Effect of metal implants and metal artifacts on back‐projected two‐dimensional entrance fluence determined by EPID dosimetry

Abstract Purpose To evaluate the errors caused by metal implants and metal artifacts in the two‐dimensional entrance fluences reconstructed using the back‐projection algorithm based on electronic portal imaging device (EPID) images. Methods The EPID in the Varian VitalBeam accelerator was used to acquire portal dose images (PDIs), and then commercial EPID dosimetry software was employed to reconstruct the two‐dimensional entrance fluences based on computed tomography (CT) images of the head phantoms containing interchangeable metal‐free/titanium/aluminum round bars. The metal‐induced errors in the two‐dimensional entrance fluences were evaluated by comparing the γ results and the pixel value errors in the metal‐affected regions. We obtained metal‐artifact‐free CT images by replacing the voxel values of non‐metal inserts with those of metal inserts in metal‐free CT images to evaluate the metal‐artifact‐induced errors. Results The γ passing rates (versus PDIs obtained without a phantom in the beam field (PDIair), 2%/2 mm) for the back‐projected two‐dimensional entrance fluences of phantoms containing titanium or aluminum (BPTi/BPAl) were reduced from 92.4% to 90.5% and 90.6%, respectively, relative to the metal‐free phantom (BPmetal‐free). Titanium causes more severe metal artifacts in CT images than aluminum, and its removal resulted in a 0.0022 CU (median) reduction in the pixel value of BPTi artifact‐free relative to BPTi in the metal‐affected region. Moreover, the mean absolute error (MAE) and root mean square error (RMSE) decreased from 0.0050 CU and 0.0063 CU to 0.0034 CU and 0.0040 CU, respectively (vs. BPmetal‐free). Conclusion Metal implants increase the errors in back‐projected two‐dimensional entrance fluences, and metals with higher electron densities cause more errors. For high‐electron‐density metal implants that produce severe metal artifacts (e.g., titanium), removing metal artifacts from the CT images can improve the accuracy of the two‐dimensional entrance fluences reconstructed by back‐projection algorithms.


INTRODUCTION
During radiotherapy, anatomy changes, setup errors and accelerator dose output errors can cause the actual absorbed dose in vivo to differ from that calculated by the treatment planning system (TPS) based on the planning computed tomography (CT) images, which can affect patients' treatment efficacy and safety.][3][4][5][6] In vivo three-dimensional (3D) dose reconstruction during treatment is the most critical DGRT technique.One promising approach involves the combination of back-projection and forward-calculation algorithms based on electronic portal imaging device (EPID) images. 7During the patient's radiotherapy, EPID images are acquired first.Then, the patient's CT images or cone beam computed tomography (CBCT)-based synthetic CT images are input into a back-projection algorithm to reconstructed the two-dimensional (2D) entrance fluence.Finally, the in vivo 3D dose distribution for the patient is obtained using forward-calculation algorithms via the TPS based on the reconstructed 2D entrance fluence.This novel radiotherapy technique allows the estimation of the patient's in vivo dose distribution for each treatment fraction without additional radiation exposure.Despite the challenges of obtaining accurate results, this technique has the potential to improve radiotherapy efficacy and reduce adverse effects by allowing timely adjustment of the treatment plan, and extensive research has been conducted on this topic.Hansen et al. obtained the primary fluence distribution within patients by back-projecting the EPID images to CT images and then convolved the primary fluence distribution with the dose deposition kernel to calculate the in vivo 3D dose distribution, achieving errors of no more than 2% compared to measurements obtained by film and thermoluminescence dosimeters. 8Jarry et al. utilized the Monte Carlo algorithm to back-project the EPID images and reconstruct the in vivo dose distribution. 9The reconstructed dose distribution of the intensity modulated radiotherapy (IMRT) plans achieved a  passing rate (5%/3 mm) of 90%−96% relative to the Monte Carlo calculation, and a  passing rate of 80%−85% relative to the film measurements.Van Uytven et al. developed a model-based 3D in vivo dose reconstruction algorithm that combined the back projection algorithm of EPID images with a forward-calculation algorithm. 7he algorithm achieved high chi pass rates (2%/2 mm) of 97.6%-99.7%for volumetric modulated arc therapy (VMAT) and dynamic IMRT plans.
The CT values in the patient's CT images can be converted to relative electron density (RED) distributions using a CT value-RED calibration curve, which is used as the fundamental data for back-projection calculations based on the EPID images.This enables the derivation of the 2D entrance fluence and forms the basis for utilizing forward-calculation algorithms to acquire 3D in vivo dose distributions.][12][13][14] As a result, the reconstructed image may show bright and dark stripes, which can affect the accuracy of the RED distribution information obtained from the scan.In our previous study, we showed that metal artifacts caused by metal dentures can greatly reduce the dose accuracy in the OARs and nearby planning target volumes (PTVs). 15Metals and metal artifacts in CT images can also affect the accuracy of the 2D entrance fluence reconstructed by back-projection algorithms and EPID images.However, to our knowledge, no studies have been conducted on this topic.
In this study, we acquired both metal-containing and metal-free CT images, as well as the corresponding EPID images of an anthropomorphic head phantom, by replacing its cylindrical inserts.To assess the impact of metal artifacts, we replaced the voxel values of the nonmetal inserts in the metal-free CT images with those of the metal inserts.This allowed us to obtain CT images that were completely free of metal artifacts.We utilized a commercial in vivo EPID dosimetry software to perform back-projection calculations based on various EPID images using different CT images.By comparing the  results of the 2D entrance fluence for each group, as well as the pixel value differences in the metalaffected regions, we determined the impact of different metal types and their metal artifacts on the accuracy of the back-projection calculation, and elucidated the underlying principles.

