Effect of VERO pan‐tilt motion on the dose distribution

Abstract Tumor tracking is an option for intra‐fractional motion management in radiotherapy. The VERO gimbal tracking system creates a unique beam geometry and understanding the effect of the gimbal motion in terms of dose distribution is important to assess the dose deviation from the reference conditions. Beam profiles, output factors (OF) and percentage depth doses (PDD) were measured and evaluated to investigate this effect. In order to find regions affected by the pan‐tilt motion, synthesized 2D dose distributions were generated. An evaluation of the 2D dose distribution with the reference position was done using dose difference criteria 1%–4%. The OF and point dose at central axis were measured and compared with the reference position. Furthermore, the PDDs were measured using a special monitoring approach to filtering inaccurate points during the acquisition. Beam profiles evaluation showed that the effect of pan‐tilt at inline direction was stronger than at the crossline direction. The maximum average deviation of the full width half maximum (FWHM), flatness, symmetry, penumbra left and right were 0.39 ± 0.25 mm, 0.62 ± 0.50%, 0.76 ± 0.59%, 0.22 ± 0.16 mm, and 0.19 ± 0.15 mm respectively. The ÔF and the measured dose average deviation were <0.5%. The mechanical accuracies during the PDD measurements were 0.28 ± 0.09 mm and 0.21 ± 0.09 mm for pan and tilt and pan or tilt position. The PDD average deviations were 0.58 ± 0.26 % and 0.54 ± 0.25 % for pan‐or‐tilt and pan‐and‐tilt position respectively. All the results showed that the deviation at pan and tilt position are higher than pan or tilt. The most influences were observed for the penumbra region and the shift of radiation beam path.

the patient and estimate the target motion coordinate during treatment. 1,2 The predicted target coordinates are passed to the gimbal head controller of the accelerator, which adapts accordingly to compensate the target motion. Eventually, the reduced intra-fractional uncertainties will potentially shrink CTV-PTV margins. 3 In comparison to other motion mitigation strategies, the treatment time can potentially be reduced since the beam is delivered continuously while the target is in motion. [1][2][3][4][5][6][7][8][9][10] Instead of moving its gantry or multi leaf collimator (MLC) leaves for tracking, VERO swings the gimbal head. It has its own center of rotation, which is located at 40 mm below the source. 1,2 Therefore, the geometry of the beam during tracking is different from a common oblique beam, which is created by moving the linac gantry. The gimbal rotation is currently not supported by available treatment planning systems (TPS) [3][4][5][6][7][8] and thus potentially leads to an inaccurate treatment delivery. Such systematic errors will not be noticeable during the dose calculation. Currently, the gimbal tracking dose calculation is performed on a stationary CT without considering the gimbal's motion. Dose calculation is thus relying only on shifting of the target into the radiation field, 3 which is not giving a similar radiation path of the beam. Some dosimetry studies showed that the gimbal motions will not affect the beam profile characteristics, i.e., beam profile and penumbra agreed within 1%/1 mm. 5,6 Furthermore, deviations in output factor (OF), percentage depth dose (PDD) and 2D dose distribution were not observed. 5 All the previous studies used films as their primary detectors. 5,6 The aim of this work was to investigate the effect of pan-tilt motions during treatment on the delivered dose distribution in a water phantom. However, the situation is more complex in the real clinical condition, since the patient surface, tissue density, and tumor motion direction will greatly influence the dose calculation and the treatment accuracy during the treatment. A comprehensive evaluation regarding the effect of the VERO's gimbal motion on fundamental dosimetry properties such as beam profile, OF, and PDD was performed to provide a better understanding of the gimbal motion effects on the delivered dose. Furthermore, it will help medical physicists to estimate the accuracy of treatment delivery. [11][12][13][14][15] Especially, if the tracking treatment is combined with other complex treatments such as intensity modulated radiotherapy (IMRT), or wavearc 16 treatments.

