{"id":"https://openalex.org/W2057022062","doi":"https://doi.org/10.1109/tbme.2012.2197680","title":"A Minimal Model of Tumor Growth Inhibition in Combination Regimens Under the Hypothesis of No Interaction Between Drugs","display_name":"A Minimal Model of Tumor Growth Inhibition in Combination Regimens Under the Hypothesis of No Interaction Between Drugs","publication_year":2012,"publication_date":"2012-07-13","ids":{"openalex":"https://openalex.org/W2057022062","doi":"https://doi.org/10.1109/tbme.2012.2197680","mag":"2057022062","pmid":"https://pubmed.ncbi.nlm.nih.gov/22575633"},"language":"en","primary_location":{"id":"doi:10.1109/tbme.2012.2197680","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tbme.2012.2197680","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/A5081448028","display_name":"Paolo Magni","orcid":"https://orcid.org/0000-0002-8931-4676"},"institutions":[{"id":"https://openalex.org/I25217355","display_name":"University of Pavia","ror":"https://ror.org/00s6t1f81","country_code":"IT","type":"education","lineage":["https://openalex.org/I25217355"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"P. Magni","raw_affiliation_strings":["Dipartimento di Ingegneria Industriale edell'Informazione, Universita degli Studi di Pavia, Pavia, Italy. paolo.magni@unipv.it","Dipt. di Ing. Ind. e dell'Inf., Univ. degli Studi di Pavia, Pavia, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria Industriale edell'Informazione, Universita degli Studi di Pavia, Pavia, Italy. paolo.magni@unipv.it","institution_ids":["https://openalex.org/I25217355"]},{"raw_affiliation_string":"Dipt. di Ing. Ind. e dell'Inf., Univ. degli Studi di Pavia, Pavia, Italy","institution_ids":["https://openalex.org/I25217355"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067125095","display_name":"Nadia Terranova","orcid":"https://orcid.org/0000-0002-0033-3695"},"institutions":[{"id":"https://openalex.org/I25217355","display_name":"University of Pavia","ror":"https://ror.org/00s6t1f81","country_code":"IT","type":"education","lineage":["https://openalex.org/I25217355"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"N. Terranova","raw_affiliation_strings":["Dipartimento di Ingegneria Industriale e dellInformazione, Universit\u00e0 degli Studi di Pavia, Pavia, Italy","Dipt. di Ing. Ind. e dell'Inf., Univ. degli Studi di Pavia, Pavia, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria Industriale e dellInformazione, Universit\u00e0 degli Studi di Pavia, Pavia, Italy","institution_ids":["https://openalex.org/I25217355"]},{"raw_affiliation_string":"Dipt. di Ing. Ind. e dell'Inf., Univ. degli Studi di Pavia, Pavia, Italy","institution_ids":["https://openalex.org/I25217355"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087395773","display_name":"Filippo Del Bene","orcid":"https://orcid.org/0000-0001-8551-2846"},"institutions":[{"id":"https://openalex.org/I4210127540","display_name":"Nerviano Medical Sciences","ror":"https://ror.org/038mzt421","country_code":"IT","type":"company","lineage":["https://openalex.org/I4210127540"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"F. Del Bene","raw_affiliation_strings":["Accelera Srl, Italy","Accelera Srl, Nerviano, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Accelera Srl, Italy","institution_ids":[]},{"raw_affiliation_string":"Accelera Srl, Nerviano, Italy","institution_ids":["https://openalex.org/I4210127540"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039445562","display_name":"Massimiliano Germani","orcid":"https://orcid.org/0000-0001-8286-9954"},"institutions":[{"id":"https://openalex.org/I4210127540","display_name":"Nerviano Medical Sciences","ror":"https://ror.org/038mzt421","country_code":"IT","type":"company","lineage":["https://openalex.org/I4210127540"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"M. Germani","raw_affiliation_strings":["Accelera Srl, Italy","Accelera Srl, Nerviano, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Accelera Srl, Italy","institution_ids":[]},{"raw_affiliation_string":"Accelera Srl, Nerviano, Italy","institution_ids":["https://openalex.org/I4210127540"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017270452","display_name":"Giuseppe De Nicolao","orcid":"https://orcid.org/0000-0002-3712-9911"},"institutions":[{"id":"https://openalex.org/I25217355","display_name":"University of Pavia","ror":"https://ror.org/00s6t1f81","country_code":"IT","type":"education","lineage":["https://openalex.org/I25217355"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"G. De Nicolao","raw_affiliation_strings":["Dipartimento di Ingegneria Industriale e dellInformazione, Universit\u00e0 degli Studi di Pavia, Pavia, Italy","Dipt. di Ing. Ind. e dell'Inf., Univ. degli Studi di Pavia, Pavia, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria Industriale e dellInformazione, Universit\u00e0 degli Studi di Pavia, Pavia, Italy","institution_ids":["https://openalex.org/I25217355"]},{"raw_affiliation_string":"Dipt. di