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B Tilg

Publications and source records attributed to B Tilg.

10 recordsLinked to original sources
PubMed2001

An iterative algorithm for myocardial activation time imaging.

An iterative algorithm based on a general regularization scheme for nonlinear ill-posed problems in Hilbert scales (method A) is applied to the magnetocardiographic inverse problem imaging the surface myocardial activation time map. This approach is compared to an algorithm using an optimization routine for nonlinear ill-posed problems based on Tikhonov's approach of second order (method B). Method A showed good computational performance and the scheme for determining the proper regularization parameter lambda was found to be easier than in case of method B. The formulation is applied to magnetocardiographic recordings from a patient suffering from idiopathic ventricular tachycardia in which a sinus rhythm sequence was followed by a ventricular extrasystolic beat.

Algorithms↗
PubMed2000

A bidomain model based BEM-FEM coupling formulation for anisotropic cardiac tissue.

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.

Animals↗
PubMed1999

Application of high-order boundary elements to the electrocardiographic inverse problem.

Eight-noded quadrilateral boundary elements are applied to the electrocardiographic inverse problem as an example for high-order boundary elements. It is shown that the choice of the shape functions used for approximation of the potentials has a remarkable influence on the solution obtained if the number of electrodes is smaller than the number of primary source points (under-determined equation system). Three different formulations are investigated considering a concentric spheres problem where an analytic solution is available: (a) the isoparametric formulation; (b) the quasi-first-order formulation; and (c) the pseudo-subparametric formulation as a new method. In a second step the pseudo-subparametric formulation (which provided the best results in the test problem) is applied to real word data. The transmembrane potential pattern of a 40 years old female suffering from severe heart failure and ventricular tachycardia after large anterior wall myocardial infarction is reconstructed for one time instant. Furthermore, an algorithm for the calculation of the transfer matrix is presented which avoids restrictions to the boundary element mesh caused by the placement of the electrodes.

Adult↗
PubMed1999

Two-dimensional Fourier representation used in the bioelectric forward problem.

The objective of this paper is the application of two-dimensional discrete Fourier transformation for solving the integral equation of the bioelectric forward problem. Therefore, the potential, the source term, and the integral equation kernel are assumed to be sampled at evenly spaced intervals. Thus the continuous functions of the problem domain can be expressed by their two-dimensional discrete Fourier transform in the spatial frequency domain. The method is applied to compute the surface potential generated by an eccentric dipole in a homogeneous spherical conducting medium. The integral equation for the potential is solved in the spatial frequency domain and the value of the potential at the sampling points is obtained from inverse Fourier transformation. The solution of the presented method is compared to both, an analytic solution and a solution gained from applying the boundary element method. Isoparametric quadrilateral boundary elements are used for modeling the spherical volume conductor in the boundary element solution, while in the two-dimensional Fourier transformation method the volume conductor is represented by a parametric boundary surface approximation.

Computer Simulation↗
PubMed1998

Analytical validation of the BEM--application of the BEM to the electrocardiographic forward and inverse problem.

The objective of this study is to analytically validate a boundary element (BE) formulation for the relationship between the transmembrane potential on the heart's surface and the potential on the body surface applying a concentric spherical test geometry. The relative difference (reldif) between the potential on the outer sphere of the test geometry computed analytically and numerically is determined by 3.59% for the coarse discretization (48 BEs) and by 0.46% in the case of the finer subdivision (192 BEs). In the inverse problem, the transmembrane potential on the inner sphere is estimated numerically from the electric potential on the outer sphere by using a minimum-norm least-square approach. The relative differences found are 20.2% when no measurement noise is added and 26.4% in the presence of 2% additional Gaussian noise. The BE formulation is also applied to real world data for solving the electrocardiographic inverse problem. A normal volunteer's inhomogeneous thorax (outer thorax surface, surfaces of the lungs, epicardial heart surface) is modelled by 424 BEs. The same inverse method is then applied in order to reconstruct the transmembrane potential on the epicardium from the measured body surface potential (BSP) data during normal ventricular depolarisation.

