A constraint-normalized robustness index for HDR brachytherapy

Geometric uncertainties in high-dose-rate brachytherapy, including applicator displacement, catheter deflection, and interstitial needle spread, produce dose deviations that are patient and plan specific. Unlike external beam radiotherapy, where robustness evaluation frameworks are increasingly standardized, high dose rate brachytherapy lacks a normalized aggregate metric for quantifying plan sensitivity to geometric perturbations.

To define a bounded, dimensionless robustness index for per-fraction evaluation of high dose rate brachytherapy plans that is normalized to clinically meaningful dose-limit constraints, incorporates dose-dependent penalty sensitivity, and provides both a full-scenario severity measure and a dose-threshold-filtered variant.

Geometric perturbation scenarios (translations, rotations, radial expansion/contraction, catheter deflection, and combined modes) are applied to source dwell positions. For each organ at risk, a convex-transformed, constraint-normalized penalty quantifies the fraction of the remaining margin to the dose-limit constraint consumed per scenario. For target volumes, a prescription-normalized piecewise penalty captures under-coverage and excessive dose escalation. The Robustness Index is defined as one minus the mean scenario penalty, yielding a value in [0,1].

The framework produces structure-independent, interpretable indices where a Robustness Index $\approx 0.90$ indicates that scenarios consume on average only 10% of the normalized remaining margin to the dose-limit constraint. A threshold-filtered variant evaluates robustness among only those scenarios that exceed a clinically specified dose level.

The proposed robustness index provides a standardized, clinically anchored metric for high dose rate brachytherapy plan evaluation under geometric uncertainty, complementing existing dose volume histogram based reporting with a single interpretable number per structure.