Abstract
Cone-beam computed tomography (CBCT) using an “on-board” x-ray imaging device integrated into a radiation therapy system has recently been made available for patient positioning, target localization, and adaptive treatment planning. One of the challenges for gantry mounted image-guided radiation therapy (IGRT) systems is the slow acquisition of projections for cone-beam CT (CBCT), which makes them sensitive to any patient motion during the scans. Aiming at motion artifact reduction, four-dimensional CBCT (4D CBCT) techniques have been introduced, where a surrogate for the target’s motion profile is utilized to sort the cone-beam data by respiratory phase. However, due to the limited gantry rotation speed and limited readout speed of the on-board imager, fewer than 100 projections are available for the image reconstruction at each respiratory phase. Thus, severe undersampling streaking artifacts plague 4D CBCT images. In this paper, the authors propose a simple scheme to significantly reduce the streaking artifacts. In this method, a prior image is first reconstructed using all available projections without gating, in which static structures are well reconstructed while moving objects are blurred. The undersampling streaking artifacts from static structures are estimated from this prior image volume and then can be removed from the phase images using gated reconstruction. The proposed method was validated using numerical simulations, experimental phantom data, and patient data. The fidelity of stationary and moving objects is maintained, while large gains in streak artifact reduction are observed. Using this technique one can reconstruct 4D CBCT datasets using no more projections than are acquired in a 60 s scan. At the same time, a temporal gating window as narrow as 100 ms was utilized. Compared to the conventional 4D CBCT reconstruction, streaking artifacts were reduced by 60% to 70%.
Keywords: cone-beam CT, image-guided radiation therapy
INTRODUCTION
Cone-beam computed tomography (CBCT) is a powerful imaging tool in image-guided interventions (IGI)1, 2, 3 and image-guided radiation therapy (IGRT).4, 5, 6 It provides volumetric information for accurate target localization in IGRT and a three-dimensional vasculature roadmap in IGI. However, when a moving organ such as the lung or heart is scanned, motion artifacts often significantly degrade the image quality and restrict the use of CBCT.
Recently, four-dimensional CBCT (4D CBCT) was introduced to reduce respiratory motion artifacts.7, 8, 9, 10, 11 The respiratory motion profile is extracted using an external device or directly from the cone-beam projection data set. The motion profile is then utilized to guide the data sorting. The acquired cone-beam projection data are partitioned into several respiratory phases, typically 8–10 phases. However, due to the limited gantry rotation speed and frame rate of the flat-panel imager, the total number of cone-beam projections acquired in one gantry rotation is limited (i.e., typically ∼600 projections). Thus, after the respiratory phase sorting, less than 100 cone-beam projections are available for the reconstruction of each respiratory phase. In addition, the cone-beam projections are often bunched into several clusters in 4D CBCT. This bunched sampling pattern increases the artifact level in the reconstructed images. In fact, when the same number of cone-beam projections are utilized, streaking artifacts in the case of bunched sampling are much more severe than when using uniform angular sampling. Consequently, significant streaking artifacts were observed in 4D CBCT images.12, 13, 14, 15 When the gating window is narrowed, i.e., gated into more than ten phases, the artifact level increases, potentially reducing the clinical value of 4D CBCT images.
In order to reduce the streaking artifacts in 4D CBCT, several interesting schemes were recently proposed. The first scheme is to significantly increase the current gantry rotation speed so that the gantry rotation time is shorter than the breathing period. To achieve this, subsecond per gantry rotation is required, which is very difficult to implement using the current treatment gantry. Since higher speeds are not permitted according the International Electrotechnical Commission recommendation, in order to increase the data view angle sampling, multiple-gantry rotation and slow-gantry rotation schemes were investigated.12, 14 The drawback of these schemes is that the data acquisition time is quite long, increasing the risk of inadvertent patient motion. Additionally, from a clinical standpoint, the patient throughput is reduced. Another scheme is to combine deformable image registration with the cone-beam image reconstruction.13 Besides the removal of the streaking artifacts, another interesting feature of this method is the enhancement of the signal-to-noise ratio (SNR). This method depends on the accuracy of the registration, which can be influenced by the inconsistency between planning CT and CBCT images. Also, the registration procedure is time consuming and there is potential loss of spatial resolution for this method.
