Modeling of Flow in an In Vitro Aneurysm Model

123 Pages·2015·2.55 MB·English

by  Qing Hao

University of Miami
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2010-12-16
Modeling of Flow in an In Vitro Aneurysm Model:
A Fluid-Structure Interaction Approach
Qing Hao
University of Miami, [email protected]
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UNIVERSITY OF MIAMI

MODELING OF FLOW IN AN IN VITRO ANEURYSM MODEL: A FLUID-
STRUCTURE INTERACTION APPROACH

By

Qing Hao

A DISSERTATION

Submitted to the Faculty
of the University of Miami
in partial fulfillment of the requirements for
the degree of Doctor of Philosophy

Coral Gables, Florida

December 2010
©2010
Qing Hao
All Rights Reserved
UNIVERSITY OF MIAMI

A dissertation submitted in partial fulfillment of
the requirements for the degree of
Doctor of Philosophy

MODELING OF FLOW IN AN IN VITRO ANEURYSM MODEL: A FLUID-
STRUCTURE INTERACTION APPROACH

Qing Hao

Approved:

________________ _________________
Baruch B. Lieber, Ph.D. Terri A. Scandura, Ph.D.
Professor of Bimedical Engineering Dean of the Graduate School

________________ _________________
Weiyong Gu, Ph.D. Chun-Yuh Huang, Ph.D.
Professor of Bimedical Engineering Assistant Professor of
Biomedical Engineering

________________
Danny Bluestein, Ph.D.
Professor of Biomedical Engineering
SUNY Stony Brook
HAO, QING (Ph.D., Biomedical Engineering)
Modeling of Flow in an vitro Aneurysm Model: (December 2010)
A Fluid-Structure Interaction Approach

Abstract of a dissertation at the University of Miami.

Dissertation supervised by Professor Baruch B. Lieber
No. of pages in text. (111)

Flow velocity field, vorticity and circulation and wall shear stresses were simulated
by FSI approach under conditions of pulsatile flow in a scale model of the rabbit elastin-
induced aneurysm. The flow pattern inside the aneurysm sac confirmed the in vitro
experimental findings that in diastole time period the flow inside the aneurysm sac is a
stable circular clock-wise flow, while in systole time period higher velocity enters into
the aneurysm sac and during systole and diastole time period an anti-clock circular flow
pattern emerged near the distal neck; in the 3-D aneurysm sac, the kinetic energy per
point is about 0.0002 (m2/s2); while in the symmetrical plane of the aneurysm sac, the
kinetic energy per point is about 0.00024 (m2/s2). In one cycle, the shape of the
intraaneurysmal energy profile is in agreement with the experimental data; The shear
stress near the proximal neck experienced higher shear stress (peak value 0.35 Pa) than
the distal neck (peak value 0.2 Pa), while in the aneurysm dome, the shear stress is
always the lowest (0.0065 Pa). The ratio of shear stresses in the proximal neck vs. distal
neck is around 1.75, similar to the experimental findings that the wall shear rate ratio of
proximal neck vs. distal neck is 1.5 to 2.
ACKNOWLEDGEMENTS

I would like to thank Dr. Baruch B. Lieber for his invaluable guidance and
advising throughout this journey. I would have not finished without his help.

I also would like to thank Adina staff for their technical support and help in the
email communications. Special thanks go to the members of our research group in Miami
for the discussions.

Finally, my profound thanks to my family, my father, Hao Chuanjing, and my
mother, Xiao Guifang for their support, patience and love.
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TABLE OF CONTENTS

Page

LIST OF FIGURES ..................................................................................................... v

LIST OF TABLES ....................................................................................................... ix

Chapter

1 INTRODUCTION ......................................................................................... 1
1.1 Stroke and Cerebral Aneurysm …………………………………………… 1
1.2 Current Treatment of Cerebral Aneurysm…………………………………. 4
1.3 The Development of Flow Divertor ……………………………………. 7
1.4 The Study Goal …………………………………………………………. 15

