# Histogram analysis of diffusion-weighted imaging with a fractional order calculus model in breast cancer: diagnostic performance and associations with prognostic factors

## TL;DR

This study shows that a new imaging model called FROC can help distinguish breast cancer from benign tumors and is linked to important cancer markers.

## Contribution

The study introduces a fractional order calculus model for diffusion-weighted imaging, showing its diagnostic performance and associations with breast cancer biomarkers.

## Key findings

- FROC histogram metrics showed diagnostic performance comparable to ADC in differentiating benign and malignant breast lesions.
- FROC parameters were significantly associated with ER/PR status, proliferation, and nodal involvement in breast cancer.
- FROC-based analysis captures microstructural heterogeneity not captured by traditional ADC metrics.

## Abstract

This study aims to evaluate the diagnostic performance of diffusion-weighted imaging (DWI) with a fractional order calculus (FROC) model for differentiating breast lesions and to explore the associations between FROC/apparent diffusion coefficient (ADC)-derived diffusion metrics and prognostic biomarkers and molecular subtypes in breast cancer.

This retrospective study included 147 patients with 159 histopathology-confirmed lesions who underwent multi-b DWI using simultaneous multi-slice (SMS) readout-segmented echo-planar imaging (rs-EPI) at 3.0 T. Whole-lesion histograms were computed for mono-exponential ADC and FROC parameters (D, β, μ). The Mann–Whitney U test was used to compare the histogram metrics of each diffusion parameter between the benign and malignant groups and between groups with different prognostic biomarkers and molecular subtypes. The Kruskal–Wallis test was used to compare the histogram metrics of each DWI-derived parameter among the different molecular subtypes. The Spearman rank correlation analysis was employed to characterize correlations between diffusion parameters and prognostic biomarkers. The diagnostic performance of each DWI-derived parameter in differentiating breast lesions was assessed using receiver operating characteristic (ROC) analysis.

Interobserver reproducibility was excellent (intra-class correlation coefficient 0.827–0.928). Central tendency histogram metrics (10th, 90th percentiles, mean, median) of ADC and FROC parameters were higher in benign than malignant lesions, whereas skewness (all models) and entropy/kurtosis (ADC, D, μ) were lower in benign lesions (all p < 0.05, except β-skewness). The histogram metrics of ADC-median, DFROC-mean, and DFROC-median showed similar diagnostic performance. The values of ADC-mean, DFROC-10%, DFROC-mean, DFROC-median, βFROC-10%, βFROC-mean, and βFROC-median were significantly lower in the estrogen receptor (ER)-positive group compared with those in the ER-negative group. The tumors with progesterone receptor (PR)-negative status showed significantly higher βFROC-10%, βFROC-mean, and βFROC-median values than those of tumors with PR-positive status. The values of DFROC-skewness, βFROC-10%, and βFROC-mean exhibited significant differences in differentiating the triple-negative and luminal subtypes.

FROC-based histogram analysis yields diagnostic performance comparable to ADC for benign vs. malignant classification, while providing richer associations with ER/PR status, proliferation, and nodal involvement, reflecting microstructural heterogeneity not captured by mono-exponential diffusion.