Improving dual‐panel in‐beam PET imaging for proton therapy monitoring using 3D U‐Net

Abstract

Background

In‐beam positron emission tomography (PET) integrates dedicated detectors into proton therapy systems, enabling real‐time acquisition of proton‐induced positron‐emitting activity. By pre‐delivering a subset of single‐energy proton spots as probes, in‐beam PET has the potential to support online proton range verification and may inform subsequent spot delivery. However, the limited acquisition time and low yields of positron emitters result in noisy reconstructed images, and the open geometry of dual‐panel PET further introduces stretching artifacts.

Purpose

To address these issues, this study proposed a 3D U‐Net‐based post‐processing method to enhance in‐beam PET image quality and evaluated its feasibility through Monte Carlo simulations and preliminary experimental validation.

Methods

Thirteen head computed tomography (CT) phantoms were irradiated with horizontally and vertically incident single‐energy probes, representing two scenarios in which beams passed through relatively homogeneous and heterogeneous tissues. A phantom‐level split was used, with seven CT phantoms for training, two for validation, and four held‐out CT phantoms for testing. Proton probes in 3×3, 5×5, 7×7, and 9×9 spot patterns were simulated, with each spot delivering 2×10⁷ protons. In‐beam PET acquisition was performed for 30 s. Unfiltered reconstructed PET images were used as network inputs, and ground‐truth activity distributions served as labels. Gaussian‐filtered PET images served as the baseline for performance evaluation. Image quality was quantified by peak signal‐to‐noise ratio (PSNR) and structural similarity index (SSIM), and proton range verification accuracy was evaluated by absolute range error (ARE). Additional simulations with CT density perturbations were conducted to evaluate sensitivity to proton range shifts. Preliminary experimental validation was performed using an all‐digital PET prototype and polymethyl methacrylate (PMMA) phantoms.

Results

For horizontal beams, median PSNR values increased from 21.4–23.9 to 35.2–37.4, median SSIM values increased from 0.450–0.621 to 0.906–0.961, and median ARE values decreased from 1.05–1.18 mm to 0.52–0.73 mm. For vertical beams, median PSNR values improved from 21.9–23.2 to 29.2–34.1, median SSIM values improved from 0.480–0.560 to 0.745–0.895, and median ARE values decreased from 1.80–2.40 mm to 1.50–1.73 mm. The proposed method also demonstrated improved sensitivity to simulated range shifts and consistent improvements on experimental PET data.

Conclusion

These findings demonstrate the preliminary feasibility of using 3D U‐Net‐based post‐processing to enhance dual‐panel in‐beam PET image quality and improve PET‐based proton range verification.

1. INTRODUCTION

Proton therapy offers superior dose conformity by depositing the highest radiation dose within the Bragg peak, thereby enabling precise tumor targeting while sparing surrounding healthy tissues. ¹ However, the steep dose gradients near the Bragg peak make proton therapy highly sensitive to range uncertainties, particularly when critical structures lie distal to the target volume. ² Consequently, in vivo proton range verification is crucial to ensure treatment safety and guide beam delivery. ³

Among the noninvasive techniques for in vivo range verification, positron emission tomography (PET) is well established, relying on the detection of proton‐induced positron‐emitting activity. ⁴ Proton range can be verified by comparing the PET‐measured activity distribution with a reference activity distribution obtained according to the treatment plan using Monte Carlo simulation ⁵ or analytical algorithms. ⁶ Based on scanner positioning relative to the treatment system, PET monitoring in proton therapy can be categorized as in‐beam, ⁷ in‐room, ⁸ or offline. ⁹ Among these, in‐beam PET is considered the most promising, as it integrates detectors directly into the treatment system to measure activity during or immediately after irradiation. This configuration maximizes the detection of short‐lived positron emitters and eliminates the need for patient repositioning as well as minimizes biological washout effects. ¹⁰ , ¹¹ , ¹² To accommodate beam passage and patient treatment couch movement, in‐beam PET systems typically employ open geometries, such as partial‐ring PET, ¹³ dual‐head PET, ¹⁴ , ¹⁵ , ¹⁶ , ¹⁷ , ¹⁸ OpenPET, ¹⁹ , ²⁰ and multi‐layer plastic scintillators Jagiellonian PET. ²¹ The dual‐head design has been most extensively studied and clinically tested due to its relative ease of construction and integration.

