Physics-aware geometric deep learning for pre-planning dosimetric feasibility in Gamma Knife radiosurgery

In Gamma Knife stereotactic radiosurgery (SRS), achieving optimal dosimetric outcomes is physically constrained by complex tumor geometry. While the Gradient Index (GI) and Conformity Index (CI) define plan quality, the volume receiving [Formula: see text] and Shot Density dictate patient safety and efficiency. Current volumetric heuristics fail to capture the topological irregularities that govern these parameters. This study introduces a physics-aware Geometric Deep Learning framework to simultaneously predict quality, safety, and complexity metrics directly from surface topology. Methods: Utilizing the Vestibular-Schwannoma-SEG dataset [Formula: see text], tumor manifolds were converted into physics-aware point clouds enriched with 12-dimensional feature vectors, including surface normals and radial curvature. A multi-task PointNet-based architecture, termed "GammaPoint-Net," was developed to regress GI, CI, [Formula: see text], and Shot Density. The framework was benchmarked against 3D Voxel-based CNNs, standard volumetric regression, conventional machine-learning regressors trained on handcrafted 3D shape descriptors (Random Forest, Support Vector Regression, and XGBoost), and point-based architectures using 5-fold cross-validation. GammaPoint-Net achieved superior predictive accuracy across all objectives ([Formula: see text]), significantly outperforming volumetric baselines [Formula: see text]. Ablation studies confirmed that incorporating differential geometric features reduced the mean absolute error by 46%. GammaPoint-Net also outperformed the strongest handcrafted shape-descriptor baseline (XGBoost augmented with curvature moments, [Formula: see text]; paired Wilcoxon [Formula: see text] ). Saliency mapping demonstrated that the network autonomously identifies high-curvature surface protrusions as the primary drivers of dosimetric degradation. GammaPoint-Net demonstrates that surface topology, rather than volume, is the fundamental determinant of radiosurgical plan quality. This framework provides an instantaneous, interpretable pre-planning assessment, enabling physicists to anticipate plan difficulty and toxicity risks prior to optimization.