Improving the accuracy of the boundary element method by the use of second-order interpolation functions [EEG modeling application]

The boundary element method (BEM) is a widely used method to solve biomedical electromagnetic volume conduction problems. The commonly used formulation of this method uses constant interpolation functions for the potential and flat triangular surface elements. Linear interpolation for the potential...

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Bibliographic Details
Published in:IEEE transactions on biomedical engineering 2000-10, Vol.47 (10), p.1336-1346
Main Authors: Frijns, J.H.M., de Snoo, S.L., Schoonhoven, R.
Format: Article
Language:English
Subjects:
Accuracy
Algorithms
Associate members
Biological and medical sciences
Biomedical imaging
Boundary element method
Boundary element methods
Brain modeling
Conductors
Distributed computing
Electrical engineering
Electrodiagnosis. Electric activity recording
Electroencephalography
Electromyography
Finite element analysis
Functions
Geometry
Humans
Interpolation
Inverse problems
Investigative techniques, diagnostic techniques (general aspects)
Linear Models
Mathematical models
Medical sciences
Miscellaneous. Technology
Models, Neurological
Signal Processing, Computer-Assisted
Studies
Testing
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Summary:The boundary element method (BEM) is a widely used method to solve biomedical electromagnetic volume conduction problems. The commonly used formulation of this method uses constant interpolation functions for the potential and flat triangular surface elements. Linear interpolation for the potential on a flat triangular mesh turned out to yield a better accuracy. In this paper, the authors introduce quadratic interpolation functions for the potential and quadratically curved surface elements, resulting from second-order spatial interpolation. Theoretically, this results in an accuracy that is inversely proportional to the third power of element size. The method is tested on a four concentric sphere geometry, representative for electroencephalogram modeling, and compared to previous solutions of this problem in literature. In addition, a cylindrical test configuration is used. It is concluded that the use of quadratic interpolation functions for the potential and of quadratically curved surface elements in BEM results in a significant increase in accuracy and in some cases even a reduction of the computation time with the same number of nodes involved in the calculations.
ISSN:0018-9294
1558-2531
DOI:10.1109/10.871407