Placenta
Volume 31, Issue 1 , Pages 44-52 , January 2010

A Mathematical Model of Intervillous Blood Flow in the Human Placentone

  • I.L. Chernyavsky

      Affiliations

    • Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK
    • ,
  • O.E. Jensen

      Affiliations

    • Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK
    • ,
  • L. Leach

      Affiliations

    • Centre for Integrated Systems Biology and Medicine, School of Biomedical Sciences, University of Nottingham, Queen's Medical Centre, E Floor Medical School, Nottingham NG7 2UH, UK
    • Corresponding Author InformationCorresponding author. Tel.: +44 115 823 0175; fax: +44 115 823 0142.

,Accepted 3 November 2009.

References 

  1. Freese UE. The uteroplacental vascular relationship in the human. Am J Obstet Gynecol. 1968;101:8–16
  2. Ramsey EM. Uteroplacental circulation during labor. Clin Obstet Gynecol. 1968;11:78–95
  3. Reynolds SRM. Derivation of the vascular elements in the fetal cotyledon of the hemochorial placenta: a contribution to the theory of placental morphogenesis. Anat Rec. 1967;157:43–46
  4. Wilkin P. Contribution to the study of the fetal placental circulation. Gynécol et Obstét. 1954;53:239–263[in French]
  5. Wigglesworth JS. Vascular organization of the human placenta. Nature. 1967;216:1120–1121
  6. Schuhmann RA. Placentone structure of the human placenta. In:  Kaufmann P,  King B editor. Structural and functional organization of the placenta. Bibliotheca anatomica. vol. 22:Karger; 1982;p. 46–57
  7. Benirschke K, Kaufmann P, Baergen RN. Pathology of the human placenta. 5th ed. Springer; 2006;1050 pp.
  8. Freese UE. Vascular relations of placental exchange areas in primates and man. In:  Longo LD,  Bartels H editor. Respiratory gas exchange and blood flow in the placenta. Bethesda, MD: Nat. Inst. Child Health Hum. Dev.; 1972;p. 31–60
  9. Boyd JD, Hamilton WJ. The human placenta. Cambridge: W.Heffer&Sons Ltd; 1970;365 pp.
  10. Schröder HJ. Comparative aspects of placental exchange functions. Eur J Obstet Gynecol Reprod Biol. 1995;63:81–90
  11. Kirschbaum TH, Shapiro NZ. A mathematical model of placental oxygen transfer. J Theor Biol. 1969;25:380–402
  12. Faber JJ. Application of the theory of heat exchangers to the transfer of inert materials in placentas. Circ Res. 1969;24:221–234
  13. In:  Longo LD,  Bartels H editor. Respiratory gas exchange and blood flow in the placenta. Bethesda, MD: Nat. Inst. Child Health Hum. Dev.; 1972;570 pp
  14. Bartels H, Moll W. Passage of inert substances and oxygen in the human placenta. Pflügers Arch Eur J Physiol. 1964;280:165–177
  15. Hill E, Power G, Longo L. A mathematical model of carbon dioxide transfer in the placenta and its interaction with oxygen. Am J Physiol. 1973;224:283–299
  16. Lardner TJ. A model for placental oxygen exchange. J Biomech. 1975;8:131–134
  17. Erian FF, Corrsin S, Davis SH. Maternal, placental blood flow: a model with velocity-dependent permeability. J Biomech. 1977;10:807–814
  18. Schmid-Schönbein H. Conceptional proposition for a specific microcirculatory problem: maternal blood flow in hemochorial multivillous placentae as percolation of a “porous medium”. Trophoblast Res. 1988;3:17–38
  19. Guilbeau EJ, Reneau DD, Knisely MH. The effects of placental oxygen consumption and the contractions of labor on fetal oxygen supply: a steady and unsteady state mathematical simulation. In:  Longo LD,  Bartels H editor. Respiratory gas exchange and blood flow in the placenta. Bethesda, MD: Nat. Inst. Child Health Hum. Dev.; 1972;p. 297–342
  20. Heilmann L, Grebner H, Mattheck C, Ludwig H. Mathematical, clinical, and laboratory study of hemodynamic changes in the placental circulation. Arch Gynecol Obstet. 1979;227:303–313
