{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:14:18Z","timestamp":1777446858237,"version":"3.51.4"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"7-8","license":[{"start":{"date-parts":[[2021,6,11]],"date-time":"2021-06-11T00:00:00Z","timestamp":1623369600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,6,11]],"date-time":"2021-06-11T00:00:00Z","timestamp":1623369600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["Grant Number 81771927"],"award-info":[{"award-number":["Grant Number 81771927"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Med Biol Eng Comput"],"published-print":{"date-parts":[[2021,8]]},"DOI":"10.1007\/s11517-021-02366-2","type":"journal-article","created":{"date-parts":[[2021,6,11]],"date-time":"2021-06-11T04:04:14Z","timestamp":1623384254000},"page":"1417-1430","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Lagrangian-averaged vorticity deviation of spiraling blood flow in the heart during isovolumic contraction and ejection phases"],"prefix":"10.1007","volume":"59","author":[{"given":"Ke","family":"Yang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shiqian","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hui","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dhanjoo N.","family":"Ghista","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Oluwarotimi W.","family":"Samuel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8600-1105","authenticated-orcid":false,"given":"Kelvin K. L.","family":"Wong","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,6,11]]},"reference":[{"issue":"1","key":"2366_CR1","doi-asserted-by":"publisher","first-page":"86","DOI":"10.1016\/j.echo.2009.09.007","volume":"23","author":"A Kheradvar","year":"2010","unstructured":"Kheradvar A, Houle H, Pedrizzetti G, Tonti G, Belcik T, Ashraf M, Lindner JR, Gharib M, Sahn D (2010) Echocardiographic particle image velocimetry: a novel technique for quantification of left ventricular blood vorticity pattern. J Am Soc Echocardiogr 23(1):86\u201394","journal-title":"J Am Soc Echocardiogr"},{"issue":"1","key":"2366_CR2","doi-asserted-by":"publisher","first-page":"8","DOI":"10.1097\/01.mat.0000249870.44625.22","volume":"53","author":"A Kheradvar","year":"2007","unstructured":"Kheradvar A, Milano M, Gharib M (2007) Correlation between vortex ring formation and mitral annulus dynamics during ventricular rapid filling. ASAIO J 53(1):8\u201316","journal-title":"ASAIO J"},{"issue":"8","key":"2366_CR3","doi-asserted-by":"publisher","first-page":"1495","DOI":"10.1007\/s10439-009-9709-y","volume":"37","author":"KKL Wong","year":"2009","unstructured":"Wong KKL, Kelso RM, Worthley SG, Sanders P, Mazumdar J, Abbott D (2009) Cardiac flow analysis applied to phase contrast magnetic resonance imaging of the heart. Ann Biomed Eng 37(8):1495\u20131515","journal-title":"Ann Biomed Eng"},{"issue":"16","key":"2366_CR4","doi-asserted-by":"publisher","first-page":"6305","DOI":"10.1073\/pnas.0600520103","volume":"103","author":"M Gharib","year":"2006","unstructured":"Gharib M, Rambod E, Kheradvar A, Sahn DJ, Dabiri JO (2006) Optimal vortex formation as an index of cardiac health. Proc Natl Acad Sci 103(16):6305\u20136308","journal-title":"Proc Natl Acad Sci"},{"issue":"2","key":"2366_CR5","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1142\/S0219519409002924","volume":"9","author":"DN Ghista","year":"2009","unstructured":"Ghista DN, Li L, Chua LP et al (2009) Mechanism of left ventricular pressure increase during isovolumic contraction, and determination of its equivalent myocardial fibers orientation. Journal Mechanics Medicine and Biology 9(2):177\u2013198","journal-title":"Journal Mechanics Medicine and Biology"},{"issue":"6","key":"2366_CR6","first-page":"59","volume":"22","author":"SC Chapra","year":"2013","unstructured":"Chapra SC (2013) Numerical methods for engineers[J]. Mcgraw-Hill Publ Comp 22(6):59\u201368","journal-title":"Mcgraw-Hill Publ Comp"},{"issue":"12","key":"2366_CR7","doi-asserted-by":"publisher","first-page":"124501","DOI":"10.1115\/1.4025385","volume":"135","author":"J