We have developed a spline-based Laplacian estimator over an arbitrarily shaped surface of a volume conductor and tested its applicability to Laplacian electrocardiogram (ECG) mapping. In the newly developed algorithm, estimation of the parameters associated with the spline Laplacian is formulated by seeking the general inverse of a transfer matrix. Only one spline-parameter needs to be determined through regularization in order to estimate the realistic geometry surface Laplacian from the body surface potentials. It has been demonstrated that the rich knowledge on regularization in the inverse problems can be directly applied to estimate the spline Laplacian ECG (LECG), such as the discrepancy principle. Computer simulations have been conducted to validate the new approach in a spherical volume conductor and test the feasibility of mapping cardiac electrical sources in a realistic geometry heart-torso model. The present results demonstrate that the realistic geometry spline LECG can be estimated conveniently from the body surface potentials, is more robust against measurement noise and has better performance than the conventional five-point local Laplacian estimator.
Bibliographical noteFunding Information:
Manuscript received May 3, 2001; revised September 28, 2001. This work was supported in part by the National Science Foundation (NSF) under CAREER Award BES-9875344, in part by the American Heart Association under Grant 0140132N, and in part by a grant from UIC/CRB. Asterisk indicates corresponding author. *B. He is with the Departments of Bioengineering and Electrical and Computer Engineering, University of Illinois at Chicago, MC-063, SEO 218, 851 S. Morgan Street, Chicago, IL 60607 USA (e-mail: email@example.com).
- Body surface Laplacian mapping
- Inverse problem
- Laplacian ECG
- Realistic geometry
- Spline Laplacian
- Surface Laplacian