{"id":"https://openalex.org/W2610895895","doi":"https://doi.org/10.3390/e19050209","title":"Ensemble Averages, Soliton Dynamics and Influence of Haptotaxis in a Model of Tumor-Induced Angiogenesis","display_name":"Ensemble Averages, Soliton Dynamics and Influence of Haptotaxis in a Model of Tumor-Induced Angiogenesis","publication_year":2017,"publication_date":"2017-05-04","ids":{"openalex":"https://openalex.org/W2610895895","doi":"https://doi.org/10.3390/e19050209","mag":"2610895895"},"language":"en","primary_location":{"id":"doi:10.3390/e19050209","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e19050209","pdf_url":"https://www.mdpi.com/1099-4300/19/5/209/pdf?version=1493900614","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/19/5/209/pdf?version=1493900614","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051606797","display_name":"L. L. Bonilla","orcid":"https://orcid.org/0000-0002-7687-8595"},"institutions":[{"id":"https://openalex.org/I50357001","display_name":"Universidad Carlos III de Madrid","ror":"https://ror.org/03ths8210","country_code":"ES","type":"education","lineage":["https://openalex.org/I50357001"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Luis Bonilla","raw_affiliation_strings":["Department of Materials Science and Engineering, G. Mill\u00e1n Institute for Fluid Dynamics, Nanoscience, and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Legan\u00e9s, Spain"],"raw_orcid":"https://orcid.org/0000-0002-7687-8595","affiliations":[{"raw_affiliation_string":"Department of Materials Science and Engineering, G. Mill\u00e1n Institute for Fluid Dynamics, Nanoscience, and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Legan\u00e9s, Spain","institution_ids":["https://openalex.org/I50357001"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080788620","display_name":"Manuel Carretero","orcid":"https://orcid.org/0000-0002-3517-4241"},"institutions":[{"id":"https://openalex.org/I50357001","display_name":"Universidad Carlos III de Madrid","ror":"https://ror.org/03ths8210","country_code":"ES","type":"education","lineage":["https://openalex.org/I50357001"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Manuel Carretero","raw_affiliation_strings":["Department of Materials Science and Engineering, G. Mill\u00e1n Institute for Fluid Dynamics, Nanoscience, and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Legan\u00e9s, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Materials Science and Engineering, G. Mill\u00e1n Institute for Fluid Dynamics, Nanoscience, and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Legan\u00e9s, Spain","institution_ids":["https://openalex.org/I50357001"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067996209","display_name":"Filippo Terragni","orcid":"https://orcid.org/0000-0002-6113-0824"},"institutions":[{"id":"https://openalex.org/I50357001","display_name":"Universidad Carlos III de Madrid","ror":"https://ror.org/03ths8210","country_code":"ES","type":"education","lineage":["https://openalex.org/I50357001"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Filippo Terragni","raw_affiliation_strings":["Department of Materials Science and Engineering, G. Mill\u00e1n Institute for Fluid Dynamics, Nanoscience, and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Legan\u00e9s, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Materials Science and Engineering, G. Mill\u00e1n Institute for Fluid Dynamics, Nanoscience, and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Legan\u00e9s, Spain","institution_ids":["https://openalex.org/I50357001"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5051606797"],"corresponding_institution_ids":["https://openalex.org/I50357001"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.7884,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.70051943,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"19","issue":"5","first_page":"209","last_page":"209"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9998999834060669,"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":0.9998999834060669,"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/T10422","display_name":"Angiogenesis and VEGF in Cancer","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10379","display_name":"Cellular Mechanics and Interactions","score":0.9846000075340271,"subfield":{"id":"https://openalex.org/subfields/1307","display_name":"Cell Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/angiogenesis","display_name":"Angiogenesis","score":0.6924718022346497},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.5188707113265991},{"id":"https://openalex.org/keywords/soliton","display_name":"Soliton","score":0.49042245745658875},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4893597960472107},{"id":"https://openalex.org/keywords/chemotaxis","display_name":"Chemotaxis","score":0.45923101902008057},{"id":"https://openalex.org/keywords/extracellular-matrix","display_name":"Extracellular matrix","score":0.45465612411499023},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.4244348108768463},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.414310485124588},{"id":"https://openalex.org/keywords/biological-system","display_name":"Biological system","score":0.3237583339214325},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.25213974714279175},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.23517045378684998},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.16475069522857666},{"id":"https://openalex.org/keywords/cell-biology","display_name":"Cell biology","score":0.11097133159637451},{"id":"https://openalex.org/keywords/cancer-research","display_name":"Cancer research","score":0.08958464860916138}],"concepts":[{"id":"https://openalex.org/C2780394083","wikidata":"https://www.wikidata.org/wiki/Q539568","display_name":"Angiogenesis","level":2,"score":0.6924718022346497},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.5188707113265991},{"id":"https://openalex.org/C87651913","wikidata":"https://www.wikidata.org/wiki/Q464949","display_name":"Soliton","level":3,"score":0.49042245745658875},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4893597960472107},{"id":"https://openalex.org/C54166955","wikidata":"https://www.wikidata.org/wiki/Q658145","display_name":"Chemotaxis","level":3,"score":0.45923101902008057},{"id":"https://openalex.org/C189165786","wikidata":"https://www.wikidata.org/wiki/Q193825","display_name":"Extracellular