{"id":"https://openalex.org/W4412171098","doi":"https://doi.org/10.1109/tmi.2025.3587636","title":"Flow-Rate-Constrained Physics-Informed Neural Networks for Flow Field Error Correction in 4-D Flow Magnetic Resonance Imaging","display_name":"Flow-Rate-Constrained Physics-Informed Neural Networks for Flow Field Error Correction in 4-D Flow Magnetic Resonance Imaging","publication_year":2025,"publication_date":"2025-07-10","ids":{"openalex":"https://openalex.org/W4412171098","doi":"https://doi.org/10.1109/tmi.2025.3587636","pmid":"https://pubmed.ncbi.nlm.nih.gov/40638348"},"language":"en","primary_location":{"id":"doi:10.1109/tmi.2025.3587636","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tmi.2025.3587636","pdf_url":null,"source":{"id":"https://openalex.org/S58069681","display_name":"IEEE Transactions on Medical Imaging","issn_l":"0278-0062","issn":["0278-0062","1558-254X"],"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 Medical Imaging","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/A5101314792","display_name":"Jihun Kang","orcid":"https://orcid.org/0000-0001-5455-6651"},"institutions":[{"id":"https://openalex.org/I165507594","display_name":"Kangwon National University","ror":"https://ror.org/01mh5ph17","country_code":"KR","type":"education","lineage":["https://openalex.org/I165507594"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Jihun Kang","raw_affiliation_strings":["Department of Smart Health Science and Technology, Kangwon National University, Chuncheon, Republic of Korea"],"raw_orcid":"https://orcid.org/0000-0001-5455-6651","affiliations":[{"raw_affiliation_string":"Department of Smart Health Science and Technology, Kangwon National University, Chuncheon, Republic of Korea","institution_ids":["https://openalex.org/I165507594"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065640419","display_name":"Eui Cheol Jung","orcid":null},"institutions":[{"id":"https://openalex.org/I165507594","display_name":"Kangwon National University","ror":"https://ror.org/01mh5ph17","country_code":"KR","type":"education","lineage":["https://openalex.org/I165507594"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Eui Cheol Jung","raw_affiliation_strings":["Kangwon Institute of Inclusive Technology, Kangwon National University, Chuncheon, Republic of Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Kangwon Institute of Inclusive Technology, Kangwon National University, Chuncheon, Republic of Korea","institution_ids":["https://openalex.org/I165507594"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058190632","display_name":"Hyun Jung Koo","orcid":"https://orcid.org/0000-0001-5640-3835"},"institutions":[{"id":"https://openalex.org/I116631150","display_name":"Ulsan College","ror":"https://ror.org/02tec3785","country_code":"KR","type":"education","lineage":["https://openalex.org/I116631150"]},{"id":"https://openalex.org/I2801680663","display_name":"Asan Medical Center","ror":"https://ror.org/03s5q0090","country_code":"KR","type":"healthcare","lineage":["https://openalex.org/I2801680663","https://openalex.org/I4210167194"]},{"id":"https://openalex.org/I40542001","display_name":"University of Ulsan","ror":"https://ror.org/02c2f8975","country_code":"KR","type":"education","lineage":["https://openalex.org/I40542001"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Hyun Jung Koo","raw_affiliation_strings":["Department of Radiology, Asan Medical Center, University of Ulsan College of Medicine, Seoul, Republic of Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Radiology, Asan Medical Center, University of Ulsan College of Medicine, Seoul, Republic of Korea","institution_ids":["https://openalex.org/I40542001","https://openalex.org/I2801680663","https://openalex.org/I116631150"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004642940","display_name":"Dong Hyun Yang","orcid":"https://orcid.org/0000-0001-5477-558X"},"institutions":[{"id":"https://openalex.org/I116631150","display_name":"Ulsan College","ror":"https://ror.org/02tec3785","country_code":"KR","type":"education","lineage":["https://openalex.org/I116631150"]},{"id":"https://openalex.org/I2801680663","display_name":"Asan Medical Center","ror":"https://ror.org/03s5q0090","country_code":"KR","type":"healthcare","lineage":["https://openalex.org/I2801680663","https://openalex.org/I4210167194"]},{"id":"https://openalex.org/I40542001","display_name":"University of Ulsan","ror":"https://ror.org/02c2f8975","country_code":"KR","type":"education","lineage":["https://openalex.org/I40542001"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Dong Hyun Yang","raw_affiliation_strings":["Department of Radiology, Asan Medical Center, University of Ulsan College of Medicine, Seoul, Republic of Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Radiology, Asan Medical