Research process
As shown in Figure 1, we conducted this study in five steps.First, we acquired the metal-free phantom, Tiand Al-containing phantoms and their corresponding CT images (CT metal-free , CT Ti , CT Al ) by replacing the inserts in the anthropomorphic head phantom.The images of the latter two phantoms contained metal artifacts (Figure 1.I).We also obtained the CT images of the Ti-containing and Al-containing phantoms without metal artifacts by replacing the voxel values of the non-metal inserts in CT metal-free with the voxel values of the corresponding metals (Figure 1.I, Figure S1).Second, we designed separate treatment plans for the brain and nasopharynx (Figure 1.II).Third, we obtained the portal dose image (PDI) predicted by the TPS without a phantom in the beam field (PDI predicted ), the measured PDI without a phantom in the beam field (PDI air ), and the measured PDIs with metal-free, Ti-containing and Al-containing phantoms in the beam field (PDI metal-free /PDI Ti /PDI Al ) based on the EPID images (Figure 1.III).Fourth, we calculated the 2D entrance fluences in the isocenter plane based on the measured PDI and the corresponding CT images using the back-projection algorithm and the inverse square law (Figure 1.IV).Fifth, we analyzed the effect of different metal materials on the back-projection accuracy and the effect of metal artifact reduction (MAR) on the error using  analysis and pixel value error comparison in the metal-affected region (Figure 1.V).

Anthropomorphic phantom
We employed a heterogeneous anthropomorphic head phantom, the CIRS ATOM 701-B dosimetry phantom (Figure 1.I), as a substitute for a live patient's head in our study.This particular phantom is outfitted with 5 mm diameter cylindrical inserts that can be interchanged at various locations.To simulate human heads with different metal implants, we replaced the inserts with titanium and aluminum alloy counterparts (Figure 1.I).

Acquisition and preprocessing of CT images
The CT images were captured with a GE Discovery RT helical CT scanner (General Electric Company, MA, USA), employing a tube voltage of 120 kV, a slice thickness of 2.5 mm, an image resolution of 0.572 mm × 0.572 mm, and a depth of 16 bits.To eliminate errors caused by air noise in the images during the back-projection calculation, voxel values beyond the skin were designated as −1000 HU.
The REDs for the titanium and aluminum alloys were 3.73 and 2.43, respectively.The metal CT values of these alloys were derived based on CT images containing the corresponding titanium and aluminum alloys, with CT values of 8746 HU and 2640 HU, respectively.High RED value metals, such as titanium, induce severe metal artifacts in CT images that degrade image quality and accuracy.Existing commercial MAR algorithms (e.g., GE's SmartMAR, Philips' O-MAR, and Siemens' iMAR) cannot completely eliminate these artifacts and may introduce new artifacts (Figure S2).To obtain the true RED distribution of the metal-containing phantom, we simulated artifact-free CT images by replacing the voxel values of the non-metal inserts in the CT images of the metal-free phantom with those of titanium and aluminum, respectively (Figure S1).These images (CT Ti artifact-free and CT Al artifact-free ) contained titanium and aluminum voxels, respectively, without any metal artifacts.

Designing radiotherapy treatment plans
Based on the CT metal-free images, two sets of dynamic IMRT plans with seven and nine beam fields were designed for the brain and nasopharynx using the TPS (Eclipse 15.6, AXB15.6.06 algorithm) (Figure 1.II).The beam angles were averaged over 360 • .The brain clinical target volume (CTV) was outlined as a 2.5 cm in diameter circle.The PTVs were obtained by externalizing the CTV contours by 4 cm, covering approximately the entire brain tissue in each slice to ensure that each beam field passed through all metal rods, thus creating a uniform dose distribution.The CTV and gross target volume (GTV) of the nasopharyngeal carcinoma were outlined to mimic a real patient's target volume.The PTV and planning gross target volume (PTV-G) were obtained by externalizing the CTV and GTV contours by 5 mm each.The OAR contours were outlined by referencing a real patient's anatomy.For the seven-field and nine-field brain plans, the prescribed dose for PTV was 6000 cGy in 30 treatment fractions.For the seven-field and nine-field nasopharynx plans, the prescribed doses for the PTV and PTV-G were 6006 cGy and 7029 cGy in 33 treatment fractions, respectively.These plans were replicated with the same multileaf collimator (MLC) and monitor unit (MU) parameters for CT Ti , CT Ti artifact-free , CT Al , and CT Al artifact-free .

