Rd. Throne et Lg. Olson, A GENERALIZED EIGENSYSTEM APPROACH TO THE INVERSE PROBLEM OF ELECTROCARDIOGRAPHY, IEEE transactions on biomedical engineering, 41(6), 1994, pp. 592-600
We develop a new approach to the ill-conditioned inverse problem of el
ectrocardiography 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 eigenprob
lem, 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 le
ast squares fit to the measured body surface potentials is used to det
ermine 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 th
an the number of finite element nodes on the body surface, and the num
ber of modes employed in the expansion can be adjusted to reduce error
s due to noise.