Computational fluid dynamics (CFD) models have become very effective tools for predicting the flow field within the carotid bifurcation, and for understanding the relationship between local hemodynamics, and the initiation and progression of vascular wall pathologies. As prescribing proper boundary conditions can affect the solutions of the equations governing blood flow, in this study, we investigated the influence to assumptions regarding the outflow boundary conditions in an image-based CFD model of human carotid bifurcation. Four simulations were conducted with identical geometry, inlet flow rate, and fluid parameters. In the first case, a physiological time-varying flow rate partition at branches along the cardiac cycle was obtained by coupling the 3D model of the carotid bifurcation at outlets with a lumped-parameter model of the downstream vascular network. Results from the coupled model were compared with those obtained by imposing three fixed flow rate divisions (50/50, 60/40, and 70/30) between the two branches of the isolated 3D model of the carotid bifurcation. Three hemodynamic wall parameters were considered as indicators of vascular wall dysfunction. Our findings underscore that the overall effect of the assumptions done in order to simulate blood flow within the carotid bifurcation is mainly in the hot-spot modulation of the hemodynamic descriptors of atherosusceptible areas, rather than in their distribution. In particular, the more physiological, time-varying flow rate division deriving from the coupled simulation has the effect of damping wall shear stress (WSS) oscillations (differences among the coupled and the three fixed flow partition models are up to 37.3% for the oscillating shear index). In conclusion, we recommend to adopt more realistic constraints, for example, by coupling models at different scales, as in this study, when the objective is the outcome prediction of alternate therapeutic interventions for individual patients, or to test hypotheses related to the role of local fluid dynamics and other biomechanical factors in vascular diseases.
1.
Giddens
, D. P.
, Zarins
, C. K.
, and Glagov
, S.
, 1993, “The Role of Fluid Mechanics in the Localization and Detection of Atherosclerosis
,” ASME J. Biomech. Eng.
0148-0731, 115
(4B
), pp. 588
–595
.2.
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 Behaviour and Relationship to Atherosclerosis
,” Atherosclerosis
0021-9150, 110
(2
), pp. 225
–240
.3.
Caro
, C. G.
, Fitz
, G. J.
, and Schroter
, R. C.
, 1971, “Atheroma and Arterial Wall Shear. Observation, Correlation and Proposal of a Shear Dependent Mass Transfer Mechanism for Atherogenesis
,” Proc. R. Soc. London, Ser. B
0962-8452, 177
, pp. 109
–133
.4.
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 and Oscillating Shear Stress
,” Arteriosclerosis
, 5
(3
), pp. 293
–302
.5.
Karino
, T.
, 1986, “Microscopic Structure of Disturbed Flows in the Arterial and Venous System, and Its Implication in the Localization of Vascular Disease
,” Int. Angiol
0392-9590, 5
(4
), pp. 297
–313
.6.
Malek
, A. M.
, Alper
, S. L.
, and Izumo
, S.
, 1999, “Hemodynamic Shear Stress and Its Role in Atherosclerosis
,” JAMA, J. Am. Med. Assoc.
0098-7484, 282
, pp. 2035
–2042
.7.
Davies
, P. F.
, Polacek
, D. C.
, Shi
, C.
, and Helmke
, B. P.
, 2002, “The Convergence of Hemodynamics, Genomics, and Endothelial Structure in Studies of the Focal Origin of Atherosclerosis
,” Biorheology
0006-355X, 39
, pp. 299
–306
.8.
Caro
, C. G.
, Fitz
, G. J.
, and Schroter
, R. C.
, 1969, “Arterial Wall Shear and Distribution of Early Atheroma in Man
,” Nature (London)
0028-0836, 223
, pp. 1159
–1161
.9.
Ma
, P.
, Li
, X.
, and Ku
, D. N.
, 1997, “Convective Mass Transfer at the Carotid Bifurcation
,” J. Biomech.
0021-9290, 30
, pp. 565
–571
.10.
Friedman
, M. H.
, Bargeron
, C. B.
, Deters
, O. J.
, Hutchins
, G. M.
, and Mark
, F. F.
, 1987, “Correlation Between Wall Shear and Intimal Thickness at a Coronary Artery Branch
,” Atherosclerosis
0021-9150, 68
, pp. 27
–33
.11.
Steinman
, D. A.
, 2002, “Image-Based Computational Fluid Dynamics Modelling in Realistic Arterial Geometries
,” Ann. Biomed. Eng.
0090-6964, 124
(2
), pp. 166
–175
.12.