In‐beam PET has been investigated for online verification ¹² , ¹⁵ , ²² , ²³ , ²⁴ , ²⁵ and may have potential relevance to adaptive proton therapy workflows in which partial spot delivery is monitored within a treatment session. ²⁶ , ²⁷ , ²⁸ , ²⁹ Nevertheless, its image quality remains limited by two major factors. First, the short acquisition time and inherently low yields of positron emitters result in poor counting statistics and noisy reconstructed images. Second, the open scanner geometry causes incomplete angular sampling, producing stretching reconstruction artifacts. Time‐of‐flight (TOF) information can mitigate noise and artifacts, but improvements are constrained by the current system‐level TOF resolution of ∼200 ps. While further advances of TOF resolution are theoretically possible, they remain technologically challenging and costly. ³⁰ Alternative approaches using statistical iterative reconstruction with prior‐based regularization, such as maximum‐a‐posteriori reconstruction incorporating total variation ³¹ or median‐root prior, ³² have shown promise but face challenges in optimizing data‐dependent regularization parameters. ³³

Recently, deep learning has emerged as a powerful tool for PET image enhancement, particularly in low‐dose denoising. ³⁴ , ³⁵ Early pioneering studies demonstrated that deep learning can achieve comparable image quality using as little as 0.5% of standard ¹⁸F‐FDG activity. ³⁶ Beyond image denoising, deep learning has been successfully applied to correct spatially variant deformations in dual‐panel breast PET reconstructions, where U‐Net significantly reduced stretching artifacts and improved quantitative performance. ³⁷ This suggests the potential for addressing the challenges of dual‐panel in‐beam PET. Specifically, U‐Net's encoder‐decoder structure with skip connections has the potential to simultaneously mitigate noise from poor counting statistics and correct for the spatially variant stretching artifacts inherent to the limited angular sampling. Moreover, contextual information across adjacent slices might help restore the complex activity distributions generated by proton beams in tissues. In fact, in proton therapy monitoring, Sano et al. ³⁸ employed a residual U‐Net to denoise 2D PET images reconstructed by back‐projection at the detector mid‐plane. Although their approach did not account for the full 3D spatial distribution of proton‐induced positron‐emitting activity, it confirmed the potential of deep learning for improving in‐beam PET image quality and range verification accuracy.

This study proposed and evaluated a 3D U‐Net‐based post‐processing method to simultaneously reduce noise and mitigate artifacts in dual‐panel in‐beam PET reconstructions. To support the development of PET‐based online range verification, with potential relevance to adaptive proton therapy, we focused on PET monitoring of single‐energy proton beams. Through comprehensive Monte Carlo simulations, we assessed the proposed method's performance in terms of both image quality and proton range verification accuracy across relatively homogeneous and heterogeneous anatomical scenarios. Furthermore, preliminary experimental validation using an all‐digital PET prototype was conducted to assess the feasibility of the proposed approach under experimental measurement conditions.

2. MATERIALS AND METHODS

2.1. Proton spot irradiation and in‐beam PET imaging

In pencil beam spot scanning proton therapy, a treatment plan consists of multiple energy layers, each containing spots delivered at the same beam energy. Motivated by possible future PET‐based online range verification workflows, this study considered a simplified scenario in which a subset of single‐energy spots is delivered as probe irradiations, followed by in‐beam PET data acquisition. Any use of the PET‐derived range information to modify subsequent delivery would require a dedicated treatment‐plan‐based adaptive framework. The present study did not implement treatment‐plan adaptation, spot‐weight correction, dose recalculation, treatment‐plan re‐optimization, beam‐control integration, or decision thresholds for adaptive intervention. Instead, this study focused on evaluating whether the proposed 3D U‐Net‐based post‐processing method can improve dual‐panel in‐beam PET image quality and PET‐based range verification accuracy.