EPID equipment and imaging dosimetry calibration procedures
For this study, we used the Varian VitalBeam linear accelerator (Varian Medical Systems, CA, USA) equipped with 60 pairs of MLCs and an a-Si 1200 portal imager to acquire EPID images.The a-Si 1200 portal imager measures 40 × 40 cm 2 , and the EPID images have a size of 1190 × 1190 pixels with a resolution of 0.336 mm.The EPID detector was fixed at a distance of 160 cm from the source for this study.
To ensure the accuracy of the EPID images, it is necessary to calibrate the dose of the imaging system at the accelerator workstation following the Varian Technical Reference Guide.The calibration process includes five sequential steps, dark field, flood field, pixel correction, beam profile, and dose normalization, which are all carried out in the MV image calibration mode of the workstation.Throughout the calibration process, the flat panel detector must be maintained at a fixed distance of 160 cm from the source, and the X-ray energy should be set to 6 MV.For the beam profile calibration step, a reference is established using a 40 × 40 cm 2 field at a depth of 5 cm in water.In portal dosimetry, it is common to use the convention of 1 MU delivered at 100 cm to a 10 × 10 cm 2 field.Since the detector was located 160 cm from the source in this study, a target MU of 1 was used in the dose normalization step, and the reference dose was set to 0.391 calibrated unit (CU) according to the inverse square law.

Acquisition of the PDIs
In this study, the EPID detector was positioned at a source-to-detector distance (SDD) of 160 cm.For consistent comparison, all the PDI images and backprojected 2D entrance fluences were converted to the isocenter plane (SDD = 100 cm) with a size of 1190×1190 pixels and a resolution of 0.21 mm using the inverse square law. Figure 1.III illustrates the process of obtaining different PDIs.First, the TPS calculates the predicted PDI (PDI predicted ) based on the treatment plan parameters without any phantom in the beam field (Figure 1.IIIa).Then, after delivering the plan, the EPID acquires the actual PDI in air (PDI air ) without any phantom in the beam field (Figure 1.IIIb), and the PDIs with three different phantoms in the beam field, the metal-free (PDI metal-free ) phantom, Ti-containing (PDI Ti ) phantom, and Al-containing phantom (PDI Al ) (Figure 1.IIIc).

Acquisition of the 2D entrance fluence above the phantom
We used the commercial in vivo EPID dosimetry software called KylinRay-Dose4D (SuperAccuracy Science & Technology Co., Ltd, Nanjing, China) to implement the back-projection algorithm and reconstruct the 2D entrance fluence.The software is based on the following principle and procedure.The photons received on the flat plane of the EPID are split into primary and scattered rays.The gradients at the field edge differ significantly, resulting in a more pronounced differences in the grayscale distribution gradients of the primary and scattered rays at the field edges in the EPID images.Based on this feature, the software calculates the scattered ray distribution at the EPID flat plane and subtracts the scattered ray grayscale image from the total grayscale image to obtain the grayscale image generated by the primary rays.Then, the primary ray intensity distribution at the EPID top surface is obtained by deconvolution.Next, the equivalent water thickness of the photon penetration phantom is obtained based on the CT information, and the photon energy spectrum and the mass attenuation coefficient of the substance are combined to obtain the photon penetration phantom attenuation coefficient using a fast Monte Carlo calculation method based on GPU parallelism. 16Finally, 2D entrance fluence at the human or phantom surface is reconstructed by applying the inverse square law and correcting for the photon beam attenuation. 17,18The calculation grid size of KylinRay-Dose4D corresponded to a PDI size of 1190 × 1190 pixels and a resolution of 0.21 mm at the isocenter plane.
In clinical applications, it is desirable to use online CT images of the patients (or phantoms) acquired before each treatment for back-projection calculations rather than the planning CT images obtained at the time of setup because the patient's anatomical structures and positions may vary between the initial setup and each treatment.However, our radiotherapy center has only one CBCT scanner that can provide online images.Although we previously developed a method to convert CBCT images into synthetic CT images with reduced metal artifacts, the RED information in the synthetic CT images may not be completely accurate, which may introduce additional errors in the back-projection calculation. 15,19In this study, we used a simulated phantom with a rigid structure and no anatomical variations.The phantom contained only the head region, which was easy to set up, and the setup error in all directions were less than 1 mm.Therefore, we assumed that using the planning CT image of the phantom instead of the online image in the back-projection calculation was sufficiently accurate.
The 2D entrance fluences were reconstructed from different combinations of PDIs and CT images (Figure 1.IV).We denoted the 2D entrance fluences reconstructed based on PDI metal-free and CT metal-free as BP metal-free .We denoted the 2D entrance fluences reconstructed based on PDI Ti /PDI Al and CT Ti /CT Al (with metal artifacts) as BP Ti /BP Al .Finally, we denoted the 2D entrance fluences reconstructed based on PDI Ti /PDI Al and CT Ti artifact-free /CT Al artifact-free (without metal artifacts) were referred to as BP Ti artifact-free /BP Al artifact-free .

