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Deep learning-based in vivo dose verification from proton-induced secondary-electron-bremsstrahlung images with various count level

      Highlights

      • Bremsstrahlung imaging is a promising method for range verification of proton beam.
      • A deep learning model was applied to overcome problems for bremsstrahlung imaging.
      • U-Net model was trained to predict proton dose images from bremsstrahlung images.
      • The trained model can predict dose images within 2.1 mm range/width error.

      Abstract

      Purpose

      Proton-induced secondary-electron-bremsstrahlung (SEB) imaging is a promising method for estimating the ranges of particle beam. However, SEB images do not directly represent dose distributions of particle beams. In addition, the ranges estimated from measured images were deviated because of limited spatial resolutions of the developed x-ray camera as well as statistical noise in the images. To solve these problems, we proposed a method for predicting high-resolution dose images from SEB images with various count level using a deep learning (DL) approach for range and width verification.

      Methods

      In this study, we adopted the double U-Net model, which is a previously proposed deep convolutional network model. The first U-Net model in the double U-Net model was used to denoise the SEB images with various count level. The first U-Net model for denoising was trained on 8000 pairs of SEB images with various count level and noise-free images which were created by a sophisticated in-house developed model function. The second U-Net model for dose prediction was trained using 8000 pairs of denoised SEB images from the first U-Net model and high-resolution dose images generated by Monte Carlo simulation.

      Results

      For both simulation and measurement data, the trained DL model could successfully predict high-resolution dose images which showed a clear Bragg peak and no statistical noise. The difference of the range and width was less than 2.1 mm, even from the SEB images measured with a decrease in the number of irradiated protons to less than 11% of 3.2 × 1011 protons.

      Conclusions

      High-resolution dose images from measured and simulated SEB images were successfully predicted by using the trained DL model for protons. Our proposed DL model was feasible to predict dose images accurately even with smaller number of irradiated protons.

      Keywords

      1. Introduction

      In particle therapy, range verification is important to monitor the location of Bragg peak and dose distribution in a human body. A number of studies have tried to verify the range or dose distributions of particle beams by detecting the induced positrons [
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      Range verification system using positron emitting beams for heavy-ion radiotherapy.
      ,
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      ,
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      • Cirrone G.A.P.
      • Cuttone G.
      • Del Guerra A.
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      Preliminary results of an in-beam PET prototype for proton therapy.
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      ] or prompt gamma photons [
      • Min C.H.
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      Prompt gamma measurements for locating dose falloff region in proton therapy.
      ,
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      Prompt gamma detection for range verification in proton therapy.
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      Prompt gamma imaging with a slit camera for real-time range control in proton therapy.
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      • et al.
      Prompt gamma imaging of proton pencil beams at clinical dose rate.
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      • et al.
      First clinical application of a prompt gamma based in vivo proton range verification system.
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      • Ammar C.
      • Frey K.
      • Bauer J.
      • Melzig C.
      • Chiblak S.
      • Hildebrandt M.
      • et al.
      Comparing the biological washout of β+-activity induced in mice brain after 12C-ion and proton irradiation.
      ,
      • Wrońska A.
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      • Bednarczyk P.
      • Gazdowicz G.
      • et al.
      Prompt-gamma emission in GEANT4 revisited and confronted with experiment.
      ]. Proton-induced positron emitter imaging suffers the washout effect. Yamaguchi et al. have proposed a monitoring method which measures the secondary-electron-bremsstrahlung (SEB) produced during particle beam irradiation [
      • Yamaguchi M.
      • Torikai K.
      • Kawachi N.
      • Shimada H.
      • Satoh T.
      • Nagao Y.
      • et al.
      Beam range estimation by measuring bremsstrahlung.
      ,

      Yamaguchi M, Torikai K, Kawachi N, Shimada H, Satoh T, Nagao Y, Fujimaki S, Kokubun M, Watanabe S, Takahashi T, Arakawa K, Kamiya T, Nakano T. Corrigendum: Beam range estimation by measuring bremsstrahlung (2012 Phys. Med. Biol. 57 2843), Phys Med Biol 2016; 61: 3638–44.

      ]. The SEB is emitted by secondary electrons that are deflected in the electric field of an atomic nucleus while losing the kinetic energy of secondary electrons. The production mechanism of SEB is different from that of prompt gamma photons and positrons produced in nuclear reactions. Since the SEB is produced simultaneously with the irradiation of particle beam, the washout effect is not a problem. In addition, the SEB is relatively easier to detect by gamma cameras than higher energy prompt gamma photons emitted by positron annihilations or nuclear reactions. Dedicated low-energy x-ray cameras were developed and tested during particle-beam irradiations for detecting the SEB, and the cameras could be used to image the beam distributions [
      • Yamaguchi M.
      • Torikai K.
      • Kawachi N.
      • Shimada H.
      • Satoh T.
      • Nagao Y.
      • et al.
      Beam range estimation by measuring bremsstrahlung.
      ,

      Yamaguchi M, Torikai K, Kawachi N, Shimada H, Satoh T, Nagao Y, Fujimaki S, Kokubun M, Watanabe S, Takahashi T, Arakawa K, Kamiya T, Nakano T. Corrigendum: Beam range estimation by measuring bremsstrahlung (2012 Phys. Med. Biol. 57 2843), Phys Med Biol 2016; 61: 3638–44.

