{"id":"https://openalex.org/W2077234559","doi":"https://doi.org/10.1007/s10288-008-0083-7","title":"Mathematical optimization in intensity modulated radiation therapy","display_name":"Mathematical optimization in intensity modulated radiation therapy","publication_year":2008,"publication_date":"2008-08-14","ids":{"openalex":"https://openalex.org/W2077234559","doi":"https://doi.org/10.1007/s10288-008-0083-7","mag":"2077234559"},"language":"en","primary_location":{"id":"doi:10.1007/s10288-008-0083-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10288-008-0083-7","pdf_url":null,"source":{"id":"https://openalex.org/S4210191715","display_name":"4OR","issn_l":"1614-2411","issn":["1614-2411","1619-4500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"4OR","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"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/A5019869178","display_name":"Matthias Ehrgott","orcid":"https://orcid.org/0000-0003-4648-4066"},"institutions":[{"id":"https://openalex.org/I154130895","display_name":"University of Auckland","ror":"https://ror.org/03b94tp07","country_code":"NZ","type":"education","lineage":["https://openalex.org/I154130895"]}],"countries":["NZ"],"is_corresponding":true,"raw_author_name":"Matthias Ehrgott","raw_affiliation_strings":["Department of Engineering Science, The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand","Department of Engineering Science; The University of Auckland; Auckland New Zealand"],"affiliations":[{"raw_affiliation_string":"Department of Engineering Science, The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand","institution_ids":["https://openalex.org/I154130895"]},{"raw_affiliation_string":"Department of Engineering Science; The University of Auckland; Auckland New Zealand","institution_ids":["https://openalex.org/I154130895"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076667327","display_name":"\u00c7i\u011fdem G\u00fcler","orcid":null},"institutions":[{"id":"https://openalex.org/I153267046","display_name":"University of Kaiserslautern","ror":"https://ror.org/04zrf7b53","country_code":"DE","type":"education","lineage":["https://openalex.org/I153267046"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"\u00c7i\u011fdem G\u00fcler","raw_affiliation_strings":["Department of Mathematics, Technical University of Kaiserslautern, Postfach 3049, 67653, Kaiserslautern, Germany","Department of Mathematics, Technical University of Kaiserslautern, Kaiserslautern, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Technical University of Kaiserslautern, Postfach 3049, 67653, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I153267046"]},{"raw_affiliation_string":"Department of Mathematics, Technical University of Kaiserslautern, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I153267046"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111683448","display_name":"Horst W. Hamacher","orcid":null},"institutions":[{"id":"https://openalex.org/I153267046","display_name":"University of Kaiserslautern","ror":"https://ror.org/04zrf7b53","country_code":"DE","type":"education","lineage":["https://openalex.org/I153267046"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Horst W. Hamacher","raw_affiliation_strings":["Department of Mathematics, Technical University of Kaiserslautern, Postfach 3049, 67653, Kaiserslautern, Germany","Department of Mathematics, Technical University of Kaiserslautern, Kaiserslautern, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Technical University of Kaiserslautern, Postfach 3049, 67653, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I153267046"]},{"raw_affiliation_string":"Department of Mathematics, Technical University of Kaiserslautern, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I153267046"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063710454","display_name":"Lizhen Shao","orcid":"https://orcid.org/0000-0002-5605-5540"},"institutions":[{"id":"https://openalex.org/I154130895","display_name":"University of Auckland","ror":"https://ror.org/03b94tp07","country_code":"NZ","type":"education","lineage":["https://openalex.org/I154130895"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"Lizhen Shao","raw_affiliation_strings":["Department of Engineering Science, The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand","Department of Engineering Science; The University of Auckland; Auckland New Zealand"],"affiliations":[{"raw_affiliation_string":"Department of Engineering Science, The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand","institution_ids":["https://openalex.org/I154130895"]},{"raw_affiliation_string":"Department of Engineering Science; The University of Auckland; Auckland New