Thirteen head computed tomography (CT) images were used as digital phantoms and irradiated with horizontally and vertically incident single‐energy probes, representing two scenarios with beams passing through relatively homogeneous and heterogeneous tissues. For each orientation, proton probes were simulated in 3×3, 5×5, 7×7, and 9×9 spot patterns, with a spacing of 5.0 mm. Each spot delivered 2×10⁷ protons, resulting in a maximum probe dose of less than 0.5 Gy. Proton energies ranged from 80.5 MeV to 131.6 MeV with 25 discrete energy levels. For each CT phantom and each discrete proton energy, single‐energy spot probes were delivered from randomly selected incident positions. Probes that exited the CT phantom, were close to the CT boundary, or lacked a complete distal fall‐off within the CT volume were excluded during post‐processing. Consequently, the retained samples covered all 25 proton energy levels but were not uniformly distributed across energy bins. The largest difference between the most and least populated bins, expressed as a percentage of the average bin count, was 19%, 25%, 31%, and 55% for the 3×3, 5×5, 7×7, and 9×9 spot patterns, respectively. Spot sizes were modeled as a single Gaussian distribution with a standard deviation varying from 4.65 to 3.31 mm, decreasing with increasing proton energy. Energy straggling was modeled as a Gaussian distribution with a standard deviation of 0.3%. The representative dose distributions for the 3×3 and 9×9 spot patterns are shown in Figure 1a,b, respectively.

FIGURE 1.

Representative dose distributions of single‐energy proton probes irradiating a CT phantom in horizontal and vertical orientations. (a) Dose distribution from a probe consisting of 3×3 spots. (b) Dose distribution from a probe consisting of 9×9 spots.

PET imaging was simulated with a dual‐panel in‐beam PET scanner modeled based on compact digital PET detectors. ³⁹ The scanner consisted of two parallel detector panels with adjustable spacing. In this study, the spacing was fixed at 40 cm to match human head dimensions. Each panel contained 16×10 detector modules, with each module comprising a 6×6 array of 3.9×3.9×20 mm³ LYSO scintillators. The scanner provided an effective detection area of approximately 40.8×25.5 cm², and a TOF resolution of 249 ps.

For Monte Carlo simulations, tissue compositions were derived from CT Hounsfield units. Proton‐induced positron‐emitting activity distributions were calculated using the filtering method proposed by Parodi and Bortfeld. ⁴⁰ The isotopes considered in this study included ¹⁰C, ¹¹C, ¹³N, ¹⁴O, ¹⁵O, ¹⁷F, ³⁸K, and ³⁰P. The distributions of these isotopes were summed to form a total activity distribution, which served as the radioactive source for in‐beam PET simulations performed in GATE. Although longer PET acquisition times capture more positron‐emitting signals, shorter times are preferable for online dose verification. Therefore, the acquisition time was set to 30 seconds in this study. In GATE, an energy window of 425–650 keV and a coincidence time window of 2.0 ns were applied to generate coincidence events. The output was converted into list‐mode data containing TOF information and reconstructed using the TOF list‐mode maximum likelihood expectation maximization (MLEM) algorithm with 10 iterations. The system response matrix was computed on the fly using the Siddon algorithm accelerated by a graphics processing unit (GPU). Attenuation corrections were conducted based on the CT images. The reconstructed PET images had a matrix size of 96×120×80 voxels with dimensions of 2.35×2.35×2.35 mm³. No post‐reconstruction Gaussian smoothing was applied before the reconstructed images were used as inputs to the 3D U‐Net. For baseline evaluation, Gaussian‐filtered PET images were generated separately by applying a Gaussian filter with a standard deviation of 3.0 mm to the reconstructed PET images.

2.2. Calculation of activity range

Dose and activity intensity diminish near the lateral edges of the proton beam, reducing the reliability of range verification. Considering this spatial dependency, a selective processing approach was implemented. For each probe, the 3D dose distribution was normalized to its maximum value, and depth‐dose curves were extracted along the beam axis at different lateral positions. Range verification was performed only for curves whose maximum dose exceeded a threshold of 0.25. Figure 2a shows a slice of the 3D dose distribution for a 9×9 spot probe, together with depth‐dose curves at three representative positions (P1, P2, P3). Figure 2b presents the corresponding positron‐emitting activity distribution and depth‐activity curves. For P1 and P2, where the maximum dose exceeded the 0.25 threshold, PET‐based range verification was performed. In contrast, verification was omitted for P3 due to its sub‐threshold maximum dose.

FIGURE 2.

