(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 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.

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.

Valves with gaps in the adaptive mesh

(a)arotic valve	(b)tricuspid valve
(c)pulmonary valve	(d)mitral valve

Boundary Detection (download the adaptive tetra mesh with boundary detection)

aortic valve	tricuspid valve	pulmonary valve	mitral valve