In this paper, we propose a simple scheme to reduce the streaking artifacts in 4D CBCT. In this scheme, we reconstruct a prior image using all of the cone-beam projection data without gating. The image volume is then reprojected back at each view angle to generate a motion contaminated CBCT data set. The respiratory signal is used to gate the true data set and the reprojected data set. The difference projections generated from these two data sets (i.e., subtraction in projection space) is then reconstructed to generate a difference image for each respiratory phase using the cone-beam reconstruction algorithm developed by Feldkamp, Davis, and Kress (FDK).16 The difference image is added back to the prior image reconstructed using all projections to generate the final 4D CBCT image volume for each respiratory phase. This scheme was proposed to mitigate streaking artifacts for possible cardiac scans in early the 1980s.17, 18 Due to the limitations of the data acquisition system and other requirements in cardiac scanning, this simple method seems to be forgotten very soon after its development. There are two major reasons to limit the use of this algorithm in cardiac CT imaging. First, the correction scheme does not remove all of the streaking artifacts. The residual streaking artifacts may still limit the diagnostic value of the corrected images. Namely, the corrected cardiac CT images are still not clinically acceptable. Second, the noise level in the corrected images is primarily determined by the undersampled projections. Thus, the CNR in the corrected images is still limited and the final image is not suitable for diagnostic purposes. However, in image-guided radiation therapy, the more important issue is how to track the moving object accurately such that the final trajectory of the moving object can be used to guide the radiation delivery. In this case, the requirement on image quality can be compromised. But the temporal resolution is the major factor which should not be compromised. Therefore, this correction scheme is usable in 4D CBCT in image-guided radiation therapy. In this paper, we adapt the idea to the 4D CBCT case and demonstrate its potential practical value using numerical simulations and experimental phantom studies. This method provides a means to reduce streaking artifacts when using a very narrow respiratory gating window.
METHODS AND MATERIALS
Flow chart of the proposed algorithm
We will first describe the algorithm conceptually and then discuss the implementation strategy. For lung cancer patients, multiple organs move during the respiratory motion. But the outmost tissues of the patient and bony structures like spine, sternum, and ribs are static or quasi-static. Due to the high x-ray attenuation of the bony structures, these structures generate severe streaking artifacts that degrade the image quality. The key observation in the proposed method is that the undersampling streaking artifacts from the static structures can be estimated and then reduced. In order to do so, we first reconstruct a prior three-dimensional image volume using all of the acquired projection data without gating. Then we reproject the reconstructed image volume at the same view angles where the cone-beam projection data were acquired. Two image volumes can be reconstructed for each respiratory phase using both gated measured projections and gated reprojected projections. These two image volumes are contaminated by the undersampling streaking artifacts. But the pattern of undersampling streaking artifacts is very similar in these two image volumes. Thus, a subtraction of these two images will cancel the undersampling streaking artifacts that are due to static objects. At the same time, the static structures will also be cancelled after the subtraction. As a consequence, we are left with an image of the moving components which cannot be cancelled by the subtraction. We then combine this subtraction image which contains motion information of the moving objects with the prior image which contains the static structures. Therefore, by combining these two image volumes we generate an image volume with suppressed streaking artifacts for each respiratory phase. Since the FDK image reconstruction algorithm is linear with respect to the input data, it is more convenient to conduct the subtraction in projection data and directly reconstruct the difference image and add this result back to the prior image volume. The flow chart of the algorithm is presented in Fig. 1.
Figure 1.
Flow chart of the proposed correction algorithm.
Reprojection method and data filtering procedure for data processing
Several reprojection algorithms have been developed and published in literature.19, 20, 21, 22 In this paper, Siddon’s ray-driven forward projection method was used to calculate the reprojections from the prior image.22 The projection value of each ray is computed as a weighted summation of the intensities of voxels on the path of the ray. The weight is the intersection length of the ray with each individual voxels. The major computation load in ray-driven forward projection is to calculate those intersection lengths. In Siddon’s method, the image volume is treated as orthogonal sets of equally spaced, parallel planes rather than individual elements. The intersection lengths are computed based on the intersections of a given ray and these planes. An advantage of the using this method is that the computation complexity is significantly decreased.
