On the evaluation of mobile target trajectory between four‐dimensional computer tomography and four‐dimensional cone‐beam computer tomography

Abstract Purpose For mobile lung tumors, four‐dimensional computer tomography (4D CT) is often used for simulation and treatment planning. Localization accuracy remains a challenge in lung stereotactic body radiation therapy (SBRT) treatments. An attractive image guidance method to increase localization accuracy is 4D cone‐beam CT (CBCT) as it allows for visualization of tumor motion with reduced motion artifacts. However, acquisition and reconstruction of 4D CBCT differ from that of 4D CT. This study evaluates the discrepancies between the reconstructed motion of 4D CBCT and 4D CT imaging over a wide range of sine target motion parameters and patient waveforms. Methods A thorax motion phantom was used to examine 24 sine motions with varying amplitudes and cycle times and seven patient waveforms. Each programmed motion was imaged using 4D CT and 4D CBCT. The images were processed to auto segment the target. For sine motion, the target centroid at each phase was fitted to a sinusoidal curve to evaluate equivalence in amplitude between the two imaging modalities. The patient waveform motion was evaluated based on the average 4D data sets. Results The mean difference and root‐mean‐square‐error between the two modalities for sine motion were −0.35 ± 0.22 and 0.60 mm, respectively, with 4D CBCT slightly overestimating amplitude compared with 4D CT. The two imaging methods were determined to be significantly equivalent within ±1 mm based on two one‐sided t tests (p < 0.001). For patient‐specific motion, the mean difference was 1.5 ± 2.1 (0.8 ± 0.6 without outlier), 0.4 ± 0.3, and 0.8 ± 0.6 mm for superior/inferior (SI), anterior/posterior (AP), and left/right (LR), respectively. Conclusion In cases where 4D CT is used to image mobile tumors, 4D CBCT is an attractive localization method due to its assessment of motion with respect to 4D CT, particularly for lung SBRT treatments where accuracy is paramount.


| INTRODUCTION
Since the introduction of image-guided radiation therapy (IGRT), many imaging modalities have been employed to increase the accuracy at which mobile lung tumors are treated. These modalities include megavoltage (MV) cone-beam computed tomography (CBCT), kilovoltage (kV) CBCT, tomotherapy MV computed tomography (CT), and room mounted kV planar imaging with or without fiducials. [1][2][3][4][5] Given that lung cancer is the leading cause of cancer death in the United States as reported by the National Cancer Institute, 6  The accuracy at which targets may be localized from utilization of the 4D CBCT image acquisition makes it an appealing candidate for lung stereotactic body radiation therapy (SBRT) image guidance.
With SBRT, the dose per fraction is much higher than that used in conventional radiotherapy treatments, and far fewer fractions are used, leading to a more potent biological effect. 11,12 Because the dose per fraction is high, dose gradients must be steep to minimize unnecessary toxicity to normal tissues surrounding the treatment site, and target localization must be very accurate to ensure no geographic miss. With respect to target localization, 4D CBCT has been shown to better localize mobile lung tumors while maintaining comparable image quality when compared with traditional 3D CBCT image guidance techniques used in lung treatment protocols. 7,13 Application of SBRT to certain lung cancers has been shown to be as effective as conventional radiation therapy with the added benefit of patient convenience in much shorter treatment times. 14,15 It has also become a viable alternative to surgically inoperable patients and those with oligometastatic disease. 16,17 By increasing the confidence of localization with 4D CBCT, these outcomes may further improve.
To recognize the benefits 4D CBCT may provide, it is important to understand how 4D CBCT target trajectories compare with those at simulation. Often, patients are simulated with a 4D CT image acquisition. The 4D CT is employed to learn about the target's path and excursion and allow for accurate delineation of the mobile target. Because the treatment plan is based upon the motion at simulation, it is important to establish how the target trajectory acquired from the 4D CT compares with that during treatment of the 4D CBCT to ensure proper dose coverage. Previously, differences in 4D CT and 4D CBCT evaluation of target motion for patient respiratory patterns have been explored. [18][19][20] These studies have found potential discrepancies between the two imaging modalities in the presence of patient respiration where breathing irregularity is common. It is challenging though to determine if these discrepancies are due to patient-related factors or inherent differences in the imaging modalities. Additionally, 4D CT has been shown to suffer from motion artifacts leading to 4D CBCT better evaluating target volumes when using a motion phantom with a few different sinusoidal and patient specific motion parameters. 21 Lastly, phantom target motion between the two imaging modalities has been shown to be comparable but with very few different motion parameters explored. 22 These studies, however, have not explored how a wide variety of combinations of amplitude and cycle time for the target motion affect the agreement between 4D CT and 4D CBCT evaluation of target trajectories and where evaluation is hindered due to artifacts. Additionally, it is unclear if previously studied discrepancies in target motion evaluation are inherent to the two modalities or due to patient specific factors such as breathing irregularity. This study poses two aims, (a) to investigate several combinations of target amplitude and cycle time on a dynamic thorax phantom using sine motion to remove the variability of patient respiration and evaluating if the two modalities are equivalent within a given difference interval and (b) evaluate the motion measured using previous patient breathing waveforms to simulate patient breathing.