Zealand","institution_ids":["https://openalex.org/I154130895"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5019869178"],"corresponding_institution_ids":["https://openalex.org/I154130895"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":9.4423,"has_fulltext":false,"cited_by_count":74,"citation_normalized_percentile":{"value":0.98212956,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"6","issue":"3","first_page":"199","last_page":"262"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10358","display_name":"Advanced Radiotherapy Techniques","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10358","display_name":"Advanced Radiotherapy Techniques","score":1.0,"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/T10522","display_name":"Medical Imaging Techniques and Applications","score":0.9994000196456909,"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"}},{"id":"https://openalex.org/T11176","display_name":"Radiation Therapy and Dosimetry","score":0.9965000152587891,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/multileaf-collimator","display_name":"Multileaf collimator","score":0.9267375469207764},{"id":"https://openalex.org/keywords/intensity","display_name":"Intensity (physics)","score":0.6033508777618408},{"id":"https://openalex.org/keywords/radiation-therapy","display_name":"Radiation therapy","score":0.5525868535041809},{"id":"https://openalex.org/keywords/intensity-modulation","display_name":"Intensity modulation","score":0.5439706444740295},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48170071840286255},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4805234372615814},{"id":"https://openalex.org/keywords/collimator","display_name":"Collimator","score":0.4715844690799713},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.45434945821762085},{"id":"https://openalex.org/keywords/medical-physics","display_name":"Medical physics","score":0.4406629502773285},{"id":"https://openalex.org/keywords/beam","display_name":"Beam (structure)","score":0.41982632875442505},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3484381437301636},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.343711256980896},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.314769446849823},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.26245513558387756},{"id":"https://openalex.org/keywords/linear-particle-accelerator","display_name":"Linear particle accelerator","score":0.23932403326034546},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.1302262842655182},{"id":"https://openalex.org/keywords/surgery","display_name":"Surgery","score":0.07648515701293945}],"concepts":[{"id":"https://openalex.org/C161471255","wikidata":"https://www.wikidata.org/wiki/Q374703","display_name":"Multileaf collimator","level":4,"score":0.9267375469207764},{"id":"https://openalex.org/C93038891","wikidata":"https://www.wikidata.org/wiki/Q1061524","display_name":"Intensity (physics)","level":2,"score":0.6033508777618408},{"id":"https://openalex.org/C509974204","wikidata":"https://www.wikidata.org/wiki/Q180507","display_name":"Radiation therapy","level":2,"score":0.5525868535041809},{"id":"https://openalex.org/C48925448","wikidata":"https://www.wikidata.org/wiki/Q6044344","display_name":"Intensity modulation","level":4,"score":0.5439706444740295},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48170071840286255},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4805234372615814},{"id":"https://openalex.org/C2779200277","wikidata":"https://www.wikidata.org/wiki/Q1164658","display_name":"Collimator","level":2,"score":0.4715844690799713},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.45434945821762085},{"id":"https://openalex.org/C19527891","wikidata":"https://www.wikidata.org/wiki/Q1120908","display_name":"Medical physics","level":1,"score":0.4406629502773285},{"id":"https://openalex.org/C168834538","wikidata":"https://www.wikidata.org/wiki/Q3705329","display_name":"Beam (structure)","level":2,"score":0.41982632875442505},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3484381437301636},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.343711256980896},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.314769446849823},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26245513558387756},{"id":"https://openalex.org/C180048950","wikidata":"https://www.wikidata.org/wiki/Q836828","display_name":"Linear particle accelerator","level":3,"score":0.23932403326034546},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.1302262842655182},{"id":"https://openalex.org/C141071460","wikidata":"https://www.wikidata.org/wiki/Q40821","display_name":"Surgery","level":1,"score":0.07648515701293945},{"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/C96834759","wikidata":"https://www.wikidata.org/wiki/Q750463","display_name":"Phase