Garcia","year":"2013","unstructured":"Garcia J, Larose E, Pibarot P, Kadem L (2013) On the evaluation of vorticity using cardiovascular magnetic resonance velocity measurements. J Biomech Eng 135(12):124501\u2013124506","journal-title":"J Biomech Eng"},{"issue":"10","key":"2366_CR8","doi-asserted-by":"publisher","first-page":"3598","DOI":"10.1007\/s00330-015-4186-1","volume":"26","author":"D Hirtler","year":"2016","unstructured":"Hirtler D, Garcia J, Barker AJ, Geiger J (2016) Assessment of intracardiac flow and vorticity in the right heart of patients after repair of tetralogy of Fallot by flow-sensitive 4D MRI. Eur Radiol 26(10):3598\u20133607","journal-title":"Eur Radiol"},{"issue":"9","key":"2366_CR9","doi-asserted-by":"publisher","first-page":"e0139025","DOI":"10.1371\/journal.pone.0139025","volume":"10","author":"JV Spiczak","year":"2015","unstructured":"Spiczak JV, Crelier G, Giese D, Kozerke S, Maintz D, Bunck AC (2015) Quantitative analysis of vortical blood flow in the thoracic aorta using 4D phase contrast MRI. PLoS One 10(9):e0139025","journal-title":"PLoS One"},{"issue":"1","key":"2366_CR10","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1002\/jmri.23793","volume":"37","author":"S Nordmeyer","year":"2013","unstructured":"Nordmeyer S, Riesenkampff E, Messroghli D, Kropf S, Nordmeyer J, Berger F, Kuehne T (2013) Four-dimensional velocity-encoded magnetic resonance imaging improves blood flow quantification in patients with complex accelerated flow. J Magn Reson Imaging 37(1):208\u2013216","journal-title":"J Magn Reson Imaging"},{"issue":"2","key":"2366_CR11","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1510\/icvts.2008.195859","volume":"9","author":"A Frydrychowicz","year":"2009","unstructured":"Frydrychowicz A, Berger A, Stalder AF, Markl M (2009) Preliminary results by flow-sensitive magnetic resonance imaging after Tiron David I procedure with an anatomically shaped ascending aortic graft. Interact Cardiovasc Thorac Surg 9(2):155\u2013158","journal-title":"Interact Cardiovasc Thorac Surg"},{"issue":"4","key":"2366_CR12","doi-asserted-by":"publisher","first-page":"1542","DOI":"10.1002\/mrm.24802","volume":"71","author":"R Lorenz","year":"2014","unstructured":"Lorenz R, Bock J, Barker AJ, Knobelsdorff-Brenkenhoff FV, Wallis W, Korvink JG et al (2014) 4D flow magnetic resonance imaging in bicuspid aortic valve disease demonstrates altered distribution of aortic blood flow helicity. Magn Reson Med 71(4):1542\u20131553","journal-title":"Magn Reson Med"},{"key":"2366_CR13","doi-asserted-by":"publisher","first-page":"H2764","DOI":"10.1152\/ajpheart.00540.2006","volume":"292","author":"L Zhong","year":"2007","unstructured":"Zhong L, Tan RS, Ghista DN, EYK N, Chua LP, Kassab GS (2007) Validation of a novel noninvasive cardiac index of left ventricular contractility in patients. American Journal of Physiology-Heart Circulatory Physiology 292:H2764\u2013H2772","journal-title":"American Journal of Physiology-Heart Circulatory Physiology"},{"issue":"3","key":"2366_CR14","doi-asserted-by":"publisher","first-page":"500","DOI":"10.1007\/s00348-005-0085-6","volume":"40","author":"A Etebari","year":"2006","unstructured":"Etebari A, Vlachos PP (2006) Improvements on the accuracy of derivative estimation from DPIV velocity measurements. Exp Fluids 40(3):500\u2013502","journal-title":"Exp Fluids"},{"issue":"1","key":"2366_CR15","doi-asserted-by":"publisher","first-page":"541","DOI":"10.1002\/mrm.26687","volume":"79","author":"J Sotelo","year":"2018","unstructured":"Sotelo J, Urbina J, Valverde I, Mura J, Tejos C, Irarrazaval P, Andia ME, Hurtado DE, Uribe S (2018) Three-dimensional quantification of vorticity and helicity from 3D cine PC-MRI using finite-element interpolations. Magn Reson Med 79(1):541\u2013553","journal-title":"Magn Reson Med"},{"key":"2366_CR16","unstructured":"Zienkiewicz OC, Taylor RL, Zhu JZ (2005) The finite element method: its basis and fundamentals, 6th