Effects of collimator angle, couch angle, and starting phase on motion‐tracking dynamic conformal arc therapy (4D DCAT)

Abstract Purpose The aim of this study was to find an optimized configuration of collimator angle, couch angle, and starting tracking phase to improve the delivery performance in terms of MLC position errors, maximal MLC leaf speed, and total beam‐on time of DCAT plans with motion tracking (4D DCAT). Method and materials Nontracking conformal arc plans were first created based on a single phase (maximal exhalation phase) of a respiratory motion phantom with a spherical target. An ideal model was used to simulate the target motion in superior‐inferior (SI), anterior‐posterior (AP), and left‐right (LR) dimensions. The motion was decomposed to the MLC leaf position coordinates for motion compensation and generating 4D DCAT plans. The plans were studied with collimator angle ranged from 0° to 90°; couch angle ranged from 350°(−10°) to 10°; and starting tracking phases at maximal inhalation (θ=π/2) and exhalation (θ=0) phases. Plan performance score (PPS) evaluates the plan complexity including the variability in MLC leaf positions, degree of irregularity in field shape and area. PPS ranges from 0 to 1, where low PPS indicates a plan with high complexity. The 4D DCAT plans with the maximal and the minimal PPS were selected and delivered on a Varian TrueBeam linear accelerator. Gafchromic‐EBT3 dosimetry films were used to measure the dose delivered to the target in the phantom. Gamma analysis for film measurements with 90% passing rate threshold using 3%/3 mm criteria and trajectory log files were analyzed for plan delivery accuracy evaluation. Results The maximal PPS of all the plans was 0.554, achieved with collimator angle at 87°, couch angle at 350°, and starting phase at maximal inhalation (θ=π/2). The maximal MLC leaf speed, MLC leaf errors, total leaf travel distance, and beam‐on time were 20 mm/s, 0.39 ± 0.16 mm, 1385 cm, and 157 s, respectively. The starting phase, whether at maximal inhalation or exhalation had a relatively small contribution to PPS (0.01 ± 0.05). Conclusions By selecting collimator angle, couch angle, and starting tracking phase, 4D DCAT plans with the maximal PPS demonstrated less MLC leaf position errors, lower maximal MLC leaf speed, and shorter beam‐on time which improved the performance of 4D motion‐tracking DCAT delivery.


| INTRODUCTION
Dynamic conformal arc therapy (DCAT) technique has been implemented in linear accelerator (linac) based stereotactic body radiotherapy (SBRT) for patients with Stage I/II non-small-cell lung cancer (NSCLC). [1][2][3][4][5][6][7][8][9] One advantage of DCAT technique is the robust and transferable treatment methodology in planning, which is capable of reproducing the same or similar optimized planning results on different planning systems. [7][8][9][10] Compared to three-dimensional (3D) conformal radiation therapy (3DCRT), DCAT has been proven to achieve higher target dose conformity and normal tissue dose sparing as well as shorter beam-on time for dose delivery. 9, 10 Rauschenbach et al. 10 stated that DCAT should remain an alternative to 3DCRT in facilities that do not have VMAT or IMRT. Shi et al. 11 have successfully implemented DCAT technique into clinical use for lung SBRT. They reported that the plan quality of DCAT met the RTOG protocols.
Ouyang et al. 12 reported that combining flattening filter free beams and DCAT provides promising improvements in NSCLC SBRT treatment in both plan quality and treatment planning efficiency. In addition, unlike VMAT, tumor coverage is not affected by MLC interplay effect.
Although hypo-fractionated radiotherapy has demonstrated capability of providing high local control rates (85%-98%) in several phase I/II trials, [13][14][15][16][17][18][19] blurred dose caused by tumor motion entails an increased risk of normal tissue toxicity. 20, 21 Shimizu et al. 22 reported lung tumor motion in SI direction was up to 24 mm. Several studies reported over 10 mm tumor motion in AP and LR directions. [23][24][25] Zhao and colleagues 26 reported dose deviation with motion is larger for smaller lung tumor (i.e., gross target volume is less than 10 cm 3 in their study). Therefore, it is especially important to manage respiratory motion in hypo-fractionated lung SBRT to ensure more accurate dose delivery. Tumor motion tracking is a recent development toward improving dose delivery quality. Compared with the common techniques of motion management such as respiratory gating and forced shallow breathing, motion-tracking technique provides shorter treatment delivery time and requires less patient co-operation and causes less patient discomfort. [27][28][29] The effects of plan parameters in motion tracking have not been fully studied. Several studies implemented motion tracking with dynamic MLC treatment delivery for either Varian or Elekta linac and reported improved target dose coverage without significantly increasing the total treatment time. [30][31][32][33][34][35] Sawant et al. developed lung tumor motion compensation method where target motion that is decomposed to the beam's eye view (BEV) is dependent on collimator, gantry, and couch angles. 30 Different combinations of collimator and couch angles will result in different tracking complexity which affects the delivery performance. Therefore, optimization of collimator and couch trajectories may reduce the possibility of having plans running at the mechanical limits of the linac, which can improve the treatment efficiency and robustness. 36,37 In most published studies on VMAT plans with motion tracking, collimator, and couch angles for plans were set at 90°and 0°, respectively, which has been shown to be favorable for MLC tracking because the MLC leaf motion direction is parallel to target motion in superiorinferior (SI) direction. 30,32,34,35 However, for (3D) motion tracking, this collimator angle may not be the optimal solution for motion tracking.
In this study, we investigated the effects of collimator angle and couch angle on the performance, including MLC leaf position errors, MLC leaf speed, and total beam-on time of DCAT plans with motion tracking (i.e., 4D DCAT). In addition, we also evaluated the effect of different starting tracking phases on 4D DCAT performance.