matrix","level":2,"score":0.45465612411499023},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.4244348108768463},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.414310485124588},{"id":"https://openalex.org/C186060115","wikidata":"https://www.wikidata.org/wiki/Q30336093","display_name":"Biological system","level":1,"score":0.3237583339214325},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.25213974714279175},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.23517045378684998},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.16475069522857666},{"id":"https://openalex.org/C95444343","wikidata":"https://www.wikidata.org/wiki/Q7141","display_name":"Cell biology","level":1,"score":0.11097133159637451},{"id":"https://openalex.org/C502942594","wikidata":"https://www.wikidata.org/wiki/Q3421914","display_name":"Cancer research","level":1,"score":0.08958464860916138},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C170493617","wikidata":"https://www.wikidata.org/wiki/Q208467","display_name":"Receptor","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e19050209","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e19050209","pdf_url":"https://www.mdpi.com/1099-4300/19/5/209/pdf?version=1493900614","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:a2cc7cb488734e1b907c68115577d694","is_oa":true,"landing_page_url":"https://doaj.org/article/a2cc7cb488734e1b907c68115577d694","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,"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":"Entropy, Vol 19, Iss 5, p 209 (2017)","raw_type":"article"},{"id":"pmh:oai:e-archivo.uc3m.es:10016/27872","is_oa":true,"landing_page_url":"http://hdl.handle.net/10016/27872","pdf_url":null,"source":{"id":"https://openalex.org/S4306400817","display_name":"e-Archivo (Carlos III University of Madrid)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I50357001","host_organization_name":"Universidad Carlos III de Madrid","host_organization_lineage":["https://openalex.org/I50357001"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"research article"},{"id":"pmh:oai:mdpi.com:/1099-4300/19/5/209/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e19050209","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy; Volume 19; Issue 5; Pages: 209","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e19050209","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e19050209","pdf_url":"https://www.mdpi.com/1099-4300/19/5/209/pdf?version=1493900614","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6348767563","display_name":null,"funder_award_id":"C2-2-P","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G6917588612","display_name":null,"funder_award_id":"MTM2014-56948-C2-2-P","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G8383522679","display_name":null,"funder_award_id":"-C2-2-P","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"}],"funders":[{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2610895895.pdf","grobid_xml":"https://content.openalex.org/works/W2610895895.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W1412973526","https://openalex.org/W1965949654","https://openalex.org/W1972161075","https://openalex.org/W1973546194","https://openalex.org/W1976904080","https://openalex.org/W1978139448","https://openalex.org/W2000315161","https://openalex.org/W2018589752","https://openalex.org/W2034600723","https://openalex.org/W2044979535","https://openalex.org/W2048195900","https://openalex.org/W2063722569","https://openalex.org/W2064701790","https://openalex.org/W2068072750","https://openalex.org/W2102113729","https://openalex.org/W2122913894","https://openalex.org/W2132985539","https://openalex.org/W2144026946","https://openalex.org/W2150853563","https://openalex.org/W2161590805","https://openalex.org/W2164878073","https://openalex.org/W2279134460","https://openalex.org/W2286871334","https://openalex.org/W2419218429","https://openalex.org/W2519393355","https://openalex.org/W2561725266","https://openalex.org/W2568293135"],"related_works":["https://openalex.org/W1596865785","https://openalex.org/W2085357479","https://openalex.org/W2417007386","https://openalex.org/W1993973863","https://openalex.org/W2388783242","https://openalex.org/W1135436615","https://openalex.org/W2975251372","https://openalex.org/W2313472050","https://openalex.org/W2102113319","https://openalex.org/W4379383422"],"abstract_inverted_index":{"In":[0],"this":[1,74],"work,":[2],"we":[3],"present":[4],"a":[5,100,119,157],"numerical":[6,149],"study":[7,158],"of":[8,11,22,55,70,87,95,106,109,113,137,142,151,159],"the":[9,20,50,62,71,107,128,134,140,143,152,160],"influence":[10],"matrix":[12,64],"degrading":[13],"enzyme":[14],"(MDE)":[15],"dynamics":[16],"and":[17,58,85,155],"haptotaxis":[18,59,138],"on":[19,139],"development":[21],"vessel":[23,114,145],"networks":[24],"in":[25,73,104],"tumor-induced":[26],"angiogenesis.":[27],"Avascular":[28],"tumors":[29],"produce":[30],"growth":[31,56],"factors":[32],"that":[33],"induce":[34],"nearby":[35],"blood":[36,66],"vessels":[37],"to":[38,61,90],"emit":[39],"sprouts":[40,47],"formed":[41],"by":[42,52,79,127,147,156],"endothelial":[43],"cells.":[44],"These":[45],"capillary":[46],"advance":[48,141],"toward":[49],"tumor":[51],"chemotaxis":[53],"(gradients":[54],"factor)":[57],"(adhesion":[60],"tissue":[63],"outside":[65],"vessels).":[67],"The":[68,116],"motion":[69,124],"capillaries":[72],"constrained":[75],"space":[76],"is":[77,99,125],"modelled":[78],"stochastic":[80,153],"processes":[81],"(Langevin":[82],"equations,":[83],"branching":[84],"merging":[86],"sprouts)":[88],"coupled":[89],"continuum":[91],"equations":[92],"for":[93],"concentrations":[94],"involved":[96],"substances.":[97],"There":[98],"complementary":[101],"deterministic":[102],"description":[103],"terms":[105],"density":[108],"actively":[110],"moving":[111],"tips":[112],"sprouts.":[115],"latter":[117],"forms":[118],"stable":[120],"soliton-like":[121],"wave":[122],"whose":[123],"influenced":[126],"different":[129],"taxis":[130],"mechanisms.":[131],"We":[132],"show":[133],"delaying":[135],"effect":[136],"angiogenic":[144],"network":[146],"direct":[148],"simulations":[150],"process":[154],"soliton":[161],"motion.":[162]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2017-05-12T00:00:00"}
