Abstract

Genesis and onset of atherosclerosis are greatly influenced by hemodynamic forces. Two-phase transient computational fluid dynamic (CFD) simulations are performed using a mixture theory model for blood, and a transport equation for low-density lipoprotein (LDL), in idealized and patient-derived abdominal aorta to predict the sites at risk for atherosclerosis. Flow patterns at different time instants and relevant hemodynamic indicators—wall shear stress (WSS)-based (time-averaged wall shear stress (TAWSS), oscillatory shear index (OSI), and relative residence time (RRT)), and LDL concentration—are used concurrently to predict the susceptible sites of atherosclerosis. In the case of idealized geometry, flow recirculations are observed on the posterior wall opposite the superior mesenteric artery and below the renal bifurcations. Low TAWSS, high OSI, high RRT and high concentration of LDL are observed in these regions. This suggests that in idealized abdominal aorta, the posterior wall proximal to the renal artery junction is more prone to atherosclerosis. This matches qualitatively with the experimental and simulation data in the literature. In the case of patient-derived geometry, flow reversal, low TAWSS, high OSI and high RRT are observed infrarenal on the anterior wall. Further, high concentration of LDL is observed at the same location on the anterior wall suggesting anterior wall distal to the renal artery junction is more prone to atherosclerosis. These findings demonstrate the use of a novel method to predict the sites at risk for atherosclerosis in geometries where complexities like junctions and curvature play a major role.

References

References
1.
World Health Organization
,
2017
, “World Heart Day,” World Health Organization, Geneva, Switzerland, accessed Dec. 18, 2019, www.who.int/cardiovascular_diseases/world-heart-day/en/
2.
Prabhakaran
,
D.
,
Singh
,
K.
,
Roth
,
G. A.
,
Banerjee
,
A.
,
Pagidipati
,
N. J.
, and
Huffman
,
M. D.
,
2018
, “
Cardiovascular Diseases in India Compared With the United States
,”
J. Am. Coll. Cardiol.
,
72
(
1
), pp.
79
95
.10.1016/j.jacc.2018.04.042
3.
Ross
,
R.
,
1999
, “
Atherosclerosis'an Inflammatory Disease
,”
N. Engl. J. Med.
,
340
(
2
), pp.
115
126
.10.1056/NEJM199901143400207
4.
Rimmer
,
J. M.
, and
Gennari
,
F. J.
,
1993
, “
Atherosclerotic Renovascular Disease and Progressive Renal Failure
,”
Ann. Intern. Med.
,
118
(
9
), pp.
712
719
.10.7326/0003-4819-118-9-199305010-00010
5.
Safian
,
R. D.
, and
Textor
,
S. C.
,
2001
, “
Renal-Artery Stenosis
,”
N. Engl. J. Med.
,
344
(
6
), pp.
431
442
.10.1056/NEJM200102083440607
6.
Derkx
,
F.
, and
Schalekamp
,
M.
,
1994
, “
Renal Artery Stenosis and Hypertension
,”
Lancet
,
344
(
8917
), pp.
237
239
.10.1016/S0140-6736(94)93002-3
7.
Conlon
,
P. J.
,
Little
,
M. A.
,
Pieper
,
K.
, and
Mark
,
D. B.
,
2001
, “
Severity of Renal Vascular Disease Predicts Mortality in Patients Undergoing Coronary Angiography
,”
Kidney Int.
,
60
(
4
), pp.
1490
1497
.10.1046/j.1523-1755.2001.00953.x
8.
Tyralla
,
K.
, and
Amann
,
K.
,
2003
, “
Morphology of the Heart and Arteries in Renal Failure
,”
Kidney Int.
,
63
, pp.
S80
S83
.10.1046/j.1523-1755.63.s84.1.x
9.
Hiatt
,
W. R.
,
Regensteiner
,
J.
, and
Hirsch
,
A. T.
,
2001
,
Peripheral Arterial Disease Handbook
,
CRC Press
, Boca Raton, FL.
10.
Langille
,
B.
, and
O'Donnell
,
F.
,
1986
, “
Reductions in Arterial Diameter Produced by Chronic Decreases in Blood Flow Are Endothelium-Dependent
,”
Science
,
231
(
4736
), pp.
405
407
.10.1126/science.3941904
11.
Zarins
,
C. K.
,
Zatina
,
M. A.
,
Giddens
,
D. P.
,
Ku
,
D. N.
, and
Glagov
,
S.
,
1987
, “
Shear Stress Regulation of Artery Lumen Diameter in Experimental Atherogenesis
,”
J. Vasc. Surg.
,
5
(
3
), pp.
413
420
.10.1016/0741-5214(87)90048-6
12.
