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This study quantifies the cross-sectional association between three-dimensional carotid bifurcation geometry and pro-atherogenic flow and identifies anatomical biomarkers for non-invasive risk stratification.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Methods<\/jats:title>\n                    <jats:p>Geometric analyses included 346 carotid bifurcations, comprising 240 stenosed and 106 non-stenosed bifurcations. Patient-specific CFD was performed in 176 bifurcations: 101 stenosed and 75 non-stenosed. Eight geometric descriptors, including a new offset flow divider capturing bifurcation apex asymmetry, and four ICA bulb hemodynamic indices (TAWSS, OSI, RRT, BFI) were extracted; logistic and linear regression assessed the association of geometry with (i) stenosis presence and (ii) pro-atherogenic flow.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>\n                      Bifurcation angle, ICA angle, tortuosity, and offset flow divider were significantly elevated in stenosed bifurcations (all\n                      <jats:inline-formula>\n                        <jats:alternatives>\n                          <jats:tex-math>$$p&lt;0.001$$<\/jats:tex-math>\n                          <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                            <mml:mrow>\n                              <mml:mi>p<\/mml:mi>\n                              <mml:mo>&lt;<\/mml:mo>\n                              <mml:mn>0.001<\/mml:mn>\n                            <\/mml:mrow>\n                          <\/mml:math>\n                        <\/jats:alternatives>\n                      <\/jats:inline-formula>\n                      ); a four-feature geometric model showed moderate discrimination between stenosed and non-stenosed bifurcations (cross-validated\n                      <jats:inline-formula>\n                        <jats:alternatives>\n                          <jats:tex-math>$$\\textrm{AUROC}=0.767$$<\/jats:tex-math>\n                          <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                            <mml:mrow>\n                              <mml:mtext>AUROC<\/mml:mtext>\n                              <mml:mo>=<\/mml:mo>\n                              <mml:mn>0.767<\/mml:mn>\n                            <\/mml:mrow>\n                          <\/mml:math>\n                        <\/jats:alternatives>\n                      <\/jats:inline-formula>\n                      ). The post-stenotic expansion ratio was more strongly associated with local flow disturbance than the degree of luminal narrowing. In non-stenosed bifurcations, multivariable geometric models explained 49 to\n                      <jats:inline-formula>\n                        <jats:alternatives>\n                          <jats:tex-math>$$60\\%$$<\/jats:tex-math>\n                          <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                            <mml:mrow>\n                              <mml:mn>60<\/mml:mn>\n                              <mml:mo>%<\/mml:mo>\n                            <\/mml:mrow>\n                          <\/mml:math>\n                        <\/jats:alternatives>\n                      <\/jats:inline-formula>\n                      of the variance in the flow-normalized low-TAWSS, elevated-OSI, and elevated-RRT outcomes, with bulb area and area ratio providing the largest independent contributions, indicating that geometric variation is strongly associated with candidate pro-atherogenic flow patterns even in the absence of detectable luminal narrowing.\n                    <\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusions<\/jats:title>\n                    <jats:p>Carotid geometry carries two complementary signals: markers of disease presence (bifurcation angle, ICA angle) and candidate anatomical substrates of pro-atherogenic flow in still-non-stenosed bifurcations (bulb area, area ratio). Together with the post-stenotic expansion ratio, these geometric features define a compact, image-derivable set of candidate biomarkers for future early carotid risk stratification.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1007\/s10439-026-04417-x","type":"journal-article","created":{"date-parts":[[2026,10,19]],"date-time":"2026-10-19T19:44:06Z","timestamp":1792439046000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Hemodynamic and Geometrical Parameters Associated with Carotid Artery Stenosis: A Cross-Sectional Study Using 4D Flow MRI and CFD"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-8864-6988","authenticated-orcid":false,"given":"Ali","family":"Mokhtari","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ariel","family":"Bergmann","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christoph","family":"Strecker","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jonathan","family":"Andrae","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andreas","family":"Harloff","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dominik","family":"Obrist","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,10,19]]},"reference":[{"key":"4417_CR1","first-page":"e28","volume":"129.3","author":"AS Go","year":"2014","unstructured":"Go, A. 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Eng.\u00a038(8):e3630, 2022.","journal-title":"International Journal for Numerical Methods in Biomedical Engineering"}],"container-title":["Annals of Biomedical Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10439-026-04417-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10439-026-04417-x","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10439-026-04417-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,19]],"date-time":"2026-10-19T19:44:09Z","timestamp":1792439049000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10439-026-04417-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10,19]]},"references-count":48,"alternative-id":["4417"],"URL":"https:\/\/doi.org\/10.1007\/s10439-026-04417-x","relation":{},"ISSN":["0090-6964","1573-9686"],"issn-type":[{"value":"0090-6964","type":"print"},{"value":"1573-9686","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,10,19]]},"assertion":[{"value":"18 May 2026","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 October 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 October 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare that they have no relevant financial or non-financial conflict of interest to disclose.","order":1,"name":"Ethics","label":"Conflict of interest","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The original imaging studies from which the carotid 4D flow MRI dataset was derived were approved by the Ethics Committee of the University of Freiburg, Germany and written informed consent was obtained from all participants. The work was performed in accordance with the Declaration of Helsinki. The present manuscript reports a secondary, retrospective analysis of fully anonymized data drawn from those original studies.","order":2,"name":"Ethics","label":"Ethical approval","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable, as no individual person\u2019s data are included in this manuscript.","order":3,"name":"Ethics","label":"Consent for Publication","group":{"name":"EthicsHeading","label":"Declarations"}}]}}