Noisy probing dose facilitated dose prediction for pencil beam scanning proton therapy: Physics enhances generalizability

Abstract

Background:

Accurate and efficient dose calculation is essential for online adaptive planning in proton therapy. Deep learning (DL) has shown promising dose prediction results for pencil beam scanning proton therapy (PBSPT) in recent years, but existing DL-based dose prediction methods still suffer from limited generalizability and an inability to effectively handle outlier clinical cases. This may lead to inaccurate dose delivery to targets or excessive irradiation to organs at risk (OARs), thereby compromising the safety and efficacy of online adaptive proton therapy.

Purpose:

To design a physics-aware and generalizable AI-based PBSPT dose prediction method that incorporates underlying physics to enhance generalizability, particularly in handling outlier clinical cases.

Methods:

This study analyzed PBSPT plans of 103 prostate (93 for training and 10 for testing) and 78 lung cancer patients (68 for training and 10 for testing) from our institution, with each case comprising CT images and structure sets. Using the doses generated by our Monte Carlo-based dose engine as the reference standard, we compared three methods: the region of interest (ROI)-based method, the beam mask and sliding window method, and the proposed noisy probing dose method, which rapidly generates a low-statistics dose via uniformly weighted spots on an expanded spot-placement target volume without optimization. To evaluate the generalizability of these methods to rare treatment planning scenarios,12 cases with uncommon beam angles or prescription doses were used to assess their performance, which was evaluated using dose-volume histogram (DVH) indices, 3D Gamma passing rates (3%/2 mm/10%), and Dice coefficients for dose agreement, while prediction times were measured to gauge model efficiency.

Results:

The proposed noisy probing dose method consistently outperformed the ROI-based and beam mask baselines across all evaluated metrics, with more accurate dose agreement and superior generalizability. For DVH indices, the noisy probing dose method achieved the smallest deviation in clinical target volume (CTV) dose coverage: in prostate cancer, CTV D98 deviation was reduced by 45% (from 0.53 ± 0.22 Gy [RBE] for ROI-based) and 29% (from 0.41 ± 0.28 Gy [RBE] for beam mask) to 0.29 ± 0.06 Gy [RBE]; in lung cancer, similar improvements were observed, with CTV D98 deviations reduced to 0.34 ± 0.12 Gy [RBE]. The 3D Gamma passing rates improved to 99.65% ± 1.15% for prostate targets and 97.04% ± 1.17% for lung targets. The dice coefficients of the 90% iso-dose lines were also the highest with the noisy probing dose method (prostate: 0.983 ± 0.005; lung: 0.967 ± 0.01). For the 12 outlier cases, the noisy probing dose method maintained superior generalizability, yielding higher 3D Gamma passing rates (prostate targets: 96.79% ± 0.83%, OARs: 94.29% ± 1.01%; lung targets: 93.38% ± 1.34%, OARs: 93.95% ± 1.32%), demonstrating robust generalizability to rare clinical scenarios. The dose predictions for all testing cases were completed within 0.3 seconds.

Conclusions:

A novel noisy probing dose method was proposed for PBSPT dose prediction in prostate and lung cancer patients. By embedding more proton-specific physics, this method demonstrated an improvement in the generalizability of dose prediction.

1 |. INTRODUCTION

Pencil beam scanning proton therapy (PBSPT) has become the state of the art delivery technique in proton therapy, offering superior dose conformity and reduced normal tissue exposure compared with photon-based radiotherapy.^1–8 However, its strong sensitivity to range and setup uncertainties necessitates highly accurate dose calculation.^9–14 With the rise of advanced techniques such as online-adaptive radiotherapy, FLASH, grid therapy, and robust optimization, there is increasing demand for faster yet reliable treatment planning to enable clinical feasibility.^15–28

Artificial intelligence (AI) has shown promise in accelerating treatment planning, particularly in optimal planning dose generation (i.e., dose prediction).²⁹ AI-based models can rapidly estimate complex optimal dose distributions within seconds, making them attractive alternatives to conventional dose calculation and optimization.^27,30,31 Most existing work has focused on photon modalities, where models typically predict voxel-wise dose directly from CT images and region-of-interest (ROI) contours.^32–36 While accurate, such approaches rely heavily on large, homogeneous datasets with consistent beam settings, limiting generalizability across diverse clinical scenarios.²⁹ This challenge is especially pronounced in PBSPT, where beam numbers, angles, and prescription schemes vary substantially across patients and institutions, making it impractical to develop separate models for every beam configuration.

