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PyDoseRT Proton: A GPU Pencil-Beam Engine with a Convolutional Residual-Correction Network for Fast Proton Dose Calculation
Lukas Zimmermann, Hermann Fuchs, Attila Simkó, Gerd Heilemann
TL;DR
The paper addresses the need for proton dose calculation that is fast enough for iterative planning yet more accurate than analytical pencil-beam methods near heterogeneities. PyDoseRT Proton combines a differentiable proton PB engine with a learned residual correction toward Monte Carlo accuracy; the submitted CT configuration achieved strong preliminary-test dose-prediction metrics.
Problem
Monte Carlo transport is accurate but too slow for iterative planning, while analytical pencil-beam algorithms degrade in lung and at bone/air interfaces.
Method
PyDoseRT Proton couples a proton PB engine calibrated to Monte Carlo with a compact convolutional network that learns an additive residual while retaining an explicit physics baseline.
Results
The submitted CT configuration obtained beamlet MAE 0.0066, image-z IDD distance 0.0025, plan MAE 0.0049, 98.30% gamma pass rate (1%/1 mm), and DVH error 0.460.
Takeaways & Limitations
The learned correction and correct anatomical support drive patient-dose accuracy beyond the analytical baseline, while differentiability enables future gradient-based treatment-planning workflows.
Takeaways & Limitations
The evaluation used only eight cases for local model selection, tuning, and reporting, and MRI results additionally depend on synthetic-CT quality.
Abstract
from arXiv · showhide
Architecture category. Hybrid method: a physics-based analytical pencil-beam (PB) dose engine followed by a 3-D convolutional residual-correction network (RepVGG-U-Net). We addressed the DoseRAD2026 proton dose-prediction task with PyDoseRT Proton, a GPU-accelerated engine implemented in PyTorch and augmented by a learned residual toward Monte Carlo (MC) accuracy. A double-Gaussian PB kernel was calibrated to GATE/Geant4 integrated depth doses in water in two stages: a classical per-energy curve fit, then a gradient-based fit of the full 3-D dose through the PyTorch physics engine as it retains a differentiable execution path for gradient-based optimization of dose-dependent objectives. The engine computes each beamlet on a beam's-eye-view (BEV) lattice with variance-preserving Gaussian splitting, an analytic nuclear halo, and a Fermi-Eyges heterogeneity term, then rotates the result into the patient frame. Additionally, a compact residual U-Net predicts an additive correction in BEV space. It is conditioned on voxelwise material-label embeddings, a discrete energy embedding and spot size. The same model was used for all anatomical sites (thoracic and abdominal). It was trained with a patient-space L1 objective emphasizing the scored high-dose region and multi-scale BEV deep supervision. The submitted CT configuration obtained preliminary-test beamlet MAE 0.0066, image-z IDD distance 0.0025, plan MAE 0.0049, 98.30\% gamma pass rate (1\%/1 mm), and DVH error 0.460.
1 Introduction
PyDoseRT Proton combines a fast analytical proton pencil-beam engine with a learned residual toward Monte Carlo accuracy, targeting dose calculation suitable for iterative planning and heterogeneous anatomy.
- Monte Carlo transport is accurate but too slow for iterative planning, while analytical pencil-beam methods are fast but degrade in lung and bone/air interfaces.
- The method couples a proton pencil-beam engine calibrated to Monte Carlo water data with a compact convolutional network that predicts an additive residual.
- A zero-initialized residual preserves the analytical solution as an explicit physics baseline instead of predicting dose directly from anatomy.
2 Methods
The system uses BEV-space physics and residual learning, with differentiable calibration, material-aware conditioning, and patient-space training supported by multi-scale BEV supervision.
- Data and workflow: The dose corrector was trained on 67 cases using planning-CT-derived SPR, material labels, density, plan geometry, and Monte Carlo reference dose.
- Data and workflow: Patient data are transformed into beam’s-eye-view coordinates for analytical dose calculation and learned correction, then mapped back to the patient grid.