2 NUMERICAL METHODS AND MODEL VALIDATIONS ...................... 20
2.1 The Governing Equations of Fluid Mechanics .......................................... 20
2.2 Solid Mechanics ......................................................................................... 25
2.3 Boundary and Initial Conditions ................................................................ 28
2.4 Model Validation ....................................................................................... 29

3 ANEURYSM FSI MODEL AND RESULTS ................................................. 39
3.1 The Silicone Replica 3-D Model .............................................................. 39
3.2 Governing Equations and Boundary Conditions ...................................... 40
3.3 Results ....................................................................................................... 43

4 DISCUSSION .................................................................................................. 97

5 CONCLUSIONS.............................................................................................. 103

REFERENCES………………………………………………………………….…… 105
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LIST OF FIGURES

Figure 1-1. Velocity field inside the aneurysm……………………………………......18

Figure 1-2. CFD simulation for a side wall aneurysm...................................................19

Figure 2-1. Comparison between the analytical and numerical solutions for steady
(Poisuille) flow in a rigid tube……………………..………………………………….35

Figure 2-2. Comparison between the analytical and numerical solution for pulsatile
(Womersley flow) velocity profiles in rigid tube……………………….…………….36

Figure 2-3. Comparison between the analytical and numerical solution for pulsatile
(Womersley flow) axial velocity profiles in an elastic tube…………………………..37

Figure 2-4. Radial velocity profile for a point on the inner wall of the tube and axially
located in the center of the tube during one pulsatile cycle…………………………...38

Figure 3-1. The fluid part of the aneurysm model constructed in SolidWorks……….49

Figure 3-2. The solid part of the aneurysm model constructed in SolidWorks.………50

Figure 3-3. The coarsest meshes for the fluid part (a), and solid part (b)..……………51

Figure 3-4. The aneurysm sac mesh in Mesh Set # 3, and the location of dome element,
proximal element and distal element…..………………………………………………52

Figure 3-5. Average flow rate in the descending aorta (a), and in the vertebral artery (b)
as a function of mesh sizes that shown in table 3-1………….. ……………………… 53

Figure 3-6. Waveforms of flow rate into the model and pressures at the inlet and outlets
of the model (a). Pressure difference between the inlet and outlet (b).………………..54

Figure 3-7. Flow rates in the branches: (a) ascending aorta; (b) descending aorta; (c) right
subclavian artery, of the aneurysm model……………………………………………...55

Figure 3.7. Flow rates in the branches: (d) left subclavian; (e) left common carotid artery;
(f) vertebral artery, of the aneurysm model…………………………………………….56

Figure 3-8. The velocity field in the aneurysm model at time t/T=0.132 (velocity units are
m/s). The velocity scale is shown by the vector above the color scale…………………….57
v
Figure 3-9. The velocity field in the aneurysm model at time t/T=0.132 (velocity units are
m/s). The velocity scale is shown by the vector above the color scale………………...…58

Figure 3-10. The velocity field inside the aneurysm sac at t/T =0.042 (orange triangles in the
top inset). The velocity scale is shown by the vector above the color scale……………...59

Figure 3-11. The velocity field inside the aneurysm sac at t/T =0.102 (orange triangles in the
top inset). The velocity scale is shown by the vector above the color scale………………60

Figure 3-12. The velocity field inside the aneurysm sac at t/T =0.132 (orange triangles in the
top inset). The velocity scale is shown by the vector above the color scale………………61

Figure 3-13. The velocity field inside the aneurysm sac at t/T =0.162 (orange triangles in the
top inset). The velocity scale is shown by the vector above the color scale………………62

Figure 3-14. The velocity field inside the aneurysm sac at t/T =0.192 (orange triangles in the
top inset). The velocity scale is shown by the vector above the color scale………………63

Figure 3-15. The velocity field inside the aneurysm sac at t/T =0.252 (orange triangles in the
top inset). The velocity scale is shown by the vector above the color scale……………….64