Electrocardiography↗
PubMed1997

Magnetic source imaging in the human heart: estimating cardiac electrical sources from simulated and measured magnetocardiogram data.

The estimation of pseudo primary current dipoles on a 2D-manifold in the atrial and ventricular myocardium and septum, and of the transmembrane potential on the endocardium and epicardium, from the magnetic heart field is investigated. The human thorax surrounding the heart is modelled by an inhomogeneous boundary element volume conductor model, including the outer thorax surface and the surfaces of the lungs. The influence of the blood mass is neglected. In the inverse problem Tikhonov's regularisation is applied. The regularisation parameter is determined by the L-curve method. An algorithm for iterative improvement is applied to estimate the pseudo primary current dipoles. Synthetic magnetic field and electric potential data are generated using a cellular automaton model of the entire human heart. Real world magnetic field data for a normal subject are analysed to demonstrate the practicability and effectiveness of the presented method.

Algorithms↗
PubMed1995

An iterative approach on magnetic source imaging within the human cortex--a simulation study.

A simulation study on magnetic source imaging within the human brain from a synthetic evoked magnetic field is presented. An inhomogeneous boundary element (BE) head model (cortex cerebrospinal fluid) was built up from real magnetic resonance imaging (MRI) cross-sections. In the forward problem, one or two rotating primary current dipoles (PCDs) are located at arbitrary sites within the auditory cortices. The PCDs should represent focal and distributed neural activities, respectively. The reconstruction space (predefined by a priori morphological information) is defined as a surface within the three-dimensional cortical volume, with an averaged distance of 0.005 m to the outer cortex surface. The reconstructed pseudo primary current dipoles (PPCDs) are not restricted to any particular direction. The observation space consists of two concave surfaces closely above the scalp. Each observation surface contains 37 observation points. An iterative Wiener filter estimation (WFE) is applied in order to reconstruct PPCD distribution from simulated magnetic field data. This iterative WFE approach enables the simultaneous localization of focal and distributed activities. Aspects on the correlation between neural activities are not investigated within this paper.

Algorithms↗
PubMed1995

A simulation study on magnetic source imaging with a realistic model of the entire human heart.

A computer model study on magnetic source imaging from magnetocardiographic data is presented using a cellular automaton model of the entire human heart in the so-called forward problem. A homogeneous boundary element (BE) torso is built up from real magnetic resonance imaging (MRI) cross-sections. The heart model, which has a realistic anatomical shape, is positioned inside the BE torso. In the forward problem the spread of excitation is simulated by applying a modified Huygen's propagation principle. The magnetocardiogram (MCG) and electrocardiogram (ECG) can then be computed following the bidomain theory. From the simulated MCG data, pseudo primary current dipole (PPCD) estimation within the electrically active tissue is performed. The reconstruction space is defined as a surface in the middle of the atrial and ventricular myocardium and septum. The observation space consists of two mutually perpendicular planes closely above the torso surface on the frontal and the left lateral side, respectively. An iterative minimum-norm approach is applied in order to reconstruct PPCD distributions. The errors in PPCD estimation arising from noisy data and regularization algorithms are investigated in more detail.

Computer Simulation↗
PubMed1994

[Simulation of a one-dimensional impulse transmission along a heart muscle fiber with varied intracellular specific resistance--unidirectional block].

The subject of this study is the modeling of the spread of excitation along a ventricular myocardial fibre based on the one-dimensional "cable" (transmission line) theory. In particular the influence of a varying intracellular c resistivity, R, and of the extracellular potassium concentration [K]o on the propagation is investigated. The membrane model used is the Luo-Rudy model, with which such cellular phenomena as supernormal excitability and Wenckebach pattern can be simulated. The specific resistivity, R, comprises the resistivity of the myoplasm and that of the gap junction. The phenomen of the unidirectional block (UDB) can be simulated in the ischaemic/non-ischaemic transitional zone. Here, the resistivity peak within the ischaemic border zone--caused by collagenous tissue--in combination with a gradient of the R along the fibre-plays a basic role. This simulation study makes it evident that variations in the R-profile have a considerably greater effect on the propagation of a stimulus than variations in the [K]o-profile.

Collagen↗