Abnormal arterial flows by a distributed model of the fetal circulation

Recasting Current Knowledge of Human Fetal Circulation: The Importance of Computational Models

Computational hemodynamic simulations are becoming increasingly important for cardiovascular research and clinical practice, yet incorporating numerical simulations of human fetal circulation is relatively underutilized and underdeveloped. The fetus possesses unique vascular shunts to appropriately distribute oxygen and nutrients acquired from the placenta, adding complexity and adaptability to blood flow patterns within the fetal vascular network. Perturbations to fetal circulation compromise fetal growth and trigger the abnormal cardiovascular remodeling that underlies congenital heart defects. Computational modeling can be used to elucidate complex blood flow patterns in the fetal circulatory system for normal versus abnormal development. We present an overview of fetal cardiovascular physiology and its evolution from being investigated with invasive experiments and primitive imaging techniques to advanced imaging (4D MRI and ultrasound) and computational modeling. We introduce the theoretical backgrounds of both lumped-parameter networks and three-dimensional computational fluid dynamic simulations of the cardiovascular system. We subsequently summarize existing modeling studies of human fetal circulation along with their limitations and challenges. Finally, we highlight opportunities for improved fetal circulation models.

A review study of fetal circulatory models to develop a digital twin of a fetus in a perinatal life support system

BACKGROUND

Preterm birth is the main cause of neonatal deaths with increasing mortality and morbidity rates with decreasing GA at time of birth. Currently, premature infants are treated in neonatal intensive care units to support further development. However, the organs of, especially, extremely premature infants (born before 28 weeks of GA) are not mature enough to function optimally outside the womb. This is seen as the main cause of the high morbidity and mortality rates in this group. A liquid-filled incubator, a so-called PLS system, could potentially improve these numbers for extremely premature infants, since this system is designed to mimic the environment of the natural womb. To support the development and implementation of such a complex system and to interpret vital signals of the fetus during a PLS system operation, a digital twin is proposed. This mathematical model is connected with a manikin representing the digital and physical twin of the real-life PLS system. Before developing a digital twin of a fetus in a PLS system, its functional and technical requirements are defined and existing mathematical models are evaluated.

METHOD AND RESULTS

This review summarizes existing 0D and 1D fetal circulatory models that potentially could be (partly) adopted for integration in a digital twin of a fetus in a PLS system based on predefined requirements. The 0D models typically describe hemodynamics and/or oxygen transport during specific events, such as the transition from fetus to neonate. Furthermore, these models can be used to find hemodynamic differences between healthy and pathological physiological states. Rather than giving a global description of an entire cardiovascular system, some studies focus on specific organs or vessels. In order to analyze pressure and flow wave profiles in the cardiovascular system, transmission line or 1D models are used. As for now, these models do not include oxygen transport.

CONCLUSION

This study shows that none of the models identified in literature meet all the requirements relevant for a digital twin of a fetus in a PLS system. Nevertheless, it does show the potential to develop this digital twin by integrating (parts) of models into a single model.

Hypothesized pathogenesis of acardius acephalus, acormus, amorphus, anceps, acardiac edema, single umbilical artery, and pump twin risk prediction

Background

Acardiac twinning complicates monochorionic twin pregnancies in ≈2.6%, in which arterioarterial (AA) and venovenous placental anastomoses cause a reverse circulation between prepump and preacardiac embryos and cessation of cardiac function in the preacardiac. Literature suggested four acardiac body morphologies in which select (groups of) organs fail to develop, deteriorate, or become abnormal: acephalus (≈64%, [almost] no head, part of body, legs), amorphus (≈22%, amorphous tissue lump), anceps (≈10%, cranial bones, well‐developed), and acormus (≈4%, head only). We sought to develop hypotheses that could explain acardiac pathogenesis, its progression, and develop methods for clinical testing.

