Numerical Simulations of Aortic Blood Flow with a Bicuspid Aortic Valve Público
Blum, Ruth Davis (2010)
Abstract
One of the most common congenital heart defects is bicuspid aortic valve (BAV), occurring in about 1% to 2% of the population. In patients with BAV the aortic valve deviates from normal in that it only has two leaflets instead of three. BAV can result in altered hemodynamics and decreased performance of the valve, which in turn can lead to serious complications, such as aortic dilation, stenosis, regurgitation, aneurysms, dissection and infective endocarditis. This research focuses on understanding the pathology behind one complication associated with bicuspid aortic valves in particular: aortic dilation . This is primarily because aortic dilation is correlated to greatly increased risk for further complications such as aortic regurgitation, formation of an aortic aneurysm or aortic dissection.
The framework to which the present work belongs is a project for investigating the fluid dynamics in the ascending aorta of patients with BAV in order to reveal the hemodynamic mechanisms possibly causing aortic dilation in some patients and not others. Differences in BAV morphologies due to the fusion of different combinations of cusps and different inlet sizes were considered, and an idealized geometry of the aorta was used. This investigation was conducted via three-dimensional computational models that are able to provide reliable evaluation of various hemodynamic and anatomical parameters, relevant for prediction and quantification of aortic dilation.
It was found that as the size of the inlet decreases, the velocity, pressure and wall shear stress all increase in the ascending aorta. Blood vessel wall remodeling is associated with prolonged increases of pressure and flow rate, and so narrow inlets may be correlated with aortic dilation. It is unclear how the fusion of different leaflets is correlated with pathologies of the aortic arch, but when coupled with a small inlet, rotated inlets induce asymmetry of the blood flow. At this point in the research it can be concluded that there is something inherent with blood flow in the aortic arch in models with bicuspid aortic valves that is intrinsically different from the normal tricuspid aortic valve flow. Additionally, this flow differs depending on the specific morphology of the bicuspid aortic valve under investigation.
Table of Contents
CONTENTS
1. Introduction
…………………………………………………………
1
1.1
Background
…………………………………………...………….
1
1.2 Significance ……………………………………………….....……. 2
1.3 Prior Studies ……………………………………………………..... 4
1.4 Summary ……………………………………………………......... 6
2. Methods
……………………………………………………..………..
8
2.1 Computational Fluid Dynamics …………….…………….. 8
2.2 Starting Assumptions ………………………….…………….. 10
2.3 The Mathematical Model ……………………………………. 15
2.4 Quantitative Analysis ………………………………………... 18
2.5 Numerical Approximation ………..…………………....... 19
2.6 Summary ……………………………………………....………….. 21
3. Results
…………………………………………………….…………..
22
4. Discussion
……………………………………………………………
34
5. Conclusion
……………………………………………………………
37
6. Glossary
…………………………………………………….…………
39
7. Bibliography
……………………………………………………….
41
ILLUSTRATIONS
Figures
1.1 A normal aortic valve ………………………..................……………….. 1
1.2 A bicuspid aortic valve ……………………….................………………. 2
2.1 Five degrees of freedom of the inlet condition ……………....…. 12
2.2 Illustration of the three possible leaflet fusions ………....……… 13
2.3 Inlet rotation angles used to describe the different
fusions of leaflets ……………………………………....................……………. 14
2.4 Inlet to the aorta
……………………...................…………………………
14
2.5 Model of a carotid bifurcation, illustrating a typical
computational domain
……………………………..........................……….
16
2.6 Parabolic velocity profile prescribed at the inlet section
of
the computational domain
…………………………......................……...
17
2.7 The time-varying flow rate
………………………...............…………..
18
2.8 Images of meshes ……………………………...................………………. 22
3.1 Velocity profile at peak systole …………………………..............…… 23
3.2 Location of cross-sectional velocity slice …………..........………… 24
3.3 Velocity cross-section profile at top of aortic arch
during peak systole
………………............................………………………
25
3.4 Pressure pattern during peak systole ………………………….......... 26
3.5 Wall shear stress pattern during peak systole ………….....……… 27
3.6 Location of three different cross-sectional slices for
which the isolines were computed
……………....................……………
29
3.7 Velocity isolines for an inlet radius of 1.05 cm at
peak
systole
………………..................................…………………………………….
29
3.8 Velocity isolines for an inlet radius of 0.45 cm at
peak
systole
…………………………….................................…………………………
30
3.9 Location of slices of velocity and pressure patterns
in realistic geometry
……………………………….........................………...
32
3.10 Velocity patterns in realistic geometry at peak systole
……….. 32
3.11 Pressure pattern in realistic geometry at peak systole
………… 33
3.12 Wall shear stress in realistic geometry at peak systole ………… 34
Equations
E. 1 Navier-Stokes equations ……………………………………….. 15
E. 2 Strain rate ………………………………………………………........ 15
E. 3 Cauchy stress tensor ………………………………………...…… 17
E. 4 Prescribed velocity profile ……………………………….……… 17
E. 5 Time-varying flow rate ……………………………………..……. 17
E. 6 Wall shear stress ………………………………………………...... 19
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