- Pencil-beam engine: Each beamlet uses water-equivalent depth, variance-preserving 81-way Gaussian splitting, a double-Gaussian halo, and a Fermi–Eyges heterogeneity term.
- Residual correction: The RepVGG–U-Net predicts an additive residual in BEV space and conditions it on continuous inputs, material information, energy, and spot width; residual heads are zero-initialized.
- MRI pathway and post-processing: The same dose model processes MRI cases after independently generated synthetic CT, and the corrected BEV dose is rotated back, densified, and support-masked on the patient grid.
- Training: The primary loss is computed after inverse rotation in patient space, while auxiliary decoder predictions receive masked, peak-normalized L1 supervision at multiple BEV scales.
3 Results
Results show that calibration choices, anatomical support, and training duration materially affected proton-dose accuracy, while the selected hybrid model achieved strong validation and preliminary hidden-test performance. The evidence also identifies thoracic cases and MRI synthetic-CT generation as important remaining limitations.
- 3.1 Water calibration: 0.16% mean MAE and 99.8% local gamma pass rate were achieved by the 108 LUT in matched water benchmarks.The 109 refit converged cleanly but did not improve patient-validation dose accuracy.
- 3.1 Water calibration: 11.6% lower mean beam MAE, 7.9% lower IDD distance, and 7.1% lower plan MAE were obtained with the 108-generation LUT versus 107.The comparison includes increased fitted-energy coverage and removal of an unstable 142.06-MeV entry; matched 108-versus-109 changes were negligible.
- 3.2 Architecture selection: 7.5–7.6% lower high-dose MAE than scalar or Fourier energy representations and 10.8% lower than omitting energy were observed for the learned energy embedding.GroupNorm was better in five of six matched normalization pairs, but short screens were not exhaustive.
- 3.3 Validation set (8 held-out patients): 0.00571 MAE and 0.00463 IDD distance were reached by v2 in the full pre-mask-update evaluation, while thoracic errors remained larger than abdominal errors.The integral ratio of 0.988 indicated a small residual under-response rather than exact dose conservation.
- 3.3 Validation set (8 held-out patients): 5.12% lower beam MAE and 8.99% lower IDD distance were achieved after corrected-mask retraining for 27 epochs, improving both metrics across all eight held-out cases.The run used the corrected topological mask and the same recipe retrained from scratch with a longer schedule.
- 3.4 Preliminary hidden-test results: 3.0% CT beam-MAE improvement and 8.0% CT IDD improvement followed retraining, whereas MRI improved by 0.5% in beam MAE and not at all in IDD distance.Because MRI uses the same dose model after synthetic-CT generation, the remaining MRI limitation was attributed to the MR-to-CT front end.
4 Discussion
The discussion identifies learned correction and anatomical support as major accuracy drivers, while highlighting residual far-halo under-response and limits on the challenge evidence. Differentiability broadens the engine’s potential reuse, but plan optimization was not evaluated.
- Accuracy drivers: The learned correction and correct anatomical support drive accuracy more than increasing water-phantom histories beyond 10^8.The 10^8 calibration removes instability and noise seen at 10^7, while 10^9 does not measurably improve patient dose.
- Accuracy drivers: The topological mask explains much of the late IDD and plan-level gain, so remaining error is not attributable solely to the lateral kernel.
- Model limitations: Residual far-halo under-response persists, especially at high energy, and widening the lateral fit window can overestimate halo dose.This indicates a shape/support trade-off in the double-Gaussian model rather than simple spatial truncation.
- Scope of differentiability: Differentiability makes the forward model reusable for gradient-based treatment-planning workflows with dose-derived objectives.The challenge results demonstrate differentiable kernel calibration, not plan optimization.
- Study limitations: The study is limited by eight local model-selection cases, tuning and reporting on the same validation cohort, and incomplete runtime provenance for the final CT artifact.Checkpoint selection by validation high-dose MAE is insensitive to IDD distance, which is non-monotonic during training.
- Reproducibility: The proton dose engine, challenge container, training code, evaluation scripts, and model definitions are planned for availability in a separate repository.