Bruce Hopenfeld1. 1. Angel Medical Systems, Tinton Falls, New Jersey, USA. brhopenfeld@yahoo.com
Abstract
BACKGROUND: In some cases, it may be necessary to combine distinct finite element meshes into a single system. The present work describes a scheme for coupling a finite element mesh, which may have curvilinear elements, to a voxel based finite element mesh. METHODS: The method is described with reference to a sample problem that involves combining a heart, which is defined by a curvilinear mesh, with a voxel based torso mesh. The method involves the creation of a temporary (scaffolding) mesh that couples the outer surface of the heart mesh to a voxel based torso mesh. The inner surface of the scaffolding mesh is the outer heart surface, and the outer surface of the scaffolding mesh is defined by the nodes in the torso mesh that are nearest (but outside of) the heart. The finite element stiffness matrix for the scaffolding mesh is then computed. This stiffness matrix includes extraneous nodes that are then removed, leaving a coupling matrix that couples the original outer heart surface nodes to adjacent nodes in the torso voxel mesh. Finally, a complete system matrix is assembled from the pre-existing heart stiffness matrix, the heart/torso coupling matrix, and the torso stiffness matrix. RESULTS: Realistic body surface electrocardiograms were generated. In a test involving a dipole embedded in a spherical shell, relative error of the scheme rapidly converged to slightly over 4%, although convergence thereafter was relatively slow. CONCLUSION: The described method produces reasonably accurate results and may be best suited for problems where computational speed and convenience have a higher priority than very high levels of accuracy.
BACKGROUND: In some cases, it may be necessary to combine distinct finite element meshes into a single system. The present work describes a scheme for coupling a finite element mesh, which may have curvilinear elements, to a voxel based finite element mesh. METHODS: The method is described with reference to a sample problem that involves combining a heart, which is defined by a curvilinear mesh, with a voxel based torso mesh. The method involves the creation of a temporary (scaffolding) mesh that couples the outer surface of the heart mesh to a voxel based torso mesh. The inner surface of the scaffolding mesh is the outer heart surface, and the outer surface of the scaffolding mesh is defined by the nodes in the torso mesh that are nearest (but outside of) the heart. The finite element stiffness matrix for the scaffolding mesh is then computed. This stiffness matrix includes extraneous nodes that are then removed, leaving a coupling matrix that couples the original outer heart surface nodes to adjacent nodes in the torso voxel mesh. Finally, a complete system matrix is assembled from the pre-existing heart stiffness matrix, the heart/torso coupling matrix, and the torso stiffness matrix. RESULTS: Realistic body surface electrocardiograms were generated. In a test involving a dipole embedded in a spherical shell, relative error of the scheme rapidly converged to slightly over 4%, although convergence thereafter was relatively slow. CONCLUSION: The described method produces reasonably accurate results and may be best suited for problems where computational speed and convenience have a higher priority than very high levels of accuracy.