{"id":"https://openalex.org/W2418467709","doi":"https://doi.org/10.3390/s16060858","title":"Improving the Accuracy of Laplacian Estimation with Novel Variable Inter-Ring Distances Concentric Ring Electrodes","display_name":"Improving the Accuracy of Laplacian Estimation with Novel Variable Inter-Ring Distances Concentric Ring Electrodes","publication_year":2016,"publication_date":"2016-06-10","ids":{"openalex":"https://openalex.org/W2418467709","doi":"https://doi.org/10.3390/s16060858","mag":"2418467709","pmid":"https://pubmed.ncbi.nlm.nih.gov/27294933"},"language":"en","primary_location":{"id":"doi:10.3390/s16060858","is_oa":true,"landing_page_url":"https://doi.org/10.3390/s16060858","pdf_url":"https://www.mdpi.com/1424-8220/16/6/858/pdf?version=1465541836","source":{"id":"https://openalex.org/S101949793","display_name":"Sensors","issn_l":"1424-8220","issn":["1424-8220"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sensors","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1424-8220/16/6/858/pdf?version=1465541836","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011899697","display_name":"Oleksandr Makeyev","orcid":"https://orcid.org/0000-0003-2648-0500"},"institutions":[{"id":"https://openalex.org/I142089014","display_name":"Din\u00e9 College","ror":"https://ror.org/03rbsqr59","country_code":"US","type":"education","lineage":["https://openalex.org/I142089014"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Oleksandr Makeyev","raw_affiliation_strings":["Department of Mathematics, Din\u00e9 College, Tsaile, AZ 86556, USA"],"raw_orcid":"https://orcid.org/0000-0003-2648-0500","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Din\u00e9 College, Tsaile, AZ 86556, USA","institution_ids":["https://openalex.org/I142089014"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043967761","display_name":"Walter G. Besio","orcid":"https://orcid.org/0000-0003-2752-5483"},"institutions":[{"id":"https://openalex.org/I17626003","display_name":"University of Rhode Island","ror":"https://ror.org/013ckk937","country_code":"US","type":"education","lineage":["https://openalex.org/I17626003"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Walter Besio","raw_affiliation_strings":["Department of Electrical, Computer, and Biomedical Engineering, University of Rhode Island, Kingston, RI 02881, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical, Computer, and Biomedical Engineering, University of Rhode Island, Kingston, RI 02881, USA","institution_ids":["https://openalex.org/I17626003"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5011899697"],"corresponding_institution_ids":["https://openalex.org/I142089014"],"apc_list":{"value":2400,"currency":"CHF","value_usd":2598},"apc_paid":{"value":2400,"currency":"CHF","value_usd":2598},"fwci":1.6409,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.82225078,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"16","issue":"6","first_page":"858","last_page":"858"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10660","display_name":"Conducting polymers and applications","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/2507","display_name":"Polymers and Plastics"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10660","display_name":"Conducting polymers and applications","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/2507","display_name":"Polymers and Plastics"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11472","display_name":"Analytical Chemistry and Sensors","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/1502","display_name":"Bioengineering"},"field":{"id":"https://openalex.org/fields/15","display_name":"Chemical Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11434","display_name":"Electrochemical Analysis and Applications","score":0.9886000156402588,"subfield":{"id":"https://openalex.org/subfields/1603","display_name":"Electrochemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/electrode","display_name":"Electrode","score":0.7385482788085938},{"id":"https://openalex.org/keywords/concentric","display_name":"Concentric","score":0.7272496223449707},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.6994086503982544},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.6634451746940613},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.6400606036186218},{"id":"https://openalex.org/keywords/truncation-error","display_name":"Truncation