      ,
      • Yamaguchi M.
      • Nagao Y.
      • Ando K.
      • et al.
      Secondary-electron-bremsstrahlung imaging for proton therapy.
      ,
      • Ando K.
      • Yamaguchi M.
      • Yamamoto S.
      • Toshito T.
      • Kawachi N.
      Develop- ment of a low-energy x-ray camera for the imaging of secondary electron bremsstrahlung x-ray emitted during proton irradiation for range estimation.
      ,
      • Yamaguchi M.
      • Nagao Y.
      • Ando K.
      • Yamamoto S.
      • Sakai M.
      • Parajuli R.K.
      • et al.
      Imaging of monochromatic beams by measuring secondary electron bremsstrahlung for carbon-ion therapy using a pinhole x-ray camera.
      ,
      • Yamamoto S.
      • Yamaguchi M.
      • Akagi T.
      • Sasano M.
      • Kawachi N.
      Development of a YAP(Ce) camera for the imaging of secondary electron bremsstrahlung x-ray emitted during carbon-ion irradiation toward the use of clinical conditions.
      ,
      • Yamamoto S.
      • Yamaguchi M.
      • Akagi T.
      • Kitano M.
      • Kawachi N.
      Sensitivity improvement of YAP(Ce) cameras for imaging of secondary electron bremsstrahlung x-rays emitted during carbon-ion irradiation: problem and solution.
      ].
      Although the beam distributions of particle-ions could be imaged by the cameras, they were different from the dose distributions for two major reasons. First, the SEB distributions have no Bragg peak because the SEB energy was lower at Bragg peak region along the beam path. Second, most of the SEB would be attenuated in human body because of their low energy in comparison to prompt gamma photons. In addition, the images measured by the current x-ray camera suffered from the limited spatial resolutions and high statistical noises because of the inevitable low count condition [
      • Yamaguchi M.
      • Torikai K.
      • Kawachi N.
      • Shimada H.
      • Satoh T.
      • Nagao Y.
      • et al.
      Beam range estimation by measuring bremsstrahlung.
      ,

      Yamaguchi M, Torikai K, Kawachi N, Shimada H, Satoh T, Nagao Y, Fujimaki S, Kokubun M, Watanabe S, Takahashi T, Arakawa K, Kamiya T, Nakano T. Corrigendum: Beam range estimation by measuring bremsstrahlung (2012 Phys. Med. Biol. 57 2843), Phys Med Biol 2016; 61: 3638–44.

      ,
      • Yamaguchi M.
      • Nagao Y.
      • Ando K.
      • et al.
      Secondary-electron-bremsstrahlung imaging for proton therapy.
      ,
      • Ando K.
      • Yamaguchi M.
      • Yamamoto S.
      • Toshito T.
      • Kawachi N.
      Develop- ment of a low-energy x-ray camera for the imaging of secondary electron bremsstrahlung x-ray emitted during proton irradiation for range estimation.
      ,
      • Yamaguchi M.
      • Nagao Y.
      • Ando K.
      • Yamamoto S.
      • Sakai M.
      • Parajuli R.K.
      • et al.
      Imaging of monochromatic beams by measuring secondary electron bremsstrahlung for carbon-ion therapy using a pinhole x-ray camera.
      ,
      • Yamamoto S.
      • Yamaguchi M.
      • Akagi T.
      • Sasano M.
      • Kawachi N.
      Development of a YAP(Ce) camera for the imaging of secondary electron bremsstrahlung x-ray emitted during carbon-ion irradiation toward the use of clinical conditions.
      ,
      • Yamamoto S.
      • Yamaguchi M.
      • Akagi T.
      • Kitano M.
      • Kawachi N.
      Sensitivity improvement of YAP(Ce) cameras for imaging of secondary electron bremsstrahlung x-rays emitted during carbon-ion irradiation: problem and solution.
      ]. These issues deteriorated the performance of the estimation of the ranges and widths of the beams in the measured SEB images [
      • Yamaguchi M.
      • Torikai K.
      • Kawachi N.
      • Shimada H.
      • Satoh T.
      • Nagao Y.
      • et al.
      Beam range estimation by measuring bremsstrahlung.
      ,

      Yamaguchi M, Torikai K, Kawachi N, Shimada H, Satoh T, Nagao Y, Fujimaki S, Kokubun M, Watanabe S, Takahashi T, Arakawa K, Kamiya T, Nakano T. Corrigendum: Beam range estimation by measuring bremsstrahlung (2012 Phys. Med. Biol. 57 2843), Phys Med Biol 2016; 61: 3638–44.