Methods

We used qualitatively described pathophysiology during development, including twin‐specific AA and Hyrtl's anastomoses, the short umbilical cord syndrome, high capillary permeability, properties of spontaneous aborted embryos, and Pump/Acardiac umbilical venous diameter (UVD) ratios.

Results

We propose that each body morphology has a specific pathophysiologic pathway. An acephalus acardius may be larger than an anceps, verifiable from UVD ratio measurements. A single umbilical artery develops when one artery, unconnected to the AA, vanishes due to flow reduction by Hyrtl's anastomotic resistance. Acardiac edema may result from acardiac body hypoxemia combined with physiological high fetal capillary permeability, high interstitial compliance and low albumin synthesis. Morphological changes may occur after acardiac onset. Pump twin risk follows from UVD ratios.

Conclusion

Our suggested outcomes agree reasonably well with reported onset, incidence, and progression of acardiac morphologies. Guidance for clinical prediction and testing requires ultrasound anatomy/circulation study, from the first trimester onward.

Impact of ductus arteriosus constriction and restrictive foramen ovale on global hemodynamics for term fetuses with d-TGA

The ductus arteriosus (DA) constriction and restrictive foramen ovale (FO) are known as the leading cause of compromise and death of fetuses with dextro-transposition of the great arteries (d-TGA). Although the d-TGA fetal hemodynamics is of great importance in making diagnosis and management of the congenital heart defect, it remains poorly understood, particularly in terms of abnormal DA and FO. In this study, we developed a closed-loop 0-1D multiscale model of the fetal cardiovascular system (CVS) specified for the d-TGA circulation and conducted a systematic study of the impact of the DA constriction and restrictive FO on fetal hemodynamics. We found that the DA constriction led to a pronounced increase in the pulmonary artery pressure, pulmonary and mitral valve (PV and MV) regurgitation as well as left heart volume; the restrictive FO was responsible for reducing MV E/A ratio, ie, the ratio of peak early filling and late diastolic filling velocities, and PV peak systolic flow (PSV) but could increase both aortic valve (AV) PSV and aortic isthmus systolic index (ISI). Moreover, the amount of blood flowing through the DA was observed equivalent to that through the FO; the influence of DA constriction on the cerebral and placental perfusions are larger than that of the FO. Our results demonstrate that the proposed fetal cardiovascular model may be a useful tool for studying the underlying mechanisms associated with d-TGA fetal circulation and providing insights into its complex physiology and pathology.

A Review of Biomechanics Analysis of the Umbilical-Placenta System With Regards to Diseases

Placenta is an important organ that is crucial for both fetal and maternal health. Abnormalities of the placenta, such as during intrauterine growth restriction (IUGR) and pre-eclampsia (PE) are common, and an improved understanding of these diseases is needed to improve medical care. Biomechanics analysis of the placenta is an under-explored area of investigation, which has demonstrated usefulness in contributing to our understanding of the placenta physiology. In this review, we introduce fundamental biomechanics concepts and discuss the findings of biomechanical analysis of the placenta and umbilical cord, including both tissue biomechanics and biofluid mechanics. The biomechanics of placenta ultrasound elastography and its potential in improving clinical detection of placenta diseases are also discussed. Finally, potential future work is listed.

Multiscale and multimodal imaging of utero-placental anatomy and function in pregnancy

Placental structures at the nano-, micro-, and macro scale each play important roles in contributing to its function. As such, quantifying the dynamic way in which placental structure evolves during pregnancy is critical to both clinical diagnosis of pregnancy disorders, and mechanistic understanding of their pathophysiology. Imaging the placenta, both exvivo and invivo, can provide a wealth of structural and/or functional information. This review outlines how imaging across modalities and spatial scales can ultimately come together to improve our understanding of normal and pathological pregnancies. We discuss how imaging technologies are evolving to provide new insights into placental physiology across disciplines, and how advanced computational algorithms can be used alongside state-of-the-art imaging to obtain a holistic view of placental structure and its associated functions to improve our understanding of placental function in health and disease.

