gradient is developed, the Hyrtl anastomosis rebuilds the pressure gradients in the affected artery and redistributes blood flow from the unaffected artery to the affected one to improve placental perfusion. In conclusion, the Hyrtl anastomosis plays the role of either a safety valve or a pressure stabilizer between the umbilical arteries at the placental insertion.
- umbilical artery
- fetal blood circulation
- biofluid simulations
- discordant blood flow
the placenta is a vital organ that maintains fetomaternal exchange of oxygen, nutrients, and waste products during fetal development. Fetal blood to the placenta is provided by a pair of umbilical arteries that arise from the fetus internal iliac arteries. Naturally, it is assumed that umbilical blood flow is equal in both arteries, and consequently, they are expected to perfuse similar volumes of placental territories. However, Doppler measurements of velocity waveforms and post-labor evaluations revealed cases of discordant umbilical arteries (6, 8, 13, 24), which may be attributed to significant differences in either arterial diameter or the placental volume supplied by these arteries. It was also observed that the degree of discordance is largely reduced as pregnancy advances, probably due to the maturation of the Hyrtl anastomosis between the umbilical arteries (16).
The Hyrtl anastomosis is a common connection between the umbilical arteries in most human placentas (Fig. 1A). The anatomic structure of this anastomosis is of a large variability, but it was always found in the vicinity of the cord insertion (18, 19). Generally, it was hypothesized that the Hyrtl anastomosis plays an active role in the regulation and distribution of fetal blood flow to the placenta (27). It was speculated that it equalizes the blood pressure between the territories supplied by the umbilical arteries (17). It was also considered as a shunt (e.g., safety valve) in case of partial compression of the placenta during uterine contractions or occlusion of one umbilical artery (2, 17). Nevertheless, the hemodynamic characteristics of Hyrtl anastomosis in fetoplacental circulation have not been evaluated. Accordingly, a computational study has been developed for quantitative analysis of the functional role of Hyrtl anastomosis in distribution of fetal circulation in case of discordant blood flow in the umbilical arteries.
Description of the model.
Hyrtl anastomosis may be either a single connecting vessel or a fusion between the umbilical arteries (18, 27). The majority of the anastomoses (up to 90%) are of a single connecting tube, which may be transverse or oblique to the arteries (26). The physical model for the present study was chosen to be an H-type anastomosis. Thus the two umbilical arteries are represented by two straight tubes until the cord insertion in the placenta, and the Hyrtl anastomosis is included by a transverse connection (Fig. 1B). The diameters, D1 = D2 = 4 mm, and arterial length, 80 mm, where Lup = Ldown = 40 mm of the umbilical arteries, as well as the geometry of the Hyrtl anastomosis (Danast = 4 mm, Lanast = 8 mm), were chosen from averaged morphometric data (17–19, 25). The downstream resistance of the arterial vasculature in the placental territories, which are supplied by each umbilical artery, is represented by a cylindrical porous media of length Lporous = 20 mm (Fig. 1B). The resistances of the porous cylinders downstream of arteries 1 and 2 are R1 and R2, respectively. The length of the upstream segment of the model (Lup) was chosen to ensure a parabolic velocity distribution in the vicinity of the anastomosis. The length of the downstream segment (Ldown) was chosen to ensure reduction of the parabolic velocity distribution into a uniform flow (i.e., plug flow) when fetal blood arrives to the porous media. In this study we assumed that fetal blood flow in the umbilical arteries may be simulated by a unidirectional steady flow into the placental vasculature.
