A generalized eigensystem approach to the inverse problem of electrocardiography

We develop a new approach to the ill-conditioned inverse problem of electrocardiography which employs finite element techniques to generate a truncated eigenvector expansion to stabilize the inversion. Ordinary three-dimensional isoparametric finite elements are used to generate the conductivity matrix for the body. We introduce a related eigenproblem, for which a special two-dimensional isoparametric area matrix is used, and solve for the lowest eigenvalues and eigenvectors. The body surface potentials are expanded in terms of the eigenvectors, and a least squares fit to the measured body surface potentials is used to determine the coefficients of the expansion. This expansion is then used directly to determine the potentials on the surface of the heart. The number of measurement points on the surface of the body can be less than the number of finite element nodes on the body surface, and the number of modes employed in the expansion can be adjusted to reduce errors due to noise.