2.A | Measurement geometry and setup
As shown in Fig. 1, the VERO gimbal can be swung to inline/ tilt (A ! C) and crossline/pan (A ! B) direction using its center of rotation (COR). A target tracking utilizing the gimbal motion creates a unique beam geometry as shown in Fig. 2. Unlike the common oblique beam geometry, the gimbal geometry creates a longer source surface distance (SSD) and a larger effective field size (FS). The gimbal can track a moving target up to a maximum tracking distance TD ð Þ ¼ 41:9 mm away from the isocenter at a pan or tilt directions, which is equal to an angle (a) of pan or tilt of 2.5 degree (Fig. 1).
Moreover, a maximum gimbal position at a pan and tilt position (A ! D) will result in a relative angle of the gimbal to the water surface of 3.5 degree (Fig. 1). This creates an SSD increase of 1.83 mm compared to the reference. Since beam profile, OF and PDD are influenced by the FS and SSD, 17,18 both parameter changes could leads to a deviation of the reference dosimetry parameters.
All measurements in this study were carried out using BLUE PHANTOM 2 (IBA Dosimetry GmbH, Schwarzenbruck, Germany) and a microDiamond single crystal detector (T60019, PTW-Freiburg GmbH, Freiburg, Germany). The reference condition was defined at pan and tilt angle 0 o . Moreover, the PDDs and profile measurements were done using an output resolution of 1 mm and the field detector reading was normalized at a depth of 15 mm.
The central axis (CAX) position played an important role during the measurement since it was used as a reference to determine the scanning region. Moreover, it ensured that the scanning profile was always intersected at the CAX position ( Figs. 1 and 2). Therefore, the PDD scan direction, as well as the OF depth, were always along the CAX beam path. The coordinates of the CAX at a certain depth (d) were determined by calculating the tracking angle (a) based on the TD of the gimbal at pan-tilt angle (Fig. 1) using the COR SSD at the reference position, which was 960 mm: The gimbal center of rotation is located 40 mm below the radiation source, which creates an SSD 960 mm without pan or tilt.

2.B | Beam profile and output factor
Beam profiles were measured as described in Table 1

2.C | Percentage depth dose
A similar approach as the OF measurements was applied to determine the start-stop position for the PDD measurements. The start and stop positions on the CAX were calculated using Eqs. (1) and (2) at a depth of 300 mm and 0 mm respectively. The 3D dose scan mode was used for the PDD measurement.
A dry run test was performed prior the measurement to ensure a detector position at CAX of the beam. The test also functioned as detector positioning consistency and mechanical movement quality control of the BLUE PHANTOM 2 during the 3D dose scan mode. After the initial dry run test, it was found that the mechanical movement of the detector arms was not always smooth, which could create a positioning inaccuracy. This Additionally, r was calculated by projecting the measurement directional vector A 2 B 2 ! into the scanning line directional vector The distance of r was determined by dividing the crossproduct of both vectors with the magnitude of the scanning vector The effective measurement depth (d eff: ) was determined by calculating its relative distance to the CAX coordinate: Measurement point coordinate at inline (YÞ, crossline X ð Þ direction and depth d ð Þ were obtained from the measurement software output.

2.D | 2D dose distribution synthesis
Beam geometry properties for the beam profile, PDD and OF measurements at pan-tilt position, with a being the pan-tilt angle according to the tracking distance (TD). The beam profiles, PDDs and OFs were measured from point F 1 to F 2 , B 1 to B 2 , and at A 1 respectively. The isocenter(ISO 1 and ISO 2 ) is separated with the target plane during tracking, due to the fix distance of the isocenter. The PDD assessments were obtained by comparing the dose difference at each depth according to Table 1 to the reference condition. The comparison was performed at depths beyond 15 mm or the build-up region to avoid large uncertainties of the depth dose distribution close to the water surface due to electron scattering created by the beam-shaping aperture above the water surface. 20,21 The calculated 2D dose distributions from inline and crossline measurements were assessed pixel-by-pixel. The approach was performed to study the effect of pan-tilt movements on the dose distribution profile and to identify the region that is mostly influenced by the movement. The assessment was conducted using full field measurements using a 2% threshold as the limit of the radiation field.

2.E | Data analysis
Secondly, the evaluation was done using 80% of the physical field size at the corresponding depth of measurement, which represents the effective field size for treatment.

3.A | Profile characteristics and output factor
Calculation of beam profile characteristics, i.e., FWHM, flatness, symmetry, and penumbra were calculated and compared with the reference condition. Figure 3 is an example of the D at pan-tilt positions À41.9 mm and 41.9 mm. The penumbra left and right shows similar patterns and values, therefore only the left penumbra is shown in Fig. 3.
Similar results were found at other pan-tilt position as seen in The OF deviation shows a decreasing trend from 10 mm 9 10 mm to 100 mm 9 100 mm field size and then an increasing trend toward 150 mm 9 150 mm. The dose measured during the OF measurements during pan-tilt were lower than at the reference position. The average deviation of the measured dose at pan and tilt is slightly higher than at pan or tilt position, which was less than 0.1%.

