Angle dependent dose transformer algorithm for fast proton therapy dose calculations

TL;DR

ADoTA introduces an angle-aware, transformer-augmented 3D U-Net for proton dose calculation that eliminates per-beamlet grid reorientation by encoding a fast Gaussian beamlet projection conditioned on energy. Trained on $108$ CTs and tested on $50$, it achieves MC-level accuracy with gamma pass rates around $99\%$ across thoracic and abdominal/pelvic sites while reducing end-to-end computation by about $86\%$ compared with reinterpolation-based methods. The model integrates voxel-level and depth-dose losses, uses energy-conditioned tokens, and demonstrates robust performance across energies and beam angles, enabling faster, online adaptive proton therapy workflows. These results support practical deployment for rapid plan evaluation and robust dose-influence matrix construction in heterogeneous anatomies, with clear paths for grid-agnostic extensions and GPU-accelerated preprocessing.

Abstract

Accurate 3D dose calculation for Pencil Beam Scanning Proton Therapy (PBSPT) is typically performed with Monte Carlo (MC) engines, but their runtimes limit adaptive workflows and repeated evaluations. Current deep-learning proton dose engines often require orthogonality between proton rays and the CT grid, forcing computationally expensive beamlet-wise 3D reinterpolation. We propose the Angle-dependent Dose Transformer Algorithm (ADoTA), which eliminates grid rotation by augmenting the model input with a fast analytical beamlet-shape projection that explicitly encodes beam direction. The model was trained on CT data from 108 patients to predict beamlet dose distributions for initial energies of $70$--$270\,\mathrm{MeV}$ over an $80\times110\,\mathrm{mm}^2$ field, and tested on an independent cohort of 50 patients. On the test set, gamma pass rates $(1\%,3\,\mathrm{mm})$ were $99.40\pm0.86\%$ (thorax) and $99.87\pm0.23\%$ (abdomen/pelvis). Single-beamlet inference took $1.72\pm0.8\,\mathrm{ms}$. By avoiding reinterpolation, end-to-end 3D dose computation was reduced by $\approx86\%$ relative to the fastest published reinterpolation-based methods. For full treatment plans, gamma pass rates $Γ(2\%,2\,\mathrm{mm})$ with a 10\% dose cut-off reached $98.4\%$ (lung) and $98.9\%$ (prostate). ADoTA provides an angle-aware deep-learning proton dose engine that preserves MC-level accuracy across heterogeneous anatomies while substantially reducing computational overhead.

Figures (15)

• Figure 1: Dataset split (CT Images level) introduced to train, validate and test developed model.
• Figure 2: Sampling process for training records $r_i$. For each spot position $(\mathrm{SP}_x,\;\mathrm{SP}_y)$, two virtual source positions are defined: the nominal $S_{\mathrm{v}}$ and the translated $S'_{\mathrm{v}}$. For each source position, simulations are performed at two distinct proton energies. This configuration ensures that the dataset encompasses both angular and energy variability.
• Figure 3: Overview of the Angle-dependent Dose Transformer Algorithm (ADoTA). The model takes as input a concatenated batch of CT grids and beamlet shape projection representations, $(\mathbf{V_{\mathrm{crop}}} | \mathbf{\Phi}_{\mathrm{crop}})$, together with the corresponding batch of proton beamlet mean energies, $\boldsymbol{\epsilon}$. The encoder generates the latent space $\mathcal{L}_{\mathrm{E}}$, which is conditioned by energy token $\epsilon_{T}$ to form the energy-conditioned latent space $\mathcal{L}_{\mathrm{C}}$. After positional embedding and transformer encoding, the output $\mathcal{L}_{\mathrm{C, D}}$ is reshaped and cropped into the 3D latent volume $\mathcal{L}_{\mathrm{D}_{\mathrm{cropp}}}$. The decoder, connected to the encoder via residual connections HeDeepRecognition, reconstructs the spatially aligned batch of dose distributions $\hat{\mathbf{D}}_{\mathrm{crop}}$. Figure represents processing of the batch element.
• Figure 4: Distribution of gamma pass rate $\Gamma(2\%,2,\mathrm{mm},10\%)$ and relative dose error $\rho$ on the lung and abdominal/pelvic beamlet test datasets. For each distribution, markers indicate the minimum, mean, and maximum values across the corresponding test samples.
• Figure 5: The best performing case in the lung test set. Beamlet initial energy: 76.68 MeV. $\mathrm{MAPE} = 3.84\%$, $\Gamma(2\%, 2\mathrm{mm}, 10\%)=100.0\%$. The first three rows display the 3D dose distributions calculated by MCsquare (first row) and ADoTA (second row), along with the absolute percentage difference between them (third row). The axial and sagittal planes are centered on the voxel containing the Bragg peak. The fourth row presents the normalized IDD profiles for both the MCsquare and ADoTA distributions. The final three rows show the beam's eye view at selected depths, as indicated by the red markers in the upper rows. Only voxels receiving a dose above 10 % of the maximum deposited dose are included in the MAPE calculation. This visualization layout is consistent for Figures \ref{['fig:lung_best']}-\ref{['fig:pelvic_worst']}.