Ing. Ind. e dell'Inf., Univ. degli Studi di Pavia, Pavia, Italy","institution_ids":["https://openalex.org/I25217355"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5158,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.64718615,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"59","issue":"8","first_page":"2161","last_page":"2170"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9998000264167786,"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":0.9998000264167786,"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/T11016","display_name":"Monoclonal and Polyclonal Antibodies Research","score":0.9973999857902527,"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/T10211","display_name":"Computational Drug Discovery Methods","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6140403747558594},{"id":"https://openalex.org/keywords/drug","display_name":"Drug","score":0.5156470537185669},{"id":"https://openalex.org/keywords/drug-administration","display_name":"Drug administration","score":0.47410067915916443},{"id":"https://openalex.org/keywords/pharmacology","display_name":"Pharmacology","score":0.46727263927459717},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.4389491379261017},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34957242012023926},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.3482653796672821},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3360607624053955},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.27598851919174194}],"concepts":[{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6140403747558594},{"id":"https://openalex.org/C2780035454","wikidata":"https://www.wikidata.org/wiki/Q8386","display_name":"Drug","level":2,"score":0.5156470537185669},{"id":"https://openalex.org/C2987276129","wikidata":"https://www.wikidata.org/wiki/Q12140","display_name":"Drug administration","level":2,"score":0.47410067915916443},{"id":"https://openalex.org/C98274493","wikidata":"https://www.wikidata.org/wiki/Q128406","display_name":"Pharmacology","level":1,"score":0.46727263927459717},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4389491379261017},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34957242012023926},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.3482653796672821},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3360607624053955},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.27598851919174194},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D000818","descriptor_name":"Animals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000818","descriptor_name":"Animals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000818","descriptor_name":"Animals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000970","descriptor_name":"Antineoplastic Agents","qualifier_ui":"Q000494","qualifier_name":"pharmacology","is_major_topic":false},{"descriptor_ui":"D000970","descriptor_name":"Antineoplastic Agents","qualifier_ui":"Q000494","qualifier_name":"pharmacology","is_major_topic":false},{"descriptor_ui":"D000970","descriptor_name":"Antineoplastic Agents","qualifier_ui":"Q000494","qualifier_name":"pharmacology","is_major_topic":false},{"descriptor_ui":"D004347","descriptor_name":"Drug Interactions","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D004347","descriptor_name":"Drug Interactions","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D004347","descriptor_name":"Drug Interactions","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":"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":true},{"descriptor_ui":"D008954","descriptor_name":"Models, Biological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008954","descriptor_name":"Models, Biological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D009374","descriptor_name":"Neoplasms, Experimental","qualifier_ui":"Q000188","qualifier_name":"drug therapy","is_major_topic":false},{"descriptor_ui":"D009374","descriptor_name":"Neoplasms, Experimental","qualifier_ui":"Q000188","qualifier_name":"drug therapy","is_major_topic":false},{"descriptor_ui":"D009374","descriptor_name":"Neoplasms, Experimental","qualifier_ui":"Q000188","qualifier_name":"drug therapy","is_major_topic":false},{"descriptor_ui":"D009374","descriptor_name":"Neoplasms, Experimental","qualifier_ui":"Q000473","qualifier_name":"pathology","is_major_topic":false},{"descriptor_ui":"D009374","descriptor_name":"Neoplasms, Experimental","qualifier_ui":"Q000473","qualifier_name":"pathology","is_major_topic":false},{"descriptor_ui":"D009374","descriptor_name":"Neoplasms, Experimental","qualifier_ui":"Q000473","qualifier_name":"pathology","is_major_topic":false},{"descriptor_ui":"D023041","descriptor_name":"Xenograft Model Antitumor Assays","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D023041","descriptor_name":"Xenograft Model Antitumor Assays","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D023041","descriptor_name":"Xenograft