A stochastic model for early placental development

Maternal affective symptoms and sleep quality have sex-specific associations with placental topography

BACKGROUND

The impacts of prenatal maternal affective symptoms on the placental structure are not well-established. Employing Geographic Information System (GIS) spatial autocorrelation, Moran's I, can help characterize placental thickness uniformity/variability and evaluate the impacts of maternal distress on placental topography.

METHODS

This study (N = 126) utilized cohort data on prenatal maternal affective symptoms and placental 2D and 3D morphology. Prenatal maternal depression, stress, anxiety and sleep quality were scored for each trimester using the Edinburgh Postnatal Depression Scale (EPDS), Stressful Life Event Scale (SLE), Penn State Worry Questionnaire (PSWQ), and Pittsburgh Sleep Quality Index (PSQI), respectively. Placental shape was divided into Voronoi cells and thickness variability among these cells was computed using Moran's I for 4-nearest neighbors and neighbors within a 10 cm radius. Sex-stratified Spearman correlations and linear regression were used to study associations between mean placental thickness, placental GIS variables, placental weight and the average score of each maternal variable.

RESULTS

For mothers carrying boys, poor sleep was associated with higher mean thickness (r = 0.308,p = 0.035) and lower placental thickness uniformity (r = -0.36,p = 0.012). Lower placental weight (r = 0.395,p = 0.003), higher maternal depression (r = -0.318,p = 0.019) and worry/anxiety (r = -0.362,p = 0.007) were associated with lower placental thickness uniformity for mothers carrying girls.

LIMITATIONS

The study is exploratory and not all GIS models were developed. Excluding high-risk pregnancies prevented investigating pregnancy complications related hypotheses. A larger sample size is needed for greater confidence for clinical application.

CONCLUSIONS

Placental topography can be studied using GIS theory and has shown that prenatal maternal affective symptoms and sleep have sex-specific associations with placental thickness.

Determinants of low birth weight among newborns delivered in China: a prospective nested case-control study in a mother and infant cohort

This nested case-control study aimed to investigate the determinants of low birth weight among newborn babies delivered in Shenzhen, Guangdong, China. We recorded socio-demographic data, health status before pregnancy, pregnancy outcomes and complications in a Shenzhen mother and infant cohort. Among 8951 cases, 401 (4.48%) had low birth weight and 1.65% were full-term with LBW. Maternal body mass index, family income, history of pregnancy, hypertension before pregnancy, vaginal bleeding in 1^st trimester, pregnancy-related diabetes, hypertension, placenta previa, placental abruption, premature rupture of membrane, oligohydramnios, and placental types were significantly associated with low birth weight (P < 0.05). In this study, high-risk and mainly preventable factors were linked to low birth weight. Adequate antenatal care, proper maternal nutrition and implementation of proven strategies to prevent high-risk factors may be effective ways to reduce the incidence of low birth weight.

The Role of the 3Rs for Understanding and Modeling the Human Placenta

Modeling the physiology of the human placenta is still a challenge, despite the great number of scientific advancements made in the field. Animal models cannot fully replicate the structure and function of the human placenta and pose ethical and financial hurdles. In addition, increasingly stricter animal welfare legislation worldwide is incentivizing the use of 3R (reduction, refinement, replacement) practices. What efforts have been made to develop alternative models for the placenta so far? How effective are they? How can we improve them to make them more predictive of human pathophysiology? To address these questions, this review aims at presenting and discussing the current models used to study phenomena at the placenta level: in vivo, ex vivo, in vitro and in silico. We describe the main achievements and opportunities for improvement of each type of model and critically assess their individual and collective impact on the pursuit of predictive studies of the placenta in line with the 3Rs and European legislation.