Schematic of the data processing procedure for extracting depth‐activity curves and calculating the activity range. (a) Transverse slice of the dose distribution and depth‐dose curves extracted along the proton beam direction. (b) Corresponding slice of the activity distribution and depth‐activity curves extracted along the beam direction. (c) Calculation of the activity range, defined as the average depth of multiple points on the distal falling edge of the normalized depth‐activity curve.

To calculate the activity range, each depth‐activity curve was individually normalized using the following formula:

$$y=\frac{y}{{\sum }_{i=1}^M\left(y_i\right)}\times N,N=\left|\left\{y_i\in y|y_i>\max (y)\times 0.3\right\}\right|$$ (1)

where y represents the depth‐activity vector of length M, and N denotes the number of elements in y that exceed 30% of its maximum value. This normalization approach is more robust than using the maximum value alone. The activity range was then defined as the average depth of multiple points along the distal fall‐off of the normalized depth‐activity curve. These points corresponded to activity intensity ranging from 0.3 to 0.7 in increments of 0.05, as illustrated in Figure 2c. Using the multi‐point average improved reliability compared to using a single depth point.

2.3. Neural network architecture and training

The U‐Net architecture has gained significant popularity across various domains due to its robust encoder‐decoder structure. In this study, we employed a four‐stage 3D U‐Net for PET image post‐processing. The unfiltered reconstructed PET images were used as inputs, and the positron‐emitting activity distributions were used as labels. As shown in Figure 3, the 3D U‐Net consists of a left‐side encoder and a right‐side decoder. Each stage of the encoder and decoder contains two 3×3×3 convolutional layers, each followed by group normalization (GN) and a rectified linear unit (ReLU) activation function. The encoder incorporates a 2×2×2 max‐pooling operation with a stride of two for downsampling, while the decoder uses transposed convolution for upsampling. Skip connections link corresponding encoder and decoder stages. At the final decoder layer, a 1×1×1 convolution followed by a ReLU generates the output.

FIGURE 3.

Architecture of the 3D U‐Net used in this study.

To balance overall image quality and localization accuracy of the distal fall‐off of the activity distribution, a hybrid loss function was used, defined as follows:

$$\mathrm{Loss}=L_1(\mathrm{image})+10\times L_1(\mathrm{RO}{\mathrm{I}}_1)+20\times L_1(\mathrm{RO}{\mathrm{I}}_2)$$ (2)

where L₁ (image) denotes the voxel‐wise L1 distance between the true and predicted images, while L ₁(ROI₁) and L ₁(ROI₂) represent voxel‐wise L1 distances within specific regions of interest (ROIs). ROI₁ comprises voxels within the depth‐activity curves used for range verification. ROI₂ is a subset of ROI₁, restricted to voxels between the distal starting and ending positions. As illustrated in Figure 2c, the distal starting and ending positions are defined as the activity range minus and plus five voxels, respectively.

The model development dataset consisted of nine CT phantoms, of which seven phantoms were used for training and two phantoms were used for validation. For each beam orientation, 3200, 2500, 1800, and 1300 probes with 3×3, 5×5, 7×7, and 9×9 spot patterns, respectively, were generated for training. In the validation dataset, 800, 625, 450, and 325 probes were generated for the corresponding spot patterns. Each probe corresponds to a single 3D PET volume. Two separate models were trained for different beam orientations. The models were implemented in PyTorch and trained on an NVIDIA A100 GPU. Training used the Adam optimizer with a batch size of 12. The learning rate was initially set to 2×10⁻⁴ and linearly decreased to 2×10⁻⁵ over 300 epochs. The model with the lowest validation loss was selected for testing.

2.4. Performance evaluation

Model performance was assessed using the four held‐out head CT phantoms, which were not involved in any stage of model development. For each beam orientation, 1600, 1300, 900, and 650 probes with 3×3, 5×5, 7×7, and 9×9 spot patterns, respectively, were generated for the held‐out test dataset. The performance of the 3D U‐Net‐based PET image post‐processing was evaluated from two perspectives. First, the peak signal‐to‐noise ratio (PSNR) and structural similarity index (SSIM) were employed to evaluate the similarity between the PET images and the positron‐emitting activity distributions. To ensure that the SSIM assessment reflects the quality of the signal region without interference from near‐zero background, we employed a masked SSIM approach. Specifically, we used 1% of the maximum voxel value to extract the smallest bounding box around the target region, computed the SSIM map, and then averaged only over the masked voxels. Second, the accuracy of range verification was assessed using the absolute range error (ARE), defined as the absolute difference between the PET imaging activity range and the true positron‐emitting activity range. All reported baseline PSNR, SSIM, and ARE values correspond to the Gaussian‐filtered PET images, whereas all reported values for the proposed method correspond to the U‐Net‐predicted PET images.