For rays passing through the static objects only, the reprojection values should be, in theory, identical to the measured projection values. However, these two values may deviate from each other in practice. Several causes can contribute to this difference, for example, the discretization, noise, numerical errors, etc. When a subtraction is performed, nonzero difference projections are obtained and, consequently, streaking artifacts may appear in the reconstructed difference images. The worst case scenario is the subtraction at the boundaries between high contrast objects such as bones and the soft-tissues. At these boundaries, inevitable numerical errors will cause significant mismatch in the subtracted projection data. In this work, we applied a 3×3 low-pass median filter to the difference projections to mitigate the potential discrepancies caused by numerical errors.
Dynamic phantoms in numerical simulations
A two-dimensional dynamic chest phantom, as shown in Fig. 2, was used in our simulations and the fan-beam geometry was utilized. This phantom is composed of 16 ellipses with parameters given in the Appendix. The object inside the right cavity moves along the horizontal direction and simultaneously changes its vertical semi-axis length to simulate the tumor motion and deformation during respiratory motion. The maximal displacement along the horizontal direction is 40 mm and the vertical axis length varies from 30 to 50 mm. The breathing period was assumed to be 4 s. Data acquisition time of the Varian Trilogy system (i.e., 60 s) was assumed in our simulations and 600 projections were simulated in a full scan.
Figure 2.
Motion phantom (a) and blurred image reconstructed from all available projections without gating (b).
Experimental motion phantom
In order to evaluate the proposed streaking artifacts reduction algorithm, a motion phantom was constructed and scanned in this work. Two vertebra were inserted into the cavity of a 13 cm diameter plastic cylinder within a foam support. Five ulna bones were attached outside of the cylinder to simulate the ribs. A 2 cm diameter plastic sphere which can move simultaneously in the superior-inferior (SI) and anterior-posterior (AP) directions was used to simulate the respiratory motion of a tumor motion. The plastic ball contains a small air cavity and was attached to linear stages via a plastic rod. In this study, the maximal displacements (from peak to valley) were 2 cm in the SI direction and 1 cm in the AP direction. The displacement followed a triangle motion profile, as shown in Fig. 3. The breathing period used in this study was 5.3 s.
Figure 3.
Motion profile used in the experiment.
A second phantom was built in which three objects could move simultaneously to simulate the multiple organs motion in respiratory motion. In this phantom, three plastic objects (one plastic ball and two plastic rods) were attached to the linear stages and move in SI (2 cm) and AP (1 cm) directions. The motion period was programmed to be 4.2 s.
Experimental data acquisition system
The cone-beam projection data of the motion phantom were acquired using the Varian Trilogy treatment system (Varian Medical Systems, Palo Alto, CA). An on-board kV x-ray source and a flat panel detector are mounted to the linac gantry. When the gantry rotates, a series of 2D projections can be acquired and a 3D volume can be reconstructed from these projections using the standard FDK image reconstruction algorithm.16 By incorporation of a respiratory signal, 4D CBCT can be performed on this system. The phantom was scanned using parameters of 125 kVp, 80 mA, and 12 ms pulse width. In total, 640 projections were acquired over a 60 s rotation through 360°. The detector size is 397.3×298 mm2. The detector is read out at 1024×768 pixels with a pixel size of 388×388 μm2. In order to reduce the computation load, a 2×2 binning was used such that a 512×384 detector matrix was utilized.
A NaI(Tl) detector with a photomultiplier tube (PMT) was placed close to but outside of the x-ray field of view. This NaI detector functioned as an x-ray on signal. A temporal stamp was then achieved for each projection. This signal was sent to a personal computer so that it could be synchronized with the motion signal. The proper phase was then assigned for each projection based on these two synchronized signals.
Patient scan
A lung cancer patient was scanned at the Memorial Sloan Kettering Cancer Center using the Varian Trilogy system and an RPM respiratory gating system (Varian Medical System, Palo Alto, CA). Typical scanning parameters, 125 kVp, 80 mA, and 25 ms, were used. The patient was scanned using half-fan mode to achieve a larger field of view (FOV) and the commercial bow-tie filter was attached to the x-ray tube. In half-fan mode, the flat panel detector was shifted 14.7 cm to one end. Both the RPM signal and the x-ray on signal were recorded for gated reconstruction. In total 636 projections were acquired over a 60 s gantry rotation through 360°.
