D. Potyagaylo, W. H. W. Schulze, and O. Dössel. Solving the transmembrane potential based inverse problem of ECG under physiological constraints on the solution range. In Biomedizinische Technik / Biomedical Engineering, vol. 57(s1) , pp. 170, 2012
In this paper we propose an iteratively regularized Gauss-Newton method to solve the inverse ECG problem and efficiently choose the parameter of regularization. The classical stopping criterium for this regularization technique Morozov discrepancy principle, cannot be used in our application because the noise level estimate and problem model error are typically not available. We formulate the stopping rule based on the statistical formulation of the parameter and the physiological nature of the sought solution. With Laplace operator as a regularization matrix, the regularization parameter can be seen as an indirect measure of deviation in the solution: smaller parameters lead to a broader solution range. From our knowledge about electrophysiology of the heart we can assume values of −85 mV and +25 mV as a lower and an upper estimates for transmembrane potentials. Under this assumption we stop Gaus-Newton iteration as soon as the difference between solution smallest and largest values achieves 110 mV. Three simulation protocols confirm our ansatz: the proposed method was compared with the commonly used in the feld L-curve based Tikhonov method, showing superior performance during an initial phase of an ectopic heart activation sequence.
W. H. W. Schulze, D. Potyagaylo, and O. Dössel. Activation time imaging in the presence of myocardial ischemia: Choice of initial estimates for iterative solvers. In Computing in Cardiology, 2011, vol. 39, pp. 961-964, 2012
In this work, a simulation study is performed that demonstrates how activation times of cardiac action potentials can be reconstructed from body surface potential maps (BSPMs). An extrasystole is simulated in the ventricles, which are affected by myocardial ischemia or necrosis, and the related BSPM is calculated. Initial estimates are required for iterative algorithms that solve the related non-linear reconstruction problem. As a good initial estimate is essential for a proper reconstruction, the robustness of two methods is tested against the influence of pathological conditions: the critical times method and a linear timeintegral based method. While the first method extrapolates activation times into inactive tissue in this study, the latter carves out ischemic or necrotic tissue as homogeneous regions. In an outlook, a concept for the combination of both methods is proposed.