A mathematical model of umbilical venous pulsation

Pulsations in the fetal heart propagate through the precordial vein and the ductus venosus but are normally not transmitted into the umbilical vein. Pulsations in the umbilical vein do occur, however, in early pregnancy and in pathological conditions. Such transmission into the umbilical vein is poorly understood. In this paper we hypothesize that the mechanical properties and the dimensions of the vessels do influence the umbilical venous pulsations, in addition to the magnitude of the pressure and flow waves generated in the fetal atria. To support this hypothesis we established a mathematical model of the umbilical vein/ductus venosus bifurcation. The umbilical vein was modeled as a compliant reservoir and the umbilical vein pressure was assumed to be equal to the stagnation pressure at the ductus venosus inlet. We calculated the index of pulsation of the umbilical vein pressure ((max-min)/mean), the reflection and transmission factors at the ductus venosus inlet, numerically and with estimates. Typical dimensions in the physiological range for the human fetus were used, while stiffness parameters were taken from fetal sheep. We found that wave transmission and reflection in the umbilical vein ductus venosus bifurcation depend on the impedance ratio between the umbilical vein and the ductus venosus, as well as the ratio of the mean velocity and the pulse wave velocity in the ductus venosus. Accordingly, the pulsations initiated by the fetal heart are transmitted upstream and may arrive in the umbilical vein with amplitudes depending on the impedance ratio and the ratio between the mean velocity and the pulse wave velocity in the ductus venosus.     

Effect of NO, phenylephrine, and hypoxemia on ductus venosus diameter in fetal sheep

To study the regulation of the ductus venosus (DV) inlet in vivo, we measured the effect of vasoactive substances and hypoxemia on its diameter in nine fetal sheep in utero at 0.9 gestation under ketamine-diazepam anesthesia. Catheters were inserted into an umbilical vein and a fetal common carotid artery, and a flowmeter was placed around the umbilical veins. Ultrasound measurements of the diameter of the fetal DV during normoxic baseline conditions [fetal arterial PO(2) (PaO(2)) 24 mmHg] were compared with measurements during infusion of sodium nitroprusside (SNP; 1.3, 2.6, and 6.5 microg. kg(-1). min(-1)) or the alpha(1)-adrenergic agonist phenylephrine (6.5 microg. kg(-1). min(-1)) into the umbilical vein or during hypoxemia (fetal Pa(O(2)) reduced to 10 mmHg). SNP increased the DV inlet diameter by 23%, but phenylephrine had no effect. Hypoxemia caused a 61% increase of the inlet diameter and a distension of the entire vessel. We conclude that the DV inlet is tonically constricted, because nitric oxide dilates it but an alpha(1)-adrenergic agonist does not potentiate constriction. Hypoxemia causes a marked distension of the entire DV.     

Pressure pulses and flow velocities in central veins of the anesthetized sheep fetus

The pressure drop and pressure pulses in the isthmus of the ductus venosus (DV) in fetal sheep have not been measured directly and related to flow. In eight acutely anesthetized fetal sheep, a 3-Fr tip pressure transducer (TP) was inserted from the external jugular into the umbilical vein (UV). Ultrasound Doppler flow velocities, TP position, and intravenous pressures were recorded in the UV, DV, and inferior vena cava (VC) while the TP was withdrawn. Flow was steady in the UV, but small pressure fluctuations (<0.4 mmHg) could be detected. Time-averaged pressure dropped 1.9 mmHg (mean; 0.5-3.3 mmHg 95% confidence interval) across the DV isthmus. Pressure pulses increased from 1.7 mmHg (mean; 1.2-2.1 mmHg 95% confidence interval) in the DV to 3.9 mmHg (mean; 1.8-6.0 mmHg 95% confidence interval) in the inferior VC. The pressure wave from the heart arrived later [0.053 s (mean; 0.025-0.080 s 95% confidence interval)] in the isthmus of the DV than in the diaphragmatic inferior VC, indicating a wave velocity of approximately 1.1 m/s. At all locations, pressures and flow velocities were inversely related.     

