# Presentation: 095282

## Constructing Hexahedral Meshes of Abdominal Aortic Aneurysms for Use in Finite Element Modeling

- CT scans were segmented and triangular surface meshes generated using Amira.
- Antiga and Steinman’s method (2004) for automatically extracting parameterized representations of blood vessel walls was extended for AAAs.
**Extraction of centerlines**
- Obtain approximation of medial axis by calculating the Voronoi diagram
- Solve Eikonal equation over the Voronoi diagram using the fast marching algorithm
- ∇ T = 1 / R(x)
- Find centerlines by backtracking along path of steepest descent
- Antiga and Steinman’s implementation in the Visualization Toolkit (VTK) was extended using Visual C++ .NET.

**Constructing Hexahedral Meshes of Abdominal Aortic Aneurysms for Use in Finite Element Modeling**

**Rowena Ong**
- Kara Kruse, MSE
- Research Alliance in Math and Science
- Computational Sciences and Engineering Division, Oak Ridge National Laboratory
- http://www.csm.ornl.gov/Internships/abstracts/RowenaOng.pdf

- The Research Alliance in Math and Science program is sponsored by the Mathematical, Information, and Computational Sciences Division, Office of Advanced Scientific Computing Research, U.S. Department of Energy.  The work was performed at the Oak Ridge National Laboratory, which is managed by UT-Battelle, LLC under Contract No. De-AC05-00OR22725. **T**his work has been authored by a contractor of the U.S. Government, accordingly, the U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for U.S. Government purposes.

**CONCLUSIONS**
- When complete, this program will automatically generate quality hexahedral meshes of AAAs, including iliac bifurcation and distinguishing between inner surface of thrombus and outer arterial wall.
- These meshes may be used in fluid-solid interaction models in the future, potentially giving more accurate results than fluid or structural models and providing insight into how the iliac bifurcation and thrombus affect AAA formation.
- This method could be applied to both vascular and pulmonary modeling to improve finite element analysis at bifurcations.

**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.

**INTRODUCTION**
- Abdominal Aortic Aneurysms (AAAs) are a leading cause of death in the U.S.  Finite element models are being developed to help physicians predict location and risk of rupture.
- Current finite element models of AAAs do not include both iliac bifurcation and thrombus, which may significantly affect fluid flow and wall stress (Fig. 1).
- Generation of a high-quality finite element mesh with regular elements is difficult at the bifurcation.
- Purpose of this project: To generate quality hexahedral meshes of AAAs, including iliac bifurcation and distinguishing between the inner surface of the thrombus and the arterial wall, so that finite element analysis can be performed.

- Fig. 1. AAA anatomy

- Fig. 2. Mesh representation of an AAA. The thrombus is represented by the volume between the two surfaces.

**RESULTS**
- Results for one patient’s dataset:

- Fig. 3. CT images of AAA were segmented.  (Only one slice shown here.)

**Generation of parameterized surface**
- Longitudal mapping
- Solve following equation over the surface mesh using finite element method
- Δ f = 0 (where Δ is LaPlace-Beltrami operator)
- Circumferential mapping
- Use angular coordinates with respect to the centerline
**Generate hexahedral mesh **
- Use sweeping algorithm