To enhance the overall accuracy, generalizability, and interpretability of the dose prediction models, the input data need to be expanded to include patient-specific physics information, which is the subject of this work. To date, there have been primarily three different approaches for AI-based dose prediction in radiation therapy: Approach 1 relies solely on prior treatment plan data (CT, contours, and dose distributions) to develop purely data-driven prediction engines. While potentially accurate given abundant and diverse data, such models lack physics interpretability and may produce outputs inconsistent with underlying proton dose characteristics.^{32–35,37,38} Approach 2 integrates conventional physics-based methods by generating approximate or noisy optimal dose distributions with analytical or Monte Carlo simulations, which are then refined by AI. Although this improves physical plausibility, it requires complex and time-consuming dose optimization, undermining the speed advantage of AI.^39–42 Approach 3 introduces beam configuration information (e.g., beam angles) alongside patient anatomy. This partially mitigates limitations of pure data-driven models but demands highly heterogeneous training data across parameter space, which is rarely achievable in single-institution datasets.^43–46 The resulting model still lacks physics interpretability as well.

While photon dose prediction can often be achieved with geometric considerations alone, PBSPT is more challenging due to proton-specific physical interactions with tissue heterogeneities, making robust generalizable models difficult to establish.^37,38,45,47 Recent studies have attempted to improve PBSPT dose prediction using beam masks or sliding-window augmentation, but their accuracy and adaptability remain constrained.⁴⁵

The objective of this study is to develop a physics-aware, generalizable AI-based PBSPT dose prediction framework. We propose a novel input feature, the noisy probing dose, derived directly from spot energy layers and spacing without requiring dose optimization. This feature encodes essential proton physics information, providing interpretability and enhancing model generalizability across diverse beam settings. Compared with conventional ROI- or beam mask-based methods, the noisy probing dose approach demonstrates superior accuracy and robustness, including in outlier cases with uncommon beam angles or prescriptions, supporting its potential for routine clinical application.

2 |. MATERIAL AND METHODS

2.1 |. Data collection

For this study, we selected 103 prostate cancer patients and 78 lung cancer patients who were previously treated with PBSPT at our facility using our in-house patient search engine. For each disease site, 10 patients were randomly selected as an independent test set for final performance evaluation, while the remaining 93 prostate and 68 lung cancer cases were used for model development, with approximately 80% allocated for training and 20% for validation. The target and organ at risk (OAR) delineations were examined and approved by experienced radiation oncologists. The prescribed dose was 70.0 Gy[RBE] in 28 fractions for prostate cancer, while for lung cancer it ranged from 50.0 Gy[RBE] to 60.0 Gy[RBE], administered over 25 to 30 fractions. Individualized treatment plans were developed for each patient, taking into account their unique anatomy, using different beam angles and configurations. All treatment plans were optimized using a Single Field Optimization (SFO) technique. The in-house treatment planning system (TPS), Shiva,^{8,12,16,22,23,26} employing a Virtual Particle Monte Carlo (VPMC) dose engine,⁴⁸ was used to generate the planning dose distributions. A total of 2×10⁷ histories were used to ensure a statistical uncertainty of less than 1%. Dose-volume constraints for both prostate and lung cases adhered to the clinical protocols of our institution.

2.2 |. Data preprocessing

First, the CT scans, structure sets, and dose DICOM files computed by VPMC (considered to be the ground truth dose distributions) for each patient were extracted and converted into 3D matrices. These 3D matrices were first resampled to a 2.5 mm grid from their original resolution, and subsequently rigidly aligned to a reference case chosen for the corresponding site to ensure data consistency. We normalized the CT HU number and the dose matrices to have a mean value of 0 and a variance of 1. A bounding box of dimensions 350 × 450 × 550, centered on the target, was used to crop the images, ensuring that all regions potentially impacting the dose distribution were included in the model training for all data. Zero padding was used in instances where the processed matrices’ dimension was smaller than the cropping box.

Next, we generated a 3D binary bitmask for each ROI, designating a value of 1 for voxels within the contour and 0 for those outside. For prostate cases, ROIs comprised CTV, bladder, spaceOAR, left/right femoral head, penile bulb, and rectum. For lung cases, they included CTV, spinal cord, spinal cord prv, esophagus, heart, and total lung. Therefore, after preprocessing, each patient’s aligned and cropped data was represented by CT matrices, contour mask matrices, and dose matrices.