Computational modeling of the interactions between the maternal and fetal circulations in human pregnancy

In pregnancy, fetal growth is supported by its placenta. In turn, the placenta is nourished by maternal blood, delivered from the uterus, in which the vasculature is dramatically transformed to deliver this blood an ever increasing volume throughout gestation. A healthy pregnancy is thus dependent on the development of both the placental and maternal circulations, but also the interface where these physically separate circulations come in close proximity to exchange gases and nutrients between mum and baby. As the system continually evolves during pregnancy, our understanding of normal vascular anatomy, and how this impacts placental exchange function is limited. Understanding this is key to improve our ability to understand, predict, and detect pregnancy pathologies, but presents a number of challenges, due to the inaccessibility of the pregnant uterus to invasive measurements, and limitations in the resolution of imaging modalities safe for use in pregnancy. Computational approaches provide an opportunity to gain new insights into normal and abnormal pregnancy, by connecting observed anatomical changes from high-resolution imaging to function, and providing metrics that can be observed by routine clinical ultrasound. Such advanced modeling brings with it challenges to scale detailed anatomical models to reflect organ level function. This suggests pathways for future research to provide models that provide both physiological insights into pregnancy health, but also are simple enough to guide clinical focus. We the review evolution of computational approaches to understanding the physiology and pathophysiology of pregnancy in the uterus, placenta, and beyond focusing on both opportunities and challenges. This article is categorized under: Reproductive System Diseases >Computational Models.

A panel of criteria for comprehensive assessment of severity of ultraviolet B radiation-induced non-melanoma skin cancers in SKH-1 mice

The study of causes and cures for ultraviolet B radiation (UVB)-induced non-melanoma skin cancers (NMSC) has been greatly facilitated by use of the albino SKH-1 hairless mice. These mice develop multiple tumors of different sizes and the severity of cancer is often measured by one or more of the four criteria, namely the prevalence, multiplicity, area and volume of tumors. However, there are inherent limitations of each criterion: the prevalence and number do not account for size differences among tumors, area measurement ignores the tumor height, and volume measurement overcompensates for the height at the cost of planar dimensions. Here, using our dataset from an ongoing NMSC study, we discuss the limitations of these four criteria, and suggest refinements in measuring prevalence. We recommend the use of three more criteria, namely the Knud Thomsen tridimensional surface that apportions optimal weightage to three tumor dimensions, weekly occurrence of new tumors and tumor growth-rate to reveal initiation and growth of tumors in early and late phase of NMSC development, respectively. Together, use of this comprehensive panel of seven criteria can provide an accurate assessment of severity of NMSC and lead to a testable hypothesis whether the experimental manipulation of mice has affected the early initiation or growth phase of NMSC tumors.

Associations Between the Features of Gross Placental Morphology and Birthweight

The placenta plays a critical role in regulating fetal growth. Recent studies suggest that there may be sex-specific differences in placental development. The purpose of our study was to evaluate the associations between birthweight and placental morphology in models adjusted for covariates and to assess sex-specific differences in these associations. We analyzed data from the Stillbirth Collaborative Research Network's population-based case-control study conducted between 2006 and 2008, which recruited cases of stillbirth and population-based controls in 5 states. Our analysis was restricted to singleton live births with a placental examination (n = 1229). Characteristics of placental morphology evaluated include thickness, surface area, difference in diameters, shape, and umbilical cord insertion site. We used linear regression to model birthweight as a function of placental morphology and covariates. Surface area had the greatest association with birthweight; a reduction in surface area of 83 cm2, which reflects the interquartile range, is associated with a 260.2-g reduction in birthweight (95% confidence interval, -299.9 to -220.6), after adjustment for other features of placental morphology and covariates. Reduced placental thickness was also associated with lower birthweight. These associations did not differ between males and females. Our results suggest that reduced placental thickness and surface area are independently associated with lower birthweight and that these relationships are not related to sex.

Associations Between Features of Placental Morphology and Birth Weight in Dichorionic Twins

Low birth weight is associated with perinatal and long-term morbidity and mortality, and may be a result of abnormal placental development and function. In studies of singletons, associations have been reported between features of placental morphology and birth weight. Evaluating similar associations within twin pairs offers a unique opportunity to control for key confounders shared within a twin pair, including gestational age, parental characteristics, and intrauterine environment. Data from 3 studies in the United States that were completed from 2012 to 2013, 2006 to 2008, and 1959 to 1966 were used in our analysis of 208 sets of dichorionic twins with unfused placentas. We used linear regression to model difference in birth weight within a twin pair as a function of differences in placental characteristics (i.e., thickness, 2-dimensional surface area, intraplacental difference in diameter). After controlling for sex discordance, a 75.3- cm2 difference in placental surface area, which reflects the interquartile range, was associated with a difference in birth weight of 142.1 g (95% confidence interval (CI): 62.9, 221.3). The magnitude of the association also may be larger for same-sex male pairs than same-sex female pairs (males: 265.8 g, 95% CI: 60.8, 470.8; females: 133.0 g, 95% CI: 15.7, 250.3). Strong associations between surface area and birth weight are consistent with reported results for singleton pregnancies.

