Demonstration of "discontinuities" in the time derivatives of body surface potentials, and their prospective role in noninvasive imaging of the ventricular surface activation map

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Abstract
The ill-posed nature of the inverse electrocardiography problem has necessitated use of regularization techniques as a means of rendering epicardial potential maps. Significant inaccuracies are introduced by such methods (on the order of 50% error relative to the actual map), due to imposition of the regularizing functionals. It has been previously shown that the generator of topological changes in epicardial potential maps during ventricular activation is of much lower order than the epicardial maps themselves, yet sufficiently constrains the full ventricular surface activation mapping problem so as to obviate the need for further regularization. The mathematical formalism for reconstructing this generator has previously been presented under the assumption of negligible depolarization wavefront thickness, and requires identification and processing of "step discontinuities" predicted to occur in body surface potential derivatives. Using principal component analysis and spatial averaging methods, we have examined this fundamental prediction of the formalism in the context of a nonzero depolarization wavefront thickness (leading to prediction of dominant body surface potential derivative deflections with rise times comparable to those of ventricular electrogram intrinsic deflections). Studies of the body surface potential data obtained in three normal subjects supports the predictions of the theory, thereby suggesting the possible usefulness of the approach as an alternative to traditional regularization methods.