Inverse solution in electrocardiography: determining epicardial from body surface maps by using the finite element method

A new method of determining epicardial potentials from body surface maps is presented. Epicardial potentials can be estimated via the forward transfer matrix computed by using the finite element method. Due to smoothing and decrease in value in potential distribution of the body surface, the inverse problem involved becomes, in nature, ill-conditioned and direct application of the usual inversion technique will give an extremely oscillatory solution. Therefore, in order to obtain a practically meaningful solution, an appropriate regularizing procedure must be developed and, in the present paper, an effective regularization based on the generalized inverse matrix is proposed and its usefulness is demonstrated. Numerical experiments suggest that if the epicardial map includes high components of spatial frequency the inverted epicardial map will have poor resolution. This is especially true at the epicardial surface distant from the body surface, such as on the diaphragmatic side of the ventricle. If the epicardial maps have to be inverted over the entire region of the epicardium with a clinically allowable accuracy, about 180 body surface lead points and 3 significant figures in the measurements of body surface potentials will be needed.