The use of temporal information in the regularization of the inverse problem of electrocardiography

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Abstract
The inverse problem of electrocardiography is solved in order to reconstruct electrical events within the heart from information measured noninvasively on the body surface. These electrical events can be deduced from measured epicardial potentials; therefore, a noninvasive method of recovering epicardial potentials from body surface data is useful in clinical and experimental work. The ill-posed nature of this problem necessitates the use of regularization in the solution procedure. Inversion using Tikhonov zero-order regularization, a quasi-static method, had been employed previously and was able to reconstruct, with relatively good accuracy, important events in cardiac excitation (maxima, minima, etc.). Taking advantage of the fact that the process of cardiac excitation is continuous in time, one can incorporate information from the time progression of excitation in the regularization procedure using the Twomey technique. Methods of this type were tested on data obtained from a human-torso tank in which a beating canine heart was placed in the correct human anatomical position. The results show a marked improvement in the inverse solution when these temporal methods are used, and demonstrate that important physiological events (e.g., right ventricular breakthrough) not detected by the quasi-static approach, are reconstructed using these methods. In addition, the results indicate that as the time interval between sampled maps is reduced, the quality of the solutions that use this temporal regularization is greatly improved.