{"id":"https://openalex.org/W4392236249","doi":"https://doi.org/10.3389/fonc.2024.1328147","title":"Optimizing linear energy transfer distribution in intensity-modulated proton therapy using the alternating direction method of multipliers","display_name":"Optimizing linear energy transfer distribution in intensity-modulated proton therapy using the alternating direction method of multipliers","publication_year":2024,"publication_date":"2024-02-28","ids":{"openalex":"https://openalex.org/W4392236249","doi":"https://doi.org/10.3389/fonc.2024.1328147","pmid":"https://pubmed.ncbi.nlm.nih.gov/38482200","pmcid":"https://www.ncbi.nlm.nih.gov/pmc/articles/10932999"},"language":"en","primary_location":{"id":"doi:10.3389/fonc.2024.1328147","doi":"https://doi.org/10.3389/fonc.2024.1328147","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fonc.2024.1328147","pdf_url":"https://www.frontiersin.org/journals/oncology/articles/10.3389/fonc.2024.1328147/pdf","source":{"id":"https://openalex.org/S2596394214","display_name":"Frontiers in Oncology","issn_l":"2234-943X","issn":["2234-943X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Oncology","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.frontiersin.org/journals/oncology/articles/10.3389/fonc.2024.1328147/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068699006","display_name":"Qingkun Fan","orcid":"https://orcid.org/0000-0002-8596-9982","observed_orcids":["https://orcid.org/0000-0002-8596-9982","https://orcid.org/0009-0004-8347-1912"]},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qingkun Fan","raw_affiliation_strings":["School of Mathematics and Statistics, Wuhan University, Wuhan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Wuhan University, Wuhan, China","institution_ids":["https://openalex.org/I37461747"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100339498","display_name":"Xiaoyuan Zhang","orcid":"https://orcid.org/0000-0002-2090-2381","observed_orcids":["https://orcid.org/0000-0002-2090-2381"]},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoyuan Zhang","raw_affiliation_strings":["School of Mathematics and Statistics, Wuhan University, Wuhan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Wuhan University, Wuhan, China","institution_ids":["https://openalex.org/I37461747"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5092410366","display_name":"Riao Dao","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Riao Dao","raw_affiliation_strings":["School of Physics and Technology, Wuhan University, Wuhan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Physics and Technology, Wuhan University, Wuhan, China","institution_ids":["https://openalex.org/I37461747"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102632279","display_name":"Yujia Qian","orcid":"https://orcid.org/0009-0005-8332-5306","observed_orcids":["https://orcid.org/0009-0005-8332-5306"]},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yujia Qian","raw_affiliation_strings":["School of Physics and Technology, Wuhan University, Wuhan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Physics and Technology, Wuhan University, Wuhan, China","institution_ids":["https://openalex.org/I37461747"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078388333","display_name":"Lewei Zhao","orcid":"https://orcid.org/0000-0002-1050-3184","observed_orcids":["https://orcid.org/0000-0002-1050-3184"]},"institutions":[{"id":"https://openalex.org/I4210128757","display_name":"Corewell Health William Beaumont University Hospital","ror":"https://ror.org/03artm726","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I4210128757","https://openalex.org/I4392738273"]},{"id":"https://openalex.org/I4210161894","display_name":"Corewell Health Trenton Hospital","ror":"https://ror.org/058sakv40","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I4210161894","https://openalex.org/I4392738273"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lewei Zhao","raw_affiliation_strings":["Department of Radiation Oncology, Corewell Health William Beaumont University Hospital, Royal Oak, MI, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Radiation Oncology, Corewell Health William Beaumont University Hospital, Royal Oak, MI, United States","institution_ids":["https://openalex.org/I4210128757","https://openalex.org/I4210161894"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100339643","display_name":"Xiaoqiang Li","orcid":"https://orcid.org/0000-0003-2463-8298","observed_orcids":["https://orcid.org/0000-0003-2463-8298"]},"institutions":[{"id":"https://openalex.org/I4210128757","display_name":"Corewell Health William Beaumont University Hospital","ror":"https://ror.org/03artm726","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I4210128757","https://openalex.org/I4392738273"]},{"id":"https://openalex.org/I4210161894","display_name":"Corewell Health Trenton Hospital","ror":"https://ror.org/058sakv40","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I4210161894","https://openalex.org/I4392738273"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xiaoqiang Li","raw_affiliation_strings":["Department of Radiation Oncology, Corewell Health William Beaumont University Hospital, Royal Oak, MI, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Radiation Oncology, Corewell Health William Beaumont University Hospital, Royal Oak, MI, United States","institution_ids":["https://openalex.org/I4210128757","https://openalex.org/I4210161894"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068845250","display_name":"Xuanfeng Ding","orcid":"https://orcid.org/0000-0002-1733-6278","observed_orcids":["https://orcid.org/0000-0002-1733-6278"]},"institutions":[{"id":"https://openalex.org/I4210128757","display_name":"Corewell Health William Beaumont University Hospital","ror":"https://ror.org/03artm726","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I4210128757","https://openalex.org/I4392738273"]},{"id":"https://openalex.org/I4210161894","display_name":"Corewell Health Trenton Hospital","ror":"https://ror.org/058sakv40","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I4210161894","https://openalex.org/I4392738273"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xuanfeng Ding","raw_affiliation_strings":["Department of Radiation Oncology, Corewell Health William Beaumont University Hospital, Royal Oak, MI, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Radiation Oncology, Corewell Health William Beaumont University Hospital, Royal Oak, MI, United States","institution_ids":["https://openalex.org/I4210128757","https://openalex.org/I4210161894"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109761207","display_name":"Gang Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210129222","display_name":"Wuhan Union Hospital","ror":"https://ror.org/0371fqr87","country_code":"CN","type":"healthcare","lineage":["https://openalex.org/I4210129222"]},{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Gang Liu","raw_affiliation_strings":["Cancer Center, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, China","Hubei Key Laboratory of Precision Radiation Oncology, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Cancer Center, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, China","institution_ids":["https://openalex.org/I4210129222","https://openalex.org/I47720641"]},{"raw_affiliation_string":"Hubei Key Laboratory of Precision Radiation Oncology, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, China","institution_ids":["https://openalex.org/I4210129222","https://openalex.org/I47720641"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087271666","display_name":"Shuyang Dai","orcid":"https://orcid.org/0000-0002-2824-8521","observed_orcids":["https://orcid.org/0000-0002-2824-8521"]},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]},{"id":"https://openalex.org/I4210129222","display_name":"Wuhan Union Hospital","ror":"https://ror.org/0371fqr87","country_code":"CN","type":"healthcare","lineage":["https://openalex.org/I4210129222"]},{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shuyang Dai","raw_affiliation_strings":["Hubei Key Laboratory of Precision Radiation Oncology, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, China","School of Mathematics and Statistics, Wuhan University, Wuhan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hubei Key Laboratory of Precision Radiation Oncology, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, China","institution_ids":["https://openalex.org/I4210129222","https://openalex.org/I47720641"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Wuhan University, Wuhan, China","institution_ids":["https://openalex.org/I37461747"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5087271666","https://openalex.org/A5109761207"],"corresponding_institution_ids":["https://openalex.org/I37461747","https://openalex.org/I4210129222","https://openalex.org/I47720641"],"apc_list":{"value":3295,"currency":"USD","value_usd":3295},"apc_paid":{"value":3295,"currency":"USD","value_usd":3295},"fwci":3.1766,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.92280803,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"14","issue":null,"first_page":"1328147","last_page":"1328147"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11176","display_name":"Radiation Therapy and Dosimetry","score":0.9545999765396118,"subfield":{"id":"https://openalex.org/subfields/2740","display_name":"Pulmonary and Respiratory Medicine"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T11176","display_name":"Radiation Therapy and Dosimetry","score":0.9545999765396118,"subfield":{"id":"https://openalex.org/subfields/2740","display_name":"Pulmonary and Respiratory Medicine"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T10358","display_name":"Advanced Radiotherapy Techniques","score":0.04320000112056732,"subfield":{"id":"https://openalex.org/subfields/3108","display_name":"Radiation"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11395","display_name":"Radiopharmaceutical Chemistry and Applications","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/intensity-modulated-proton-therapy","display_name":"intensity-modulated proton therapy","score":0.968999981880188},{"id":"https://openalex.org/keywords/alternating-direction-method-of-multipliers","display_name":"alternating direction method of multipliers","score":0.9769999980926514},{"id":"https://openalex.org/keywords/nonconvex-optimization","display_name":"non-convex optimization","score":0.8539999723434448},{"id":"https://openalex.org/keywords/brain-cancer","display_name":"brain cancer","score":0.7429999709129333},{"id":"https://openalex.org/keywords/liver-cancer","display_name":"liver cancer","score":0.9980000257492065},{"id":"https://openalex.org/keywords/prostate-cancer","display_name":"prostate cancer","score":0.8539999723434448},{"id":"https://openalex.org/keywords/rectal-sparing","display_name":"rectal sparing","score":0.4169999957084656}],"concepts":[{"id":"https://openalex.org/C48925448","wikidata":"https://www.wikidata.org/wiki/Q6044344","display_name":"Intensity modulation","level":4,"score":0.5401611924171448},{"id":"https://openalex.org/C86611320","wikidata":"https://www.wikidata.org/wiki/Q1699996","display_name":"Linear energy transfer","level":3,"score":0.498859167098999},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.49577030539512634},{"id":"https://openalex.org/C93038891","wikidata":"https://www.wikidata.org/wiki/Q1061524","display_name":"Intensity (physics)","level":2,"score":0.4910469055175781},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4891360104084015},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.48774343729019165},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.47799673676490784},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.46441811323165894},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4608108699321747},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.43438538908958435},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4210493564605713},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4048589766025543},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37478578090667725},{"id":"https://openalex.org/C2989005","wikidata":"https://www.wikidata.org/wiki/Q214963","display_name":"Nuclear medicine","level":1,"score":0.33627957105636597},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23592400550842285},{"id":"https://openalex.org/C153385146","wikidata":"https://www.wikidata.org/wiki/Q18335","display_name":"Radiation","level":2,"score":0.1559128761291504},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.15374386310577393},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.15361732244491577},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.15221834182739258},{"id":"https://openalex.org/C89631360","wikidata":"https://www.wikidata.org/wiki/Q1428766","display_name":"Phase noise","level":2,"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/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0},{"id":"https://openalex.org/C96834759","wikidata":"https://www.wikidata.org/wiki/Q750463","display_name":"Phase modulation","level":3,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3389/fonc.2024.1328147","doi":"https://doi.org/10.3389/fonc.2024.1328147","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fonc.2024.1328147","pdf_url":"https://www.frontiersin.org/journals/oncology/articles/10.3389/fonc.2024.1328147/pdf","source":{"id":"https://openalex.org/S2596394214","display_name":"Frontiers in Oncology","issn_l":"2234-943X","issn":["2234-943X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Oncology","raw_type":"journal-article"},{"id":"pmh:oai:pubmedcentral.nih.gov:10932999","doi":null,"is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/10932999","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC10932999/pdf/fonc-14-1328147.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Front Oncol","raw_type":"Text"},{"id":"pmid:38482200","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/38482200","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,"listed_in":[],"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":"Frontiers in oncology","raw_type":"Journal Article"},{"id":"pmh:oai:doaj.org/article:c9fbf1d668b54c8db23b0f7df0019349","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/c9fbf1d668b54c8db23b0f7df0019349","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":"Frontiers in Oncology, Vol 14 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3389/fonc.2024.1328147","doi":"https://doi.org/10.3389/fonc.2024.1328147","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fonc.2024.1328147","pdf_url":"https://www.frontiersin.org/journals/oncology/articles/10.3389/fonc.2024.1328147/pdf","source":{"id":"https://openalex.org/S2596394214","display_name":"Frontiers in Oncology","issn_l":"2234-943X","issn":["2234-943X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Oncology","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/3","display_name":"Good