      ,
      • Yamaguchi M.
      • Nagao Y.
      • Ando K.
      • et al.
      Secondary-electron-bremsstrahlung imaging for proton therapy.
      ,
      • Ando K.
      • Yamaguchi M.
      • Yamamoto S.
      • Toshito T.
      • Kawachi N.
      Develop- ment of a low-energy x-ray camera for the imaging of secondary electron bremsstrahlung x-ray emitted during proton irradiation for range estimation.
      ,
      • Yamaguchi M.
      • Nagao Y.
      • Ando K.
      • Yamamoto S.
      • Sakai M.
      • Parajuli R.K.
      • et al.
      Imaging of monochromatic beams by measuring secondary electron bremsstrahlung for carbon-ion therapy using a pinhole x-ray camera.
      ,
      • Yamamoto S.
      • Yamaguchi M.
      • Akagi T.
      • Sasano M.
      • Kawachi N.
      Development of a YAP(Ce) camera for the imaging of secondary electron bremsstrahlung x-ray emitted during carbon-ion irradiation toward the use of clinical conditions.
      ,
      • Yamamoto S.
      • Yamaguchi M.
      • Akagi T.
      • Kitano M.
      • Kawachi N.
      Sensitivity improvement of YAP(Ce) cameras for imaging of secondary electron bremsstrahlung x-rays emitted during carbon-ion irradiation: problem and solution.
      ].
      To overcome these limitations of the SEB imaging, we have applied a deep learning (DL) approach to the dose distribution prediction from the measured SEB images for carbon-ions in the previous study [
      • Yamaguchi M.
      • Liu C.-C.
      • Huang H.-M.
      • Yabe T.
      • Akagi T.
      • Kawachi N.
      • et al.
      Dose image prediction for range and width verifications from carbon ion-induced secondary electron bremsstrahlung x-rays using deep learning workflow.
      ]. The predicted images by the DL approach showed a good agreement with dose distributions of carbon-ions [
      • Yamaguchi M.
      • Liu C.-C.
      • Huang H.-M.
      • Yabe T.
      • Akagi T.
      • Kawachi N.
      • et al.
      Dose image prediction for range and width verifications from carbon ion-induced secondary electron bremsstrahlung x-rays using deep learning workflow.
      ]. However, the DL approach was applied for only SEB images of carbon-ions and it was not clear whether this approach can be applied to SEB images of protons. Furthermore, the DL model was trained using fixed and high number of counts of SEB images and it was necessary to mitigate the effects of different statistical noise levels in the SEB images when the number of counts varies between different patients. High statistical noise or low-count condition in the SEB images leads to uncertainty in the particle’s range directly estimated from the measured SEB images. In addition, images with different noise properties as input to the trained DL model may degrade the performance of predicting dose distribution for the range and width verification.
      To clarify these points, we tried to predict high-resolution dose image from the SEB images with various count level using double U-Net model for protons. U-Net is an encoder-decoder based convolutional network. It learns both local and global feature information from the input image to predict the target image [
      • Ronneberger O.
      • Fischer P.
      • Brox T.
      ]. Each U-Net model in double U-Net model has 18 convolutional layers and total number of trainable parameters is about five million. The first U-Net model eliminates the statical noises in the SEB images while training the SEB images for various count level. The second U-Net model predicts the high-resolution dose images from the first U-Net model’s outputs (denoised images of SEB) to solve the problems of limited spatial resolutions of the SEB images and nonlinearity between SEB and proton-dose.

