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

transcript

Rowena OngVanderbilt University

Mentor: Kara KruseComputational Sciences and Engineering Division

August 11, 2004

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

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

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

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

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

Segment

Thrombus

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

Obtain CT scans of AAA Generate surfaces

Outer surface

Inner surface

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

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

Methods3. Build hexahedral mesh of thrombus and lumen using sweeping algorithm

ResultsFrom actual patient data

CT scans segmented Outer and inner surfaces generated

Results: Voronoi diagrams

Inner surface Outer surface

Results: Centerlines

Results: Splitting lines

Results: Parametric representation

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 Research

U.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.

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

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