2.8
Error assessment  analysis is a widely used approach to assess the accuracy of dose distributions.The methodology of  analysis is explained in detail in the TG-218 report. 20We conducted  analysis based on an external 1 cm region of the MLC complete irradiation area outline (MLC CIAO) for each field corresponding to different PDIs and back-projected 2D entrance fluences using Varian's portal dosimetry (PD) system.The PD system's improved  evaluation calculation algorithm, absolute normalization mode, and global  evaluation with a threshold of 10% were employed in the analysis.To determine the  passing rate, mean  value, and percentage of  values greater than 1.5, we utilized three different criteria: 3%/3 mm, 3%/2 mm, and 2%/2 mm.We also evaluated the pixel-level differences in the back-projected 2D entrance fluences in the metalaffected regions for each group.Our analysis included three comparisons: (1) We used PDI air as a reference to compare the differences among all backprojected 2D entrance fluences; (2) we used BP metal-free as a reference to compare the effects of different metal types on the back-projection accuracy and to evaluate the effect of MAR in CT images on error reduction; and (3) we directly compared the back-projected 2D entrance fluences (BP Ti/Al and BP Ti artifact-free/Al artifact-free ) obtained before and after MAR in CT images and quantified the differences in the metal-affected region.The results of these comparisons are presented as violin plots,and we calculated the mean absolute error (MAE) and root mean square error (RMSE) for the pixel value differences in the first two comparisons.
In Equations ( 1) and ( 2), I 1 and I 2 denote the two images to be compared, and I 1,i and I 2,i denote to the CU values of the i-th pixel in images I 1 and I 2 , respectively.We calculated the difference between the PDI air and PDI Ti /PDI Al to identify metal-affected regions in the back-projected 2D entrance fluences.X-rays passing through metal inserts are subject to higher attenuation, resulting in lower pixel values in metal-affected regions than in non-metal regions in the difference image.To determine the metal-affected regions, we calculated the percentile of pixel values in the difference images.After comparing the results, we determined that pixels with values below the third percentile should be identified as metal-affected regions because most of these pixels were within the area affected by metal in the back-projected 2D entrance fluences.
We used IBM SPSS Statistics software 21 to analyze significant differences between related data sets.For non-normally distributed data, we applied the Wilcoxon signed-rank tests, while for normally distributed data, we used t-tests.The median and interquartile range (IQR) were used for skewed data, and the mean and standard deviation (SD) were used for normal data.