Moyle
, K. R.
, Antiga
, L.
, and Steinman
, D. A.
, 2006, “Inlet Conditions for Image-Based CFD Models of the Carotid Bifurcation: Is It Reasonable to Assume Fully Developed Flow?
,” ASME J. Biomech. Eng.
0148-0731, 128
(3
), pp. 371
–379
.13.
Ford
, M. D.
, Xie
, Y. J.
, Wasserman
, B. A.
, and Steinman
, D. A.
, 2008, “Is Flow in the Common Carotid Artery Fully Developed?
,” Physiol. Meas
0967-3334, 29
(11
), pp. 1335
–1349
.14.
Wake
, A. K.
, Oshinski
, J. N.
, Tannenbaum
, A. R.
, and Giddens
, D. P.
, 2009, “Choice of In Vivo Versus Idealized Velocity Boundary Conditions Influences Physiologically Relevant Flow Patterns in a Subject-Specific Simulation of Flow in the Human Carotid Bifurcation
,” ASME J. Biomech. Eng.
0148-0731, 131
(2
), p. 021013
.15.
Lee
, S. W.
, and Steinman
, D. A.
, 2007, “On the Relative Importance of Rheology for Image-Based CFD Models of the Carotid Bifurcation
,” ASME J. Biomech. Eng.
0148-0731, 129
(2
), pp. 273
–278
.16.
Thomas
, J. B.
, Milner
, J. S.
, and Steinman
, D. A.
, 2002, “On the Influence of Vessel Planarity on Local Hemodynamics at the Human Carotid Bifurcation
,” Biorheology
0006-355X, 39
(3–4
), pp. 443
–448
.17.
Thomas
, J. B.
, Milner
, J. S.
, Rutt
, B. K.
, and Steinman
, D. A.
, 2003, “Reproducibility of Image-Based Computational Fluid Dynamics Models of the Human Carotid Bifurcation
,” Ann. Biomed. Eng.
0090-6964, 31
(2
), pp. 132
–141
.18.
Perktold
, K.
, and Rappitsch
, G.
, 1995, “Computer Simulation of Local Blood Flow and Vessel Mechanics in a Compliant Carotid Artery Bifurcation Model
,” J. Biomech.
0021-9290, 28
(7
), pp. 845
–856
.19.
Zhao
, S. Z.
, Ariff
, B.
, Long
, Q.
, Hughes
, A. D.
, Thom
, S. A.
, Stanton
, A. V.
, and Xu
, X. Y.
, 2002, “Inter-Individual Variations in Wall Shear Stress and Mechanical Stress Distributions at the Carotid Artery Bifurcation of Healthy Humans
,” J. Biomech.
0021-9290, 35
(10
), pp. 1367
–1377
.20.
Formaggia
, L.
, Veneziani
, A.
, and Vergara
, C.
, 2008, “A New Approach to Numerical Solution of Defective Boundary Value Problems in Incompressible Fluid Dynamics
,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal.
0036-1429, 46
(6
), pp. 2769
–2794
.21.
Augst
, A. D.
, Barratt
, D. C.
, Hughes
, A. D.
, Thom
, S. A.
, and Xu
, X. Y.
, 2003, “Various Issues Relating to Computational Fluid Dynamics Simulations of Carotid Bifurcation Flow Based on Models Reconstructed From Three-Dimensional Ultrasound Images
,” Proc. Inst. Mech. Eng., Part H: J. Eng. Med.
0954-4119, 217
(5
), pp. 393
–403
.22.
Long
, Q.
, Xu
, X. Y.
, Ariff
, B.
, Thom
, S. A.
, Hughes
, A. D.
, and Stanton
, A. V.
, 2000, “Reconstruction of Blood Flow Patterns in a Human Carotid Bifurcation: A Combined CFD and MRI Study
,” J. Magn. Reson Imaging
1053-1807, 11
, pp. 299
–311
.23.
Younis
, H. F.
, Kaazempur-Mofrad
, M. R.
, Chan
, R. C.
, Isasi
, A. G.
, Hinton
, D. P.
, Chau
, A. H.
, Kim
, L. A.
, and Kamm
, R. D.
, 2004, “Hemodynamics and Wall Mechanics in Human Carotid Bifurcation and Its Consequences for Atherogenesis: Investigation of Interindividual Variation
,” Biomech. Model. Mechanobiol.
1617-7959, 3
(1
), pp. 17
–32
.24.
Augst
, A. D.
, Ariff
, B.
, Thom
, S. A. M.
