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.

Department of Mathematics FNSPE Czech Technical University Prague Trojanova 13 Prague 2 12000 Czech Republic Mathematical Institute University of Oxford Woodstock Road Oxford UK

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

Mathematical Institute University of Oxford Woodstock Road Oxford UK

Nuffield Department of Obstetrics and Gynaecology University of Oxford Oxford UK Fetal Medicine Unit John Radcliffe Hospital Oxford UK

School of Mathematics University of Manchester Oxford Road Manchester UK

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Warrander L, Batra G, Bernatavicius G, Greenwood S, Dutton P, Jones R, Sibley C, Heazell A. 2012. Maternal perception of reduced fetal movements is associated with altered placental structure and function. PLoS ONE 7, e34851 (10.1371/journal.pone.0034851) PubMed DOI PMC

Salafia C, Maas E, Thorp J, Eucker B, Pezzullo J, Savitz D. 2005. Measures of placental growth in relation to birth weight and gestational age. Am. J. Epidemiol. 162, 991–998. (10.1093/aje/kwi305) PubMed DOI

Yampolsky M, Salafia C, Shlakhter O, Haas D, Eucker B, Thorp J. 2009. Centrality of the umbilical cord insertion in a human placenta influences the placental efficiency. Placenta 30, 1058–1064. (10.1016/j.placenta.2009.10.001) PubMed DOI PMC

Kajantie E, Thornburg K, Eriksson J, Osmond C, Barker D. 2010. In preeclampsia, the placenta grows slowly along its minor axis. Int. J. Dev. Biol. 54, 469–473. (10.1387/ijdb.082833ek) PubMed DOI

Barker D, Thornburg K, Osmond C, Kajantie E, Eriksson J. 2010. The surface area of the placenta and hypertension in the offspring in later life. Int. J. Dev. Biol. 54, 525–530. (10.1387/ijdb.082760db) PubMed DOI PMC

Eriksson J, Kajantie E, Thornburg K, Osmond C, Barker D. 2011. Mother's body size and placental size predict coronary heart disease in men. Eur. Heart J. 32, 2297–2303. (10.1093/eurheartj/ehr147) PubMed DOI PMC

Burton G, Jauniaux E. 2011. The placenta and human developmental programming, ch. 13, pp. 161–171. Cambridge, UK: Cambridge University Press.

Chernyavsky I, Jensen O, Leach L. 2010. A mathematical model of intervillous blood flow in the human placentone. Placenta 31, 44–52. (10.1016/j.placenta.2009.11.003) PubMed DOI

Yampolsky M, Salafia C, Shlakhter O, Haas D, Eucker B, Thorp J. 2008. Modeling the variability of shapes of a human placenta. Placenta 29, 790–797. (10.1016/j.placenta.2008.06.005) PubMed DOI PMC

Guiot C, Pianta P, Todros T. 1992. Modelling the feto-placental circulation: I. A distributed network predicting umbilical haemodynamics throughout pregnancy. Ultrasound Med. Biol. 18, 535–544. (10.1016/0301-5629(92)90068-L) PubMed DOI

Pijnenborg R, Vercruysse L, Hanssens M. 2006. The uterine spiral arteries in human pregnancy: facts and controversies. Placenta 27, 939–958. (10.1016/j.placenta.2005.12.006) PubMed DOI

Swanson K, Rockne R, Claridge J, Chaplain M, Alvord E, Jr, Anderson A. 2011. Quantifying the role of angiogenesis in malignant progression of gliomas: in silico modeling integrates imaging and histology. Cancer Res. 71, 7366–7375. (10.1158/0008-5472.CAN-11-1399) PubMed DOI PMC

Boyd J, Hamilton W. 1970. The human placenta, vol. 212. Cambridge, UK: Heffer & Sons.

Meekins J, Pijnenborg R, Hanssens M, MCFadyen I, van Asshe A. 1994. A study of placental bed spiral arteries and trophoblast invasion in normal and severe pre-eclamptic pregnancies. BJOG 101, 669–674. (10.1111/j.1471-0528.1994.tb13182.x) PubMed DOI

Kloeden P, Platen E. 1992. Numerical solution of stochastic differential equations. Applications of Mathematics, vol. 23. Berlin, Germany: Springer.

Milstein G. 1995. Numerical integration of stochastic differential equations. Mathematics and Its Applications, vol. 313. Dordrecht, The Netherlands: Springer.

Page K. 1993. The physiology of the human placenta, ch. 1, p. 10 London: University College London Press.

Schuhmann R, Stoz F, Maier M. 1988. Histometric investigations in placentones (materno-fetal circulation units) of human placentae. In Placental vascularization and blood flow, pp. 3–16. Berlin, Germany: Springer.

Wooding P, Burton G. 2008. Comparative placentation: structures, functions and evolution, ch. 8, p. 209 Berlin, Germany: Springer.

