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Objectives: This study aimed to assess the potential role of 3-dimensional (3D) fractal dimension (FD) derived from contrast-enhanced CT images in predicting microvascular invasion (MVI) in patients with hepatocellular carcinoma (HCC).
Materials And Methods: This retrospective study included 655 patients with surgically confirmed HCC from two medical centers (training set: 406 patients; internal test set: 170 patients; external test set: 79 patients). Box-counting algorithms were used to compute 3D FD values from portal venous phase images. Univariable and multivariable logistic regression analyses identified independent predictors. The model's area under the curve (AUC) was calculated. Recurrence-free survival (RFS) and overall survival (OS) were evaluated using the Kaplan-Meier method.
Results: Patients with MVI-positive HCC demonstrated significantly higher FD values compared to those with MVI-negative HCC (p < 0.01). The FD achieved AUCs of 0.786 (95% CI: 0.713-0.849) in the internal test set and 0.776 (95% CI: 0.669-0.874) in the external test set. A combined model incorporating alpha-fetoprotein, tumor size, tumor number, and FD showed superior diagnostic performance for MVI prediction compared to the clinical model, with AUCs of 0.795 (95% CI: 0.720-0.860) vs 0.752 (95% CI: 0.670-0.825) in the internal test set, and 0.826 (95% CI: 0.721-0.915) vs 0.739 (95% CI: 0.613-0.849) in the external test set. Patients stratified as high-risk MVI exhibited significantly worse RFS and OS outcomes compared to low-risk MVI patients (p < 0.05).
Conclusion: The 3D FD values differed significantly between MVI-positive and MVI-negative HCC patients. Integrating FD into the clinical model enhanced MVI prediction accuracy and may help identify patients at high risk.
Key Points: Question The predictive value of three-dimensional (3D) fractal dimension (FD) derived from contrast-enhanced CT images for identifying MVI-positive HCC remains unclear. Findings Quantitative indicators derived from fractal analysis were able to predict MVI. The developed model demonstrated improved performance when incorporating fractal dimension. Clinical relevance Fractal analysis based on contrast-enhanced CT is a feasible approach for evaluating MVI and provides additional clinical value for prognostic assessment. It may serve as a reference for preoperative MVI estimation and assist clinicians in executing more tailored therapies.
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http://dx.doi.org/10.1007/s00330-025-11878-6 | DOI Listing |
ACS Omega
September 2025
Department of Chemistry, American University of Beirut, P.O. Box 11-0236, Riad El-Solh, 1107 2020 Beirut, Lebanon.
Fractal growth in reaction-diffusion frameworks (RDF) offers a powerful paradigm for understanding self-assembly in chemical and materials systems. However, its connection to diffusion-limited aggregation (DLA) remains underexplored. Here, we present the first quantitative demonstration of RDF-driven fractal crystallization of benzoic acid (BA), revealing a direct correlation among fractal dimension, diffusion rate, and gel-matrix chemistry.
View Article and Find Full Text PDFSoft Matter
September 2025
Nestlé Product Technology Centre, York, YO31 8FY, UK.
Particles with some degree of hydrophilicity are known to aggregate when directly dispersed in non-aqueous media. Proteins are generally insoluble in oil and have complex surface properties, but they may form networks in oil like more simple colloidal particles, depending on particle size and surface hydrophilicity. Here, the particle size of pea protein isolate (PPI) particles in oil was reduced to submicron sizes by stirred media milling.
View Article and Find Full Text PDFJ Cancer Res Ther
September 2025
Department of Interventional Ultrasound, The Senior Department of Oncology, The Fifth Medical Center of PLA General Hospital, Beijing 100039, China.
Background: Noninvasive and functional tumor vascular system imaging at the microscopic scale is greatly significant. Using animal models, we investigated the feasibility of using superresolution ultrasound (SR-US) imaging to visualize and quantify the microvessels during tumor growth.
Methods: This study established nine rabbit VX2 tumor models.
Front Neurosci
August 2025
School of Mathematics and Statistics Science, Ludong University, Yantai, China.
Epilepsy is a neurological disorder affecting ~50 million patients worldwide (30% refractory cases) with complex dynamical behavior governed by nonlinear differential equations. Seizures severely impact patients' quality of life and may lead to serious complications. As a primary diagnostic tool, electroencephalography (EEG) captures brain dynamics through non-stationary time series with measurable chaotic and fractal properties.
View Article and Find Full Text PDFJ Phys Condens Matter
September 2025
Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 Barrackpore Trunk Road, Kolkata-700108, Kolkata, Kolkata, West Bengal, 700108, INDIA.
Quasiperiodic systems are known to exhibit localization transitions in low dimensions, wherein all electronic states become localized beyond a critical disorder strength. Interestingly, recent studies have uncovered a reentrant localization (RL) phenomenon: upon further increasing the quasiperiodic modulation strength beyond the localization threshold, a subset of previously localized states can become delocalized again within a specific parameter window. While RL transitions have been primarily explored in systems with simple periodic modulations, such as dimerized or long-range hopping integrals, the impact of more intricate or correlated hopping structures on RL behavior remains largely elusive.
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