Model Antitumor Assays","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D045744","descriptor_name":"Cell Line, Tumor","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D045744","descriptor_name":"Cell Line, Tumor","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D045744","descriptor_name":"Cell Line, Tumor","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D051379","descriptor_name":"Mice","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D051379","descriptor_name":"Mice","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D051379","descriptor_name":"Mice","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D055808","descriptor_name":"Drug Discovery","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D055808","descriptor_name":"Drug Discovery","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D055808","descriptor_name":"Drug Discovery","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false}],"locations_count":2,"locations":[{"id":"doi:10.1109/tbme.2012.2197680","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tbme.2012.2197680","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:22575633","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/22575633","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}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Good health and well-being","score":0.8500000238418579,"id":"https://metadata.un.org/sdg/3"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320322874","display_name":"Universit\u00e0 degli Studi di Pavia","ror":"https://ror.org/00s6t1f81"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1969763365","https://openalex.org/W1972699120","https://openalex.org/W1981904850","https://openalex.org/W1984913351","https://openalex.org/W1991829344","https://openalex.org/W2019895529","https://openalex.org/W2060737851","https://openalex.org/W2074642772","https://openalex.org/W2104119864","https://openalex.org/W2105510646","https://openalex.org/W2111264921","https://openalex.org/W2128943895","https://openalex.org/W2158733752","https://openalex.org/W2161559302","https://openalex.org/W2223501982","https://openalex.org/W2409392632","https://openalex.org/W6675813461"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2352495365","https://openalex.org/W4251067554","https://openalex.org/W2069998960","https://openalex.org/W2033571057","https://openalex.org/W2320266418","https://openalex.org/W3199476259","https://openalex.org/W2397868246","https://openalex.org/W4231040959"],"abstract_inverted_index":{"One":[0],"important":[1],"issue":[2],"in":[3,21,31,84],"the":[4,12,15,62,87,106,139,151,162,176,180,190,193,200],"preclinical":[5],"development":[6],"of":[7,14,52,90,108,126,154,164,192,203],"an":[8,165],"anticancer":[9],"drug":[10,56,141],"is":[11,101,120,147,159],"assessment":[13],"compound":[16],"under":[17,113],"investigation":[18],"when":[19],"administered":[20],"combination":[22,116],"with":[23],"other":[24],"drugs.":[25,205],"Several":[26],"experiments":[27,57],"are":[28,43],"routinely":[29],"conducted":[30],"xenograft":[32],"mice":[33],"to":[34,61,71,77,103,183,199],"evaluate":[35],"if":[36],"drugs":[37,110],"interact":[38],"or":[39],"not.":[40],"Experimental":[41],"data":[42],"generally":[44],"qualitatively":[45],"analyzed":[46],"on":[47,175],"empirical":[48],"basis.":[49],"The":[50,118,143],"ability":[51],"deriving":[53],"from":[54,122],"single":[55,99,140],"a":[58,98,123,184],"reference":[59],"response":[60],"joint":[63],"administrations,":[64],"assuming":[65],"no":[66],"interaction,":[67],"and":[68,80,111,131,167],"comparing":[69],"it":[70],"real":[72],"responses":[73],"would":[74],"be":[75],"key":[76],"recognize":[78],"synergic":[79],"antagonist":[81],"compounds.":[82],"Therefore,":[83],"this":[85,114],"paper,":[86],"minimal":[88,124],"model":[89,119,181,187,198],"tumor":[91,144],"growth":[92,145],"inhibition":[93],"(TGI),":[94],"previously":[95],"developed":[96],"for":[97,105,138],"drug,":[100],"reformulated":[102],"account":[104],"effects":[107],"noninteracting":[109,204],"simulate,":[112],"hypothesis,":[115],"regimens.":[117],"derived":[121],"set":[125],"basic":[127],"assumptions":[128,174],"that":[129,158,188],"include":[130],"extend":[132],"those":[133],"formulated":[134],"at":[135],"cellular":[136],"level":[137],"administration.":[142],"dynamics":[146],"well":[148],"approximated":[149],"by":[150],"deterministic":[152],"evolution":[153],"its":[155],"expected":[156],"value":[157],"obtained":[160],"through":[161],"solution":[163],"ordinary":[166],"several":[168],"partial":[169],"differential":[170],"equations.":[171],"Under":[172],"suitable":[173],"cell":[177],"death":[178],"process,":[179],"reduces":[182],"lumped":[185],"parameter":[186],"represents":[189],"extension":[191],"very":[194],"popular":[195],"Simeoni":[196],"TGI":[197],"combined":[201],"administration":[202]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-01-13T01:12:25.745995","created_date":"2025-10-10T00:00:00"}