, Xu
, X. Y.
, and Hughes
, A. D.
, 2007, “Analysis of Complex Flow and the Relationship Between Blood Pressure, Wall Shear Stress, and Intima-Media Thickness in the Human Carotid Artery
,” Am. J. Physiol. Heart Circ. Physiol.
0363-6135, 293
, pp. H1031
–H1037
.25.
Tan
, F. P.
, Soloperto
, G.
, Bashford
, S.
, Wood
, N. B.
, Thom
, S.
, Hughes
, A.
, and Xu
, X. Y.
, 2008, “Analysis of Flow Disturbance in a Stenosed Carotid Artery Bifurcation Using Two-Equation Transitional and Turbulence Models
,” ASME J. Biomech. Eng.
0148-0731, 130
(6
), p. 061008
.26.
Hyun
, S.
, Kleinstreuer
, C.
, and Archie
, J. P.
, 2003, “Computational Analysis of Effects of External Carotid Artery Flow and Occlusion on Adverse Carotid Bifurcation Hemodynamics
,” J. Vasc. Surg.
0741-5214, 37
(6
), pp. 1248
–1254
.27.
Blanco
, P. J.
, Pivello
, M. R.
, Urquiza
, S. A.
, and Feijóo
, R. A.
, 2009, “On the Potentialities of 3D-1D Coupled Models in Hemodynamics Simulations
,” J. Biomech.
0021-9290, 42
(7
), pp. 919
–930
.28.
Redaelli
, A.
, and Montevecchi
, F. M.
, 1996, “Computational Evaluation of Intraventricular Pressure Gradients Based on a Fluid-Structure Approach
,” ASME J. Biomech. Eng.
0148-0731, 118
(4
), pp. 529
–537
.29.
Formaggia
, L.
, Nobile
, F.
, Quarteroni
, A.
, and Veneziani
, A.
, 1999, “Multiscale Modelling of the Circulatory System: A Preliminary Analysis
,” Comput. Visualization Sci.
1432-9360, 2
, pp. 75
–83
.30.
Formaggia
, L.
, Lamponi
, D.
, Tuveri
, M.
, and Veneziani
, A.
, 2006, “Numerical Modeling of 1D Arterial Networks Coupled With a Lumped Parameters Description of the Heart
,” Comput. Methods Biomech. Biomed. Eng.
1025-5842, 9
(5
), pp. 273
–288
.31.
Urquiza
, S. A.
, Blanco
, P. J.
, Vénere
, M. J.
, and Feijóo
, R. A.
, 2006, “Multidimensional Modelling for the Carotid Artery Blood Flow
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 195
, pp. 4002
–4017
.32.
Migliavacca
, F.
, Balossino
, R.
, Pennati
, G.
, Dubini
, G.
, Hsia
, T. Y.
, de Leval
, M. R.
, and Bove
, E. L.
, 2006, “Multiscale Modelling in Biofluidynamics: Application to Reconstructive Pediatric Cardiac Surgery
,” J. Biomech.
0021-9290, 39
(6
), pp. 1010
–1020
.33.
Balossino
, R.
, Pennati
, G.
, Migliavacca
, F.
, Formaggia
, L.
, Veneziani
, A.
, Tuveri
, M.
, and Dubini
, G.
, 2009, “Computational Models to Predict Stenosis Growth in Carotid Arteries: Which Is the Role of Boundary Conditions?
,” Comput. Methods Biomech. Biomed. Eng.
1025-5842, 12
(1
), pp. 113
–123
.34.
Antiga
, L.
, Piccinelli
, M.
, Botti
, L.
, Ene-Iordache
, B.
, Remuzzi
, A.
, and Steinman
, D. A.
, 2008, “An Image-Based Modelling Framework for Patient-Specific Computational Hemodynamics
,” Med. Biol. Eng. Comput.
0140-0118, 46
(11
), pp. 1097
–1112
.35.
Marshall
, I.
, Papathanasopoulou
, P.
, and Wartolowska
, K.
, 2004, “Carotid Flow Rates and Flow Division at the Bifurcation in Healthy Volunteers
,” Physiol. Meas.
, 25
(3
), pp. 691
–697
.36.
Westerhof
, N.
, Lankhaar
, J. W.
, and Westerhof
, B. E.
, 2009, “The Arterial Windkessel
,” Med. Biol. Eng. Comput.
0140-0118, 47
(2
), pp. 131
–141
.37.
Quarteroni
, A.
, Ragni
, S.