  21. Costa A, Costantino M, Fumero R. Oxygen exchange mechanisms in the human placenta: mathematical modelling and simulation. J Biomed Eng. 1992;14:385–389
  22. Burton G, Woods A, Jauniaux E, Kingdom J. Rheological and physiological consequences of conversion of the maternal spiral arteries for uteroplacental blood flow during human pregnancy. Placenta. 2009;30:473–482
  23. Bear J. Dynamics of fluids in porous media. Dover Publications; 1988;784 pp.
  24. Batchelor GK. An introduction to fluid dynamics. Cambridge Math. Lib., Cambridge Univ. Press; 2000;635 pp.
  25. Moll W, Wallenburg HCS, Kastendieck E, Voslar M. The flow resistance of the spiral artery and the related intervillous space in the rhesus monkey placenta. Pflügers Arch Eur J Physiol. 1978;377:225–228
  26. Borell U, Fernström I, Ohlson L, Wiqvist N. An arteriographic study of the blood flow through the uterus and the placenta at midpregnancy. Acta Obstet Gynecol Scand. 1965;44:22–31
  27. Soghomonians A, Barakat AI, Thirkill TL, Blankenship TN, Douglas GC. Effect of shear stress on migration and integrin expression in macaque trophoblast cells. Biochim Biophys Acta, Mol Cell Res. 2002;1589:233–246
  28. Hempstock J, Bao YP, Bar-Issac M, Segaren N, Watson AL, Charnock-Jones DS, et al. Intralobular differences in antioxidant enzyme expression and activity reflect the pattern of maternal arterial bloodflow within the human placenta. Placenta. 2003;24:517–523
  29. Konje JC, Huppertz B, Bell SC, Taylor DJ, Kaufmann P. 3-dimensional colour power angiography for staging human placental development. Lancet. 2003;362:1199–1201
  30. Abramowicz J, Sheiner E. Ultrasound of the placenta: a systematic approach. part II: functional assessment (Doppler). Placenta. 2008;29:921–929
  31. Mayhew TM. Patterns of villous and intervillous space growth in human placentas from normal and abnormal pregnancies. Eur J Obstet Gynecol Reprod Biol. 1996;68:75–82
  32. Popel AS, Johnson PC. Microcirculation and hemorheology. Annu Rev Fluid Mech. 2005;37:43–69
  33. Aifantis EC. Towards a rational modeling for the human placenta. Math Biosci. 1978;40:281–301
  34. Wilbur WJ, Power GG, Longo LD. Water exchange in the placenta: a mathematical model. Am J Physiol Regul Integr Comp Physiol. 1978;235:R181–R199
  35. Schröder H. Fluid shift across the placenta: III. Application of a computer model of passive placental transfer. Placenta. 1982;3:349–357
  36. Groome LJ. A theoretical analysis of the effect of placental metabolism on fetal oxygenation under conditions of limited oxygen availability. Biosystems. 1991;26:45–56
  37. Banerjee RK, Kwon O, Vaidya VS, Back LH. Coupled oxygen transport analysis in the avascular wall of a coronary artery stenosis during angioplasty. J Biomech. 2008;41:475–479
  38. Roos MW, Sperber GO. A diffusion model of cerebral microischemia. Exp Neurol. 1997;147:142–150
  39. Prendergast CH, Parker KH, Gray R, Venkatesan S, Bannister P, Castro-Soares J, et al. Glucose production by the human placenta in vivo. Placenta. 1999;20:591–598
  40. Espinoza J, Romero R, Mee Kim Y, Kusanovic JP, Hassan S, Erez O, et al. Normal and abnormal transformation of the spiral arteries during pregnancy. J Perinat Med. 2006;34:447–458
  41. Moore KL, Persaud TVN. The developing human: clinically oriented embryology. 7th ed. Philadelphia: Saunders; 2003;560 pp.
  42. Milne-Thomson LM. Theoretical hydrodynamics. 5th ed. New York: Macmillan; 1968;743 pp

PII: S0143-4004(09)00347-6

doi: 10.1016/j.placenta.2009.11.003

Placenta
Volume 31, Issue 1 , Pages 44-52 , January 2010

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