2.3 |. Generation of noisy probing dose

Given the substantial impact of beam configurations on dose distributions in PBSPT, we proposed the noisy dose probing method to enhance the physics awareness of the AI model. First, a so-called spot-placement target volume (STV) was generated, as is typical for proton therapy treatment planning at our clinic. The STV is formed by a uniform expansion of planning target volume (PTV) for initial spot arrangement to allow for at least one spot outside the PTV. Next, spots were placed throughout the STV, layer by layer, with a constant spot spacing of 5 mm. With each spot weight set to 1, the probing dose is calculated using a low number of protons with VPMC. Since multiple scenarios are not needed and a low number of protons are used (1/1000 of the number of protons commonly used for conventional influence matrix calculation), the probing dose can be generated with a substantially reduced computational cost, while introducing only negligible additional memory overhead compared to calculating the dose influence matrix in conventional treatment planning. The selection of this 1/1000 ratio represents a strategic trade-off between computational efficiency and the preservation of structural physical priors; it is intended to ensure sufficient beam path connectivity for the network to extract essential dosimetric features while maintaining a fast simulation speed suitable for adaptive workflows.

2.4 |. Framework of the model and model training

Our chosen model framework was a fully integrated 3D U-Net, capable of handling multichannels of 3D matrix input. The network architecture utilizes 3×3×3 convolutional kernels throughout. The number of filters starts at 64 in the first layer and doubles at each down-sampling step, reaching 512 at the bottleneck, with a symmetric decoder path that halves the filters at each up-sampling level. These 3D input matrices were composed of the pre-processed CT matrices, contour bitmask matrices, and noisy probing dose matrices. Their combination varied based on the applied training strategy. The model’s objective was to generate a 3D dose matrix output aligned with the ground-truth dose matrix. In terms of clinical trials and implementation, this trained model can be integrated into our in-house TPS, Shiva,^10,11 to evaluate the predicted planning dose and facilitate potential replanning, as illustrated in Figure 1. The model training was conducted using the Smooth L1 loss function,^49,50 and the Adam optimizer with an initial learning rate of 1×10⁻⁴. To ensure repeatability and technical reproducibility, all model training and evaluations were implemented using fixed random seeds for weight initialization and data shuffling. To ensure a fair comparison, identical network architectures and hyperparameters were applied to all baseline models. Furthermore, the model’s robustness was validated against independent datasets and uncommon clinical scenarios (e.g., different beam configurations and prescriptions) to ensure consistent performance across varying clinical protocols. Detailed training procedures, including optimization strategies and data augmentation techniques, are provided in the Appendix Method S1 and Table A1.

FIGURE 1.

Workflow of proposed plan dose generation. (a) AI workflow with probing dose (bottom) compared to the traditional workflow with influence matrix and inverse optimization (top). (b) Diagram of noisy probing dose facilitated AI-based dose prediction for pencil beam scanning proton therapy.

2.5 |. Ablation study

To assess the impact of each component of the proposed strategies, three experiments were designed. Experiment 1 utilized CT images and contour bitmasks as input channels for model training as used in the conventional ROI-based method. Experiment 2 adds the beam mask and sliding window technique to the CT images and contour bitmasks from Experiment 1. The 3D beam masks were created using raytracing, and the sliding window approach, which randomly masks out a cube of 3 × 3 × 3 voxels for each batch during training, prompts the model to focus on improving fine details in subsequent batches, ultimately enhancing the overall dose prediction precision across the dataset.^27,45 Experiment 3 added the noisy probing dose technique to the model training, besides the methods used in Experiment 2 defined as the noisy probing dose method. A set of 10 prostate cancer and 10 lung cancer cases were used to evaluate the performance of each experiment. The ablation study allows for measuring the improvement in dose prediction versus the method used.

In assessing the accuracy of the dose prediction, three distinct evaluation metrics were employed. Firstly, DVH indices were used which include D2 and D98 for the CTV, mean dose (Dmean) for bladder, spaceOAR, femoral heads, penile bulb, rectum, esophagus, heart, and total lung, and maximum dose (Dmax) for spinal cord, spinal cord prv. Next, we employed the global 3D Gamma passing rate with a criterion of 3%/2 mm/10% to demonstrate the 3D spatial dose distribution consistency between the predicted dose and the ground-truth dose in targets, ROI, and BODY (outside all ROIs), respectively. Lastly, we evaluated the 3D spatial dose distribution consistency through the Dice coefficients of the volumes enclosed by the iso-dose lines (with dose values ranging from 10% to 90% of the prescription dose with an increment of 10%) between the predicted and the ground truth dose distributions.