      2. Material and methods

      2.1 Measurement of SEB images during proton beam irradiations

      The measurements of the SEB images were performed in the spot scanning room of the Nagoya Proton Therapy Center [
      • Toshito T.
      • Omachi C.
      • Kibe Y.
      • Sugai H.
      • Hayashi K.
      • Shibata H.
      • et al.
      A proton therapy system in Nagoya proton therapy center.
      ]. For the measurements of SEB images during proton beam irradiations, we used a low-energy YAlO3: Ce (YAP (Ce)) x-ray camera [
      • Yamamoto S.
      • Yamaguchi M.
      • Akagi T.
      • Kitano M.
      • Kawachi N.
      Sensitivity improvement of YAP(Ce) cameras for imaging of secondary electron bremsstrahlung x-rays emitted during carbon-ion irradiation: problem and solution.
      ]. The x-ray camera used a 0.5 mm thick, 20 mm × 20 mm YAP (Ce) plate that was optically coupled to a 25-mm square high quantum efficiency cross-wire anode-type position sensitive photomultiplier tube (PS-PMT) (R8900-100-C12, Hamamatsu Photonics, Japan) [
      • Yamamoto S.
      • Yamaguchi M.
      • Akagi T.
      • Kitano M.
      • Kawachi N.
      Sensitivity improvement of YAP(Ce) cameras for imaging of secondary electron bremsstrahlung x-rays emitted during carbon-ion irradiation: problem and solution.
      ]. By using a thin YAP(Ce) scintillator, low-energy SEB can be detected efficiently, while high-energy photons such as prompt gamma photons or annihilation radiation of positrons can penetrate the scintillator and reduce the background components in measured images. The detector was contained in a 2.0 cm thick tungsten to shield high-energy photons such as prompt gamma photons and annihilation radiation of positrons, and a 1.5 mm diameter pinhole collimator was placed in front of the imaging detector.
      In previous study, the intrinsic spatial resolution of low energy x-ray camera was evaluated by measuring of ∼35 keV x-ray from 137Cs point source [
      • Yamamoto S.
      • Yamaguchi M.
      • Akagi T.
      • Kitano M.
      • Kawachi N.
      Sensitivity improvement of YAP(Ce) cameras for imaging of secondary electron bremsstrahlung x-rays emitted during carbon-ion irradiation: problem and solution.
      ]. The intrinsic spatial resolution was ∼1.6 mm full width at half maximum (FWHM). The system spatial resolution of the camera with a pinhole collimator was obtained ∼20 mm FWHM at 30 cm from the collimator surface to point source [
      • Yamamoto S.
      • Yamaguchi M.
      • Akagi T.
      • Kitano M.
      • Kawachi N.
      Sensitivity improvement of YAP(Ce) cameras for imaging of secondary electron bremsstrahlung x-rays emitted during carbon-ion irradiation: problem and solution.
      ]. Considering the magnification of the image, the spatial resolution of the measured image is expected to be ∼26 mm FWHM for this imaging experiment.
      The output analog waveforms of camera from six cross-wire anodes for the x-direction and y-direction of the PS-PMT were weight-summed by amplifiers to produce four analog waveforms. The weight-summed waveforms were converted to digital signals by four 100 MHz analog-to-digital converters (ADCs). The digitized signals were digitally integrated and used for position determination based on a gravity calculation. The calculated position signals were used to produce a 44 × 44 matrix image with a 0.45 mm pixel size. In order to acquire clear images of the beam shape, the energy window of the camera was set from 30 keV to 60 keV [
      • Ando K.
      • Yamaguchi M.
      • Yamamoto S.
      • Toshito T.
      • Kawachi N.
      Develop- ment of a low-energy x-ray camera for the imaging of secondary electron bremsstrahlung x-ray emitted during proton irradiation for range estimation.
      ,
      • Yamaguchi M.
      • Nagao Y.
      • Ando K.
      • Yamamoto S.
      • Sakai M.
      • Parajuli R.K.
      • et al.
      Imaging of monochromatic beams by measuring secondary electron bremsstrahlung for carbon-ion therapy using a pinhole x-ray camera.
      ,
      • Yamamoto S.
      • Yamaguchi M.
      • Akagi T.
      • Sasano M.
      • Kawachi N.
      Development of a YAP(Ce) camera for the imaging of secondary electron bremsstrahlung x-ray emitted during carbon-ion irradiation toward the use of clinical conditions.
      ,
      • Yamamoto S.
      • Yamaguchi M.
      • Akagi T.
      • Kitano M.
      • Kawachi N.
      Sensitivity improvement of YAP(Ce) cameras for imaging of secondary electron bremsstrahlung x-rays emitted during carbon-ion irradiation: problem and solution.
      ]. The acquired images of 44 pixel × 44 pixels were cropped to 40 × 40 pixels in the center of the image for the DL.
      Fig. 1 shows a schematic drawing (A) and a photo (B) of the set-up for imaging the SEB using the x-ray camera. With the YAP(Ce) x-ray cameras, we conducted imaging experiments of SEB during irradiation of proton beams to the phantom. The energy window of the camera was set from 30 keV to 60 keV to measure low-energy SEB. The distance from the x-ray camera to the center of the phantom was 42 cm. Proton beam was irradiated to the center of a water phantom of which outer size was 20 cm (horizontal) × 20 cm (vertical) × 10 cm (depth) from the upper side with a clinical proton therapy system (Hitachi, Japan). The SEB was imaged during irradiation of proton beam for one of the three different beam energies, 100.2 MeV, 119.3 MeV and 139.3 MeV-proton.
      Figure thumbnail gr1
      Fig. 1Schematic drawing (A) and a photo (B) of imaging the SEB during irradiation of proton beams to water phantom. X and Y axes in (B) indicate directions of measured images.
      Imaging by the x-ray camera was conducted dynamic acquisition mode (20 s acquisition × 9 frames) while water phantom was irradiated with pencil beam protons. The number of protons irradiated to the phantom for 20 s was ∼ 3.5 × 1010 protons. This number of protons corresponds to 21, 26, and 30 Gy at the Bragg peak for 100.2, 119.3, and 139.3 MeV-protons, which were calculated by the treatment planning system. The measured dynamic SEB images were summed to produce images with different acquisition times and used for DL testing. Some of the measured SEB images with different acquisition times for 119.3 MeV protons were shown in Fig. 2.
      Figure thumbnail gr2
      Fig. 2Measured images of SEB with different acquisition times for 119.3 MeV protons.