Center, University of Ulsan College of Medicine, Seoul, Republic of Korea","institution_ids":["https://openalex.org/I40542001","https://openalex.org/I2801680663","https://openalex.org/I116631150"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085001294","display_name":"Hojin Ha","orcid":"https://orcid.org/0000-0001-6476-2889"},"institutions":[{"id":"https://openalex.org/I165507594","display_name":"Kangwon National University","ror":"https://ror.org/01mh5ph17","country_code":"KR","type":"education","lineage":["https://openalex.org/I165507594"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Hojin Ha","raw_affiliation_strings":["Department of Mechanical and Biomedical Engineering, Kangwon National University, Chuncheon, Republic of Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Biomedical Engineering, Kangwon National University, Chuncheon, Republic of Korea","institution_ids":["https://openalex.org/I165507594"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5101314792"],"corresponding_institution_ids":["https://openalex.org/I165507594"],"apc_list":null,"apc_paid":null,"fwci":2.3965,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.88934102,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"44","issue":"12","first_page":"5155","last_page":"5171"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10378","display_name":"Advanced MRI Techniques and Applications","score":0.9980000257492065,"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"}},"topics":[{"id":"https://openalex.org/T10378","display_name":"Advanced MRI Techniques and Applications","score":0.9980000257492065,"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/T10821","display_name":"Cardiovascular Function and Risk Factors","score":0.9528999924659729,"subfield":{"id":"https://openalex.org/subfields/2705","display_name":"Cardiology and Cardiovascular 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/T11778","display_name":"Electrical and Bioimpedance Tomography","score":0.951200008392334,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.6228770017623901},{"id":"https://openalex.org/keywords/magnetic-resonance-imaging","display_name":"Magnetic resonance imaging","score":0.5842435956001282},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4574086666107178},{"id":"https://openalex.org/keywords/magnetic-field","display_name":"Magnetic field","score":0.44647538661956787},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.439073383808136},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.39255398511886597},{"id":"https://openalex.org/keywords/nuclear-magnetic-resonance","display_name":"Nuclear magnetic resonance","score":0.3894578814506531},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38106435537338257},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.29055649042129517},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.24114474654197693},{"id":"https://openalex.org/keywords/radiology","display_name":"Radiology","score":0.09199324250221252},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.0916125476360321},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08821433782577515}],"concepts":[{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.6228770017623901},{"id":"https://openalex.org/C143409427","wikidata":"https://www.wikidata.org/wiki/Q161238","display_name":"Magnetic resonance imaging","level":2,"score":0.5842435956001282},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4574086666107178},{"id":"https://openalex.org/C115260700","wikidata":"https://www.wikidata.org/wiki/Q11408","display_name":"Magnetic field","level":2,"score":0.44647538661956787},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.439073383808136},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.39255398511886597},{"id":"https://openalex.org/C46141821","wikidata":"https://www.wikidata.org/wiki/Q209402","display_name":"Nuclear magnetic resonance","level":1,"score":0.3894578814506531},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38106435537338257},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.29055649042129517},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.24114474654197693},{"id":"https://openalex.org/C126838900","wikidata":"https://www.wikidata.org/wiki/Q77604","display_name":"Radiology","level":1,"score":0.09199324250221252},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0916125476360321},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08821433782577515}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D001021","descriptor_name":"Aortic Valve","qualifier_ui":"Q000000981","qualifier_name":"diagnostic imaging","is_major_topic":false},{"descriptor_ui":"D001021","descriptor_name":"Aortic Valve","qualifier_ui":"Q000000981","qualifier_name":"diagnostic imaging","is_major_topic":false},{"descriptor_ui":"D001021","descriptor_name":"Aortic