The inverse problem in electrocardiography on a spherical model

摘要

An inverse problem in electrocardiography, that computes potential distribution on the surface of the heart from potential distribution on the body surface, is studied analytically on concentric spheres model. No symmetry on potential distribution is assumed. The solution to the inverse problem is unique, but inherently very unstable. This paper focuses on two aspects of the inverse problem. First, the magnitude of the instability of the inverse solution is demonstrated by using the exact form of the inverse solution, a regularization method based on parameters directly related to measurable variables is presented, and upper and lower bounds on the error estimate of regularized solution are derived for specific choice of the regularization parameters. Second, the optimal selection of measurements sites for approximation of body surface potentials by means of spherical quadrature is considered. In particular, the problem of optimal distribution of nodes that lead to a quadrature of highest possible degree of exactness is investigated. The study implies that commonly used uniform distributions of nodes are not optimal. Furthermore, it is shown that in certain cases increasing the number of measurements does not improve the accuracy of the inverse solution. This result has been verified by experimental studies published in the literature.