2.A | Phantom motion
To perform this study, the Computerized Imaging Reference Systems (CIRS, Norfolk, VA) dynamic thorax phantom model 008A was employed. Figure 1 shows the phantom used in this study, with 4D CT and 4D CBCT axial slices demonstrating the phantom's geometry.
The Trio PC Motion library was used to alter the motion parameters of the phantom.

2.B | Sine motion
The imaging rod with a 2-cm diameter soft tissue equivalent target was selected. The sine motion signal was used with cycle times and amplitudes chosen based on practical respiratory rates and previously observed motion amplitudes from a large sample of lung cancer patients. 23,24 This resulted in amplitudes in the superior-inferior (SI) directions of 3, 5, 7, 9, 11, 13, 15, 17, and 19 mm. Each parameter was paired with cycle times of 3, 5, and 7 s except for 3, 5, 17, and 19 mm.

2.D | 4D CT acquisition
The process used for 4D CT simulation of lung SBRT patients at our institution was followed. The 4D CT data sets were acquired with a cine scan using a GE lightspeed 16-slice CT scanner with a rotation time of 1 s, slice thickness of 2.5 mm, and pixel spacing of 1.27 mm.
Surface imaging was used as a marker of respiratory phase for retrospective 4D binning using CRAD (Uppsala, Sweden) Sentinel. A  1.5 s. This is consistent with clinical practice where the additional time margin ensures full capture of the respiratory cycle in the presence of variable respiratory rates. Once the 4D CT data were acquired, it was exported and reconstructed using GE Advantage 4D (GE Healthcare, Chicago, IL). All 10 phase CT image sets were exported for analysis.

2.E | 4D CBCT acquisition
Elekta's kV CBCT system (XVI) was used on the VersaHD LINAC to obtain the 4D CBCT data sets employing the Symmetry imaging protocol (Elekta, Stockholm, Sweden). A high-contrast object is required to accurately bin the images into the appropriate respiratory phase.
A bolus was added to the end of the imaging rod acting as a highcontrast object to reduce discrepancies in phase sorting as shown by Liang et al. 8 The configuration of the added bolus on the imaging rod is shown Fig. 1. The 4D CBCT scanning protocol consisted of the acquisition of 975 frames (20 mA and 16 ms per frame) over a 200°counterclockwise arc of gantry rotation. Elekta's F0 filter and S20 collimators were used. Images were reconstructed with a nominal slice thickness and pixel spacing of 1 mm. All phases from the 4D CBCT were DICOM exported through MOSAIQ to be processed offline.

