Improving the Accuracy of Laplacian Estimation with Novel Variable Inter-Ring Distances Concentric Ring Electrodes
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 rec...
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doaj-abdb7253ea2340b7805600bd4eb2a2c92020-11-25T00:59:55ZengMDPI AGSensors1424-82202016-06-0116685810.3390/s16060858s16060858Improving the Accuracy of Laplacian Estimation with Novel Variable Inter-Ring Distances Concentric Ring ElectrodesOleksandr Makeyev0Walter G. Besio1Department of Mathematics, Diné College, Tsaile, AZ 86556, USADepartment of Electrical, Computer, and Biomedical Engineering, University of Rhode Island, Kingston, RI 02881, USANoninvasive 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.http://www.mdpi.com/1424-8220/16/6/858noninvasiveelectrophysiologyelectroencephalographysensorsmultipolarconcentric ring electrodesLaplacianfinite element methodmodeling |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Oleksandr Makeyev Walter G. Besio |
spellingShingle |
Oleksandr Makeyev Walter G. Besio Improving the Accuracy of Laplacian Estimation with Novel Variable Inter-Ring Distances Concentric Ring Electrodes Sensors noninvasive electrophysiology electroencephalography sensors multipolar concentric ring electrodes Laplacian finite element method modeling |
author_facet |
Oleksandr Makeyev Walter G. Besio |
author_sort |
Oleksandr Makeyev |
title |
Improving the Accuracy of Laplacian Estimation with Novel Variable Inter-Ring Distances Concentric Ring Electrodes |
title_short |
Improving the Accuracy of Laplacian Estimation with Novel Variable Inter-Ring Distances Concentric Ring Electrodes |
title_full |
Improving the Accuracy of Laplacian Estimation with Novel Variable Inter-Ring Distances Concentric Ring Electrodes |
title_fullStr |
Improving the Accuracy of Laplacian Estimation with Novel Variable Inter-Ring Distances Concentric Ring Electrodes |
title_full_unstemmed |
Improving the Accuracy of Laplacian Estimation with Novel Variable Inter-Ring Distances Concentric Ring Electrodes |
title_sort |
improving the accuracy of laplacian estimation with novel variable inter-ring distances concentric ring electrodes |
publisher |
MDPI AG |
series |
Sensors |
issn |
1424-8220 |
publishDate |
2016-06-01 |
description |
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. |
topic |
noninvasive electrophysiology electroencephalography sensors multipolar concentric ring electrodes Laplacian finite element method modeling |
url |
http://www.mdpi.com/1424-8220/16/6/858 |
work_keys_str_mv |
AT oleksandrmakeyev improvingtheaccuracyoflaplacianestimationwithnovelvariableinterringdistancesconcentricringelectrodes AT waltergbesio improvingtheaccuracyoflaplacianestimationwithnovelvariableinterringdistancesconcentricringelectrodes |
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