Deep learning-based synthetic dose-weighted LET map generation for intensity modulated proton therapy

Abstract The advantage of proton therapy as compared to photon therapy stems from the Bragg peak effect, which allows protons to deposit most of their energy directly at the tumor while sparing healthy tissue. However, even with such benefits, proton therapy does present certain challenges. The biological effectiveness differences between protons and photons are not fully incorporated into clinical treatment planning processes. In current clinical practice, the relative biological effectiveness (RBE) between protons and photons is set as constant 1.1. Numerous studies have suggested that the RBE of protons can exhibit significant variability. Given these findings, there is a substantial interest in refining proton therapy treatment planning to better account for the variable RBE. Dose-average linear energy transfer (LETd) is a key physical parameter for evaluating the RBE of proton therapy and aids in optimizing proton treatment plans. Calculating precise LETd distributions necessitates the use of intricate physical models and the execution of specialized Monte-Carlo simulation software, which is a computationally intensive and time-consuming progress. In response to these challenges, we propose a deep learning based framework designed to predict the LETd distribution map using the dose distribution map. This approach aims to simplify the process and increase the speed of LETd map generation in clinical settings. The proposed CycleGAN model has demonstrated superior performance over other GAN-based models. The mean absolute error (MAE), peak signal-to-noise ratio and normalized cross correlation of the LETd maps generated by the proposed method are 0.096 ± 0.019 keV μm−1, 24.203 ± 2.683 dB, and 0.997 ± 0.002, respectively. The MAE of the proposed method in the clinical target volume, bladder, and rectum are 0.193 ± 0.103, 0.277 ± 0.112, and 0.211 ± 0.086 keV μm−1, respectively. The proposed framework has demonstrated the feasibility of generating synthetic LETd maps from dose maps and has the potential to improve proton therapy planning by providing accurate LETd information.


Introduction
Proton therapy has an advantage over conventional photon therapy because of the proton beam Bragg peak effect (Goitein 1985, Baumann et al 2020).The Bragg peak effect allows a proton to deposit most of its energy in the tumor while sparing normal tissues because there is essentially no exit dose beyond the Bragg Peak.Proton therapy offers advantages, but it does come with uncertainty due to different dose effects compared to conventional photon radiotherapy.Bragg Peak positioning is strongly dependent on the accurate estimation of the proton range, which can be complicated by variations in tissue composition and density within the patient's body, introducing uncertainties that are not typically encountered with photon therapy (Paganetti 2012).cross-validation approach in our methodology.In this process, our patient dataset was evenly divided into five subsets.During each iteration of the validation, a single subset of patients was selected as the test dataset, with the remaining four subsets used for training.This procedure was repeated five times, each time with a different subset serving as the test dataset, thereby ensuring that each patient's data was included in the test dataset exactly once.Emory IRB review board approval was obtained, and informed consent was not required for this Health Insurance Portability and Accountability Act (HIPAA) compliant retrospective analysis.Three DL models were compared in our study: the pixel-to-pixel GAN, the Wasserstein CycleGAN, and our proposed CycleGAN.These DL models were trained using 2D transverse slices and were subsequently evaluated based on quantitative parameters.

Proposed cycleGAN based framework
The detailed framework is shown in figure 1.The dose distribution map for the patient was derived from the TPS of RayStation 10B (RaySearch Lab., Stockholm, Sweden).Conversely, the LET d distribution map was produced using a Monte Carlo (MC) engine in RayStation 12 A (RaySearch Lab., Stockholm, Sweden), which has been validated against FLUKA simulation reference.

