title: Image-Based Modeling of Blood Flow and Oxygen Transfer in Feto-Placental Capillaries.
abstract: During pregnancy, oxygen diffuses from maternal to fetal blood through villous trees in the placenta. In this paper, we simulate blood flow and oxygen transfer in feto-placental capillaries by converting three-dimensional representations of villous and capillary surfaces, reconstructed from confocal laser scanning microscopy, to finite-element meshes, and calculating values of vascular flow resistance and total oxygen transfer. The relationship between the total oxygen transfer rate and the pressure drop through the capillary is shown to be captured across a wide range of pressure drops by physical scaling laws and an upper bound on the oxygen transfer rate. A regression equation is introduced that can be used to estimate the oxygen transfer in a capillary using the vascular resistance. Two techniques for quantifying the effects of statistical variability, experimental uncertainty and pathological placental structure on the calculated properties are then introduced. First, scaling arguments are used to quantify the sensitivity of the model to uncertainties in the geometry and the parameters. Second, the effects of localized dilations in fetal capillaries are investigated using an idealized axisymmetric model, to quantify the possible effect of pathological placental structure on oxygen transfer. The model predicts how, for a fixed pressure drop through a capillary, oxygen transfer is maximized by an optimal width of the dilation. The results could explain the prevalence of fetal hypoxia in cases of delayed villous maturation, a pathology characterized by a lack of the vasculo-syncytial membranes often seen in conjunction with localized capillary dilations.
authors: School of Mathematics, University of Manchester, Manchester, M13 9PL, United Kingdom.
authors: Philip
authors: http://orcid.org/0000-0001-5788-3826
authors: P
authors: Pearce
authors: Maternal and Fetal Health Research Centre, Institute of Human Development, University of Manchester, Manchester, United Kingdom.|Maternal and Fetal Health Research Centre, St. Mary's Hospital, Central Manchester University Hospitals NHS Foundation Trust, Manchester Academic Health Science Centre, Manchester, M13 9WL, United Kingdom.
authors: Paul
authors: P
authors: Brownbill
authors: Department of Biomathematics, Institute of Physiology, v.v.i., Academy of Sciences of the Czech Republic, Prague, Czech Republic.
authors: Jiří
authors: J
authors: Janáček
authors: Institute of Histology and Embryology, First Faculty of Medicine, Charles University, Albertov 4, CZ-12801 Prague 2, Czech Republic.
authors: Marie
authors: M
authors: Jirkovská
authors: Department of Biomathematics, Institute of Physiology, v.v.i., Academy of Sciences of the Czech Republic, Prague, Czech Republic.
authors: Lucie
authors: L
authors: Kubínová
authors: School of Mathematics, University of Manchester, Manchester, M13 9PL, United Kingdom.
authors: Igor L
authors: IL
authors: Chernyavsky
authors: School of Mathematics, University of Manchester, Manchester, M13 9PL, United Kingdom.
authors: Oliver E
authors: OE
authors: Jensen
mesh_terms: D001775:Blood Circulation; D002196:Capillaries / Q000378:metabolism / Q000502:physiology*; D002824:Chorionic Villi / Q000196:embryology; D004058:Diffusion; D005260:Female; D005333:Fetus / Q000098:blood supply*; D006801:Humans; D021621:Imaging, Three-Dimensional; D008954:Models, Biological; D010100:Oxygen / Q000378:metabolism*; D010920:Placenta / Q000098:blood supply*; D011247:Pregnancy
chemical_list: D010100:Oxygen