Velocity profiles in the human ductus venosus: a numerical fluid structure interaction study

The veins distributing oxygenated blood from the placenta to the fetal body have been given much attention in clinical Doppler velocimetry studies, in particular the ductus venosus. The ductus venosus is embedded in the left liver lobe and connects the intra-abdominal portion of the umbilical vein (IUV) directly to the inferior vena cava, such that oxygenated blood can bypass the liver and flow directly to the fetal heart. In the current work, we have developed a mathematical model to assist the clinical assessment of volumetric flow rate at the inlet of the ductus venosus. With a robust estimate of the velocity profile shape coefficient (VC), the volumetric flow rate may be estimated as the product of the time-averaged cross-sectional area, the time-averaged cross-sectional maximum velocity and the VC. The time average quantities may be obtained from Doppler ultrasound measurements, whereas the VC may be estimated from numerical simulations. The mathematical model employs a 3D fluid structure interaction model of the bifurcation formed by the IUV, the ductus venosus and the left portal vein. Furthermore, the amniotic portion of the umbilical vein, the right liver lobe and the inferior vena cava were incorporated as lumped model boundary conditions for the fluid structure interaction model. A hyperelastic material is used to model the structural response of the vessel walls, based on recently available experimental data for the human IUV and ductus venous. A parametric study was constructed to investigate the VC at the ductus venosus inlet, based on a reference case for a human fetus at 36 weeks of gestation. The VC was found to be \(0.687\,\pm \,0.023\) (Mean \(\pm \) SD of parametric case study), which confirms previous studies in the literature on the VC at the ductus venosus inlet. Additionally, CFD simulations with rigid walls were performed on a subsection of the parametric case study, and only minor changes in the predicted VCs were observed compared to the FSI cases. In conclusion, the presented mathematical model is a promising tool for the assessment of ductus venosus Doppler velocimetry.     

Simulation of pressure drop and energy dissipation for blood flow in a human fetal bifurcation.

The pressure drop from the umbilical vein to the heart plays a vital part in human fetal circulation. The bulk of the pressure drop is believed to take place at the inlet of the ductus venosus, a short narrow branch of the umbilical vein. In this study a generalized Bernoulli formulation was deduced to estimate this pressure drop. The model contains an energy dissipation term and flow-scaled velocities and pressures. The flow-scaled variables are related to their corresponding spatial mean velocities and pressures by certain shape factors. Further, based on physiological measurements, we established a simplified, rigid-walled, three-dimensional computational model of the umbilical vein and ductus venosus bifurcation for stationary flow conditions. Simulations were carried out for Reynolds numbers and umbilical vein curvature ratios in their respective physiological ranges. The shape factors in the Bernoulli formulation were then estimated for our computational models. They showed no significant Reynolds number or curvature ratio dependency. Further, the energy dissipation in our models was estimated to constitute 24 to 31 percent of the pressure drop, depending on the Reynolds number and the curvature ratio. The energy dissipation should therefore be taken into account in pressure drop estimates.     

Role of ductus venosus in distribution of umbilical blood flow in human fetuses during second half of pregnancy

Color Doppler sonography was used to study umbilical and ductus venosus (DV) flow in 137 normal fetuses between 20 and 38 wk of gestation. Hepatic flows were also evaluated. In all parts of the venous circulation examined, blood flow increased significantly with advancing gestational age. The weight-specific amniotic umbilical flow did not change significantly during gestation (120 +/- 44 ml. min(-1). kg(-1)), whereas DV flow decreased significantly (from 60 to 17 ml. min(-1). kg(-1)). The percentage of umbilical blood flow shunted through the DV decreased significantly (from 40% to 15%); consequently, the percentage of flow to the liver increased. The right lobe flow changed from 20 to 45%, whereas the left lobe flow was approximately constant (40%). These changes are related to different patterns of growth of the umbilical veins and DV diameters. The present data support the hypothesis that the DV plays a less important role in shunting well-oxygenated blood to the brain and myocardium in late normal pregnancy than in early gestation, which leads to increased fetal liver perfusion.     

