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An assessment of ductus venosus tapering and wave transmission from the fetal heart

  • Leif Rune HellevikEmail author
  • J. Vierendeels
  • T. Kiserud
  • N. Stergiopulos
  • F. Irgens
  • E. Dick
  • K. Riemslagh
  • P. Verdonck
Original Paper

Abstract

Pressure and flow pulsations in the fetal heart propagate through the precordial vein and the ductus venosus (DV) but are normally not transmitted into the umbilical vein (UV). Pulsations in the umbilical vein do occur, however, in early pregnancy and in pathological conditions. Such transmission into the umbilical vein is not well understood. In particular, the effect of the impedance changes in the DV due to its tapered geometry is not known. This paper presents a mathematical model that we developed to study the transmission of pulsations, originating in the fetal heart, through the DV to the umbilical vein. In our model, the tapered geometry of the DV was found to be of minor importance and the only effective reflection site in the DV appears to be at the DV inlet. Differences between the DV inlet and outlet flow were also found to be minor for medium to large umbilical vein–DV diameter ratios. Finally, the results of a previously proposed lumped model were found to agree well with the present model of the DV–umbilical vein bifurcation.

Keywords

Wave propagation Ductus venosus Reflection 

References

  1. Acharya G, Kiserud T (1999) Pulsations of the ductus venosus blood velocity and diameter are more pronounced at the outlet than at the inlet. Eur J Obstet Gynecol Reprod Biol 84:149–154CrossRefGoogle Scholar
  2. Anderson D, Tannehill H, Pletcher R (1984) Computational fluid mechanics and heat transfer. Hemisphere Publishing Co., New YorkzbMATHGoogle Scholar
  3. Baschat A, Cosmi E, Bilardo C et al (2007) Predictors of neonatal outcome in early-onset placental dysfunction. Obstet Gynecol 109: 253–261Google Scholar
  4. Baschat A, Guclu S, Kush M, Gembruch U, Weiner C, Harman C (2004) Venous doppler in the prediction of acid-base status of growth-restricted fetuses with elevated placental blood flow resistance. Am J Obstet Gynecol 1991: 277–284CrossRefGoogle Scholar
  5. Behrman RE, Lees MH, Peterson EN, Lannoy CW, Seeds AE (1970) Distribution of the circulation in the normal and asphyxiated fetal primate. Am J Obstet Gynecol 108: 956–959Google Scholar
  6. Bellotti M, Pennati G, De Gasperi C, Battaglia F, Ferrazzi E (2000) Role of ductus venosus in distribution of umbilical flow in human fetuses during second half of pregnancy. Am J Physiol 279: H1256–H1263Google Scholar
  7. Borrell A, Antolin E, Costa D, Farre M, Martinez J, Fortuny A (1998) Abnormal ductus venosus blood flow in trisomy 21 fetuses during early pregnancy. Am J Obstet Gynecol 179: 1612–1617CrossRefGoogle Scholar
  8. Coceani F, Olley P (1988) The control of cardiovascular shunts in the fetal and perinatal period. Can J Pharmacol 66: 1129–1134Google Scholar
  9. Courant R, Friedrichs KO, Lewy H (1928) Über die Differenzengleichungen der Mathematischen Physik. Math Ann 100: 32zbMATHCrossRefMathSciNetGoogle Scholar
  10. Ebbing C, Rasmussen S, Kiserud T (2008a) Fetal celiac and splenic artery flow velocity and pulsatility index: longitudinal reference ranges and evidence for vasodilatation at a low portocaval pressure gradient. Ultrasound Obstet Gynecol 32:663–672CrossRefGoogle Scholar
