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This study developed and validated a three-dimensional multimodal fractal dynamic model (FRAC-3D) that integrates spatial metabolism, cytoarchitecture, and blood perfusion, aiming to non-invasively identify MVI status preoperatively and evaluate patient prognosis.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Methods<\/jats:title>\n                    <jats:p>\n                      Utilizing a retrospective nested cohort design, stabilized inverse probability of treatment weighting (sIPTW) was applied to the derivation cohort (\n                      <jats:italic>n<\/jats:italic>\n                      \u2009=\u2009100) for baseline debiasing. A core cohort of 145 patients with complete PET\/CT, CE-MRI, and DWI imaging was ultimately included. Spatial metabolic fractal dimension (FD_PET), architectural fractal dimension (FD_ADC), and perfusion fractal acceleration (Afd_MRI) were extracted to construct the FRAC-3D model. The model\u2019s discrimination, calibration, and clinical benefit were validated in an independent temporal validation cohort (\n                      <jats:italic>n<\/jats:italic>\n                      \u2009=\u200945).\n                    <\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>\n                      Multivariable analysis confirmed that FD_ADC is the strongest independent predictor of MVI (OR\u2009=\u20093.85, 95% CI: 2.45\u20136.04,\n                      <jats:italic>P<\/jats:italic>\n                      \u2009&lt;\u20090.001). The FRAC-3D model achieved an AUC of 0.938 and a negative predictive value of 96.2% in the validation cohort. Compared with the dual-modal model, FRAC-3D significantly improved risk restratification (continuous NRI\u2009=\u20090.425,\n                      <jats:italic>P<\/jats:italic>\n                      \u2009&lt;\u20090.001). A \u201chighly chaotic\u201d imaging phenotype, identified based on fractal feature clustering, demonstrated an MVI incidence as high as 96.7% and a median recurrence-free survival (RFS) of only 5.2 months.\n                    <\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusion<\/jats:title>\n                    <jats:p>Through the cross-validation of multidimensional biophysical features, the FRAC-3D model enables high-precision preoperative prediction of MVI status. This study advances the perioperative assessment of CRLM from traditional \u2018static anatomical metrics\u2019 into a novel dimension of \u2018microenvironmental dynamic evolution\u2019, providing a robust, physics-driven tool for individualized surgical margin planning and the precise stratification of targeted neoadjuvant therapy.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1186\/s12967-026-08712-y","type":"journal-article","created":{"date-parts":[[2026,7,27]],"date-time":"2026-07-27T09:33:52Z","timestamp":1785144832000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Three-dimensional multimodal fractal dynamics integrating spatial metabolism, cytoarchitecture, and perfusion for preoperative prediction of microvascular invasion in colorectal liver metastases"],"prefix":"10.1186","volume":"24","author":[{"given":"Ziyi","family":"Guo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9389-731X","authenticated-orcid":false,"given":"Chao","family":"Guo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhengran","family":"Lu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kailin","family":"Zou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongnan","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,7,27]]},"reference":[{"issue":"12","key":"8712_CR1","doi-asserted-by":"publisher","first-page":"1208","DOI":"10.1016\/S1470-2045(13)70447-9","volume":"14","author":"B Nordlinger","year":"2013","unstructured":"Nordlinger B, Sorbye H, Glimelius B, Poston GJ, Schlag PM, Rougier P, et al. 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