2.6 |. Uncommon cases test

To further assess the model’s generalizability, we selectively identified six uncommon prostate and lung clinical cases that were not included in the training data, consisting of two plans with different dose prescriptions not included in the model training data, two plans with different beam numbers and angles not included in the model training data, and two plans with different prescriptions and beam configurations. For each case, predicted dose distributions were generated using the models from three experiments, and the Gamma passing rates (3%/2 mm/10%) were calculated relative to the ground truth dose distributions in the target, OARs, and BODY regions.

3 |. RESULTS

3.1 |. Dose distribution comparison

Figure 2a and 2c provide a graphical representation of the truth and predicted dose distributions derived from each of the three experiments. The figure further illustrates the differences in dose distribution within the respective planes between the predicted and the ground truth dose for the example patients.

FIGURE 2.

Comparisons of the predicted dose distributions as derived from three distinct experiments juxtaposed against the ground truth doses. (a) An example prostate case in the axial plane. (b) The DVH of an example prostate case. (c) An example lung case in the sagittal plane. (d) The DVH of an example lung case. Solid line: ground-truth dose; dash line: predicted dose from Experiment 1, dash dot line: predicted dose from Experiment 2; dot line: predicted dose from Experiment 3.

3.2 |. DVH comparison

Figure 2b and 2d indicate an improved accuracy in dose prediction when the beam mask and sliding window model was employed relative to the ROI model, with further enhancement observed when the noisy probing dose model was used, as compared to the beam mask and sliding window method.

All DVH metrics in Experiment 3 achieved the most favorable results for the CTV and OAR regions in both prostate and lung cancer patients (Figure 3a and Table 1). The absolute deviations of CTV D98 was 0.34 ± 0.12 Gy [RBE] for lung cancer patients and 0.29 ± 0.06 Gy [RBE] for prostate cancer patients. Meanwhile, the CTV D2 values were 0.49 ± 0.44 Gy [RBE] and 0.47 ± 0.25 Gy [RBE].

FIGURE 3.

(a) Boxplot (depicting the minimum, first quartile, median, third quartile, and maximum values) showcasing the absolute divergence of the DVH indices for targets and OARs between the ground truth and predicted doses from three distinct experiments for prostate and lung test cases. In the diagram, experiment 1, experiment 2, and experiment 3 are represented by colors red, blue, and green, respectively. (b) 3D gamma passing rates (3%/2 mm/10%) within targets, OARs, and the BODY (targets and OARs excluded) for prostate and lung test cases, with 10 cases from each testing group represented by green circles. The dotted lines in the figure symbolize the trend of the average value for all the test cases within each respective group.

TABLE 1.

Detailed DVH indices for experiments 1 and 2, and experiment 3.