Zarins
,
C. K.
,
Giddens
,
D. P.
,
Bharadvaj
,
B.
,
Sottiurai
,
V. S.
,
Mabon
,
R. F.
, and
Glagov
,
S.
,
1983
, “
Carotid Bifurcation Atherosclerosis. Quantitative Correlation of Plaque Localization With Flow Velocity Profiles and Wall Shear Stress
,”
Circ. Res.
,
53
(
4
), pp.
502
514
.10.1161/01.RES.53.4.502
13.
Malek
,
A. M.
,
Alper
,
S. L.
, and
Izumo
,
S.
,
1999
, “
Hemodynamic Shear Stress and Its Role in Atherosclerosis
,”
JAMA
,
282
(
21
), pp.
2035
2042
.10.1001/jama.282.21.2035
14.
Les
,
A. S.
,
Shadden
,
S. C.
,
Figueroa
,
C. A.
,
Park
,
J. M.
,
Tedesco
,
M. M.
,
Herfkens
,
R. J.
,
Dalman
,
R. L.
, and
Taylor
,
C. A.
,
2010
, “
Quantification of Hemodynamics in Abdominal Aortic Aneurysms During Rest and Exercise Using Magnetic Resonance Imaging and Computational Fluid Dynamics
,”
Ann. Biomed. Eng.
,
38
(
4
), pp.
1288
1313
.10.1007/s10439-010-9949-x
15.
Shadden
,
S. C.
, and
Arzani
,
A.
,
2015
, “
Lagrangian Postprocessing of Computational Hemodynamics
,”
Ann. Biomed. Eng.
,
43
(
1
), pp.
41
58
.10.1007/s10439-014-1070-0
16.
Sazonov
,
I.
,
Khir
,
A. W.
,
Hacham
,
W. S.
,
Boileau
,
E.
,
Carson
,
J. M.
,
van Loon
,
R.
,
Ferguson
,
C.
, and
Nithiarasu
,
P.
,
2017
, “
A Novel Method for Non-Invasively Detecting the Severity and Location of Aortic Aneurysms
,”
Biomech. Model. Mechanobiol.
,
16
(
4
), pp.
1225
1242
.10.1007/s10237-017-0884-8
17.
Yang
,
C.
,
Tang
,
D.
,
Yuan
,
C.
,
Hatsukami
,
T. S.
,
Zheng
,
J.
, and
Woodard
,
P. K.
,
2007
, “
In Vivo/Ex Vivo MRI-Based 3D Non-Newtonian FSI Models for Human Atherosclerotic Plaques Compared With Fluid/Wall-Only Models
,”
Comput. Model. Eng. Sci.
, 19(3), p. 233.https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2750911/
18.
Liu
,
B.
, and
Tang
,
D.
,
2011
, “Influence of Non-Newtonian Properties of Blood on the Wall Shear Stress in Human Atherosclerotic Right Coronary Arteries,”
Mol. Cell. Biomech.
, 8(1), p.
73
.10.3970/mcb.2011.008.073
19.
Silva
,
T.
,
Sequeira
,
A.
,
Santos
,
R. F.
, and
Tiago
,
J.
,
2013
, “
Mathematical Modeling of Atherosclerotic Plaque Formation Coupled With a Non-Newtonian Model of Blood Flow
,”
Conference Papers in Mathematics
,
2013
, pp.
1
14
.10.1155/2013/405914
20.
Weddell
,
J. C.
,
Kwack
,
J.
,
Imoukhuede
,
P.
, and
Masud
,
A.
,
2015
, “Hemodynamic Analysis in an Idealized Artery Tree: Differences in Wall Shear Stress Between Newtonian and Non-Newtonian Blood Models,”
PloS one
, 10(4).10.1371/journal.pone.0124575
21.
Menichini
,
C.
,
Cheng
,
Z.
,
Gibbs
,
R. G.
, and
Xu
,
X. Y.
,
2018
, “
A Computational Model for False Lumen Thrombosis in Type B Aortic Dissection Following Thoracic Endovascular Repair
,”
J. Biomech.
,
66
, pp.
36
43
.10.1016/j.jbiomech.2017.10.029
22.
Ameenuddin
,
M.
, and
Anand
,
M.
,
2019
, “
CFD Analysis of Hemodynamics in Idealized Abdominal Aorta-Renal Artery Junction: Preliminary Study to Locate Atherosclerotic Plaque
,”
Comput. Res. Model.
,
11
(
4
), pp.
695
706
.10.20537/2076-7633-2019-11-4-695-706
23.
Jung
,
J.
, and
Hassanein
,
A.
,
2008
, “
Three-Phase CFD Analytical Modeling of Blood Flow
,”
Med. Eng. Phys.
