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

Proton arc therapy (PAT) is an emerging and promising modality in radiotherapy, offering improved dose distribution and treatment robustness over intensity-modulated proton therapy. Yet, identifying the optimal energy layer (EL) sequence remains challenging due to the intensive computational demand and prolonged treatment delivery time. This study proposes an unsupervised deep learning model for fast EL pre-selection that minimizes EL switch (ELS) time while maintaining high plan quality. We introduce a novel data representation method, spot-count representation, which encodes the number of proton spots intersecting the target and organs at risk (OAR) in a matrix structured by sorted gantry angles and energy layers. This representation serves as the input of an U-Net style architecture, SPArc_dl, which is trained using a tri-objective function: maximizing spot-counts on target, minimizing spot-counts on OAR, and reducing ELS time. The model is evaluated on 35 nasopharyngeal cancer cases, and its performance is compared to SPArc_particle_swarm (SPArc_ps). SPArc_dl produces EL pre-selection that significantly improves both plan quality and delivery efficiency. Compared to SPArc_ps, it enhances the conformity index by 0.1 (p<0.01), reduces the homogeneity index by 0.71 (p<0.01), lowers the brainstem mean dose by 0.25 (p<0.01), and shortens the ELS time by 37.2% (p < 0.01). The results unintentionally reveal employing unchanged ELS is more time-wise efficient than descended ELS. SPArc_dl's inference time is within 1 second. However, SPArc_dl plan demonstrates limitation in robustness. The proposed spot-count representation lays a foundation for incorporating unsupervised deep learning approaches into EL pre-selection task. SPArc_dl is a fast tool for generating high-quality PAT plans by strategically pre-selecting EL to reduce delivery time while maintaining excellent dosimetric performance.