Blood flow and transport in the human placenta

The placenta is a multi-functional organ that exchanges blood gases and nutrients between a mother and her developing fetus. In humans, fetal blood flows through intricate networks of vessels confined within villous trees, the branches of which are bathed in pools of maternal blood. Fluid mechanics and transport processes play a central role in understanding how these elaborate structures contribute to the function of the placenta, and how their disorganization may lead to disease. Recent advances in imaging and computation have spurred significant advances in simulations of fetal and maternal flows within the placenta, across a range of lengthscales. Models describe jets of maternal blood emerging from spiral arteries into a disordered and deformable porous medium, and solute uptake by fetal blood flowing through elaborate three-dimensional capillary networks. We survey recent developments and emerging challenges in modeling flow and transport in this complex organ.

Placental Dysfunction Underlies Increased Risk of Fetal Growth Restriction and Stillbirth in Advanced Maternal Age Women

Pregnancies in women of advanced maternal age (AMA) are susceptible to fetal growth restriction (FGR) and stillbirth. We hypothesised that maternal ageing is associated with utero-placental dysfunction, predisposing to adverse fetal outcomes. Women of AMA (≥35 years) and young controls (20-30 years) with uncomplicated pregnancies were studied. Placentas from AMA women exhibited increased syncytial nuclear aggregates and decreased proliferation, and had increased amino acid transporter activity. Chorionic plate and myometrial artery relaxation was increased compared to controls. AMA was associated with lower maternal serum PAPP-A and sFlt and a higher PlGF:sFlt ratio. AMA mice (38-41 weeks) at E17.5 had fewer pups, more late fetal deaths, reduced fetal weight, increased placental weight and reduced fetal:placental weight ratio compared to 8-12 week controls. Maternofetal clearance of 14C-MeAIB and 3H-taurine was reduced and uterine arteries showed increased relaxation. These studies identify reduced placental efficiency and altered placental function with AMA in women, with evidence of placental adaptations in normal pregnancies. The AMA mouse model complements the human studies, demonstrating high rates of adverse fetal outcomes and commonalities in placental phenotype. These findings highlight placental dysfunction as a potential mechanism for susceptibility to FGR and stillbirth with AMA.

On the mathematical modelling of tumor-induced angiogenesis

An angiogenic system is taken as an example of extremely complex ones in the field of Life Sciences, from both analytical and computational points of view, due to the strong coupling between the kinetic parameters of the relevant branching - growth - anastomosis stochastic processes of the capillary network, at the microscale, and the family of interacting underlying biochemical fields, at the macroscale. To reduce this complexity, for a conceptual stochastic model we have explored how to take advantage of the system intrinsic multiscale structure: one might describe the stochastic dynamics of the cells at the vessel tip at their natural microscale, whereas the dynamics of the underlying fields is given by a deterministic mean field approximation obtained by an averaging at a suitable mesoscale. But the outcomes of relevant numerical simulations show that the proposed model, in presence of anastomosis, is not self-averaging, so that the ``propagation of chaos" assumption cannot be applied to obtain a deterministic mean field approximation. On the other hand we have shown that ensemble averages over many realizations of the stochastic system may better correspond to a deterministic reaction-diffusion system.

Solitonlike attractor for blood vessel tip density in angiogenesis

Recently, numerical simulations of a stochastic model have shown that the density of vessel tips in tumor-induced angiogenesis adopts a solitonlike profile [Sci. Rep. 6, 31296 (2016)2045-232210.1038/srep31296]. In this work, we derive and solve the equations for the soliton collective coordinates that indicate how the soliton adapts its shape and velocity to varying chemotaxis and diffusion. The vessel tip density can be reconstructed from the soliton formulas. While the stochastic model exhibits large fluctuations, we show that the location of the maximum vessel tip density for different replicas follows closely the soliton peak position calculated either by ensemble averages or by solving an alternative deterministic description of the density. The simple soliton collective coordinate equations may also be used to ascertain the response of the vessel network to changes in the parameters and thus to control it.

