A multiplicity of secondary flow morphologies is produced in the arterial network due to complexities in geometry (such as curvature, branching, and tortuosity) and pulsatility in the blood flow. In clinical literature, these morphologies have been called “spiral blood flow structures” and have been associated with a protective role toward arterial wall damage in the ascending and abdominal aorta. Persistent secondary flow (vortical) structures as observed experimentally in planar cross sections have been associated with flow instabilities. This study presents the results of two rigorous in vitro experimental investigations of secondary flow structures within a 180-deg bent tube model of curved arteries. First, phase-averaged, two-component, two-dimensional, particle image velocimetry (2C-2D PIV) experiments were performed at the George Washington University. Second, phase-locked, three-component, three-dimensional magnetic resonance velocimetry (3C-3D MRV) measurements were done at the Richard M. Lucas Center at Stanford University. Under physiological (pulsatile) inflow conditions, vortical patterns of a variety of scales, swirl magnitudes (strengths), and morphologies were found. A continuous wavelet transform (CWT) algorithm (pivlet 1.2) was developed for coherent structure detection and applied to out-of-plane vorticity (ω) fields. Qualitative comparisons of coherent secondary flow structures from the PIV and magnetic resonance velocimetry (MRV) data were made. In addition to the qualitative depiction of such planar vortical patterns, a regime map has also been presented. The phase dependence of the secondary flow structures under physiological flow conditions and the concomitant 3D nature of these vortical patterns required the full resolution of the flow field achieved by MRV techniques.

References

References
1.
Womersley
,
J. R.
,
1955
, “
Method for the Calculation of Velocity, Rate of Flow and Viscous Drag in Arteries When the Pressure Gradient Is Known
,”
J. Physiol.
,
1
, pp.
553
563
.
2.
Lyne
,
W. H.
,
1971
, “
Unsteady Viscous Flow in a Curved Pipe
,”
J. Fluid Mech.
,
45
, pp.
13
31
.
3.
Dean
,
W. R.
,
1927
, “
Note on the Motion of a Fluid in a Curved Pipe
,”
Philos. Mag. Series 7
,
4
(20), pp.
208
223
.
4.
Dean
,
W. R.
,
1928
, “
The Streamline Motion of a Fluid in a Curved Pipe
,”
Philos. Mag. Series 7
,
5
(30), pp.
673
695
.
5.
Siggers
,
J. H.
, and
Walters
,
S. L.
,
2008
, “
Unsteady Flows in Pipes With Finite Curvature
,”
J. Fluid Mech.
,
600
, pp.
133
165
.
6.
Ault
,
J. T.
,
Chen
,
K. K.
, and
Stone
,
H. A.
,
2015
, “
Downstream Decay of Fully Developed Dean Flow
,”
J. Fluid Mech.
,
777
, pp.
219
244
.
7.
Zamir
,
M.
,
2000
,
The Physics of Pulsatile Flow
(Biological Physics Series),
Springer
,
Heidelberg, Germany
.
8.
Fung
,
Y. C.
,
1996
,
Biomechanics: Circulation
,
2 ed.
,
Springer
,
Heidelberg, Germany
.
9.
Hamakiotes
,
C. C.
, and
Berger
,
S. A.
,
1988
, “
Fully Developed Pulsatile Flow in a Curved Pipe
,”
J. Fluid Mech.
,
195
, pp.
23
55
.
10.
Bulusu
,
K. V.
, and
Plesniak
,
M. W.
,
2015
, “
Shannon Entropy-Based Wavelet Transform Method for Autonomous Coherent Structure Identification in Fluid Flow Field Data
,”
Entropy
,
17
(
10
), pp.
6617
6642
.
11.
Waters
,
S. L.
, and
Pedley
,
T. J.
,
1999
, “
Oscillatory Flow in a Tube of Time-Dependent Curvature. Part 1. Perturbation to Flow in a Stationary Curved Tube
,”
J. Fluid Mech.
,
383
, pp.
327
352
.
12.
Pedley
,
T. J.
,
1980
,
The Fluid Mechanics of Large Blood Vessels
,
Cambridge University Press
, New York.
13.
Zalosh
,
R. G.
, and
Nelson
,
W. G.
,
1973
, “
Pulsating Flow in a Curved Tube
,”
J. Fluid Mech.
,
59
(
4
), pp.
693
705
.
14.
