{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,3]],"date-time":"2026-08-03T04:09:15Z","timestamp":1785730155868,"version":"3.56.0"},"reference-count":47,"publisher":"Wiley","issue":"9","license":[{"start":{"date-parts":[[2021,7,27]],"date-time":"2021-07-27T00:00:00Z","timestamp":1627344000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["aapm.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Medical Physics"],"published-print":{"date-parts":[[2021,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:sec><jats:title>Purpose<\/jats:title><jats:p>The aim of this paper is to propose a fracture model for human ribs based on acoustic emission (AE) data. The accumulation of microcracking until a macroscopic crack is produced can be monitored by AE. The macrocrack propagation causes the loss of the structural integrity of the rib.<\/jats:p><\/jats:sec><jats:sec><jats:title>Methods<\/jats:title><jats:p>The AE technique was used in in vitro bending tests of human ribs. The AE data obtained were used to construct a quantitative model that allows an estimation of the failure stress from the signals detected. The model predicts the ultimate stress with an error of less than 3.5% (even at stresses 15% lower than failure stress), which makes it possible to safely anticipate the failure of the rib.<\/jats:p><\/jats:sec><jats:sec><jats:title>Results<\/jats:title><jats:p>The percolation theory was used to model crack propagation. Moreover, a quantitative probability\u2010based model for the expected number of AE signals has been constructed, incorporating some ideas of percolation theory. The model predicts that AE signals associated with micro\u2010failures should exhibit a vertical asymptote when stress increases. The occurrence of this vertical asymptote was attested in our experimental observations. The total number of microfailures detected prior to the failure is <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp15082-math-0001.png\" xlink:title=\"urn:x-wiley:00942405:media:mp15082:mp15082-math-0001\"\/> and the ultimate stress is <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp15082-math-0002.png\" xlink:title=\"urn:x-wiley:00942405:media:mp15082:mp15082-math-0002\"\/> MPa. A significant correlation (<jats:italic>p<\/jats:italic>\u00a0&lt;\u00a00.0001) between <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp15082-math-0003.png\" xlink:title=\"urn:x-wiley:00942405:media:mp15082:mp15082-math-0003\"\/> and the predicted value is found, using only the first <jats:italic>N<\/jats:italic>\u00a0=\u00a030\u00a0micro\u2010failures (correlation improves for <jats:italic>N<\/jats:italic> higher).<\/jats:p><\/jats:sec><jats:sec><jats:title>Conclusions<\/jats:title><jats:p>The measurements and the shape of the curves predicted by the model fit well. In addition, the model parameters seem to explain quantitatively and qualitatively the distribution of the AE signals as the material approaches the macroscopic fracture. Moreover, some of these parameters correlate with anthropometric variables, such as age or Body Mass Index. The proposed model could be used to predict the structural failure of ribs subjected to bending.<\/jats:p><\/jats:sec>","DOI":"10.1002\/mp.15082","type":"journal-article","created":{"date-parts":[[2021,7,10]],"date-time":"2021-07-10T08:16:59Z","timestamp":1625905019000},"page":"5540-5548","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["A predictive model for fracture in human ribs based on in vitro acoustic emission data"],"prefix":"10.1002","volume":"48","author":[{"given":"Silvia","family":"Garc\u00eda\u2010Vilana","sequence":"first","affiliation":[{"name":"UPC RMEE\u2010GRABI Barcelona Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David","family":"S\u00e1nchez\u2010Molina","sequence":"additional","affiliation":[{"name":"UPC RMEE\u2010GRABI Barcelona 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