2.5. Evaluation of range shift sensitivity

In the simulation framework, proton probes irradiated different regions of the CT phantoms with varying beam energies, which inherently resulted in different proton ranges. To further evaluate the capability of the proposed method to detect proton range deviations, additional simulations were conducted by introducing density perturbations into the CT phantoms. Specifically, the density of soft tissue was modified by −5% and +5% to simulate proton range uncertainties caused by stopping power estimation errors. For these simulations, the CT phantoms with density perturbations were irradiated using the same probe locations and energies as those in the held‐out test dataset, enabling direct comparison between nominal and perturbed conditions. To balance experimental scope and computational cost, three representative proton beam energies (90.6, 108.4, and 124.2 MeV) were selected for the range shift evaluation. To quantify the sensitivity of the proposed method to range deviations, a linear regression model was used to fit the imaging activity range shift as a function of the true activity range shift. The coefficient of determination (R ²) and root mean square error (RMSE) were used as metrics to evaluate fitting accuracy.

2.6. Preliminary experimental validation

The U‐Net model trained on the simulated datasets for horizontally incident probes was applied to enhance experimentally reconstructed PET images. The experiment was conducted using a ProBeam360°proton therapy system and an all‐digital PET prototype. The PET prototype has the same detector module structure as the dual‐panel in‐beam PET modeled in the simulation. The prototype consists of 12 detector panels arranged in a circular geometry with a diameter of 30 cm, as illustrated in Figure 4a. Each detector panel comprises 2×12 detector modules, resulting in an overall panel size of approximately 51×306 mm². In the simulation, the dual‐panel in‐beam PET provides a detection coverage angle of approximately 64 degrees, as shown in Figure 4c. To maintain a comparable detection coverage in the experiment, only a subset of detector modules was used for data acquisition, resulting in an effective coverage angle of approximately 60 degrees, as illustrated in Figure 4b. In the experiment, 120 MeV proton beams were delivered to polymethyl methacrylate (PMMA) phantoms using spot patterns of 3×3, 5×5, 7×7, and 9×9. The PMMA phantom had dimensions of 6×6×15 cm³ and a density of 1.18 g/cm³. For each irradiation, the monitor unit (MU) per spot was set to 1000, resulting in a higher delivered dose than that used in the simulations. To achieve comparable statistical noise levels between experimental and simulated PET images, coincidence events were randomly sampled from the experimental list‐mode data. Specifically, 4000, 11,000, 22,000, and 36,000 coincidence events were sampled for the 3×3, 5×5, 7×7, and 9×9 spot patterns, respectively. This sampling strategy ensured that the statistical uncertainty in the experimental PET activity distributions was approximately equivalent to that obtained from Monte Carlo simulations. The random sampling procedure was repeated 100 times to generate multiple independent realizations of the PET data, enabling a robust statistical evaluation of the proposed method. Given that the elemental composition and density of PMMA phantoms are known, the positron activity distribution generated via Monte Carlo simulation served as the reference activity distribution for quantitative evaluation.

FIGURE 4.

(a) Photograph of the all‐digital PET prototype. (b) Transverse view of the PET prototype with the detector modules used for data acquisition highlighted in red. (c) Transverse view of the dual‐panel in‐beam PET simulated in this study.

3. RESULTS

3.1. Evaluation of PET reconstructed image quality

Figures 5 and 6 show representative examples of the true activity distributions, Gaussian‐filtered PET images, and predicted PET images for horizontal and vertical beam irradiation of CT phantoms. For horizontal beams, most probes traversed the relatively homogeneous brain region, producing uniform distributions of proton‐induced positron‐emitting activity. In contrast, vertical probes passed through the heterogeneous nasopharynx, resulting in more complex activity distributions. Due to the ill‐posed nature of PET reconstruction and limited coincidence event statistics, the Gaussian‐filtered PET images exhibited a blotchy appearance and noticeable noise. Stretching artifacts also appeared in slices perpendicular to the PET detector panels because of limited angular sampling, obscuring low‐activity regions within cavities. By comparison, the PET images predicted by the 3D U‐Net were more consistent with the true activity distributions, with noise and artifacts substantially suppressed.