health and well-being","score":0.8048999905586243}],"study_designs":[],"awards":[{"id":"https://openalex.org/G1584704688","display_name":null,"funder_award_id":"12005072","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4392236249.pdf","grobid_xml":"https://content.openalex.org/works/W4392236249.grobid-xml"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W1515726259","https://openalex.org/W1974015666","https://openalex.org/W1985075815","https://openalex.org/W2035306925","https://openalex.org/W2040145532","https://openalex.org/W2045079045","https://openalex.org/W2047890536","https://openalex.org/W2051434435","https://openalex.org/W2076605490","https://openalex.org/W2079250348","https://openalex.org/W2086479790","https://openalex.org/W2116345430","https://openalex.org/W2158918353","https://openalex.org/W2163678892","https://openalex.org/W2199020630","https://openalex.org/W2244987555","https://openalex.org/W2333432395","https://openalex.org/W2513819086","https://openalex.org/W2516454733","https://openalex.org/W2604380817","https://openalex.org/W2764174300","https://openalex.org/W2770163048","https://openalex.org/W2770989174","https://openalex.org/W2904834068","https://openalex.org/W2936183363","https://openalex.org/W2944932571","https://openalex.org/W2946000200","https://openalex.org/W3002590463","https://openalex.org/W3027372991","https://openalex.org/W3034433855","https://openalex.org/W3036401222","https://openalex.org/W3093052621","https://openalex.org/W3133818332","https://openalex.org/W3175701890","https://openalex.org/W3178514503","https://openalex.org/W3211606847","https://openalex.org/W3215869515","https://openalex.org/W4200161526","https://openalex.org/W4292363360","https://openalex.org/W4296691843","https://openalex.org/W4301014524","https://openalex.org/W4318947317","https://openalex.org/W4324295759","https://openalex.org/W4376648868"],"related_works":["https://openalex.org/W2770989174","https://openalex.org/W2513819086","https://openalex.org/W2116345430","https://openalex.org/W3036401222","https://openalex.org/W1979002387","https://openalex.org/W3034433855","https://openalex.org/W2920596991","https://openalex.org/W7164002307","https://openalex.org/W3175701890","https://openalex.org/W4387207547"],"abstract_inverted_index":{"Purpose":[0],"This":[1,220],"study":[2,221],"develop":[3],"a":[4,62,153,225],"novel":[5,35],"linear":[6],"energy":[7],"transfer":[8],"(LET)":[9],"optimization":[10,37,53,71,78,230],"method":[11,27,38],"for":[12,159,228],"intensity-modulated":[13],"proton":[14],"therapy":[15],"(IMPT)":[16],"with":[17,42,93,231],"minimum":[18],"monitor":[19],"unit":[20],"(MMU)":[21],"constraint":[22,63,234],"using":[23,128],"the":[24,44,48,52,57,70,74,77,83,87,94,110,113,129,140,160,163,169,180,183,189,201,204,210,232],"alternating":[25],"direction":[26],"of":[28,112,142,148],"multipliers":[29],"(ADMM).":[30],"Material":[31],"and":[32,47,55,86,103,118,243],"methods":[33],"The":[34,116,137],"LET":[36,49,88,119,149,165,185,206,229],"(ADMM-LET)":[39],"was":[40,66],"proposed":[41,114],"(1)":[43],"dose":[45,84,117,155],"objective":[46,50,54],"as":[51,61,224],"(2)":[56],"non-convex":[58],"MMU":[59,95,233],"threshold":[60],"condition.":[64],"ADMM":[65],"used":[67],"to":[68,108,125,176,197,216],"solve":[69],"problem.":[72],"In":[73],"ADMM-LET":[75,122,143,223],"framework,":[76],"process":[79],"entails":[80],"iteratively":[81],"solving":[82],"sub-problem":[85],"sub-problem,":[89],"simultaneously":[90],"ensuring":[91],"compliance":[92],"constraint.":[96],"Three":[97],"representative":[98],"cases,":[99],"including":[100],"brain,":[101],"liver,":[102],"prostate":[104,202],"cancer,":[105],"were":[106,123],"utilized":[107],"evaluate":[109],"performance":[111],"method.":[115,135],"distributions":[120],"from":[121,173,194,213],"compared":[124],"those":[126],"obtained":[127],"published":[130],"iterative":[131],"convex":[132],"relaxation":[133],"(ICR-LET)":[134,175,196,215],"Results":[136],"results":[138],"demonstrate":[139],"superiority":[141],"over":[144],"ICR-LET":[145],"in":[146,235,240],"terms":[147],"distribution":[150],"while":[151],"achieving":[152],"comparable":[154],"distribution.":[156],"More":[157],"specifically,":[158],"brain":[161],"case,":[162,182,203],"maximum":[164],"(unit:":[166,186,207],"keV/\u00b5m)":[167,187,208],"at":[168,188,209],"optic":[170],"nerve":[171],"decreased":[172,212],"5.45":[174],"1.97":[177],"(ADMM-LET).":[178,199,218],"For":[179,200],"liver":[181],"mean":[184,205],"clinical":[190],"target":[191],"volume":[192],"increased":[193],"4.98":[195],"5.50":[198],"rectum":[211],"2.65":[214],"2.14":[217],"Conclusion":[219],"establishes":[222],"new":[226],"approach":[227],"IMPT,":[236],"offering":[237],"potential":[238],"improvements":[239],"treatment":[241],"outcomes":[242],"biological":[244],"effects.":[245]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":2}],"updated_date":"2026-10-29T09:56:32.521200","created_date":"2024-03-05T00:00:00"}