Location	Metric	Experiment 1 (Mean ± SD)	Experiment 2 (Mean ± SD)	Experiment 3 (Mean ± SD)
Lung	CTV D98	0.74 ± 0.18 Gy[RBE]	0.54 ± 0.19 Gy[RBE]	0.34 ± 0.12 Gy[RBE]
	CTV D2	0.94 ± 0.44 Gy[RBE]	0.62 ± 0.44 Gy[RBE]	0.49 ± 0.44 Gy[RBE]
	Esophagus Dmean	0.51 ± 0.30 Gy[RBE]	0.42 ± 0.22 Gy[RBE]	0.38 ± 0.28 Gy[RBE]
	Heart Dmean	0.48 ± 0.21 Gy[RBE]	0.48 ± 0.16 Gy[RBE]	0.41 ± 0.18 Gy[RBE]
	Lung_total Dmean	0.45 ± 0.21 Gy[RBE]	0.37 ± 0.17 Gy[RBE]	0.36 ± 0.21 Gy[RBE]
	SpinalCord Dmax	0.95 ± 0.19 Gy[RBE]	0.67 ± 0.13 Gy[RBE]	0.45 ± 0.18 Gy[RBE]
	SpinalCord PRV Dmax	1.20 ± 0.27 Gy[RBE]	0.94 ± 0.28 Gy[RBE]	0.68 ± 0.14 Gy[RBE]
Prostate	CTV D98	0.53 ± 0.22 Gy[RBE]	0.41 ± 0.28 Gy[RBE]	0.29 ± 0.06 Gy[RBE]
	CTV D2	0.81 ± 0.25 Gy[RBE]	0.60 ± 0.25 Gy[RBE]	0.47 ± 0.25 Gy[RBE]
	Bladder Dmean	0.30 ± 0.21 Gy[RBE]	0.28 ± 0.18 Gy[RBE]	0.27 ± 0.23 Gy[RBE]
	Femoral_head_L Dmean	0.45 ± 0.25 Gy[RBE]	0.32 ± 0.25 Gy[RBE]	0.31 ± 0.24 Gy[RBE]
	Femoral_head_R Dmean	0.47 ± 0.22 Gy[RBE]	0.33 ± 0.24 Gy[RBE]	0.31 ± 0.22 Gy[RBE]
	Penile_bulb Dmean	0.74 ± 0.30 Gy[RBE]	0.67 ± 0.32 Gy[RBE]	0.57 ± 0.33 Gy[RBE]
	Rectum Dmean	0.49 ± 0.31 Gy[RBE]	0.49 ± 0.33 Gy[RBE]	0.42 ± 0.23 Gy[RBE]
	SpaceOAR Dmean	0.51 ± 0.22 Gy[RBE]	0.36 ± 0.12 Gy[RBE]	0.19 ± 0.08 Gy[RBE]

Additionally, the absolute variations in Dmean and Dmax for OARs from the three experiments were all within the clinically acceptable limits. Experiment 2 reduced the Dmean absolute deviation by ~0.15 Gy[RBE] for most OARs compared to Experiment 1, with a further decrease of ~0.1 Gy[RBE] in Experiment 3. Similarly, the Dmax absolute deviations for the spinal cord and spinal cord PRV were also the lowest in Experiment 3. Using the noisy probing dose method, the improvements observed in Experiment 3 showed consistent trends with p < 0.05.

Specifically, the absolute deviations of Dmean for SpaceOAR—an implant utilized in prostate cancer patients treated with PBSPT for rectal protection—were further improved in Experiment 3 (0.19 ± 0.08 Gy [RBE]). This signifies that even in the presence of the implant (a non-human factor), the dose prediction accuracy remained commendable.

3.3 |. 3D gamma passing rates evaluation

Figure 3b demonstrates improved Gamma passing rates for targets, OARs, and BODY in Experiment 2 relative to Experiment 1, with a particularly marked improvement in BODY. In Experiment 3, the 3D Gamma passing rates exhibited an additional increment of approximately 1.7% for target volumes and an average improvement of 2.9% for OARs and BODY, compared to those observed in Experiment 2 (see Table 2). The 3D Gamma passing rate improvement showed consistent trends with p < 0.05 using noisy probing dose method.

TABLE 2.

3D gamma passing rates (3%/2 mm/10%) for experiments 1 and 2, and experiment 3.

Cohort	Location	Organ	Experiment 1 (Mean ± SD)	Experiment 2 (Mean ± SD)	Experiment 3 (Mean ± SD)
Common test cases	Lung	Targets	91.55% ± 1.27%	95.34% ± 1.17%	97.04% ± 1.17%
		OARs	88.78% ± 1.83%	93.02% ± 1.66%	95.92% ± 1.66%
		BODY	83.79% ± 1.01%	90.93% ± 1.29%	93.83% ± 1.29%
	Prostate	Targets	95.03% ± 1.18%	97.95% ± 1.15%	99.65% ± 1.15%
		OARs	91.15% ± 1.53%	95.01% ± 1.21%	97.91% ± 1.21%
		BODY	84.81% ± 1.36%	92.75% ± 1.40%	95.65% ± 1.40%
Uncommon test cases	Lung	Targets	85.93% ± 2.01%	90.08% ± 1.34%	93.38% ± 1.34%
		OARs	83.42% ± 1.76%	89.45% ± 1.32%	93.95% ± 1.32%
		BODY	77.49% ± 1.05%	86.53% ± 1.32%.	91.03% ± 1.32%
	Prostate	Targets	89.32% ± 1.45%	93.48% ± 1.51%	96.78% ± 1.51%
		OARs	85.87% ± 1.73%	91.15% ± 1.13%	95.65% ± 1.13%
		BODY	79.19% ± 2.03%	88.71% ± 1.12%	93.21% ± 1.12%

