{"id":"https://openalex.org/W2778551157","doi":"https://doi.org/10.1109/tbme.2017.2785342","title":"EEG for Current With Two-Dimensional Support","display_name":"EEG for Current With Two-Dimensional Support","publication_year":2017,"publication_date":"2017-12-21","ids":{"openalex":"https://openalex.org/W2778551157","doi":"https://doi.org/10.1109/tbme.2017.2785342","mag":"2778551157","pmid":"https://pubmed.ncbi.nlm.nih.gov/29989944"},"language":"en","primary_location":{"id":"doi:10.1109/tbme.2017.2785342","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tbme.2017.2785342","pdf_url":null,"source":{"id":"https://openalex.org/S5240358","display_name":"IEEE Transactions on Biomedical Engineering","issn_l":"0018-9294","issn":["0018-9294","1558-2531"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Biomedical Engineering","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057085378","display_name":"George Dassios","orcid":"https://orcid.org/0000-0002-1738-1693"},"institutions":[{"id":"https://openalex.org/I174878644","display_name":"University of Patras","ror":"https://ror.org/017wvtq80","country_code":"GR","type":"education","lineage":["https://openalex.org/I174878644"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"George Dassios","raw_affiliation_strings":["Department of Chemical Engineering, University of Patras"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Chemical Engineering, University of Patras","institution_ids":["https://openalex.org/I174878644"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007372240","display_name":"A. S. Fokas","orcid":"https://orcid.org/0000-0002-5881-802X"},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Athanassios S. Fokas","raw_affiliation_strings":["Department of Applied Mathematics and Theoretical Physics, University of Cambridge and also with the Department of Electrical Engineering University of Southern California"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Theoretical Physics, University of Cambridge and also with the Department of Electrical Engineering University of Southern California","institution_ids":["https://openalex.org/I1174212"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025129267","display_name":"Parham Hashemzadeh","orcid":"https://orcid.org/0000-0001-7597-6970"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Parham Hashemzadeh","raw_affiliation_strings":["Department of Applied Mathematics and Theoretical Physics, University of Cambridge"],"raw_orcid":"https://orcid.org/0000-0001-7597-6970","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Theoretical Physics, University of Cambridge","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054387045","display_name":"Richard M. Leahy","orcid":"https://orcid.org/0000-0002-7278-5471"},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Richard M. Leahy","raw_affiliation_strings":["Department of Electrical Engineering, University of Southern California, Los Angeles, CA, USA"],"raw_orcid":"https://orcid.org/0000-0002-7278-5471","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.399,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.62556727,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"65","issue":"9","first_page":"2101","last_page":"2108"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10241","display_name":"Functional Brain Connectivity Studies","score":0.6208000183105469,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10241","display_name":"Functional Brain Connectivity Studies","score":0.6208000183105469,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.09059999883174896,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.05739999935030937,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/current","display_name":"Current (fluid)","score":0.6441783308982849},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5730165839195251},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.5471535921096802},{"id":"https://openalex.org/keywords/electroencephalography","display_name":"Electroencephalography","score":0.529444694519043},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5013508796691895},{"id":"https://openalex.org/keywords/scalp","display_name":"Scalp","score":0.4941308796405792},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4828527569770813},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.363323450088501},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3299027979373932},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3129957616329193},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3007841110229492},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.29696792364120483},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.24217694997787476},{"id":"https://openalex.org/keywords/neuroscience","display_name":"Neuroscience","score":0.17481282353401184},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10960268974304199},{"id":"https://openalex.org/keywords/psychology","display_name":"Psychology","score":0.08782321214675903}],"concepts":[{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.6441783308982849},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5730165839195251},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5471535921096802},{"id":"https://openalex.org/C522805319","wikidata":"https://www.wikidata.org/wiki/Q179965","display_name":"Electroencephalography","level":2,"score":0.529444694519043},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5013508796691895},{"id":"https://openalex.org/C2778515351","wikidata":"https://www.wikidata.org/wiki/Q9622","display_name":"Scalp","level":2,"score":0.4941308796405792},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4828527569770813},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.363323450088501},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3299027979373932},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3129957616329193},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3007841110229492},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.29696792364120483},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.24217694997787476},{"id":"https://openalex.org/C169760540","wikidata":"https://www.wikidata.org/wiki/Q207011","display_name":"Neuroscience","level":1,"score":0.17481282353401184},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10960268974304199},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.08782321214675903},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C105702510","wikidata":"https://www.wikidata.org/wiki/Q514","display_name":"Anatomy","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D001921","descriptor_name":"Brain","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D001921","descriptor_name":"Brain","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D001921","descriptor_name":"Brain","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D001931","descriptor_name":"Brain