Birdsey T, Boyd R, Sibley C, Greenwood S. 1997. Microvillous membrane potential (Em) in villi from first trimester human placenta: comparison to Em at term. Am. J. Physiol. 273, R1519–R1528. PubMed

Kido A, Kataoka M, Koyama T, Yamamoto A, Saga T, Togashi K. 2010. Changes in apparent diffusion coefficients in the normal uterus during different phases of the menstrual cycle. Br. J. Radiol. 83, 524–528. (10.1259/bjr/11056533) PubMed DOI PMC

Klamkin M. 1971. Elementary approximations to the area of n-dimensional ellipsoids. Am. Math. Mon. 78, 280–283. (10.2307/2317530) DOI

Esmaelzadeh S, Rezaei N, HajiAhmadi M. 2004. Normal uterine size in women of reproductive age in Northern Islamic Republic of Iran. Eastern Mediterranean Health J. 10, 437–441. PubMed

Callen P. 1994. Ultrasonography in obstetrics and gynecology. Philadelphia, PA: Saunders.

Berman M, Cohen H. (eds). 1997. Diagnostic medical sonography: obstetrics and gynecology, vol. 1 Philadelphia, PA: Lippincott Williams & Wilkins.

Sanders R, Winter T. 1991. Clinical sonography: a practical guide. Philadelphia, PA: Lippincott Williams & Wilkins.

Warwick W, Banister D. 1989. Gray‘s anatomy. London, UK: Churchill Livingstone.

Heazell A, et al. 2010. Comparing placentas from normal and abnormal pregnancies In Proc. 2010 UK Mathematics-in-Medicine Study Group. www.maths-in-medicine.org/uk/2010/placentas/report.pdf.

Sherman T. 1981. On connecting large vessels to small. The meaning of Murray's law. J. Gen. Physiol. 78, 431–453. (10.1085/jgp.78.4.431) PubMed DOI PMC

Sengers B, Please C, Lewis R. 2010. Computational modelling of amino acid transfer interactions in the placenta. Exp. Physiol. 95, 829–840. (10.1113/expphysiol.2010.052902) PubMed DOI

Gill J, Salafia C, Grebenkov D, Vvedensky D. 2011. Modeling oxygen transport in human placental terminal villi. J. Theor. Biol. 291, 33–41. (10.1016/j.jtbi.2011.09.008) PubMed DOI

Gordon Z, Eytan O, Jaffa A, Elad D. 2007. Fetal blood flow in branching models of the chorionic arterial vasculature. Ann. NY. Acad. Sci. 1101, 250–265. (10.1196/annals.1389.037) PubMed DOI

Luria O, Bar J, Kovo M, Golan A, Barnea O. 2010. Feto-maternal interaction: a mathematical model simulating placental response in hypertensive disorders of pregnancy. Reprod. Sci. 17, 963–969. (10.1177/1933719110376091) PubMed DOI

van den Wijngaard J, Westerhof B, Ross M, Van Gemert M. 2007. A mathematical model of twin-twin transfusion syndrome with pulsatile arterial circulations. Am. J. Physiol. 292, R1519–R1531. (10.1152/ajpregu.00534.2006) PubMed DOI

Sebire N, Jain V, Talbert D. 2004. Spiral artery associated restricted growth (SPAARG): a computer model of pathophysiology resulting from low intervillous pressure having fetal programming implications. Pathophysiology 11, 87–94. (10.1016/j.pathophys.2004.06.003) PubMed DOI

Pathak S, Hook E, Hackett G, Murdoch E, Sebire N, Jessop F, Lees C. 2010. Cord coiling, umbilical cord insertion and placental shape in an unselected cohort delivering at term: relationship with common obstetric outcomes. Placenta 31, 963–968. (10.1016/j.placenta.2010.08.004) PubMed DOI

Biswas S, Ghosh S, Chhabra S. 2008. Surface area of chorionic villi of placentas: an index of intrauterine growth restriction of fetuses. J. Obstetr. Gynaecol. Res. 34, 487–493. (10.1111/j.1447-0756.2008.00719.x) PubMed DOI

Biswas S, Ghosh S. 2008. Gross morphological changes of placentas associated with intrauterine growth restriction of fetuses: a case control study. Early Hum. Dev. 84, 357–362. (10.1016/j.earlhumdev.2007.09.017) PubMed DOI

Gordon Z, Elad D, Almog R, Hazan Y, Jaffa A, Eytan O. 2007. Anthropometry of fetal vasculature in the chorionic plate. J. Anat. 211, 698–706. (10.1111/j.1469-7580.2007.00819.x) PubMed DOI PMC

Baergen R. 2011. Manual of pathology of the human placenta, ch. 15, p. 270 Berlin, Germany: Springer.

Salafia C, Yampolsky M. 2009. Metabolic scaling law for fetus and placenta. Placenta 30, 468–471. (10.1016/j.placenta.2008.12.013) PubMed DOI PMC

Billington W. 1971. Biology of the trophoblast. Adv. Reprod. Physiol. 5, 27–66. PubMed

Ferretti C, Bruni L, Dangles-Marie V, Pecking A, Bellet D. 2007. Molecular circuits shared by placental and cancer cells, and their implications in the proliferative, invasive and migratory capacities of trophoblasts. Hum. Reprod. Update 13, 121–141. (10.1093/humupd/dml048) PubMed DOI

Schwartz N, Mandel D, Shlakhter O, Coletta J, Pessel C, Trimor-Tritsch I, Salafia C. 2011. Placental morphologic features and chorionic surface vasculature at term are highly correlated with 3-dimensional sonographic measurements at 11 to 14 weeks. J. Ultrasound Med. 30, 1171–1178. PubMed