Quantifying the spatial information loss of Dose-Volume Histograms in Gamma Knife radiosurgery via unsupervised 3D dose geometry embedding.

Dose-Volume Histograms (DVH) discard spatial information by summarizing 3D distributions into 1D curves. This study quantifies this loss in Gamma Knife radiosurgery and introduces TopoGK, a novel unsupervised deep learning framework capturing full 3D dose geometry. Ninety-six vestibular schwannoma plans were analyzed. Dose grids were tumor-centered, resampled to [Formula: see text] voxels, and normalized to [Formula: see text]. A 3D Convolutional Variational Autoencoder compressed each dose-mask volume into a 64dimensional spatial embedding. Spatial information loss was quantified by comparing pairwise DVH and latent distances both globally and within volume-stratified subgroups. Physical validation employed hotspot center-of-mass displacement, gradient anisotropy, and a novel Spatial Discordance Index (SDI). Five-fold cross-validation ensured generalizability. A linear PCA baseline was included for comparison. The correlation between DVH and spatial similarity was weak ([Formula: see text] within volume-matched pairs). Among DVH-matched pairs, the hotspot exhibited a median physical displacement of 2.81 mm (90th percentile: 4.69 mm), and 61.8-76.5% exceeded heuristic geometric SDI thresholds. Multivariate regression ([Formula: see text]; volume-adjusted [Formula: see text]) confirmed that the learned embedding is driven by spatial metrics-hotspot displacement ([Formula: see text]) and anisotropy ( [Formula: see text]) rather than DVH ([Formula: see text]). Held-out reconstruction SSIM reached [Formula: see text]. TopoGK outperformed PCA in spatial correlation ( [Formula: see text] 0.451 vs. 0.287). DVH similarity does not guarantee spatial dose equivalence. The proposed framework provides a physically validated spatial fingerprint capturing geometric variations invisible to conventional plan evaluation. As a proof-of-concept in single-fraction vestibular schwannoma radiosurgery, these results motivate further investigation toward spatially-aware quality assurance in stereotactic radiosurgery.