The physical domain of the problem is a network of rigid three-dimensional (3-D) tubes. Fetal blood flow into the placenta is assumed to be steady, incompressible, and laminar with no-slip conditions at the walls. Accordingly, the continuity and Navier-Stokes equations are (1) (2) where U is the velocity vector, P is the fluid pressure, and ρ and υ are the fluid density and kinematical viscosity, respectively. The last term on the right-hand side of Eq. 2 represents the dissipative force of the porous media at the peripheral end of the umbilical arteries. The viscous resistance coefficient 1/α is given by Blevins (3) as (3) where R is the resistance, A is the cross-sectional area, L is the length of the porous cylinders, and μ is the viscosity. For simulations, the resistance of normal placental territories downstream of each umbilical artery is assumed to be RN = 4,325 × 105 N·s·m−5 (0.053 mmHg·ml−1·min), where the subscript N stands for “normal” (15). For fetal blood at body temperature, we used ρ = 1,060 kg·m3 and μ = 0.004 kg·m−1·s−1 (7, 23).
Normally, fetal blood flow into the placenta during the third trimester is at a rate of QN = 500 ml/min. Accordingly, if the umbilical arteries are identical, the averaged flow rate through each is 250 ml/min (11). Hence, for the normal symmetric case, we assumed that the flow into each artery is Q1 = Q2 = 250 ml/min. The published data for arterial pressure in the umbilical arteries ranges between 2,665 and 10,665 Pa (20–80 mmHg) (20, 28, 29). For the present model (Fig. 1B), we assumed that the normal inlet pressure is Pinlet-N = 5,150 Pa (38.6 mmHg), similar to the data of Weiner et al. (29). The outlet of the model is assumed to be at the level of fetal capillaries within the cotyledons; hence, Poutlet = 1,200 Pa (9 mmHg) (14, 15).
To explore the role of the anastomosis in cases of discordant umbilical arteries, it is necessary to simulate cases with different boundary conditions due to discordant fetal blood flow in the umbilical arteries. The variability of such cases is enormous, and thus we investigated two limiting states. In the first state, we assumed that the total fetal blood flow into the placenta is constant and divided between the umbilical arteries. Hence, any reduction of the input flow rate to one artery leads to a corresponding increase in the second one. This state may be considered as if the umbilical arteries are supplied by a flow generator (FG) and is described mathematically by Q1 + Q2 = QN. In the second state, we assumed that the pressure at the inlet to both umbilical arteries is always identical, independently of downstream resistance variations. This state may be considered as if the umbilical arteries are supplied by a pressure generator (PG) and is described mathematically by Pinlet-1 = Pinlet-2 = Pinlet-N for each artery.
Plan of numerical simulations.
The normal fetal blood flow in two identical umbilical arteries was simulated by Q1 = Q2 = QN/2, Pinlet 1 = Pinlet-2 = Pinlet-N, and R1 = R2 = RN. To simulate cases of discordant blood flow in the umbilical arteries and the resulting contribution of the Hyrtl anastomosis, we assumed two general options. In the first option, the flow into one artery is smaller than into the other one because of either geometry differences between the arteries or some upstream pathology (4, 9, 21). We assumed that the input flow rate may decrease by 20 or 40% of the normal flow. In the second option, the umbilical arteries supply placental territories of different resistances to fetal blood flow (12, 23). We assumed cases of 30, 60, and 100% increase in placental resistance to artery 1, whereas the resistance to artery 2 remained RN. A summary of all simulations of discordant fetal blood flow in the umbilical arteries is provided in Table 1. Evaluation of blood flow distribution due to the Hyrtl anastomosis was done for both states of FG and PG boundary conditions. The results for two independent umbilical arteries without the anastomosis (i.e., a single uniform tube) were computed for the given inlet flow rate and the outlet pressure (Poutlet).
The governing equations were simultaneously solved by implementing the finite volume computational fluid dynamics package FLUENT (Fluent, Lebanon, NH). The Euler implicit algorithm was used to solve the partial differential equations in a segregated manner. A spatially second-order upwind discretization scheme was used to minimize numerical dissipation. The 3-D geometry of the umbilical arteries and their connection via the Hyrtl anastomosis was converted into a discrete mesh with GAMBIT (Fluent). The mesh was composed of 880,193 cells to ensure a parabolic velocity profile in the midst of the anastomosis. For the ‘normal symmetric case, a single umbilical artery consisted of only 249,644 cells. The mesh volume density was much larger in the vicinity of the anastomosis.