Figure 3-16. The velocity field inside the aneurysm sac at t/T =0.282 (orange triangles in the
top inset). The velocity scale is shown by the vector above the color scale……………….65

Figure 3-17. The velocity field inside the aneurysm sac at t/T =0.312 (orange triangles in the
top inset). The velocity scale is shown by the vector above the color scale……………….66

Figure 3-18. The velocity field inside the aneurysm sac at t/T =0.342 (orange triangles in the
top inset). The velocity scale is shown by the vector above the color scale……………….67

Figure 3-19. The velocity field inside the aneurysm sac at t/T =0.410 (orange triangles in the
top inset). The velocity scale is shown by the vector above the color scale……….………68

Figure 3-20. The velocity field inside the aneurysm sac at t/T =0.5975 (orange triangles in the
top inset). The velocity scale is shown by the vector above the color scale……………….69

Figure 3-21. The velocity field inside the aneurysm sac at t/T =0.6275 (orange triangles in the
top inset). The velocity scale is shown by the vector above the color scale. ………………70

Figure 3-22. The velocity field inside the aneurysm sac at t/T =0.6875 (orange triangles in the
top inset). The velocity scale is shown by the vector above the color scale. .………………71

Figure 3-23. The velocity field inside the aneurysm sac at t/T =0.8075 (orange triangles in the
top inset). The velocity scale is shown by the vector above the color scale. .………………72

Figure 3-24. Contours of vorticity in the plane of symmetry of the aneurysm (x-y plane) at
t/T =0.012…………………………………………………………………………………….73

vi
Figure 3-25. Contours of vorticity in the plane of symmetry of the aneurysm (x-y plane) at
t/T =0.042……………………………………………………………………………….74

Figure 3-26. Contours of vorticity in the plane of symmetry of the aneurysm (x-y plane) at
t/T =0.057………………………………………………………………………………..75

Figure 3-27. Contours of vorticity in the plane of symmetry of the aneurysm (x-y plane) at
t/T =0.102………………………………………………………………………………..76

Figure 3-28. Contours of vorticity in the plane of symmetry of the aneurysm (x-y plane) at
t/T =0.132 ………………………………………………………………………………77

Figure 3-29. Contours of vorticity in the plane of symmetry of the aneurysm (x-y plane) at
t/T =0.162……………………………………………………………………………….78

Figure 3-30. Contours of vorticity in the plane of symmetry of the aneurysm (x-y plane) at
t/T =0.192……………………………………………………………………………….79

Figure 3-31. Contours of vorticity in the plane of symmetry of the aneurysm (x-y plane) at
t/T =0.2………………………………………………………………………………….80

Figure 3-32. Contours of vorticity in the plane of symmetry of the aneurysm (x-y plane) at
t/T =0.252……………………………………………………………………………….81

Figure 3-33. Contours of vorticity in the plane of symmetry of the aneurysm (x-y plane) at
t/T =0.282……………………………………………………………………………….82

Figure 3-34. Contours of vorticity in the plane of symmetry of the aneurysm (x-y plane) at
t/T =0.312……………………………………………………………………………….83

Figure 3-35. Contours of vorticity in the plane of symmetry of the aneurysm (x-y plane) at
t/T =0.342………………………………………………………………………………..84

Figure 3-36. Contours of vorticity in the plane of symmetry of the aneurysm (x-y plane) at
t/T =0.35………………………………………………………………………………….85

Figure 3-37. Contours of vorticity in the plane of symmetry of the aneurysm (x-y plane) at
t/T =0.41………………………………………………………………………………….86

Figure 3-38. Contours of vorticity in the plane of symmetry of the aneurysm (x-y plane) at
t/T =0.53………………………………………………………………………………….87

Figure 3-39. Contours of vorticity in the plane of symmetry of the aneurysm (x-y plane) at
t/T =0.5975 ……………………………………………………………………………….88

Figure 3-40. Contours of vorticity in the plane of symmetry of the aneurysm (x-y plane) at
t/T =0.6275………………………………………………………………………………..89

vii