The three dimensionally curved aortic arch is modeled as a portion of a helical pipe. Pulsatile blood flow therein is calculated assuming helical symmetry and an experimentally measured pressure pulse. Appropriate values for the Womersley and Reynolds numbers are taken from allometric scaling relations for a variety of body masses. The flow structure is discussed with particular reference to the wall shear, which is believed to be important in the inhibition of atheroma. It is found that nonplanar curvature limits the severity of flow separation at the inner bend, and reduces spatial variation of wall shear. [S0148-0731(00)00402-7]

1.
Caro
,
C. G.
,
Fitz-Gerald
,
J. M.
, and
Schroter
,
R. C.
,
1971
, “
Atheroma and Arterial Wall Shear: Observation, Correlation and Proposal of a Shear Dependent Mass Transfer Mechanism of Atherogenesis
,”
Proc. R. Soc. London, Ser. B
,
177
, pp.
109
159
.
2.
Caro
,
C. G.
,
Doorly
,
D. J.
,
Tarnawski
,
M.
,
Scott
,
K. T.
,
Long
,
Q.
, and
Dumoulin
,
C. L.
,
1996
, “
Non-planar Curvature and Branching of Arteries and Non-planar-type of Flow
,”
Proc. R. Soc. London, Ser. A
,
452
, pp.
185
197
.
3.
Zabielski
,
L.
, and
Mestel
,
A. J.
,
1998
, “
Steady Flow in a Helically Symmetric Pipe
,”
J. Fluid Mech.
,
370
, pp.
297
320
.
4.
Zabielski
,
L.
, and
Mestel
,
A. J.
,
1998
, “
Unsteady Blood Flow in a Helically Symmetric Pipe
,”
J. Fluid Mech.
,
370
, pp.
321
345
.
5.
Childress, S., Landman, M., and Strauss, H., 1989, “Steady Motion With Helical Symmetry at Large Reynolds Number,” in: Proc. IUTAM Symp. on Topological Fluid Dynamics, H. K. Moffatt and A. Tsinober, eds., Cambridge University Press, pp. 216–224.
6.
Dean
,
W. R.
,
1928
, “
The Streamline Motion of Fluid in a Curved Pipe
,”
Philos. Mag.
,
30
, pp.
673
695
.
7.
Lyne
,
W. H.
,
1970
, “
Unsteady Viscous Flow in a Curved Pipe
,”
J. Fluid Mech.
,
45
, pp.
13
31
.
8.
Schmidt-Nielsen, K., 1984, Scaling: Why Is Animal Size So Important? Cambridge University Press.
9.
Chandran
,
K. B.
,
1993
, “
Flow Dynamics in the Human Aorta
,”
ASME J. Biomech. Eng.
,
115
, pp.
611
616
.
10.
Stahl
,
W. R.
,
1968
, “
Scaling of Respiratory Variables in Mammals
,”
J. Appl. Phys.
,
22
, pp.
453
460
.
11.
Pedley, T. J., 1978, “The Fluid Mechanics of Circulatory Systems,” Comparative Physiology—Water, Ions and Fluid Mechanics, Schmidt-Nielsen, Bolis, and Maddrell, eds., pp. 283–301.
12.
Clark, A. J., 1927, Comparative Physiology of the Heart, MacMillan, New York.
13.
Kleiber
,
M.
,
1932
, “
Body Size and Metabolism
,”
Hilgardia
,
6
, pp.
315
353
.
14.
Smith
,
F. T.
,
1976
, “
Steady Motion in a Curved Pipe
,”
Proc. R. Soc. London, Ser. A
,
347
, pp.
345
370
.
15.
Parker, K. H., 1998, private communication, Imperial College, London.
16.
McDonald, D. A., 1990, Blood Flow in Arteries, The Camelot Press Ltd., Southampton, United Kingdom.
17.
Kilner
,
P. J.
,
Yanz
,
G. Z.
,
Mohiaddin
,
R. H.
,
Firmin
,
D. N.
, and
Longmore
,
D. B.
,
1993
, “
Helical and Retrograde Secondary Flow Patterns in the Aortic Arch Studied by Three-Dimensional Magnetic Resonance Velocity Mapping
,”
Circulation
,
5
, pp.
2235
2247
.
18.
Axel, L., McLean, M., Tarnawski, M., Doorly, D. J., Dumoulin, C. L., and Caro, C. G., 1996, “Magnetic Resonance Imaging of Helical Flows,” Proc. Society of Magnetic Resonance 4th Scientific Meeting, New York.
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