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Sensors 2016, 16(6), 858; doi:10.3390/s16060858

Improving the Accuracy of Laplacian Estimation with Novel Variable Inter-Ring Distances Concentric Ring Electrodes

1
Department of Mathematics, Diné College, Tsaile, AZ 86556, USA
2
Department of Electrical, Computer, and Biomedical Engineering, University of Rhode Island, Kingston, RI 02881, USA
*
Author to whom correspondence should be addressed.
Academic Editors: Steffen Leonhardt and Daniel Teichmann
Received: 26 February 2016 / Revised: 2 June 2016 / Accepted: 7 June 2016 / Published: 10 June 2016
(This article belongs to the Special Issue Noninvasive Biomedical Sensors)
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Abstract

Noninvasive concentric ring electrodes are a promising alternative to conventional disc electrodes. Currently, the superiority of tripolar concentric ring electrodes over disc electrodes, in particular, in accuracy of Laplacian estimation, has been demonstrated in a range of applications. In our recent work, we have shown that accuracy of Laplacian estimation can be improved with multipolar concentric ring electrodes using a general approach to estimation of the Laplacian for an (n + 1)-polar electrode with n rings using the (4n + 1)-point method for n ≥ 2. This paper takes the next step toward further improving the Laplacian estimate by proposing novel variable inter-ring distances concentric ring electrodes. Derived using a modified (4n + 1)-point method, linearly increasing and decreasing inter-ring distances tripolar (n = 2) and quadripolar (n = 3) electrode configurations are compared to their constant inter-ring distances counterparts. Finite element method modeling and analytic results are consistent and suggest that increasing inter-ring distances electrode configurations may decrease the truncation error resulting in more accurate Laplacian estimates compared to respective constant inter-ring distances configurations. For currently used tripolar electrode configuration, the truncation error may be decreased more than two-fold, while for the quadripolar configuration more than a six-fold decrease is expected. View Full-Text
Keywords: noninvasive; electrophysiology; electroencephalography; sensors; multipolar; concentric ring electrodes; Laplacian; finite element method; modeling noninvasive; electrophysiology; electroencephalography; sensors; multipolar; concentric ring electrodes; Laplacian; finite element method; modeling
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Makeyev, O.; Besio, W.G. Improving the Accuracy of Laplacian Estimation with Novel Variable Inter-Ring Distances Concentric Ring Electrodes. Sensors 2016, 16, 858.

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