{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T09:25:01Z","timestamp":1790760301227,"version":"4.1.0"},"reference-count":64,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2019,11,11]],"date-time":"2019-11-11T00:00:00Z","timestamp":1573430400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Anatomy"],"published-print":{"date-parts":[[2020,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Blood flow rate (<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/joa13119-math-0002.png\" xlink:title=\"urn:x-wiley:00218782:media:joa13119:joa13119-math-0002\"\/>) in relation to arterial lumen radius (<jats:italic>r<jats:sub>i<\/jats:sub><\/jats:italic>) is commonly modelled according to theoretical equations and paradigms, including Murray\u2019s Law (<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/joa13119-math-0003.png\" xlink:title=\"urn:x-wiley:00218782:media:joa13119:joa13119-math-0003\"\/> \u221d <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/joa13119-math-0004.png\" xlink:title=\"urn:x-wiley:00218782:media:joa13119:joa13119-math-0004\"\/>) and da Vinci\u2019s Rule (<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/joa13119-math-0005.png\" xlink:title=\"urn:x-wiley:00218782:media:joa13119:joa13119-math-0005\"\/> \u221d <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/joa13119-math-0006.png\" xlink:title=\"urn:x-wiley:00218782:media:joa13119:joa13119-math-0006\"\/>). Wall shear stress (<jats:italic>\u03c4<\/jats:italic>) is independent of <jats:italic>r<jats:sub>i<\/jats:sub><\/jats:italic> with Murray\u2019s Law (<jats:italic>\u03c4<\/jats:italic>\u00a0\u221d\u00a0<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/joa13119-math-0007.png\" xlink:title=\"urn:x-wiley:00218782:media:joa13119:joa13119-math-0007\"\/>) and decreases with da Vinci\u2019s Rule (<jats:italic>\u03c4<\/jats:italic>\u00a0\u221d\u00a0<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/joa13119-math-0008.png\" xlink:title=\"urn:x-wiley:00218782:media:joa13119:joa13119-math-0008\"\/>). These paradigms are tested empirically with a meta\u2010analysis of the relationships between <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/joa13119-math-0009.png\" xlink:title=\"urn:x-wiley:00218782:media:joa13119:joa13119-math-0009\"\/> and <jats:italic>r<jats:sub>i<\/jats:sub><\/jats:italic> in seven major arteries of the human cephalic circulation from 19 imaging studies in which both variables were presented. The analysis shows that <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/joa13119-math-0010.png\" xlink:title=\"urn:x-wiley:00218782:media:joa13119:joa13119-math-0010\"\/> \u221d <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/joa13119-math-0011.png\" xlink:title=\"urn:x-wiley:00218782:media:joa13119:joa13119-math-0011\"\/> and <jats:italic>\u03c4<\/jats:italic>\u00a0\u221d\u00a0<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/joa13119-math-0012.png\" xlink:title=\"urn:x-wiley:00218782:media:joa13119:joa13119-math-0012\"\/>, more consistent with da Vinci\u2019s Rule than Murray\u2019s Law. This meta\u2010analysis provides standard values for <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/joa13119-math-0013.png\" xlink:title=\"urn:x-wiley:00218782:media:joa13119:joa13119-math-0013\"\/>, <jats:italic>r<jats:sub>i<\/jats:sub><\/jats:italic> and <jats:italic>\u03c4<\/jats:italic> in the human cephalic arteries that may be a useful baseline in future investigations. On average, the paired internal carotid arteries supply 75%, and the vertebral arteries supply 25%, of total brain blood flow. The internal carotid arteries contribute blood entirely to the anterior and middle cerebral arteries and also partly to the posterior cerebral arteries via the posterior communicating arteries of the circle of Willis. On average, the internal carotid arteries provide 88% of the blood flow to the cerebrum and the vertebral arteries only 12%.<\/jats:p>","DOI":"10.1111\/joa.13119","type":"journal-article","created":{"date-parts":[[2019,11,11]],"date-time":"2019-11-11T14:34:44Z","timestamp":1573482884000},"page":"522-530","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Blood flow rate and wall shear stress in seven major cephalic arteries of humans"],"prefix":"10.1111","volume":"236","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3395-0059","authenticated-orcid":false,"given":"Roger S.","family":"Seymour","sequence":"first","affiliation":[{"name":"School of Biological Sciences Faculty of Sciences University of Adelaide Adelaide SA 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