Heart Model with Valves

The construction of the human heart model is important for the development of cardiovascular surgical procedures based on simulations of patient-specific models using finite element method. We are trying to construct a tetrahedral heart model with some necessary components, such as aorta, veins, four chambers (left, right atriums and ventricles), heart valves, muscles, etc. The extended Dual Contouring method is used here to build the tetrahedral heart model from volumetric imaging data.

1. Anatomical charts of the human heart (Figure 1)

Figure 1: Heart Anatomy Model from [6]

2. Simplified heart model (Figure 2)

A simplified surface heart model (triangular mesh*, Figure 2, download triangular mesh) is used to construct the tetrahedral mesh. Comparing with Figure 1, we can see there are four heart valves (aortic valve, pulmonary valve, mitral valve and tricuspid valve) and one valve of foramen ovale (I am not sure if it is the correct name). (* With permission of New York University, © Copyright 1994-2003.)

Original model Modified model

Figure 2: Simplified Heart Model

(a) (b) (c) (d)

(e)

Figure 3: Valves – (a) aortic valve; (b) tricuspid valve;

In our finite element model of the human heart, the aortic valve, the tricuspid valve, the pulmonary valve and the mitrial valve should have gaps between its cuspid components, which allow blood flow through the valves. We modified the original valve models (Figure 3 (a ~ d)) to obtain gaps.

(a) (b) (c) (d)

Original (e) Modified (e)

Figure 4: Valves with gaps – (a) aortic valve; (b) tricuspid valve;

3. Tetrahedral meshes of the heart model

Considering all the components in the simplified heart model as only one object. First convert the triangular surface mesh into volumetric data using signed distance method, then extract triangular surface meshes (download triangular mesh) and tetrahedral meshes from it.

· Heart model with valves, no valve gaps (download tetrahedral mesh)

(a) (b) (c)

Figure 5: Tetrahedral meshes of the heart model. (a) – viewed from outside;

(b) – inner structure (wireframe); (c) a cross section of the tetrahedral mesh of the heart.

Heart model with valves gaps (download the adaptive triangular mesh) (download the adaptive tetrahedral mesh)

In order to keep all the features of the complicated human heart model (like valves, chambers and blood vessels), and at the same time minimize the number of elements for efficient finite element calculation, we choose adaptive tetrahedral meshes. The valve areas are set the finest level, features based on the Eucliean error function are identified and preserved. Those areas with thin walls are refined to keep the correct topology. The following mesh is extracted from a signed distance function dataset with the resolution of 257^3. Bad valve gaps shown in Figure 7 are introduced because the current resolution is not high enough.

Figure 6: Adaptive tetrahedral mesh for the heart model with valve gaps. The top row shows the boundary in wire frame, the meshes in valve areas are finest; The bottom left is viewed from outside; The bottom right shows a cross section of the adaptive tetrahedral mesh, the valves have finest mesh, features are identified using the Eucliean error function, and preserved by the mesh adaptivity.

(a) (b)

Figure 7: Valves with gaps in the adaptive mesh.

4. Boundary and Material Detection (download the adaptive tetra mesh with boundary detection)

aortic valve tricuspid valve

pulmonary valve mitral valve

Figure 8: Boundary detection in the adaptive mesh.

Figure 9: Material detection in a heart model with the replace mitral valve.

5. Data Format (*.raw)

Triangular Mesh:

36410 159199 // # of vertices (nvert), # of triangle (ntri)

-14.649727 6.947823 -39.802671 // x, y, z coordinates of the 0^th vertex

10.669823 30.016861 -5.444489 // x, y, z coordinates of the 1^th vertex

…

6.884521 59.296120 2.071411 // x, y, z coordinates of the (nvert-2)^th vertex

9.898041 59.586449 2.049690 // x, y, z coordinates of the (nvert-1)^th vertex

6 5 7 // the three vertices which construct the 0^th triangle

5 4 7 // the three vertices which construct the 1^th triangle

…

20207 20211 20219 // the three vertices which construct the (ntri-2)^th triangle

20207 20219 20212 // the three vertices which construct the (ntri-1)^th triangle

Tetrahedral Mesh:

