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The use of the simulation results as a priori information to solve the inverse problem of electrocardiography for a patient

In the present work the epicardial potential distribution for an individual patient provided by the solution of the linear inverse problem of electrocardiography are shown. To obtain the solution, the Twomey regularization as well as the stochastic regularization were used. Both methods require a priori estimations. These estimations were provided by means of simulation of the cardiac activity on a personalized electrophysiological model of the patient. To estimate the quality of the results provided by each method, the inverse problem was solved with the simulated ECG, the solution being compared with the epicardial potentials obtained from the simulation. Twomey regularization tends to provide the better correspondence than the conventional Tikhonov 0-order regularization. The stochastic regularization provides the best correspondence with the reference data, being the most time-consuming of all the methods under consideration. Solving the inverse problem of electrocardiography provides a physician with the useful information about the electrophysiological processes in the heart of a patient

Imaging of Bioelectric Sources in the Heart Using a Cellular Automaton Model

The approach to solve the inverse problem of electrocardiography presented here is using a computer model of the individual heart of a patient. It is based on a 3D-MRI dataset. Electrophysiologically important tissue classes are incorporated using rules. Source distributions inside the heart are simulated using a cellular automaton. Finite element method is used to calculate the corresponding body surface potential map. Characteristic parameters like duration and amplitude of transmembrane potential or velocity of propagation are optimized for selected tissue classes or regions in the heart so that simulated data fit to the measured data. This way the source distribution and its time course of an individual patient can be reconstructed

Comparison of regularization techniques for the reconstruction of transmembrane potentials in the heart.

Computer simulations to reconstruct the transmembrane potential distribution were performed for an anisotropic finite element model of the heart. Transmembrane potential was reconstructed in the form of 3D patches. Test patterns generated with a cellular automaton were used. Tikhonov 0-order and 2-order reconstruction techniques were compared. Tikhonov 2-order regularization was shown to deliver better solutions; this is demonstrated by the inspection of the source space of the inverse problem and by the comparison of the correlation coefficients between the reconstructed and original distributions. Time information was incorporated into the regularization.

Comparison of macroscopic models of excitation and force propagation in the heart.

Computer aided simulations of the heart provide knowledge of phenomena, which are commonly neither visible nor measurable with current techniques. This knowledge can be applied e.g. in cardiologic diagnosis and therapy. A variety of models was created to reconstruct cardiac processes, e.g. electrical propagation and force development. In this work different macroscopic models were compared, i.e. models based on excitation-diffusion equations and cellular automata. The comparison was carried out concerning reconstruct-ability of cardiac phenomena, mathematical and biophysical foundation as well as computational expense. Particularly, the reconstruct-ability of electromechanic feedback mechanisms was examined. Perspectives for further developments and improvements of models were given.

Simulation study of the effect of modelling errors on the solution of inverse cardiac source imaging problem using realistic source patterns

The effect of the modelling errors on the solution of the inverse problem of electrocardiography is investigated. The electrocardiographic signal is simulated using a finite element model of the human torso and realistic source patterns gained with a cellular automaton. Noise is added to simulated measurements and the inverse problem is solved. The modelling errors consist of false conductivity assumptions, changed anisotropy ratio of skeletal muscles and geometric errors. The effect of modelling errors on optimal regularization parameter determination is investigated. The changes in muscle anisotropy and heart position are shown to have the highest effect on reconstructed epicardial potentials. CRESO (Composite REsidual and Smoothing Operator) and L-curve criteria for optimal regularization parameter estimation are compared.

THE EFFECT OK CARDIAC ANISOTROPY ON THE RECONSTRUCTION OF TRANSMEMBRANE VOLTAGES IN THE HEART

S U M M A K Y : Computer simulations vvcre carricd out to iiivcshgatc the cflcct of anisotropy of cardiac muscle on thc iccons t ruc t ion of transmembrane voltagcs from mulh-cl iunncl electrocardiograms (ECO). An c.\perimental study was performed to reconstruct the truMsmcmbrane voltages in the myocardium from real measurement data. Realistic cardiac anisotropy was assigncd to the segmentcd MR1 dataset. Ineluding the realistic cardiac anisotropy in anatomical models can improve the quality of non-invasive cardiac souree imaging.

Linearization approach for impedance reconstruction in human body from surface potentials measurements

The paper describes a fast and simple method to find the deviation of impedance of different tissues from the average values known from the literature. A technique similar to the Electrical Impedance Tomography is used assuming the geometry of organs to be known. To find the individual impedance deviations, we assume that the change of the surface potentials depends linearly on a small (up to 10%) conductivity change. In that case one can find the individual impedance deviations by an inverse-matrix multiplication. The results of numerical simulations demonstrate the successfull reconstruction of impedance deviations up to 10% from the average value for several tissues simultaneously.

Investigation of the source space of electrocardiography and magnetocardiography using isotropic and anisotropic thorax models

Noninvasive Imaging of the bioelectric processes on the heart using Electrocardiography (ECG) and Magnetocardiography (MCG) data is a widely discussed research topic of the recent years. The source space of ECG is compared with the source space of MCG and vice versa to investigate the difference of information content of these mapping techniques for source imaging purposes. The approach allows the calculation of the intersection and non-intersection part (the calculation of silent sources) of MCG (ECG) in comparison to ECG (MCG). The investigation was carried out on a Finite Element model which was constructed from a magnetic resonance imaging (MRI) dataset of a volunteer. Anisotropic fibre orientation was applied to myocardium to investigate its effect on the differences of the source spaces.

DETERMINING THE EXTENT AND SITE OF INFARCTION BY NONINVASIVE CARDIAC SOURCE IMAGING

w l κ» re .v dcsignates the vector of potentials on the luules of cpicardium (or the veetor of transmembrane voluiges on the nodes within heart tissue), b vector of Potentials on the body surface, and A is known s a /«/</-//>/</ /w//n.v, describing the relation between the iibove t wo vcciors. The latter carries the exhaustive Informat ion about the geometrie and electric properties of human body. The l imitat ion of the precision of measurements, s well s the loss of Information caused by discretization, leads to the distortion and instability of reconstruction results [ 11 . In this work we estimate the limits of such reconstruction.

Evaluating the Reconstruction Limits and the Effect of Modeling Errors in Noninvasive Cardiac Source Imaging

The subject of the inverse problem of electrocardiographs is to obtain quantitative information about the electrical act ivi ty of the heart using e. g. the model of equivalent cardiac sources. An important formulation ol t he inverse problem is to model the cardiac sources as an epicardial potential distribution. Discretization of t he forward electric problem leads to the linear relationship between the vector of epicardial potentials χ and the vector h of the potentials at the torso surface: