# Improved differentiation of prostate cancer using advanced diffusion models: a comparative study of mono-exponential, fractional-order-calculus, and multi-compartment models

## TL;DR

This study compares advanced diffusion models for prostate cancer detection and finds that multi-compartment models improve accuracy in risk classification.

## Contribution

The study introduces a comparative evaluation of multi-compartment and fractional-order-calculus diffusion models for prostate cancer risk stratification.

## Key findings

- The MC model's F2 and C1 + F2 parameters showed the highest AUCs for low vs. intermediate-risk PCa differentiation.
- Combining MC and FROC models improved accuracy in classifying intermediate vs. high-risk PCa.
- ADC demonstrated strong correlations with several parameters but was less effective in challenging classifications.

## Abstract

This study aims to compare the performance of mono-exponential (Mono), fractional-order-calculus (FROC), and multi-compartment (MC) diffusion models in differentiating prostate lesions, including benign prostatic hyperplasia (BPH) and prostate cancer (PCa), as well as classifying PCa by clinical significance and risk levels.

\A prospective study was conducted with 224 men (aged 50–80) undergoing 3 T MR imaging. Regions of interest (ROIs) analyses were performed on quantitative parameters from Mono, FROC, and MC models. These parameters were evaluated for their ability to distinguish BPH from PCa, clinically significant (CS) from clinically insignificant (CInS) PCa, and among PCa risk levels. Group differences were assessed using the Mann–Whitney U test and Kruskal–Wallis test, followed by post-hoc Dunn’s test. ROC curves were plotted, and AUC was calculated. Logistic regression was used for parameter combinations, and performance was evaluated via 1000 bootstrap samples. The correlation between parameter pairs was analyzed. The image quality and PCa detection capability were also evaluated visually.

In distinguishing PCa from BPH, the F1, ADC, and D parameters from the three models achieved high AUCs of 0.92, 0.91, and 0.91, respectively. For differentiating CS-PCa from CInS-PCa, the F2 parameter and the combination of C1 + F2 from the MC model showed the highest AUCs (0.75 and 0.76). In assessing PCa risk levels, F2 and C1 + F2 from the MC model showed the highest AUCs (0.73 and 0.74) for low vs. intermediate-risk PCa. For intermediate vs. high-risk PCa, F1, F1F2, and β + F1F2 from MC and FROC models had the highest AUCs (0.66, 0.66, and 0.71). In addition, ADC was strongly or moderately correlated to D, μ, F1, F1F2, F3, C1 and C3, and not correlated to β and F2. ADC and C1 demonstrated high image quality and strong PCa detection capability.

Advanced diffusion models, particularly the MC model, demonstrated a significant improvement over ADC in differentiating prostate lesions, especially between low and intermediate-risk PCa, between intermediate and high-risk PCa, and between clinically significant and insignificant PCa. Comparable performance was observed in distinguishing BPH from PCa among three models. Moreover, the combination of MC and FROC models further enhanced differentiation accuracy, particularly in the more challenging classifications between intermediate and high-risk PCa, where ADC alone proved inadequate. These results highlight the potential clinical value of MC model and combining MC and FROC models for more precise PCa risk stratification.