# Presentation: 320540

## 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**

**Notes:**
“From year to year we look at Nature with new eyes.”
Henry David Thoreau, Journal IX, 156 (December 4, 1856)
Generally regarded as a literary figure, Thoreau showed a lasting interest in science. He belonged to the Boston Natural History Society from 1850 onwards, read widely in the scientific literature of his day, and published one the first scholarly discussions on forest succession. (Some historians rate Thoreau as one of the founders of ecology.)

## 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

## Introduction: What does AAA modeling involve?

- Using equations to model wall stress and/or fluid flow through AAA
- Three basic parts:
- Equations modeling fluid flow and/or wall stress
- 3D reconstruction of AAA from CT scans
- Finite element analysis to numerically solve equations

- Cassada, Barnes, & Lilly, 2003

## 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

## 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

- 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**

## 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

## Methods

- 1. Segment CT scans and generate triangular surface meshes using Amira

**Obtain CT scans of AAA**

**Generate surfaces**

**Outer surface**

**Inner surface**

## 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

## 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

## Methods

- 3. Build hexahedral mesh of thrombus and lumen using sweeping algorithm

## Results

- From actual patient data

- CT scans segmented

- Outer and inner surfaces generated

## Results: Voronoi diagrams

- Inner surface

- Outer surface

## Results: Centerlines

- Inner surface

- Outer surface

## Results: Splitting lines

- Inner surface

- Outer surface

## Results: Parametric representation

- Inner surface

- Outer surface

## Results: Parametric Representation

- Close-up of bifurcation

## 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**

## 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**

## 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

## 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 ResearchU.S. Department of Energy
- Through the Research Alliance for Math and Science (RAMS)

## 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.