Abstract: This poster presents technical details to generate an adaptive and quality tetrahedral finite element mesh of a human heart. 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 to assist
the boundary and material layer detection. For the patient-specific model, some boundary points are selected from MRI images, and connected using cubic splines and lofting to segment the 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 Mesher (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 will be used in simulating the electrical activity of the heart.
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, Northwestern Univ.
#
ME, Polytechnic Univ.
‡
Simula Research Lab, Norway
* Please contact jessica@ices.utexas.edu for further information.
References
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.
5. Acknowledgements: Thank NYU for providing the educational polygonal heart model, Helena Hanninen from
Helsinki Univ. Central Hospital in Finland for MRI scanned data.
13
th
International Meshing Roundtable, Williamsburg, Virginia, September 19-22, 2004
aortic valve tricuspid valve pulmonary valve mitral valve
1. An Educational Model
Fig. 1. Heart Anatomy Model from [4]
1.1 Model Acquisition
An educational polygonal model is modified 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.
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
We first select some points in each slice of the MRI data, then connect them smoothly
using cubic splines and lofting. In this way, we 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 will be used in the simulation of the electronic activity of the heart.
Fig. 2. The original model from NYU* and the modified
model. Note*: With permission of New York University, Copyright 1994-2004.
aortic valve pulmonary valvetricuspid valve mitral valve
Original foramen ovale Modified foramen ovale
Original Model Modified 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.
Fig. 3. Boundary Detection
Fig. 4. Material Layer Detection
1.4 Application and Results
Before material layer detection After material layer detection
Application: The heart model is put inside a cubic
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.
2. A Patient-specific Model
Volume rendering
The heart inside the human body
Manually digitized slicesRaw MRI data Continuous model
The heart model with extensions The heart model immersed in the fluid mesh
Fig. 5. The resulting adaptive and quality tetrahedral mesh for the cardiac model and the
heart model used in the simulation of blood flow.
Smooth shading
Smooth shading + wireframe
A cross section of tetrahedral mesh
Fig. 6. Interior/exterior meshes of a patient-specific heart.