RESULTS
The results in Table 1 show that PDI air has a higher γ passing rate, lower mean γ value, and lower percentage of γ > 1.5 than PDI predicted .This indicates that the EPID is accurately calibrated and that the difference between the measured and calculated values is minimal.Tables 2-4 present the γ passing rate, mean γ value, and percentage of γ > 1.5 for all groups of backprojected 2D entrance fluences (vs.PDI air ) at 2%/2 mm and the corresponding statistical results.The γ results at 3%/3 mm and 3%/2 mm are shown in Table S1.All three γ results were within the tolerance limits recommended by TG-218 for BP metal-free , demonstrating that the backprojection algorithm used in this study is clinically acceptable for a metal-free phantoms. 20However, compared to BP metal-free , all three γ results were significantly worse (p < 0.01 or p < 0.001, Wilcoxon signed-rank test) for the back-projected 2D entrance fluences of the metal-contacting phantom.BP Ti artifact-free had significantly lower mean  values than BP Ti (p < 0.05, Wilcoxon signed-rank test, Table 4) for most beam fields (Figure S3).However, the other  results did not show significant differences among BP Ti , BP Ti artifact-free , BP Al , and BP Al artifact-free (p > 0.05, Wilcoxon signed-rank test).
The accuracy of the back-projected 2D entrance fluence for the metal-containing phantom depends on several factors, such as the CT image quality, mechanical errors, absolute dose errors, positional errors, and errors in the back-projection algorithm.Therefore, using PDI air as a reference for  analysis does not adequately reflect the effects of different metals and metal artifacts on the back-projection algorithm.To isolate the effects of metal and metal artifacts from other factors, we used BP metal-free , which corresponds to the metal-free phantom, as the reference for  analysis.Tables 5-7 show that there was no significant difference (p > 0.05,Wilcoxon signed-rank test) between BP Al and BP Al artifact-free for all three  criteria, indicating that aluminum-induced metal artifacts had negligible effects on the accuracy of the back-projected 2D entrance fluence.In contrast, BP Ti artifact-free had significantly better  results than BP Ti for all three criteria (p < 0.001, Wilcoxon signed-rank test), indicating that titaniuminduced metal artifacts had substantial impacts on the accuracy of the back-projected 2D entrance fluence and that removing these artifacts considerably improved the accuracy.In addition, BP Ti had significantly worse  results than BP Al and BP Al artifact-free for all three criteria (p < 0.001, Wilcoxon signed-rank test), while BP Ti artifact-free did not differ significantly from BP Al and BP Al artifact-free in terms of the mean  value (p > 0.05, paired t test).This implies that titanium and its metal artifacts in CT images introduce more errors in the backprojected 2D entrance fluence than aluminum and that eliminating these artifacts reduces the error, leading to PDI air : portal dose image without the phantom in air.a: The distribution of the skewed data is presented using the median and IQR.BP metal-free : 2D entrance fluences obtained using the back-projection algorithm for a phantom without metal.BP Ti and BP Al : 2D entrance fluences obtained using the back-projection algorithm for phantoms containing titanium/aluminum rods; the corresponding CT images contain metal artifacts.BP Ti artifact-free and BP Al artifact-free : 2D entrance fluences obtained using the back-projection algorithm for phantoms containing titanium/aluminum rods; the corresponding CT images do not contain metal artifacts.***: p value < 0.001.The  analysis results in the table represent the statistical findings for all fields across the four radiation treatment plans designed for this study.
values more consistent with the aluminum-containing phantom (mean  value).
In the  analysis, the accuracy of the 2D entrance fluence corresponding to the beam field is determined for the entire image.However, focusing on the metalaffected regions allows us to better identify errors caused by metal and metal artifacts.Figure 2 compares the pixel-level differences in the back-projected 2D entrance fluence in the metal-affected region with respect to different reference images.In Figure 2a, PDI air is used as the reference, and the results show that BP metal-free has the smallest difference (median 0.0035 CU) and the narrowest distribution.BP Al and BP Al artifact-free have slightly larger differences but similar distributions to BP metal-free .BP Ti has the largest difference (median 0.0069 CU) and the widest distribution, which can be reduced by considering BP Ti artifact-free (median 0.0051 CU).In Figure 2b, BP metal-free is used as the reference, and the results show that BP Al and BP Al artifact-free have negligible differences (median 0.0004 and 0.0008 CU, respectively) and narrow distributions in the metal-affected region.BP Ti The distribution of the skewed data is presented using the median and IQR.BP metal-free : 2D entrance fluences obtained using the back-projection algorithm for a phantom without metal.BP Ti and BP Al : 2D entrance fluences obtained using the back-projection algorithm for phantoms containing titanium/aluminum rods and the corresponding CT images contain metal artifacts.BP Ti artifact-free and BP Al artifact-free : 2D entrance fluences obtained using the back-projection algorithm for phantoms containing titanium/aluminum rods and the corresponding CT images do not contain metal artifacts.**: p value<0.01.***: p value<0.001.The  analysis results in the table represent the statistical findings for all fields across the four radiation treatment plans designed for this study.The distribution of the skewed data is presented using the median and IQR.BP metal-free : 2D entrance fluences obtained using the back-projection algorithm for a phantom without metal.BP Ti nd BP Al : 2D entrance fluences obtained using the back-projection algorithm for phantoms containing titanium/aluminum rods; the corresponding CT images contain metal artifacts.BP Ti artifact-free and BP Al artifact-free : 2D entrance fluences obtained using the back-projection algorithm for phantoms containing titanium/aluminum rods and the corresponding CT images do not contain metal artifacts.*: p value < 0.05.***: p value < 0.001.The  analysis results in the table represent the statistical findings for all fields across the four radiation treatment plans designed for this study.

