A new method for regularization of the inverse problem of electrocardiography

The inverse problem of electrocardiography (specifically, that part concerned with the computation of the ventricular surface activation isochrones) is shown to be formally equivalent to the problem of identification and measurement of discontinuities in derivatives of body surface potentials. This is based on the demonstration that such measurements allow localization of the relative extrema of the ventricular surface activation map (given a forward problem solution), which in turn restricts the space of admissible solution maps to a compact set. Although the inverse problem and the problem of identifying derivative discontinuities are both ill-posed, it is possible that the latter may be more easily or justifiably resolved with available information, particularly as current methods for regularizing the inverse problem typically rely on a regularization parameter chosen in an a posteriori fashion. An example of the power of the approach is the demonstration that a recent Uniform Dipole Layer Hypothesis-based method for producing the ventricular surface activation map is largely independent on that hypothesis and capable in principle of generating maps that are very similar in a precise sense to those that would result from the usual epicardial potential formulation (assuming the latter were capable of producing intrinsic deflections in computed epicardial electrograms sufficiently steep to accurately compute the activation map). This is consistent with the preliminary success of the former method, despite the significant inaccuracy of its underlying assumption.