Mapping","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D001931","descriptor_name":"Brain Mapping","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D001931","descriptor_name":"Brain Mapping","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D004569","descriptor_name":"Electroencephalography","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D004569","descriptor_name":"Electroencephalography","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D004569","descriptor_name":"Electroencephalography","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D006257","descriptor_name":"Head","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D006257","descriptor_name":"Head","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D006257","descriptor_name":"Head","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008954","descriptor_name":"Models, Biological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008954","descriptor_name":"Models, Biological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008954","descriptor_name":"Models, Biological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012815","descriptor_name":"Signal Processing, Computer-Assisted","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D012815","descriptor_name":"Signal Processing, Computer-Assisted","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D012815","descriptor_name":"Signal Processing, Computer-Assisted","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":3,"locations":[{"id":"doi:10.1109/tbme.2017.2785342","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tbme.2017.2785342","pdf_url":null,"source":{"id":"https://openalex.org/S5240358","display_name":"IEEE Transactions on Biomedical Engineering","issn_l":"0018-9294","issn":["0018-9294","1558-2531"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Biomedical Engineering","raw_type":"journal-article"},{"id":"pmid:29989944","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/29989944","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":"IEEE transactions on bio-medical engineering","raw_type":null},{"id":"pmh:oai:europepmc.org:5677948","is_oa":false,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/6393112","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1755984640","display_name":null,"funder_award_id":"EP/N014588/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G3433025165","display_name":null,"funder_award_id":"R01 EB009048","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4013382746","display_name":null,"funder_award_id":"EP/N006593/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6333403462","display_name":null,"funder_award_id":"EP/H051309/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7353819589","display_name":null,"funder_award_id":"R01 NS089212","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G871495995","display_name":null,"funder_award_id":"EP/H04261X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1605773447","https://openalex.org/W1967345698","https://openalex.org/W1973275441","https://openalex.org/W1984614893","https://openalex.org/W1988354434","https://openalex.org/W2014502281","https://openalex.org/W2016980059","https://openalex.org/W2021787435","https://openalex.org/W2046973056","https://openalex.org/W2053595213","https://openalex.org/W2070312562","https://openalex.org/W2084333685","https://openalex.org/W2091623371","https://openalex.org/W2100028360","https://openalex.org/W2115175655","https://openalex.org/W2135595031","https://openalex.org/W2145309136","https://openalex.org/W2166073443","https://openalex.org/W2731873610","https://openalex.org/W4210809295","https://openalex.org/W4231545543","https://openalex.org/W4241074797"],"related_works":["https://openalex.org/W2366370005","https://openalex.org/W75765767","https://openalex.org/W2963794791","https://openalex.org/W1927677835","https://openalex.org/W1489221585","https://openalex.org/W2372248139","https://openalex.org/W1823792310","https://openalex.org/W2012449959","https://openalex.org/W2111079319","https://openalex.org/W3015866773"],"abstract_inverted_index":{"OBJECTIVE:":[0],"The":[1,199,235],"inverse":[2,251,259],"problem":[3],"of":[4,24,52,55,69,82,88,109,157,183,202,211,214,222,231,247],"computing":[5],"the":[6,22,25,39,46,53,56,60,66,79,83,86,89,93,105,110,125,129,142,154,165,170,173,181,188,192,203,219,227,232,240,245,250,254,262,267],"neuronal":[7],"current":[8,28,57,84,90,174,204],"density":[9],"from":[10,65],"scalp":[11,31,40,143,167],"EEG":[12,41,61,94],"is":[13,19],"highly":[14],"ill-posed.":[15],"In":[16],"part,":[17],"this":[18],"due":[20],"to":[21,45,218,238],"nonuniqueness":[23],"mapping":[26,268],"between":[27],"sources":[29,43],"and":[30,107,120,134,159,209,221],"potentials.":[32],"We":[33,162],"develop":[34,73],"an":[35],"explicit":[36],"formula":[37,75],"for":[38,42,141,145,153,195,256],"constrained":[44],"cortical":[47],"surface":[48,220],"in":[49,169,176,180,249],"terms":[50],"only":[51,78],"components":[54,230],"that":[58,76,91,102,164,172,265],"affect":[59],"signal.":[62],"METHODS:":[63],"Starting":[64],"quasi-static":[67],"form":[68],"Maxwell's":[70],"equations,":[71],"we":[72,138],"a":[74,146,177,212,223],"involves":[77],"\"visible\"":[80,200],"part":[81,87,201],"(i.e.,":[85],"affects":[92],"measurements),":[95],"as":[96,98,150,152],"well":[97,151],"certain":[99,224],"auxiliary":[100,263],"functions":[101,264],"depend":[103],"on":[104],"topology":[106],"conductivity":[108],"3-D":[111,193],"domains":[112],"$\\Omega":[113,116,118,121],"_c$":[114],",":[115],"_f$,":[117],"_b$,":[119],"_s$,":[122],"which":[123],"model":[124],"spaces":[126],"occupied":[127],"by":[128],"cerebrum,":[130],"cerebrospinal":[131],"fluid,":[132],"bone,":[133],"scalp,":[135],"respectively.":[136],"RESULTS:":[137],"derive":[139],"expressions":[140],"potential":[144,189,255],"general":[147],"nested":[148],"topology,":[149],"special":[155],"case":[156,171],"spherical":[158,178],"ellipsoidal":[160],"surfaces.":[161],"verify":[163],"resulting":[166,236],"potential,":[168],"resides":[175],"shell":[179],"cerebrum":[182],"thickness":[184],"$2\\delta$,":[185],"agrees":[186],"with":[187],"obtained":[190],"via":[191],"formulation":[194],"$\\delta":[196],"=10^{-8}\\text{m}$.":[197],"CONCLUSION:":[198],"can":[205,269],"be":[206,270],"explicitly":[207],"characterized":[208],"consists":[210],"combination":[213],"its":[215],"component":[216],"normal":[217],"function":[225],"generating":[226],"remaining":[228],"tangential":[229],"current.":[233],"SIGNIFICANCE:":[234],"ability":[237],"restrict":[239],"source":[241],"space":[242],"greatly":[243],"reduces":[244],"degree":[246],"ambiguity":[248],"solutions,":[252,260],"offering":[253],"more":[257],"stable":[258],"since":[261],"define":[266],"computed":[271],"efficiently":[272],"using":[273],"standard":[274],"numerical":[275],"methods.":[276]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}