Evaluation of gantry angle during respiratory‐gated VMAT using triggered kilovoltage x‐ray image

Abstract Respiratory‐gated volumetric modulated arc therapy (gated VMAT) involves further complexities to the dose delivery process because the gantry rotation must repeatedly stop and restart according to the gating signals. In previous studies, the gantry rotation performances were evaluated by the difference between the plan and the machine log. However, several reports pointed out that log analysis does not sufficiently replicate the machine performance. In this report, a measurement‐based quality assurance of the relation between the gantry angle and gate‐on or gate‐off using triggered kilovoltage imaging and a cylinder phantom with 16 ball bearings is proposed. For the analysis, an in‐house program that estimates and corrects the phantom offset was developed. The gantry angle in static and gated arc delivery was compared between the machine log and the proposed method. The gantry was set every 5 deg through its full motion range in static delivery, and rotated at three speeds (2, 4 and 6 deg s‐1) with different gating intervals (1.5 or 3.0 s) in gated arc delivery. The mean and standard deviation of the angular differences between the log and the proposed method was −0.05 deg ± 0.12 deg in static delivery. The mean of the angular difference was within ±0.10 deg and the largest difference was 0.41 deg in gated arc delivery. The log records the output of the encoder so that miscalibration and mechanical sagging will be disregarded. However, the proposed method will help the users to detect the mechanical issues due to the repeated gantry stops and restarts in gated VMAT.

the respiratory cycle. [1][2][3] Recently, a technique combining respiratory gating and volumetric modulated arc therapy (gated VMAT) is applied for thoracic and abdominal tumors. [4][5][6] Gated VMAT can deliver a dose to the target volume with high conformity despite the presence of respiratory motion. 7 However, this technique involves further complexities to the dose delivery process because the gantry rotation must repeatedly stop and restart according to the gating signals. When respiration reaches the gate-off phase, the radiation beam is turned off. However, the gantry slightly overruns from the intended stop position, and then the gantry is rewound to the restart position before the next gate-on phase. When the gantry rotation speed is fast and/or the interval between beam-off and beam-on is short, the accuracy of the gantry angle may deteriorate. Regarding the accuracy of the gantry angle, the American Association of Physicists in Medicine Task Group 142 Report recommends ±1 deg as an acceptable criterion. 8 In previous studies evaluating the machine performance of gated VMAT, the difference between the planned and the recorded gantry angle was analyzed using the machine log. Nicolini et al. reported that systematic delivery errors between the ungated and various gated conditions were not observable in the machine log (monitor unit, gantry angle or multileaf collimator positions). On the other hand, the gamma-index passing rates between the planned and the measured dose distributions were changed within 2 % depending on the number of beam interruptions. 9 Qian et al. found that the logbased dose reconstruction faithfully realized the measurement of ion chamber array in gated VMAT under a variety of periodic respiration situations. 10 The dose verification can evaluate machine performance comprehensively, however the mechanical issue due to the repeated stops and restarts of the gantry are not assured independently. Several reports discussed the log analysis and pointed out that log does not sufficiently replicate the machine performance. [11][12][13] Therefore, measurement-based quality assurance (QA) must be performed. A recent report on gantry angle analysis using radiochromic film concluded that the gantry angle error was smaller than 0.5 deg under a gantry rotation speed of 2.3 deg s -1 . Hubley et al. selected a slower gantry rotation speed so that the film-based QA is achieved with a high signal-to-noise ratio. 14 However, the gantry rotation speeds in gated VMAT vary irregularly from its maximum of 6.0 deg s -1 to slower speeds. For gantry angular analysis under actual conditions, a more sensitive device than radiochromic film is required.
This report proposes a new method of using a kilovoltage (kV) imaging system and a cylinder phantom for measurement-based QA of the gantry angle, and presents a comparison between measurement-based QA and log analysis.

