The surface Laplacian operator of the potentials on a bounded volume conductor has a unique inverse

Author

Van Oosterom, Adriaan

Author_Institution

Dept. of Cardiology, Lausanne Univ., Switzerland

Volume

53

Issue

7

fYear

2006

fDate

7/1/2006 12:00:00 AM

Firstpage

1449

Lastpage

1450

Abstract

In the discussion on the use of the surface Laplacian (SL) of the distribution of bioelectric potentials on the body surface, the question remained open whether a complete specification of the SL of the potential over the surface bounding a volume conductor would uniquely specify the potential on that surface up to a constant. This paper reports that this is indeed the case. In addition, it is shown that the integral of the SL over a closed surface is zero, a property that may serve as a check on the accuracy of any numerical approximation of the SL.

Keywords

Laplace equations; bioelectric potentials; bioelectric potentials; bounded volume conductor; inverse operator; surface Laplacian operator; Bioelectric phenomena; Cardiology; Conductors; Eigenvalues and eigenfunctions; Electric potential; Electrocardiography; Helium; Laplace equations; Thorax; Transmission line matrix methods; Body surface potentials; inverse operator; surface Laplacian; Algorithms; Body Surface Potential Mapping; Brain; Brain Mapping; Computer Simulation; Diagnosis, Computer-Assisted; Electric Conductivity; Electroencephalography; Heart Conduction System; Models, Cardiovascular; Models, Neurological;

fLanguage

English

Journal_Title

Biomedical Engineering, IEEE Transactions on

Publisher

ieee

ISSN

0018-9294

Type

jour

DOI

10.1109/TBME.2006.875713

Filename

1643418