Probabilistic quality assurance of biopsy DVH thresholds in HDR prostate brachytherapy under localization uncertainty

MR-US guided biopsies support biologic correlation in HDR prostate brachytherapy, but steep dose gradients and millimeter-scale localization uncertainty limit the validity of nominal biopsy doses.

To assess how localization uncertainty affects the robustness of biopsy DVH dose thresholds in HDR prostate brachytherapy and to quantify the nominal dose margins corresponding to 95% pass probabilities.

Twenty-seven biopsies from 15 HDR monotherapy patients were reconstructed as sets of $1mm$ voxels and sampled on the clinical HDR dose lattice. Localization uncertainty was modeled with 10 000 Monte Carlo trials per biopsy using isotropic 3D Gaussian translations ( $\sigma =1.25mm$ ) plus an axial tissue-deficit offset. For each voxel we computed nominal and Monte Carlo summaries of dose and dose gradient magnitude; for each biopsy we evaluated DVH metrics $D_{2\%}$ , $D_{50\%}$ , $D_{98\%}$ , and $V_{150\%}$ . For four robustness thresholds, Monte Carlo pass probabilities $p_b$ were related to nominal distance-from-threshold using logistic models, and geometric, spatial, and radiomics predictors were tested as secondary covariates.

The pooled voxel-dose and dose-gradient distributions were broad, positively skewed, and consistent with log-normal models. Nominal voxel-level doses tended to be higher than localization-perturbed samples, with mean absolute per-trial $|\Delta D_{b,v,t}|\approx 7.6\mathrm{Gy}$ . Margin-only logistic models captured most of the variability in pass probabilities; the nominal margins required for a 95% pass probability were $\approx 6\mathrm{Gy}$ ( $D_{98\%}$ ), $21\mathrm{Gy}$ ( $D_{50\%}$ ), $49\mathrm{Gy}$ ( $D_{2\%}$ ), and 49 percentage points ( $V_{150\%}$ ). Adding geometric, spatial, or radiomics predictors altered these margins only modestly. Along biopsy cores, mean absolute dose differences between voxel pairs approached $\approx 10\mathrm{Gy}$ at separations of $1$ - $1.5cm$ , indicating decorrelation on that scale.

Localization uncertainty causes nominal biopsy DVH metrics to systematically overestimate Monte Carlo-propagated doses. The reported 95% margins should be interpreted as biopsy-scale robustness buffers under the stated uncertainty model, not as clinically prescriptive focal-boost increments. Dose decorrelated over distances of order $1$ - $1.5cm$ along biopsy cores, supporting spatially explicit, Monte Carlo-based reporting when interpreting biopsy dosimetry in HDR prostate brachytherapy.