An Approach to Inverse Calculation of Epicardial Potentials from Body Surface Maps1

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Abstract
The inverse problem of evaluating epicardial potentials from a knowledge of heart and torso geometry as well as body surface potentials is here formulated as a problem in control theory. As is well known, such an inverse problem is ill-posed and a regularization technique has been devised to overrun this difficulty. The resulting regularized problem is well-posed and requires the minimization of a cost function including, besides the square distance of any predicted surface potential distribution from the experimental one, a regularization term involving the second derivatives of the identified epicardial potentials. The results here presented were obtained on a model problem for a plane geometry. Surface potentials generated by multipoles and perturbated with a noise level reflecting both instrumentation and electrode placement uncertainties were fitted by the proposed method and 'epicardial potentials' were determined with a maximum sum square relative error of 15%. The results suggest that by introducing suited regularity constraints, the a priori difficulties inherent to the problem of computing epicardial potentials from torso potentials, can be overcome.

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