Valve","qualifier_ui":"Q000000981","qualifier_name":"diagnostic imaging","is_major_topic":false},{"descriptor_ui":"D001022","descriptor_name":"Aortic Valve Insufficiency","qualifier_ui":"Q000000981","qualifier_name":"diagnostic imaging","is_major_topic":false},{"descriptor_ui":"D001022","descriptor_name":"Aortic Valve Insufficiency","qualifier_ui":"Q000000981","qualifier_name":"diagnostic imaging","is_major_topic":false},{"descriptor_ui":"D001022","descriptor_name":"Aortic Valve Insufficiency","qualifier_ui":"Q000000981","qualifier_name":"diagnostic imaging","is_major_topic":false},{"descriptor_ui":"D001022","descriptor_name":"Aortic Valve Insufficiency","qualifier_ui":"Q000503","qualifier_name":"physiopathology","is_major_topic":false},{"descriptor_ui":"D001022","descriptor_name":"Aortic Valve Insufficiency","qualifier_ui":"Q000503","qualifier_name":"physiopathology","is_major_topic":false},{"descriptor_ui":"D001022","descriptor_name":"Aortic Valve Insufficiency","qualifier_ui":"Q000503","qualifier_name":"physiopathology","is_major_topic":false},{"descriptor_ui":"D001024","descriptor_name":"Aortic Valve Stenosis","qualifier_ui":"Q000000981","qualifier_name":"diagnostic imaging","is_major_topic":false},{"descriptor_ui":"D001024","descriptor_name":"Aortic Valve Stenosis","qualifier_ui":"Q000000981","qualifier_name":"diagnostic imaging","is_major_topic":false},{"descriptor_ui":"D001024","descriptor_name":"Aortic Valve Stenosis","qualifier_ui":"Q000000981","qualifier_name":"diagnostic imaging","is_major_topic":false},{"descriptor_ui":"D001024","descriptor_name":"Aortic Valve Stenosis","qualifier_ui":"Q000503","qualifier_name":"physiopathology","is_major_topic":false},{"descriptor_ui":"D001024","descriptor_name":"Aortic Valve Stenosis","qualifier_ui":"Q000503","qualifier_name":"physiopathology","is_major_topic":false},{"descriptor_ui":"D001024","descriptor_name":"Aortic Valve Stenosis","qualifier_ui":"Q000503","qualifier_name":"physiopathology","is_major_topic":false},{"descriptor_ui":"D001783","descriptor_name":"Blood Flow Velocity","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D001783","descriptor_name":"Blood Flow Velocity","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D001783","descriptor_name":"Blood Flow Velocity","qualifier_ui":"Q000502","qualifier_name":"physiology","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":"D008279","descriptor_name":"Magnetic Resonance Imaging","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":true},{"descriptor_ui":"D008279","descriptor_name":"Magnetic Resonance Imaging","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":true},{"descriptor_ui":"D008279","descriptor_name":"Magnetic Resonance Imaging","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D019047","descriptor_name":"Phantoms, Imaging","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D019047","descriptor_name":"Phantoms, Imaging","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D019047","descriptor_name":"Phantoms, Imaging","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D021621","descriptor_name":"Imaging, Three-Dimensional","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":true},{"descriptor_ui":"D021621","descriptor_name":"Imaging, Three-Dimensional","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":true},{"descriptor_ui":"D021621","descriptor_name":"Imaging, Three-Dimensional","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":true}],"locations_count":2,"locations":[{"id":"doi:10.1109/tmi.2025.3587636","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tmi.2025.3587636","pdf_url":null,"source":{"id":"https://openalex.org/S58069681","display_name":"IEEE Transactions on Medical Imaging","issn_l":"0278-0062","issn":["0278-0062","1558-254X"],"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 Medical Imaging","raw_type":"journal-article"},{"id":"pmid:40638348","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/40638348","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 medical imaging","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2253499925","display_name":null,"funder_award_id":"RS-2023-00218630","funder_id":"https://openalex.org/F4320328359","funder_display_name":"Ministry of Science and ICT, South Korea"},{"id":"https://openalex.org/G3102109511","display_name":null,"funder_award_id":"2710086063","funder_id":"https://openalex.org/F4320328359","funder_display_name":"Ministry of Science and ICT, South Korea"},{"id":"https://openalex.org/G433077157","display_name":null,"funder_award_id":"2021R1I1A3040346","funder_id":"https://openalex.org/F4320321408","funder_display_name":"Ministry of Education"},{"id":"https://openalex.org/G5687394423","display_name":null,"funder_award_id":"RS-2024-00336999","funder_id":"https://openalex.org/F4320328359","funder_display_name":"Ministry