{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T19:32:33Z","timestamp":1776886353818,"version":"3.51.2"},"reference-count":37,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2013,3,22]],"date-time":"2013-03-22T00:00:00Z","timestamp":1363910400000},"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":[[2013,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Fundamental mathematical relationships are widespread in biology yet there is little information on this topic with regard to human limb bone lengths and none related to human limb bone volumes. Forty\u2010six sets of ipsilateral upper and lower limb long bones and third digit short bones were imaged by computed tomography. Maximum bone lengths were measured manually and individual bone volumes calculated from <jats:styled-content style=\"fixed-case\">computed tomography<\/jats:styled-content> images using a stereologic method. Length ratios of femur\u00a0:\u00a0tibia and humerus\u00a0:\u00a0ulna were remarkably similar (1.21 and 1.22, respectively) and varied little (&lt;7%) between individuals. The volume ratio of femur\u00a0:\u00a0tibia was approximately half that of humerus\u00a0:\u00a0ulna (1.58 and 3.28, respectively; <jats:italic>P<\/jats:italic>\u00a0&lt;\u00a00.0001). Lower limb bone volume ratios varied much more than upper limb ratios. The relationship between bone length and volume was found to be well described by power laws, with R<jats:sup>2<\/jats:sup> values ranging from 0.983 to 0.995. The most striking finding was a logarithmic periodicity in bone length moving from distal to proximal up the limb (upper limb \u03bb =\u00a00.72, lower limb \u03bb\u00a0=\u00a00.93). These novel data suggest that human limb bone lengths and volumes follow fundamental and highly conserved mathematical relationships, which may contribute to our understanding of normal and disordered growth, stature estimation, and biomechanics.<\/jats:p>","DOI":"10.1111\/joa.12041","type":"journal-article","created":{"date-parts":[[2013,3,23]],"date-time":"2013-03-23T07:56:22Z","timestamp":1364025382000},"page":"526-537","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":35,"title":["Fundamental ratios and logarithmic periodicity in human limb bones"],"prefix":"10.1111","volume":"222","author":[{"given":"Alexis","family":"Pietak","sequence":"first","affiliation":[{"name":"Department of Chemical Engineering Queen's University Kingston Ontario Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Siyan","family":"Ma","sequence":"additional","affiliation":[{"name":"Department of Anatomy Otago School of Medical 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