the effect of artery bifurcation angles on fluid flow and wall shear stress in the middle cerebral artery

98 Pages·2015·2.92 MB·English

by  Zachary Ramey Jones

THE EFFECT OF ARTERY BIFURCATION ANGLES ON FLUID FLOW AND
WALL SHEAR STRESS IN THE MIDDLE CEREBRAL ARTERY

A Thesis
Presented to
the Faculty of California Polytechnic State University,
San Luis Obispo

In Partial Fulfillment
of the Requirements for the Degree
Master of Science in Biomedical Engineering

by
Zachary Ramey Jones
December 2014
©2014
Zachary Ramey Jones
ALL RIGHTSRESERVED

ii
COMMITTEEMEMBERSHIP

TITLE: The Effect of Artery Bifurcation Angles on Fluid
Flow and Wall Shear Stress in the Middle Cerebral
Artery

AUTHOR: Zachary Ramey Jones

DATE SUBMITTED: December 2014

COMMITTE CHAIR: David Clague, Ph.D., Associate Professor,
Department of Biomedical & General Engineering

COMMITTEE MEMBER: Scott Hazelwood, Ph.D., Associate Professor,
Department of Biomedical & General Engineering

COMMITTEE MEMBER: Dan Walsh, Ph.D., Associate Professor,
Department of Biomedical & General Engineering

iii
ABSTRACT
The Effect of Artery Bifurcation Angles on Fluid Flow and Wall
Shear Stress in the Middle Cerebral Artery

Zachary Ramey Jones

Saccular aneurysms are the abnormal plastic deformation of veins and arteries
that can lead to lethal thrombus genesis or internal hemorrhaging. Medication and
surgery greatly reduce the mortality rates, but treatment is limited by predicting who
will develop aneurysms. A common location for saccular aneurysm genesis is at the
main middle cerebral artery (MCA) bifurcation. The main MCA bifurcation is
comprised of the M1 MCA segment, parent artery, and two M2 segments, daughter
arteries. Studies have found that the lateral angle (LA) ratio of the MCA bifurcation
is correlated with aneurysm formation. The LA ratio is defined as the angle between
the M1 and the larger M2 divided by the angle between the M1 and the smaller M2.
When the LA ratio is equal to 1, perfectly symmetrical, no aneurysms are found at the
MCA bifurcation. When the LA ratio is greater than 1.6, aneurysms are commonly
found at the MCA bifurcation. In the research described here, varying MCA
bifurcation angles were compared to uncover any changes to fluid flow and wall
shear stress that could stimulate aneurysm growth. Eight pre-aneurysm MCA
bifurcation models were created in SolidWorks® using 120 degrees, 90 degrees, and
60 degrees as the angle between the M1 and the larger M2. LA ratios of 1, 1.6 and
2.2 were then used to characterize the other branch angle (60 degrees with a LA ratio
of 1 was excluded). These models were imported into COMSOL Multiphysics®
where the laminar fluid flow module was used to simulate non-Newtonian blood
flow. Fluid flow profiles showed little to no change between the models. Shear
stress changed when the LA ratio was increased, but the changed varied between the
120, 90 and 60 degree models. 120 degree models had a 3.87% decrease in max
shear stress with a LA ratio of 2.2 while the 90 degree models had 7.5% decrease in
max shear stress with a LA ratio of 2.2. Each daughter artery had distinct areas of
high shear stress when the LA ratio equaled 1. Increasing the LA ratio or decreasing
the bifurcation angle caused the areas of shear stress to merge together. Increasing
LA ratio caused shear stress to decrease and spread around the MCA bifurcation. The
reduction in max wall shear stress for high LA ratios supports current aneurysm
genesis hypothesizes, but additional testing is required before bifurcation geometries
can be used to predicted aneurysm genesis.
iv
TABLE OF CONTENTS

LIST OF TABLES ...................................................................................................... vii
LIST OF FIGURES ................................................................................................... viii
CHAPTER 1: INTRODUCTION ..................................................................................1
1.1: Thesis Overview ........................................................................................ 1
1.2: Motivation .................................................................................................. 2
1.3: Previous Aneurysm Studies ....................................................................... 3
CHAPTER 2: BACKGROUND ....................................................................................7
2.1: Artery Physiology ...................................................................................... 7
2.2: Aneurysm Physiology and Pathology ........................................................ 9
2.3: Middle Cerebral Artery Bifurcation Characterization ............................. 14
2.4: Loading Conditions.................................................................................. 20
2.5: Rheology and Shear Stress ...................................................................... 29
CHAPTER 3: MODELING METHODS.....................................................................36
3.1: Modeling Overview ................................................................................. 36
3.2: Fluid Flow Module and Loading Conditions ........................................... 37
3.3: Geometries of Model ............................................................................... 40
3.4: Meshing ................................................................................................... 43
3.5: PIV Settings ............................................................................................. 46
CHAPTER 4: RESULTS .............................................................................................48
4.1: Initial Testing ........................................................................................... 48
4.2: Model Validation ..................................................................................... 49
4.3: Fluid Flow ................................................................................................ 51
4.4: Wall Shear Stress ..................................................................................... 53
CHAPTER 5: DISCUSSION .......................................................................................61
CHAPTER 6: CONCLUSION ....................................................................................64
REFERENCES ............................................................................................................66
APPENDICES
APPENDIX A: GEOMETRIES FOR SOLIDWORKS MODELS .................70
APPENDIX B: FLOW PROFILE AND SHEAR STRESS PLOTS ...............74
v
APPENDIX C: MATLAB CODE FOR WINDKESSEL MODEL .................82
APPENDIX D: COMSOL PIV INSTRUCTIONS ..........................................85
APPENDIX E: LIVELINKtm AND SOLIDWORKS® ...................................88