Quantification of streaking artifacts
In order to quantify the level of streaking artifacts in a reconstructed image, the total variation (TV) of the image can be introduced as a figure of merit, which is defined as
| (1) |
A larger TV value corresponds to stronger streaking artifacts. Since the 4D CBCT images are currently reconstructed using the standard FDK algorithm, the degree of streaking artifacts reduction is compared with the FDK algorithm. A streak reduction ratio (SRR) is introduced to quantify the relative level of streaking artifacts:
| (2) |
Note that the intrinsic variations of an image itself have been included in the above streaks reduction factor. In numerical phantom experiments, the above definition can be slightly modified to account for the variation of the true image (ITRUTH):
| (3) |
From this definition, the numerical value calculated from SRR is lower than it would be when the ground truth variation is subtracted. In numerical simulations, Eq. 3 will be utilized to quantify streaking reduction factor while Eq. 2 will be utilized to quantify the streaking reduction factor for experimental studies since the ground truth is difficult to extract in reality.
RESULTS
Phantom experiments: Numerical studies
Numerical simulations were performed to validate the proposed artifact correction algorithm. The 600 projections were first sorted into ten groups according to the motion profile, which is equivalent to a temporal resolution of 400 ms (the period of motion is 4 s). Given uniform motion and uniform view sampling, the number of available projections for each phase is the same (i.e., 600∕10=60). The prior image was reconstructed using all projections without gating was shown in Fig. 2b. The moving target is blurred by the motion and no temporal information is contained within this image. Images of individual phases were then reconstructed from sorted projections using both the conventional fan beam filtered backprojection (FBP) reconstruction method23 and our correction algorithm. Results are presented in Fig. 4. The display window for Figs. 45678 is [−0.005 0.08] mm−1. Using the gating technique, temporal information is recovered and motion blurring is significantly less pronounced than the image reconstructed without gating. But strong view aliasing streaking artifacts are observed in the FBP images due to the view undersampling (only 60 projections available for each phase). Using our correction algorithm, the view aliasing artifacts are effectively mitigated and the temporal information is also retained. For the image of phase 25%, residual motion blurring is present when we sort the data into ten phases. In order to reduce the residual motion artifacts, the projection data were gated into 20 phases (or 200 ms temporal resolution) and images were reconstructed using both algorithms. From the results in Fig. 5, we can see that image quality can be retained while the temporal resolution was improved and thus few motion blurring artifacts are present in the reconstructed images. Difference images between the images reconstructed using the correction algorithm and the ground truth have also been presented in Fig. 5 (bottom row).
Figure 4.
Simulation studies with a 60 s gantry rotation and a 400 ms temporal resolution. Images were reconstructed using FBP (top row) and our new algorithm (bottom row) at phases of 0%, 25%, and 45%.
Figure 5.
Simulation studies with a 60 s gantry rotation and a 200 ms temporal resolution. Images were reconstructed using FBP (top row) and our new algorithm (central row) at phases of 0%, 25%, and 45%. The bottom row shows the difference between images at the central row and the ground truth.
Figure 6.
Comparison between uniform sampling (left) and bunching sampling (right) patterns for the same number of view angles.
Figure 7.
Simulation studies with a 120 s gantry rotation and a 400 ms temporal resolution. Images were reconstructed using FBP (top row) and our new algorithm (bottom row) at phases of 0%, 25%, and 45%.
Figure 8.
Simulation studies with a 120 s gantry rotation and 200 ms temporal resolution. Images were reconstructed using FBP (top row) and our new algorithm (bottom row) at phases of 0%, 25%, and 45%.
As shown in the above results, although the number of projections per phase is halved when the scans are gated into 20 phases than 10 phases, the overall image quality is not significantly affected. Obviously, the moving object is blurred more in the ten phases gating case but the global image artifacts are due to the bunched sampling pattern in 4D CBCT. Instead of uniform sampling, projections for each phase are bunched into several groups. The grouped projections are uniformly distributed and the number of groups is roughly equal to the number of breathing cycles acquired during data acquisition. Due to the high correlation of projections inside each group, the actual gain in projection information is much less than a factor of 2.
