<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({64}^{3}\)</EquationSource> </InlineEquation> voxels, and normalized to <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({\text{D}}_{max}\)</EquationSource> </InlineEquation>. 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 (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(=0.132;\text{r}=0.109\)</EquationSource> </InlineEquation> 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 (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\({\text{R}}^{2}=0.621\)</EquationSource> </InlineEquation>; volume-adjusted <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\({\text{R}}^{2}=0.487\)</EquationSource> </InlineEquation>) confirmed that the learned embedding is driven by spatial metrics-hotspot displacement (<InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\upbeta =0.47\)</EquationSource> </InlineEquation>) and anisotropy ( <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\upbeta =0.18\)</EquationSource> </InlineEquation>) rather than DVH (<InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\upbeta =0.10\)</EquationSource> </InlineEquation>). Held-out reconstruction SSIM reached <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(0.943\pm 0.018\)</EquationSource> </InlineEquation>. TopoGK outperformed PCA in spatial correlation ( <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\({\text{r}}_{\text{C}\text{O}\text{M}}=\)</EquationSource> </InlineEquation> 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.</p>

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

期刊论文
发表日期：

2026年7月20日

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Omar Hamzaoui,
Yassine Oulhouq,
Mohammed Rezzoug,
Mustapha Zerfaoui,
Dikra Bakkari,
Abdeslem Rrhioua

摘要

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 \({64}^{3}\) voxels, and normalized to \({\text{D}}_{max}\) . 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 ( \(=0.132;\text{r}=0.109\) 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 ( \({\text{R}}^{2}=0.621\) ; volume-adjusted \({\text{R}}^{2}=0.487\) ) confirmed that the learned embedding is driven by spatial metrics-hotspot displacement ( \(\upbeta =0.47\) ) and anisotropy ( \(\upbeta =0.18\) ) rather than DVH ( \(\upbeta =0.10\) ). Held-out reconstruction SSIM reached \(0.943\pm 0.018\) . TopoGK outperformed PCA in spatial correlation ( \({\text{r}}_{\text{C}\text{O}\text{M}}=\) 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.