49 例先天性胎儿心脏疾病的静脉导管血流频谱分析

目的：不同的胎儿先天性心脏疾病通过不同的作用机制影响到胎儿心脏功能,会引起胎儿体内血循环的不同改变。静脉导 管是胎儿血循环中重要的组成,也会随之出现相应的频谱改变。通过对49 例合并先天性心脏疾病胎儿的静脉导管血流频谱及参 数进行分析,研究胎儿不同类型心脏疾病对静脉导管（DV）血流频谱的影响。方法：选取2009 年1 月至2012 年12 月间我们在产 前超声检查中发现的49 例合并先天性心脏疾病的胎儿,分别测量DV血流频谱并进行参数分析,根据DV频谱是否正常分为两 组。结果：DV频谱正常组有29 例(59.18%),表现为S 波、a 波的流速和方向正常,PVIV 及DVRI指标位于正常范围。DV频谱异 常组有20 例,表现为S波流速降低、a 波缺失或反向,PVIV 及DVRI升高。结论：DV血流频谱和参数是评价胎儿心功能的良好 指标。不同种类胎儿心脏发育异常对胎儿心功能影响的作用机制不同,其DV频谱也有着不同改变。通过对DV频谱的波形和参 数分析,了解胎儿心脏异常的病生理机制,评价其严重程度和预后,这对于指导临床诊疗有着重要意义。     

49例先天性胎儿心脏疾病的静脉导管血流频谱分析

目的：不同的胎儿先天性心脏疾病通过不同的作用机制影响到胎儿心脏功能,会引起胎儿体内血循环的不同改变。静脉导管是胎儿血循环中重要的组成,也会随之出现相应的频谱改变。通过对49例合并先天性心脏疾病胎儿的静脉导管血流频谱及参数进行分析,研究胎儿不同类型心脏疾病对静脉导管（DV）血流频谱的影响。方法：选取2009年1月至2012年12月间我们在产前超声检查中发现的49例合并先天性心脏疾病的胎儿,分别测量DV血流频谱并进行参数分析,根据DV频谱是否正常分为两组。结果：DV频谱正常组有29例（59.18%）,表现为S波、a波的流速和方向正常,PVIV及DVRI指标位于正常范围。DV频谱异常组有20例,表现为S波流速降低、a波缺失或反向,PVIV及DVRI升高。结论：DV血流频谱和参数是评价胎儿心功能的良好指标。不同种类胎儿心脏发育异常对胎儿心功能影响的作用机制不同,其DV频谱也有着不同改变。通过对DV频谱的波形和参数分析,了解胎儿心脏异常的病生理机制,评价其严重程度和预后,这对于指导临床诊疗有着重要意义。     

Blood flow in the umbilical vein in normal pregnancy]

Blood flow through the umbilical vein was measured with Doppler's technique in 206 pregnant women with normal course of pregnancy. Flow rate index, vein diameter and total blood flow per unit of fetal weigh have been calculated. It was found, that the blood flow rate and umbilical vein diameter increase with the growth of the normal pregnancy.     

Effects of chronic instrumentation on fetal growth

Chronically-instrumented fetal sheep are a commonly used animal model for the study of fetal growth and metabolism. In the current study, we wanted to test the hypothesis that instrumentation alone would alter fetal growth patterns. Thirty-two animals in three groups were used: (i) non-instrumented animals (n = 10); (ii) instrumented with catheters in the maternal and fetal femoral artery and vein and electromagnetic flow probes on the main uterine arteries (n = 10): (iii) animals instrumented as group 2, but with the addition of a doppler flow probe on the common umbilical artery and a common umbilical vein catheter (n = 12). Animals in group 2 and 3 were monitored until 137 to 140 days of gestation, at which time they were sacrificed for fetal morphometric measurements. Instrumentation significantly (P less than 0.05) decreased fetal body weight, length, and thymus weights. Liver-to-body ratios increased (P less than 0.05) in both surgically-instrumented groups. The addition of the umbilical artery doppler flow probe and an umbilical venous catheter did not lead to any further alterations in fetal growth. The current study demonstrates that surgical instrumentation alone can lead to significant alterations in fetal growth.     

