A stochastic model for early placental development.
In the human, placental structure is closely related to placental function and consequent pregnancy outcome. Studies have noted abnormal placental shape in small-for-gestational-age infants which extends to increased lifetime risk of cardiovascular disease. The origins and determinants of placental shape are incompletely understood and are difficult to study in vivo. In this paper, we model the early development of the human placenta, based on the hypothesis that this is driven by a chemoattractant effect emanating from proximal spiral arteries in the decidua. We derive and explore a two-dimensional stochastic model, and investigate the effects of loss of spiral arteries in regions near to the cord insertion on the shape of the placenta. This model demonstrates that disruption of spiral arteries can exert profound effects on placental shape, particularly if this is close to the cord insertion. Thus, placental shape reflects the underlying maternal vascular bed. Abnormal placental shape may reflect an abnormal uterine environment, predisposing to pregnancy complications. Through statistical analysis of model placentas, we are able to characterize the probability that a given placenta grew in a disrupted environment, and even able to distinguish between different disruptions.
School of Mathematics, University of Manchester, Oxford Road, Manchester, UK simon.cotter@manchester.ac.uk.
Simon L
SL
Cotter
Department of Mathematics, FNSPE, Czech Technical University in Prague, Trojanova 13, Prague 2 12000, Czech Republic Mathematical Institute, University of Oxford, Woodstock Road, Oxford, UK.
Václav
V
Klika
Mathematical Institute, University of Oxford, Woodstock Road, Oxford, UK.
Laura
L
Kimpton
Nuffield Department of Obstetrics and Gynaecology, University of Oxford, Oxford, UK Fetal Medicine Unit, John Radcliffe Hospital, Oxford, UK.
Sally
S
Collins
Institute of Human Development, Maternal and Fetal Health Research Centre, University of Manchester, Manchester, UK Maternal and Fetal Health Research Centre, St Mary's Hospital, Central Manchester University Hospitals NHS Foundation Trust, Manchester Academic Health Science Centre, Manchester, UK.
Alexander E P
AE
Heazell
D003198:Computer Simulation; D047108:Embryonic Development / Q000502:physiology*; D005260:Female; D006801:Humans; D008954:Models, Biological; D015233:Models, Statistical; D018919:Neovascularization, Physiologic / Q000502:physiology; D038081:Organogenesis / Q000502:physiology*; D010100:Oxygen / Q000378:metabolism*; D010920:Placenta / Q000196:embryology*; D010929:Placentation; D011247:Pregnancy; D013269:Stochastic Processes; D014469:Umbilical Arteries / Q000502:physiology*
D010100:Oxygen
mathematical modelling; placental development; placental shape; spiral artery; stochastic dynamics