,
30
(
1
), pp.
91
103
.10.1016/j.medengphy.2006.12.004
24.
Marieb
,
E. N.
, and
Hoehn
,
K.
,
2007
,
Human Anatomy & Physiology
,
Pearson Education
, San Francisco, CA.
25.
Charm
,
S.
, and
Kurland
,
G.
,
1965
, “
Viscometry of Human Blood for Shear Rates of 0-100,000 Sec- 1
,”
Nature
,
206
(
4984
), pp.
617
618
.10.1038/206617a0
26.
Thurston
,
G. B.
,
1972
, “
Viscoelasticity of Human Blood
,”
Biophys. J.
,
12
(
9
), pp.
1205
1217
.10.1016/S0006-3495(72)86156-3
27.
Thurston
,
G. B.
,
1979
, “
Rheological Parameters for the Viscosity Viscoelasticity and Thixotropy of Blood
,”
Biorheology
,
16
(
3
), pp.
149
162
.10.3233/BIR-1979-16303
28.
Rajagopal
,
K. R.
, and
Tao
,
L.
,
1995
,
Mechanics of Mixtures
, Vol.
35
,
World Scientific
, Farrer road, Singapore.
29.
Massoudi
,
M.
,
2003
, “
Constitutive Relations for the Interaction Force in Multicomponent Particulate Flows
,”
Int. J. Nonlinear Mech.
,
38
(
3
), pp.
313
336
.10.1016/S0020-7462(01)00064-6
30.
Humphrey
,
J. D.
, and
Rajagopal
,
K. R.
,
2002
, “
A Constrained Mixture Model for Growth and Remodeling of Soft Tissues
,”
Math. Models Methods Appl. Sci.
,
12
(
3
), pp.
407
430
.10.1142/S0218202502001714
31.
Lemon
,
G.
,
King
,
J. R.
,
Byrne
,
H. M.
,
Jensen
,
O. E.
, and
Shakesheff
,
K. M.
,
2006
, “
Mathematical Modelling of Engineered Tissue Growth Using a Multiphase Porous Flow Mixture Theory
,”
J. Math. Biol.
,
52
(
5
), pp.
571
594
.10.1007/s00285-005-0363-1
32.
Wu
,
W.
-T.,
Aubry
,
N.
, and
Massoudi
,
M.
,
2013
, “Channel Flow of a Mixture of Granular Materials and a Fluid,”
ASME
Paper No. IMECE2013-65385.10.1115/IMECE2013-65385
33.
Atkin
,
R. J.
, and
Craine
,
R. E.
,
1976
, “
Continuum Theories of Mixtures: Applications
,”
IMA J. Appl. Math.
,
17
(
2
), pp.
153
207
.10.1093/imamat/17.2.153
34.
Ameenuddin
,
M.
,
Anand
,
M.
, and
Massoudi
,
M.
,
2019
, “
Effects of Shear-Dependent Viscosity and Hematocrit on Blood Flow
,”
Appl. Math. Comput.
,
356
, pp.
299
311
.10.1016/j.amc.2019.03.028
35.
Brooks
,
D. E.
,
Goodwin
,
J. W.
, and
Seaman
,
G. V.
,
1970
, “
Interactions Among Erythrocytes Under Shear
,”
J. Appl. Physiol.
,
28
(
2
), pp.
172
177
.10.1152/jappl.1970.28.2.172
36.
Ku
,
D. N.
,
Giddens
,
D. P.
,
Zarins
,
C. K.
, and
Glagov
,
S.
,
1985
, “
Pulsatile Flow and Atherosclerosis in the Human Carotid Bifurcation. positive Correlation Between Plaque Location and Low Oscillating Shear Stress
,”
Arteriosclerosis
,
5
(
3
), pp.
293
302
.10.1161/01.ATV.5.3.293
37.
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
.10.1152/ajpheart.00897.2003
38.
Sharifi
,
A.
, and
Niazmand
,
H.
,
2015
, “
Analysis of Flow and LDL Concentration Polarization in Siphon of Internal Carotid Artery: Non-Newtonian Effects
,” 
Comput. Biol. Med.
,
65
, pp.
93
102
.10.1016/j.compbiomed.2015.08.002
39.
Gabriel
,
S. A.
,
Ding
,
Y.
, and
Feng
,
Y.
,
2018
, “
Modelling the Period-Average Transport of Species Within Pulsatile Blood Flow
,”
J. Theor. Biol.
,
457
, pp.
258
269
.10.1016/j.jtbi.2018.07.006
40.
Sun
,
N.