Mending a broken heart: In vitro, in vivo and in silico models of congenital heart disease

Birth defects contribute to ∼0.3% of global infant mortality in the first month of life, and congenital heart disease (CHD) is the most common birth defect among newborns worldwide. Despite the significant impact on human health, most treatments available for this heterogenous group of disorders are palliative at best. For this reason, the complex process of cardiogenesis, governed by multiple interlinked and dose-dependent pathways, is well investigated. Tissue, animal and, more recently, computerized models of the developing heart have facilitated important discoveries that are helping us to understand the genetic, epigenetic and mechanobiological contributors to CHD aetiology. In this Review, we discuss the strengths and limitations of different models of normal and abnormal cardiogenesis, ranging from single-cell systems and 3D cardiac organoids, to small and large animals and organ-level computational models. These investigative tools have revealed a diversity of pathogenic mechanisms that contribute to CHD, including genetic pathways, epigenetic regulators and shear wall stresses, paving the way for new strategies for screening and non-surgical treatment of CHD. As we discuss in this Review, one of the most-valuable advances in recent years has been the creation of highly personalized platforms with which to study individual diseases in clinically relevant settings.

Pressure and Flow Relations in the Systemic Arterial Tree Throughout Development From Newborn to Adult

Objective: Distributed models of the arterial tree allow studying the effect of physiological and pathophysiological changes in the vasculature on hemodynamics. For the adult, several models exist; however, a model encompassing the full age range from newborn to adult was until now lacking. Our goal is to describe a complete distributed hemodynamic model for normal development from newborn to adult. Methods: The arterial system was modeled by 121 segments characterized by length, radius, wall thickness, wall stiffness, and wall viscosity. The final segments ended in three-element Windkessels. All parameters were adapted based on body height and weight as a function of age as described in the literature. Results: Pressures and flows are calculated as a function of age at sites along the arterial tree. Central to peripheral transfer functions are given. Our results indicate that peripheral pressure in younger children resembles central pressure. Furthermore, total arterial compliance, inertance and impedance are calculated. Findings indicate that the arterial tree can be simulated by using a three-element Windkessel system. Pulse wave velocity in the aorta was found to increase during development. Conclusions: The arterial system, modeled from newborn to adult bears clinical significance, both for the interpretation of peripheral measured pressure in younger and older children, and for using a Windkessel model to determine flow from pressure measurements.

The biomechanics of the umbilical cord Wharton Jelly: Roles in hemodynamic proficiency and resistance to compression

The umbilical cord is a complex structure containing three vessels, one straight vein and two coiled arteries, encased by the Wharton Jelly (WJ) a spongy structure made of collagen and hydrated macromolecules. Fetal blood reaches the placenta through the arteries and flows back to the fetus through the vein. The role of the WJ in maintaining cord circulation proficiency and the ultimate reason for arterial coiling still lack of reasonable mechanistic interpretations. We performed biaxial tension tests and evidenced significant differences in the mechanical properties of the core and peripheral WJ. The core region, located between the arteries and the vein, resulted rather stiffer close to the fetus. Finite element modelling and optimization based inverse method were used to create 2D and 3D models of the cord and to simulate stress distribution in different hemodynamic conditions, compressive loads and arterial coiling. We recorded a facilitated stress transmission from the arteries to the vein through the soft core of periplacental WJ. This condition generates a pressure gradient that boosts the venous backflow circulation towards the fetus. Peripheral WJ allows arteries to act as pressure buffering chambers during the cardiac diastole and helps to dissipate compressive forces away from vessels. Altered WJ biomechanics may represent the structural basis of cord vulnerability in many high-risk clinical conditions.