Computational simulations of discordant flow in the umbilical arteries were performed by imposing on artery 1 either an increased placental resistance at the downstream end or a reduced inlet blood flow due to some upstream pathology, while artery 2 was subjected to normal blood flow. To simplify the presentation of the results, we investigated the pressure distributions along the central axis of each umbilical artery as being representative of the 3-D distribution of arterial pressure. The results of blood flow in the umbilical arteries when artery 1 feeds placental territories with increased resistance are depicted in Fig. 2 for numerical simulations with and without the Hyrtl anastomosis compared with the normal case of identical arteries feeding a symmetric placenta. The results for the model with the anastomosis are presented for boundary conditions of either FG or PG.
In the absence of the anastomosis, increased placental resistance by 30, 60, and 100% at the peripheral end of artery 1 (while Q1 = 250 ml/min) resulted in significant increases in the pressures up to 20, 41, and 70%, respectively (Fig. 2, A and C). Note that the static pressure at the junction that simulates the insertion of the umbilical artery in the placenta was elevated, whereas the slope of the pressure along the artery was practically identical. This pattern is due to the increased placental resistance that increases the pressure drop along the porous media that represents the placenta but does not change the pressure drop along the artery segment. On the other hand, when the anastomosis was included in the model using the FG boundary conditions, the increase in pressures was only 10, 19, and 28%, respectively, whereas use of the PG boundary conditions yielded pressure distributions along the vessel that were almost identical to the normal symmetric case (Fig. 2C). As blood flows through the anastomosis from artery 1 into artery 2, which is feeding placental territories with normal resistance (R2 = RN), the pressure drop along the central axis of artery 2 is also increasing due to increased blood flow through the porous cylinder (Fig. 2B). For the simulation with FG boundary conditions, the pressures in artery 2 demonstrated an increase of 9, 16, and 24% compared with normal symmetric placenta, as the resistance of the placental territories of artery 1 increased by 1.3, 1.6, and 2.0, respectively.
The corresponding redistribution of blood flow via the Hyrtl anastomosis is demonstrated in Fig. 3. The results are shown for the different increased resistance of R1 normalized by RN. The differences between inlet and outlet flow rates of the umbilical arteries due to the flow through the anastomosis are given in Fig. 3, A and B, for the simulations with FG and PG boundary conditions, respectively. It is clearly demonstrated that the anastomosis is distributing the inlet blood flow by transferring some of the blood flow of artery 1 into artery 2. The flow rate through the anastomosis itself is depicted in Fig. 3C, which demonstrates the increased blood flow rate through the anastomosis (QHA) as the resistance of the placental territories supplied by artery 1 is increased. The diverting of blood flow from artery 1 into artery 2 decreased the pressure drop between the anastomoses and the placental territories of artery 1, which would otherwise be larger when R1 is increased.
The pressure distributions along the central axis of the umbilical arteries for 20 and 40% reduced flow rate at the inlet to artery 1 due to an upstream pathology are shown in Fig. 4 for cases with and without Hyrtl anastomosis compared with the normal case. In the absence of the anastomosis, reduction in the flow rate into artery 1 significantly reduced the pressures along the tube with a maximal decrease of 16 and 32% for 20 and 40% reduction of inlet flow, respectively (Fig. 4, A and C). However, when the anastomosis was present in the model using the FG boundary conditions, blood flow was redistributed from artery 2 into artery 1 and the axial pressure drop demonstrated a maximal decrease of only 2 and 4%, respectively (Fig. 4A). Use of the PG boundary conditions similarly yielded a maximal decrease in pressure drop of 3 and 7%, respectively (Fig. 4C). The variations of the corresponding pressure distributions along the central axis of artery 2 compared with the normal identical arteries feeding a symmetric placenta were very small (Fig. 4B). The corresponding largest increase in pressure drop in artery 2 due to redistribution of some blood into artery 1 was only 2 and 5%, respectively, for simulation with the FG boundary conditions.