Singh
,
M. P.
,
1974
, “
Entry Flow in a Curved Pipe
,”
J. Fluid Mech.
,
65
(
3
), pp.
517
539
.
15.
Smith
,
F. T.
,
1975
, “
Pulsatile Flow in Curved Pipes
,”
J. Fluid Mech.
,
71
(
part 1
), pp.
15
42
.
16.
Yao
,
L. S.
, and
Berger
,
S. A.
,
1975
, “
Entry Flow in a Curved Pipe
,”
J. Fluid Mech.
,
67
(
1
), pp.
177
196
.
17.
Bulusu
,
K. V.
, and
Plesniak
,
M. W.
,
2013
, “
Secondary Flow Morphologies Due to Model Stent-Induced Perturbations in a 180-degree Curved Tube During Systolic Deceleration
,”
Exp. Fluids
,
54
(
3
), p.
1493
.
18.
Bulusu
,
K. V.
,
Hussain
,
S.
, and
Plesniak
,
M. W.
,
2014
, “
Determination of Secondary Flow Morphologies by Wavelet Analysis in a Curved Artery Model With Physiological Inflow
,”
Exp. Fluids
,
55
(
11
), p.
1832
.
19.
Mallubhotla
,
H.
,
Belfort
,
G.
,
Edelstein
,
W. A.
, and
Early
,
T. A.
,
2001
, “
Dean Vortex Stability Using Magnetic Resonance Flow Imaging and Numerical Analysis
,”
AIChE J.
,
47
(
5
), pp.
1126
1139
.
20.
Evegren
,
P.
,
Fuchs
,
L.
, and
Revstedt
,
J.
,
2010
, “
On the Secondary Flow Through Bifurcating Pipes
,”
Phys. Fluids
,
22
(
10
), p.
103601
.
21.
Sengupta
,
P. P.
,
Burke
,
R.
,
Khandheria
,
B. K.
, and
Belohlavek
,
M.
,
2008
, “
Following the Flow in Chambers
,”
Heart Failure Clin.
,
4
(
3
), pp.
325
332
.
22.
Stonebridge
,
P. A.
,
Hoskins
,
P. R.
,
Allan
,
P. L.
, and
Belch
,
J. F.
,
1996
, “
Spiral Laminar Flow in vivo
,”
Clin. Sci. (London)
,
91
(
1
), pp.
17
21
.
23.
Stonebridge
,
P.
, and
Brophy
,
C. M.
,
1991
, “
Spiral Laminar Flow in Arteries?
,”
Lancet
,
338
(
8779
), pp.
1360
1361
.
24.
Houston
,
J. G.
,
Gandy
,
S. J.
,
Sheppard
,
D. G.
,
Dick
,
J. B.
,
Belch
,
J. J.
, and
Stonebridge
,
P. A.
,
2003
, “
Two-Dimensional Flow Quantitative MRI of Aortic Arch Blood Flow Patterns: Effect of Age, Sex, and Presence of Carotid Atheromatous Disease on Prevalence of Spiral Blood Flow
,”
J. Magn. Reson. Imaging
,
18
(
2
), pp.
169
174
.
25.
Houston
,
J. G.
,
Gandy
,
S. J.
,
Milne
,
W.
,
Dick
,
J. B.
,
Belch
,
J. J.
, and
Stonebridge
,
P. A.
,
2004
, “
Spiral Laminar Flow in the Abdominal Aorta: A Predictor of Renal Impairment Deterioration in Patients With Renal Artery Stenosis?
,”
Nephrol Dial. Transplant.
,
19
(
7
), pp.
1786
1791
.
26.
Berger
,
S. A.
, and
Jou
,
L.-D.
,
2000
, “
Flows in Stenotic Vessels
,”
Annu. Rev. Fluid Mech.
,
32
(
1
), pp.
347
382
.
27.
Barakat
,
A. I.
, and
Lieu
,
D. K.
,
2003
, “
Differential Responsiveness of Vascular Endothelial Cells to Different Types of Fluid Mechanical Shear Stress
,”
Cell Biochem. Biophys.
,
38
(
3
), pp.
323
344
.
28.
White
,
C. R.
, and
Frangos
,
J. A.
,
2010
, “
The Shear Stress of It All: The Cell Membrane and Mechanochemical Transduction
,”
Philos. Trans. R. Soc. B
,
362
, pp.
1459
1467
.
29.
Melchior
,
B.