Mathematical modelling of the maternal cardiovascular system in the three stages of pregnancy

In this study, a mathematical model of the female circulation during pregnancy is presented in order to investigate the hemodynamic response to the cardiovascular changes associated with each trimester of pregnancy. First, a preliminary lumped parameter model of the circulation of a non-pregnant female was developed, including the heart, the systemic circulation with a specific block for the uterine district and the pulmonary circulation. The model was first tested at rest; then heart rate and vascular resistances were individually varied to verify the correct response to parameter alterations characterising pregnancy. In order to simulate hemodynamics during pregnancy at each trimester, the main changes applied to the model consisted in reducing vascular resistances, and simultaneously increasing heart rate and ventricular wall volumes. Overall, reasonable agreement was found between model outputs and in vivo data, with the trends of the cardiac hemodynamic quantities suggesting correct response of the heart model throughout pregnancy. Results were reported for uterine hemodynamics, with flow tracings resembling typical Doppler velocity waveforms at each stage, including pulsatility indexes. Such a model may be used to explore the changes that happen during pregnancy in female with cardiovascular diseases.

Normal Pregnancy Is Associated with Changes in Central Hemodynamics and Enhanced Recruitable, but Not Resting, Endothelial Function

Introduction. Flow-mediated dilation (FMD), low flow-mediated constriction (L-FMC), and reactive hyperemia-related changes in carotid-to-radial pulse wave velocity (ΔPWVcr%) could offer complementary information about both “recruitability” and “resting” endothelial function (EF). Carotid-to-femoral pulse wave velocity (PWVcf) and pulse wave analysis-derived parameters (i.e., AIx@75) are the gold standard methods for noninvasive evaluation of aortic stiffness and central hemodynamics. If healthy pregnancy is associated with both changes in resting and recruitable EF, as well as in several arterial parameters, it remains unknown and/or controversial. Objectives. To simultaneously and noninvasively assess in healthy pregnant (HP) and nonpregnant (NP) women central parameters in conjunction with “basal and recruitable” EF, employing new complementary approaches. Methods. HP (n = 11, 34.2 ± 3.3 weeks of gestation) and age- and cardiovascular risk factors-matched NP (n = 22) were included. Aortic blood pressure (BP), AIx@75, PWVcf, common carotid stiffness, and intima-media thickness, as well as FMD, L-FMC, and ΔPWVcr %, were measured. Results. Aortic BP, stiffness, and AIx@75 were reduced in HP. ΔPWVcr% and FMD were enhanced in HP in comparison to NP. No differences were found in L-FMC between groups. Conclusion. HP is associated with reduced aortic stiffness, central BP, wave reflections, and enhanced recruitable, but not resting, EF.

Preeclampsia Is Associated with Increased Central Aortic Pressure, Elastic Arteries Stiffness and Wave Reflections, and Resting and Recruitable Endothelial Dysfunction

Introduction. An altered endothelial function (EF) could be associated with preeclampsia (PE). However, more specific and complementary analyses are required to confirm this topic. Flow-mediated dilation (FMD), low-flow-mediated constriction (L-FMC), and hyperemic-related changes in carotid-radial pulse wave velocity (PWVcr) offer complementary information about “recruitability” of EF. Objectives. To evaluate, in healthy and hypertensive pregnant women (with and without PE), central arterial parameters in conjunction with “basal and recruitable” EF. Methods. Nonhypertensive (HP) and hypertensive pregnant women (gestational hypertension, GH; preeclampsia, PE) were included. Aortic blood pressure (BP), wave reflection parameters (AIx@75), aortic pulse wave velocity (PWVcf) and PWVcr, and brachial and common carotid stiffness and intima-media thickness were measured. Brachial FMD and L-FMC and hyperemic-related change in PWVcr were measured. Results. Aortic BP and AIx@75 were elevated in PE. PE showed stiffer elastic but not muscular arteries. After cuff deflation, PWVcr decreased in HP, while GH showed a blunted PWVcr response and PE showed a tendency to increase. Maximal FMD and L-FMC were observed in HP followed by GH; PE did not reach significant arterial constriction. Conclusion. Aortic BP and wave reflections as well as elastic arteries stiffness are increased in PE. PE showed both “resting and recruitable” endothelial dysfunctions.

