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Numerical Analysis of Blood Flow Through the Human Carotid Artery
BifurcationBachelor’s Thesis
by Athanasios MargaritisAEM: 5516
Supervisor: Anestis I. Kalfas, Associate Professor
Aristotle University of ThessalonikiFaculty of Engineering
School of Mechanical EngineeringLaboratory of Fluid Mechanics and
Turbomachinery
Contents• Introduction• Literature Survey• Methods• Results• Discussion• ConclusionsoLimitationsoSuggestions for Further Research
Numerical Analysis of Blood Flow Through the Human Carotid Artery Bifurcation
Aristotle University of Thessaloniki
Athanasios Margaritis
Laboratory of Fluid Mechanics and Turbomachinery
IntroductionThe purpose of this study
• Engineering Diploma First Cycle Thesis (Bachelor’s Thesis)• Atherosclerotic diseases are the main cause of mortality – morbidity• Blood flow through Carotid Artery important for atherogenesis• Study flow through the Carotid Artery using Measurements, Imaging and
CFD• Target: use CFD for prognosis, diagnosis and treatment of
cardiovascular diseases
Aristotle University of Thessaloniki
Athanasios Margaritis
Laboratory of Fluid Mechanics and Turbomachinery
Numerical Analysis of Blood Flow Through the Human Carotid Artery Bifurcation
IntroductionThe stages of this study
• Six 3D geometries reconstructed using 2D MRI images from 3 volunteers• Geometry correction and computational mesh generation using
ANSA• Universal average periodic boundary conditions coded in
MATLAB and C• Solution using commercial CFD software, ANSYS Fluent• Results presentation using ANSYS CFD-Post and μΕΤΑ
Aristotle University of Thessaloniki
Athanasios Margaritis
Laboratory of Fluid Mechanics and Turbomachinery
Numerical Analysis of Blood Flow Through the Human Carotid Artery Bifurcation
Literature SurveyPrevious Studies Reviewed
• Numerous relevant previous studies (since 1960, intensified after 2000)• CFD applications for studying of blood flow through the arterial tree or carotid
artery• Studies of wave propagation through the arterial tree• Research on arterial wall properties (elasticity, viscoelasticity, compliance
etc.)
• Differences regarding simulation models• Viscosity model: Newtonian or Non-Newtonian (usually
Carreau-Yassuda)• Fluid-Structure Interactions: Included or Not (arterial wall compliance and
elasticity)• Blood Phases: Single or Multiple phases of blood• Boundary Conditions: Patient-specific or Universal, Shape of velocity
profiles• Indexes: WSS, RRT, OSI, etc. and their
validity and correlations
(1/2)
Aristotle University of Thessaloniki
Athanasios Margaritis
Laboratory of Fluid Mechanics and Turbomachinery
Numerical Analysis of Blood Flow Through the Human Carotid Artery Bifurcation
Literature SurveyGeneral Observations
• Previous research results suggest• Low, oscillating Wall Shear Stress regions on the outer wall of the Internal
Carotid Artery, in correlation with sinus size• Peak maximum values of Wall Shear Stress at the bifurcation apex, during
the end of the systolic acceleration phase of the cardiac cycle• Minor effect of blood’s viscosity model
• Previous studies have established physiological ranges for results• Appropriate models for simulating blood flow have been widely
tested
(2/2)
Aristotle University of Thessaloniki
Athanasios Margaritis
Laboratory of Fluid Mechanics and Turbomachinery
Numerical Analysis of Blood Flow Through the Human Carotid Artery Bifurcation
MethodsImaging and Reconstruction Techniques
• 2D cross-sectional images from 3 healthy subjects (208 from each)• Semi-automatic segmentation and 3D geometry reconstruction
(ITK-SNAP)• Manual corrections• Irrelevant vessels removal• Imaging errors and anomalies smoothing
• Exportation to Stereolithography (STL) file
(1/7)
Aristotle University of Thessaloniki
Athanasios Margaritis
Laboratory of Fluid Mechanics and Turbomachinery
Numerical Analysis of Blood Flow Through the Human Carotid Artery Bifurcation
MethodsIn-vivo MRA Example Images
(2/7)
Aristotle University of Thessaloniki
Athanasios Margaritis
Laboratory of Fluid Mechanics and Turbomachinery
Numerical Analysis of Blood Flow Through the Human Carotid Artery Bifurcation
Figure 1. Side view of the carotid artery region of Subject 1 (Kalozoumis, 2009).