The corresponding variation of inlet and outlet flow rates as a function of the reduced flow rates into artery 1 are given in Fig. 5, A and B. For upstream discordant arterial flow, the anastomosis compensated the missing flow rate in artery 1 by transferring some of the blood from artery 2 into artery 1 (Fig. 5A). In the case of upstream pathologies, the efficacy of the anastomosis is demonstrated by the significant increase of blood flow through the anastomosis as the inlet flow rate into artery 1 decreased (Fig. 5C).
Hyrtl anastomosis between the umbilical arteries is present in the majority of pregnant women just upstream of the insertion into the placenta. In this work we performed a quantitative analysis of the role of this anastomosis in equilibrating the pressure gradients in discordant umbilical blood flow in the arteries and the corresponding redistribution of blood perfusion into the placenta. We have selected for analysis two possible situations that lead to discordant umbilical blood flow: increased resistance of the placental territories supplied by one of the arteries and reduced blood flow into one of the umbilical arteries due to increased upstream resistance. The simulations presented demonstrate the different physical role of Hyrtl anastomosis in equilibration of discordant umbilical blood flow due to different causes.
The numerical prediction of pressure distribution along the axis of the umbilical arteries when the peripheral resistance of placental territories to one of them is increased (Fig. 2, A and C) demonstrates the role of the anastomosis as a safety valve for releasing highly developed pressures in one side. We compared the pressure distribution along the central axis of artery 1 for a case of R1 = 2RN with that of the averaged area pressure distribution along the axis and found that both curves were practically identical. This supports the use of the pressure at the central axis as a representative pressure. When the placenta is partially occluded to fetal blood flow (e.g., R1 > RN; R2 = RN), inlet pressure in artery 1 may rise up to 70% (for R1 = 2RN) with respect to the reference normal in the absence of the Hyrtl anastomosis. For simulations with the FG boundary conditions, the maximal rise is only 28%. Nevertheless, existence of the anastomosis largely reduces this pressure rise to values very close to the normal model when PG boundary conditions are incorporated (Fig. 2C). The inlet pressure in the unaffected artery ( i.e., artery 2) is also increasing in the predictions with FG boundary conditions (Fig. 2B), because additional blood flow is supplied via the anastomosis just before the outlet into the placenta. The efficacy of the anastomosis increases when the resistance of placenta territory increases, and more blood is transferred into other territories fed by the unaffected artery (Fig. 3).
In this study, we solved the governing equations for two limiting cases of PG and FG boundary conditions. The FG condition corresponds to a generator with infinite internal resistance (Rgenerator → ∞), whereas the PG condition corresponds to a generator with negligible internal resistance (Rgenerator → 0) (5). In reality, fetal heart is the generator that supplies arterial blood into the umbilical arteries and may have a finite resistance (0 < Rgenerator < ∞). Thus real cases are most likely to fall within the hatched area between the lines for PG and FG (Fig. 3C). Moreover, if the resistance to blood flow through the anastomosis increases (for example, a very small anastomosis diameter), the hatched area in Fig. 3C becomes narrower and moves downward toward the abscissa. In the absence of Hyrtl anastomosis (Ranast → ∞), QHA becomes zero.
The placenta is an organ that develops to maturity, along with the umbilical cord, within a relatively short time. When significant discordant arterial blood flow is being developed in the umbilical cord, it has been found in a single placenta with nonanastomosing umbilical arteries that the larger artery supplied a larger volume of placental territories (10). Similarly, an averaged asymmetry of ∼1:2 between placental areas supplied by each umbilical artery was observed in 61 placentas with Hyrtl anastomoses (25). When discordant flow is being developed due to increased resistance at the placental territories of one artery, the concomitant development of a Hyrtl anastomosis induces more blood supply to the other artery and thereby more blood to its placental territories. As a result, the placental territories supplied by the more efficient artery are expected to develop larger volumes with increased exchange surfaces than those supplied by the affected artery. In fact, this pattern of development was observed in a relatively old study of 78 placentas with Hyrtl anastomoses (22).
