Direct inference of heart-surface potentials from body-surface potentials has been the goal of most recent work on electrocardiographic inverse solutions. We developed and tested indirect methods for inferring heart-surface potentials based on estimation of regularized multipole sources. Regularization was done using Tikhonov, constrained-least-squares, and multipole-truncation techniques. These multipole-equivalent methods (MEMs) were compared to the conventional mixed boundary-value method (BVM) in a realistic torso model with up to 20% noise added to body-surface potentials and ±1 cm error in heart position and size. Optimal regularization was used for all inverse solutions. The relative error of inferred heart-surface potentials of the MEM was significantly less (p < 0.05) than that of the BVM using zeroth-order Tikhonov regularization in 10 of the 12 cases tested. These improvements occurred with a fourth-degree (24 coefficients) or smaller multipole moment. From these multipole coefficients, heart-surface potentials can be found at an unlimited number of heart-surface locations. Our indirect methods for estimating heart-surface potentials based on multipole inference appear to offer significant improvement over the conventional direct approach.


Electrical and Computer Engineering

Keywords and Phrases

Constrained least squares; Inverse electrocardiology; Multipole expansion; Vkhonov regularization

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version

Final Version

File Type





© 2004 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Jul 2004