  11. Ebbing C, Rasmussen S, Kiserud T (2008) Hepatic artery hemodynamics suggest operation of a buffer response in the human fetus. Reprod Sci 15: 166–178CrossRefGoogle Scholar
  12. Edelstone D, Rudolph A, Heymann M (1980) Effect of hypoxemia and decreasing umbilical flow on liver and ductus venosus blood flows in fetal lambs. Am J Physiol 238:H656–H663Google Scholar
  13. Fernandez R, De Witt K, Botwin M (1976) Pulsatile flow through a bifurcation with applications to arterial disease. J Biomech 9: 575CrossRefGoogle Scholar
  14. Gembruch U, Krapp M, Baumann P (1995) Changes of venous blood flow velocity waveforms in fetuses with supraventricular tachycardia. Ultrasound Obstet Gynecol 5: 392–399CrossRefGoogle Scholar
  15. Gudmundsson S, Huhta JC, Wood DC, Tulzer G, Cohen AW, Weiner S (1991) Venous doppler ultrasonography in the fetus with nonimmune hydrops. Am J Obstet Gynecol 164: 33–37Google Scholar
  16. Haugen G, Hanson M, Kiserud T, Crozier S, Inskip H, Godfrey K (2005) Fetal liver-sparing cardiovascular adaptations linked to mother’s slimness and diet. Circ Res 96: 12–14CrossRefGoogle Scholar
  17. Hecher K, Ville Y, Snijders R, Nicolaides K (1995) Doppler studies of the fetal circulation in twin-twin transfusion syndrome. Ultrasound Obstet Gynecol 5: 318–324CrossRefGoogle Scholar
  18. Hellevik LR, Kiserud T, Irgens F, Stergiopulos N, Hanson M (1998a) Mechanical properties of the fetal ductus venosus and the umbilical vein. Heart Vessels 13(4): 175–180CrossRefGoogle Scholar
  19. Hellevik LR, Kiserud T, Irgens F, Ytrehus T, Eik-Nes SH (1998b) Simulation of pressure drop and energy dissipation for blood flow in a human fetal bifurcation. J Biomech Eng 120(4): 455–462CrossRefGoogle Scholar
  20. Hellevik LR, Stergiopulos N, Kiserud T, Rabben S, Eik-Nes SH, Irgens F (2000) A mathematical model of umbilical venous pulsation. J Biomech 33(9): 1123–1130CrossRefGoogle Scholar
  21. Jouppila P, Kirkinen P, Puukka R (1986) Correlation between umbilical vein blood flow and umbilical blood viscosity in normal and complicated pregnancies. Arch Gynecol 237: 191–197CrossRefGoogle Scholar
  22. Kiserud T (1999) Hemodynamics of the ductus venosus. Eur J Obstet Gynecol Reprod Biol 84:149–154CrossRefGoogle Scholar
  23. Kiserud T, Crowe C, Hanson M (1998) Ductus venosus agenesis prevents transmission of central venous pulsation to the umbilical vein in fetal sheep. Ultrasound Obstet Gynecol 11: 190–194CrossRefGoogle Scholar
  24. Kiserud T, Ebbing C, Kessler J, Rasmussen S (2006) Fetal cardiac output, distribution to the placenta, and impact of placental compromise. Ultrasound Obstet Gynecol 28: 126–136CrossRefGoogle Scholar
  25. Kiserud T, Eik-Nes S, Blaas HG, Hellevik L (1991) Ultrasonographic velocimetry of the fetal ductus venosus. Lancet 338: 1412–1414CrossRefGoogle Scholar
  26. Kiserud T, Eik-Nes SH, Blaas HG, Hellevik LR, Simensen B (1994) Ductus venosus blood velocity and the umbilical circulation in the seriously growth retarded fetus. Ultrasound Obstet Gynecol 4: 109–114CrossRefGoogle Scholar
  27. Kiserud T, Eik-Nes SH, Hellevik LR, Blaas HG (1993) Ductus venosus blood velocity changes in fetal cardiac diseases. J Matern Fetal Invest 3: 15–20Google Scholar
  28. Kiserud T, Ozaki T, Nishina H, Rodeck C, Hanson M (2000a) Effect of no, phenylephrine and hypoxemia on the ductus venosus diameter in the fetal sheep. Am J Physiol 279: H1166–H1171Google Scholar