In a more recent study of the fetal vasculature of 210 placentas, only a few were found to have symmetric placental pools supplied by identical umbilical arteries (1). In 67% of the placentas, discordant umbilical arteries were observed with the larger artery supplying larger placental surface. The ratio between these surfaces was 1:2 in 39% of the casts, 1:3 in 15%, and 1:4 in 8%. Similarly, it also was found that discordance in the diameters of the umbilical arteries is associated with abnormal insertion of the umbilical cord in the placenta (19). In fact, French investigators (cited in Ref. 19) observed that marginal insertion of the umbilical cord is more likely in cases of discordant umbilical arteries or a single umbilical artery. Thus the Hyrtl anastomosis may be considered as a guard that redirects fetal blood flow to induce development of an asymmetric placenta that will ensure optimal performance during embryonic development.
When blood flow rate in artery 1 is much smaller than in artery 2 due to some upstream pathology or arteries with different diameters, the pressure drop in artery 1 is much smaller in the absence of the Hyrtl anastomosis (Fig. 4, A and C). A drop of 16 and 32% of the maximal values of the normal artery was observed for 20 and 40% reduction of the inlet blood flow, respectively. When the Hyrtl anastomosis is present, it is compensating for the flow rate in artery 1 by redistributing the blood flow between arteries 1 and 2, and thereby the pressure drop in artery 1 is reelevated nearly to the normal values. Namely, the decrease of 16 and 32% in pressure is reduced in the presence of an anastomosis to only 2 and 4% for the FG boundary conditions (Fig. 4A) and to 3 and 7% for the PG boundary conditions (Fig. 4C), respectively. If Ranast is increased, the hatched area in Fig. 5C becomes narrower and moves toward the abscissa. In the absence of Hyrtl anastomosis (Ranast → ∞), QHA becomes zero. Again, the anastomosis is acting as a pressure equilibrator and restores the outlet flow as if the umbilical arteries are normal (Fig. 5C).
In the present model, we assumed for the Hyrtl anastomosis an idealized geometry of a perpendicular single tube connecting the parallel umbilical arteries (Fig. 1B). This assumption is based on observations in real placentas, which have reported that Hyrtl anastomosis was mostly (up to 90%) a single true connection between the arteries (26). In terms of hemodynamic characteristics, the H-type model represents the geometry of a single connecting tube. In the case of an inclined anastomosis, there may be an additional pressure drop, but it is very small and has negligible effects on the overall flow pattern. Thus the H-type Hyrtl anastomosis is a good representative model for all cases of a single connecting tube anastomosis. Similarly, in cases where the Hyrtl anastomosis is a fenestration or a fusion between the arteries (up to 10% of the observed placentas; Ref. 26) the anastomosis resistance to blood flow is much smaller than that of the H-type, and its functional performance will largely improve.
In conclusion, we conducted for the first time a quantitative analysis of the hemodynamic characteristics of fetal blood flow through the Hyrtl anastomosis in the mature placenta. The results of this study clearly demonstrate the important functional role of the Hyrtl anastomosis in regulating arterial blood flow in discordant arteries to equilibrate the pressure gradients in the arteries before insertion into the placenta. When placental territories of one artery impose increase resistance to fetal blood flow, the Hyrtl anastomosis redistributes the blood flow into the second artery to reduce the large pressure gradients that are developed in the affected artery. As a result, the placental territories with rich blood supply are likely to be developed into larger volumes than the part with increased resistance to maintain fetal well being. When one of the arteries conducts a smaller blood flow into the placenta and a relatively smaller pressure gradient is developed, Hyrtl anastomosis rebuilds pressure gradients in the affected artery and redistributes blood flow from the unaffected artery to the affected one to improve placental perfusion.
This work was partially supported by a grant from the Nicholas and Elizabeth Slezak Super Center for Cardiac Research and Biomedical Engineering at Tel Aviv University.
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- Copyright © 2007 the American Physiological Society