FIGURE 5.

Representative examples of true activity distributions, Gaussian‐filtered PET images, and predicted PET images for horizontal beam irradiation of CT phantoms with 9×9 and 3×3 spot probes. White dashed lines in the true activity distribution indicate the positions where activity curves were extracted.

FIGURE 6.

Representative examples of true activity distributions, Gaussian‐filtered PET images, and predicted PET images for vertical beam irradiation of CT phantoms with 9×9 and 3×3 spot probes. White dashed lines in the true activity distribution indicate the positions where activity curves were extracted.

To quantify the improvement in image quality, PSNR and SSIM values were calculated for both Gaussian‐filtered and predicted PET images. Figure 7 presents the statistical distributions using violin plots. In all cases, the predicted PET images showed higher PSNR and SSIM values, with increased medians and quartiles. For horizontal beams, the median PSNR values across all spot patterns increased from 21.4–23.9 to 35.2–37.4, and the median SSIM values increased from 0.450–0.621 to 0.906–0.961. For vertical beams, the median PSNR values improved from 21.9–23.2 to 29.2–34.1, and the median SSIM values improved from 0.480–0.560 to 0.745–0.895.

FIGURE 7.

Violin plots showing the statistical distributions of PSNR and SSIM values for the Gaussian‐filtered PET reconstructed images and the predicted images. Each plot displays the median (white dot), 25^th and 75^th percentiles (box edges), and blue dashed lines representing the trend of the medians.

3.2. Evaluation of range verification accuracy

Figure 8 shows representative spatial distributions of the true activity range and the corresponding ARE values across cross‐sections perpendicular to the proton beam. For horizontal beams, which traversed relatively homogeneous tissue, the distal fall‐off of activity was smooth and regular. The ARE values for the Gaussian‐filtered PET images were generally below 3 mm, with localized regions reaching 5 mm. For the predicted PET images, ARE values were mostly reduced to below 2 mm. In contrast, vertical beams passed through the heterogeneous nasopharynx, producing greater spatial variation in the distal fall‐off of activity. Consequently, the ARE values for the Gaussian‐filtered PET images mostly exceeded 5 mm. The proposed U‐Net‐based method yielded lower ARE values and improved the accuracy of range verification.

FIGURE 8.

Representative examples of the true activity range and ARE values across cross‐sections perpendicular to the proton beam. The left column shows the true activity range, while the middle and right columns show ARE for the Gaussian‐filtered PET images and the predicted PET images, respectively.

The violin plots in Figure 9 present the statistical distributions of the ARE values for both Gaussian‐filtered PET images and predicted PET images. In all cases, the predicted PET images yielded lower ARE values, with reduced medians and quartiles. For horizontal beams, the median ARE values across all spot patterns decreased from 1.05–1.18 mm to 0.52–0.73 mm, and the third quartile values decreased from 1.88–2.11 mm to 0.96–1.34 mm. For vertical beams, the median ARE values across all spot patterns were reduced from 1.80–2.40 mm to 1.50–1.73 mm, and the third quartile values decreased substantially from 3.67–5.17 mm to 3.01–3.75 mm.

FIGURE 9.

Violin plots showing the statistical distributions of ARE values for the Gaussian‐filtered PET images and the predicted images. Each plot displays the median (white dot), 25^th and 75^th percentiles (box edges), and blue dashed lines representing the trend of the medians.

3.3. Results of range shift sensitivity evaluation

Figure 10 presents the scatter plots of the imaging activity range shifts versus the true activity range shifts for all probes. In all cases, the proposed method improved the linear correlation between the imaging activity range shifts and the true activity range shifts, as indicated by decreased RMSE and increased R ². Specifically, for horizontal beam irradiation, R ² increased from 0.741 to 0.901, while RMSE decreased from 2.02 to 1.24 mm. For vertical beam irradiation, a more modest improvement was observed, with R² increasing from 0.428 to 0.517, and RMSE decreasing from 2.79 to 2.52 mm.