  29. Kiserud T, Rasmussen S, Skulstad S (2000b) Blood flow and degree of shunting through the ductus venosus in the human fetus. Am J Obstet Gynecol 182: 147–153CrossRefGoogle Scholar
  30. Kiserud T, Stratford L, Hanson M (1997) Umbilical flow distribution to the liver and ductus venosus: an in vitro investigation of the fluid dynamic mechanisms in the fetal sheep. Am J Obstet Gynecol 177: 86–90CrossRefGoogle Scholar
  31. Lingman G, Laurin J, Maršál K (1986) Circulatory changes in fetuses with imminent asphyxia. Biol Neonate 49: 66–73CrossRefGoogle Scholar
  32. MacCormack R (1969) The effect of viscosity in hypervelocity impact cratering. AIAA Pap No. 69–354Google Scholar
  33. Pennati G, Bellotti M, Ferrazzi E, Rigano S, Garberi A (1997) Hemodynamic changes across the human ductus venosus: a comparison between clinical findings and mathematical calculations. Ultrasound Obstet Gynecol 9: 383–391CrossRefGoogle Scholar
  34. Pythoud F (1996) Analysis of wave reflections in the arterial system. PhD thesis, École Polytechnique Fédérale de LausanneGoogle Scholar
  35. Raines J, Jaffrin M, Shapiro A (1974) A computer simulation of arterial dynamics in the human leg. J Biomech 7: 77–91CrossRefGoogle Scholar
  36. Rizzo G, Arduini D, Romanini C (1992) Umbilical vein pulsations: a physiologic finding in early gestation. Am J Obstet Gynecol 167(3): 675–677Google Scholar
  37. Tchirikov M, Kertschanska S, Schroder H (2003) Differential effects of cathecholamines on vascular rings from ductus venosus and intrahepatic veins of fetal sheep. J Physiol 548(Pt 2): 519–526CrossRefGoogle Scholar
  38. Tchirikov M, Kertschanska S, Sturenberg H, Schroder H (2002) Liver blood perfusion as a possible instrument for fetal growth regulation. Placenta 23: S153–S158CrossRefGoogle Scholar
  39. Tchirikov MSH, Kertschanska S (2001) Obstruction of ductus venosus stimulates cell proliferation in organs of fetal sheep. Placenta 22: 24–31CrossRefGoogle Scholar
  40. White FM (1988) Fluid mechanics chap 6.9. Mechanical engineering series, 2nd edn. McGraw-Hill, New YorkGoogle Scholar
  41. Womersley J (1957) An elastic tube theory of pulse transmission and oscillatory flow in mammalian arteries. Technical Report WADC Technical Report TR 56-614, Wright Air Development Center, Wright Patterson Air Force Base, OhioGoogle Scholar
  42. Young D, Tsai F (1973) Flow characteristics in models of arterial stenoses-II. unsteady flow. J Biomech 6: 547–559CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Leif Rune Hellevik
    • 1
    Email author
  • J. Vierendeels
    • 2
  • T. Kiserud
    • 3
    • 4
  • N. Stergiopulos
    • 5
  • F. Irgens
    • 1
  • E. Dick
    • 2
  • K. Riemslagh
    • 2
  • P. Verdonck
    • 6
  1. 1.Biomechanics Division, Department of Structural EngineeringThe Norwegian University of Science and Technology (NTNU)TrondheimNorway
  2. 2.Department of Flow, Heat and Combustion MechanicsGhent UniversityGhentBelgium
  3. 3.Department of Obstetrics and GynecologyHaukeland University HospitalBergenNorway
  4. 4.Department of Clinical MedicineUniversity of BergenBergenNorway
  5. 5.Biomedical Engineering Laboratory, EPFLLausanneSwitzerland
  6. 6.Institute Biomedical Technology Ghent UniversityGhentBelgium

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