Edition. Butterworth-Heinemann"},{"issue":"12","key":"2366_CR17","doi-asserted-by":"publisher","first-page":"2652","DOI":"10.1007\/s10439-012-0615-3","volume":"40","author":"J T\u00f6ger","year":"2012","unstructured":"T\u00f6ger J, Kanski M, Carlsson M, Kovacs SJ, S\u00f6derlind G, Arheden H et al (2012) Vortex ring formation in the left ventricle of the heart: analysis by 4D flow MRI and Lagrangian coherent structures. Ann Biomed Eng 40(12):2652\u20132662","journal-title":"Ann Biomed Eng"},{"issue":"1","key":"2366_CR18","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1186\/s12968-014-0078-9","volume":"16","author":"MSM Elbaz","year":"2014","unstructured":"Elbaz MSM, Calkoen EE, Westenberg JJM, Lelieveldt BPF, Wroest AA, Geest R (2014) Vortex flow during early and late left ventricular filling in normal subjects: quantitative characterization using retrospectively-gated 4D flow cardiovascular magnetic resonance and three-dimensional vortex core analysis. J Cardiovasc Magn Reson 16(1):78\u201390","journal-title":"J Cardiovasc Magn Reson"},{"issue":"6","key":"2366_CR19","doi-asserted-by":"publisher","first-page":"705","DOI":"10.1016\/j.jcmg.2008.06.008","volume":"1","author":"GR Hong","year":"2008","unstructured":"Hong GR, Pedrizzetti G, Tonti G, Li P, Wei Z, Kim JK, Baweja A, Liu S, Chung N, Houle H, Narula J, Vannan MA (2008) Characterization and quantification of vortex flow in the human left ventricle by contrast echocardiography using vector particle image velocimetry. J Am Coll Cardiol Img 1(6):705\u2013717","journal-title":"J Am Coll Cardiol Img"},{"key":"2366_CR20","doi-asserted-by":"publisher","first-page":"3396","DOI":"10.1002\/mrm.28361","volume":"84","author":"C Kr\u00e4uter","year":"2020","unstructured":"Kr\u00e4uter C, Reiter U, Reiter C, Nizhnikava V, Masana M, Schmidt A, Fuchsj\u00e4ger M, Stollberger R, Reiter G (2020) Automated mitral valve vortex ring extraction from 4D-flow MRI. Magn Reson Med 84:3396\u20133408","journal-title":"Magn Reson Med"},{"issue":"7","key":"2366_CR21","first-page":"136","volume":"795","author":"G Haller","year":"2015","unstructured":"Haller G, Hadjighasem A, Farazmand M, Huhn F (2015) Defining coherent vortices objectively from the vorticity. J Fluid Mech 795(7):136\u2013173","journal-title":"J Fluid Mech"},{"issue":"4","key":"2366_CR22","first-page":"380","volume":"51","author":"JE Hall","year":"2006","unstructured":"Hall JE (2006) Textbook of medical physiology. Quarterly Journal of Experimental Physiology & Cognate Medical Sciences 51(4):380\u2013381","journal-title":"Quarterly Journal of Experimental Physiology & Cognate Medical Sciences"},{"issue":"5","key":"2366_CR23","doi-asserted-by":"publisher","first-page":"1441","DOI":"10.1016\/S0735-1097(98)00379-9","volume":"32","author":"L Schmitz","year":"1998","unstructured":"Schmitz L, Koch H, Bein G, Brockmeier K (1998) Left ventricular diastolic function in infants, children, and adolescents. Reference values and analysis of morphologic and physiologic determinants of echocardiographic Doppler flow signals during growth and maturation[J]. J Am Coll Cardiol 32(5):1441\u20131448","journal-title":"J Am Coll Cardiol"},{"issue":"2","key":"2366_CR24","doi-asserted-by":"publisher","first-page":"174","DOI":"10.1016\/j.medengphy.2009.11.007","volume":"32","author":"KKL Wong","year":"2010","unstructured":"Wong KKL, Tu J, Kelso RM, Worthley SG, Sanders P, Mazumdar J, Abbott D (2010) Cardiac flow component analysis. Med Eng Phys 32(2):174\u2013188","journal-title":"Med Eng Phys"},{"issue":"3","key":"2366_CR25","first-page":"160","volume":"255","author":"M Raffel","year":"2017","unstructured":"Raffel M, Willert CE, Wereley ST, Kompenhans J (2017) Particle image velocimetry a practical guide[J]. Experimental Fluid Mechanics 255(3):160\u2013162","journal-title":"Experimental Fluid Mechanics"},{"issue":"5","key":"2366_CR26","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1016\/j.jjcc.2019.05.005","volume":"74","author":"A Kheradvar","year":"2019","unstructured":"Kheradvar A, Rickers C, Morisawa D, Kim M, Hong GR, Pedrizzetti G (2019) Diagnostic and prognostic significance of cardiovascular