Dosimetric analysis along core-needle biopsies in prostate HDR brachytherapy
Objective. Develop a probabilistic framework that maps high-dose-rate brachytherapy dose and dose-gradient magnitude onto MR-informed, TRUS-guided prostate core-needle biopsies, explicitly propagating millimetre-scale localization uncertainty. Approach. We reconstructed two representative second-fraction biopsy cores, voxelized them at 1mm3, and registered them to the clinical 1×1×0.5mm3 dose lattice. Spatial uncertainty from registration, segmentation, and biopsy length mismatch was modelled as NT=10 000 rigid translations sampled from N(0,σ2I) with σ=1.25mm, plus an independent axial shift along the core. For each voxel we obtained Monte Carlo distributions of dose D and dose-gradient magnitude G=‖∇D‖, distributional DVHs, Δ-metrics comparing nominal to probability-weighted summaries, and spatial summaries including axial length-scale dose-difference curves and voxel-pair contrast maps. Main results. Two exemplar second-fraction cores from a representative patient, selected as mechanistic exemplars of steep- versus low-gradient dose environments, showed right-skewed trialwise dose distributions in high-gradient segments, with widened uncertainty bands and larger nominal-summary discrepancies in the steep-gradient core. In that core, the typical per-trial perturbation in mapped dose was substantially larger (median |ΔDb,v,t|≈7Gy versus ≈1Gy in the low-gradient core). Length-scale curves increased with axial separation and then plateaued, indicating centimetre-scale along-core spatial structure in these exemplars; voxel-pair maps highlighted both near-uniform subsegments and voxel pairs achieving prescribed inter-voxel contrast. Significance. The framework converts biopsy localization uncertainty into probability-weighted voxel- and core-level dose descriptors and interpretable Δ-metrics that separate nominal bias from propagated variability. These estimands can be used to assess feasibility for dose-biology studies, guide selection or pairing of subsegments with specified homogeneity or contrast, and provide dose and gradient covariates for Raman, biochemical, and genomic assays, including settings where ex vivo biopsy orientation or integrity is partially lost. Cohort-level dosimetric characterization and robustness analyses are outside the scope of this exemplar-focused paper.