TA B L E 6
has a larger difference (median 0.0038 CU) and a wider distribution, which can also be reduced by BP Ti artifact-free (median 0.0013 CU).In Figure 2c, BP Al and BP Ti are used as references for their corresponding artifact-free images, and the results show that BP Al artifact-free images have approximately no difference (median 0.0002 CU) and a very narrow distributions in the metal-affected regions, while BP Ti artifact-free has a negative difference (median −0.0022 CU) and a wider distribution, indicating a greater reduction in pixel values due to the removal of Ti-induced metal artifacts.The mean and SD are used to describe the distribution of normally distributed data, while the median and IQR are used for skewed data.In the case of BP Ti , despite the skewness of the data, the contrast was reported using the mean and SD.The pixel-level MAE and RMSE of the back-projected 2D entrance fluences for each beam field versus PDI air in the metal-affected regions are presented in Table 8.The MAE and RMSE values for BP Al and BP Al artifact-free were slightly higher than those for BP metal-free , whereas the MAE and RMSE values for BP Ti and BP Ti artifact-free were considerably increased.The errors for BP Al and BP Al artifact-free were comparable, while BP Ti artifact-free showed substantially lower MAE and RMSE values than BP Ti .When BP metal-free was used as the reference, the error comparison among BP Al , BP Al artifact-free , BP Ti and BP Ti artifact-free showed similar trends (Table 9).Compared to the MAE and RMSE values for BP Ti , the MAE and RMSE values for BP Ti artifact-free decreased from 0.0050 CU to 0.0034 CU and from 0.0063 CU to 0.0040 CU, respectively, compared to BP Ti .
Figure 3 illustrates the effect of metal and metal artifacts on the back-projected 2D entrance fluences for field seven in the nine-field plans for the brain and nasopharynx cases, respectively.The back-projected 2D entrance fluences for other beam fields are shown in Figures S4-S7.Metal inserts attenuate and scatter more X-rays, resulting in lower PDI pixel values in the metal-affected region than in the PDI metal-free (blue regions in Figure 3d and i).In the brain case (upper part of Figure 3), the metal-affected region (elliptical dashed line) has a darker red color in Figures 3a and b, indicating larger discrepancies between BP Ti and BP metal-free , and between BP Ti artifact-free and BP metal-free , respectively.The lighter red color in Figure 3b than in Figure 3a suggests that correcting the metal artifacts in the CT images can reduce the errors in the back-projected 2D entrance fluence in the metal-affected regions.The predominantly blue color in Figure 3c (pink dashed ellipse) shows that BP Ti artifact-free has a much smaller absolute error in the metal-affected region than BP Ti .The profile of pixel error values in Figure 3e further confirms that BP Ti has higher error values and a wider distribution of error pixels in the F I G U R E 3 (a) and (f) Dose difference maps between BP Ti and BP metal-free .(b) and (g) Dose difference maps between BP Ti artifact-free and BP metal-free .(c) and (h) Difference maps of absolute dose errors of BP Ti and BP Ti artifact-free relative to BP metal-free .In (a), (b), (f), and (g), the darker red color indicates larger errors in the back-projected 2D entrance fluence for the Ti-containing phantom than for the metal-free phantom, while the darker blue color indicates the opposite.In (c) and (h), the darker blue color indicates smaller absolute errors in BP Ti artifact-free than in BP Ti , using the BP metal-free as a reference, while the darker red color indicates the opposite.(d) and (i) Dose difference maps of PDI Ti and PDI metal-free .The blue area in the images represents the metal region.(e) and (j) Error value profiles of BP Ti / BP Ti artifact-free / BP Al / BP Al artifact-free relative to BP metal-free , and pixel value difference profiles of PDI Ti / PDI Al relative to PDI metal-free .These curves correspond to the red lines passing through the metal region in the small image in the upper left corner.The error in the metal region in BP Ti is larger than that in BP Ti artifact-free .The black arrows in (e) and (j) indicate the error caused by metal artifacts in BP Ti .metal-affected region than BP Ti artifact-free (green dashed box and black dashed ellipse).For the aluminum case, there is no substantial difference between BP Al artifact-free and BP Al in the metal-affected region, and both have smaller errors than BP Ti artifact-free and BP Ti .A similar pattern is observed for the nasopharyngeal case (lower part of Figure 3).
The mechanism of how metal artifacts affect the back projection algorithm (Figure 4) was investigated by comparing the CT value distribution around a metal insert before and after MAR.The case with the aluminum insert had a lower RED value (Figure 4f, j, o and p) and caused weak metal artifacts in CT Al (Figure 4c, m, n and p), resulting in a small difference in the sum of the CT values between CT Al and CT Al artifact-free (185 ± 1014 HU for CT Al − CT Al artifact-free along the x-axis direction in Figure 4q).The case with the titanium insert had a higher RED value (Figure 4 h, l, o and p) and caused severe metal artifacts in CT Ti (Figure 4d and n-p), leading to a large difference in the sum of the CT values between CT Ti and CT Ti artifact-free (5518±5600 HU for CT Ti − CT Ti artifact-free along the x-axis direction in Figure 4q).

