A new approach is proposed to solve bioelectric inverse problems by employing the surface Laplacian of the bioelectrical potential. A theoretical investigation was conducted to test the feasibility of epicardial inverse imaging of cardiac electrical activity. A two-sphere homogeneous volume conductor model, where the inner sphere represents the epicardium and the outer sphere the body surface, was used. Radial and tangential current dipoles were used to approximate localized wavefronts propagating from the endocardium to the epicardium, and ectopic myocardial activities. The epicardial potential distribution was reconstructed from the body surface Laplacians with the aid of the Tikhonov zero-order regularization technique, which then was compared with the results obtained from the body surface potentials using the same regularization scheme. The two inverse solutions were compared qualitatively via visual inspection of the reconstructed epicardial potential maps, and quantitatively by examining relative errors and correlation coefficients between the 'true' and the reconstructed epicardial potentials. Both qualitative and quantitative results indicate that the surface Laplacians play a positive role in improving the ill-posed nature of the bioelectric inverse problem, which would enhance our capability of reconstructing important epicardial events such as extrema in the epicardial potential distribution. The present theoretical study suggests that the Laplacian-based inverse imaging technique may have important applications to epicardial inverse imaging and other bioelectric inverse imaging.
Bibliographical noteFunding Information:
Manuscript received November 3, 1995; revised April 23, 1996 and October 7, 1996. This work was supported in part by a grant from The Whitaker Foundation, in part by a grant from the University of Illinois at Chicago Campus Research Board and the Pittsburgh Supercomputing Center through the NIH National Center for Research Resources under Grant 2 P41 RR06009. Asterisk indicates corresponding author. *B. He is with the Department of Electrical Engineering and Computer Science and Bioengineering Program, The University of Illinois at Chicago, SEO 1120, MC 154, 851 South Morgan Street, Chicago, IL 60607 USA (e-mail: firstname.lastname@example.org).
- Body surface Laplacian map
- Epicardial potential inverse solution
- Inverse problem
- Laplacian inverse imaging