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

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 2 Introduction: What are abdominal aortic aneurysms (AAAs)?  Ballooning of aorta caused by weakened vessel walls  If untreated, vessel walls may rupture  AAAs 13 th leading cause of death in U.S.  Mortality rate ~80% for ruptured AAAs

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 3 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 stress 2.3D reconstruction of AAA from CT scans 3.Finite element analysis to numerically solve equations Cassada, Barnes, & Lilly, 2003

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 4 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

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 5  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

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 6 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

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 7 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

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 8 Methods 2. 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, 2004 Antigua, Ene-Iordache, 2003

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 9 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

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 10 Methods 3. Build hexahedral mesh of thrombus and lumen using sweeping algorithm

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 11 Results From actual patient data CT scans segmented Outer and inner surfaces generated

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 12 Results: Voronoi diagrams Inner surface Outer surface

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 13 Results: Centerlines Inner surface Outer surface

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 14 Results: Splitting lines Inner surface Outer surface

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 15 Results: Parametric representation Inner surface Outer surface

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 16 Results: Parametric Representation Close-up of bifurcation

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 17 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

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 18 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

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 19 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

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 20 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 Division Office of Advanced Scientific Computing Research U.S. Department of Energy Through the Research Alliance for Math and Science (RAMS)

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 21 References  Antiga, L. and D. Steinman Robust and Objective Decomposition and Mapping of Bifurcating Vessels. IEEE Trans. on Medical Imaging, 23(6):  Antiga, L., B. Ene-Iordache, A. Remuzzi 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,  Antiga, L Patient-Specific Modeling of Geometry and Blood Flow in Large Arteries. PhD Thesis.  Angenent, S., S. Haker, A. Tannenbaum, & R. Kikinis On the Laplace–Beltrami Operator and Brain Surface Flattening. IEEE Trans. on Medical Imaging, 18(8):