2.F.1 | Sine motion
Determining target trajectory throughout the different phases of respiration was conducted with an in-house python code to process the images. Phase images were imported and organized into a 4D matrix then converted to binary images using the Otsu thresholding method. 25 Erosion followed by dilation was applied in some instances to remove noise-based objects. After image processing, the approximate coordinates of the target centroid were selected using a built-in slice viewer. The binary data set was then labeled to find each object in the data set. The target object was determined by minimizing the Euclidean distance between the previously selected coordinates that approximated the centroid using the slice viewer and the centroid of each labeled object. Image processing and labeling was done almost exclusively using the skimage library. 26 The coordinates and centroid of the concluded object depicting the target were stored to segment the target and for centroid determination and curve fitting.
Sinusoidal curve fitting of each phase's centroid was used to measure the motion amplitude. Segmentation was employed to visually inspect if the target was properly found in each phase using the same slice viewer in the axial and coronal planes. Data were fit using SciPy library's least squares with an optimization function minimizing the difference between the variable sine function parameters (amplitude, frequency, phase shift, and vertical shift) and the data points of the centroid position for each respiratory phase. 27 Curve fitted amplitudes were then compared between the two imaging modalities. Additionally, a second method of amplitude evaluation was employed because curve fitting was unacceptable in the presence of motion artifacts in a few motion combinations. This method used the average CT of the 4D CT data set with a window level and width of −400 and 1500, respectively, to measure amplitude through visual inspection.
The concluded curve fitted amplitudes were evaluated to determine equivalence between the two imaging modalities. Equivalence was tested by the two one-sided t-test (TOST) method. 28,29 The upper and lower limits used for the TOST were 1 and −1 mm, respectively. The 1-mm range was chosen due to the setup error considered acceptable in SBRT treatments. 30 Additionally, coefficients of correlation and determination between the true amplitude programmed and both imaging methods were employed.

2.F.2 | Patient waveforms
Target motion evaluation for simulated patient respiratory motion scenarios was based on average 4D CT and 4D CBCT data sets.
Individual phase data were not used due to many phases being too noisy or containing artifacts due to the irregularity between cycles.
Data sets were imported into python and interpolated to allow auto segmentation to 0.1 mm of accuracy. The interpolated data sets were binarized based on manual threshold values representing the most visually appropriate contour. The dimensions of these contours were used to determine the amplitudes in the SI, AP, and LR directions.

3.A | Sine motion
The progression of binarizing the 4D data sets to visual inspection of the target being properly found by segmentation in the axial and coronal planes is illustrated in Fig. 3.
The programmed phantom motion parameters and corresponding amplitudes from sinusoidal curve fitting extracted from the 4D CT and 4D CBCT data sets appear in Table 1  The mean difference between the two modalities was −0.35 ± 0.22 mm, representing a small but significant bias of 4D CBCT overestimating amplitude with respect to 4D CT. Additionally, root-mean-square-error was determined to be 0.60 mm. The two imaging methods were determined to be significantly equivalent within this interval (p < 0.001) based on the two TOSTs used.
The amplitude difference between measurements versus the programmed amplitude, equivalence limits, and mean difference with error is shown in Fig. 5.
The correlation coefficients between the true amplitudes programmed at the phantom and curve fitted amplitudes of 4D CT and 4D CBCT were 0.9958 and 0.9976, respectively. Similarly, the coefficient of determination (R 2 ) was 0.9917 for 4D CT and 0.9953 for 4D CBCT. Figure 6 shows the measured amplitude from curve fitting versus the programmed amplitude for 4D CT and 4D CBCT with linear regression.

3.B | Patient waveforms
The target size, measured amplitudes, and difference in amplitudes between 4D CT and 4D CBCT for simulated patient respiratory motion are shown in Table 2. The mean difference was 1.5 ± 2.1, 0.4 ± 0.3, and 0.8 ± 0.6 mm for SI, AP, and LR, respectively. In the SI direction, the mean difference was 0.8 ± 0.6 with the exclusion of the outlier shown in Table 2 for Patient 3.

