Complexity analysis of VMAT prostate plans: insights from dimensionality reduction and information theory techniques

Abstract Introduction: Volumetric Modulated Arc Therapy (VMAT) is a state-of-the-art prostate cancer treatment, defined by high dose gradients around targets. Its unique dose shaping incurs hidden complexity, impacting treatment deliverability, carcinogenesis, and machine strain. This study compares various aperture-based VMAT complexity indices in prostate cases using principal component and mutual information analyses. It suggests essential properties for an ideal complexity index from an information-theoretic viewpoint. Material and methods: The following ten complexity indices were calculated in 217 VMAT prostate plans: circumference over area (CoA), edge metric (EM), equivalent square field (ESF), leaf travel (LT), leaf travel modulation complexity score for VMAT (LTMCSV), mean-field area (MFA), modulation complexity score (standard MCS and VMAT variant MCSV), plan irregularity (PI), and small aperture score (SAS5mm). Principal component analysis (PCA) was applied to explore the correlations between the metrics. The differential entropy of all metrics was also calculated, along with the mutual information for all 45 metric pairs. Results: Whole-pelvis plans had greater complexity across all indices. The first three principal components explained 96.2% of the total variance. The complexity metrics formed three groups with similar conceptual characteristics, particularly ESF, LT, MFA, PI, and EM, SAS5mm. The differential entropy varied across the complexity metrics (PI having the smallest vs. EM the largest). Mutual information analysis (MIA) confirmed some metrics’ interdependence, although other pairs, such as LTMCSV/SAS5mm, LT/MCSV, and EM/SAS5mm, were found to share minimal MI. Conclusions: There are many complexity indices for VMAT described in the literature. PCA and MIA analyses can uncover significant overlap among them. However, this is not entirely reducible through dimensionality reduction techniques, suggesting that there also exists some reciprocity. When designing predictive models of quality assurance metrics, PCA and MIA may prove useful for feature engineering.