The pressure drop from the umbilical vein to the heart plays a vital part in human fetal circulation. The bulk of the pressure drop is believed to take place at the inlet of the ductus venosus, a short narrow branch of the umbilical vein. In this study a generalized Bernoulli formulation was deduced to estimate this pressure drop. The model contains an energy dissipation term and flow-scaled velocities and pressures. The flow-scaled variables are related to their corresponding spatial mean velocities and pressures by certain shape factors. Further, based on physiological measurements, we established a simplified, rigid-walled, three-dimensional computational model of the umbilical vein and ductus venosus bifurcation for stationary flow conditions. Simulations were carried out for Reynolds numbers and umbilical vein curvature ratios in their respective physiological ranges. The shape factors in the Bernoulli formulation were then estimated for our computational models. They showed no significant Reynolds number or curvature ratio dependency. Further, the energy dissipation in our models was estimated to constitute 24 to 31 percent of the pressure drop, depending on the Reynolds number and the curvature ratio. The energy dissipation should therefore be taken into account in pressure drop estimates.

1.
Back
L.
,
Cho
Y.
, and
Crawford
D.
,
1986
, “
Phasic and spatial pressure measurements in a femoral artery branch model for pulsatile flow
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
108
, pp.
251
258
.
2.
Behrman
R. E.
,
Lees
M. H.
,
Peterson
E. N.
,
de Lannoy
C. W.
, and
Seeds
S. A.
,
1970
, “
Distribution of the circulation in the normal and asphyxiated fetal primate
,”
Am. J. Obstet. Gynecol.
, Vol.
108
, pp.
956
959
.
3.
Blanc
W.
,
1960
, “
Premature closure of the ductus venosus
,”
Am. J. Dis. Child.
, Vol.
100
, p.
572
572
.
4.
Chako
A.
, and
Reynolds
S.
,
1953
, “
Embryonic development in the human of the sphincter of the ductus venosus
,”
Anat. Rec.
, Vol.
151
, pp.
151
173
.
5.
Chang
L.
, and
Tarbell
J.
,
1988
, “
A numerical study of flow in curved tubes simulating coronary arteries
,”
J. Biomech.
, Vol.
27
, p.
927
927
.
6.
Cho
Y.
,
Back
L.
, and
Crawford
D.
,
1985
, “
Experimental investigation of branch flow ratio, angle and Reynolds number effects of the pressure and flow fields in arterial branch models
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
107
, pp.
257
267
.
7.
Collins, M., and Xu, X., 1990, “A predictive scheme for flow in arterial bifurcations: comparison with laboratory measurements,” in: F. Mosora, C. G. Caro, E. Krause, C. Baquey, and R. Pelissier, eds., Biomechanical Transport Processes, pp. 125–133, New York.
8.
Edelstone
D. I.
,
Rudolph
A. M.
, and
Heymann
M. A.
,
1978
, “
Liver and ductus venosus blood flows in fetal lambs in utero
,”
Circ. Res.
, Vol.
42
, pp.
426
433
.
9.
Edelstone
D. I.
, and
Rudolph
A. M.
,
1979
, “
Preferential streaming of ductus venosus blood to the brain and heart in fetal lambs
,”
Am. J. Physiol.
, Vol.
237
, pp.
H724–H729
H724–H729
.
10.
Fernandez
R.
,
De Witt
K.
, and
Botwin
M.
,
1976
, “
Pulsatile flow through a bifurcation with applications to arterial disease
,”
J. Biomech.
, Vol.
9
, p.
575
575
.
11.
Fluent, 1991, User’s guide, version 4.0.
12.
Guiot
C.
,
Pianta
P. G.
, and
Todros
T.
,
1992
, “
Modelling the feto-placental circulation: 1. a distributed network predicting umbilical haemodynamics throughout pregnancy
,”
Ultrasound Med. Biol.
, Vol.
18
, No.
6–7
, pp.
535
544
.
13.
Hatle
L.
,
Brubakk
A.
,
Tromsdal
A.
, and
Angelsen
B.
,
1978
, “
Non-invasive assessment of pressure drop in mitral stenosis by doppler ultrasound
,”
Br. Heart J.
, Vol.
40
, pp.
131
140
.
14.
Holen
J.
,
Aaslid
R.
,
Landmark
K.
, and
Simonsen
S.
,
1976
, “
Determination of pressure gradient in mitral stenosis with a non-invasive ultrasound doppler technique
,”
Acta Med. Scand.
, Vol.
199
, pp.
455
460
.
15.
Huisman
T.
,
Stewart
P.
, and
Wladimiroff
J.
,
1992
, “
Ductus venosus blood flow velocity waveforms in the human fetus—a Doppler study
,”
Ultrasound Med. Biol.
, Vol.
18
, pp.
33
37
.
16.
Jouppila
P.
,
Kirkinen
P.
, and
Puukka
R.
,
1986
, “
Correlation between umbilical vein blood flow and umbilical blood viscosity in normal and complicated pregnancies
,”
Arch. Gynecol.
, Vol.
237
, pp.
191
197
.
17.
Kiserud
T.
,
Eik-Nes
S.
,
Blaas
H.
, and
Hellevik
L.
,
1991
, “
Ultrasonographic velocimetry in the fetal ductus venosus
,”
Lancet
, Vol.
388
, pp.
1412
1414
.
18.
Kiserud
T.
,
Eik-Nes
S.
,
Hellevik
L.
, and
Blaas
H.
