Dynamic gating window technique for the reduction of dosimetric error in respiratory‐gated spot‐scanning particle therapy: An initial phantom study using patient tumor trajectory data

Abstract Spot‐scanning particle therapy possesses advantages, such as high conformity to the target and efficient energy utilization compared with those of the passive scattering irradiation technique. However, this irradiation technique is sensitive to target motion. In the current clinical situation, some motion management techniques, such as respiratory‐gated irradiation, which uses an external or internal surrogate, have been clinically applied. In surrogate‐based gating, the size of the gating window is fixed during the treatment in the current treatment system. In this study, we propose a dynamic gating window technique, which optimizes the size of gating window for each spot by considering a possible dosimetric error. The effectiveness of the dynamic gating window technique was evaluated by simulating irradiation using a moving target in a water phantom. In dosimetric characteristics comparison, the dynamic gating window technique exhibited better performance in all evaluation volumes with different effective depths compared with that of the fixed gate approach. The variation of dosimetric characteristics according to the target depth was small in dynamic gate compared to fixed gate. These results suggest that the dynamic gating window technique can maintain an acceptable dose distribution regardless of the target depth. The overall gating efficiency of the dynamic gate was approximately equal or greater than that of the fixed gating window. In dynamic gate, as the target depth becomes shallower, the gating efficiency will be reduced, although dosimetric characteristics will be maintained regardless of the target depth. The results of this study suggest that the proposed gating technique may potentially improve the dose distribution. However, additional evaluations should be undertaken in the future to determine clinical applicability by assuming the specifications of the treatment system and clinical situation.


| INTRODUCTION
The number of proton therapy systems that implement the spotscanning irradiation technique has been increasing in recent years worldwide. The spot-scanning technique possesses advantages including high conformity to the target and efficient energy utilization compared with those of the passive scattering irradiation technique. In spot-scanning technique, all or most protons will be delivered to the patients, although many protons are blocked/collimated out in the passive scattering technique. In addition, spot-scanning enables intensity-modulated particle therapy because the intensity (MU, time or fluence) of each spot can be easily modulated. 1,2 However, this irradiation technique is sensitive to target motion. Because the dose is delivered spot-by-spot, local under-and over-dosages inside the target volume can be created owing to the interplay effect between the pencil beam and tumor motion. Thus, management of respiratory motion of the tumor is essential especially for the spot-scanning particle therapy. Various motion management techniques, which use an external surrogate [3][4][5][6][7][8][9][10] or an internal fiducial marker, 11,12 have been clinically applied. External surrogates, such as monitoring of the abdominal motion with a laser displacement sensor, are used to obtain a respiratory signal. Thus, the treatment beam is gated only when the respiratory signal is within the predefined region, which is called gating window. However, external motion is not necessarily correlated with internal motion during treatment. [13][14][15] For example, it has been reported that the frequency of baseline shift/drift can increase with longer treatment time. 16 To realize beam gating with internal target motion monitoring, real-time image gated proton therapy (RGPT) has been developed. 11,12 In RGPT, as in real-time tumor-tracking therapy (RTRT) during photon therapy, 17,18 two orthogonal fluoroscopic images are continuously acquired during the treatment, and a three-dimensional position of the internal fiducial marker, which is inserted in or near the tumor is obtained in real-time. The treatment beam irradiates only when the fiducial marker is within the three-dimensional region, i.e., the gating window. It has been reported that clinically acceptable dose can be delivered with a fixed gate of ±2 mm during RGPT. 11,19 During this treatment technique, patient position can be corrected if the baseline shift has occurred. 20 In both external and internal surrogatebased gating, the size of the gating window is fixed during the treatment in the current treatment system. Dosimetric error can be reduced more by decreasing the size of the gating window. However, treatment time can be prolonged because the gating efficiency is lower.
Total dose distribution is constituted from the spots for which the doses are different during spot-scanning particle therapy. For example, by assuming that the spread-out Bragg peak (SOBP) is constructed from multiple Bragg peaks, the dosimetric error in a distal layer will be large compared with that in a proximal layer for the same positional error of the spot. This means that the size of the gating window can be optimized for each spot. In this study, we propose the dynamic gating window technique, which optimizes the size of the gating window for each spot by considering the possible dosimetric error. Although a treatment system with a dynamic gating window technique function is not available for clinical applications, the implementation of this function can be addressed by software/ hardware modifications, as described in the discussion section. The purpose of this study is to show the effectiveness of the dynamic gating window technique by evaluating the dosimetric error and the gating efficiency by simulating irradiation of the moving target in a water phantom. As an initial study, the target was assumed to be a cubic region. Target motion was simulated using the actual three-dimensional trajectory data, which were obtained during lung RTRT.

