Three-dimensional multimodal fractal dynamics integrating spatial metabolism, cytoarchitecture, and perfusion for preoperative prediction of microvascular invasion in colorectal liver metastases

Background Accurately predicting microvascular invasion (MVI) preoperatively remains a core challenge for precision surgical decision-making in patients with colorectal liver metastases (CRLM). 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. Methods Utilizing a retrospective nested cohort design, stabilized inverse probability of treatment weighting (sIPTW) was applied to the derivation cohort ( n = 100) 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’s discrimination, calibration, and clinical benefit were validated in an independent temporal validation cohort ( n = 45). Results Multivariable analysis confirmed that FD_ADC is the strongest independent predictor of MVI (OR = 3.85, 95% CI: 2.45–6.04, P < 0.001). 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 = 0.425, P < 0.001). A “highly chaotic” 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. Conclusion 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 ‘static anatomical metrics’ into a novel dimension of ‘microenvironmental dynamic evolution’, providing a robust, physics-driven tool for individualized surgical margin planning and the precise stratification of targeted neoadjuvant therapy.