Proposed cycleGAN architecture
Traditional adversarial network methods, such as generative adversarial networks (GANs), are founded on two sub-networks: a generator and a discriminator, operating in opposing directions.Given two training datasetsfor instance, a dose map and a LET d map-an initial mapping is learned to generate an image that resembles an LET d map from a dose map image, referred to as a synthetic LET d map image in this study.The generator's task is to create a synthetic LET d map image from the dose map image that is convincing enough to deceive the discriminator into identifying it as a genuine LET d map image.Conversely, the discriminator's training objective is to minimize the judgment error within its network and to amplify its capacity to discern a genuine LET d map image from a synthetic LET d map image.The generator and discriminator networks compete against each other during the training process.This competition fosters the improvement of each network's capabilities, leading to a more accurate synthetic LET d map in this study (Goodfellow et al 2020).
The CycleGAN, developed by Zhu et al (2017) is a novel approach for unpaired image-to-image translation based on the GAN framework.Its superiority over traditional DL networks in generating synthetic images has been affirmed by various research studies (Lei et al 2019, Harms et al 2020, Brou Boni et al 2021).The proposed CycleGAN consists of two sub-networks: two U-net based generators and two discriminators.Their architecture detail information are shown in figures 2(a) and (b).The structure of the generators and discriminators was specifically designed and tailored to accommodate the unique characteristics of these datasets and the intended Convolutional neural networks (CNNs) that incorporate residual blocks have demonstrated impressive results in image-to-image translation tasks (He et al 2016), particularly when the source and target images share substantial similarity.This is akin to the relationship between dose and LET d map images.Detailed information of residual block in generator is shown in figure 3.Each residual block consists of a residual connection and multiple hidden layers.Although the residual block doesn't alter the size of the feature map, it facilitates network optimization and enhances performance in image-to-image translation tasks.

Compound loss function
CycleGAN generator loss function can be divided into three parts, an adversarial loss also called GAN loss, cycle consistency loss and identity loss (Zhu et al 2017).The adversarial loss function, which relies on the output of The CycleGAN discriminator loss consists of two parts, the fake loss and real loss, and they are shown in equations ( 10) and (11).The total discriminator loss function is shown in equation (12).Where I noise represents a generated noise image where each voxel possesses a random value between 0 and 1, l is the weight parameters which is set as 0.5 in this work

Data acquisition and preprocess
The data set consisted of 50 patients diagnosed with early-stage prostate cancer, all of whom received proton SBRT at the Emory Proton Therapy Center.Out of these, 41 patients were designated as the training dataset, while the remaining 9 patients were used as the application dataset.All the patients received a total dosage of 36.25 Gy RBE , administered over 5 fractions.Each treatment plan incorporated four beams: two horizontal opposed beams and two anterior oblique beams set at +/− 45-degree angle from the horizontal level.The two horizontally opposed beams accounted for 70% of the total doses.All treatment plans were optimized using the RayStation treatment planning system V10B (Raysearch Lab, Stockholm, Sweden).As per clinical practice, we planned on the clinical target volume (CTV) with robust optimization accounting for an uncertainty of ±3.5% in range and 5 mm (3 mm in posterior) in 6 orthogonal directions for setup.Single field optimization (SFO) strategies were mostly utilized in the treatment planning process.The total dose maps were produced with Monte Carlo dose engine implemented in RayStation V10B.All treatment plans shared the same dose grid, with a resolution of 0.3 cm × 0.