2.A | Respiratory three-dimensional motion phantom and model
The QUASAR TM respiratory motion phantom (Modus Medical Device Inc., Canada) and a Cedar cylindrical insert with a 30 mm off-centered spherical target (22 mm diameter) for simulating 3D respiratory motion was used in this study (Fig. 1). A rotational stage hinged the insert with the phantom motor which allows the target to rotate with 60°of total motion range as it translates. As shown in Fig. 2, the target motion is the composite of reciprocating motion in the SI direction (z axis) and rotational motion in LR (left-right, x axis) and AP (anteriorposterior, y axis) plane. The target motion model is then given by where A z 0 = 20 mm was the peak-to-peak target motion amplitude, was the maximal rotational angle of the insert. The off-center distance q was 30 mm. s is the breathing cycle period and was set to 6 s. ; x , ; y , and ; z are the starting phase for motion tracking, and ranged from maximal exhalation phases (; ¼ 0) to maximal inhalation (; ¼ p=2).

2.B.2 | Motion-tracking plans
The 4D DCAT plans were generated by applying the lung tumor motion-tracking algorithm. The motion-tracking method was based on a priori known rigid sinusoidal motion model that was projected to the BEV and compensated by MLC leaves.
For motion parallel to the direction of leaf travel, MLC m; n ð Þ, the position of leaf "m" of CP "n" in the nontracking DCAT plan was transformed using: where the motion compensation along MLC leaf travel direction, MLC k , is described in Appendix A. For motion perpendicular to the direction of leaf travel, all in-field MLC leaves would be shifted laterally according to the motion direction by the following equation: where the motion compensation that is perpendicular to MLC leaf   As shown in Appendix A, motion projected to the BEV is dependent on collimator angle, couch angle, and starting phase. Therefore, PPS can be expressed as eq. 6.
MCS ranges from 0 to 1, and it approaches 0 for increasing degree of treatment plan complexity. 39 Fig. 1(c)]. An inhouse developed program was used to track the markers and display the positions of the markers in real-time. Before each delivery, we calibrated the cameras and software to ensure the coordinates were consistent. When the tracking program was initiated, it focused on the markers and would change the tracking square color from yellow to red when the target reached to a specific breathing phase for beam initiation. In order to provide enough time for human response to manually turn on the beam, it would become yellow to green and remain for one-second before it turned to red (i.e., the starting point for 4D DCAT delivery).
During delivery, the verification system compared actual target position with the planned one. Once the discrepancy was higher than the tolerance (i.e., 1 mm), delivery would be paused in order to avoid significant de-synchronization between MLC tracking and target motion.
Gafchromic EBT3 film was embedded in the target for dose mea- 4D DCAT with the minimal PPS, respectively ( Fig. 9 and Table 3).
Differences in dosimetric indices to the organs such as spinal cord and lung are also listed in Table 3. There was a minimal difference in heart doses between the two 4D DCAT plans.

| DISCUSSION
Ideally, for a nontracking DCAT plan, when the isocenter is at the target geometric center and the target shape is symmetrical, the target projection to the MLC coordinates at each CP should be identical. In this case, the ideal PPS for nontracking DCAT plans with different collimator and couch angles should be equal to one. In reality, since the target contour generated in the TPS was not a perfect sphere, it resulted in the variation in target projection at each CP (i.e., slight MLC shape variation at each CP). Therefore, PPS results were slightly less than one but also very close to one among different nontracking plans in the study. For the 4D DCAT plans, on the other hand, the PPS values were significantly smaller than one, with a best score of 0.554 in the study. It indicated an increased complexity when carrying out motion tracking using dynamic MLC technique. Compared to the optimization results using 1°gantry angle increment (maximal PPS: 0.554), when using 2°and 5°increments for optimizations, the maximal PPS of 4D DCAT plans were 0.554 and 0.543, respectively. Therefore, similar optimization results can be achieved with higher gantry angle increment (e.g., <5°in this study) which reduces the total optimization time.
The error bars in Fig. 5 show relatively small variation in measurement of delivered plans, which indicates that all plan parameters   For an irregular shaped tumor with more complicated motion pattern, one would expect the beam aperture difference and target motion between adjacent CPs be larger. Therefore, plan with the minimal PPS will be expected to have more leaf errors during tracking since more leaves will be moving at the maximal speed.
Passing rates of all the film measurements are higher than 90% threshold when using 3%/3 mm criteria, which demonstrates the reliability of the synchronization method using manual beam initiation and cameras for target motion monitoring. Failed points (i.e., yellow and red points) in Fig. 7 indicate motion blurring caused by de-synchronization during dose delivery.  rately catch the motion as predicted in the tracking simulation. One solution is to reduce the maximal leaf speed limit to a lower level in motion-tracking algorithm so that MLC leaves can move more smoothly without affecting dose rate. One disadvantage of slowing down leaf speed is that the total delivery time will be longer.
In addition to de-synchronization, motion-tracking accuracy is affected by the tracking method for motion perpendicular to the leaf travel direction. Since the MLC leaf width in the central 8 cm field is 2.5 mm, the motion will not be compensated if the amplitude is less than 2.5 mm.
Falk and colleagues 28

ACKNOWLEDG MENTS
The authors thank Dr. Daryl Nazareth and Dr. Lalith Kumaraswamy from Roswell Park Cancer Insitute, Buffalo, NY, who provided expertise that greatly assisted the study.

CONFLI CT OF INTEREST
None.