2.A | Experimental setup
As shown in Fig. 1, a QA phantom (IsoCal, Varian Medical Systems, Palo Alto, CA, USA) was mounted on the tip of the linac (TrueBeam ver.2.5, Varian Medical Systems, Palo Alto, CA, USA) couch and aligned with the room lasers. The IsoCal phantom is a hollow cylinder with 16 tungsten-carbide ball bearings (BBs) arranged at a specified position. 15 While the purpose of this phantom is to calibrate between the isocenter and the image center, 16 it was used to determine the gantry angle in this study. The phantom images were acquired by the "triggered imaging" mode using the on-board kV imager at the source-detector distance (SDD) of 150 cm. The active area is 40 cm × 30 cm and the pixel size is 0.39 mm in this imaging mode. The images were sampled at the moment of gate-on or gate-F I G . 1. The experimental setup for the gantry angle analysis. The IsoCal phantom was mounted on the treatment couch and aligned with the room lasers. The gating signals were supplied to TrueBeam using the real-time position management system and model 008PL moving phantom.

2.B | Determination of the gantry angle
To determine the gantry angle, the projected coordinate of ith BB on the imager X i calc ; Y i calc ð Þfor given gantry angle θ and the sourcedetector distance Z was calculated in advance. The coordinate of ith BB (x i , y i , z i ) in the reference coordinate system defined by IEC61217 was transformed with the matrix for translation and rota- The image of BBs was acquired using the on-board kV imager.
After the global thresholding process, the projected coordinate Þof ith BB was measured. In this process, the imager sag was corrected with premeasured coordinates of the projected image from every 5 deg of gantry angle for one BB that was arranged at the isocenter. 17 The gantry angle (θ img ) was determined by the least squares minimization using the following formula, where n is the number of BBs within a region of interest (ROI) that is defined as 512 × 768 pixels and placed on the center of the projected image, P i and P i calc are the measured and the calculated coordinates for ith BB. The data processing was performed using an inhouse program on MATLAB (R2017a, Mathworks, Natick, MA, USA). Figure 2 shows the image to determine the gantry angle. By calculation of θ img using one BB inside the ROI, the resolution of angle per pixel (Δθ img ) varies from 0.11 deg to 0.17 deg. When n BBs are inside the ROI, the estimated angular resolution (Δθ img ) can be calculated using the following equation.
As shown in Fig. 2, θ img is determined with images of at least six BBs, so the angular resolution can be estimated within 0.07 deg.

2.C | Comparison in static delivery
In order to evaluate the method given in Section 2.B, θ img was compared with gantry angle θ log recorded in the trajectory log file (ver. 3.0, Varian Medical Systems, Palo Alto, CA, USA). The triggered kV images were acquired every 5 deg of the gantry angle through its full extent (from −180 deg to 180 deg), and θ inc was measured simultaneously using a digital inclinometer (DP-90, Niigata Seiki Co., Niigata, Japan) attached to the gantry head. θ log was also compared with θ inc to confirm the gantry angle only in static delivery.
Distributions of the angular differences between θ inc and θ log or θ img and θ log in the range of the gantry angle from −180 deg to 180 deg every 5 deg.
The mean and SD of the difference between θ img and θ log at the moment of gate-on and gate-off during gated arc delivery. In the case of the gate-off moment, θ img was corrected 0.

2.D | Comparison during gated arc delivery
The gantry was rotated at speeds of 2, 4 or 6 deg s -1 in the clockwise (CW) or counterclockwise (CCW) direction, beam-on time was set at 3.0 s and the interval time was set at 1.5 or 3.0 s, respectively. These conditions reproduce actual gantry rotation speeds and realistic patterns for fast and/or normal breathing in gated VMAT.
The combination of maximum gantry rotation speed of 6.0 deg s -1 and short interval time of 1.5 s was assumed to be the heaviest load in clinical practice. θ img was determined using the image that was sampled at the moment of gate-on or gate-off. θ log was determined using the status log of gate-on and gate-off that was recorded in 20 ms intervals.  Table 1 shows the mean and SD of the angular difference between θ img and θ log at the moment of gate-on or gate-off. In the gate-on mode, the angular difference was within 0.30 deg and it was independent of the gantry rotation speed and the interval time. In the gate-off mode, the angular difference increased with the gantry rotation speed.

3.B | Comparison during gated arc delivery
The reason is that the gantry is stationary until triggered in the gate-on mode, but the gantry is rotating and the image is sampled in 50 ms ± 2% after being triggered in the gate-off mode. It was confirmed that the rotation speed was constant within 50 ms by the log analysis.
Therefore, it is necessary for θ img to correct 0.1, 0.2 or 0.3 deg for rotation speed 2, 4 or 6 deg s -1 , respectively. After the correction, the mean of the angular difference was within ±0.10 deg and it became independent of the gantry rotation speed in the gate-off mode.

| DISCUSSION
To evaluate the gantry angle during respiratory-gated VMAT, a new measurement-based QA was proposed. The gantry angle was determined with specific positions of BBs on the triggered kV image. The IsoCal phantom is suitable for the proposed method because the BBs are arranged exactly in it. Other phantoms in which the BB arrangement is known may also be adapted to the proposed method.
In the previous study, the gantry angle was evaluated using radiochromic film or a cine electronic portal imaging device (cine-EPID) image. 14,18,19 Radiochromic film is a low sensitivity device so that a slow rotation speed was required for sampling. 14 The cine-EPID has large time uncertainty due to a slower sampling rate of 2.5 Hz and the initial EPID frame will be lost. 18 Consequently, this makes it ble offset x Ã T and z Ã T can be determined using the following equation, where m is the number of representative gantry angles, and α is the ratio of source-axis distance (SAD) to SDD. In contrast, δY is affected by only the longitudinal displacement y T . Therefore, the probable offset y Ã T is determined using the following equation, For given phantom settings, x Ã T ; y Ã T ; z Ã T À Á can be quantified The gantry angle is determined using Eq. (2). Figure 4(b) shows the difference between θ img and θ log after the phantom offset correction. The mean and SD of the difference was decreased to −0.05 deg ± 0.12 deg even though the phantom offset is 0.5 or 1.0 mm. This result suggests that the gantry angle can be evaluated independently from the phantom setting by the proposed method.
The correction for phantom rotation has not been implemented yet, so the phantom rotation was adjusted with a six degrees of freedom couch in this study.
In previous studies evaluating the machine performance of gated VMAT, several authors analyzed the difference between the planned and the recorded gantry angle using the machine log. 9,10 However, the machine log records the output of the encoder, so that the uncertainty due to the miscalibration and mechanical sagging will be disregarded. Moreover, the log is recorded discretely with the same sampling interval, so it has a discrepancy depending on the gantry rotation speed. These uncertainties of log analysis were not discussed in previous reports, so they should be confirmed with the measure- in other gating conditions. The proposed method will become important for detecting mechanical issues due to repeated gantry stops and restarts in gated VMAT even if patient-specific dose verification is replaced by log analysis.

| CONCLUSIONS
Several authors have evaluated the difference between the planned and the recorded gantry angle by log analysis for respiratory-gated VMAT. However, log analysis detects only the output of the encoder so that miscalibration and mechanical sagging will be disregarded.
Measurement-based QA of the gantry angle using the kV imaging system and cylindrical phantom with 16 BBs was proposed and it was compared with log analysis in this report. The proposed method acquired images with a short sampling time; consequently, the gantry angle can be sampled synchronously with gate-on or gate-off moment at maximum gantry rotation speed. The proposed method will become important for detecting mechanical issues due to repeated gantry stops and restarts in gated VMAT even if patientspecific dose verification is replaced by log analysis.

ACKNOWLEDG MENTS
This work was supported by JSPS KAKENHI Grant Number JP19K17186.

CONFLI CT OF INTEREST
We have no conflict of interest to declare.