      2.2 Image dataset for DL training

      To generate SEB images for DL training, we utilized the model function described in Ref. [
      • Yamaguchi M.
      • Liu C.-C.
      • Huang H.-M.
      • Yabe T.
      • Akagi T.
      • Kawachi N.
      • et al.
      Dose image prediction for range and width verifications from carbon ion-induced secondary electron bremsstrahlung x-rays using deep learning workflow.
      ] that simulates realistic x-ray camera images with the energy window of 30 keV to 60 keV deposited in the YAP(Ce) scintillator. In the present study we fixed the parameter γ_y of the Voigt profile included in the SEB profile along the beam axis, at 0. This restriction prohibits the SEB profile along the beam axis from having significant values in the region deeper than the range, thus allowing the model to better reproduce the experimental values. The projections of the experimental data for 180 s irradiation and the model curves simulated using the model function on x-axis (perpendicular to the beam direction) and y-axis (parallel to the beam direction) are shown in Fig. 3. For all three energies, the model curves could resemble the experimental data. In this study, energy dependences of the parameters of the model function are represented as parabolic functions by fitting the deduced values of the parameters.
      Figure thumbnail gr3
      Fig. 3Projections of the experimental data (blue lines) and the model curves simulated using the model function (red curves) on x- (a) and y-axis (b). The left, central, and right panels represent for the incident energies of 139.3, 119.3, and 100.2 MeV, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
      As mentioned in Ref. [
      • Yamaguchi M.
      • Liu C.-C.
      • Huang H.-M.
      • Yabe T.
      • Akagi T.
      • Kawachi N.
      • et al.
      Dose image prediction for range and width verifications from carbon ion-induced secondary electron bremsstrahlung x-rays using deep learning workflow.
      ], the dose distributions were prepared directly by Monte Carlo (MC) simulations using the Particle and Heavy Ion Transport code System (PHITS) [
      • Sato T.
      • Iwamoto Y.
      • Hashimoto S.
      • Ogawa T.
      • Furuta T.
      • Abe S.-I.
      • et al.
      Features of Particle and Heavy Ion Transport code System (PHITS) version 3.02.
      ] version 3.10 because the computational burden for the calculation of dose distributions is much smaller than that for the SEB images. These MC simulated dose images were also used as the ground truth images for evaluating the U-Net model predicted images.

      2.3 DL-based denoising and dose prediction for SEB images

      2.3.1 Neural network architecture

      The DL model composed of two standard U-Net models [
      • Ronneberger O.
      • Fischer P.
      • Brox T.
      ] to overcome the issues mentioned above for SEB imaging. Both U-Net models were same architecture as shown in Fig. 4. The architecture of each U-net model consists of encoding process and decoding process. The encoding process consists of two 3 × 3 convolutions layer with rectified linear units (ReLU) and a 2 × 2 max pooling with stride 2 for down-sampling, while the decoding process consists of 2 × 2 deconvolutions with stride 2 and two 3 × 3 convolutions with ReLU. In addition, a 1 × 1 convolutional layer with ReLU as an activation function was applied as a last layer of each U-Net model. The feature maps are copied and concatenated via the skip connections to the convolutional layers at each down- and up-sampling step between encoding and decoding process, respectively. The first U-Net was used to denoise the SEB images with different count into noise-free images. The second U-Net was used to convert the denoised images into dose images with super-resolution. For the second U-Net model, the input images (first U-Net’s outputs, denoised images of SEB) were up-sampled by a factor of five to match the size of the target image (200 × 200 dose image).
      Figure thumbnail gr4
      Fig. 4Double U-Nets model architecture for denoising of SEB images and converting into high-resolution dose images.

      2.3.2 Network training

      First, we trained a first U-Net model to denoise SEB images with different count level as inputs and noise-free images as targets. Next, the second U-Net model was trained to predict a high-resolution dose image from the denoised images obtained by the first U-Net as inputs and dose image as the target.
      For training and validation of DL models, total 9500 datasets of SEB images (difference count and noise free images) were created by randomly setting the proton energy, irradiation position and number of irradiated protons using in-house model functions. Nine hundred and fifty high-resolution dose images corresponding to these SEB images were simulated by MC. These simulated datasets were split into 8000 simulated pairs as training data, 1500 pairs as validation data.
      The loss function was defined as the mean square error (MSE) between the predicted images and the target images. The MSE loss was minimized by the Adam algorithm with initial learning rate 10−3, beta_1 = 0.9, and beta_2 = 0.999. The learning rate was decayed by multiply of a factor of 0.1 if there is no improvement in validation loss for 5 epochs. Early stopping was used to stop the training and avoiding overfitting if there is no improvement in validation loss for 10 epochs in training model. The batch size was 10. These network models were implemented using Keras and PlaidML as a backend, and were trained on a Radeon Pro 580 (8 GB) graphic processing unit.

      2.4 DL model performance evaluation

      To evaluate the trained DL model’s performance depending on the count level in the SEB images, we prepared 300 datasets from the simulation for testing data. The 300 datasets of SEB images were generated by changing the irradiated number of protons from 10% (3.2 × 1010 protons) to 100% (3.2 × 1011 protons) using in-house model function. These datasets were divided into ten groups with different number of protons to evaluate the DL performance depending on the count level in the SEB images. In addition to the simulation data, we predicted dose images from the measured SEB images with the difference count level to demonstrate the transferability and feasibility of trained DL model by simulation images on real measured images. 27 measured images for testing data were obtained by varying the irradiation time of protons from 20 s (∼3.5 × 1010 protons irradiation) to 180 s (∼3.2 × 1011 protons irradiation) with 20 s intervals for 100.2, 119.3 and 139.3 MeV-proton. All of these SEB image counts were divided by the number of irradiated protons to normalize the intensity of the images for DL training and testing.

