{"id":"https://openalex.org/W3135214040","doi":"https://doi.org/10.1016/j.rinp.2021.103992","title":"Optimal control of hyperthermia thermal damage based on tumor configuration","display_name":"Optimal control of hyperthermia thermal damage based on tumor configuration","publication_year":2021,"publication_date":"2021-03-07","ids":{"openalex":"https://openalex.org/W3135214040","doi":"https://doi.org/10.1016/j.rinp.2021.103992","mag":"3135214040"},"language":"en","primary_location":{"id":"doi:10.1016/j.rinp.2021.103992","doi":"https://doi.org/10.1016/j.rinp.2021.103992","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.rinp.2021.103992","pdf_url":"https://www.sciencedirect.com/science/article/pii/S2211379721001613/pdf","source":{"id":"https://openalex.org/S2764941219","display_name":"Results in Physics","issn_l":"2211-3797","issn":["2211-3797"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","jufo-1","norway-1","oarl","poland-70"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Results in Physics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.sciencedirect.com/science/article/pii/S2211379721001613/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108667530","display_name":"Reza Roohi","orcid":"https://orcid.org/0000-0003-2071-4089","observed_orcids":["https://orcid.org/0000-0003-2071-4089"]},"institutions":[{"id":"https://openalex.org/I4400600978","display_name":"Fasa University","ror":"https://ror.org/03a77cf20","country_code":"IR","type":"education","lineage":["https://openalex.org/I4400600978"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"R. Roohi","raw_affiliation_strings":["Department of Mechanical Engineering, Fasa University, Fasa, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Fasa University, Fasa, Iran","institution_ids":["https://openalex.org/I4400600978"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074418418","display_name":"Mohammad Heydari","orcid":"https://orcid.org/0000-0001-6764-4394","observed_orcids":["https://orcid.org/0000-0001-6764-4394","https://orcid.org/0000-0002-2169-9485","https://orcid.org/0000-0002-8051-492X"]},"institutions":[{"id":"https://openalex.org/I204490172","display_name":"Shiraz University of Technology","ror":"https://ror.org/04bxa3v83","country_code":"IR","type":"education","lineage":["https://openalex.org/I204490172"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"M.H. Heydari","raw_affiliation_strings":["Department of Mathematics, Shiraz University of Technology, Shiraz, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shiraz University of Technology, Shiraz, Iran","institution_ids":["https://openalex.org/I204490172"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015962889","display_name":"Zakieh Avazzadeh","orcid":"https://orcid.org/0000-0003-2257-1798","observed_orcids":["https://orcid.org/0000-0003-2257-1798"]},"institutions":[{"id":"https://openalex.org/I69356397","display_name":"Xi\u2019an Jiaotong-Liverpool University","ror":"https://ror.org/03zmrmn05","country_code":"CN","type":"education","lineage":["https://openalex.org/I69356397"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Z. Avazzadeh","raw_affiliation_strings":["Department of Applied Mathematics, Xi\u2019an Jiaotong-Liverpool University, Suzhou, 215123 Jiangsu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Xi\u2019an Jiaotong-Liverpool University, Suzhou, 215123 Jiangsu, China","institution_ids":["https://openalex.org/I69356397"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5015962889","https://openalex.org/A5074418418"],"corresponding_institution_ids":["https://openalex.org/I204490172","https://openalex.org/I69356397"],"apc_list":{"value":1200,"currency":"USD","value_usd":1200},"apc_paid":{"value":1200,"currency":"USD","value_usd":1200},"fwci":1.1524,"has_fulltext":true,"cited_by_count":17,"citation_normalized_percentile":{"value":0.76785612,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"23","issue":null,"first_page":"103992","last_page":"103992"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.4088999927043915,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.4088999927043915,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10958","display_name":"Ultrasound and Hyperthermia Applications","score":0.3181000053882599,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11565","display_name":"Thermoelastic