error","score":0.4764290750026703},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.47626540064811707},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.47419339418411255},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.417961984872818},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.4084101915359497},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.387050986289978},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3273395895957947},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31585609912872314},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.18280106782913208},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.1611175239086151},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.07262015342712402}],"concepts":[{"id":"https://openalex.org/C17525397","wikidata":"https://www.wikidata.org/wiki/Q176140","display_name":"Electrode","level":2,"score":0.7385482788085938},{"id":"https://openalex.org/C90296322","wikidata":"https://www.wikidata.org/wiki/Q619776","display_name":"Concentric","level":2,"score":0.7272496223449707},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.6994086503982544},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.6634451746940613},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.6400606036186218},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.4764290750026703},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.47626540064811707},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.47419339418411255},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.417961984872818},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.4084101915359497},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.387050986289978},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3273395895957947},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31585609912872314},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.18280106782913208},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.1611175239086151},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.07262015342712402},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3390/s16060858","is_oa":true,"landing_page_url":"https://doi.org/10.3390/s16060858","pdf_url":"https://www.mdpi.com/1424-8220/16/6/858/pdf?version=1465541836","source":{"id":"https://openalex.org/S101949793","display_name":"Sensors","issn_l":"1424-8220","issn":["1424-8220"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sensors","raw_type":"journal-article"},{"id":"pmid:27294933","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/27294933","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sensors (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:digitalcommons.uri.edu:ele_facpubs-1054","is_oa":true,"landing_page_url":"https://digitalcommons.uri.edu/ele_facpubs/55","pdf_url":null,"source":{"id":"https://openalex.org/S4377196359","display_name":"Digital Commons - URI (University of Rhode Island)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I17626003","host_organization_name":"University of Rhode Island","host_organization_lineage":["https://openalex.org/I17626003"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Department of Electrical, Computer, and Biomedical Engineering Faculty Publications","raw_type":"text"},{"id":"pmh:oai:doaj.org/article:abdb7253ea2340b7805600bd4eb2a2c9","is_oa":true,"landing_page_url":"https://doaj.org/article/abdb7253ea2340b7805600bd4eb2a2c9","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Sensors, Vol 16, Iss 6, p 858 (2016)","raw_type":"article"},{"id":"pmh:oai:europepmc.org:3901895","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/4934284","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"},{"id":"pmh:oai:mdpi.com:/1424-8220/16/6/858/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/s16060858","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Sensors; Volume 16; Issue 6; Pages: 858","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/s16060858","is_oa":true,"landing_page_url":"https://doi.org/10.3390/s16060858","pdf_url":"https://www.mdpi.com/1424-8220/16/6/858/pdf?version=1465541836","source":{"id":"https://openalex.org/S101949793","display_name":"Sensors","issn_l":"1424-8220","issn":["1424-8220"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sensors","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7107907909","display_name":null,"funder_award_id":"1R21NS061335\u201001A2","funder_id":"https://openalex.org/F4320337359","funder_display_name":"National Institute of Neurological Disorders and Stroke"},{"id":"https://openalex.org/G8519910372","display_name":null,"funder_award_id":"0933596","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8532750081","display_name":null,"funder_award_id":"175\u2010B5E7","funder_id":"https://openalex.org/F4320308691","funder_display_name":"Arizona Space Grant Consortium"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320308691","display_name":"Arizona Space Grant Consortium","ror":"https://ror.org/054zw2979"},{"id":"https://openalex.org/F4320337359","display_name":"National Institute of Neurological Disorders and Stroke","ror":"https://ror.org/01s5ya894"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2418467709.pdf","grobid_xml":"https://content.openalex.org/works/W2418467709.