Unconstrained Inverse Electrocardiography: Epicardial Potentials

The inverse problem in electrocardiography is attacked via the development of a model appropriate for the computation of epicardial potentials from a knowledge of heart and torso geometry as well as surface potentials. The model takes the form of an integral equation of the first kind in which the kernel is interpreted as a Green's function. A theoretical investigation of system independence in the presence of error is developed, and two techniques for the theoretical consideration of system independence are examined. Application of these two techniques to concentric spherical systems indicates that spheres with ratios of inner-to-outer radii less than 0.5 contain less than twenty independent parameters in the presence of realistic noise levels. The number of independent parameters deteriorates rapidly as this ratio falls below 0.5. These results suggest that it is not feasible to determine epicardial potentials from torso potentials by using unconstrained solutions.