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

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Abstract 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: Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models Models of Systems Properties and Processes > Mechanistic Models Physiology > Mammalian Physiology in Health and Disease
An illustration of some of the different scales of imaging available to modeling studies, and models that have been published that cover these scales. Top: shows computational models that aim to predict function at scales reflective of the images below them. Left to right: (a) Gill et al. (2011) predicted nutrient concentration in villous structures (reproduced with permission), (b) model of shear stress over terminal villi (reproduced under Creative Commons Attribution License, Lecarpentier et al. (2016)), (c) a model of the branching structure of feto‐placental vasculature (Clark et al., 2015; Tun et al., 2019), (d) predictions of velocity streamlines in a porous media model of IVS blood flow with local permeability a function of villous tree structure (Lin et al., 2016), (e) an illustration of the typical structure of transmission line models often used to predict Doppler waveforms. Bottom: shows a range of uteroplacental imaging technologies. From left to right: (f) A histological cross‐section of term placental villi with vessels filled with red blood cells visible, (g) a micro‐CT image of a placental region with blood vessels injected with contrast agent; (h) a magnetic resonance T2 relaxation map of near‐term placentae (reproduced under Creative Commons Attribution License, Aughwane et al. (2019)); (i) a 3D ultrasound placental volume at 20 weeks of gestation, (j) an umbilical artery Doppler waveform at 20 weeks of gestation. All sample images not previously published were collected following ethical approval (f,g—NTX/12/06/057/AM08, i,j—University of Auckland Human Participants Ethics Committee, 011317)
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Computational models of the interface between maternal and fetal circulations (the intervillous space) used to determine the shear stress experienced by the syncytiotrophoblast. Left: a porous media model showing blood velocity. Models such as this can be viewed as a volume averaging of the underlying physics in which the complicated underlying structure of the villous trees has been “smeared out”. Right: A Navier–Stokes model using physiological geometry obtained from imaging experiments showing shear stress. This type of model is directly solving the underlying equations governing the physics of fluid flow on the prescribed geometry and hence can capture the spatial variations in shear stress that exist due to the complex underlying structure of the villous trees. Navier–Stokes models can only capture a small part of the placentome whereas porous media models can be used to capture these regional variations but are unable to capture spatial variations due to the structure of the villous trees as these details have been “smeared out” in by volume averaging. Panels are modified from Lecarpentier et al. (2016), which was published under the Creative Commons Attribution License
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Computational models of the uterine vasculature often focus on mechanisms by which uterine artery Doppler waveforms are influenced by uteroplacental structure. Top: shows how uterine artery Doppler typically changes in pregnancy, with early gestation waveforms being characterized by a “notch”. Most models of this system follow an electrical circuit analogy, representing blood vessels as capacitor‐resistor pairs. Bottom left: Early models of this system lumped together with the uteroplacental vascular system into one and predicted the notch reflects a high resistance/compliance in the downstream uterine vasculature, specifically the spiral arteries. Bottom right: More recent anatomical models have suggested that the upstream uterine vasculature, particularly the radial arteries and arteriovenous anastomoses can impact on observed Doppler waveforms, complicating interpretation of these waveforms clinically
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Mathematical modeling of the trophoblast plugs that at least partially occlude spiral arteries in the first trimester of pregnancy have suggested possible mechanisms for plug dispersal. Agent‐based models of trophoblast behaviors coupled with continuum porous media models have suggested that weaknesses in the plug, which may be caused by asymmetries or cell death lead to localized high flow/shear regions, which lead to channel formation in the plug and a cycle of plug dispersal. Despite a strong focus on cell‐based modeling in developmental biology, these techniques have not widely been applied in studies of the pregnant uterus or placenta
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Top: Schematic diagram of the placental villous tree around the outside of which maternal blood circulates. Bottom: Zoomed in inset of materno‐fetal interface demonstrating the anatomy of individual placental villi, which contain fetal blood vessels and are surrounded by a bilayer of epithelial trophoblast cells. Extravillous trophoblasts can be seen migrating out of the placental villi and invading into the maternal decidua, where a subset of these (endovascular trophoblasts) remodel the spiral arteries from tightly coiled tubes on the left, to wide conduits on the right. Endovascular trophoblasts can also be seen forming a trophoblast plug in the center artery. Anatomy of the larger upstream uterine vessels that remodel in a trophoblast independent manner, as well as the arterio‐venous anastomoses is shown
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Physiology > Mammalian Physiology in Health and Disease
Models of Systems Properties and Processes > Mechanistic Models
Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models

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