, and
Frangos
,
J. A.
,
2010
, “
Shear-Induced Endothelial Cell-Cell Junction Inclination
,”
Am. J. Physiol. Cell Physiol.
,
299
(
3
), pp.
C621
C629
.
30.
Caro
,
C. G.
,
Fitz-Gerald
,
J. M.
, and
Schroter
,
C.
,
1971
, “
Atheroma and Arterial Wall Shear. Observation, Correlation and Proposal of a Shear Dependent Mass Transfer Mechanism for Atherogenesis
,”
Proc. R. Soc. London B
,
177
(
1046
), pp.
109
159
.
31.
Hoi
,
Y.
,
Zhou
,
Y.-Q.
,
Zhang
,
X.
,
Henkelman
,
R. M.
, and
Steinman
,
D. A.
,
2011
, “
Correlation Between Local Hemodynamics and Lesion Distribution in a Novel Aortic Regurgitation Murine Model of Atherosclerosis
,”
Ann. Biomed. Eng.
,
39
(
5
), pp.
1414
1422
.
32.
Friedman
,
M. H.
,
2009
, “
Variability of Arterial Wall Shear Stress, Its Dependence on Vessel Diameter and Implications for Murray's Law
,”
Atherosclerosis
,
203
(
1
), pp.
47
48
.
33.
Himburg
,
H. A.
,
Grzybowski
,
D. M.
,
Hazel
,
A. L.
,
LaMack
,
J. A.
,
Li
,
X.-M.
, and
Friedman
,
M. H.
,
2004
, “
Spatial Comparison Between Wall Shear Stress Measures and Porcine Arterial Endothelial Permeability
,”
Am. J. Physiol. Heart Circ. Physiol.
,
286
(
5
), pp.
H1916
H1922
.
34.
Himburg
,
H. A.
,
Dowd
,
S. E.
, and
Friedman
,
M. H.
,
2007
, “
Frequency-Dependent Response of the Vascular Endothelium to Pulsatile Shear Stress
,”
Am. J. Physiol. Heart Circ. Physiol.
,
293
(
1
), pp.
H645
H653
.
35.
Himburg
,
H. A.
, and
Friedman
,
M. H.
,
2006
, “
Correspondence of Low Mean Shear and High Harmonic Content in the Porcine Iliac Arteries
,”
ASME. J. Biomed. Eng.
,
128
(
6
), pp.
852
856
.
36.
Glenn
,
A. L.
,
2011
, “
Classification of Secondary Vortices in a Curved Pipe Model of an Artery
,” M.S. thesis, The George Washington University, Washington, DC.
37.
Glenn
,
A. L.
,
Bulusu
,
K. V.
,
Shu
,
F.
, and
Plesniak
,
M. W.
,
2012
, “
Secondary Flow Structures Under Stent-Induced Perturbations for Cardiovascular Flow in a Curved Artery Model
,”
Int. J. Heat Fluid Flow
,
35
, pp.
76
83
.
38.
van Wyk
,
S.
,
Wittberg
,
L. P.
,
Bulusu
,
K. V.
,
Fuchs
,
L.
, and
Plesniak
,
M. W.
,
2015
, “
Non-Newtonian Perspectives on Pulsatile Blood-Analog Flows in a 180-degree Curved Artery Model
,”
Phys. Fluids
,
27
(
7
), p.
071901
.
39.
Timité
,
B.
,
Castelian
,
C.
, and
Peerhossaini
,
H.
,
2010
, “
Pulsatile Viscous Flow in a Curved Pipe: Effects of Pulsation on the Development of Secondary Flow
,”
Int. J. Heat Fluid Flow
,
31
(
5
), pp.
879
896
.
40.
Boiron
,
O.
,
Deplano
,
V.
, and
Pelissier
,
R.
,
2007
, “
Experimental and Numerical Studies on the Starting Effect on the Secondary Flow in a Bend
,”
J. Fluid Mech.
,
574
, pp.
109
129
.
41.
Jarrahi
,
M.
,
Castelain
,
C.
, and
Peerhossain
,
H.
,
2011
, “
Secondary Flow Patterns and Mixing in Laminar Pulsating Flow Through a Curved Pipe
,”
Exp. Fluids
,
50
(
6
), pp.
1539
1558
.
42.
Rindt
,
C. M. M.
,
van Steenhoven
,
A. A.
,
Janssen
,
J. D.
, and
Vossers
,
G.
