Inverse solutions for electric and potential field imaging

Abstract

One of the fundamental problems in theoretical electrocardiography can be characterized by an inverse problem. In this paper, we present new methods for achieving better estimates of heart surface potential distributions in terms of torso potentials through an inverse procedure. First, an adaptive meshing algorithm is described which minimizes the error in the forward problem due to spatial discretization. We have found that since the inverse problem relies directly on the accuracy of the forward solution, adaptive meshing produces a more accurate inverse transfer matrix. Secondly, we introduce a new local regularization procedure. This method works by breaking the global transfer matrix into sub-matrices and performing regularization only on those sub-matrices which have large condition numbers. Furthermore, the regularization parameters are specifically 'tuned' for each sub-matrix using an a priori scheme based on the L-curve method. This local regularization method provides substantial increases in accuracy when compared to global regularization schemes. Finally, we present specific examples of the implementation of these schemes using models derived from magnetic resonance imaging data from a human subject.