Characterization of the in vivo wall shear stress environment of human fetus umbilical arteries and veins

The endothelial cells of the umbilical vessels are frequently used in mechanobiology experiments. They are known to respond to wall shear stress (WSS) of blood flow, which influences vascular growth and remodeling. The in vivo environment of umbilical vascular WSS, however, is not well characterized. In this study, we performed detailed characterization of the umbilical vascular WSS environments using clinical ultrasound scans combined with computational simulations. Doppler ultrasound scans of 28 normal human fetuses from 32nd to 33rd gestational weeks were investigated. Vascular cross-sectional areas were quantified through 3D reconstruction of the vascular geometry from 3D B-mode ultrasound images, and flow velocities were quantified through pulse wave Doppler. WSS in umbilical vein was computed with Poiseuille’s equation, whereas WSS in umbilical artery was obtained via computational fluid dynamics simulations of the helical arterial geometry. Results showed that blood flow velocity for umbilical artery and vein did not correlate with vascular sizes, suggesting that velocity had a very weak trend with or remained constant over vascular sizes. Average WSS for umbilical arteries and vein was 2.81 and 0.52 Pa, respectively. Umbilical vein WSS showed a significant negative correlation with the vessel diameter, but umbilical artery did not show any correlation. We hypothesize that this may be due to differential regulation of vascular sizes based on WSS sensing. Due to the helical geometry of umbilical arteries, bending of the umbilical cord did not significantly alter the vascular resistance or WSS, unlike that in the umbilical veins. We hypothesize that the helical shape of umbilical arteries may be an adaptation feature to render a higher constancy of WSS and flow in the arteries despite umbilical cord bending.     

Safety Indices during Fetal Echocardiography at the Time of First-Trimester Scan Are Machine Dependent

The aim of our study was to evaluate the thermal index (TI) and mechanical index (MI), during the assessment of the fetal heart at the time of first-trimester scan, with different ultrasound machines. This was part of an observational study conducted in patients undergoing routine first-trimester screening. Cases were examined with Voluson E8 or 730Pro scanners using 2–8 MHz transabdominal probes. TI and MI were retrieved from the saved displays while in gray mode, color flow mapping and pulsed-wave (PW) Doppler examinations of the fetal heart and also from the ductus venosus (DV) assessment. We evaluated 552 fetal cardiac examinations, 303 (55%) performed with Voluson E8 and 249 (45%) with Voluson 730Pro ultrasound machines. The gray-scale exam of the heart and the PW Doppler DV assessment had TI values significantly lower for the Voluson E8 group (median, 0.04 vs. 0.2 and 0.1 vs. 0.2, respectively). The MI values from gray-scale and color flow mapping of the heart were significantly lower (median, 0.6 vs, 1.2 and 0.7 vs. 1) and for PW Doppler exam of the tricuspid flow were significantly higher (median 0.4 vs. 0.2) in the Voluson E8 group. The TI values from Doppler examinations of the heart, either color flow or PW imaging and MI values from DV assessment were not significantly different between the two groups. A different (newer) generation of ultrasound equipment provides lower or at least the same safety indices for most of the first-trimester heart examinations.     