and Magnetoelastic Phenomena","score":0.12039999663829803,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hyperthermia","display_name":"hyperthermia","score":0.9710000157356262},{"id":"https://openalex.org/keywords/optimal-control","display_name":"optimal control","score":0.8320000171661377},{"id":"https://openalex.org/keywords/thermal-damage","display_name":"thermal damage","score":0.777999997138977},{"id":"https://openalex.org/keywords/arrhenius-model","display_name":"Arrhenius model","score":0.8949999809265137},{"id":"https://openalex.org/keywords/tumor-ablation","display_name":"tumor ablation","score":0.6489999890327454},{"id":"https://openalex.org/keywords/energy-minimization","display_name":"energy minimization","score":0.6830000281333923}],"concepts":[{"id":"https://openalex.org/C2779949491","wikidata":"https://www.wikidata.org/wiki/Q242165","display_name":"Hyperthermia","level":2,"score":0.7370230555534363},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.5987389087677002},{"id":"https://openalex.org/C2909953478","wikidata":"https://www.wikidata.org/wiki/Q564872","display_name":"Hyperthermia Treatment","level":3,"score":0.5309169888496399},{"id":"https://openalex.org/C186725500","wikidata":"https://www.wikidata.org/wiki/Q327092","display_name":"Bioheat transfer","level":3,"score":0.5303068161010742},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4778197109699249},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4728532135486603},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46309804916381836},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.4627189040184021},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.45050859451293945},{"id":"https://openalex.org/C204530211","wikidata":"https://www.wikidata.org/wiki/Q752823","display_name":"Thermal","level":2,"score":0.41501671075820923},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.3751673400402069},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2865387797355652},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.26324284076690674},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.20711135864257812},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17345082759857178},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/j.rinp.2021.103992","doi":"https://doi.org/10.1016/j.rinp.2021.103992","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.rinp.2021.103992","pdf_url":"https://www.sciencedirect.com/science/article/pii/S2211379721001613/pdf","source":{"id":"https://openalex.org/S2764941219","display_name":"Results in Physics","issn_l":"2211-3797","issn":["2211-3797"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","jufo-1","norway-1","oarl","poland-70"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Results in Physics","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:399d530d817148b09d8aa682f8dfe357","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/399d530d817148b09d8aa682f8dfe357","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,"listed_in":[],"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":"Results in Physics, Vol 23, Iss , Pp 103992- (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1016/j.rinp.2021.103992","doi":"https://doi.org/10.1016/j.rinp.2021.103992","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.rinp.2021.103992","pdf_url":"https://www.sciencedirect.com/science/article/pii/S2211379721001613/pdf","source":{"id":"https://openalex.org/S2764941219","display_name":"Results in Physics","issn_l":"2211-3797","issn":["2211-3797"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","jufo-1","norway-1","oarl","poland-70"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Results in Physics","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/3","score":0.7246000170707703,"display_name":"Good health and well-being"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3135214040.pdf","grobid_xml":"https://content.openalex.org/works/W3135214040.