3.B | Mechanical movement monitoring
Unlike the profile measurements, the PDD measurements were more complex with respect to phantom mechanical movements since the detector positioning involved more than one motor. The measurement involving one motor movement did not show any positioning deviation since vector A 2 B 2 ! and B 1 B 2 ! will always overlap with a resulting deviation of r ¼ 0 (Fig. 2). Moreover, the other two motors will lock itself, as a result the remaining motor movement will always be on its vector direction.
The dry run test showed unsmoothed mechanical movement since the motion was based on more than one motor. Maintaining the distance r of the measured point to the nominal scanning line less than 0.5 mm resulted in a mean positioning accuracy of 0.21 AE 0.09 mm and 0.28 AE 0.09 mm for 2 and 3 axes movements during the PDD measurement (Fig. 6), respectively. The PDD average deviations at all field sizes at pan-tilt position were less than 1% (Fig. 8). Figure 8 also shows that the average deviations at pan and tilt are higher than at pan or tilt position, since the SSD is longer than the pan or tilt position.

3.D | The 2D dose distribution
The synthesized dose distribution resulting from multiplying an inline and crossline dose profile at a corresponding depth has been compared with the calculated dose profile from the treatment planning system. The comparisons showed the smallest and largest mean difference between the synthesized and calculated dose profile of À0.1 AE 1.9% and 0.7 AE 0.7% respectively. The synthesized 2D dose distributions comparisons with the reference were evaluated using a pixel-to-pixel comparison and a criteria 1%-4% dose deviation was used to evaluate the dose distribution. Figure 9 shows that most of the profiles had less than 95% of the point that passed the criteria.
The pixel-by-pixel comparisons showed that the mean dose deviation was less than 1% with high dose deviations at the penumbra regions (Fig. 10), resulting in high standard deviations of its mean dose difference. Removing the penumbra region by comparing only 80% of the full field size for further evaluation showed that the and tilt were higher than pan or tilt as shown in Table 2, and the values show a decreasing trend as the depth increases.

3.E | The radiation path
The radiation paths of pan-tilt are shown in Fig. 11. The position of the dose distribution is shifted according to the pan-tilt position which depends on the pan-tilt angle as described in Eqs. (1) and (2).
The radiation path at CAX is shifted compare with its reference positions, as well as the dose distribution above and below the SAD