Impact of increased hematocrit on right ventricular afterload in response to chronic hypoxia

Chronic hypoxia causes chronic mountain sickness through hypoxia-induced pulmonary hypertension (HPH) and increased hematocrit. Here, we investigated the impact of increased hematocrit and HPH on right ventricular (RV) afterload via pulmonary vascular impedance. Mice were exposed to chronic normobaric hypoxia (10% oxygen) for 10 (10H) or 21 days (21H). After baseline hemodynamic measurements, ∼500 μl of blood were extracted and replaced with an equal volume of hydroxyethylstarch to normalize hematocrit and all hemodynamic measurements were repeated. In addition, ∼500 μl of blood were extracted and replaced in control mice with an equal volume of 90% hematocrit blood. Chronic hypoxia increased input resistance (Z0 increased 82% in 10H and 138% in 21H vs. CTL; P < 0.05) and characteristic impedance (ZC increased 76% in 10H and 109% in 21H vs. CTL; P < 0.05). Hematocrit normalization did not decrease mean pulmonary artery pressure but did increase cardiac output such that both Z0 and ZC decreased toward control levels. Increased hematocrit in control mice did not increase pressure but did decrease cardiac output such that Z0 increased. The paradoxical decrease in ZC with an acute drop in hematocrit and no change in pressure are likely due to inertial effects secondary to the increase in cardiac output. A novel finding of this study is that an increase in hematocrit affects the pulsatile RV afterload in addition to the steady RV afterload (Z0). Furthermore, our results highlight that the conventional interpretation of ZC as a measure of proximal artery stiffness is not valid in all physiological and pathological states.

A computational model of the fetal circulation to quantify blood redistribution in intrauterine growth restriction

Intrauterine growth restriction (IUGR) due to placental insufficiency is associated with blood flow redistribution in order to maintain delivery of oxygenated blood to the brain. Given that, in the fetus the aortic isthmus (AoI) is a key arterial connection between the cerebral and placental circulations, quantifying AoI blood flow has been proposed to assess this brain sparing effect in clinical practice. While numerous clinical studies have studied this parameter, fundamental understanding of its determinant factors and its quantitative relation with other aspects of haemodynamic remodeling has been limited. Computational models of the cardiovascular circulation have been proposed for exactly this purpose since they allow both for studying the contributions from isolated parameters as well as estimating properties that cannot be directly assessed from clinical measurements. Therefore, a computational model of the fetal circulation was developed, including the key elements related to fetal blood redistribution and using measured cardiac outflow profiles to allow personalization. The model was first calibrated using patient-specific Doppler data from a healthy fetus. Next, in order to understand the contributions of the main parameters determining blood redistribution, AoI and middle cerebral artery (MCA) flow changes were studied by variation of cerebral and peripheral-placental resistances. Finally, to study how this affects an individual fetus, the model was fitted to three IUGR cases with different degrees of severity. In conclusion, the proposed computational model provides a good approximation to assess blood flow changes in the fetal circulation. The results support that while MCA flow is mainly determined by a fall in brain resistance, the AoI is influenced by a balance between increased peripheral-placental and decreased cerebral resistances. Personalizing the model allows for quantifying the balance between cerebral and peripheral-placental remodeling, thus providing potentially novel information to aid clinical follow up.