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W1971075293","https://openalex.org/W1996052867","https://openalex.org/W1997940993","https://openalex.org/W2000144812","https://openalex.org/W2012597904","https://openalex.org/W2047821137","https://openalex.org/W2048856724","https://openalex.org/W2049376437","https://openalex.org/W2060473871","https://openalex.org/W2103233901","https://openalex.org/W2408478130","https://openalex.org/W2494775221","https://openalex.org/W2609290290","https://openalex.org/W2761829277","https://openalex.org/W2768876099","https://openalex.org/W2782302440","https://openalex.org/W2787959293","https://openalex.org/W2793831519","https://openalex.org/W2796202420","https://openalex.org/W2802603505","https://openalex.org/W2804275880","https://openalex.org/W2810254856","https://openalex.org/W2896776383","https://openalex.org/W2902587778","https://openalex.org/W2906334757","https://openalex.org/W2913661051","https://openalex.org/W2914047918","https://openalex.org/W2922224456","https://openalex.org/W2945250210","https://openalex.org/W2950708086","https://openalex.org/W2963108065","https://openalex.org/W2967370425","https://openalex.org/W4298060601","https://openalex.org/W6608670542"],"related_works":["https://openalex.org/W1619012091","https://openalex.org/W2183987696","https://openalex.org/W2049279242","https://openalex.org/W2331547677","https://openalex.org/W4389060576","https://openalex.org/W4384700526","https://openalex.org/W7070286994","https://openalex.org/W2977897651","https://openalex.org/W2073310163","https://openalex.org/W1966881525"],"abstract_inverted_index":{"Improvement":[0],"and":[1,11,46,101,106,114,138,196,202,221],"optimization":[2],"of":[3,7,74,152,165,172,215,228,261,276],"hyperthermia":[4,28,65,97],"as":[5,156],"one":[6],"the":[8,33,55,60,72,81,84,107,121,125,134,140,150,163,170,181,183,190,210,213,229,234,244,252,262,282],"most":[9],"effective":[10],"conventional":[12],"cancer":[13],"treatments":[14],"have":[15],"been":[16],"tackled":[17],"by":[18,149,208],"many":[19],"researchers":[20],"in":[21,80,226],"recent":[22],"years.":[23],"The":[24,144,258],"main":[25,259],"benchmark":[26],"for":[27,64,194],"treatment":[29,66],"is":[30,93,117,129,147,176,224,238,256,265],"to":[31,37,41,48,54,71,120,131,212,219,242],"elevate":[32],"cancerous":[34,75,115],"tissue":[35],"temperature":[36,136,231],"a":[38,153,157,247],"specified":[39],"level":[40,110,137],"initiate":[42],"damage":[43,53,109],"or":[44,169],"ablation":[45],"simultaneously":[47,132],"prevent":[49],"any":[50],"irreversible":[51],"thermal":[52,141,167,174],"surrounding":[56],"healthy":[57,113],"cells.":[58,76],"Therefore,":[59],"heat":[61,90,191],"source":[62,91,192],"pattern":[63],"should":[67],"be":[68],"adjusted":[69],"according":[70,119],"distribution":[73,193],"To":[77],"do":[78],"this,":[79],"present":[82],"study":[83],"fractional":[85,271],"bioheat":[86],"equation":[87],"with":[88,99],"unknown":[89],"term":[92],"implemented.":[94],"Two":[95],"different":[96],"scenarios":[98],"single":[100,195],"dual":[102,197],"tumors":[103],"are":[104],"considered":[105],"appropriate":[108],"at":[111],"both":[112],"tissues":[116],"planned":[118],"Arrhenius":[122],"model.":[123],"Moreover,":[124],"optimal":[126,184],"control":[127,185],"criterion":[128],"set":[130],"produce":[133],"goal":[135],"minimize":[139],"power":[142,175],"consumption.":[143],"mentioned":[145],"task":[146],"accomplished":[148],"definition":[151],"priority":[154,211],"coefficient":[155],"weight":[158],"function":[159,237],"which":[160,279],"determines":[161],"whether":[162],"establishment":[164],"desired":[166,230],"field":[168,232],"reduction":[171],"applied":[173,216],"more":[177],"important.":[178],"Based":[179],"on":[180,251],"results,":[182,246],"approach":[186],"can":[187],"precisely":[188],"determine":[189],"tumor":[198],"cases":[199],"(with":[200],"1.03":[201],"0.13%":[203],"deviation":[204,223],"error,":[205],"respectively).":[206],"Whereas,":[207],"shifting":[209],"minimization":[214],"energy,":[217],"up":[218],"23.1":[220],"38.7%":[222],"observed":[225],"formation":[227],"(while":[233],"overall":[235],"cost":[236],"minimized).":[239],"In":[240],"order":[241],"investigate":[243],"numerical":[245],"computational":[248],"method":[249,264],"based":[250],"Legendre":[253],"cardinal":[254],"functions":[255],"proposed.":[257],"advantage":[260],"proposed":[263],"that":[266],"it":[267],"transforms":[268],"solving":[269,274],"such":[270],"models":[272],"into":[273],"systems":[275],"algebraic":[277],"equations":[278],"greatly":[280],"simplify":[281],"problem.":[283]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":5}],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2021-03-15T00:00:00"}