To demonstrate that the bunching sampling pattern is not an efficient sampling method, we include a numerical simulation here. The same phantom as that in Fig. 2a but without motion was used. In this simulation, 120 projections were first evenly distributed into a full 2π angular range. In this case, the angular difference between two projections was uniformly 2π∕120. The same number of projections was then bunched into 15 clusters and these clusters are evenly distributed into the angular range of 2π. The angular difference between the centers of two neighboring clusters is then 2π∕15 while the angular difference between two projections inside a cluster was 2π∕600. Images were reconstructed from both sampling patterns and are shown in Fig. 6. Although the same number of projections was used, the image reconstructed from the uniform sampling pattern has much less streaking artifacts than that reconstructed from the clustered projections.
In order to improve the sampling density, slow-gantry rotation (SGR) and multiple-gantry rotation (MGR) schemes were proposed by other investigators.12, 14 Numerical simulations were also conducted to validate our correction algorithm for the SGR scheme. Gantry rotation time from 1 min to 4 min was simulated and we kept the same detector read out speed (10.7 frames per second) and breathing period. Results for 2 min gantry rotation are presented in Figs. 78. Compared with the results of a 60 s gantry rotation time, the quality of the corrected image is improved with a 120 s gantry rotation.
The streak reduction ratios (SRR) defined in Eq. 3 were utilized to quantify the reduction ratios. The SRR was calculated for both images reconstructed with FBP algorithm and images reconstructed using the proposed correction algorithm at different gantry rotation time. In each case, the SRR was calculated for all phases and the mean value and standard deviations of the SRR were calculated (Fig. 9).
Figure 9.
Streak reduction ratios for images gated into 20 phases (a) and 10 phases (b).
From the above results, it is seen that the streaks are significantly reduced with a reduction ratio of about 80% when the proposed correction algorithm was used for both the state-of-the-art gantry rotation speed (1 min) and the newly proposed gantry slow down scheme (2 to 4 min). When the slow gantry scheme was simulated, the streaking artifacts reduction ratio is from 20% to 40%, which is smaller than the correction scheme.
Phantom experiments: Motion phantom studies
The breathing period in the physical phantom study is 5.3 s and the gantry rotation time is 60 s. During the data acquisition period, cone-beam projection data are acquired over 11–12 respiratory cycles. Using the acquired projections, we gated the data into about 50 phases such that there is only one projection in each respiratory cycle. In this case, we only have 11–12 projections for each respiratory phase. The results are presented in Fig. 10. The three image slices (axial, sagittal, and coronal slices, respectively) in the top row were reconstructed using the standard FDK cone-beam reconstruction algorithm from all projections without gating. These images are blurred due to motion and no temporal information is contained within these images. The images in the middle row are the corresponding image slices reconstructed for the respiratory phase 0%. The moving object was almost completely hidden in the strong streaking artifacts background. The images reconstructed using our correction algorithm are presented in the bottom row. The streaking artifacts are effectively reduced such that the moving objects are clearly visible. Simultaneously, motion artifacts are also effectively eliminated by using a narrow gating window. This may be appreciated by comparing the ungated scan with the results of the new algorithm.
Figure 10.
4D CBCT images of a physical phantom. Top row shows images reconstructed from all views without gating; middle row shows images reconstructed using FDK with phase gating (95 ms temporal window); bottom row shows images reconstructed using our new algorithm at the same phase as middle row. From left to right are images of axial, sagittal, and coronal views. The selected phase center for images at middle and bottom rows is 10%. The display window for all images is [0,0.04] mm−1.
In these studies, a temporal gating window of 95 ms, which is the time between two adjacent projections, was utilized. For 4D CBCT, this temporal gating window can be treated as the temporal resolution for theoretical analysis. Thus, the temporal resolution for 4D CBCT with our correction algorithm can be as high as 95 ms.
In order to demonstrate the dynamic information, three coronal images at phases 9.5%, 32%, and 50% are presented in Fig. 11. Note that the motion was in both SI and AP directions, so for coronal images, the sphere was moving up∕down and in∕out of the plane.
Figure 11.
Coronal view of images reconstructed using our new algorithm at phases of 9.5%, 32%, and 50% to demonstrate the dynamics. The display window is [0,0.04] mm−1.
The cone-beam projection data can also be gated using a wider temporal window, for example, we gated the projections into ten phases, which corresponds to an effective temporal window of 530 ms. Images are presented in Fig. 12. Images in the top row were reconstructed using the conventional FDK image reconstruction algorithm and the images in the bottom row were reconstructed using our correction algorithm. Since a wider temporal window was used, the moving object is more blurred in this case compared with the images in Fig. 10. For the image reconstructed using the conventional FDK algorithm, although more projections are available to reconstruct each phase, the improvement in image quality is not significant.