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W156208504","https://openalex.org/W570534109","https://openalex.org/W642655741","https://openalex.org/W1964945061","https://openalex.org/W1968934910","https://openalex.org/W1982815617","https://openalex.org/W1990679932","https://openalex.org/W1990826987","https://openalex.org/W1991857916","https://openalex.org/W2006608018","https://openalex.org/W2007016537","https://openalex.org/W2013334615","https://openalex.org/W2022988565","https://openalex.org/W2056144146","https://openalex.org/W2059686755","https://openalex.org/W2065758313","https://openalex.org/W2068240508","https://openalex.org/W2068529368","https://openalex.org/W2112026471","https://openalex.org/W2122585109","https://openalex.org/W2129491824","https://openalex.org/W2129890330","https://openalex.org/W2134073536","https://openalex.org/W2141089798","https://openalex.org/W2141220100","https://openalex.org/W2143760165","https://openalex.org/W2147833007","https://openalex.org/W2148701578","https://openalex.org/W2150471971","https://openalex.org/W2153208799","https://openalex.org/W2153499236","https://openalex.org/W2155309225","https://openalex.org/W2167883296","https://openalex.org/W2210053795","https://openalex.org/W2237420642","https://openalex.org/W2327316415","https://openalex.org/W2416582535","https://openalex.org/W4285719527","https://openalex.org/W4300116097","https://openalex.org/W6686257947","https://openalex.org/W6701545369","https://openalex.org/W6716630685","https://openalex.org/W6845181502"],"related_works":["https://openalex.org/W2040666836","https://openalex.org/W2238041693","https://openalex.org/W2112774109","https://openalex.org/W125347959","https://openalex.org/W1990789772","https://openalex.org/W2536422707","https://openalex.org/W24145419","https://openalex.org/W2036329708","https://openalex.org/W2073514592","https://openalex.org/W138907054"],"abstract_inverted_index":{"Noninvasive":[0],"concentric":[1,17,55,104],"ring":[2,18,56,105],"electrodes":[3,19,57],"are":[4,132,147],"a":[5,34,59,109,197],"promising":[6],"alternative":[7],"to":[8,62,134,169],"conventional":[9],"disc":[10,21],"electrodes.":[11,106],"Currently,":[12],"the":[13,65,77,89,95,159,181,192],"superiority":[14],"of":[15,27,36,47,64],"tripolar":[16,121,178],"over":[20],"electrodes,":[22],"in":[23,25,33,163],"particular,":[24],"accuracy":[26,46],"Laplacian":[28,48,66,96,166],"estimation,":[29],"has":[30],"been":[31],"demonstrated":[32],"range":[35],"applications.":[37],"In":[38],"our":[39],"recent":[40],"work,":[41],"we":[42],"have":[43],"shown":[44],"that":[45,151],"estimation":[49,63],"can":[50],"be":[51,185],"improved":[52],"with":[53,73],"multipolar":[54],"using":[58,76,108],"general":[60],"approach":[61],"for":[67,82,191],"an":[68],"(n":[69,122,127],"+":[70,79,112],"1)-polar":[71],"electrode":[72,130,155,179],"n":[74,83],"rings":[75],"(4n":[78,111],"1)-point":[80,113],"method":[81,142],"\u2265":[84],"2.":[85],"This":[86],"paper":[87],"takes":[88],"next":[90],"step":[91],"toward":[92],"further":[93],"improving":[94],"estimate":[97],"by":[98],"proposing":[99],"novel":[100],"variable":[101],"inter-ring":[102,119,137,153,172],"distances":[103,120,138,154,173],"Derived":[107],"modified":[110],"method,":[114],"linearly":[115],"increasing":[116,152],"and":[117,125,144,149],"decreasing":[118],"=":[123,128],"2)":[124],"quadripolar":[126,193],"3)":[129],"configurations":[131,156],"compared":[133,168],"their":[135],"constant":[136,171],"counterparts.":[139],"Finite":[140],"element":[141],"modeling":[143],"analytic":[145],"results":[146],"consistent":[148],"suggest":[150],"may":[157,184],"decrease":[158,199],"truncation":[160,182],"error":[161,183],"resulting":[162],"more":[164,187,195],"accurate":[165],"estimates":[167],"respective":[170],"configurations.":[174],"For":[175],"currently":[176],"used":[177],"configuration,":[180],"decreased":[186],"than":[188,196],"two-fold,":[189],"while":[190],"configuration":[194],"six-fold":[198],"is":[200],"expected.":[201]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