FIGURE 10.

Scatter plots of the imaging activity range shifts versus the true activity range shifts for all proton probes. The linear regression models are shown by red lines, with R ² values and RMSE values indicated in each plot. (a) Gaussian‐filtered PET imaging activity range shifts for horizontal beam irradiation. (b) Predicted PET imaging activity range shifts for horizontal beam irradiation. (c) Gaussian‐filtered PET imaging activity range shifts for vertical beam irradiation. (d) Predicted PET imaging activity range shifts for vertical beam irradiation.

3.4. Results of preliminary experimental validation

Figure 11 shows representative examples of the simulated reference activity distributions, the Gaussian‐filtered PET images, and the predicted PET images when proton beams irradiated the PMMA phantoms. Similar to the simulation results, the Gaussian‐filtered PET images exhibited noticeable noise and stretching artifacts. After post‐processing with the 3D U‐Net model, the predicted PET images became more consistent with the reference activity distributions, with higher PSNR and SSIM values. Figure 12 presents the statistical distributions of PSNR, SSIM, and ARE using violin plots. For all proton spot probes, the predicted PET images exhibited higher PSNR and SSIM values and lower ARE values. Specifically, the median PSNR values across all spot patterns increased from 18.8–22.9 to 25.9–32.6. The median SSIM values increased from 0.433–0.647 to 0.681–0.922, while the median ARE values decreased from 0.70–0.82 mm to 0.39–0.57 mm.

FIGURE 11.

Examples of simulated reference activity distributions, Gaussian‐filtered PET images, and predicted PET images for proton beam irradiation of PMMA phantoms using 3×3 and 9×9 spot patterns. White dashed lines in the reference activity distribution indicate the locations where activity profiles were extracted.

FIGURE 12.

Violin plots showing the statistical distributions of PSNR, SSIM and ARE values for Gaussian‐filtered PET images and predicted PET images for proton beam irradiation of PMMA phantoms. Each plot displays the median (white dot), 25^th and 75^th percentiles (box edges), and blue dashed lines representing the trend of the medians.

4. DISCUSSION

This study aimed to improve dual‐panel in‐beam PET image quality and thereby enhance PET‐based range verification accuracy. To achieve this goal, we proposed a 3D U‐Net‐based post‐processing method to simultaneously suppress noise and stretching artifacts. Simulations were conducted using single‐energy proton probes with various spot patterns irradiating both homogeneous and heterogeneous anatomical regions. The performance of the U‐Net was evaluated in terms of image quality and proton range verification accuracy. The results demonstrate that the 3D U‐Net effectively suppressed artifacts and noise, generating images more consistent with the true activity distributions. This improvement in image quality also enhanced the accuracy of range verification.

In in‐beam PET imaging, the limited number of detected coincidence events and the ill‐posed nature of the reconstruction lead to substantial statistical noise and occasional outliers in the reconstructed images. Gaussian smoothing is commonly applied to suppress high‐frequency noise and stabilize depth‐activity curve extraction for range verification, thereby improving the robustness of distal range estimation. However, excessive Gaussian smoothing inevitably introduces spatial blurring and may degrade the sharpness of the distal fall‐off, potentially affecting range estimation accuracy. In this study, the PET images input to the proposed 3D U‐Net were not Gaussian filtered. Instead, the network operates directly on noisy reconstructions and learns a data‐driven mapping to suppress noise while preserving clinically relevant spatial structures. In our quantitative evaluation, the U‐Net‐predicted images achieved higher PSNR and SSIM and lower ARE than the Gaussian‐filtered baseline images. Gaussian filtering was selected as the principal baseline because it is a commonly used and parameter‐light post‐reconstruction smoothing method for suppressing high‐frequency noise. More sophisticated regularized reconstruction or post‐processing methods were not included as primary comparators because they typically require data‐dependent parameter tuning, and a fair comparison would require a dedicated benchmark study beyond the scope of this preliminary feasibility study.