,
1991
, “
Unsteady Entrance Flow in a 90 deg Curved Tube
,”
J. Fluid Mech.
,
226
, pp.
445
474
.
43.
Sudo
,
K.
,
Sumida
,
M.
, and
Yamane
,
R.
,
1992
, “
Secondary Motion of Fully Developed Oscillatory Flow in a Curved Pipe
,”
J. Fluid Mech.
,
237
, pp.
189
208
.
44.
Eustice
,
J.
,
1910
, “
Flow of Water in Curved Pipes
,”
Proc. R. Soc. London A
,
84
(
568
), pp.
107
118
.
45.
Peterson
,
S. D.
, and
Plesniak
,
M. W.
,
2008
, “
The Influence of Inlet Velocity Profile and Secondary Flow on Pulsatile Flow in a Model Artery With Stenosis
,”
J. Fluid Mech.
,
616
, pp.
263
301
.
46.
Budwig
,
R.
,
1994
, “
Refractive Index Matching Methods for Liquid Flow Investigations
,”
Exp. Fluids
,
17
(
5
), pp.
350
355
.
47.
Yousif
,
M. Y.
,
Holdsworth
,
D. W.
, and
Poepping
,
T. L.
,
2011
, “
A Blood-Mimicking Fluid for Particle Image Velocimetry With Silicone Vascular Models
,”
Exp. Fluids
,
50
(
3
), pp.
769
774
.
48.
Deutsch
,
S.
,
Tarbell
,
J. M.
,
Manning
,
K. B.
,
Rosenberg
,
G.
, and
Fontaine
,
A. A.
,
2006
, “
Experimental Fluid Mechanics of Pulsatile Artificial Blood Pumps
,”
Annu. Rev. Fluid Mech.
,
38
(
1
), pp.
65
86
.
49.
Holdsworth
,
D.
,
Norley
,
C. J.
,
Frayne
,
R.
,
Steinman
,
D. A.
, and
Rutt
,
B. K.
,
1999
, “
Characterization of Common Carotid Artery Blood-Flow Waveforms in Normal Human Subjects
,”
Physiol. Meas.
,
20
(
3
), pp.
219
240
.
50.
Adrian
,
R. J.
,
1997
, “
Dynamic Ranges of Velocity and Spatial Resolution of Particle Image Velocimetry
,”
Meas. Sci. Technol.
,
8
(
12
), pp.
1393
1398
.
51.
Sciacchitano
,
A.
,
Neal
,
D. R.
,
Smith
,
B. L.
,
Warner
,
S. O.
,
Vlachos
,
P. P.
,
Wieneke
,
B.
, and
Scarano
,
F.
,
2014
, “
Collaborative Framework for PIV Uncertainty Quantification: Comparative Assessment of Method
,”
17th International Symposium on Applications of Laser Techniques to Fluid Mechanics
,
Lisbon
,
Portugal
, July 7–10.
52.
Elkins
,
C. J.
, and
Alley
,
M. T.
,
2007
, “
Magnetic Resonance Velocimetry: Applications of Magnetic Resonance Imaging in the Measurement of Fluid Motion
,”
Exp. Fluids
,
43
(
6
), pp.
823
858
.
53.
Pelc
,
N. J.
,
Sommer
,
G.
,
Li
,
K. C. P.
,
Brosnan
,
T. J.
,
Herfkens
,
R. J.
, and
Enzmann
,
D. R.
,
1994
, “
Quantitative Magnetic Resonance Flow Imaging
,”
Magn. Reson. Q.
,
10
(
3
), pp.
125
147
.
54.
Banko
,
A.
,
Coletti
,
F.
,
Schiavazzi
,
D.
,
Elkins
,
C.
, and
Eaton
,
J.
,
2015
, “
Three-Dimensional Inspiratory Flow in the Upper and Central Human Airways
,”
Exp. Fluids
,
56
(
6
), pp.
117
128
.
55.
Mitchell
,
D. G.
,
1999
,
MRI Principles
,
W. B. Saunders Company
, Philadelphia, PA.
56.
Pelc
,
N. J.
,
Bernstein
,
M. A.
,
Shimakawa
,
A.
, and
Glover
,
G. H.
,
1991
, “
Encoding Strategies for Three-Direction Phase Contrast MR Imaging of Flow
,”
J Magn. Reson. Imaging
,
1
(
4
), pp.
405
413
.
57.
Markl
,
M.