of Science and ICT, South Korea"},{"id":"https://openalex.org/G6574769628","display_name":null,"funder_award_id":"2022R1A2C2013272","funder_id":"https://openalex.org/F4320328359","funder_display_name":"Ministry of Science and ICT, South Korea"},{"id":"https://openalex.org/G7043230835","display_name":null,"funder_award_id":"2022R1A5A1022977","funder_id":"https://openalex.org/F4320328359","funder_display_name":"Ministry of Science and ICT, South Korea"},{"id":"https://openalex.org/G7805607083","display_name":null,"funder_award_id":"2022RIS-005","funder_id":"https://openalex.org/F4320321408","funder_display_name":"Ministry of Education"}],"funders":[{"id":"https://openalex.org/F4320321408","display_name":"Ministry of Education","ror":"https://ror.org/01p262204"},{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"},{"id":"https://openalex.org/F4320328359","display_name":"Ministry of Science and ICT, South Korea","ror":"https://ror.org/01wpjm123"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1904179231","https://openalex.org/W2029158950","https://openalex.org/W2040080333","https://openalex.org/W2051125812","https://openalex.org/W2131044382","https://openalex.org/W2233399710","https://openalex.org/W2294935900","https://openalex.org/W2892722194","https://openalex.org/W2899283552","https://openalex.org/W2901420400","https://openalex.org/W2963430933","https://openalex.org/W2963677766","https://openalex.org/W3022091210","https://openalex.org/W3098546160","https://openalex.org/W3111513394","https://openalex.org/W3120927491","https://openalex.org/W3168210391","https://openalex.org/W3201253676","https://openalex.org/W3205073660","https://openalex.org/W4206116949","https://openalex.org/W4206250312","https://openalex.org/W4220937057","https://openalex.org/W4229368245","https://openalex.org/W4318316085","https://openalex.org/W4321600083","https://openalex.org/W4379801639","https://openalex.org/W4381682243","https://openalex.org/W4387211454","https://openalex.org/W4390587344","https://openalex.org/W4391616748","https://openalex.org/W4393194546","https://openalex.org/W4400679691","https://openalex.org/W4402121976","https://openalex.org/W4416249878"],"related_works":["https://openalex.org/W2257755506","https://openalex.org/W3021493803","https://openalex.org/W2011111248","https://openalex.org/W4256129901","https://openalex.org/W2002934375","https://openalex.org/W2006468016","https://openalex.org/W2912860444","https://openalex.org/W1907269663","https://openalex.org/W3151415490","https://openalex.org/W2056020138"],"abstract_inverted_index":{"In":[0],"this":[1],"study,":[2],"we":[3],"present":[4],"enhanced":[5],"physics-informed":[6],"neural":[7],"networks":[8],"(PINNs),":[9],"which":[10],"were":[11,80],"designed":[12],"to":[13,36,51,63,82],"address":[14],"flow":[15,20,42,48,103,111,128,140,155],"field":[16,28,129],"errors":[17],"in":[18,32,38,126,143,161],"four-dimensional":[19],"magnetic":[21],"resonance":[22],"imaging":[23],"(4D":[24],"Flow":[25,27],"MRI).":[26],"errors,":[29,130],"typically":[30],"occurring":[31],"high-velocity":[33,146],"regions,":[34],"lead":[35],"inaccuracies":[37],"velocity":[39],"fields":[40],"and":[41,67,76,108,118,132,145],"rate":[43,49,141],"underestimation.":[44],"We":[45],"proposed":[46,58,136],"incorporating":[47],"constraints":[50],"ensure":[52],"physical":[53],"consistency":[54],"across":[55],"cross-sections.":[56],"The":[57,88],"framework":[59],"included":[60],"optimization":[61],"strategies":[62],"improve":[64],"convergence,":[65],"stability,":[66],"accuracy.":[68],"Artificial":[69],"viscosity":[70],"modeling,":[71],"projecting":[72],"conflicting":[73],"gradients":[74],"(PCGrad),":[75],"Euclidean":[77],"norm":[78],"scaling":[79],"applied":[81],"balance":[83],"loss":[84],"functions":[85],"during":[86],"training.":[87],"performance":[89],"was":[90],"validated":[91],"using":[92],"2D":[93],"computational":[94],"fluid":[95],"dynamics":[96],"(CFD)":[97],"with":[98,115],"synthetic":[99],"error,":[100],"in-vitro":[101],"4D":[102,110,154],"MRI":[104,112,156],"mimicking":[105],"aortic":[106,116,119],"valve,":[107],"in-vivo":[109],"from":[113],"patients":[114],"regurgitation":[117],"stenosis.":[120],"This":[121,148],"study":[122],"demonstrated":[123],"considerable":[124],"improvements":[125],"correcting":[127],"denoising,":[131],"super-resolution.":[133],"Notably,":[134],"the":[135,151,162],"PINNs":[137],"provided":[138],"accurate":[139],"reconstruction":[142],"stenotic":[144],"regions.":[147],"approach":[149],"extends":[150],"applicability":[152],"of":[153],"by":[157],"providing":[158],"reliable":[159],"hemodynamics":[160],"post-processing":[163],"stage.":[164]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2025-12-06T23:10:59.065948","created_date":"2025-10-10T00:00:00"}