Figure 2. Example of a cross-sectional MRA image of Subject 1 (Kalozoumis, 2009).
Carotid Artery
Bifurcation
Internal Carotid Arteries
External Carotid Arteries
Carotid
Shell Elemen
ts Numbe
r
Volume Elements Number
CCA Inlet
Equiv. Diameter
[mm]
ICA/CCA Diameter
Ratio
ECA/CCA
Diameter Ratio
ICA/ECA Diameter
Ratio
L1 25392 464748 5.7902 58.5% 35.1% 166%R1 24673 429366 5.7388 63.9% 31.2% 205%L2 25197 453835 6.4318 68.7% 39.0% 176%R2 24868 414471 6.3413 79.4% 45.5% 175%L3 27602 495230 6.6125 74.6% 52.1% 143%R3 24945 443211 6.6236 71.5% 54.0% 132%
MethodsComputational Mesh Generation• Mesh Independence Study
• Surface elements around 25K• Volume elements around 450K• Inflation layers
• 8 layers• First layer height of 0.01 mm• Growth factor of 1.2
• Element size between 0.3 mm and 0.5 mm (further refinement at the bifurcation apex)
• Surface geometry smoothing and shell mesh generation and refinement• Inflatable layers generation• Hexahedral volume mesh for faster convergence, equivalent
accuracy
(3/7)
Table 1. Geometric characteristics of the meshes for the 6 Carotid Arteries studied.
Aristotle University of Thessaloniki
Athanasios Margaritis
Laboratory of Fluid Mechanics and Turbomachinery
Numerical Analysis of Blood Flow Through the Human Carotid Artery Bifurcation
MethodsComputational Mesh Example (R1)
(4/7)
Aristotle University of Thessaloniki
Athanasios Margaritis
Laboratory of Fluid Mechanics and Turbomachinery
Numerical Analysis of Blood Flow Through the Human Carotid Artery Bifurcation
Figure 3. Top view (-Z direction) of the Right Carotid Artery Bifurcation of Subject 1 (R1).
Figure 4. Front view (+X direction) of the Right Carotid Artery Bifurcation of Subject 1 (R1).
Inflation layersnear the wall
Refined bifurcation apex
area
MethodsSolution Models and Parameters
• Pressure-based solver, incompressible fluid• Transient study, periodic, pulsatile flow• Coupled equation scheme, 2nd order discretization• Laminar flow model, no turbulence occurs, • Viscosity models compared: Newtonian and Carreau-Yassuda
(5/7)
Aristotle University of Thessaloniki
Athanasios Margaritis
Laboratory of Fluid Mechanics and Turbomachinery
Numerical Analysis of Blood Flow Through the Human Carotid Artery Bifurcation
MethodsBoundary Conditions Imposed
(6/7)
• Universal, average boundary conditions• According to literature
• Periodic parabolic inlet mass flux profiles, coded as UDF• Periodic pressure boundary conditions• Fixed mass flow distribution
Figure 7. Pressure inlet and outlet boundary conditions.Figure 6. Inlet volumetric flow boundary condition.
Figure 5. Parabolic inlet velocity profile.
Aristotle University of Thessaloniki
Athanasios Margaritis
Laboratory of Fluid Mechanics and Turbomachinery
Numerical Analysis of Blood Flow Through the Human Carotid Artery Bifurcation
MethodsAccuracy Evaluation – Periodicity
(7/7)
Figure 9. Periodicity of Wall Shear Stress magnitude on the outer wall of the ICA bulb.
Figure 8. Periodicity of velocity magnitude through the ICA bulb.
