Obtaining 'Good' solutions to the inverse problem of Electrocardiography
by
Josef Barnes
Griffith University

Accurate positioning of the site of a heart attack on the surface of the heart is an important diagnostic tool in patient management. From a mathematical viewpoint this revolves around the solution of differential equations governing the electric field in the human chest. The forward problem of electrocardiography is the determination of the body surface electric potential distribution given a certain heart surface distribution. The inverse problem, however, attempts to find the heart surface potential distribution from a measured body surface potential distribution. Unlike the forward problem, the inverse problem is not well-posed, meaning that many similar body surface potential distributions can give widely varying heart surface potential distributions. That is, the inverse problem is sensitive to measurement errors in the magnitudes of the potentials as well as the positions of the measurement electrodes.

A popular method for determining stable solutions to ill-posed problems is Tikhonov regularisation, where accurate solutions can be obtained by choosing the optimal regularisation parameter. Five methods for determining an approximation to the optimal regularisation parameter were compared over three different simulation models of increasing complexity. In particular, the relatively new method, Robust Generalised Cross Validation was compared against four well established methods to determine how well it performed in the inverse problem of electrocardiography.

Date received: December 3, 2009