Electron-microscopic immunolabelling of vasoactive substances in human umbilical endothelial cells and their actions in early and late pregnancy

Human umbilical vessels are devoid of nerves and therefore endothelial cells may play an important role in the control of feto-placental blood flow. The pharmacological effects of 5-hydroxytryptamine, histamine and endothelin were examined in umbilical arteries and veins from legal terminations (gestational age 8–17 weeks, n=12) and normal term vaginal deliveries (gestational age 38–41, n=12). Immunocytochemistry of human unbilical vessels indicated that 5-hydroxytryptamine, histamine and endothelin were localised in subpopulations of endothelial cells of both artery and vein in late, but not early, pregnancy. 5-Hydroxytryptamine (10 nM–30 μM) caused sustained concentration-dependent contractions in all vessels from early and late pregnancy. Histamine (0.1 μM–30 mM) also caused sustained contractions in all vessels from late pregnancy but only 27% of arteries and 41% of veins from early pregnancy responded. Endothelin (10 pM–30 nM) caused slow long-lasting contractions in all vessels from early and late pregnancy. Atrial natriuretic peptide and neuropeptide Y did not alter vascular tone. The endothelium may thus play an autocrine/paracrine role, by synthesizing and releasing the above reactive substances in late pregnancy to influence feto-placental blood flow. Received: 23 May 1995 / Accepted: 13 October 1995     

Venous responses to hypoxemia in the fetal lamb

The factors regulating umbilical venous return and its distribution between the ductus venosus and liver are poorly understood. This study was designed to determine where the major changes in resistance to umbilical venous return occur in response to fetal hypoxemia. In eight chronically-instrumented fetal lambs, during control and hypoxemic periods, we measured pressure in the descending aorta, extra-abdominal umbilical vein, portal sinus, and inferior vena cava; we also measured blood flow using radionuclide-labeled microspheres. During the control period, the umbilical arteries and placental vasculature accounted for 82% of total resistance to umbilical-placental blood flow, the umbilical veins for 11%, and the ductus venosus and liver for 7%. Hypoxemia increased resistance in the umbilical veins more than twofold, but did not affect resistance in the umbilical arteries or placenta. Although combined liver/ductus venosus resistance did not change, hepatic vascular resistance increased, and ductus venosus resistance decreased. We conclude that the major increase in resistance to umbilical venous return in response to hypoxemia resides in the umbilical veins. This increased resistance may improve maternal-fetal blood gas exchange by increasing the fetal surface area in the placenta.     

Tracheid analysis and modeling of the minor veins of the coleus and smilax leaves

Tracheid analysis was carried out on the veinlets and minor veins of the coleus (Solenostemon scutellarioides [L.] Codd) leaf. Third- to fifth-order, or minor, veins average 3.4 tracheids in tandem and they bipartition islets when these enclosed islets reach a critical size; both these features of vein length and islet size contribute to a self-similar process of vein pattern generation. An areole was calculated to be initially comprised of about ten cells making the patterning event for vein formation requiring only a few cells. An algorithmic model developed here for minor vein formation includes five production rules, and this computer model explains the 3–4 tracheids per minor vein, presence of isolated tracheids, the structure of veinlets, and the elaborate branching patterns of veinlets in coleus and other plants.     

On the presence of a ductus venosus in the fetal pig in late gestation

Evidence is presented to show that there is a functional bypass in the liver of the fetal piglet between the umbilical vein and the posterior vena cava. Injections of labelled microspheres (14 micrometer) into the umbilical vein in six fetuses in late gestation resulted in the appearance of radioactivity in the arterial blood and throughout the tissues of all piglets. About 60% of the umbilical venous blood bypassed the liver whereas in a fetal foal, injection in a similar manner, no evidence for a shunt was found. Radiographic studies confirmed the presence of a large vascular connection, equivalent to the ductus venosus, between the umbilical vein and posterior vena cava in the fetal piglet.     