Implementation and evaluation
The dose and LET d map images were fed into the network as 128 × 256 2D slices.Given that each patient has 64 slices and considering the dataset of 41 patients, there are a total of 2624 slices in the training dataset.The loss function hyperparameters l, b, g and d are set as 10, 5, 20, 5, respectively.In the original CycleGAN paper (Zhu  et al 2017), certain weights were assigned to these loss components, including the adversarial (1), cycle consistency (10), identity (5) loss.The optimal weight for the supervised loss (g d , and ) are found through hyperparameter tunning.The learning rate for Adam optimizer is set as 2e-4, and the networks are trained on an NVIDIA Geforce 4090 GPU with 24 GB of memory with a batch size of 1.During training, 4.2 GB CPU memory and 7 GB GPU memory were used for each batch optimization.Each iteration took approximately 2 min during the training phase.The training process was terminated after 600 iterations, with the training of each model taking approximately 30 h in total.In the testing phase, generating a LET d map for a single patient required about 20 s.
For the evaluation of the proposed CycleGAN and two reference models, we utilized N-fold cross validation.In this evaluation technique, data from nine patients was omitted from each dataset (both training and testing) during the training phase.The remaining data was then used as the testing dataset.This process was carried out three times, with patients randomly selected each time for this purpose.
For quantitative comparisons, synthetic LET d maps are compared with ground truth LET d maps using the mean absolute error (MAE), peak signal-to-noise ratio (PSNR) and normalized cross correlation (NCC).MAE quantifies the average pixel-wise difference between synthetic and ground-truth images.However, MAE is not adept at capturing perceptual discrepancies, making it sometimes inadequate for a holistic assessment of synthetic image quality.Thus, metrics like NCC and PSNR are often paired with MAE for a more nuanced evaluation.PSNR, predominantly used in image compression and restoration, gauges the quality of reconstructed images vis-à-vis their originals.Its simplicity has made it popular, yet its reliance on mathematical closeness sometimes misaligns with human visual perception.For instance, images with a high PSNR might visually differ, while those with a lower PSNR might appear perceptually identical.To mitigate PSNR's perceptual limitations, metrics like NCC have found utility in synthetic image assessments.NCC, a similarity metric, is particularly suited for gauging perceptual and structural resemblances, offering a complementary perspective to MAE and PSNR in evaluating synthetic imagery.
MAE measures the magnitude of the difference between the generated image and the ground truth image, as shown in equation ( 14).Where ( ) f i j , is the value of pixel ( ) i j , in the ground truth image, ( ) t i j , is the value of pixel ( ) i j , in generated image, and n n x y are the number of voxels, n z is the number of slices x y z Peak signal-to-noise ratio (PSNR) is an engineering term for the ratio between the maximum signal and the noise.PSNR is calculated with equation (15).Where MAX is the maximum signal intensity possible and MSE is the mean-squared error of the image.
The NCC is a measure of the similarity of image structures and is widely used in pattern matching and image analysis (Yoo and Han 2009).NCC is calculated with equation (16).Where s s f t are the standard deviation of the ground truth and generated images To illustrate the statistical significance of quantitative improvement by the proposed CycleGAN, paired twotailed t-tests (α = 0.05) were used for comparison of the outcomes between numerical results groups calculated from 9 patients' data in test dataset.The two-tail paired t-test can validate whether the improvement of the proposed model is significant or not compared with other reference models.
All doses and anatomical contours related to the dataset were derived from clinically approved treatment planning data.These contours were exported to MATLAB to carry out the LET d volume metrics calculation on specific ROIs, further evaluating the performance of the proposed methods in clinical practice.The mean value comparisons and LET d volume histograms calculations at 95%, 50%,10% and 5% were performed for the CTV, rectum, and bladder.For the left and right femoral heads (Fem_Head_L and Fem_Head_R), only the mean values were compared.