modulation","level":3,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10288-008-0083-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10288-008-0083-7","pdf_url":null,"source":{"id":"https://openalex.org/S4210191715","display_name":"4OR","issn_l":"1614-2411","issn":["1614-2411","1619-4500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"4OR","raw_type":"journal-article"},{"id":"pmh:oai:eprints.lancs.ac.uk:64477","is_oa":false,"landing_page_url":"https://eprints.lancs.ac.uk/id/eprint/64477/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401916","display_name":"Lancaster EPrints (Lancaster University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67415387","host_organization_name":"Lancaster University","host_organization_lineage":["https://openalex.org/I67415387"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},{"id":"pmh:oai:eprints.lancs.ac.uk:64490","is_oa":false,"landing_page_url":"https://eprints.lancs.ac.uk/id/eprint/64490/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401916","display_name":"Lancaster EPrints (Lancaster University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67415387","host_organization_name":"Lancaster University","host_organization_lineage":["https://openalex.org/I67415387"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5899999737739563,"display_name":"Good health and well-being","id":"https://metadata.un.org/sdg/3"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":217,"referenced_works":["https://openalex.org/W6587533","https://openalex.org/W26314658","https://openalex.org/W251973404","https://openalex.org/W579818984","https://openalex.org/W1502046716","https://openalex.org/W1508107180","https://openalex.org/W1509786428","https://openalex.org/W1514662726","https://openalex.org/W1542127549","https://openalex.org/W1579007511","https://openalex.org/W1580646826","https://openalex.org/W1605578879","https://openalex.org/W1634005169","https://openalex.org/W1643954602","https://openalex.org/W1692778824","https://openalex.org/W1931244053","https://openalex.org/W1965550810","https://openalex.org/W1968143413","https://openalex.org/W1970077290","https://openalex.org/W1972808802","https://openalex.org/W1973702460","https://openalex.org/W1974856723","https://openalex.org/W1974908209","https://openalex.org/W1975292370","https://openalex.org/W1976996553","https://openalex.org/W1977221038","https://openalex.org/W1977545325","https://openalex.org/W1978230327","https://openalex.org/W1979184234","https://openalex.org/W1979396664","https://openalex.org/W1979800170","https://openalex.org/W1980956836","https://openalex.org/W1981065559","https://openalex.org/W1981188846","https://openalex.org/W1981464637","https://openalex.org/W1982203567","https://openalex.org/W1983273276","https://openalex.org/W1983843138","https://openalex.org/W1984280574","https://openalex.org/W1984418711","https://openalex.org/W1986933969","https://openalex.org/W1987006437","https://openalex.org/W1988402330","https://openalex.org/W1989008336","https://openalex.org/W1989099434","https://openalex.org/W1989791750","https://openalex.org/W1990130410","https://openalex.org/W1993438515","https://openalex.org/W1993985030","https://openalex.org/W1994221325","https://openalex.org/W1994444070","https://openalex.org/W1994566350","https://openalex.org/W1994644214","https://openalex.org/W1995131613","https://openalex.org/W1997632213","https://openalex.org/W1997842792","https://openalex.org/W1999916457","https://openalex.org/W2000645326","https://openalex.org/W2000676139","https://openalex.org/W2002409241","https://openalex.org/W2003071413","https://openalex.org/W2003354876","https://openalex.org/W2003585211","https://openalex.org/W2003745243","https://openalex.org/W2004793341","https://openalex.org/W2005105648","https://openalex.org/W2006762993","https://openalex.org/W2007449041","https://openalex.org/W2008519159","https://openalex.org/W2009096120","https://openalex.org/W2009379024","https://openalex.org/W2012141640","https://openalex.org/W2012351471","https://openalex.org/W2013219706","https://openalex.org/W2014158133","https://openalex.org/W2014438224","https://openalex.org/W2014535770","https://openalex.org/W2014775907","https://openalex.org/W2015392725","https://openalex.org/W2016323057","https://openalex.org/W2016480273","https://openalex.org/W2017244914","https://openalex.org/W2018514387","https://openalex.org/W2019001529","https://openalex.org/W2020254445","https://openalex.org/W2020474603","https://openalex.org/W2020946584","https://openalex.org/W2021047551","https://openalex.org/W2021131581","https://openalex.org/W2021347862","https://openalex.org/W2021482893","https://openalex.org/W2021658156","https://openalex.org/W2023