Mathematical modeling of the female reproductive system: from oocyte to delivery

From ovulation to delivery, and through the menstrual cycle, the female reproductive system undergoes many dynamic changes to provide an optimal environment for the embryo to implant, and to develop successfully. It is difficult ethically and practically to observe the system over the timescales involved in growth and development (often hours to days). Even in carefully monitored conditions clinicians and biologists can only see snapshots of the development process. Mathematical models are emerging as a key means to supplement our knowledge of the reproductive process, and to tease apart complexity in the reproductive system. These models have been used successfully to test existing hypotheses regarding the mechanisms of female infertility and pathological fetal development, and also to provide new experimentally testable hypotheses regarding the process of development. This new knowledge has allowed for improvements in assisted reproductive technologies and is moving toward translation to clinical practice via multiscale assessments of the dynamics of ovulation, development in pregnancy, and the timing and mechanics of delivery. WIREs Syst Biol Med 2017, 9:e1353. doi: 10.1002/wsbm.1353 For further resources related to this article, please visit the WIREs website.

Soliton driven angiogenesis

Angiogenesis is a multiscale process by which blood vessels grow from existing ones and carry oxygen to distant organs. Angiogenesis is essential for normal organ growth and wounded tissue repair but it may also be induced by tumours to amplify their own growth. Mathematical and computational models contribute to understanding angiogenesis and developing anti-angiogenic drugs, but most work only involves numerical simulations and analysis has lagged. A recent stochastic model of tumour-induced angiogenesis including blood vessel branching, elongation, and anastomosis captures some of its intrinsic multiscale structures, yet allows one to extract a deterministic integropartial differential description of the vessel tip density. Here we find that the latter advances chemotactically towards the tumour driven by a soliton (similar to the famous Korteweg-de Vries soliton) whose shape and velocity change slowly. Analysing these collective coordinates paves the way for controlling angiogenesis through the soliton, the engine that drives this process.

An international network (PlaNet) to evaluate a human placental testing platform for chemicals safety testing in pregnancy

The human placenta is a critical life-support system that nourishes and protects a rapidly growing fetus; a unique organ, species specific in structure and function. We consider the pressing challenge of providing additional advice on the safety of prescription medicines and environmental exposures in pregnancy and how ex vivo and in vitro human placental models might be advanced to reproducible human placental test systems (HPTSs), refining a weight of evidence to the guidance given around compound risk assessment during pregnancy. The placental pharmacokinetics of xenobiotic transfer, dysregulated placental function in pregnancy-related pathologies and influx/efflux transporter polymorphisms are a few caveats that could be addressed by HPTSs, not the specific focus of current mammalian reproductive toxicology systems. An international consortium, "PlaNet", will bridge academia, industry and regulators to consider screen ability and standardisation issues surrounding these models, with proven reproducibility for introduction into industrial and clinical practice.

Computational modelling of placental amino acid transfer as an integrated system

Placental amino acid transfer is essential for fetal development and its impairment is associated with poor fetal growth. Amino acid transfer is mediated by a broad array of specific plasma membrane transporters with overlapping substrate specificity. However, it is not fully understood how these different transporters work together to mediate net flux across the placenta. Therefore the aim of this study was to develop a new computational model to describe how human placental amino acid transfer functions as an integrated system. Amino acid transfer from mother to fetus requires transport across the two plasma membranes of the placental syncytiotrophoblast, each of which contains a distinct complement of transporter proteins. A compartmental modelling approach was combined with a carrier based modelling framework to represent the kinetics of the individual accumulative, exchange and facilitative classes of transporters on each plasma membrane. The model successfully captured the principal features of transplacental transfer. Modelling results clearly demonstrate how modulating transporter activity and conditions such as phenylketonuria, can increase the transfer of certain groups of amino acids, but that this comes at the cost of decreasing the transfer of others, which has implications for developing clinical treatment options in the placenta and other transporting epithelia.

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First computational model of placental amino acid transfer as an integrated system

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Increased activity of a transporter does not mean increased transfer to the fetus.

