A Bidomain Model Based BEM-FEM Coupling Formulation for Anisotropic Cardiac Tissue

Abstract

A hybrid boundary element method (BEM)/finite element method (FEM) approach is proposed in order to properly consider the anisotropic properties of the cardiac muscle in the magneto- and electrocardiographic forward problem. Within the anisotropic myocardium a bidomain model based FEM formulation is applied. In the surrounding isotropic volume conductor the BEM is adopted. Coupling is enabled by requesting continuity of the electric potential and the normal of the current density across the boundary of the heart. Here, the BEM part is coupled as an equivalent finite element to the finite element stiffness matrix, thus preserving in part its sparse property. First, continuous convergence of the coupling scheme is shown for a spherical model comparing the computed results to an analytic reference solution. Then, the method is extended to the depolarization phase in a fibrous model of a dog ventricle. A precomputed activation sequence obtained using a fine mesh of the heart was downsampled and used to calculate body surface potentials and extracorporal magnetic fields considering the anisotropic bidomain conductivities. Results are compared to those obtained by neglecting in part or totally (oblique or uniform dipole layer model) anisotropic properties. The relatively large errors computed indicate that the cardiac muscle is one of the major torso inhomogeneities.

Online Noninvasive Localization of Accessory Pathways in the EP Lab

“…After transformation of the electrode coordinates into the MRI frame, the leadfield-matrix was computed. The leadfield-matrix L with dimension e × s describes the relationship between the impressed electrical sources and the (extracellular) potentials Φ in e electrodes for all time steps T [4,10]: Signal preprocessing. For estimating the AT pattern, the ECG signals representing the depolarization sequences (target ECG waves) were used as input for further computation.…”

“…The coupling of these two modalities in time and space permits the imaging of electrical function when applying bioelectromagnetical field theory and solving an ill-posed inverse problem [4,5,6,7]. The primary electrical source in the cardiac muscle is the spatio-temporal distribution of the transmembrane potential (TMP) ϕ m [4,5,8,9]. The potential on the chest surface and the potential on all other conductivity interfaces are related to ϕ m by a Fredholm integral equation of second kind.…”

“…The relationship between the impressed electrical sources and the potentials at the electrode sites on the torso surface is described by the leadfield-matrix, the solution of the forward problem of electrocardiography [4,10]. The boundary element method (BEM) -a surface integral equation approach -is, in general, applied to solve this forward problem [4,5,11]. In the electrocardiographic inverse problem, the impressed electrical source distribution is estimated from the chest surface ECG mapping data.…”

“…The potential on the chest surface and the potential on all other conductivity interfaces are related to ϕ m by a Fredholm integral equation of second kind. The relationship between the impressed electrical sources and the potentials at the electrode sites on the torso surface is described by the leadfield-matrix, the solution of the forward problem of electrocardiography [4,10]. The boundary element method (BEM) -a surface integral equation approach -is, in general, applied to solve this forward problem [4,5,11].…”

“…ECG mapping data can be acquired from the patient's chest surface with multichannel (32 up to 256 channels) biopotential recording systems. The coupling of these two modalities in time and space permits the imaging of electrical function when applying bioelectromagnetical field theory and solving an ill-posed inverse problem [4,5,6,7]. The primary electrical source in the cardiac muscle is the spatio-temporal distribution of the transmembrane potential (TMP) ϕ m [4,5,8,9].…”