, and Veneziani
, A.
, 2001, “Coupling Between Lumped and Distributed Models for Blood Flow Problem
,” Comput. Visualization Sci.
1432-9360, 4
, pp. 111
–124
.38.
Quarteroni
, A.
, and Veneziani
, A.
, 2003, “Analysis of a Geometrical Multiscale Model Based on the Coupling of ODE and PDE for Blood Flow Simulations
,” Multiscale Model. Simul.
1540-3459, 1
(2
), pp. 173
–195
.39.
Laganà
, K.
, Dubini
, G.
, Migliavacca
, F.
, Pietrabissa
, R.
, Pennati
, G.
, Veneziani
, A.
, and Quarteroni
, A.
, 2002, “Multiscale Modelling as a Tool to Prescribe Realistic Boundary Conditions for the Study of Surgical Procedures
,” Biorheology
0006-355X, 39
(3–4
), pp. 359
–364
.40.
Lee
, S. W.
, Antiga
, L.
, and Steinman
, D. A.
, 2009, “Correlations Among Indicators of Disturbed Flow at the Normal Carotid Bifurcation
,” ASME J. Biomech. Eng.
0148-0731, 131
(6
), p. 061013
.41.
Kessler
, M.
, 2002, “Biocompatibility
,” Nephrol. Dial Transplant
0931-0509, 17
(7
), pp. 32
–44
.42.
He
, X.
, and Ku
, D. N.
, 1996, “Pulsatile Flow in the Human Left Coronary Artery Bifurcation: Average Conditions
,” ASME J. Biomech. Eng.
0148-0731, 118
(1
), pp. 74
–82
.43.
Himburg
, H. A.
, Grzybowski
, D. M.
, Hazel
, A.
, 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.
0363-6135, 286
(5
), pp. H1916
–H1922
.44.
Lee
, S. W.
, Antiga
, L.
, Spence
, J. D.
, and Steinman
, D. A.
, 2008, “Geometry of the Carotid Bifurcation Predicts Its Exposure to Disturbed Flow
,” Stroke
0039-2499, 39
(8
), pp. 2341
–2347
.45.
Ford
, M. D.
, Alperin
, N.
, Lee
, S. H.
, Holdsworth
, D. W.
, and Steinman
, D. A.
, 2005, “Characterization of Volumetric Flow Rate Waveforms in the Normal Internal Carotid and Vertebral Arteries
,” Physiol. Meas.
, 26
(4
), pp. 477
–488
.46.
Olufsen
, M. S.
, 1999, “Structured Tree Outflow Condition for Blood Flow in Larger Systemic Arteries
,” Am. J. Physiol.
0002-9513, 276
, pp. H257
–H268
.47.
Veneziani
, A.
, and Vergara
, C.
, 2005, “Flow Rate Defective Boundary Conditions in Hemodynamics Simulations
,” Int. J. Numer. Methods Fluids
0271-2091, 47
(8–9
), pp. 803
–816
.48.
Spilker
, R. L.
, Feinstein
, J. A.
, Parker
, D. W.
, Reddy
, V. M.
, and Taylor
, C. A.
, 2007, “Morphometry-Based Impedance Boundary Conditions for Patient-Specific Modeling of Blood Flow in Pulmonary Arteries
,” Ann. Biomed. Eng.
0090-6964, 35
(4
), pp. 546
–559
.49.
Vignon-Clementel
, I. E.
, Figueroa
, C. A.
, Jansenc
, K. E.
, and Taylor
, C. A.
, 2006, “Outflow Boundary Conditions for Three Dimensional Finite Element Modeling of Blood Flow and Pressure in Arteries
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 195
, pp. 3776
–3796
.50.
Grinberg
, L.
, and Karniadakis
, G. E. M.
, 2008, “Outflow Boundary Conditions for Arterial Networks With Multiple Outlets
,” Ann. Biomed. Eng.
0090-6964, 36
(9
), pp. 1496
–1514
.51.
Ponzini
, R.
, Lemma
, M.
, Morbiducci
, U.
, Montevecchi
, F. M.
, and Redaelli
, A.
, 2008, “Doppler Derived Quantitative Flow Estimate in Coronary Artery Bypass Graft: A Computational Multi-Scale Model for the Evaluation of the Current Theory
,” Med. Eng. Phys.
1350-4533, 30
(7
), pp. 809
–816
.52.
Zhao
, S. Z.
, Xu
, X. Y.
, Hughes
, A. D.
, Thom
, S. A.
, Stanton
, A. V.
