[a margaritis] spoudastiki ergasia (presentation)

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





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





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)





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)





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)





MethodsIn-vivo MRA Example Images

(2/7)





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.





MethodsComputational Mesh Example (R1)

(4/7)





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)





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.





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





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)




Figure 10. Wall Shear Stress and Velocity Distributions for Subject 1 (L1 – R1).



(2/5)











(3/5)










ResultsStreamlines and Secondary Flows

(4/5)




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


ResultsLow Wall Shear Stress Regions

(5/5)




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


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)




Figure 15. Comparison of results for the Newtonian and the Carreau-Yassuda viscosity models.


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)





DiscussionRecirculation and Secondary Flows

(3/4)




• 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


DiscussionPeriodic Time Evolution

(4/4)




• 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


Conclusions




• 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


Limitations




• 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


Suggestions for Further Research




• 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


Thank you.




Dipl. Ing. Athanasios Margaritis


[a margaritis] spoudastiki ergasia (presentation)

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