{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T18:13:12Z","timestamp":1783015992050,"version":"3.54.6"},"reference-count":12,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2019,10,31]],"date-time":"2019-10-31T00:00:00Z","timestamp":1572480000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,10,31]],"date-time":"2019-10-31T00:00:00Z","timestamp":1572480000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["SN COMPUT. SCI."],"published-print":{"date-parts":[[2020,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n<jats:p>A thorough knowledge of statistical properties of the coronary artery tree is very important in cardiology. We present generalised form of Murray\u2019s law\u2014the first law that described the relationship between vessel diameters in bifurcation. We show that other frequently used laws: Huo-Kassab and Finet\u2019s rules are the special cases of its generalised form. We show theoretically that the Finet\u2019s law is met with an apparently paradoxical relationship between the lengths and diameters of the vessels. Based on the analysis of CT 3D scans, we show that in the left coronary artery the diameters and lengths of vessels are inversely proportional which explains the applicability of the Finet\u2019s law. We justify theoretically the value of coefficient defining Finet\u2019s law.<\/jats:p>","DOI":"10.1007\/s42979-019-0040-x","type":"journal-article","created":{"date-parts":[[2019,10,31]],"date-time":"2019-10-31T03:03:07Z","timestamp":1572490987000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Finet\u2019s Law as a Special Case of the Generalised Murray\u2019s Law"],"prefix":"10.1007","volume":"1","author":[{"given":"Jakub","family":"Zieli\u0144ski","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J\u0119drzej M.","family":"Nowosielski","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2019,10,31]]},"reference":[{"issue":"3","key":"40_CR1","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1073\/pnas.12.3.207","volume":"12","author":"CD Murray","year":"1926","unstructured":"Murray CD. The physiological principle of minimum work: I. The vascular system and the cost of blood volume. Proc Natl Acad Sci USA. 1926;12(3):207\u201314.","journal-title":"Proc Natl Acad Sci USA."},{"key":"40_CR2","doi-asserted-by":"publisher","first-page":"939","DOI":"10.1038\/nature01444","volume":"421","author":"KA McCulloh","year":"2003","unstructured":"McCulloh KA, Sperry JS, Adler FR. Water transport in plants obeys Murray\u2019s law. Nature. 2003;421:939\u201342.","journal-title":"Nature"},{"key":"40_CR3","doi-asserted-by":"publisher","first-page":"490","DOI":"10.4244\/EIJV3I4A87","volume":"3","author":"G Finet","year":"2008","unstructured":"Finet G, Gilard M, Perrenot B, Rioufol G, Motreff P, Gavit L, Prost R. Fractal geometry of arterial coronary bifurcations: a quantitative coronary angiography and intravascular ultrasound analysis. EuroIntervention. 2008;3:490\u20138.","journal-title":"EuroIntervention."},{"key":"40_CR4","first-page":"232","volume":"86","author":"JT Dodge Jr","year":"1992","unstructured":"Dodge JT Jr, Brown BG, Bolson EL, Dodge HT. Lumen diameter of normal human coronary arteries. Influ Age Sex Anat Var Left Ventricular Hypertrophy Circ. 1992;86:232\u201346.","journal-title":"Influ Age Sex Anat Var Left Ventricular Hypertrophy Circ."},{"key":"40_CR5","doi-asserted-by":"publisher","first-page":"845","DOI":"10.4244\/EIJV12I7A139","volume":"12","author":"P Medrano-Gracia","year":"2016","unstructured":"Medrano-Gracia P, Ormiston J, Webster M, Beier S, Young A, Ellis C, Wang C, Smedby O, Cowan B. A computational atlas of normal coronary artery anatomy. EuroIntervention. 2016;12:845\u201354.","journal-title":"EuroIntervention."},{"key":"40_CR6","doi-asserted-by":"publisher","first-page":"1244","DOI":"10.1002\/ccd.26247","volume":"87","author":"L Ellwein","year":"2016","unstructured":"Ellwein L, Marks DS, Migrino RQ, Foley WD, Sherman S, LaDisa JF Jr. Image-based quantification of 3D morphology for bifurcations in left coronary artery: Application to stent design. Catheter Cardiovasc Interv. 2016;87:1244\u201355.","journal-title":"Catheter Cardiovasc Interv."},{"key":"40_CR7","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1002\/clc.4960150613","volume":"15","author":"BF Waller","year":"1992","unstructured":"Waller BF, Orr CM, Slack JD, Pinkerton CA, Van Tassel J, Peters T. Anatomy, histology, and pathology of coronary arteries: a review relevant to new interventional and imaging techniques-Part I. Clin Cardiol. 1992;15:451\u20137.","journal-title":"Clin Cardiol."},{"key":"40_CR8","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1186\/1742-4682-3-31","volume":"3","author":"PR Painter","year":"2006","unstructured":"Painter PR, Ed\u00e9n P, Bengtsson H-U. Research Pulsatile blood flow, shear force, energy dissipation and Murray\u2019s Law. Theor. Biol Med Model. 2006;3:31.","journal-title":"Theor. Biol Med Model."},{"issue":"2","key":"40_CR9","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1016\/j.bpj.2008.09.039","volume":"96","author":"Y Huo","year":"2009","unstructured":"Huo Y, Kassab GS. A scaling law of vascular volume. Biophys J. 2009;96(2):347\u201353.","journal-title":"Biophys J."},{"key":"40_CR10","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1186\/1742-4682-6-7","volume":"6","author":"R Revellin","year":"2009","unstructured":"Revellin R, Rousset F, Baud D, Bonjour J. Extension of Murray\u2019s law using a non-Newtonian model of blood flow. Theor Biol Med Model Res. 2009;6:7.","journal-title":"Theor Biol Med Model Res."},{"key":"40_CR11","unstructured":"Hagmeijer R, Venner CH, Critical review of Murray\u2019s theory for optimal branching in fluidic networks., \narXiv.org\/abs\/1812.09706\n\n (submitted on 23 Dec 2018)"},{"issue":"Part A","key":"40_CR12","first-page":"51","volume":"19(7)","author":"G Rigatelli","year":"2018","unstructured":"Rigatelli G, Zuin M, Ronco F, Caprioglio F, Cavazzini D, Giatti S, Braggion G, Perilli S, Nguyen VT. Usefulness of the Finet law to guide stent size selection in ostial left main stenting: Comparison with standard angiographic estimation. Cardiovasc Revascularization Med. 2018;19(7)(Part A):51\u2013754.","journal-title":"Cardiovasc Revascularization Med."}],"container-title":["SN Computer Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s42979-019-0040-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s42979-019-0040-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s42979-019-0040-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,30]],"date-time":"2020-10-30T01:37:21Z","timestamp":1604021841000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s42979-019-0040-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,31]]},"references-count":12,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,1]]}},"alternative-id":["40"],"URL":"https:\/\/doi.org\/10.1007\/s42979-019-0040-x","relation":{},"ISSN":["2662-995X","2661-8907"],"issn-type":[{"value":"2662-995X","type":"print"},{"value":"2661-8907","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,10,31]]},"assertion":[{"value":"22 July 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 September 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 October 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"42"}}