Image synthetic generation performance comparison
Table 1 summarizes the numerical results of various methods applied to the generation of synthetic LET d maps.As shown in table, the proposed CycleGAN surpasses the performance of the other three models in terms of MAE, PSNR, and NCC.The pix2pixGAN demonstrates the second-best performance in terms of MAE, PSNR and NCC, whereas the performance of the Wasserstein CycleGAN is the least impressive among the methods examined.It should be noted that the calculation of MAE was only performed on voxel data points within a mask (with a dose threshold of 50 cGy RBE ), implying that the image background was not incorporated in the MAE computation.The performance of CNN is comparable to that of pix2pixGAN, though it is slightly inferior.The proposed CycleGAN demonstrates a MAE of 0.096 keV μm −1 , a value substantially smaller (approximately 3%-5%) than the typical LET d value at each voxel (around 2-3 keV μm −1 , shown in figure 4).Additionally, the proposed CycleGAN exhibits a lower standard deviation compared to the other models in terms of MAE, PSNR and NCC.
Table 2 displays the results of the two-tailed paired t-test comparing the proposed CycleGAN with the other three reference models.The results demonstrate that the proposed CycleGAN significantly outperforms the other two reference models in terms of MAE, PSNR and NCC.
Figure 4 provides a visual representation of the estimation errors generated by the reference models and our proposed CycleGAN network.The proposed CycleGAN outperforms the other three reference models.The Figure 5 presents the comparison of LET d values along a profile line passing through the rectum of a patient, as predicted by the four DL models: CNN, Pix2PixGAN, Wasserstein CycleGAN, and our proposed CycleGAN.The proposed method aligns with the ground truth better than the other two reference models.The Wasserstein CycleGAN significantly overestimates the LET d value from voxel 51 to 61, whereas the Pix2pixGAN underestimates the LET d value from voxel 53 to 60. CNN exhibits a mismatch with the ground truth data and appears to consistently underestimate the LET d values for voxels ranging from 28 to 41.
Figure 6 shows the synthetic LET d histograms generated by the proposed CycleGAN, CNN, Pix2pixGAN, and Wasserstein CycleGAN, along with the ground truth for comparison.As shown in figure 6, the proposed CycleGAN demonstrates a better match in terms of LET d value distribution when compared to the reference models.

Quantitative analysis in clinical practice
The LET d -volume metrics and mean values for the CTV and specific OARs, including the rectum, bladder, Fem_Head_L, and Fem_Head_R, are detailed in proposed CycleGAN exhibited the best performance for small volume metrics at the bladder, it was outpaced by the Wasserstein CycleGAN and Pix2pixGAN at the CTV and rectum.CNN is not evaluated in this study.Figure 7 shows the comparison of dose-linear energy transfer histogram (DLVH) for a single treatment plan, comparing the ground truth with the Pix2pixGAN, Wasserstein CycleGAN and proposed CycleGAN.
As shown in table 3, the proposed CycleGAN demonstrated superior performance in terms of large and median volume metrics at CTV, rectum and bladder, with the exception of the CTV-L 50%.Though the proposed CycleGAN exhibited the best performance for small volume metrics at the bladder, it was outpaced by the Wasserstein CycleGAN and Pix2pixGAN at the CTV and rectum.The performance of our proposed method   aligns closely with that of the reference models when evaluated at CTV-L 10% and CTV-L 5%.For the metric Rectum-L 10% , our proposed method surpasses the Wasserstein CycleGAN in performance.It aligns closely with the performance of pix2pix GAN but exhibits a reduced standard deviation.In evaluations using low-volume metrics, the relatively few data points may introduce errors, potentially obscuring the superior performance of our proposed method.

