A Mathematical Model of Intervillous Blood Flow in the Human Placentone

Chernyavsky, Igor L.; Jensen, Oliver E.; Leach, Lopa

doi:10.1016/j.placenta.2009.11.003

Cited by 69 publications

(102 citation statements)

References 29 publications

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“…For sufficiently large Da and Pe, this leads to a 'staircase' structure in the exact solution ( figure 3b,c). Leading-order solute distributions, such as those computed by Chernyavsky et al [6], fail to capture these significant local variations in the solute field.…”

Section: (B) Accuracy Of the Homogenization Approximation For Periodimentioning

confidence: 97%

“…A peripheral lobule of the human placenta was used for the histological study, as it tends to contain a single chorionic villous tree matched with a spiral artery, and is therefore more representative of a single placental circulatory unit [2,6]. A single maternal lobule, obtained from a normal full-term placenta (delivered by elective caesarian section), was frozen in nitrogen-cooled isopentane before cutting according to a systematic random sampling protocol.…”

Section: (A) Imaging and Spatial Statisticsmentioning

confidence: 99%

“…For a given Pe, there is a critical Da (see equation (A 6b)), equivalent to on May 12, 2018 http://rsta.royalsocietypublishing.org/ Downloaded from as glucose and oxygen in the placenta is the regime in which Pe is of order unity or larger [6], which we illustrate using point (5) in figure 3. In this case, the correction to C (0) develops an internal boundary layer within each unit cell.…”

Section: (B) Accuracy Of the Homogenization Approximation For Periodimentioning

confidence: 99%

“…A natural starting point in modelling maternal placental blood flow is to exploit the theory of flow in porous media [7,8]. We have recently used this approach to demonstrate the importance of the calibre of maternal spiral arteries and decidual veins in determining the overall flow resistance in a functional placental unit (or 'placentone', containing a single villous tree) and to examine the factors that optimize nutrient delivery [6].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Transport in the placenta: homogenizing haemodynamics in a disordered medium

Chernyavsky

Leach

Dryden

et al. 2011

Phil. Trans. R. Soc. A.

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The placenta is an essential component of the life-support system for the developing foetus, enabling nutrients and waste to be exchanged between the foetal and maternal circulations. Maternal blood flows between the densely packed branches of villous trees, within which are foetal vessels. Here, we explore some of the challenges in modelling maternal haemodynamic transport using homogenization approaches. We first show how two measures can be used to estimate the minimum distance over which the distribution of villous branches appears statistically homogeneous. We then analyse a simplified model problem (solute transport by a unidirectional flow past a distribution of point sinks) to assess the accuracy of homogenization approximations as a function of governing parameters (Péclet and Damköhler numbers) and the statistical properties of the sink distribution. The difference between the leading-order homogenization approximation and the exact solute distribution is characterized by large spatial gradients at the scale of individual villi and substantial fluctuations that can be correlated over lengthscales comparable to the whole domain. This study highlights the importance of quantifying errors owing to spatial disorder in multi-scale approximations of physiological systems.

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Section: (B) Accuracy Of the Homogenization Approximation For Periodimentioning

confidence: 97%

Section: (A) Imaging and Spatial Statisticsmentioning

confidence: 99%

Section: (B) Accuracy Of the Homogenization Approximation For Periodimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Transport in the placenta: homogenizing haemodynamics in a disordered medium

Chernyavsky

Leach

Dryden

et al. 2011

Phil. Trans. R. Soc. A.

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show abstract

“…Indeed, there has been a recent surge in theoretical studies of placental morphology [91][92][93] and its relation to haemodynamics and transfer function [65,67,[94][95][96][97][98]. We now have the opportunity to combine the synergy of detailed inspection of placental barrier properties ex vivo and in vitro with the power of testing key mechanisms in silico that should accelerate the development of placenta-on-a-chip and its translation to industrial and regulatory use.…”

Section: Placenta On a Chipmentioning

confidence: 99%

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

Brownbill

Chernyavsky

Bottalico

et al. 2016

Reproductive Toxicology

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Personalising cardiovascular network models in pregnancy: A two‐tiered parameter estimation approach

Carson

Warrander

Johnstone

et al. 2020

Numer Methods Biomed Eng

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Uterine artery Doppler waveforms are often studied to determine whether a patient is at risk of developing pathologies such as pre‐eclampsia. Many uterine waveform indices have been developed, which attempt to relate characteristics of the waveform with the physiological adaptation of the maternal cardiovascular system, and are often suggested to be an indicator of increased placenta resistance and arterial stiffness. Doppler waveforms of four patients, two of whom developed pre‐eclampsia, are compared with a comprehensive closed‐loop model of pregnancy. The closed‐loop model has been previously validated but has been extended to include an improved parameter estimation technique that utilises systolic and diastolic blood pressure, cardiac output, heart rate, and pulse wave velocity measurements to adapt model resistances, compliances, blood volume, and the mean vessel areas in the main systemic arteries. The shape of the model‐predicted uterine artery velocity waveforms showed good agreement with the characteristics observed in the patient Doppler waveforms. The personalised models obtained now allow a prediction of the uterine pressure waveforms in addition to the uterine velocity. This allows for a more detailed mechanistic analysis of the waveforms, eg, wave intensity analysis, to study existing clinical indices. The findings indicate that to accurately estimate arterial stiffness, both pulse pressure and pulse wave velocities are required. In addition, the results predict that patients who developed pre‐eclampsia later in pregnancy have larger vessel areas in the main systemic arteries compared with the two patients who had normal pregnancy outcomes.

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A Mathematical Model of Intervillous Blood Flow in the Human Placentone

Cited by 69 publications

References 29 publications

Transport in the placenta: homogenizing haemodynamics in a disordered medium

Transport in the placenta: homogenizing haemodynamics in a disordered medium

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

Personalising cardiovascular network models in pregnancy: A two‐tiered parameter estimation approach

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