,
Alley
,
M. T.
, and
Pelc
,
N. J.
,
2003
, “
Balanced Phase-Contrast Steady-State Free Precession (PC-SSFP): A Novel Technique for Velocity Encoding by Gradient Inversion
,”
Magn. Reson. Med.
,
49
(
5
), pp.
945
952
.
58.
Markl
,
M.
,
Bammer
,
R.
,
Alley
,
M. T.
,
Elkins
,
C. J.
,
Draney
,
M. T.
,
Barnett
,
A.
,
Moseley
,
M. E.
,
Glover
,
G. H.
, and
Pelc
,
N. J.
,
2003
, “
Generalized Reconstruction of Phase Contrast MRI: Analysis and Correction of the Effect of Gradient Field Distortions
,”
Magn. Reson. Med.
,
50
(
4
), pp.
791
801
.
59.
Jeong
,
J.
, and
Hussain
,
F.
,
1995
, “
On the Identification of a Vortex
,”
J. Fluid Mech.
,
285
, pp.
69
94
.
60.
Camussi
,
R.
, and
Guj
,
G.
,
1997
, “
Orthonormal Wavelet Decomposition of Turbulent Flows: Intermittency and Coherent Structures
,”
J. Fluid Mech.
,
348
, pp.
177
199
.
61.
Camussi
,
R.
,
2002
, “
Coherent Structure Identification From Wavelet Analysis of Particle Image Velocimetry Data
,”
Exp. Fluids
,
32
(
1
), pp.
76
86
.
62.
Kailas
,
S. V.
, and
Narasimha
,
R.
,
1999
, “
The Education of Structures From Flow Imagery Using Wavelets: Part I. The Mixing Layer
,”
Exp. Fluids
,
27
, pp.
167
174
.
63.
Schram
,
C.
, and
Riethmuller
,
M. L.
,
2001
, “
Vortex Ring Evolution in an Impulsively Started Jet Using Digital Particle Image Velocimetry and Continuous Wavelet Analysis
,”
Meas. Sci. Technol.
,
12
(
9
), pp.
1413
1421
.
64.
Farge
,
M.
,
Guezennec
,
Y.
,
Ho
,
C. M.
, and
Meneveau
,
C.
,
1990
, “
Continuous Wavelet Analysis of Coherent Structures
,” Center for Turbulence Research, Summer Program, pp.
331
348
.
65.
Varun
,
A. V.
,
Balasubraminian
,
K.
, and
Sujith
,
R. I.
,
2008
, “
An Automated Vortex Detection Scheme Using the Wavelet Transform of the d2 Field
,”
Exp. Fluids
,
45
(
5
), pp.
857
868
.
66.
Zhuang
,
Y.
, and
Baras
,
J. S.
,
1994
, “
Optimal Wavelet Basis Selection for Signal Representation
,” Technical Research Report CSHCN T.R. 94-7, Center for Satellite and Hybrid Communication Networks (CSHCN), Institute for Systems Research (ISR), University of Maryland, College Park, MD, Report No. ISR TR 1994-3.
67.
Shannon
,
C. E.
,
1948
, “
A Mathematical Theory for Communication
,”
Bell Syst. Tech. J.
,
27
(
3
), pp.
379
423
.
68.
Shu
,
F.
,
Vandenberghe
,
S.
, and
Antaki
,
J. F.
,
2009
, “
The Importance of dq/dt on the Flow Field in a Turbodynamic Pump With Pulsatile Flow
,”
Artif. Organs
,
33
(
9
), pp.
757
762
.
69.
Shu
,
F.
,
Vandenberghe
,
S.
,
Miller
,
P. J.
, and
Antaki
,
J. F.
,
2008
, “
Comprehensive Classification of Flow Patterns in a Centrifugal Blood Pump Under Pulsatile Conditions
,”
16th Congress of the International Society for Rotary Blood Pumps (ISRBP)
, Houston, TX, Vol.
33
, pp.
409
413
.
70.
Chakraborty
,
P.
,
Balachander
,
S.
, and
Adrian
,
R. J.
,
2005
, “
On the Relationships Between Local Vortex Identification Schemes
,”
J. Fluid Mech.
,
535
, pp.
189
214
.
71.
Wallace
,
J. M.
,
2009
, “
Twenty Years of Experimental and Direct Numerical Simulation Access to the Velocity Gradient Tensor: What Have We Learned About Turbulence?
,”
Phys. Fluids.
,
21
(
2
), p.
021301
.
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