The use of the spatial covariance in computing pericardial potentials

This paper investigates the incorporation of the spatial covariance of the pericardial potentials, assumed known a priori as a regularization function, when computing the pericardial potential distribution from observed body surface potentials. The resulting inverse solutions are compared with those using as a regularization function: (1) the norm of the solution, (2) the norm of the surface Laplacian of the solution, as well as with those based on using the truncated singular value decomposition. The study uses a realistic source model to simulate potentials throughout the QRS-interval. This source is placed in an anatomically accurate inhomogeneous volume conductor model of the torso. The use of a single value of the regularization parameter is shown to be feasible: for data incorporating 2% noise, the use of the spatial covariance is demonstrated to result in a relative error over the entire QRS interval as low as 10%. Major errors are demonstrated to result if the effect of the inhomogeneity of the lungs is ignored. The spatial covariance based inverse is shown to be more robust with respect to the perturbations (noise; inhomogeneity) than the other estimators included in this study.