vi
LIST OF TABLES
Table Page
I. Convergence study of fluid velocities and shear stress for 120-120 model at
0.3 second ..............................................................................................................43
II. Comparison between analytical equations and simulation results for simple
cylinder. .................................................................................................................48
III. Comparison of literature values to MCA control model .......................................49
IV. Table of averaged inlet and outlet flow rates for all models..................................53
V. Max shear stress during systole and diastole with maximum area of shear
stress at MCA bifurcation ......................................................................................56
VI. Percent change in shear stress between different models compared to 120-120
control model .........................................................................................................56
vii
LIST OF FIGURES
Figure Page
1. FEA of wall shear stress and blood velocity in a MCA bifurcation with an
aneurysm [9]. ...........................................................................................................4
2. Diagram of the Artery Layers [14]. .........................................................................8
3. Diagram of Fusiform and Saccular aneurysms [15]. .............................................10
4. Example of surgical clipping of an aneurysm at a bifurcation [20]. ......................12
5. Diagram of Cerebral Arteries [18]. The area of interest is the main MCA
bifurcation located in the middle left side of the diagram. ....................................16
6. Surgical dissection of MCA bifurcation [23]. ........................................................17
7. Representation of healthy LA and DA ratios [1]. .(a)The entire cerebral
vasculature. (b and c)Lateral angle measurements. ..............................................18
8. Representation of a MCA bifurcation with an aneurysm [1].(a)The entire
cerebral vasculature. (b and c)Lateral angle measurements. ................................19
9. Two, Three, and Four Element Windkessel Model Diagram [33]. .......................22
10. Graph comparing the 3-element Windkessel model to measured pressure in a
human aorta [35]. ...................................................................................................24
11. Example of a 3-element Windkessel model of Howe's original code for the
pressure waveform in the aorta. .............................................................................26
12. Flow Rate of blood in the MCA. ...........................................................................28
13. Simulated Windkessel cardiac pressure waveform for the MCA. .........................29
14. Hypothesized pathways for mechanical stimuli to ecNOS activation [42]. ..........33
15. Velocity profile of Idealized 2D bifurcation with non-Newtonian laminar flow ..37
16. SolidWorks model of an idealized healthy MCA bifurcation. ..............................41
17. Dimensions for 120-120 bifurcation. .....................................................................42
18. Line plot of probed shear stress at the bifurcation related to Degrees of
freedom. .................................................................................................................44
19. Mesh of the boundary and domain elements for 120°-120° model. ......................45
viii
20. (left)PIV experiment from literature. (right)Particle tracings from simulated
model......................................................................................................................50
21. Flow profile at peak systole for all bifurcation angles. (a-h) 120°-120°, 120°-
75°, 120°-54.54°, 90°-90°, 90°-56.25°, 90°-40.91°, 60°-37.5°, 60°-27-27°
respectively. ...........................................................................................................52
22. Shear Stress Comparison. (a-h) 120°-120°, 120°-75°, 120°-54.54°, 90°-90°,
90°-56.25°, 90°-40.91°, 60°-37.5°, 60°-27-27° respectively. ................................54
23. Shear stress versus Distance from bifurcation for 120° base angle. ......................57
24. Shear stress versus Distance from bifurcation for 90° base angle. ........................58
25. Shear stress versus Distance from bifurcation for 60° base angle. ........................58
26. Probed max shear stress of all models over one cardiac cycle ..............................60
27. Dimensions of 120 degree base angle model with LA ratio 1.6 (120°-75°). .........70
28. Dimensions of 120 degree base angle model with LA ratio 2.2 (120°-54.54°). ....70
29. Dimensions of 90 degree base angle model with LA ratio 1 (90°-90°) .................71
30. Dimensions of 90 degree base angle model with LA ratio 1.6 (90°-56.25°) .........71
31. Dimensions of 90 degree base angle model with LA ratio 2.2 (90°-40.91°) .........72
32. Dimensions of 60 degree base angle model with LA ratio 1.6 (60°-37.5°) ...........72
33. Dimensions of 60 degree base angle model with LA ratio 2.2 (60°-27.27°) .........73
34. (top)Velocity plot of 120 degree base angle model with LA ratio 1.0.
(bottom)Shear stress plot of 120 degree base angle model with LA ratio 1.0. ......74
35. (top)Velocity plot of 120 degree base angle model with LA ratio 1.6.
(bottom)Shear stress plot of 120 degree base angle model with LA ratio 1.6. ......75
36. (top)Velocity plot of 120 degree base angle model with LA ratio 2.2.
(bottom)Shear stress plot of 120 degree base angle model with LA ratio 2.2. ......76
37. (top)Velocity plot of 90 degree base angle model with LA ratio 1.0.
(bottom)Shear stress plot of 90 degree base angle model with LA ratio 1.0. ........77
38. (top)Velocity plot of 90 degree base angle model with LA ratio 1.6.
(bottom)Shear stress plot of 90 degree base angle model with LA ratio 1.6. ........78
39. (top)Velocity plot of 90 degree base angle model with LA ratio 2.2.
(bottom)Shear stress plot of 90 degree base angle model with LA ratio 2.2. ........79
ix
40. (top)Velocity plot of 60 degree base angle model with LA ratio 1.6.
(bottom)Shear stress plot of 60 degree base angle model with LA ratio 1.6. ........80
41. (top)Velocity plot of 60 degree base angle model with LA ratio 2.2.
(bottom)Shear stress plot of 60 degree base angle model with LA ratio 2.2. ........81
x