The inverse problem of ECG is the task of cardiac source reconstruction from the measured body surface potential maps (BSPM). It is ill posed and therefore requires regularization, which is usually applied uniformly to the whole heart geometry. In order to improve the solution quality and localize potentials extrema we propose a local regularization method: the weighting is done iteratively according to the solution spatial content. The performed test showed the ability of the new method to overcome over smoothing and to better reconstruct strong solution gradients.
D. Potyagaylo, M. Segel, W. H. W. Schulze, and O. Dössel. Noninvasive Localization of Ectopic Foci: a New Optimization Approach for Simultaneous Reconstruction of Transmembrane Voltages and Epicardial Potentials. In FIMH, LNCS 7945, pp. 166-173, 2013
The goal of ECG imaging is the reconstruction of cardiac electrical activities from the potentials measured on the thorax sur- face. The tool can gain prominent clinical value for diagnosis and pre- interventional planning. The problem is however ill-posed, i.e. it is highly sensitive to modelling and measurement errors. In order to overcome this obstacle a regularization technique must be applied. In this paper we pro- pose a new optimization based method for simultaneous reconstruction of transmembrane voltages and epicardial potentials for localizing the origin of ventricular ectopic beats.Compared to second-order Tikhonov regularization, the new approach showed superior performance in marking activated regions and provided meaningful results where Tikhonov method failed.
A new method to predict changes in a lead-field matrix induced by conductivity variations of a single body tissue is proposed. The approach is based on the princi- ple component analysis (PCA) with three initial lead-field matrices transformed to vectors as input. For each tissue blood, lungs, muscles and fat a PCA was carried out. Further, for each tissue the default conductivity value and the conductivity varied by ±50 % were used to calculate the sample lead-field matrices. The results of the PCAs in- dicate that for every tissue the first principle component suffices to predict the conductivity-induced changes in the samples. With an interpolation of the scores we addition- ally show that the prediction is not bound to the sample ma- trices but moreover every matrix within each conductivity range is possibly estimated and conclusively predicted.
ECG imaging is a non-invasive technique of characterizing the electrical activity and the corresponding excitation conduction of the heart using body surface ECG. The method may provide great opportunities in the planning of cardiac interventions and in the diagnosis of cardiac diseases. This work introduces an algorithm for the imaging of transmembrane voltages that is based on a Kalman filter with an augmented measurement model. In the latter, a regularization term is integrated as additional measurement. The filter is trained using a-priori-knowledge from a simulation model. Two effects are investigated: the influence of the training data on the reconstruction quality and the representation of a-priori knowledge in the trained covariance matrices. The proposed algorithm shows a promising quality of reconstruction and may be used in the future to introduce generic physiological knowledge in solutions of cardiac source imaging.
With ECG imaging it is possible to reconstruct cardiac electrical activity noninvasively from measurements of the electrocardiogram (ECG). To facilitate the recon- struction, an MRI- or CT- based model of the body is re- quired, which is represented as a volume conductor. A mathematically ill-posed problem is solved to reconstruct the cardiac sources from potentials collected on the body surface. To obtain a body surface potential map (BSPM) electrodes are ideally placed allover the entire thorax. In practical applications, however, the number of electrodes is limited and the placing is subject to constraints. We in- vestigate the effect of different electrode setups on the ill- posedness of the inverse problem. In particular, electrode setups are chosen to comply with constraints for female pa- tients in the catheter lab.