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Boundary Conditions for Three Placental Flow Fields That May Statistical Geometry and Topology of the Human Placenta 201 Boundary Conditions Statisticalfor GeometryThree and Topology Placental of the Human Placenta Flow Fields 201 That May Predict and Cause Intra-Uterine Growth Retardation C.G. Ball1, D. Grynspan2, A. Gruslin3 1. Department of Pathology and Laboratory Medicine, University of Ottawa / Ottawa Hospital, Ottawa, Ontario, Canada 2. Department of Pathology and Laboratory Medicine, University of Ottawa / Children’s Hospital of Eastern Ontario, Ottawa, Ontario, 3. Departments of Obstetrics and GynecologyStatistical Geometry and Topology of Cellular of the Human PlacentaMolecular Medicine, University 197 of Ottawa / Ottawa Hospital, Ottawa, Ontario, Canada Introduction The Spiral Arteries Altered end-diastolic flow in the umbilical artery is a reliable predictor of Variation in the size and shape of the spiral arteries is associated with the intrauterine growth retardation (IUGR). It appears that an earlier and more physiological state of the uterus (non-gravid, post-partum, gravid, in pre- sensitive prediction can be made when chorionic vessel flow patterns are eclampsia, etc.). In the diseased state, the causality of these morphological characterised; we hypothesize that this results from remodelling of the villous changes in the spiral arteries is not entirely known (altered trophoblastic invasion circulatory bed. However, neither the true extent nor the causative mechanism has been implicated). Nonetheless, it is postulated variations in spiral arterial of these altered flow patterns is known. In addition to the villous tree, the flow bring about other changes in the health of the uterus, fetus, and mother lacunar blood flows and the spiral arteries may also be prime suspects. (such as villous tree changes, IUGR, pre-eclampsia, and so on). Furthermore, Unfortunately, direct observation of these physical flows is restricted. the shear interactions between the blood flow and arterial walls may result in Preliminary enquiry indicates that each system may be compared to a unique additional alteration of the geometry of the spiral arteries. physical flow problem. The villous tree as a complicated flow-in-pipes system; Accordingly, it would be beneficial to precisely know the flow in the spiral arteries the lacunar pools as a porous medium flow; the spiral arteries as a wall shear in order to accurately determine uteroplacental flow, and to assess whether stress interactions problem. incipient changes in spiral arterial flow incite further local and regional pathologic changes. The Chorionic Vascular Tree Fig 1. Highlighted vasculature of theFig. chorionic 7 Six tree networksplate: a) corresponding Fig 2. to Variation the vasculature of ofthe human chorionic placentas, obtained according Fig. 5 (a) A digital photograph of the chorionic plate ofto the the placenta procedure with in handSect. tracing4.1,withtheindicatedbirthweights(Fig. which 7 Six tree networks correspondinglower panels to the)togetherwiththeir vasculature of human placentas, obtained according entropy profiles (upper panelsto). Forvasculature, the procedureeach placenta, in Sect.six the computational network4.1,withtheindicatedbirthweights( is shown in gray and the corre-lower panels)togetherwiththeir highlightsPhotograph the visible surface of vasculatureplacenta (arterieswith arterial are traced tree, here). (b)b) andand (c )c) show the hand traced Our Goals The chorionic vascular tree may be approximated to a system of flow-in-pipes. sponding triangulation shown adjacententropyarterial profilesin red tree (upper networks panels). from For each human placenta, the network is shown in gray and the corre- arterial andarterial venous and vasculature venous respectively vasculature, prior to d) computer computational aided processing. (d)Computersponding triangulation shown adjacent in red In engineering systems, these problems are normally solved empirically. generated graph showing both the arterial (red)andvenousvasculature placenta, with fetal birth weights approximation of both vascular trees (from 2). G.J. Burton et al. / Placenta 30 (2009) 473–482 1. Determine479 the extent of feasible simplification of the chorionic vascular tree. These solutions approximate losses and gains in a flow system by accounting Bearing in mind the limitations(from 2.) of a small sample size, as well as the potential for measurement errors of theBearing placental in vasculature, mind the limitations Fig. 8 shows of severala small2. features sampleDetermine of size, as an well idealised as the potential geometryResults for the fetal villous tree within the the effects of standard piping elements (i.e. elbows, tees, pumps, that placental development is even linked to adultthe health. entropy