DISCUSSION
An EPID records the spatial distribution of the X-ray fluence exiting the patient during radiotherapy, and a back-projection algorithm can be applied to the EPID  image to reconstruct the 2D entrance fluence at the patient's skin surface based on the patient's CT images.However, the presence of metal implants in the body can lead to numerous metal artifacts in the CT images, affecting the accuracy of the CT values and ultimately the accuracy of the back-projection result.Despite this issue, there are no existing studies on this topic.Therefore, in this paper, we report the errors caused by metal artifacts in CT images on back-projected 2D entrance fluences and compare the effects of different metals on these errors.We created metal-free, Ti-containing, and Al-containing phantoms by replacing the cylindrical inserts in the simulated human phantom.The planning CT images of the metal-containing phantoms had metal artifacts.For comparison, we generated synthetic CT images with metal but without metal artifacts by replacing the voxel values of the non-metal inserts in the metal-free phantom with those of Ti or Al.We used the planning CT images of the phantom to obtain the 2D entrance fluences in the back-projection calculation, assuming that the setup error was negligible (<1 mm in all directions) due to the rigid structure and easy positioning of the phantom.We acquired PDIs corresponding to the metal-free and metal-containing phantoms using the EPID system and obtained different 2D entrance fluences based on the respective CT images using commercial software (KylinRay-Dose4D).
We evaluated the error of the back-projection algorithm caused by the metal and metal artifacts and the improvement in the accuracy after removing metal artifacts from the CT images of the back-projected 2D entrance fluence by comparing the γ results and the pixel value error in the metal-affected region.
According to TG-218, the universal tolerance limit for the γ passing rate is 95% with 3%/2 mm and a 10% dose threshold. 20The γ results of BP metal-free and PDI air in this study indicate that the back-projection algorithm we used is accurate when the phantom does not contain any metals.In a study by Wendling et al., a back-projection technique was developed that achieved γ passing rates (2%/2 mm) of 99.86%-99.99% between the 2D PDIs and the measured dose distribution of the film for a homogeneous slab phantom and IMRT plan, with a mean γ value of less than 0.4. 22For the improved back-projection algorithm for non-uniform media in patients developed by Wendling et al., the average  passing rate and mean  value of the PDIs relative to the TPS calculations were 93.1% and 0.40, respectively, with 3%/3 mm and a 20% dose threshold. 23Our models demonstrate relatively competitive accuracy.
When the phantom contains metals with high RED values, such as titanium, removing metal artifacts from CT images can improve the accuracy of 2D entrance fluences in metal-affected regions obtained by backprojection algorithms.The 2D entrance fluence is reconstructed by performing a back-projection calculation using the primary beam distribution measured by the EPID system.This calculation accounts for the X-ray attenuation along the propagation path through the patient or phantom, which is determined by the RED distribution derived based on the CT values in the CT images.However, metal artifacts can distort the CT values distribution in the CT images, resulting in errors in the 2D entrance fluence in the metal-affected regions.Titanium produced many obvious metal artifacts in the CT images (Figure 4d), and the bright artifacts in CT Ti on both sides of the propagated beam (black ellipses in Figure 4h and l, black arrows in Figure 4p) led to high CT values in regions outside the geometric contours of the metal on both sides of the beam propagation direction (black dashed line in Figure 4q), resulting in errors in a larger range of pixels in the metal-affected region of the BP Ti than in the BP Ti artifact-free (black ellipses in Figure 3e and j).In addition, the bright artifacts in the metal-affected regions (pink ellipses in Figure 4h and l O R C I D Zheng Cao https://orcid.org/0000-0003-2249-5705Xiang Gao https://orcid.org/0009-0006-3605-1741Yuanji Pei https://orcid.org/0000-0002-5626-7949

F I G U R E 1
Schematic diagram.The process of this research can be divided into five parts: I. Acquisition of CT images; II.Designing of treatment plans; III.Acquisition of portal dose images with the EPID system; IV.Acquisition of the 2D entrance fluences above the phantom; and V. Error assessment.
Percentage of  >1.5 for the back-projected 2D entrance fluences of metal-containing phantoms versus BP metal-free , and the statistical results.

bF I G U R E 2
Wilcoxon signed-rank test.c Paired t test.BP metal-free : 2D entrance fluences obtained using the back-projection algorithm for a phantom without metal.BP Ti and BP Al : 2D entrance fluences obtained using the back-projection algorithm for phantoms containing titanium/aluminum rods; the corresponding CT images contain metal artifacts.BP Ti artifact-free and BP Al artifact-free : 2D entrance fluences obtained using the back-projection algorithm for phantoms containing titanium/aluminum rods and the corresponding CT images do not contain metal artifacts.**: p value<0.01.***: p value<0.001.The  analysis results in the table represent the statistical findings for all fields across the four radiation treatment plans designed for this study.Violin plots of the pixel-level differences in the metal-affected regions for (a) all back-projected 2D entrance fluences vs. PDI air , (b) metal-containing back-projected 2D entrance fluences (BP Al /BP Al artifact-free /BP Ti /BP Ti artifact-free ) vs. BP metal-free and (c) BP Ti artifact-free /BP Al artifact-free vs. BP Ti /BP Al .The median and IQR of all pixel value errors are shown in the figure.

F I G U R E 4
Schematic diagram illustrating the increased errors in the metal region in BP Ti caused by metal artifacts.The original CT images of the metal-free phantom (CT metal-free ), Al-containing phantom (CT Al ), and Ti-containing phantom (CT Ti ) are displayed in (b)-(d), with a display window of [−260, 340] HU.Magnified images of the metal regions in the blue boxes in (b)-(d) are shown in (a), (f), and (h).(e) CT image of the Al-containing phantom without metal artifacts (CT Al artifact-free ), corresponding to (f).(g) CT image of the Ti-containing phantom without metal artifacts (CT Ti artifact-free ), corresponding to (h).Color images corresponding to (e)-(h) are shown in (i)-(l), with a display window of [−800, 2000] HU. (m) Difference distribution map between CT Al artifact-free and CT Al .(n) Difference distribution map between CT Ti artifact-free and CT Ti , with a display window of [−4000, 4000] HU.The CT value profiles of the horizontal and vertical lines passing through the voxels in (i)-(l) are presented in (o) and (p), respectively.The blue arrows in (m) and (n) represent the X-ray transmission direction.(q) Sum of CT value errors between CT Ti artifact-free and CT Ti in (n) and between CT Al artifact-free and CT Al in (m) along the X-ray transmission direction.Metal artifacts due to Al were less severe than those due to Ti, and the differences in the CT values due to the metal artifacts in CT Al and CT Al artifact-free were smaller than those in CT Ti and CT Ti artifact-free .