vortex formation. J Cardiol 74(5):403\u2013411","journal-title":"J Cardiol"},{"key":"2366_CR27","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1023\/B:ELAS.0000005548.36767.e7","volume":"71","author":"IS Liu","year":"2003","unstructured":"Liu IS (2003) On the transformation property of the deformation gradient under a change of frame. J Elast 71:73\u201380","journal-title":"J Elast"},{"key":"2366_CR28","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1016\/j.jmps.2015.10.002","volume":"86","author":"G Haller","year":"2016","unstructured":"Haller G (2016) Dynamic rotation and stretch tensors from a dynamic polar decomposition. Journal of the Mechanics & Physics of Solids 86:70\u201393","journal-title":"Journal of the Mechanics & Physics of Solids"},{"key":"2366_CR29","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1007\/s12574-016-0321-5","volume":"15","author":"R Asami","year":"2017","unstructured":"Asami R, Tanaka T, Ki K et al (2017) Accuracy and limitations of vector flow mapping: left ventricular phantom validation using stereo particle image velocimetory. J Echocardiogr 15:57\u201366","journal-title":"J Echocardiogr"},{"issue":"3","key":"2366_CR30","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1063\/1.1863284","volume":"17","author":"JZ Wu","year":"2005","unstructured":"Wu JZ, Xiong AK, Yang YT (2005) Axial stretching and vortex definition. Phys Fluids 17(3):69\u201374","journal-title":"Phys Fluids"},{"issue":"6779","key":"2366_CR31","doi-asserted-by":"publisher","first-page":"759","DOI":"10.1038\/35008075","volume":"404","author":"PJ Kilner","year":"2000","unstructured":"Kilner PJ, Yang GZ, Wilkes AJ, Mohiaddin RH, Firmin DN, Yacoub MH (2000) Asymmetric redirection of flow through the heart. Nature. 404(6779):759\u2013761","journal-title":"Nature."},{"issue":"5","key":"2366_CR32","doi-asserted-by":"publisher","first-page":"H718","DOI":"10.1152\/ajpheart.00697.2013","volume":"306","author":"J Bermejo","year":"2014","unstructured":"Bermejo J, Benito Y, Alhama M, Yotti R, Mart\u00ednez-Legazpi P, del Villar CP, P\u00e9rez-David E, Gonz\u00e1lez-Mansilla A, Santa-Marta C, Barrio A, Fern\u00e1ndez-Avil\u00e9s F, del \u00c1lamo JC (2014) Intraventricular vortex properties in nonischemic dilated cardiomyopathy. American Journal of Physiology-Heart Circulatory Physiology 306(5):H718\u2013H729","journal-title":"American Journal of Physiology-Heart Circulatory Physiology"},{"issue":"7","key":"2366_CR33","doi-asserted-by":"publisher","first-page":"723","DOI":"10.1093\/ehjci\/jev035","volume":"16","author":"M Stugaard","year":"2015","unstructured":"Stugaard M, Koriyama H, Katsuki K, Masuda K, Asanuma T, Takeda Y, Sakata Y, Itatani K, Nakatani S (2015) Energy loss in the left ventricle obtained by vector flow mapping as a new quantitative measure of severity of aortic regurgitation: a combined experimental and clinical study. Eur Heart J Cardiovasc Imaging 16(7):723\u2013730","journal-title":"Eur Heart J Cardiovasc Imaging"}],"container-title":["Medical & Biological Engineering & Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11517-021-02366-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11517-021-02366-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11517-021-02366-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,27]],"date-time":"2021-07-27T03:36:02Z","timestamp":1627356962000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11517-021-02366-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,11]]},"references-count":33,"journal-issue":{"issue":"7-8","published-print":{"date-parts":[[2021,8]]}},"alternative-id":["2366"],"URL":"https:\/\/doi.org\/10.1007\/s11517-021-02366-2","relation":{},"ISSN":["0140-0118","1741-0444"],"issn-type":[{"value":"0140-0118","type":"print"},{"value":"1741-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,11]]},"assertion":[{"value":"27 September 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 April 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 June 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}