Comparison of Transmembrane and Epicardial Potential Patterns Reconstructed by a Linear Inverse Approach

Reconstruction of the electrical sources of the human heart from electrocardiographic (ECG) mapping data is called the inverse problem of electrocardiography. Based on the bidomain theory [1] the transmembrane potential φTM is considered the primary electrical source. The relation between this source and the potential on all conductivity interfaces as well as the body surface is given by a FREDHOLM integral equation of second kind (GESELOWITZ equation) which is the solution for the socalled forward problem. Assuming electrical isotropy of the myocardium during depolarization the forward problem reduces to a two dimensional scalar potential problem. In general the boundary element method [2],[3] (BEM) is employed for solving this kind of problem numerically to yield a discrete ill-posed and rank-deficient system of linear equations. Prom there in the inverse problem one can not simply invert these linear equations in order to obtain meaningful solutions for the source distribution. In fact, one has to utilize some special regularization techniques which are customized for the specific problem. Due to ill-posed ness it seems to be unfeasible to reconstruct the entire time course of the transmembrane potential at each source point, however, some clinical important features of 0 (e.g., the activation time (AT) defined as the onset of φ) are to be resolved. The common method in conjunction with the inverse problem of electrocardiography is to estimate the potential on the pericardium which is, for historical reasons, denoted as t lie epicardial potential problem. An empirical way to estimate the AT from the epicardial potential is presented in [4]. Jn this study we compare the results for the AT pattern on the epicardiuin computed from the transmembrane potential setting arid the epicardial potential sotting. The rcgularization method used wa,s proposed by GKEI:NSITE !·"']AT imaging methods «re of great clinical interest. These methods enable the reconstruction of single focal, multiple focal and more complicated activation patterns. Noninvasive imaging of ec-topic and pre-exeiterl ventricular activation may be on«· of the possible clinical applications.