,
Wood
,
N. B.
,
Hughes
,
A. D.
,
Thom
,
S. A.
, and
Xu
,
X. Y.
,
2006
, “
Fluid-Wall Modelling of Mass Transfer in an Axisymmetric Stenosis: Effects of Shear-Dependent Transport Properties
,”
Ann. Biomed. Eng.
,
34
(
7
), pp.
1119
1128
.10.1007/s10439-006-9144-2
41.
Yang
,
N.
, and
Vafai
,
K.
,
2008
, “
Low-Density Lipoprotein (LDL) Transport in an Artery–A Simplified Analytical Solution
,”
Int. J. Heat Mass Transfer
,
51
(
3–4
), pp.
497
505
.10.1016/j.ijheatmasstransfer.2007.05.023
42.
Wada
,
S.
, and
Karino
,
T.
,
2000
, “
Computational Study on LDL Transfer From Flowing Blood to Arterial Walls
,”
Clinical Application of Computational Mechanics to the Cardiovascular System
,
Springer
, Tokyo, Japan, pp.
157
173
.10.1007/978-4-431-67921-9_16
43.
Stangeby
,
D. K.
, and
Ethier
,
C. R.
,
2002
, “
Computational Analysis of Coupled Blood-Wall Arterial LDL Transport
,”
ASME J. Biomech. Eng.
,
124
(
1
), pp.
1
8
.10.1115/1.1427041
44.
Ku
,
D. N.
,
Glagov
,
S.
,
Moore
,
J. E.
, Jr.
, and
Zarins
,
C. K.
,
1989
, “
Flow Patterns in the Abdominal Aorta Under Simulated Postprandial and Exercise Conditions: An Experimental Study
,”
J. Vasc. Surg.
,
9
(
2
), pp.
309
316
.10.1016/0741-5214(89)90051-7
45.
Moore
,
J. E.
, and
Ku
,
D. N.
,
1994
, “
Pulsatile Velocity Measurements in a Model of the Human Abdominal Aorta Under Resting Conditions
,”
ASME J. Biomech. Eng.
,
116
(
3
), pp.
337
346
.10.1115/1.2895740
46.
Updegrove
,
A.
,
Wilson
,
N. M.
,
Merkow
,
J.
,
Lan
,
H.
,
Marsden
,
A. L.
, and
Shadden
,
S. C.
,
2017
, “
Simvascular: An Open Source Pipeline for Cardiovascular Simulation
,”
Ann. Biomed. Eng.
,
45
(
3
), pp.
525
541
.10.1007/s10439-016-1762-8
47.
Karino
,
T.
, and
Goldsmith
,
H. L.
,
1977
, “
Flow Behaviour of Blood Cells and Rigid Spheres in an Annular Vortex
,”
Philos. Trans. R. Soc. London B Biol. Sci.
,
279
(
967
), pp.
413
445
.10.1098/rstb.1977.0095
48.
Patrick
,
M. J.
,
Chen
,
C.-Y.
,
Frakes
,
D. H.
,
Dur
,
O.
, and
Pekkan
,
K.
,
2011
, “
Cellular-Level Near-Wall Unsteadiness of High-Hematocrit Erythrocyte Flow Using Confocal ΜPIV
,”
Exp Fluids
,
50
(
4
), pp.
887
904
.10.1007/s00348-010-0943-8
49.
Yeleswarapu
,
K. K.
,
Kameneva
,
M. V.
,
Rajagopal
,
K. R.
, and
Antaki
,
J. F.
,
1998
, “
The Flow of Blood in Tubes: Theory and Experiment
,”
Mech. Res. Commun.
,
25
(
3
), pp.
257
262
.10.1016/S0093-6413(98)00036-6
50.
Moore
,
J. E.
, Jr.
,
Xu
,
C.
,
Glagov
,
S.
,
Zarins
,
C. K.
, and
Ku
,
D. N.
,
1994
, “
Fluid Wall Shear Stress Measurements in a Model of the Human Abdominal Aorta: Oscillatory Behavior and Relationship to Atherosclerosis
,”
Atherosclerosis
,
110
(
2
), pp.
225
240
.10.1016/0021-9150(94)90207-0
51.
Taylor
,
C. A.
,
Hughes
,
T. J. R.
, and
Zarins
,
C. K.
, “
Finite Element Modeling of Three-Dimensional Pulsatile Flow in the Abdominal Aorta: Relevance to Atherosclerosis
,”
 Ann. Biomed. Eng.,
26
(
6
), pp.
975
987
.10.1114/1.140
52.
Deng
,
X.
, and
Wang
,
G.
,
2003
, “
Concentration Polarization of Atherogenic Lipids in the Arterial System
,”
Sci. China C Life Sci.
,
46
(
2
), p.
153
.https://link.springer.com/article/10.1360/03yc9017
You do not currently have access to this content.