,
1992
, “
Ductus venosusa longitudinal doppler velocimetric study of the human fetus
,”
J. Maternal Fetal Invest.
, Vol.
2
, pp.
5
11
.
19.
Kiserud
T.
,
Eik-Nes
S.
,
Hellevik
L.
, and
Blaas
H.
,
1993
, “
Ductus venosus blood velocity changes in fetal cardiac diseases
,”
J. Maternal Invest.
, Vol.
3
, pp.
15
20
.
20.
Kiserud
T.
,
Hellevik
L.
,
Eik-Nes
S.
,
Angelsen
B.
, and
Blaas
H.-G.
,
1994
, “
Estimation of the pressure gradient across the fetal ductus venosus based on doppler velocimetry
,”
Ultrasound Med. Biol.
, Vol.
20
, pp.
225
232
.
21.
Liepsch
D.
,
Moravec
S.
,
Rastogi
A.
, and
Vlachos
N.
,
1982
, “
Measurement and calculations of laminar flow in a ninety degree bifurcation
,”
J. Biomech.
, Vol.
15
, p.
473
473
.
22.
Liepsch, D., ed., 1994, Biofluid Mechanics. Proc. 3rd International Symposium, VDI Verlag.
23.
Lou, Z., and Yang, W., 1991, “A computer simulation of the blood flow at the aortic bifurcation,” Bio-Med. Mater. Eng., Vol. 173, No. 1.
24.
Lou
Z.
, and
Yang
W.
,
1992
, “
Biofluid dynamics at arterial bifurcations
,”
Crit. Rev. Biomed. Eng.
, Vol.
19
, No.
6
, pp.
455
493
.
25.
Lou, Z., and Yang, W., 1993, “A computer simulation of the non-Newtonian blood flow at the aortic bifurcation,” J. Biomech., Vol. 173, No. 1.
26.
McDonald, D. A., 1973, Blood Flow in Arteries, 2nd ed., The Camelot Press, Southampton, England.
27.
Oepkes
D.
,
Vandenbussche
F.
, and
Kanhai
H.
,
1993
, “
Fetal ductus venosus blood flow velocities before and after transfusion in red-cell alloimmunized pregnancies
,”
Obstet. Gynecol.
, Vol.
82
, pp.
237
241
.
28.
Patankar, S. V., 1980, Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corporation.
29.
Pedley, T., 1980, The Fluid Mechanics of Large Blood Vessels, Cambridge University Press.
30.
Perktold
K.
,
Nerem
R.
, and
Peter
R.
,
1991
a, “
A numerical calculation of flow in a curved tube model of the left main coronary artery
,”
J. Biomech.
, Vol.
24
, No.
3/4
, pp.
175
189
.
31.
Perktold
K.
,
Peter
R.
,
Resch
M.
, and
Langs
G.
,
1991
b, “
Pulsatile non-Newtonian blood flow in three-dimensional carotid bifurcation models: A numerical study of flow phenomena under different bifurcation angles
,”
J. Biomed. Eng.
, Vol.
13
, pp.
507
515
.
32.
Perktold
K.
,
Resch
M.
, and
Peter
R.
,
1991
c, “
Three-dimensional numerical analysis of pulsatile flow and all shear stress in the carotid artery bifurcation
,”
J. Biomech.
, Vol.
24
, No.
6
, pp.
409
420
.
33.
Perktold
K.
,
Thurner
E.
, and
Kenner
T.
,
1994
, “
Flow and stress characteristics in rigid walled and compliant carotid artery bifurcation models
,”
Med. Biol. Eng. Comp.
, Vol.
32
, pp.
19
26
.
34.
Power, H., ed., 1995, Bio-fluid Mechanics, Computational Mechanics Publications, Southampton, England.
35.
Reuderink, P., 1991, “Analysis of the flow in a 3D distensible model of the carotid artery bifurcation,” Ph.D. thesis, The Eindhoven Institute of Technology, The Netherlands.
36.
Sadeghipour, M., and Hajari, B., 1995, “Pulsatile blood flow in deformable vessels—non-Newtonian behavior,” in Proc. 1995 Bioengineering Conference, Vol. 29, pp. 345–346, ASME BED-Div.
37.
Thompson
R.
, and
Stevens
R.
,
1989
, “
Mathematical model for interpretation of doppler velocity waveform indices
,”
Med. Biol. Eng. Comput.
, Vol.
27
, pp.
269
276
.
38.
Trudinger
B.
,
Giles
W.
,
Cook
C.
,
Bomardieri
J.
, and
Collins
L.
,
1985
, “
Fetal umbilical artery flow velocity waveform and placental resistance: clinical significance
,”
Br. J. Obstet. Gynaecol.
, Vol.
92
, pp.
23
30
.
39.
van Splunder
I.
,
Stijnen
T.
, and
Wladimiroff
J.
,
1995
, “
Fetal pressure-gradient estimations across the ductus venosus in early-pregnancy using doppler ultrasonography
,”
Ultrasound Obstet. Gynecol.
Vol.
6
, No.
5
, pp.
334
339
.
40.
Ward-Smith, A., 1980, Internal fluid flow. The fluid dynamics of flow in pipes and ducts, Clarendon Press, Oxford, England.
41.
Xu
X.
, and
Collins
M.
,
1990
, “
A review of the numerical analysis of blood flow in arterial bifurcations
,”
J. Eng. Med.
, Vol.
204
, pp.
205
216
.
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