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Constructing Hexahedral Meshes of Abdominal Aortic Aneurysms for Use in Finite Element Analysis. Rowena Ong Vanderbilt University Mentor: Kara Kruse Computational Sciences and Engineering Division August 11, 2004. Introduction: What are abdominal aortic aneurysms (AAAs)?. - PowerPoint PPT Presentation
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Constructing Hexahedral Meshes of Abdominal Aortic Aneurysms for Use in Finite Element Analysis
Rowena OngVanderbilt University
Mentor: Kara KruseComputational Sciences and Engineering Division
August 11, 2004
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Introduction: What are abdominal aortic aneurysms (AAAs)?
Ballooning of aorta caused by weakened vessel walls
If untreated, vessel walls may rupture
AAAs 13th leading cause of death in U.S.
Mortality rate ~80% for ruptured AAAs
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Introduction: What does AAA modeling involve? Using equations to model wall stress and/or fluid flow
through AAA
Three basic parts:1. Equations modeling fluid flow and/or wall stress2. 3D reconstruction of AAA from CT scans3. Finite element analysis to numerically solve equations
Cassada, Barnes, & Lilly, 2003
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Introduction: Challenges of AAA Modeling
Current finite element models of AAAs do not include both iliac bifurcation and thrombus
Iliac bifurcation and thrombus may play significant role in AAA formation
Iliac bifurcation
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Generation of high-quality finite element mesh difficult at bifurcation
Why? Finite element modeling – divide
object into finite elements (blocks or tetrahedra)
Irregular geometry at bifurcation, difficult to generate regularly shaped elements
Important because irregularly shaped elements can yield inaccurate results
(Di Martino et al., 2001)
Introduction: Challenges of AAA Modeling
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Introduction
Goal of this project:
Develop a semi-automatic method for generating high-quality meshes of AAAs Including iliac bifurcation and thrombus To be used in finite element analysis
Enable researchers to explore effects of the iliac bifurcation and thrombus on AAA formation
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Methods
Segment
Thrombus
Lumen
1. Segment CT scans and generate triangular surface meshes using Amira
Obtain CT scans of AAA Generate surfaces
Outer surface
Inner surface
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Methods2. Antiga and Steinman’s method (2004) and program for
blood vessel surface generation was extended for AAAs
a. Find centerlines Compute Voronoi diagram, approximation of medial axis Compute solution to Eikonal equation ∇ T = 1 / R(x) over
Voronoi diagram using fast marching algorithm Backtrace along path of steepest descent to find centerlines
Antigua & Steinman, 2004Antigua, Ene-Iordache, 2003
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Methods
b. Decompose bifurcation into 3 parts
c. Build parametric mapping of the surface
Longitudal mapping Solve Δ f = 0 (where Δ is LaPlace-
Beltrami operator) Solve using finite element method
Circumferential mapping Use angular position of points with
respect to the centerline
Implemented in Visualization Toolkit (VTK) using Visual C++.NET
Antigua & Steinman, 2004
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Methods3. Build hexahedral mesh of thrombus and lumen using sweeping algorithm
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
ResultsFrom actual patient data
CT scans segmented Outer and inner surfaces generated
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Results: Voronoi diagrams
Inner surface Outer surface
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Results: Centerlines
Inner surface Outer surface
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Results: Splitting lines
Inner surface Outer surface
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Results: Parametric representation
Inner surface Outer surface
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Results: Parametric Representation
Close-up of bifurcation
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Accomplishments
Extended Antiga and Steinman’s code to generate parameterized surfaces for AAAs
Program generates surfaces semi-automatically and objectively
Parameterized surfaces generated for real patient data
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Future Work
Eliminate triangular area between patches in bifurcation region
Generate volumetric mesh from inner and outer surfaces
Write script to export meshes to Rhino or finite element modeling software
Build GUI for program
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Long-term benefits
Program will allow high-quality finite element meshes to be generated semi-automatically and objectively
Will enable exploration of how iliac bifurcation and thrombus affect AAA formation through finite element modeling
Give physicians another tool to help evaluate AAA rupture risk
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Acknowledgements
Research Mentor
Kara Kruse, M.S.E.
Thanks to the following for AAA data:
David C. Cassada, M.D., Michael B. Freeman, M.D., Mitchell H. Goldman, M.D.
UT Medical Center, Dept. of Vascular Surgery
Stephanie Barnes, Jennifer Lilly
This work was funded by
Mathematical, Information, & Computational Sciences DivisionOffice of Advanced Scientific Computing Research
U.S. Department of Energy
Through the Research Alliance for Math and Science (RAMS)
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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
References
Antiga, L. and D. Steinman. 2004. Robust and Objective Decomposition and Mapping of Bifurcating Vessels. IEEE Trans. on Medical Imaging, 23(6):704-713.
Antiga, L., B. Ene-Iordache, A. Remuzzi. 2003. Centerline Computation and Geometric Analysis of Branching Tubular Surfaces with Application to Blood Vessel Modeling. 11th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision, 2003.
Antiga, L. 2003. Patient-Specific Modeling of Geometry and Blood Flow in Large Arteries. PhD Thesis.
Angenent, S., S. Haker, A. Tannenbaum, & R. Kikinis. 1999. On the Laplace–Beltrami Operator and Brain Surface Flattening. IEEE Trans. on Medical Imaging, 18(8):700-711.