• Mesh Independence Study• Surface elements number• Layers number and size• Volume elements number
• Time-step Independence Study• Time-step of 0.005 ms according to
literature
• Periodicity of solution• Simulated 10 cardiac cycles• Periodicity achieved after 1st cardiac
cycle
Aristotle University of Thessaloniki
Athanasios Margaritis
Laboratory of Fluid Mechanics and Turbomachinery
Numerical Analysis of Blood Flow Through the Human Carotid Artery Bifurcation
ResultsWall Shear Stress Distribution – Subject 1
• Results for L1-R1 presented at• t=T/8 (top)• t=3T/16 (middle)• t=13T/16 (bottom)
• No recirculation or helicity during systolic acceleration• Helical flow after velocity
peak, during systolic deceleration• Low WSS on the outer walls
of the ICA bulb and ECA, due to secondary flows.
(1/5)
Aristotle University of Thessaloniki
Athanasios Margaritis
Laboratory of Fluid Mechanics and Turbomachinery
Figure 10. Wall Shear Stress and Velocity Distributions for Subject 1 (L1 – R1).
Numerical Analysis of Blood Flow Through the Human Carotid Artery Bifurcation
ResultsWall Shear Stress Distribution – Subject 2
(2/5)
Aristotle University of Thessaloniki
Athanasios Margaritis
Laboratory of Fluid Mechanics and Turbomachinery
Figure 11. Wall Shear Stress and Velocity Distributions for Subject 2 (L2 – R2).
• Results for L2-R2 presented at• t=T/8 (top)• t=3T/16 (middle)• t=13T/16 (bottom)
• No recirculation or helicity during systolic acceleration• Helical flow after velocity
peak, during systolic deceleration• Low WSS on the outer walls
of the ICA bulb and ECA, due to secondary flows.
Numerical Analysis of Blood Flow Through the Human Carotid Artery Bifurcation
ResultsWall Shear Stress Distribution – Subject 3
(3/5)
Aristotle University of Thessaloniki
Athanasios Margaritis
Laboratory of Fluid Mechanics and Turbomachinery
Figure 12. Wall Shear Stress and Velocity Distributions for Subject 3 (L3 – R3).
• Results for L3-R3 presented at• t=T/8 (top)• t=3T/16 (middle)• t=13T/16 (bottom)
• No recirculation or helicity during systolic acceleration• Helical flow after velocity
peak, during systolic deceleration• Low WSS on the outer walls
of the ICA bulb and ECA, due to secondary flows.
Numerical Analysis of Blood Flow Through the Human Carotid Artery Bifurcation
ResultsStreamlines and Secondary Flows
(4/5)
Aristotle University of Thessaloniki
Athanasios Margaritis
Laboratory of Fluid Mechanics and Turbomachinery
Figure 13. Streamlines for the LCAB and RCAB of Subjects 1,2,3 during the systolic deceleration phase of the cardiac cycle.
• Results presented during the systolic deceleration phase• Secondary and helical flows
occur downstream of the bifurcation• Smaller bifurcation angle
results in larger secondary flow regions, retained further downstream
Numerical Analysis of Blood Flow Through the Human Carotid Artery Bifurcation
ResultsLow Wall Shear Stress Regions
(5/5)
Aristotle University of Thessaloniki
Athanasios Margaritis
Laboratory of Fluid Mechanics and Turbomachinery
Figure 14. Low WSS regions for the LCAB and RCAB of Subjects 1,2,3 during the systolic deceleration phase of the cardiac cycle.
• Results presented at the peak of the systolic acceleration phase• Lowest Wall Shear Stress
regions appear on the outer walls of both the ECA and the ICA bulb• Areas correlate well with
secondary flow regions
Numerical Analysis of Blood Flow Through the Human Carotid Artery Bifurcation
DiscussionEffects of the Viscosity Model• Minor effect of blood’s viscosity
model• Near-infinite shear rate near the wall
• Non-Newtonian, Carreau-Yassuda model• Negligible variations in the results• Smoother time-variation of WSS values• Slight mitigation of extreme peak
values(minimum – maximum)
• Newtonian model accuracy is sufficient• Further research for viscosity model• For Fluid-Structure Interactions• For multiphase simulation of blood
(1/4)
Aristotle University of Thessaloniki
Athanasios Margaritis
Laboratory of Fluid Mechanics and Turbomachinery
Figure 15. Comparison of results for the Newtonian and the Carreau-Yassuda viscosity models.