Discussion
There's a growing body of evidence suggesting that LET d values could be utilized in the biological optimization of treatment plans to enhance the therapeutic ratio in proton therapy (Grassberger andPaganetti 2011, Giantsoudi et al 2013).In this work, we present a framework that utilizes a paired CycleGAN to generate synthetic LET d maps from dose maps.The work provides a detailed account of the customized paired CycleGAN structure and the specific hyperparameters employed.The proposed CycleGAN demonstrates superior performance in image synthesis evaluations, as evidenced by its better MAE, PSNR, and NCC results, compared to those of the Pix2pixGAN and Wasserstein CycleGAN.
Our work stands out as, to the best of our knowledge, it represents the first instance of using a paired CycleGAN for predicting LET d from treatment dose plans in proton radiation therapy for prostate cancer.The MAE of the proposed CycleGAN is 0.096 ± 0.019 keV μm −1 , which is approximately 5% of the most typical LET d value in our dataset (as shown in figure 4).This is also around 4%, 3%, and 2% of the mean LET d value at CTV (mean value is 2.42 keV μm −1 ), rectum (mean value is 3.21 keV μm −1 ), and bladder (mean value is 4.24 keV μm −1 ), respectively.Though we are the first to publish results on proton therapy for prostate cancer using a paired CycleGAN, we can compare its performance with other methods for predicting LET d across various anatomic sites.Pirlepesov et al developed an Artificial Neural Network (ANN) to predict the LET d map for cranial patients undergoing proton therapy (Pirlepesov et al 2022).The Root Mean Square (RMS) difference reported in their study ranges from 0.5 to 1 keV μm −1 for various OARs, whereas our proposed method achieved an RMSE of 0.57 keV μm −1 at prostate.Before the adoption of DL methods, analytical approaches were the practical options for calculating LET d to avoid the significant time and effort required for Monte Carlo simulations.Wilkens et al developed an analytical method to calculate LET d along the central axis of broad beams in water, with an observed maximum deviation of 0.5 keV μm −1 (Wilkens and Oelfke 2003).Marsolat et al suggested a correction factor for Wilkens' model, thereby improving the mean LETd deviation along the beam axis to 0.05 keV μm −1 (Marsolat et al 2016).It is important to note that these methods perform LET d calculations for a proton beam in water, a scenario significantly less complex in terms of structure and physical conditions compared to the prostate cancer patients undergoing SBRT treatments presented in this work.
LET d is a physical quantity that is difficult to measure or calculate accurately.At present, MC simulations are the golden standard for LET d calculation.However, implementing the MC method for individual patient LET d calculation involves considerable effort.This includes but is not limited to reproducing complex geometrical structures and accommodating complicated physical conditions.Various patient body sizes and the relative positioning of patients during treatment make the reproduction of precise geometry in MC software a significant challenge.Choosing the correct physical conditions for Monte Carlo simulations also poses complexity to the process.The physics involved are quite intricate; for instance, incorporating secondary protons into the simulation can alter the results compared to considering only primary protons (Kalholm et al 2021).Beyond the efforts in implementing the MC algorithm, the computational cost is another significant challenge.Most MC codes used for calculating LET d , such as Geant4-TOPAS (Polster et al 2015), are still CPUbased, which makes the simulation quite time-consuming (more than several minutes).The proposed framework addresses these challenges.Once the DL network is trained, the only necessary input is the dose plan map.From this, the network can generate a highly accurate LET d map in less than 20 s.This significant reduction in time and computational resources could greatly enhance the efficiency and applicability of proton therapy treatment planning.
