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Previously, we proposed a flow complexity parameter that provides a quantitative description of the complexity of flow patterns through calculated curvature and torsion of the flow field. The purpose of the current study was to provide an analytic solution of the flow complexity parameter and assess a possible correlation with the rupture status of cerebral aneurysms by analyzing the parameter on five ruptured and five unruptured aneurysms from anterior communicating artery. We analyzed the flow complexity parameter in jet and non\u2010jet regions in order to measure the concentration of the jet flow and the complexity of the non\u2010jet flow. We found that on average, in a ruptured case the jet region is significantly less complex (4.5 times) than the jet region in an unruptured case, while the non\u2010jet region is significantly more complex (3.5 times) than the non\u2010jet region in an unruptured case. We also found a strong positive correlation of the non\u2010jet complexity with dome volume in ruptured cases, but no correlation of jet complexity with dome volume. These findings suggest that a ruptured aneurysm has more than 4 times more concentrated inflow jet and more than 3 times more complex flow patterns in non\u2010jet region than an unruptured aneurysm. This newly implemented kinematic parameter provides a measurable degree of complexity of flow patterns in cerebral aneurysms that can better assess aneurysm rupture risk.<\/jats:p>","DOI":"10.1002\/cnm.3131","type":"journal-article","created":{"date-parts":[[2018,7,19]],"date-time":"2018-07-19T07:57:02Z","timestamp":1531987022000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Correlation of flow complexity parameter with aneurysm rupture status"],"prefix":"10.1002","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1309-9981","authenticated-orcid":false,"given":"Simona","family":"Hodis","sequence":"first","affiliation":[{"name":"Department of Mathematics Texas A&amp;M University\u2014Kingsville  Kingsville Texas"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2018,8,9]]},"reference":[{"key":"e_1_2_7_2_1","first-page":"2550","article-title":"Characterization of cerebral aneurysms for assessing risk of rupture by using patient\u2010specific computational hemodynamics models","volume":"26","author":"Cebral J","year":"2005","journal-title":"Am J Neuroradiol"},{"key":"e_1_2_7_3_1","doi-asserted-by":"publisher","DOI":"10.3174\/ajnr.A2274"},{"key":"e_1_2_7_4_1","doi-asserted-by":"publisher","DOI":"10.1161\/01.STR.0000144648.89172.0f"},{"key":"e_1_2_7_5_1","doi-asserted-by":"publisher","DOI":"10.3174\/ajnr.A3678"},{"key":"e_1_2_7_6_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2015.2467203"},{"key":"e_1_2_7_7_1","doi-asserted-by":"publisher","DOI":"10.1080\/10255842.2013.869322"},{"key":"e_1_2_7_8_1","doi-asserted-by":"publisher","DOI":"10.1063\/1.1706426"},{"key":"e_1_2_7_9_1","doi-asserted-by":"publisher","DOI":"10.1136\/neurintsurg-2014-011182"},{"key":"e_1_2_7_10_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112069000991"},{"key":"e_1_2_7_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jbiomech.2006.02.017"},{"key":"e_1_2_7_12_1","doi-asserted-by":"crossref","unstructured":"BiswasA ThompsonD HeW et al.An uncertainty\u2010driven approach to vortex analysis using oracle consensus and spatial proximity. 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