Deep learning-based dose prediction in proton beam therapy for hepatocellular carcinoma: comparison of network architectures and loss functions.

In proton beam therapy (PBT) for hepatocellular carcinoma (HCC), deep learning (DL)-based dose prediction offers clinical value by providing immediate reference dose distributions as a guideline tool for treatment planners and enabling virtual PBT dose assessment at institutions lacking PBT facilities to support clinical decision-making. This study proposes a dose gradient-aware DL training approach and a beam arrangement-free framework that predicts dose distributions from computed tomography (CT) images and target/organs-at-risk structures without requiring beam arrangement inputs. Using data from 172 HCC patients, we systematically compared 20 DL models combining five architectures with four loss functions, including a novel dose gradient-aware loss capturing PBT-specific dose distribution characteristics arising from the Bragg peak. Prediction accuracy was evaluated using dose metrics for clinical target volume, planning target volume, and normal liver, 10% dose region volume assessment, visual examination, Dice similarity coefficient (DSC) for 10% dose region, and dose-volume histogram (DVH) analysis. DL models employing dose gradient-aware loss demonstrated reduced prediction errors in target volume dose metrics, achieved the lowest errors in 10% dose region volume when combined with U-Net (MAE: 35.4 cm3, RMSE: 51.3 cm3), attained the highest DSC (0.88 ± 0.05), showed the closest DVH agreement with clinical plans for both target structures and normal liver. A comprehensive evaluation consistently confirmed the superiority of dose gradient-aware loss across all metrics, demonstrating the importance of physics-informed, dose gradient-aware learning for accurate PBT dose distribution prediction. Particularly, DL models combining simple architectures with dose gradient-aware loss predicted doses that closely approximated clinical doses in PBT.