      2.5 Quantitative evaluation metric

      As image similarity metrics, we calculated the MSE and the structural similarity index (SSIM) [
      • Wang Z.
      • Bovik A.C.
      • Sheikh H.R.
      • Simoncelli E.P.
      Image quality assessment: from error visibility to structural similarity.
      ] between MC simulated dose images (later we will describe these as ground truth images) and U-Net predicted images by the trained DL model. Moreover, depth profiles and lateral profiles were obtained with a profile of 10 pixels (∼12.0 mm) width on beam path to evaluate the absolute difference of ranges and widths of the beam between U-Net predictions and ground truth images. The range was defined as the depth position at distal falls to 80% of its maximum value. The beam width was defined as a FWHM of lateral profiles obtained at 36 mm-depth positions from the water surface.

      3. Result

      3.1 Dose image prediction from the simulation data

      To check the trained DL model’s performance depending on the count levels in the SEB images, we predicted dose images from simulated SEB images with different number of irradiated protons using the trained DL model. Then we evaluated the similarities and differences between U-Net predicted images and the grand truth images. Fig. 5(a) shows the averaged values of MSE and SSIM between ground truth image and U-Net predicted images as image similarity metric for ten groups with different number of irradiated protons from 10% (3.2 × 1010 protons) to 100% (3.2 × 1011 protons). As the number of irradiated protons decreased, MSE increased and SSIM slightly decreased. The averaged value of MSE for the 10% proton number group was 8.3 times higher than that for the 100% proton number group. The averaged value of SSIM for the 10% proton number group was 0.99 times higher than that for the 100% proton number group. Fig. 5(b) shows the absolute difference of ranges and widths of the beams for different number of irradiated protons. For the 10% proton number group, the absolute differences of ranges and widths of the beams were 2.2 mm and 0.5 mm FWHM on average, compared to 0.4 mm and 0.3 mm FWHM on average for the 100% proton number group.
      Figure thumbnail gr5
      Fig. 5MSE and SSIM between ground truth image and U-Net predicted images from 300 simulated SEB images (a) and averaged differences in ranges and widths of beams between ground truth images and U-Net predicted images from simulated SEB images (b) for ten groups with different number of irradiated protons from 10% (3.2 × 1010 protons) to 100% (3.2 × 1011 protons).
      Three examples of simulated testing data were selected to show the DL model’s performance varying with the count level in SEB images. The simulated SEB images with three different counts (100%, 50% and 10%) are shown in Fig. 6(a-c), the U-Net predicted images in Fig. 6(d-f), and the corresponding ground truth images in Fig. 6(g-i). Fig. 6(j-l) show the difference images between the U-Net predicted and ground truth images.
      Figure thumbnail gr6
      Fig. 6Simulated SEB images of 100% count (3.2 × 1011 protons) (a), 50% count (1.6 × 1011 protons) and 10% count (3.2 × 1010 protons) (c), U-Net predicted images from SEB image with 100% count (d), 50% count (e) and 10% count (f), corresponding ground truth images for 100% count (g), 50% count (h) and 10% count (i), and difference images between dose and U-Net predicted images for 100% count (j), 50% count (k) and 10% count (l).
      The depth profiles of the simulated SEB images, U-Net predicted images and ground truth images are plotted for the individual three representative data in Fig. 7(a), (b) and (c), and their lateral profiles are in Fig. 7(d), (e) and (f). In addition, the evaluated metrics of the difference between the U-Net predicted images from simulated SEB images compared with ground truth images for three count levels are summarized in Table 1.
      Figure thumbnail gr7
      Fig. 7Depth profiles for simulated SEB images, U-Net predicted dose images, MC dose (ground truth image) for 100% count level (a), for 50% count level (b) and for 10% count level (c), and lateral profiles simulated SEB images, U-Net predicted dose images, MC dose (ground truth image) for 100% count level (d), for 50% count level (e) and for 10% count level (f).
      Table 1MSE, SSIM, and difference of ranges and widths of beams for U-Net predicted images from simulated SEB images with 100% count, 50% count and 10% count compared with ground truth images.
      Metrics100% count

      (3.2 × 1011 protons)
      50% count

      (1.6 × 1011 protons)
      10% count

      (3.2 × 1010 protons)
      MSE3.28 × 10−51.78 × 10−54.40 × 10−4
      SSIM0.9980.9980.989
      Range difference0.2 mm0.9 mm1.9 mm
      Width difference0.4 mm FWHM0.1 mm FWHM0.2 mm FWHM