The profiles placenta of 13 grows placentasfor measurement and divided errors into categories of the placental of low (2–3vasculature, kg),uteroplacental normal Fig. 8 shows several blood features pool. of (3–4 kg) and high (4–5 kg) infant birth weights. In common with the placentas in contractions/expansions, etc.). However, the implied assumptions of such andevelops alongside the fetus (Fig. 1). The surface of the placenta attachedthe to entropy the profiles of 13 placentas divided into3. categoriesDetermine of lowthe (2–3uteroplacental kg), normal blood flow velocity field, using a scaled endometrium (lining) of the uterine wall is calledFig. the7,theentropiesoftheentirevasculatures[Figs. basal plate and the(3–4 surface kg) and high (4–5 kg)8(a), infant (b)] birth show weights. a much smaller In common with the placentas in engineering system may not be justifiable in the variable flow setting of the Fig. 7,theentropiesoftheentirevasculatures[Figs.experimental8(a), (b)] show model. a much smaller nearest to the fetus the chorionic plate. Between the two is a complex arborized chorionic vascular tree. Among the most difficult challenges are: vascular network through which oxygen, nutrient and waste exchange takes place. 4. Determine idealised geometries for the spiral arteries in normal gravid and G.J. Burton et al. / Placenta 30 (2009) 473–482 475 non-gravid uterus, with a goal of computing shear-wall interactions and their • determination of an idealised geometry for the vascular tree, The vascular system of the placenta consists of two arteries and one vein that form a possible effect on spiral arterial development. • understanding of the fluid dynamic effects of the pulsatile flow treelike network in the chorion with its origin placed at the umbilical cord insertion. Beyond the chorionic plate, the veins and arteries dive into the placenta with fur- • determination of an acceptable approximation for blood viscosity ther branching. In our analysis we focus on the vascular structure on the chorionic References • understanding the wall effect of the elastic blood vessels plate, which we regard as a 2D tree network. The analysis distinguishes between the 1. Ball CB, Grynspan D, Gruslin A. (2013) Porous media flow models for maternal arterial and venous vasculature. placental circulation. Annual ConclusionsMeeting of the International Federation of Placenta Utero-Placental Flow Associations, Whistler, British Columbia. 2. Bernischke K., Kaufmann P, Baergen, RN Pathology of the human placenta. 5th ed. Numerous approximations of uteroplacental blood flow and solute transport4.1 Tracing the VasculatureFig. 6. Diagrammatic representationFig (not 4. to scale)Diagrammatic of the effects of spiral artery representation conversion on the inflow of of maternal normal blood into theand intervillous space and on lobuleSpringer; architecture 2006. predicted by modelling. Dilation of the distal segment in normal pregnancies will reduce the velocity of incoming blood, and the residual momentum will carry the blood into the have been proposed as a means to uncover underlying pathophysiologic central cavity (CC) of the lobule,pathologic from where it will disperse alteration evenly through of the villousthe tree.villous Transit time tree to the uterinein response vein is estimated to be in the order3. of 25–30Burton s, allowing GJ, Woods AW, Jauniaux E, Kingdom JCP. (2009) Rheological and adequate time for oxygen exchange. The pressure of the maternal blood, indicated in mmHg by the figures in blue, will drop across the non-dilated segment of the spiral artery, the processes (of IUGR and other entities). In these efforts, analytical solutions or dimensions of which are given alongside.altered In pathological spiral pregnancies, arterial where in-flow no or very limited (as conversion predicted occurs, the maternal by 3.) blood will enter the intervillous spacephysiological at speeds of consequences of conversion of the maternal spiral arteries for ExtractingFig 3. the A: network Large informationstem villi1–2 m/s. of from The the high the Reynolds placenta number predicts is a turbulent time-consuming flow, indicated by the multi- circular arrows. We suggest that the high momentum ruptures anchoring villi (asterisked) and step process. Figure 5 illustratesdisplaces the steps others to involvedform echogenic cysticin extracting lesions (ECL) lined the by thrombus placental (brown). vas- The transit time will be reduced, so that oxygen exchange is impaired and blooduteroplacental leaves in the blood flow during human pregnancy. Placenta. 30:473-482. mathematical models are applied to approximate physical processes in the villous tree, B) Higheruterine magnification vein with a higher oxygen concentration than normal. Trophoblastic microparticulate debris (dotted)
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