# 3D fractal dimension analysis of CT imaging for microvascular invasion prediction in hepatocellular carcinoma

## TL;DR

This study shows that 3D fractal analysis of CT scans can help predict microvascular invasion in liver cancer, improving risk assessment and treatment planning.

## Contribution

The study introduces 3D fractal dimension analysis of CT images as a novel predictor for microvascular invasion in hepatocellular carcinoma.

## Key findings

- 3D fractal dimension values were significantly higher in MVI-positive HCC patients compared to MVI-negative patients.
- A combined model including fractal dimension improved MVI prediction accuracy over traditional clinical models.
- High-risk MVI patients had worse recurrence-free and overall survival outcomes.

## Abstract

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).

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.

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).

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.

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.