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Finite Element Meshing for Cardiac Analysis
Yongjie (Jessica) Zhang*, Chandrajit L. Bajaj*, Thomas J. R. Hughes*, Wing Kam Liu†, Grace Chen†, Xiaodong Wang$,
‡
‡
Marius Lysaker , Christian Tarrou
*ICES & CS, Univ. of Texas at Austin
†ME,
$ME,
Northwestern Univ.
Polytechnic Univ.
‡Simula
Research Lab, Norway
Abstract:
This poster presents details of technique to produce an adaptive and quality tetrahedral finite element mesh of a human heart. Both an educational model and a patient-specific model are constructed. There are three main steps in our mesh generation: model acquisition, mesh
extraction and boundary/material layer detection. (1) Model acquisition. Beginning from an educational polygonal model, we edit and convert it to volumetric gridded data. A component index for each cell edge and grid point is computed for assisting the boundary and material layer detection.
For the patient-specific model, we first find some points in MRI scanned data, then use cubic splines and lofting to segment MRI data. Different components are identified. (2) Mesh extraction. We extract adaptive and quality tetrahedral meshes from the volumetric gridded data using our Level
Set Boundary and Interior-Exterior (LBIE) Mesher. The mesh adaptivity is controlled by regions or using a feature sensitive error function. (3) Boundary/material layer detection. The boundary of each component and multiple material layers are identified and meshed. The extracted tetrahedral
mesh of the educational model is being utilized in the analysis of cardiac fluid dynamics via immersed continuum method, and the generated patient-specific model is used in simulating the electrical activity of the heart.
1. An Educational Model
2. A Patient-specific Model
1.4 Application and Results
We first select some points in each slice of the MRI data, then connect them smoothly using
cubic splines and lofting which is used to segment the MRI data into four regions: the
background (0), the heart muscle (81), the left ventricle (162) and the right ventricle (243). We
use the same method to generate adaptive tetrahedral meshes, which is used in the simulation
of the electronic activity of the heart.
1.1 Model Acquisition
An educational polygonal model is edited and converted into volumetric gridded data using the
signed distance method. The heart model is decomposed into twenty-two components as
shown in Table 1. Additional volume data indicating which component each grid point and
each cell edge belong to is also calculated.
Raw MRI data
Manually digitized slices
Continuous model
Tab. 1. The corresponding relationship between
the component/boundary index, components and
their colors. The heart model is decomposed into
twenty-two components as shown in Fig. 2.
aortic valve
Fig. 1. Heart Anatomy Model from [4]
tricuspid valve
pulmonary valve
mitral valve
Volume rendering
Application: The heart model is put inside a cubic
1.2 Mesh Extraction
We choose the extended Dual Contouring
method to construct the tetrahedral heart
model from volumetric gridded data [2][3]
because it takes isosurfaces as boundaries and
can generate adaptive and quality meshes for
complicated structures.
1.3 Boundary/Material Layer
Detection
container, and all the blood vessels are extended to the
container boundary. The constructed meshes is being used in
the simulation of blood flow using immersed continuum
method, the distribution of velocity, shear stress, pressure
and locations of flow recirculation are analyzed. It is useful
for the heart valve design and the understanding of blood
circulation disease.
Before material layer detection
After material layer detection
Modified Model
Original Model
Smooth shading + wireframe
The heart inside the human body
Fig. 3. Boundary Detection
A cross section of tetrahedral mesh
Fig. 4. Interior/exterior meshes of a patient-specific heart.
aortic valve
tricuspid valve
pulmonary valve
Original foramen ovale
Fig. 4. Material Layer Detection
Smooth shading
Modified foramen ovale
Fig. 2. The original model from NYU* and the modified
model. Note*: With permission of New York University, Copyright 1994-2004.
13th International Meshing Roundtable, Williamsburg, Virginia, September 19-22, 2004
References
mitral valve
The heart model with extensions
The heart model immersed in the fluid mesh
Fig. 3. The resulting adaptive and quality tetrahedral mesh for the cardiac model and the
heart model used in the simulation of blood flow.
1. Y. Zhang, C. Bajaj. Finite Element Meshing for Cardiac Analysis. ICES Technical Report 04-26, the Univ. of Texas
at Austin, 2004.
2. Y. Zhang, C. Bajaj, B.-S. Sohn. 3D Finite Element Meshing from Imaging Data. Accepted in the special issue of
CMAME on Unstructured Mesh Generation. 2004.
3. Y. Zhang, C. Bajaj, B.-S. Sohn. Adaptive and Quality 3D Meshing from Imaging Data, ACM Symposium on Solid
Modeling and Applications. pp. 286-291, Seattle, June 2003.
4. The World’s Best Anatomical Charts. Anatomical Chart Company Skokie, IL. ISBN 0-9603730-5-5.
Acknowledgements: Thank NYU for providing the educational polygonal heart model, a research group in Finland
for MRI scanned data.
* Please contact [email protected] for further information.