The goal of the inverse problem of electrocardiography is to predict
cardiac electrical activity from body surface (ECG) measurements. A
persistent challenge is the very ill-posed natures of this problem, which
one can at least partially compensate through the application of suitable
constraints. However, it is often difficult to determine a priori the best
possible constraints and especially their optimal weighting. We have begun
to utilize multielectrode catheters as a means of mapping epicardial
signals in animal models and developed an associated estimation procedure.
These signals offer a very sparse sampling of the desired solution and thus
make natural candidates for inclusion in a formulation of the inverse
problem. From these varied starting points, we have recently broadened our
studies to include a variety of constraints and to develop a framework to
incorporate these constraints synergistically. This framework includes
both regularization schemes based on the Tikhonov approach as well as
Bayesian statistical and linear estimation methods. In this presentation,
we present an overview of the problem, our solution approach, and results
comparing the effectiveness of some promising constraints. Results
suggest that statistical estimation of epicardial potentials from sparsely
sampled measurements provides a valuable source of constraint information.
Such a multimodal approach to cardiac mapping is clinically and technically
viable and offers a possible means to overcome a major remaining limitation
of inverse electrocardiography.
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