Lactate uptake by the fetal sheep liver

Lactate is produced by the sheep placenta and is an important metabolic substrate for fetal sheep. However, lactate uptake and release by the fetal liver have not been assessed directly. We measured lactate flux across the liver in 16 fetal sheep at 129 (120-138) days gestation that had catheters chronically maintained in the fetal descending aorta, inferior vena cava, right or left hepatic vein, and umbilical vein. Lactate and hemoglobin concentrations and oxygen saturation were measured in blood drawn from all vessels. Umbilical venous, portal venous, and hepatic blood flow were measured by injecting radionuclide-labeled microspheres into the umbilical vein while obtaining a reference sample from the descending aorta. We found net hepatic uptake of lactate (5.0 +/- 4.4 mg/min per 100 g liver). A large quantity of lactate was delivered to the liver (94.2 +/- 78.1 mg/min per 100 g), so that the hepatic extraction of lactate was only 7.7 +/- 6.5%. Hepatic oxygen consumption was 3.18 +/- 3.3 ml/min per 100 g, and the hepatic lactate/oxygen quotient was 2.07 +/- 1.54. There was no significant correlation between hepatic lactate uptake and hepatic lactate or glucose delivery, hepatic oxygen consumption, hepatic blood flow, hepatic glucose flux, total body oxygen consumption, arterial pH, oxygen content, or oxygen saturation. There was, however, a significant correlation between hepatic lactate uptake and umbilical lactate uptake (r = 0.74, P less than 0.005) such that net hepatic lactate uptake was nearly equivalent to that produced across the umbilical-placental circulation.(ABSTRACT TRUNCATED AT 250 WORDS)     

Nontrophoblastic placental tumors

The aim of the study was to investigate potential influence of placental tumors on fetal outcome. The study comprised 10 cases of placental tumors. The analysis included the sonographic assessment of the tumor, signs of fetal anemia, as well as signs of hemodynamic disturbances or heart failure, and intrauterine treatment. The fetal hemodynamic was examined on the basis of Doppler blood flow in the umbilical artery and vein, middle cerebral artery, and ductus venous. The evaluation of fetal heart included the measurement of heart size, blood flow through cardiac valves and the assessment of fetal heart function based on cardiovascular score. The fetal outcome was also assessed according to birthweight, gestational age at delivery, pH, Ap score at 5th minute, abnormal neurological development and the need of intrauterine therapy. Ten cases of placental tumors were prenatally detected from 1999 to 2011. Among them 7 cases of hypoechogenic, non-vascularized cysts were identified and these neither effected the hemodynamics nor complicated fetal outcome. The vascularized tumors (chorioangioma) were the cause of severe anemia and hemodynamic disturbances and these led to fetal cardiac heart failure. In all cases of vascularized tumors from 2-3 intrauterine transfusion were performed. Rich vascularized tumors (chorioangioma) may cause hemodynamic disturbances and fetal heart failure. This may require intrauterine treatment and may result in abnormal fetal outcome and neurological development.     

Immunoreactive endothelin concentrations in maternal and fetal blood

Immunoreactive-endothelin (ir-ET) concentrations were determined in peripheral maternal blood and in umbilical cord blood just after delivery. The concentrations in both the umbilical artery (2.83 +/- 1.36 pmol/l plasma, Mean +/- SD) and vein (3.37 +/- 1.53 pmol/l) were significantly higher than those found in maternal venous blood (1.43 +/- 1.02 pmol/l). On the other hand, ir-ET levels in maternal blood were not significantly different when compared with those found in non-pregnant women (1.50 +/- 0.83 pmol/l). No significant difference of ir-ET levels between the umbilical artery and vein was observed. A highly significant correlation (r = 0.60, p less than 0.01) of ir-ET levels between the umbilical artery and vein was observed. Also, a significant correlation (r = 0.48, p less than 0.01) between umbilical vein and maternal vein ir-ET levels with a weaker correlation (r = 0.36, p less than 0.05) between umbilical artery and maternal vein ir-ET levels was demonstrated. The present study indicates that ir-ET may be actively secreted in fetal circulation and the plasma levels in maternal and fetal circulation may have a possible relation.