Intrauterine growth restriction (IUGR) is one of the leading causes of perinatal mortality and can be defined as a low birth weight together with signs of chronic hypoxia or malnutrition. It is mostly due to placental insufficiency resulting in a chronic restriction of oxygen and nutrients to the fetus. IUGR leads to cardiac dysfunction in utero which can persist postnatally. Under these altered conditions, IUGR fetuses redistribute their blood in order to maintain delivery of oxygenated blood to the brain, known as brain sparing. Given that, in the fetus the aortic isthmus (AoI) is a key arterial connection between the cerebral and placental circulations, quantifying AoI blood flow has been proposed to assess this brain sparing effect in clinical practice. However, which remodeling or redistribution processes in the cardiovascular systems induce the observed changes in AoI flow in IUGR fetuses is not fully understood. We developed a computational model of the fetal circulation, including the key elements related to fetal blood redistribution. Using measured cardiac outflow profiles to allow personalization, we can recreate and better understand the blood flow changes in individual IUGR fetuses.

Mathematical model of flow through the patent ductus arteriosus

The ductus arteriosus is one of several shunts in the cardiovascular system. It is a small vessel connecting the aortic arch and pulmonary artery that allows blood to bypass the pulmonary circulation. It is open during foetal development because the foetal lungs cannot function and oxygenation of the blood occurs by exchange with the maternal blood in the placenta. Normally it closes a few days after birth; however, in a small number of people closure does not occur, leading to a condition known as patent ductus arteriosus. In this paper our aim is to investigate the resulting cardiovascular effects. We develop a mathematical model of the haemodynamics in three different idealised geometries by assuming that the entry flow is irrotational and remains so in the core until at least the shunt position. We argue that separation or diffusion of vorticity into the core flow is delayed due to the high frequency associated with the pulsatile component of the flow profile. The analysis uses complex potential theory, Schwarz-Christoffel transformations, conformal mappings and Fourier series. The main results are based on the assumption that the flow in patients with patent ductus arteriosus is similar to the flow in healthy adults, and we apply this assumption using boundary conditions that are representative of physiological values in healthy adults. The model suggests that the pressures in the aorta and pulmonary artery are likely to equalise, that the shear stress increases near the edges of the shunt and that backflow of large volumes may occur from the pulmonary artery into the aorta or towards the ventricles due to the presence of the patent shunt. Our results strongly suggest that an abnormal compensatory physiology develops in patients with patent ductus arteriosus.

Review: Feto-placental vascularization: a multifaceted approach

Doppler Ultrasound allows the in vivo study of feto-placental hemodynamics. Doppler flow velocity waveforms (FVW's) obtained from the umbilical arteries reflect downstream blood flow impedance, thus giving indirect evidence of vascular villous tree characteristics. Pulsatility Index, which quantifies FVW's, decreases throughout normal pregnancy, indicating decreasing impedance and is often higher in cases of fetal growth restriction (FGR). Different approaches (morphometrical, morphological, mathematical, immunohistochemical and molecular) have contributed to elucidation of which anomalies of the vascular villous tree underlie Doppler findings. 3D ultrasound may be useful in the study of feto-placental perfusion. However, the unsolved question is why developmental villous tree anomalies occur. Crucial to the success of future research is definition of the population studied based on the uniform and correct definition of FGR.

Computational fluid dynamic analysis of flow velocity waveform notching in umbilical arteries

Umbilical artery Doppler velocimetry waveform notching has long been associated with umbilical cord abnormalities, such as distortion, torsion, and/or compression (i.e., constriction). The physical mechanism by which the notching occurs has not been elucidated. Flow velocity waveforms (FVWs) from two-dimensional pulsatile flows in a constricted channel approximating a compressed umbilical cord are analyzed, leading to a clear relationship between the notching and the constriction. Two flows with an asymmetric, semi-elliptical constriction are computed using a stabilized finite-element method. In one case, the constriction blocks 75% of the flow passage, and in the other the constriction blocks 85%. Channel width and prescribed flow rates at the channel inflow are consistent with typical cord diameters and flow rates reported in the literature. Computational results indicate that waveform notching is caused by flow separation induced by the constriction, giving rise to a vortex (core) wave and associated eddies. Notching in FVWs based on centerline velocity (centerline FVW) is directly related to the passage of an eddy over the point of measurement on the centerline. Notching in FVWs based on maximum cross-sectional velocity (envelope FVW) is directly related to acceleration and deceleration of the fluid along the vortex wave. Results show that notching in envelope FVW is not present in flows with less than a 75% constriction. Furthermore, notching disappears as the vortex wave is attenuated at distances downstream of the constriction. In the flows with 75 and 85% constriction, notching of the envelope FVW disappears at ∼3.8 and ∼4.3 cm (respectively) downstream of the constriction. These results are of significant medical importance, given that envelope FVW is typically measured by commercial Doppler systems.