      3.2 Dose image prediction from the measured data

      To demonstrate the transferability and feasibility of trained DL model by simulation images on real measured images, we predicted dose images from the measured SEB images with the difference count level for 100.2 MeV, 119.3 MeV and 139.3 MeV-proton.
      Fig. 8(a)–(c) show the MSE and SSIM between ground truth images and U-Net predicted images for different number of irradiated protons for proton energy of 100.2 MeV, 119.3 MeV and 139.3 MeV, respectively. As the number of irradiated protons decreased, MSE increased and SSIM slightly decreased. Fig. 8(d)–(f) show the absolute difference of ranges and widths of the beams between ground truth images and U-Net predicted images for different irradiation times for proton energy of 100.2 MeV, 119.3 MeV and 139.3 MeV-protons, respectively. The absolute differences in ranges and widths of the beams were less than 2.1 mm with the number of protons more than 10 % (3.2 × 1010 protons).
      Figure thumbnail gr8
      Fig. 8MSE and SSIM between ground truth image and U-Net predicted images from measured SEB images for 100.2 MeV (a), 119.3 MeV (b) and 139.3 MeV-proton(c), and the difference in ranges and widths of beams between ground truth image and U-Net predicted images from measured data for 100.2 MeV (d), 119.3 MeV (e) and 139.3 MeV-proton (f) for different relative number of irradiated protons. The relative proton number of 100% corresponds to 3.2 × 1011 protons.
      Three measured images were shown for demonstrating the differences between ground truth images and U-Net predicted images for 20 s irradiation (∼3.5 × 1010 protons). The measured images of SEB are shown in Fig. 9(a-c), the U-Net predicted images in Fig. 9(d-f), and the corresponding ground truth images in Fig. 9 (g-i). The difference images between the U-Net predicted and groundtruth images are also shown in Fig. 9(j-l).
      Figure thumbnail gr9
      Fig. 9Measured SEB images with 20 s irradiation (∼3.5 × 1010 protons, 11% counts) for 100.2 MeV(a), 119.3 MeV(b) and 139.3 MeV-proton(c), U-Net predicted images for 100.2 MeV(d), 119.3 MeV(e) and 139.3 MeV-proton(f), corresponding ground truth images for 100.2 MeV(g), 119.3 MeV(h) and 139.3 MeV-proton(i), and difference images between dose and U-Net predicted images for 100.2 MeV(j), 119.3 MeV(k) and 139.3 MeV-proton (l).
      The depth profiles of the measured SEB images for 20 s irradiation with 100.2 MeV, 119.3 MeV and 139.3 MeV-protons, U-Net predicted images and ground truth images are plotted for the individual three representative data in Fig. 10(a), (b) and (c), and their lateral profiles are in Fig. 10(d), (e) and (f). In addition, the evaluated metrics of the difference between the U-Net predicted images from measured SEB images compared with ground truth images for three energies are summarized in Table 2.
      Figure thumbnail gr10
      Fig. 10Depth profiles for measured SEB images, ground truth images, U-Net predicted images for 100.2 MeV (a), 119.3 MeV (b) and 139.3 MeV-proton(c), and lateral profiles of U-Net predicted images from simulated SEB images, ground truth images, U-Net predicted images for 100.2 MeV (d), 119.3 MeV (e) and 139.3 MeV-proton (f).
      Table 2MSE, SSIM, and absolute difference of ranges and widths of beams for U-Net predicted images from measured images for 180 s and 20 s irradiation of 100.2 MeV, 119.3 MeV and 139.3 MeV-proton.
      Metrics180 s (100% count)20 s (11% count)Ratio of 20 s

      /180 s
      MSE: 100.2 MeV2.34 × 10−51.82 × 10−48.97
      MSE: 119.3 MeV5.49 × 10−52.76 × 10−45.04
      MSE: 139.3 MeV6.71 × 10−51.63 × 10−42.43
      SSIM: 100.2 MeV0.9970.9950.989
      SSIM: 119.3 MeV0.9970.9920.995
      SSIM: 139.3 MeV0.9930.9920.999
      Range/Width difference: 100.2 MeV0.0 mm/1.0 mm1.2 mm/1.4 mm28.4/1.4
      Range/Width difference: 119.3 MeV0.7 mm/0.3 mm2.1 mm/0.6 mm2.8/1.8
      Range/Width difference: 139.3 MeV0.4 mm/0.6 mm1.8 mm/1.3 mm4.0/2.1