Figure 12.
4D CBCT images of a physical phantom. Top row shows images reconstructed using FDK with 530 ms temporal window; bottom row shows images reconstructed using our new algorithm. From left to right are images of axial, sagittal, and coronal views. The selected phase center is 10%. The display window for all images is [0,0.04] mm−1.
Analysis of the streak reduction ratio (SRR) was also performed for the experimental studies. Equation 2 was utilized to quantify the SSRs. In this analysis, the axial slices in Figs. 1012 are selected for the comparison. The results are presented in Fig. 13.
Figure 13.
Streak reduction for physical motion phantom study using different gating apertures.
From the above results, it is clearly seen that the streaking artifacts have been reduced by about 70% when the projection data were sorted into ten phases, which corresponds to about 530 ms temporal resolution. When the projection data were sorted into more phases to improve temporal resolution, 95 ms temporal resolution in above example, the streaks reduction ratios were uniformly maintained at about 70%.
The second phantom was scanned and images were reconstructed from the measured projections. Three representative axial images are presented in Fig. 14. Temporal information can be appreciated by the appearing and disappearing of the three objects inside this slice. Images reconstructed using FDK are also presented for comparison. Streaking reduction using the correction algorithm can be well appreciated from these images.
Figure 14.
Axial images of the three moving objects reconstructed using FDK (top row) and our correction algorithm (bottom row).
PATIENT STUDY
Figure 15ashows the RPM signal amplitude. Phase information was extracted from the RPM signal and is presented in Fig. 15b. Both amplitude irregularity of the RPM signal and period irregularity from the phase information were observed for this patient. The average breathing period for this patient was about 2.5 s and data acquisition time was 60 s. Therefore, data are available for about 24 respiratory cycles for this patient.
Figure 15.
A segment of the RPM signal for this experiment (a) and the corresponding phase information (b).
A nongated reconstruction was first performed using all of the 636 measured projections to obtain a prior image volume. An axial slice and sagittal slice are shown in Fig. 16. The display window for images from Fig. 16 to Fig. 17 is [−0.03 0.03]. A 50×50×10 cm3 volume of interest was reconstructed onto a 400×400×80 matrix. A large tumor inside the right lung of this patient can be observed from these slices. From the sagittal view, it is clear that the tumor is attached to the diaphragm. The measured projections were then gated so that only one projection was picked up in each respiratory cycle. Then for a given phase, 24 projections were used to reconstruct the image volume at this given phase. Both the FDK algorithm and our correction algorithm were used to reconstruct images at each given phase. Figure 17 demonstrates an axial slice and a sagittal slice in phase 0% from both FDK reconstruction and the correction algorithm. For the FDK images, severe streaking artifacts due to undersampling contaminate the whole image. After applying the correction algorithm, these artifacts were significantly reduced and we achieved a better delineation of both the target tumor and the other anatomy. Note that both the bones and the peripheral tissues are more clearly reconstructed with the correction algorithm. Sagittal slices of the image volume reconstructed using the correction algorithm at different phases are presented in Fig. 18. Contour of the tumor has been drawn by a clinical medical physicist in these images for better visualization of the tumor motion. Since the undersampling streaking artifacts have been significantly reduced using the correction algorithm, motion of both the tumor and the diaphragm can be easily appreciated by comparing these images.
Figure 16.
Prior images reconstructed from all measured projections without gating. (a) Axial slice. (b) Sagittal slice.
Figure 17.
Gated reconstruction. Images reconstructed from FDK algorithm [(a), (c)] and our correction algorithm [(b), (d)]. Both axial slices (top row) and sagittal slices (bottom row) are shown.
Figure 18.
Sagittal images reconstructed using the correction algorithm at phases of 37.5%, 62.5%, and 77.5%.
The streak reduction ratio, as defined in Eq. 2, was calculated for each phase. The results are shown in Fig. 19. On average a 60% streak reduction is achievable using this correction algorithm for this patient study.
Figure 19.
Streak reduction ratio for the patient study.