mm) P values associated with 𝜸 analysis results for different groups of data (Wilcoxon signed-rank test) vs. BP Ti vs. BP Ti artifact-free vs. BP Al vs. BP Al artifact-free
TA B L E 1  analysis results of PDI air, with PDI predicted as the reference.a The mean and SD were used to describe the distributions of normally distributed data, while the median and IQR were used for skewed data.PDI air : portal dose image measured without the phantom in air.PDI predicted : TPS predicted portal dose image without the phantom in air.The  analysis results in the table represent the statistical findings for all fields across the four radiation treatment plans designed for this study. passing rate for the back-projected 2D entrance fluence versus PDI air , and the statistical results.
a TA B L E 2 air : portal dose image measured without the phantom in air.a:Thedistribution of the skewed data is presented using the median and IQR.BP metal-free : 2D entrance fluences obtained using the back-projection algorithm for a phantom without metal.BP Ti and BP Al : 2D entrance fluences obtained using the back-projection algorithm for phantoms containing titanium/aluminum rods; and the corresponding CT images contain metal artifacts.BP Ti artifact-free and BP Al artifact-free : 2D entrance fluences obtained using the back-projection algorithm for phantoms containing titanium/aluminum rods; the corresponding CT images do not contain metal artifacts.**:pvalue < 0.01.***:pvalue < 0.001.The  analysis results in the table represent the statistical findings for all fields across the four radiation treatment plans designed for this study.TA B L E 3Percentage of  >1.5 for the back-projected 2D entrance fluences versus PDI air , and the statistical results.

2 mm) P values associated with 𝜸 analysis results for different groups of data (Wilcoxon signed-rank test) vs. BP Ti vs. BP Ti artifact-free vs. BP Al vs. BP Al artifact-free
Mean  value for the back-projected 2D entrance fluences versus PDI air , and the statistical results.PDI air : portal dose image without the phantom in air.a: The distribution of the skewed data is presented using the median and IQR.b: Supplement figure3 shows the difference between the mean  values of BP Ti and BP Ti artifact-free corresponding to each beam field, using PDI air as a reference.BP metal-free : 2D entrance fluences obtained using the back-projection algorithm for a phantom without metal.BP Ti and BP Al : 2D entrance fluences obtained using the back-projection algorithm for phantoms containing titanium/aluminum rods; the corresponding CT images contain metal artifacts.BP Ti artifact-free and BP Al artifact-free : 2D entrance fluences obtained using the back-projection algorithm for phantoms containing titanium/aluminum rods; the corresponding CT images do not contain metal artifacts.*: p value<0.05.**: p value < 0.01.***: p value < 0.001.The  analysis results in the table represent the statistical findings for all fields across the four radiation treatment plans designed for this study. passing rate for the back-projected 2D entrance fluences of metal-containing phantoms versus BP metal-free , and the statistical results.
TA B L E 5

mm) p values associated with 𝜸 analysis results for different groups of data (Wilcoxon signed-rank test) vs. BP Ti vs. BP Ti artifact-free vs. BP Al vs. BP Al artifact-free
a :

mm) p values associated with 𝜸 analysis results for different groups of data (Wilcoxon signed-rank test or paired t test) vs. BP Ti vs. BP Ti artifact-free vs. BP Al vs. BP Al artifact-free
Mean  value for the back-projected 2D entrance fluences of metal-containing phantoms versus BP metal-free , and the statistical results.
TA B L E 7 TA B L E 8 MAE and RMSE values of the back-projected 2D entrance fluences versus PDI air in the metal-affected regions.air : portal dose image measured without the phantom in air.BP metal-free : 2D entrance fluences obtained using the back-projection algorithm for a phantom without metal.BP Ti and BP Al : 2D entrance fluences obtained using the back-projection algorithm for phantoms containing titanium/aluminum rods; the corresponding CT images contain metal artifacts.BP Ti artifact-free and BP Al artifact-free : 2D entrance fluences obtained using the back-projection algorithm for phantoms containing titanium/aluminum rods; the corresponding CT images do not contain metal artifacts.MAE: mean absolute error.RMSE: root mean square error.The table data represent the errors of metal-affected pixel points in the 2D entrance fluences of all of the fields in this study as compared to the corresponding pixel points in the PDI air . PDI