Numerical Analysis of Blood Flow Through the Human Carotid Artery Bifurcation
DiscussionWall Shear Stress Distribution
• Wall Shear Stress is the most important factor for cardiovascular diseases• Endothelium alignment and LDL accumulation and intrusion
• Current results agree with previously reported findings• Maximum values of at the bifurcation apex at the end of the
systolic acceleration phase• Lower values away from the apex and during the rest of the cardiac
cycle• Physiological values of
• Lowest values on the outer walls of ICA bulb and ECA with • Risk for atherogenesis in regions where
(2/4)
Aristotle University of Thessaloniki
Athanasios Margaritis
Laboratory of Fluid Mechanics and Turbomachinery
Numerical Analysis of Blood Flow Through the Human Carotid Artery Bifurcation
DiscussionRecirculation and Secondary Flows
(3/4)
Aristotle University of Thessaloniki
Athanasios Margaritis
Laboratory of Fluid Mechanics and Turbomachinery
• Velocity profiles are disturbed, far from parabolic near the bifurcation• Flow separation, recirculation and helical secondary flows• Near the outer walls, downstream of the bifurcation• Induced due to artery branching and curvature• During the systolic deceleration phase of the cardiac cycle
• Flow inversion occurs during diastole• Effect of bifurcation angle• High bifurcation angle leads to massive secondary flow regions, limited at
the root of each branch at the bifurcation• Low bifurcation angle leads to smaller secondary flow regions, retained
further downstream through the ICA and ECA branches, main flow close to the inner walls
Numerical Analysis of Blood Flow Through the Human Carotid Artery Bifurcation
DiscussionPeriodic Time Evolution
(4/4)
Aristotle University of Thessaloniki
Athanasios Margaritis
Laboratory of Fluid Mechanics and Turbomachinery
• Flow field variation during cardiac cycle not emphasized in previous literature• Secondary and helical flow regions after systolic acceleration peak• Maximum WSS values at the end of systolic acceleration, much
lower during the rest of the cardiac cycle• Flow inversion during diastolic phase• Shear-thinning behaviour of blood mitigates peak WSS values
Numerical Analysis of Blood Flow Through the Human Carotid Artery Bifurcation
Conclusions
Aristotle University of Thessaloniki
Athanasios Margaritis
Laboratory of Fluid Mechanics and Turbomachinery
• Insignificant variation between the Newtonian and the Carreau-Yassuda viscosity models• Minor effect mostly regarding peak WSS values• Further examination required for multiphase or FSI simulations• Negligible increase in complexity – Carreau-Yassuda may be easily used
• Wall Shear Stress distributions in perfect agreement with previous literature• Accurate models and commercial ANSYS Fluent solver
• Secondary flow regions correlate with low, oscillating WSS regions• Occur on the outer walls of the ICA and ECA branches, at the beginning of
the bifurcation
• Flow inversion may occur during the diastolic phase of the cardiac cycle
Numerical Analysis of Blood Flow Through the Human Carotid Artery Bifurcation
Limitations
Aristotle University of Thessaloniki
Athanasios Margaritis
Laboratory of Fluid Mechanics and Turbomachinery
• Universal boundary conditions instead of patient-specific measurements• Parabolic inlet velocity profile – negligible error• Fixed mass flow split and pressure differences
• Imaging and reconstruction techniques• Limited MRI accuracy• Effect of posture and operator during MRI• Manual geometry reconstruction and correction – human error
Numerical Analysis of Blood Flow Through the Human Carotid Artery Bifurcation
Suggestions for Further Research
Aristotle University of Thessaloniki
Athanasios Margaritis
Laboratory of Fluid Mechanics and Turbomachinery
• Clarification of the importance of different simulation models for each case• Turbulent or Laminar• Single-phase or Multi-phase• Newtonian or Non-Newtonian
• Implementation of fully coupled Fluid-Structure Interaction simulations• Include wave propagation phenomena
• Use of Windkessel models as boundary conditions for the arterial tree
Numerical Analysis of Blood Flow Through the Human Carotid Artery Bifurcation
Thank you.
Aristotle University of Thessaloniki
Athanasios Margaritis
Laboratory of Fluid Mechanics and Turbomachinery
Dipl. Ing. Athanasios Margaritis
Numerical Analysis of Blood Flow Through the Human Carotid Artery Bifurcation