{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:19:30Z","timestamp":1760242770862,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2016,6,10]],"date-time":"2016-06-10T00:00:00Z","timestamp":1465516800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100005731","name":"Arizona\/NASA Space Grant","doi-asserted-by":"publisher","award":["175\u2010B5E7"],"award-info":[{"award-number":["175\u2010B5E7"]}],"id":[{"id":"10.13039\/100005731","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000065","name":"National Institute of Neurological Disorders and Stroke","doi-asserted-by":"publisher","award":["1R21NS061335\u201001A2"],"award-info":[{"award-number":["1R21NS061335\u201001A2"]}],"id":[{"id":"10.13039\/100000065","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["0933596"],"award-info":[{"award-number":["0933596"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>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 \u2265 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.<\/jats:p>","DOI":"10.3390\/s16060858","type":"journal-article","created":{"date-parts":[[2016,6,10]],"date-time":"2016-06-10T07:37:41Z","timestamp":1465544261000},"page":"858","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Improving the Accuracy of Laplacian Estimation with Novel Variable Inter-Ring Distances Concentric Ring Electrodes"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2648-0500","authenticated-orcid":false,"given":"Oleksandr","family":"Makeyev","sequence":"first","affiliation":[{"name":"Department of Mathematics, Din\u00e9 College, Tsaile, AZ 86556, USA"}]},{"given":"Walter","family":"Besio","sequence":"additional","affiliation":[{"name":"Department of Electrical, Computer, and Biomedical Engineering, University of Rhode Island, Kingston, RI 02881, USA"}]}],"member":"1968","published-online":{"date-parts":[[2016,6,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/0168-5597(90)90063-J","article-title":"Emulation of somatosensory evoked potential (SEP) components with the 3-shell head model and the problem of \u201cghost potential fields\u201d when using an average reference in brain mapping","volume":"77","author":"Desmedt","year":"1990","journal-title":"Electroencephalogr. 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