The range verification was carried out by extracting depth‐activity curves along the beam direction, and its accuracy was quantified using ARE. Using this approach, proton range uncertainty is strongly determined by the fidelity of the reconstructed activity distribution. Therefore, the enhancement in PET image quality naturally leads to more accurate and reliable range verification, which is precisely the problem we wanted to address in this work. The U‐Net‐predicted PET images consistently yielded smaller ARE values, confirming the method's effectiveness. Beyond range verification, high‐quality PET images are also expected to facilitate dose reconstruction from measured PET data using analytical or deep learning approaches. Moreover, improved image clarity could aid in detecting morphological changes, such as tumor cavity filling or enlargement, by enhancing the visibility of activity distribution changes.

PET image quality is related to the number of coincidence events, which depends on proton delivery dose and PET acquisition time. Longer acquisition times can allow for lower probe doses without sacrificing image quality, whereas higher delivery doses can permit shorter acquisition times. Therefore, the delivery strategy for single‐energy probes should be optimized based on clinical requirements. In‐beam PET monitoring with such probes may hold promise for FLASH therapy employing single‐energy Bragg peak plans. A potential clinical workflow could involve first delivering a low‐dose single‐energy Bragg peak plan under in‐beam PET monitoring, followed by a standard single‐energy FLASH plan guided by the monitoring results. However, such workflows require further treatment‐plan‐based investigation.

The computational latency of the proposed processing pipeline was evaluated to assess the computational feasibility of PET image enhancement and activity‐range estimation. After PET data acquisition, PET reconstruction required approximately 0.8 s, 3D U‐Net inference required approximately 40 ms, and activity‐range estimation required approximately 0.3 s. The total post‐acquisition processing time was therefore approximately 1.1 s in our current implementation. This processing time does not include adaptive decision‐making, treatment‐plan evaluation, dose recalculation, spot‐weight correction, treatment‐plan re‐optimization, delivery‐system communication, or beam‐control integration. Therefore, it should be interpreted as the computational latency of the PET image enhancement and range‐estimation pipeline, rather than that of a complete online adaptive proton therapy workflow. Further work is needed to determine how this pipeline could be integrated into a treatment‐plan‐based adaptive proton therapy framework.

The experimental study provides a preliminary feasibility validation of the proposed method using measured PET data. However, the experimental setup had several limitations. The PMMA phantom was substantially more homogeneous than patient anatomy and did not reproduce tissue heterogeneity or complex activity distributions in clinical cases. In addition, the detector configuration only approximated the simulated dual‐panel in‐beam PET geometry, as the experimental prototype was a multi‐panel circular PET system and only a subset of modules was used for limited‐angle acquisition. Therefore, although this setup allowed us to evaluate whether the 3D U‐Net model trained on simulated data could be applied to experimentally acquired low‐count PET data, the results should be interpreted as an initial feasibility validation under simplified experimental conditions rather than as a complete validation in a clinical dual‐panel in‐beam PET system. Further investigations using heterogeneous anthropomorphic phantoms, more realistic dual‐panel geometries, multiple beam energies, and larger experimental datasets are needed.

Although the 3D U‐Net, leveraging skip connections to capture multi‐scale features, proved effective for enhancing dual‐panel in‐beam PET images, its performance in heterogeneous anatomical regions, such as the nasal cavity and skull base, was less satisfactory. These areas exhibit large variations in tissue density and composition, leading to complex secondary particle production and irregular distributions of positron‐emitting isotopes. Consequently, local range estimation errors tend to increase in regions with steep density gradients or air‐tissue interfaces. Future work may address these limitations by integrating physics‐informed priors or hybrid model‐based frameworks. In addition, limited‐angle in‐beam PET data may exhibit long‐range spatial dependencies that are not optimally captured by purely convolutional architectures. Emerging architectures incorporating attention mechanisms or transformer‐based global context modeling may offer improved capability for modeling extended spatial correlations.

5. CONCLUSION

This study proposed a 3D U‐Net‐based post‐processing method to improve dual‐panel in‐beam PET imaging and evaluated its feasibility through Monte Carlo simulations and preliminary experimental validation. The proposed 3D U‐Net mitigated noise and artifacts in reconstructed PET images and improved the accuracy of proton range verification. These results demonstrate the preliminary feasibility of using deep learning to enhance in‐beam PET image quality and range verification. Further validation using more diverse patient anatomies and larger experimental datasets will be necessary to fully assess the clinical applicability of the proposed approach.

CONFLICT OF INTEREST STATEMENT

The authors have no relevant conflicts of interest to disclose.