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Increasing transfer of certain amino acids can reduce the transfer of others.

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Amino acid composition as well as concentration determines transfer to the fetus.

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Modelling of phenylketonuria suggests inhibition by excess maternal phenylalanine.

Stochastic model of tumor-induced angiogenesis: Ensemble averages and deterministic equations

A recent conceptual model of tumor-driven angiogenesis including branching, elongation, and anastomosis of blood vessels captures some of the intrinsic multiscale structures of this complex system, yet allowing one to extract a deterministic integro-partial-differential description of the vessel tip density [Phys. Rev. E 90, 062716 (2014)]. Here we solve the stochastic model, show that ensemble averages over many realizations correspond to the deterministic equations, and fit the anastomosis rate coefficient so that the total number of vessel tips evolves similarly in the deterministic and ensemble-averaged stochastic descriptions.

Agent-based model of angiogenesis simulates capillary sprout initiation in multicellular networks

Many biological processes are controlled by both deterministic and stochastic influences. However, efforts to model these systems often rely on either purely stochastic or purely rule-based methods. To better understand the balance between stochasticity and determinism in biological processes a computational approach that incorporates both influences may afford additional insight into underlying biological mechanisms that give rise to emergent system properties. We apply a combined approach to the simulation and study of angiogenesis, the growth of new blood vessels from existing networks. This complex multicellular process begins with selection of an initiating endothelial cell, or tip cell, which sprouts from the parent vessels in response to stimulation by exogenous cues. We have constructed an agent-based model of sprouting angiogenesis to evaluate endothelial cell sprout initiation frequency and location, and we have experimentally validated it using high-resolution time-lapse confocal microscopy. ABM simulations were then compared to a Monte Carlo model, revealing that purely stochastic simulations could not generate sprout locations as accurately as the rule-informed agent-based model. These findings support the use of rule-based approaches for modeling the complex mechanisms underlying sprouting angiogenesis over purely stochastic methods.

Multiscale modelling of the feto-placental vasculature

The placenta provides all the nutrients required for the fetus through pregnancy. It develops dynamically, and, to avoid rejection of the fetus, there is no mixing of fetal and maternal blood; rather, the branched placental villi 'bathe' in blood supplied from the uterine arteries. Within the villi, the feto-placental vasculature also develops a complex branching structure in order to maximize exchange between the placental and maternal circulations. To understand the development of the placenta, we must translate functional information across spatial scales including the interaction between macro- and micro-scale haemodynamics and account for the effects of a dynamically and rapidly changing structure through the time course of pregnancy. Here, we present steps towards an anatomically based and multiscale approach to modelling the feto-placental circulation. We assess the effect of the location of cord insertion on feto-placental blood flow resistance and flow heterogeneity and show that, although cord insertion does not appear to directly influence feto-placental resistance, the heterogeneity of flow in the placenta is predicted to increase from a 19.4% coefficient of variation with central cord insertion to 23.3% when the cord is inserted 2 cm from the edge of the placenta. Model geometries with spheroidal and ellipsoidal shapes, but the same volume, showed no significant differences in flow resistance or heterogeneity, implying that normal asymmetry in shape does not affect placental efficiency. However, the size and number of small capillary vessels is predicted to have a large effect on feto-placental resistance and flow heterogeneity. Using this new model as an example, we highlight the importance of taking an integrated multi-disciplinary and multiscale approach to understand development of the placenta.

Hybrid modeling of tumor-induced angiogenesis

When modeling of tumor-driven angiogenesis, a major source of analytical and computational complexity is the strong coupling between the kinetic parameters of the relevant stochastic branching-and-growth of the capillary network, and the family of interacting underlying fields. To reduce this complexity, we take advantage of the system intrinsic multiscale structure: we describe the stochastic dynamics of the cells at the vessel tip at their natural mesoscale, whereas we describe the deterministic dynamics of the underlying fields at a larger macroscale. Here, we set up a conceptual stochastic model including branching, elongation, and anastomosis of vessels and derive a mean field approximation for their densities. This leads to a deterministic integropartial differential system that describes the formation of the stochastic vessel network. We discuss the proper capillary injecting boundary conditions and include the results of relevant numerical simulations.