DISCUSSION AND CONCLUSIONS
In this paper, a correction algorithm is proposed to correct undersampling streaking artifacts in 4D CBCT. By adding a difference image reconstructed from the difference projections (e.g., the difference between the true projection and the reprojection through a motion blurred prior image), we have demonstrated that the streaking artifacts are effectively mitigated. A quantitative metric was defined for streak artifact reduction, and the new algorithm demonstrated a 70% reduction in streak artifacts compared with standard reconstruction for phantom studies and a 60% reduction in a patient study. This correction scheme enables gating of the 4D CBCT data in very narrow temporal windows (95 ms), which significantly improves the temporal resolution of 4D CBCT. Thus, our correction scheme potentially enables accurate extraction of the motion trajectory of a tumor directly from the 4D CBCT scan. The proposed method is not sensitive to the specific form of the motion and does not require any prior knowledge of the motion profile. The simulations demonstrated that the correction algorithm works for both rigid motions and deformations of the image object.
From phantom studies and a patient study, we found that significant streaking artifacts reduction has been achieved using our correction algorithm. However, we noticed that there are still some residual artifacts in the final images. One reason for these residual artifacts is that the difference image is still reconstructed using limited number of projections. Streaking artifacts are still present in the difference image and consequently are present in the final image. The other reason is that the streaking artifacts from static structures can be significantly reduced but not completely removed. As mentioned in the previous section, the difference between the measured projection and synthesized projections that pass through only static structures may still deviate from each other. This difference can be due to discretization, numerical errors, and physical factors. Although these issues will leave residual streaking artifacts in the final images, we should notice that significant streaking artifacts reduction is still achievable. This is due to the fact that streaking artifacts originating from the moving structures are less than those originating from the static structures for the image objects studied here (e.g., images of lung cancer patients). The results from both the phantom and patient studies support this conclusion.
One limitation of this study is that we did observe density deviation in the images reconstructed with the correction algorithm. However, we also observed density deviation of the images reconstructed using the FDK algorithm. This phenomenon was also observed by other researchers.13 We believe that this is an inherent problem in the conventional linear filtered backprojection (FBP) algorithm when it is applied to highly undersampled data set. Note that the reconstruction accuracy of the FBP algorithms is only ensured when the view angle sampling satisfies a certain sampling criterion. This point deserves more systematic studies, but it is beyond the scope of this paper.
ACKNOWLEDGMENTS
The work is partially supported by National Institutes of Health through Grant Nos. R01EB 005712, R01 EB 007021, and Varian Medical Systems. The authors wish to thank Dr. Michael Speidel for his assistance in implementing the ray-tracing algorithm and thank Dr. Jerry Nickles for providing the NaI detector. Special thanks go to Dr. Gig Mageras of Memorial Sloan Kettering Cancer Center for providing the in vivo CBCT data used in this study.
APPENDIX: PARAMETERS USED FOR NUMERICAL PHANTOM
In this appendix, the detailed parameters for the numerical phantom used in this paper is given in Table 1.
Table 1.
Phantom parameters used in the simulation.
| x0(mm) | y0(mm) | Rotation angle (deg) | a(mm) | b(mm) | Density (mm−1) |
|---|---|---|---|---|---|
| 0 | 0 | 0 | 180 | 120 | 0.02 |
| 0 | 0 | 0 | 150 | 90 | −0.01 |
| 75 | 0 | 0 | 60 | 60 | −0.01 |
| 75 | 0 | 0 | 60 | 60 | −0.01 |
| 0 | 105 | 0 | 20 | 6 | 0.06 |
| 0 | −105 | 0 | 20 | 6 | 0.06 |
| 165 | 0 | 0 | 4 | 10 | 0.06 |
| −165 | 0 | 0 | 4 | 10 | 0.06 |
| 104 | 84 | 65 | 6 | 16 | 0.06 |
| 104 | −84 | 125 | 6 | 16 | 0.06 |
| −104 | 84 | −65 | 6 | 16 | 0.06 |
| −104 | −84 | −125 | 6 | 16 | 0.06 |
| 0 | 0 | 0 | 10 | 10 | 0.005 |
| 0 | 50 | 0 | 10 | 10 | −0.01 |
| 0 | −50 | 0 | 10 | 10 | 0.01 |
| 75 | 0 | 0 | 20 | 20 | 0.03 |
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