Comparative proteomic analysis of malformed umbilical cords from somatic cell nuclear transfer-derived piglets: implications for early postnatal death

Background

Somatic cell nuclear transfer (scNT)-derived piglets have high rates of mortality, including stillbirth and postnatal death. Here, we examined severe malformed umbilical cords (MUC), as well as other organs, from nine scNT-derived term piglets.

Results

Microscopic analysis revealed complete occlusive thrombi and the absence of columnar epithelial layers in MUC (scNT-MUC) derived from scNT piglets. scNT-MUC had significantly lower expression levels of platelet endothelial cell adhesion molecule-1 (PECAM-1) and angiogenesis-related genes than umbilical cords of normal scNT piglets (scNT-N) that survived into adulthood. Endothelial cells derived from scNT-MUC migrated and formed tubules more slowly than endothelial cells from control umbilical cords or scNT-N. Proteomic analysis of scNT-MUC revealed significant down-regulation of proteins involved in the prevention of oxidative stress and the regulation of glycolysis and cell motility, while molecules involved in apoptosis were significantly up-regulated. Histomorphometric analysis revealed severe calcification in the kidneys and placenta, peliosis in the liver sinusoidal space, abnormal stromal cell proliferation in the lungs, and tubular degeneration in the kidneys in scNT piglets with MUC. Increased levels of apoptosis were also detected in organs derived from all scNT piglets with MUC.

Conclusion

These results suggest that MUC contribute to fetal malformations, preterm birth and low birth weight due to underlying molecular defects that result in hypoplastic umbilical arteries and/or placental insufficiency. The results of the current study demonstrate the effects of MUC on fetal growth and organ development in scNT-derived pigs, and provide important insight into the molecular mechanisms underlying angiogenesis during umbilical cord development.

Transmission line models to simulate the impedance of the uterine vasculature during the ovarian cycle and pregnancy

OBJECTIVES

Changes in uterine vascular impedance may yield diagnostic insight into physiological and pathological changes in uterine vascular resistance and compliance during the ovarian cycle and pregnancy. Herein, our objectives were to develop models to simulate uterine vascular impedance in order to gain insight into the vascular size and stiffness changes that occur during ovarian cycling and pregnancy.

STUDY DESIGN

Two electrical analogue transmission line models were developed and evaluated based on goodness-of-fit to experimental impedance measurements, which were obtained in nonpregnant luteal and follicular phase (NP-L and NP-F) and pregnant (P) ewes (n=4-8 per group). First, an anatomically based, multi-segment, symmetric, branching transmission line model was developed. Parameter values were calculated based on experimental measurements of size and stiffness in the first three generations of the uterine arterial tree for NP-L, NP-F and P ewes. Then, a single segment transmission line model was developed and effective parameter values were optimized to best-fit the measured impedances.

RESULTS

The anatomically based multi-segment model did not yield the expected good agreement with the experimental data (R(2)<0.5 for all groups). In contrast, the impedance spectra predicted by the single segment model agreed very well with experimental data (R(2)=0.93, 0.82, and 0.84 for NP-L, NP-F and P, respectively; p<0.0001, all groups). Furthermore, the changes in the best-fit model parameters for NP-F and P compared to the NP-L were consistent with the prior literature on the effects of the ovarian cycle and pregnancy on vascular resistance and compliance. In particular, compared to NP-L, NP-F had decreased longitudinal and terminal resistance with a modest increase in compliance whereas pregnancy caused more dramatic drops in longitudinal and terminal resistance and a significant increase in compliance.