3.4 |. Dice coefficient evaluation

Appendix Figure A1 shows a progressive enhancement in average Dice coefficients across isodose lines from Experiment 1 to Experiment 3. While modest enhancements were noted in the high-percentage isodose lines, with Dice scores of 0.983 ± 0.005 for prostate and 0.967 ± 0.015 for lung, more pronounced improvements were observed in the lower-percentage isodose lines, achieving Dice scores of 0.957 ± 0.019 for prostate and 0.945 ± 0.021 for lung (see Appendix Table A2).

3.5 |. Uncommon cases test

Figure 4 displays the 3D Gamma passing rates for prostate and lung cancer uncommon cases that exhibit beam settings and dose prescriptions distinct from the training data. Experiment 2 showed superior 3D Gamma passing rates for targets, OARs, and BODY. Notedly, Gamma pass rates in Experiment 3 showed a further improvement of approximately 3.3% for targets and an average increase of 4.5% for OARs and BODY, compared to Experiment 2 (see Table 2). The improvement showed consistent trends for all uncommon cases with p < 0.05 using noisy probing dose method.

FIGURE 4.

3D Gamma passing rates (3%/2 mm/10%) within targets, OARs, and the BODY (outside ROI) for prostate and lung uncommon test cases, with 6 cases from each site represented by green circles. The dotted lines in the figure symbolize the trend of the average value for all the test cases within each respective group.

4 |. DISCUSSION

In this study, we investigated the utilization of the noisy probing dose method for dose prediction in PBSPT by comparing it with the conventional ROI-based method and the recently proposed beam mask and sliding window method. The noisy probing dose method demonstrated notable improvements in DVH index accuracy, including both D2, D98 for targets and Dmean and Dmax for OARs.

We evaluated the spatial agreement between the predicted and ground truth doses using 3D Gamma analysis and Dice coefficients. While many studies prioritize dose agreement within the ROI only, we emphasized accuracy in targets, OARs, and the BODY (outside ROI). Our novel noisy probing dose method surpassed the previously reported methods, especially outside the ROI. The consistent isodose volumes enclosed by different percentages of the prescription dose highlight its superior dose prediction both inside and outside the ROI, demonstrating a holistic grasp of the entire dose gradient.

AI models, including dose prediction, can fail or underperform clinically due to outlier cases not represented in their training dataset, like patients with uncommon beam configurations or dose prescriptions. This issue has not been fully addressed in the previous literature.^{32–35,37,38,43–46} In this study we used six outlier cases each with uncommon beam setups and/or prescription doses not existing in the model training dataset, to further test the performance of the proposed noisy probing dose model. The results indicate that when dealing with outlier cases, the 3D Gamma passing rates obtained by the conventional ROI-based method are much lower than the commonly used Gamma passing thresholds in clinics, as these models often struggle with the complex interplay between unseen beam configurations and anatomical heterogeneities. On the other hand, the Gamma passing rates obtained by the proposed noisy probing dose model approached or exceeded the commonly referenced Gamma passing thresholds of 95% for routine clinics in both target and OAR regions. Notably, for challenging lung outliers cases where the Gamma passing rate was 93.38%, the absolute dosimetric deviations remained comparatively low (e.g., CTV D98 error of 0.34 ± 0.12 Gy[RBE] as shown in Table 1, which is well within strict clinical tolerances. This suggests that the proposed model is robust in handling uncommon clinical scenarios, providing dose distributions that are either directly usable or require only minor fine-tuning optimization, effectively bridging the gap between AI prediction and clinical implementation.⁵¹ This can be explained by the fact that the noisy probing dose model carries more physics information, allowing the model to learn more knowledge about the physics interaction between protons and the medium in proton dose calculation, such as dose falloff. This implies that the model can be more generalizable than the previous methods, exhibiting robust performance even when handling outlier clinical cases.

