A High-Order Coupled Finite Element/Boundary Element Human Torso Model

where φ is the potential and σ is the conductivity tensor. The most common numerical methods used to solve this equation inside a human torso are the finite element method (FEM) [1], [2] and the boundary element method (BEM) [3]-[5]. Both techniques have their relative merits for this problem. The FEM handles the highly anisotropic muscle regions well, while the BEM is more efficient in electrically isotropic and homogeneous regions (e.g. the lungs). We propose here to utilise the strengths of each method for this problem. To that end we propose using the BEM exterior to the heart in every tissue region up to the inner skeletal muscle layer (all of which are generally regarded as electrically isotropic and homogeneous). In the skeletal muscle region, due to its high degree of anisotropy (and for simplicity the fat layer as well) we use the FEM. At this stage we are thinking in terms of trying to relate the potential distributions on the surface of the heart to those on the body surface (the "forward" problem) and vice versa (the "inverse" problem). Our aim is to ultimately include a sophisticated heart model inside the torso, in particular the model described in Nielson et al [6]. This model employs a high order (cubic Hermite) FEM procedure, designed to handle the nonlinear elastic deformations of the heart and the high degree of muscle anisotropy which affects the deformations and electrical propagation through the heart. For consistency and compatibility, the same interpolation (cubic Hermite) is used in the BEM procedure. We describe below a cubic Hermite boundary element procedure and show how this can be coupled to the FEM. We then present two and three-dimensional results showing the success, efficiency and accuracy of this high order coupled technique.