, Ariff
, B.
, and Long
, Q.
, 2000, “Blood Flow and Vessel Mechanics in a Physiologically Realistic Model of a Human Carotid Artery Bifurcation
,” J. Biomech.
0021-9290, 33
(8
), pp. 975
–984
.53.
Stroud
, J. S.
, Berger
, S. A.
, and Saloner
, D.
, 2002, “Numerical Analysis of Flow Through a Severely Stenotic Carotid Artery Bifurcation
,” ASME J. Biomech. Eng.
0148-0731, 124
, pp. 9
–20
.54.
Taylor
, C. A.
, and Figueroa
, C. A.
, 2009, “Patient-Specific Modeling of Cardiovascular Mechanics
,” Annu. Rev. Biomed. Eng.
1523-9829, 11
, pp. 109
–134
.55.
Kim
, H. J.
, Figueroa
, C. A.
, Hughes
, T. J. R.
, Jansen
, K. E.
, and Taylor
, C. A.
, 2009, “Augmented Lagrangian Method for Constraining the Shape of Velocity Profiles at Outlet Boundaries for Three-Dimensional Finite Element Simulations of Blood Flow
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 198
, pp. 3551
–3566
.56.
Grigioni
, M.
, Daniele
, C.
, Morbiducci
, U.
, Del Gaudio
, C.
, D’Avenio
, G.
, Balducci
, A.
, and Barbaro
, V.
, 2005, “A Mathematical Description of Blood Spiral Flow in Vessels: Application to a Numerical Study of Flow in Arterial Bending
,” J. Biomech.
0021-9290, 38
, pp. 1375
–1386
.57.
Liu
, X.
, Pu
, F.
, Fan
, Y.
, Deng
, X.
, Li
, D.
, and Li
, S.
, 2009, “A Numerical Study on the Flow of Blood and the Transport of LDL in the Human Aorta: The Physiological Significance of the Helical Flow in the Aortic Arch
,” Am. J. Physiol. Heart Circ. Physiol.
0363-6135, 297
, pp. H163
–H170
.58.
Morbiducci
, U.
, Ponzini
, R.
, Grigioni
, M.
, and Redaelli
, A.
, 2007, “Helical Flow as Fluid Dynamic Signature for Atherogenesis in Aortocoronary Bypass. A Numeric Study
,” J. Biomech.
0021-9290, 40
, pp. 519
–534
.59.
Morbiducci
, U.
, Lemma
, M.
, Ponzini
, R.
, Boi
, A.
, Bondavalli
, L.
, Antona
, C.
, Montevecchi
, F. M.
, and Redaelli
, A.
, 2007, “Does Flow Dynamics of the Magnetic Vascular Coupling for Distal Anastomosis in Coronary Artery Bypass Grafting Contribute to the Risk of Graft Failure?
,” Int. J. Artif. Organs
0391-3988, 30
, pp. 628
–639
.60.
Morbiducci
, U.
, Ponzini
, R.
, Rizzo
, G.
, Cadioli
, M.
, Esposito
, A.
, De Cobelli
, F.
, Del Maschio
, A.
, Montevecchi
, F. M.
, and Redaelli
, A.
, 2009, “In Vivo Quantification of Helical Blood Flow in Human Aorta by Time-Resolved Three-Dimensional Cine Phase Contrast MRI
,” Ann. Biomed. Eng.
0090-6964, 37
, pp. 516
–531
.61.
Morbiducci
, U.
, Ponzini
, R.
, Nobili
, M.
, Massai
, D.
, Montevecchi
, F. M.
, Bluestein
, D.
, and Redaelli
, A.
, 2009, “Blood Damage Safety of Prosthetic Heart Valves. Shear-Induced Platelet Activation and Local Flow Dynamics: A Fluid-Structure Interaction Approach
,” J. Biomech.
0021-9290, 42
(12
), pp. 1952
–1960
.62.
Sun
, A.
, Fan
, Y.
, and Deng
, X.
, 2009, “Numerical Investigation of Blood Flow in the Distal End of an Axis-Deviated Arterial Bypass Model
,” Biorheology
0006-355X, 46
, pp. 83
–92
.63.
Zhan
, F.
, Fan
, Y.
, and Deng
, X.
, 2010, “Swirling Flow Created in a Glass Tube Suppressed Platelet Adhesion to the Surface of the Tube: Its Implication in the Design of Small-Caliber Arterial Grafts
,” Thromb. Res.
0049-3848, 125
(5
), pp. 413
–418
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