| DISCUSSION
The application of 4D CT is considered standard protocol in SBRT treatment planning and simulation of mobile lung tumors. An showing changes in the tumor trajectory between and/or immediately prior to treatments. Because the 4D CBCT used for localization is registered to the 4D CT data used for treatment planning, it is important to determine if these two imaging modalities agree with one another in terms of target motion in a controlled setting.
In this study, equivalence between 4D CT and 4D CBCT in the absence of patient related factors was explored by collecting 4D data sets of sinusoidal motion with varying amplitudes and cycle times. There was a measurable bias, too small to be clinically meaningful, where the 4D CBCT overestimated the amplitude with respect the 4D CT. However, 4D CBCT appeared to be closer to the ground truth value programmed for the phantom. The better accuracy associated with 4D CBCT is likely due to the presence of motion artifacts in 4D CT and the difference in slice thickness and image quality between the two modalities resulting primarily from difference in image acquisition (multislice in CT vs. volumetric in CBCT). Previous research has shown and sought to reconcile the fact that at large amplitudes and fast respiratory cycles, the presence of motion artifacts in 4D CT data becomes more pronounced. 31,32 Additionally, the slice thickness for 4D CBCT was finer than 4D CT at 2 and 2.5 mm, respectively. These slice thicknesses were chosen because we wanted the results to reflect what is the most clinically relevant scenario. As for the equivalence testing, the two imaging modalities were equivalent within the −1to 1-mm limits when severe artifacts were not present. The a priori difference interval of ±1 mm was selected based on what error is generally acceptable for SBRT treatments.
Following the controlled analysis of sine motion, patient respiratory waveforms were evaluated to see how the modalities agreed with more realistic patient motion, which includes occasional breathing irregularities. The error between the two modalities increased as expected intuitively due to the variation in patient breathing, but all values remained within 2 mm of each other except for Patient 3 whose SI amplitude was severely underestimated by 4D CT. It is suspected that 4D CT may be more subject to breathing irregularities at table positions because it only spends the specified cine time at each, while 4D CBCT is less impacted due to its continuous volumetric imaging method.
For the limitations of this study, a few of the small sine amplitude, slow cycle time combinations could not be analyzed due to 4D CBCT artifacts thought to manifest from inappropriate binning.
Without being able to analyze these data sets, it is difficult to know how 4D CBCT may behave at similar motion parameters in a patient. Several 4D CT motion artifacts were also seen as the amplitude became large and cycle time decreased. This led us to explore the amplitude through observation of the average 4D CT, which is less objective than the curve fitting method. Another limitation was that some of the large amplitudes were physically constrained as to the minimum cycle times allowable by the software, requiring additional cycle time to be programmed. It is probable that the added cycle time reduced motion artifacts for these large amplitudes, and if they were not limited by programmable time constraints, the 4D CT trend of motion artifacts would have persisted. Lastly, in the evaluation of sine motion, only the SI direction was examined in this T A B L E 1 Programmed parameters of the CIRS dynamic thorax motion phantom with amplitudes from curve fits using 4D CT and 4D CBCT. The value in red indicates an abolsute difference greater than 1 mm. Abbreviations: 4D CBCT, four-dimensional cone-beam computer tomography; 4D CT, four-dimensional computer tomography; AP, anterior-posterior; LR, left-right; SI, superior-inferior.
A thorax motion phantom was used to simulate target sinusoidal and simulated patient respiratory motion to evaluate target motion measured by 4D CT and 4D CBCT. The sine motion amplitudes were measured by sinusoidal curve fits, and the patient waveform motion was measured by segmentation of the target using the average 4D data sets.
The two methods were equivalent within a 1-mm limit for sine motion, and the error did not exceed 2 mm in the case of patient waveform motion with the exception of a single outlier. In cases where 4D CT is used to image mobile tumors for simulation and treatment planning, 4D CBCT will evaluate motion within at least 2-mm accuracy of 4D CT in the absence of severe artifacts or changes in respiration between simulation and treatment, making it an attractive localization method due to its reduced motion artifacts and capability to visualize daily breathing motion. This is particularly applicable to lung SBRT treatments where less fractions and imaging are required, but the accuracy of treatment delivery is paramount. Any discrepancies between the motion observed at simulation and time of treatment may therefore be attributed to patient-related factors such as setup, significant breathing irregularity, and changing target trajectory.

ACKNOWLEDGMENTS
Research reported in this publication was supported by the National

D A T A A V A I L A B I L I T Y S T A T E M E N T
The data that support the findings of this study are available from the corresponding author upon reasonable request.