Our 3D U-Net is designed as a multi-modal integrator rather than a denoising network. Although the probing dose provides a strong dosimetric prior, it is calculated using unit spot weights and therefore does not encode clinical optimization objectives such as dose uniformity or OAR sparing. The CT, CTV and ROI masks supply essential physical and clinical constraints: the CT images provide a high-fidelity electron density reference to mitigate proton range uncertainties,⁵² while the CTV and OAR masks explicitly define prescription levels and spatial boundary conditions for dose normalization and gradient formation.⁵³ The probing dose serves as an additional physics-informed structural prior encoding beam path geometry, Bragg peak depth, and lateral dose falloff, whose incremental contribution is directly demonstrated by the statistically significant performance gains observed relative to the ROI-based baseline across all evaluation metrics, and further validated by its superior generalizability in uncommon clinical scenarios. To systematically evaluate the impact of probing dose sampling rate on model performance, we conducted experiments across four sampling conditions (1/10, 1/100, 1/1000, and 1/10 000). The results (Appendix Table A3) show that the model performance remained relatively stable from 1/10 to 1/1000, with a mean Gamma passing rate decrease of less than 1.5% for targets. A more pronounced degradation was observed at 1/10 000, particularly for lung targets, accompanied by increased inter-case variability.

For a long time, AI-based dose prediction methods, especially those directly predicting doses based on the ROI, have been considered as non-physics methods, raising concerns about their generalizability.²⁹ This leads to two concerns: the accuracy of the dose prediction results for high-precision irradiation techniques such as PBSPT, and their ability to generalize dose predictions, that is, the extent to which the model can understand and predict dose distributions accurately for some outlier clinical cases. Current research attempts to enhance the model’s accuracy and robustness by including different parameters like beam angle.^43–46 However, considering the multitude of physical parameters influencing the final dose, it’s impractical to include all of them in the model training. Moreover, adding more parameters into the model training significantly increases the model complexity, making it challenging for effective clinical deployment and resulting in possible overfitting. Our proposed noisy probing dose method took inspiration from the conventional influence matrix concept used in dose calculation and optimization. We used a noisy probing dose to represent all the physics information required by the AI-based methods, such as beam angles and dose falloff, and so forth. As Figure 1 shows, we’ve established an AI-based dose prediction workflow centered around the noisy probing dose concept.

Our results have demonstrated that the proposed noisy probing dose method can make accurate dose predictions in prostate and lung cancer patients treated with PBSPT. More importantly, the noisy probing dose method can make clinically acceptable and accurate dose predictions for uncommon clinical cases, showcasing its excellent generalizability capability stemming from the underlining physics. The results also indicate the vital role of incorporating physics to train an AI model for accurate dose predictions, particularly for improving the model’s generalizability to handle outlier cases. Additionally, compared to these two findings, our model is notable for its technical feasibility, balancing precision with ease of implementation. Drawing upon the concept and calculations of the influence matrix from traditional radiotherapy treatment planning, we employed a noisy non-modulated dose as the probing dose. This approach fully harnesses the analytical prowess of AI. While this method imbues the model with robust inherent physics logic, it also simplifies its practical application in routine clinical settings.

Despite the promising results, this study has certain limitations. First, the current model was trained on plans utilizing a specific optimization strategy (i.e., SFO). However, since the non-optimized physics-informed input (the noisy probing dose) captures the fundamental energy deposition patterns that remain invariant regardless of the optimization objectives, we expect this foundation to be extendable to broader treatment planning strategies and beam delivery techniques. To adapt the model to other centers, the probing dose generation would simply require calibration to the local beam model. Future work will involve multi-center cohorts to further evaluate the model’s scalability across diverse institutional protocols and clinical preferences. Furthermore, while a batch size of 2 was necessitated by the substantial memory footprint of high-resolution 3D tensors on our current hardware, future work will utilize multi-node distributed training to explore the potential benefits of larger batch sizes on optimization dynamics. Additionally, future research will incorporate multi-seed statistical evaluations to further characterize the framework’s numerical stability and repeatability.

5 |. CONCLUSION

In conclusion, we have developed a highly accurate PBSPT dose prediction method and have tested it in prostate and lung cancer patients based on a novel concept of noisy probing dose. This method can not only make accurate dose prediction both within and outside the ROI, but it also provides clinically acceptable dose prediction for outlier clinical cases. With more physics information included, the proposed noisy probing dose method enhances the accuracy of dose prediction for PBSPT, endowing them with excellent generalizability. It also strikes a balance between maximal accuracy and limited complexity, making it ready to be implemented clinically.

Supplementary Material

SUPPORTING INFORMATION

Additional supporting information can be found online in the Supporting Information section at the end of this article.

DATA AVAILABILITY STATEMENT

The data are available from the corresponding author upon reasonable request.