In the treatment planning of prostate cancer proton therapy, two OARs, the rectum and the bladder, are likely to present a challenge.However, the proposed method demonstrates good performance on large, medium, and small volume metrics for these OARs and the CTV, with differences smaller than 0.5 keV μm −1 .A notable exception is at the small volume metrics of the rectum where the observed difference is 0.726 keV μm −1 .This is likely due to the smaller number of data points in these metrics and the fact that the rectum itself has a higher LET d value.The maximum observed differences in the mean LET d value across all examined OARs and the CTV are less than 0.3 keV μm −1 , which means the synthetic LET d map has a good agreement with the ground truth.
Despite the promising performance of the proposed method in generating synthetic LET d maps, there are still limitations in this work.The accuracy of our proposed method is still contingent upon the quality of the ground truth, which is the LET d map generated using the vendor's internal MC code.Moreover, the trained network did not exhibit robustness across different optimization strategies.The optimization strategy of the training dataset used SFO.However, when we evaluated our trained network with a test dataset that employed a multi-field optimization (MFO) strategy, the MAE increased to 0.6 keV μm −1 .Additionally, we observed that the mean difference in the OARs and CTV exceeded 0.5 keV μm −1 .Moving forward, we aim to enrich our proposed framework by incorporating a more extensive training dataset to enhance the performance and robustness of this approach.
KBP approaches in proton therapy hold the promise of delivering the advantages observed with their application in photon treatment planning.These benefits encompass enhanced plan quality and consistency (Li et al 2017), improved treatment planning workflows (Good et al 2013, Ge andWu 2019).The advantages in proton therapy are further amplified, enabling a comparative analysis of plans between proton and traditional photon-based radiation therapy.This aids in identifying patients who are most likely to benefit from proton therapy.Our introduced framework, capable of delivering precise LET d distribution data, holds promise in integrating the KBP approach within the realm of LET d .Given that the LET d of protons rises at the distal end and there exists a robust correlation between RBE and LET d value, LET d is deemed a pivotal determinant in assessing potential variable RBE within proton therapy.LET-based optimization can ensure that critical structures are spared from this heightened biological damage.A review of the literature reveals promising indications for the broad adoption of LET-based optimization (Deng et al 2021).This optimization is contingent upon rapid and precise LET d distribution data, which our proposed methodology is equipped to furnish.Moreover, should we obtain the ground truth for the LET-based optimization plan, it would be feasible to adapt our proposed framework to synthesize the LET-based optimization plan derived from the original plan.
While the paired CycleGAN has shown commendable performance in this study, several recently developed DL models have reportedly outperformed the CycleGAN in image synthesis tasks (Ho et al 2020, Sano et al 2021), such as the diffusion denoising probabilistic model.We are motivated to incorporate more advanced DL models to further enhance the accuracy of LET d prediction in the future.The LET d map information also plays a crucial role in other anatomical sites such as head-and-neck and breast.Moving forward, it will be necessary to train the proposed model with datasets from various anatomical sites.The proposed method operates on 2D slices and does not employ a patch extraction strategy.It is conceivable that 3D patch-based models might offer improved structural preservation and more effectively capture spatial relationships across multiple dimensions.The proposed method could potentially be extended to generate LET d maps for other treatment modalities, such as Carbon-ion therapy, which is also a topic of future work.