492967","https://openalex.org/W2023531597","https://openalex.org/W2023748272","https://openalex.org/W2024008934","https://openalex.org/W2024347398","https://openalex.org/W2024777608","https://openalex.org/W2025258805","https://openalex.org/W2025464654","https://openalex.org/W2026095777","https://openalex.org/W2026510342","https://openalex.org/W2026947157","https://openalex.org/W2027444611","https://openalex.org/W2027948342","https://openalex.org/W2030295088","https://openalex.org/W2030863085","https://openalex.org/W2030993720","https://openalex.org/W2031044433","https://openalex.org/W2031186981","https://openalex.org/W2033492551","https://openalex.org/W2033806488","https://openalex.org/W2034976475","https://openalex.org/W2035111930","https://openalex.org/W2035932435","https://openalex.org/W2036975954","https://openalex.org/W2037824130","https://openalex.org/W2038265790","https://openalex.org/W2039424107","https://openalex.org/W2039710897","https://openalex.org/W2042443501","https://openalex.org/W2042642264","https://openalex.org/W2042975860","https://openalex.org/W2045223228","https://openalex.org/W2047319364","https://openalex.org/W2047588216","https://openalex.org/W2048227807","https://openalex.org/W2048555863","https://openalex.org/W2048727728","https://openalex.org/W2048905028","https://openalex.org/W2049181072","https://openalex.org/W2051237659","https://openalex.org/W2051314721","https://openalex.org/W2051434435","https://openalex.org/W2052221858","https://openalex.org/W2052387204","https://openalex.org/W2053240146","https://openalex.org/W2055955846","https://openalex.org/W2056801524","https://openalex.org/W2057126596","https://openalex.org/W2057309390","https://openalex.org/W2058186945","https://openalex.org/W2058192020","https://openalex.org/W2058610100","https://openalex.org/W2059621826","https://openalex.org/W2059732509","https://openalex.org/W2060105069","https://openalex.org/W2061630310","https://openalex.org/W2064005465","https://openalex.org/W2068706967","https://openalex.org/W2072478167","https://openalex.org/W2072620509","https://openalex.org/W2072723582","https://openalex.org/W2073826786","https://openalex.org/W2074021186","https://openalex.org/W2076310535","https://openalex.org/W2076432449","https://openalex.org/W2077037649","https://openalex.org/W2078569105","https://openalex.org/W2079124778","https://openalex.org/W2082455082","https://openalex.org/W2084991719","https://openalex.org/W2087205557","https://openalex.org/W2087859424","https://openalex.org/W2087937209","https://openalex.org/W2088703618","https://openalex.org/W2090610803","https://openalex.org/W2091985880","https://openalex.org/W2094955118","https://openalex.org/W2097512974","https://openalex.org/W2099042561","https://openalex.org/W2105284680","https://openalex.org/W2106018384","https://openalex.org/W2109037291","https://openalex.org/W2112094702","https://openalex.org/W2112918543","https://openalex.org/W2114708145","https://openalex.org/W2117801253","https://openalex.org/W2121693217","https://openalex.org/W2123893434","https://openalex.org/W2124775306","https://openalex.org/W2130289671","https://openalex.org/W2133388491","https://openalex.org/W2134393828","https://openalex.org/W2137150870","https://openalex.org/W2138599283","https://openalex.org/W2139127699","https://openalex.org/W2139899608","https://openalex.org/W2141478197","https://openalex.org/W2141983610","https://openalex.org/W2145804736","https://openalex.org/W2146875819","https://openalex.org/W2147544224","https://openalex.org/W2150593711","https://openalex.org/W2155417411","https://openalex.org/W2157771622","https://openalex.org/W2159285492","https://openalex.org/W2161660704","https://openalex.org/W2163241124","https://openalex.org/W2163646186","https://openalex.org/W2163776180","https://openalex.org/W2166010438","https://openalex.org/W2169315729","https://openalex.org/W2321466613","https://openalex.org/W2329546601","https://openalex.org/W2329579984","https://openalex.org/W2426754948","https://openalex.org/W2592227283","https://openalex.org/W2615258659","https://openalex.org/W2615797034","https://openalex.org/W2904973296","https://openalex.org/W2947966541","https://openalex.org/W3103396062","https://openalex.org/W4232414536","https://openalex.org/W4233534941","https://openalex.org/W4254913749","https://openalex.org/W4302557773"],"related_works":["https://openalex.org/W2427616200","https://openalex.org/W2021347862","https://openalex.org/W64132664","https://openalex.org/W2003071413","https://openalex.org/W2030442960","https://openalex.org/W2068380426","https://openalex.org/W2072263098","https://openalex.org/W1973615940","https://openalex.org/W2070631904","https://openalex.org/W2149503133"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