| DISCUSSION
In this study, a comprehensive investigation regarding the effect of gimbal movements and its impact on the dose distributions has been conducted. The dose distribution parameters being observed were 2D dose distribution, OF, and PDD. Observation of the dose distribution deviation could help physicists to understand the effect of gimbal movements on the delivered dose.
We measured the dose distribution at maximum pan-tilt position according to Table 1. However, there were no sufficient data F I G . 8. The PDD dose average deviation from its reference condition at all pan-tilt positions for each field size.
F I G . 9. The percentage of passed pixels at depth 50 mm using 1%-4% dose difference criteria for pan and tilt (a) and pan or tilt (b). To ease readability the data points were shifted at each field size entry. Beam profile comparison showed that the effect of pan-tilt movement at inline directions was stronger than in crossline direction (Fig. 3). Kamino et al. 2  The gimbal swing created an extended SSD and a larger field size at the water surface as shown in Fig. 2. The SSD will extend by 0.9 mm and 1.8 mm at maximum pan or tilt and pan and tilt respectively. Such movements can create a systematic increase of dose uncertainties during treatment delivery. The value of the extended SSD is close to the AAPM TG 142 17 error tolerance for the optical distance indicator (ODI) which is 2 mm. Several studies showed that a combination of extended SSD and larger field size would contribute to changes in OFs, PDD curves, and 2D dose distributions. 17,18 Relative OFs were calculated by dividing the detector reading of each field size measurement to that of the reference field size of 100 mm 9 100 mm at each pan-tilt measurements. Therefore, the OF deviation at 100 mm 9 100 mm was always zero and the deviation decreases as the field sizes changed toward the reference field size of 100 mm 9 100 mm. Due to the small deviation, the shape of the OF curves was also similar with the reference condition. Therefore, the scatter patterns that occurred during the measurements were similar with its reference condition. 18 The tolerable deviation of OFs with the reference condition was 1% 17 and the maximum deviation value of (À0.11 AE 0.33)% was still below the tolerance value. The measured dose during the OF measurement also showed a lower dose value, since the SSD was further than the reference condition. The differences were less than 0.5% except for After filtering and correcting, 22 the measured PDD data points using Eqs. (3) and (4) it was found that all PDD curves beyond the buildup region were higher than the references. The average deviations for all field sizes are 0.58 AE 0.26% and 0.54 AE 0.25% for the pan-or-tilt and pan-and-tilt position respectively. This result confirms that the gimbal movements affect the PDD curves. Figure 8 showed that combinations of the extended SSD and beam angle change caused this increase. 18 The mean deviation of the PDD curve at pan and tilt is higher than pan or tilt, which shows that pan-tilt move- The 2D dose profile evaluation using the pixel-to-pixel approach showed that only 30% of the 320 fields had > 95% points that passed dose difference criteria 1%-4%. Figure 10 showed that the penumbra region was the main contributor to the failure. The pan- tilt movements will influence the dose distribution in the penumbra region, which could create a dose difference up to 8%. Nevertheless, the mean dose deviations from the pixel-to-pixel comparison were less than 1%. Excluding the penumbra region and considering only 80% of the field size during evaluation, resulted in a similar mean dose deviation at a lower standard deviation. This concluded that the source of the high standard deviation was coming from the penumbra region. Table 2 shows that the mean deviation at pan and tilt is also higher than at pan or tilt position since the beam angle is higher at pan and tilt position. which is less than 1 mm in term of distance deviation (Fig. 3). These results indicated that the dose distribution at the target edge region and the OAR beyond the target depth would be affected the most.
Increasing the CTV-PTV margin could increase dose coverage at the CAX plane during tracking but would be contra productive with the aim of tracking treatment purpose.
The effect of gimbal motion during tracking in the current study was performed at the maximum position and could be considered a worst-case scenario. Therefore, further studies regarding the effect of gimbal motion in a real treatment setting are very important to assess the accuracy of the calculated and delivered dose distribution during the entire motion.
The pan-tilt motion effect measured in this study is limited to the ideal conditions in a water phantom. The difference of each fundamental dosimetry parameter to the reference is less than 1%. The pan-tilt motion effect measured in this study is limited to the ideal conditions in a water phantom. The difference of each fundamental dosimetry parameter to the reference is less than 1%. However, the conditions are much different in a real clinical condition due to the tumor motion direction and the shape of the patient which are not ideally represented by the phantom. The act of shifting the beam alone will not give the accurate dose calculation. The target motion during treatment will influence the dose coverage within the target and its surrounding OAR. For example, the target motion in parallel direction will create over-and under-dose of the target due to the target being no longer at the SAD point.
The dose located in the target plane was not suffering a large dose difference at ring and gantry 0 o and the dose difference was less than 1%. However, the dose above and below the target shows more dose deviation due to the path difference, and the separation of the isocenter and the target dose (Fig. 2). The edge of the beam was suffering large deviation ( Fig. 11) even though the beam shifting was applied. Taking the depth of the target as the reference CAX, the shift of the beam position above or below the target could be

4.A | Future study
More detailed works to simulate the real clinical situation are required to estimate a dose calculation closer to the real situation.
New CT datasets and MU distributions corrected for the pan-tilt position cannot be generated manually but require dynamic adjustment as part of the dose calculation. Nevertheless, this fundamental data can illustrate the effect of the pan-tilt motion in the ideal situation and can be used as a precaution how to implement the pan-tilt motion for the treatment in the absence of appropriate 4D TPS.
A feasibility study regarding the implementation of the pan and tilt motion in a TPS using image transformations of the CT data outside the TPS while implementing the ring and gantry rotations within the TPS was done. 26 Full implementation of the approach in a TPS requires transformation of the CT dataset according to the pan and tilt orientation but does not need any modification of the TPS dose calculation algorithm, which makes the implementation is much easier.

| CONCLUSION S
The dose deviation for pan and tilt motion are higher than for gimbals moved in pan or tilt due to a longer SSD and a higher pan-tit PRASETIO ET AL.
| 153 angle relative to the water surface. The impact of VERO gimbal movement on 2D dose profile, OF and PDD were less than 1%, 0.5%, and 0.5% respectively. The penumbra region is greatly influenced, at the investigated maximal gimbal motion with dose differences up to 8% against the reference position. There is also a shift of the radiation path that depends on the depth relative to the isocenter, which can influence OARs distal to the target volume.
Considering the gimbal motion in the dose calculation would be beneficial to improve the accuracy of treatment delivery.

ACKNOWLEDGMENTS
The presented work was performed by the first author HP in fulfillment of the requirements for obtaining the degree "Dr. rer.

CONF LICT OF I NTEREST
The authors declare that there are no conflicts of interest in connection with this work.