Conclusion
We proposed a framework utilizing paired CycleGAN to generate synthetic LETd maps for prostate cancer patients undergoing SBRT treatment, derived directly from the treatment dose plans.The accuracy of the proposed method was scrutinized through quantitative evaluation and compared with two other reference DL models.The method we've proposed demonstrates high accuracy and efficiency in predicting LET d maps.This framework has the potential to significantly benefit more proton therapy centers by improving treatment plan quality through RBE optimization, aided by the provision of highly accurate LET d information.

Figure 1 .
Figure 1.Proposed CycleGAN based synthetic LET d map generation framework.D Dose represents the dose image discriminator, D LET is the LET d image discriminator, G LET is the generator that generates LET d image from dose image, G Dose is the dose generator from LET d image, Dose in blue square means the original dose image, LET in blue square means the ground truth LET d image, sDose in red square means the synthetic dose image, sLET in red square means the synthetic LET d images, Supervised Loss is the added compound loss function compare to traditional cycleGAN.The ground truth dose image goes into G LET to generate sLET, while the ground truth LET d enters G Dose to generate sDose, thereby completing the cycle.The sLET and ground truth LET d enters the D LET, while the sDose and ground truth Dose enters the D Dose .
3 cm × 0.3 cm.The dose map with patient CT are shown in figures A1(a1)-(a2).The LET d is defined as equation (13), where AE ( ) x E is the proton fluence at specific distance x, and S(E) is the stopping power at specific energy.The LET d map was calculated with RayStation V12A MC code engine (RaySearch Lab., Stockholm, Sweden), which has been verified with experiment and FLUKA (AB 2021).The calculated LET d maps with patient CT were shown in figures A2(b1)-(b2).The LET d has the same voxel size with dose map, which is 0.3 cm, and the LET d is shown in the unit of 1 m - KeV m .1 A dose threshold (50 cGy RBE ) has been added for the calculated LET d .A series of Python scripts was used to extract the dose and LET d map from RayStaion into a three-dimensional matrix.Then the dose and LET d maps were exported to MATLAB R2021b (Mathworks, Natick, MA).Given that each patient has a unique CTV, both the dose and LET d maps exhibit varying image sizes, despite sharing the same spatial resolution.The DL training necessitates uniform image sizes within the training dataset.Therefore, all exported images were padded with zeros to achieve a consistent size of 128 × 256 × 64 models To assess the proposed framework, three benchmark models were employed: a CNN, the pixel-to-pixel GAN (often referred to as Pix2PixGAN), and the Wasserstein GAN.A convolutional neural network (CNN) is a DL algorithm primarily designed for tasks related to processing data with a grid-like topology, such as images.It is one of the foundational architectures behind many advancements in the domain of computer vision (O'Shea and Nash 2015).The implementation of the CNN in our research builds upon our prior publications.For a detailed insight into its implementation, readers are referred to our preceding works(Chang et  al 2022a, 2022b, Chih-Wei Chang et al 2022, Gao et al 2022, Chang et al 2023, Gao et al 2023).The primary distinction between CycleGAN and Pix2PixGAN (Isola et al 2017) is their respective generative mechanisms and.Specifically, CycleGAN operates in an unsupervised manner and employs a dual generative process, while Pix2PixGAN, on the other hand, operates in a supervised manner, using a paired dataset, and utilizes a single generative process.In our research, we leveraged the Pix2PixGAN for the synthesis of the LET d map.A visual representation of the Pix2PixGAN architecture is depicted in figure A2, with detailed structures of the U-net generator (G) and discriminator (D) shown in figures 2(a) and (b) respectively.Within the scope of our study, the Pix2PixGAN functions as a generative model, establishing a transformation from x (dose map image) to y (LET d map image).The Wasserstein CycleGAN, an extension of the classic CycleGAN, was introduced by Martin et al It integrates the Wasserstein distance metric, as described by Arjovsky et al (2017), to bolster training stability and diminish the potential for mode collapse.While the architecture of the Wasserstein CycleGAN mirrors that of the traditional CycleGAN, depicted in figure 1(b), the specifics of the generator and discriminator can be observed in figures 2(a) and (b), respectively.Additionally, the design of the residual block is illustrated in figure 3.

Figure 5 .
Figure 5.Comparison of LET d values along profiles indicated by white lines in LET d map, the ground truth LET d , and estimated by CNN, pix2pixGAN, Wasserstein CycleGAN, and proposed Cycle GAN are shown.

Figure 6 .
Figure 6.Comparison of histogram of LET d map ground truth and synthetic LET d map generated by, CNN pix2pixGAN, Wasserstein CycleGAN, and Proposed CycleGAN.

Figure 7 .
Figure 7.Comparison of LET d -volume histograms (DLVHs) for a single treatment plan, comparing the ground truth with the Pix2pixGAN, Wasserstein CycleGAN, and the proposed CycleGAN.
two discriminators, applied to both the dose-to-LET d (G LET ) generator and the LET d -to-dose generator (G Dose ), Traditional CycleGANs are designed for unpaired image-to-image translation.However, in this work, we have paired images, leading us to propose a supervised CycleGAN (referred to as the proposed Cycle GAN).The architecture of the proposed CycleGAN network is presented in figure 1, which includes an additional supervised loss function incorporated into the generator's loss function.This added supervised loss function in this study is outlined in equations (7) and (8), where ILET is the true LETd map image, IDose is the true dose map image, and the function ‖‖ 2 is the L2 norm operator.The total generator loss function is shown in equation (11), where ,

Table 1 .
Numerical results of different methods on pelvic sLET d image.

Table 2 .
P values by performing a two-sided t-test (α = 0.05) between proposed method and comparison methods for MAE and PSNR on pelvic sLETd maps.

Table 3 .
The mean LET d error and LET d -volume metrics, computed by the proposed CycleGAN, Pix2pixGAN, and Wasserstein CycleGAN at CTV and specific OARs, including the Rectum, Bladder, Fem_Head_L, and Fem_Head_R, are provided in terms of keV/μm.