Unsupervised deep learning model for fast energy layer pre-selection of delivery-efficient proton arc therapy plan optimization of nasopharyngeal carcinoma

Abstract Objective. Proton arc therapy (PAT) is an emerging and promising modality in radiotherapy, offering improved dose distribution and treatment robustness over conventional intensity-modulated proton therapy. Yet, identifying the optimal energy layer (EL) sequence remains challenging due to the high computational demand and prolonged treatment delivery time. This study proposes unsupervised deep learning for fast EL pre-selection, targeting EL switching (ELS) time and plan quality. Approach. We introduce a spot-count representation that combines structure-specific spot counts with spatial dose-influence features, organized by gantry angle and EL. A U-Net-style model, SPArc_dldp, uses this representation and water-equivalent thickness features to score candidate ELs, with training objectives based on spot counts and ELS time. We evaluated SPArc_dldp against SPArc_pso in 35 paired nasopharyngeal carcinoma cases, including nine-scenario robust optimization and evaluation. Main results. SPArc_dldp achieved a significantly higher nominal clinical target volume (CTV) conformity index (CI: 0.613±0.034 versus 0.557±0.040; p<0.001). It showed better homogeneity (HI: 0.395±0.048 versus 0.414±0.060; p=0.135). EL-selection computation took 2.218±0.022 ms for DL and 14.18±2.71 s for PSO. DL had significantly shorter ELS time (28.59±4.01 versus 72.19±5.56 s; p<0.001), but higher optic-nerve and parotid mean doses. Following robust optimization, DL had a higher CTV root-mean-square deviation dose-volume histogram area (RVH–AUC: 10.71±1.00 versus 8.69±0.73 per-fraction Gy(RBE)·%; p<0.001), indicating greater dose variation. Significance. The proposed spot-count representation supports rapid EL pre-selection for PAT planning. In this exploratory comparison, SPArc_dldp achieved higher nominal CI and shorter ELS time, alongside higher mean doses to some OARs and greater CTV dose variation.