50856 247924 // # of vertices (nvert), # of tetra (ntetra)

-21.017212 -0.283054 -33.161398 0 // x, y, z coordinates of the 0^th vertex, boundary sign

-20.773251 0.980949 -34.280157 1 // x, y, z coordinates of the 1^th vertex, boundary sign

…

6.884521 59.296120 2.071411 8 // x, y, z coordinates of the (nvert-2)^th vertex

9.898041 59.586449 2.049690 2 // x, y, z coordinates of the (nvert-1)^th vertex

6 5 7 8 // the four vertices which construct the 0^th tetrahedron (Right-Hand-Principle)

5 4 7 8 // the four vertices which construct the 1^th tetrahedron

…

20207 20211 20219 20210 // the four vertices which construct the (ntetra-2)^th tetrahedron

20207 20219 20212 20210 // the four vertices which construct the (ntetra-1)^th tetrahedron

note: boundary index = 0 means the interior vertex; boundary index >= 1 means the boundary vertex.

Boundary Index	Components	Boundary Index	Components	Boundary Index	Components
0	interior	8	pulmonary valve (red)	16	right atrium (red)
1	aortic valve (blue)	9	tricuspid valve (green)	17	right pulmonary v. (red)
2	aortic valve (purple)	10	tricuspid valve (purple)	18	inferior vena cava (orange)
3	aortic valve (green)	11	tricuspid valve (pink)	19	left atrium (orange)
4	mitral valve (red)	12	valve of foramen ovale (green)	20	right pulmonary a. (dark red)
5	mitral valve (yellow)	13	valve of foramen ovale (red)	21	aorta (blue)
6	pulmonary valve (orange)	14	right ventricle (blue)	22	outer surface (pink)
7	pulmonary valve (blue)	15	left ventricle (green)

Table 1: The correspondence between the boundary sign and components (shown in Figure 3).

Collaborators:

Wing Kam Liu (Northwestern University)
Xiaodong Wang (Polytechnic University)
Tom Hughes (ICES)

Reference:

1. Y. Zhang, C. Bajaj. Finite Element Meshing for Cardiac Analysis. ICES Technical Report 04-26, the Univ. of Texas at Austin, 2004. (pdf)

2. Y. Zhang. Tetrahedral/Hexahedral Finite Element Meshing from Volumetric Imaging Data. Ph.D. Proposal, 2003. (pdf)(ppt)

3. Y. Zhang, C. Bajaj, B-S. Sohn. 3D Finite Element Meshing from Imaging Data. Accepted in the special issue of Computer Methods in Applied Mechanics and Engineering (CMAME) on Unstructured Mesh Generation, 2004. (pdf) (html)

4. Y. Zhang, C. Bajaj and B. Sohn. Adaptive and Quality 3D Meshing from Imaging Data. Proceedings of ACM Symposium on Solid Modeling and Applications. Pages 286-291. Seattle, June 2003. (pdf)

5. Y. Zhang, C. Bajaj and B. Sohn. Adaptive Multiresolution and Quality 3D Meshing from Imaging Data. ICES & CS Technical Report, 2002.

6. The World’s Best Anatomical Charts. Anatomical Chart Company Skokie, IL. ISBN 0-9603730-5-5.

7. http://www.ices.utexas.edu/ccv --> gallery --> computational medicine --> the human heart.

8. http://ccvweb.csres.utexas.edu/ccv/projects/medx/heart/

9. Our old results (1) -- http://www.ices.utexas.edu/~jessica/medical_data/heart/Heart_Valve.htm

10. Our old results (2) -- http://www.ices.utexas.edu/~jessica/medical_data/heart/HeartModel.htm