CONCLUSIONS

The single segment transmission line model is a useful tool to examine changes in vascular structure and function that occur during the ovarian cycle and pregnancy.

Bioengineering aspects of the umbilical cord

The umbilical cord and its constituent tissues: an outer layer of amnion, porous Wharton's jelly, two umbilical arteries, and one umbilical vein, are designed to protect blood flow to the fetus during a term pregnancy. The outer amnion layer may regulate fluid pressure within the umbilical cord. The porous, fluid filled Wharton's jelly likely acts to prevent compression of the vessels. Blood flow is regulated by smooth muscle surrounding the arteries that is intermingled with a collagen based extracellular matrix (ECM). Doppler ultrasound measurements of blood flow within the umbilical cord, and at specific sites within the developing fetus, provide evidence of impaired blood flow in conditions such as preeclampsia. Mechanosensory communication between cells and the extracellular matrix (ECM) may likely result in cords possessing abnormal physical dimensions, impaired hemodynamics, and altered composition within the umbilical cord tissues. Few studies have explored the biomechanics of the intact umbilical cord, with its constituent tissues, from normal pregnancies or abnormal pregnancies, maternal or fetal complications. Here, alterations in the umbilical cord are reviewed concerning anatomical abnormalities, disease, or chromosomal alterations using sonography, Doppler ultrasound, histology, and biomolecular and biochemical analyses. This paper considers how current knowledge of the umbilical cord and its constituent tissues can be used to infer biomechanical function. In addition, the mechanical consequences of structural abnormalities and altered tissue structure or composition are discussed with a specific focus on preeclampsia.

CURRENT ASPECTS OF FETAL CARDIOVASCULAR FUNCTION

Investigation of fetal cardiac function remains a challenging task. Although the response of the heart to changes in load is well-known in animal models and the adult human, the developmental changes in fetal cardiac response remain poorly characterised. However, quantitative evaluation of cardiovascular function is important to predict the clinical course and to manage the fetus optimally. To date, the routine evaluation of fetal cardio vascular function has relied largely on Doppler echocardiography which enables an estimate of haemodynamics; newer modalities such as measurement of myocardial velocities are employed less routinely. Fetal magnetic resonance imaging still lacks the resolution necessary to contribute significantly to morphological or functional assessment of the fetal cardiovascular system.

A mathematical model of twin-twin transfusion syndrome with pulsatile arterial circulations

The twin-twin transfusion syndrome (TTTS) is a severe complication of monochorionic twin pregnancies caused by a net transfusion of blood from one twin (the donor) to the other (the recipient) through placental anastomoses. To examine the pathophysiology of TTTS evolving through clinical stages I to IV, we extended our mathematical model to include pulsating circulations propagating along the arterial tree as well as placental and cerebral vascular resistances, and arterial wall thickness and stiffness. The model demonstrates that abnormal umbilical arterial flow (TTTS stage III) in the donor twin results from increased placental resistance as well as reduced resistance in the cerebral arteries. In contrast, recipient twin abnormal umbilical arterial flow requires a significantly greater increase in placental resistance, resulting from the compressive effects of high amniotic fluid pressure. Thus simulated abnormalities of donor umbilical arterial pulsations occur in the donor more commonly and earlier than in the recipient. The “normal” staging sequence (I, II, III, IV) correlates with the presence of compensating placental anastomoses, constituting the majority of monochorionic twin placentas. However, TTTS stage III may occur before manifestations of stage II (lack of donor bladder filling), in our model correlating with severe TTTS from a single arteriovenous anastomosis, an infrequent occurring placental angioarchitecture. In conclusion, this mathematical model describes the onset and development of the four stages of TTTS, reproduces a variety of clinical manifestations, and may contribute to identifying the underlying pathophysiology of the staging sequence in TTTS.