      4. Discussion

      In this study, we have successfully predicted the high-resolution dose images from not only the simulated image but also measured SEB images for various count level using the proposed DL approach. The trained DL model achieved the performance with the difference of the ranges and widths of the beams within 1.0 mm for the measured SEB images with ∼ 3.2 x1011 protons irradiations (180 s irradiation), as listed in Table 2. The MSEs and SSIMs in that condition were smaller than 6.71 × 10−5 and larger than 0.993, respectively (Table 2), which were similar values to those for carbon-ion SEB images [
      • Yamaguchi M.
      • Liu C.-C.
      • Huang H.-M.
      • Yabe T.
      • Akagi T.
      • Kawachi N.
      • et al.
      Dose image prediction for range and width verifications from carbon ion-induced secondary electron bremsstrahlung x-rays using deep learning workflow.
      ]. These results indicated that the DL approach can be applied to SEB images of protons as well as those of carbon-ions in the previous study.
      The purpose of the first U-Net model was to denoise the SEB images with various count level. High statistical noise in the measured images leads to uncertainty in the ranges and beam width estimation for the SEB imaging. A smoothing method using a Gaussian filter is commonly used for denoising images, but this method results in a degradation of spatial resolution and the data in the steep areas of the measured image [
      • Yamamoto S.
      • Yamaguchi M.
      • Akagi T.
      • Kitano M.
      • Kawachi N.
      Sensitivity improvement of YAP(Ce) cameras for imaging of secondary electron bremsstrahlung x-rays emitted during carbon-ion irradiation: problem and solution.
      ]. Therefore, we applied the DL method to denoise the SEB images in the first step to predict the dose image for the ranges and beam width estimation. The purpose of the second U-Net model was to predict the high-resolution dose image to solve the problems of limited spatial resolutions of the measured images and nonlinearity between SEB and proton-dose.
      Even from the SEB images with smaller number of protons, our proposed DL model achieved the performance with the difference of the ranges and widths of the beams within 2.2 mm from the SEB image for simulation data (Fig. 5). Moreover, we could estimate the ranges and widths of the beams less than 2.1 mm differences from real measured images (Fig. 8). These results indicate that our proposed DL approach may be used for predicting the dose images for the real measurement data under low-count conditions, and the transferability and feasibility of trained DL model by simulation images on real measured images with different count level.
      The simulated and measured images of SEB were obtained by irradiation of the total number of 1010 ∼ 1011 protons. As shown in Fig. 2, high-count images and clear beam trajectories could be obtained under these irradiation conditions. However, these irradiation conditions were still higher than the clinical dose level (107 ∼ 108 protons/spot). To apply this approach in clinical dose level, we need to increase the sensitivity of the developed x-ray camera [
      • Yamamoto S.
      • Yamaguchi M.
      • Akagi T.
      • Kitano M.
      • Kawachi N.
      Sensitivity improvement of YAP(Ce) cameras for imaging of secondary electron bremsstrahlung x-rays emitted during carbon-ion irradiation: problem and solution.
      ] or increasing the number of x-ray cameras will be required. In addition to the dose level, we trained the SEB image data in a homogeneous water phantom in this study. In clinical situation, proton-dose distributions in patient’s body are complicated due to the change of the beam range caused by air and bone structures. DL and Machine learning approaches have been applied to predict delivered dose distributions in a patient’s body using irradiation log-files [
      • Maes D.
      • Bowen S.R.
      • Regmi R.
      • Bloch C.
      • Wong T.
      • Rosenfeld A.
      • et al.
      A machine learning-based framework for delivery error prediction in proton pencil beam scanning using irradiation log-files.
      ] and prompt gamma-ray images [
      • Liu C.C.
      • Huang H.M.
      A deep learning approach for converting prompt gamma images to proton dose distributions: a Monte Carlo simulation study.
      ] and to accelerate Monte Carlo dose calculation for treatment planning [
      • Javaid U.
      • Souris K.
      • Huang S.
      • Lee J.A.
      Denoising proton therapy Monte Carlo dose distributions in multiple tumor sites: a comparative neural networks architecture study.
      ,
      • Ciardiello A.
      • Asai M.
      • Caccia B.
      • Cirrone G.A.P.
      • Colonna M.
      • Dotti A.
      • et al.
      Preliminary results in using Deep Learning to emulate BLOB, a nuclear interaction model.
      ]. We will try to measure SEB images for spread-out Bragg Peak for the clinical dose level and to evaluate the performance of the DL estimation using SEB image data in a heterogeneous phantom such as a patient’s body.
      In this study, the SEB was measured using only one x-ray camera. To improve the sensitivity of the measurements, we will design a system with multiple x-ray cameras. Moreover, by placing the multiple x-ray cameras at different angles, we may be able to measure three-dimensional (3D) information and to reconstruct tomographic images. The measured images with multiple x-ray cameras may also be used to derive 3D dose images by DL without using the conventional reconstruction algorithms [
      • Kim K.
      • Wu D.
      • Gong K.
      Penalized PET reconstruction using deep learning prior and local linear fitting.
      ,
      • Liu C.-C.
      • Qi J.
      Higher SNR PET image prediction using a deep learning model and MRI image.
      ,
      • Shen L.
      • Zhao W.
      • L.
      Xing Patient-specific reconstruction of volumetric computed tomography images from a single projection view via deep learning.
      ].

      5. Conclusions

      High resolution dose images from measured and simulated SEB images were successfully predicted by using the trained DL model for protons. Our proposed DL model was feasible to predict dose images accurately even with smaller number of irradiated protons. Future study will focus on applying the DL model to heterogeneous targets such as patients and clinical irradiation fields in the clinical dose level for the prediction of the dose distribution.

      Declaration of Competing Interest

      The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

      Acknowledgements

      We performed this study’s proton experiments at the Nagoya Proton Therapy Center. We thank the clinical teams for granting us beam time for our experiments and the staffs who helped us prepare and carry out the irradiations. This work was supported in part by JSPS KAKENHI , Japan Grant Number JP18K19909 and JP19H00672 .

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