2.A | Dynamic gating window technique
The concept of the dynamic gating window technique is shown in Furthermore, the WEL variation owing to ΔX G and ΔY G was omitted because a simple water phantom was assumed in the dosimetric evaluation. Thus, an appropriate gate size can be determined because ΔX G , ΔY G , and ΔZ G can suppress ΔD less than the tolerance level for each spot. In this study, dosimetric evaluation was conducted with the water phantom in order to demonstrate the effectiveness of the dynamic gating window technique in simple condition as an initial study. Note that the above assumptions about WEL variation would not necessarily be applicable to actual clinical situation.
In this study, the tolerance of dosimetric error to determine the size of the gating window for each direction was set to 5%. The minimum size of the gating window in all directions was limited to 1 mm because the size should not be lower than the measurement accuracy of a typical imaging equipment. The maximum size of the gating window in the scan direction was limited to 5 mm to prevent the spot position error from being larger than the spot spacing that is used in the evaluation even if the corresponding dosimetric error was within the tolerance.

2.B.1 | Simulation condition
The effectiveness of the dynamic gating window technique was evaluated by dosimetric simulations performed with a simple mathematical water phantom. The evaluation geometry is shown in Fig. 2. In this study, the treated volume (TV), which is the volume that is planned to receive more than 95% of the prescribed dose, was set to 6 cm 3 × 6 cm 3 × 6 cm 3 . It is noted that the TV includes the clinical target volume (CTV) and the margin to consider the uncertainty of dose delivery (e.g., positioning errors and CT number uncertainty). It was assumed that the TV is constituted from a CTV and an isotropic margin of 5 mm. In this study, dosimetric characteristics were evaluated in CTVs and TVs.
Because the dose distribution is expected to be improved by the proposed technique, especially in the marginal region on distal side, dosimetric characteristics were also evaluated in the TV to reveal the effectiveness of the proposed technique. Dosimetric characteristics were examined in the CTV and TV with three different depths to evaluate the dependence of layer interval. Effective depth, SOBP range, beam energies, required numbers of layers to create a SOBP, and layer distance for each TV are summarized in Table 1. Effective depth was defined as the depth of the SOBP center. In each case, the TV was moved in the water phantom according to the three-dimensional trajectory data of lung tumor motion, which was obtained from the photon lung RTRT. The beam direction was anterior to posterior direction.
Trajectory data, which included more than 5 mm of beam and scanning directions, were selected to determine the effectiveness of the proposed technique because the dosimetric error is small with or without beam gating for the data with small motion. A total of 34 trajectory data, which were obtained from different patients, were used. Trajectory data were used iteratively in case that the data length was insufficient to irradiate the TV. The three-dimensional position of the gating window was defined as a location that provides the maximum gating efficiency in the first 20 s of trajectory data for each case because the location of the gating window in the original data was different owing to the manual setup. For comparison, evaluation was also conducted with a fixed gate. The size of gating window was fixed to ±2 mm for all directions, which is a typical setting of RTRT in clinical practice.

2.B.2 | Dose calculation
Dose distribution was calculated using a commercial technical computing tool, Mathematica (Wolfram Research, USA). In this study, a Bragg curve for each spot was modeled by Bortfeld's analytical formula. 21 For each energy, the beam width, which was measured for the Hokkaido University spot-scanning proton beam treatment system, was used.
Highland approximation was used to consider proton scattering in the water phantom. 22 The scan started from the most distal layer, and the scan depth was decreased layer by layer until the entire volume was irradiated. Furthermore, 17 × 17 spots for each layer with a spot spacing of 5 mm were used. All spots in a layer had the same dose weight.
Thus, the size of the dynamic gate for the spots in a layer was same in this evaluation. In the calculation of dose distribution, spot positions were fixed in all evaluation conditions. The evaluation regions, CTV and TV in this study, were moved in the water phantom according to the motion trajectory of the tumor. The calculation grid was 2 mm for each direction. All evaluations were conducted for one dose painting with a relative dose. Since the derivable maximum MU/spot is varied for each treatment system, the target may need to be irradiated multiple times  To simulate beam gating spot-by-spot by assuming the actual time scale, the tumor trajectory data, which were recorded at a rate of 30 times per second, were interpolated to evaluate the positional deviation of the target at each irradiation spot. In this study, machine specifications that are similar to those of the typical proton therapy system were assumed. The scan speed was fixed to 10 m/s, which corresponds to 5 ms required to move to the next spot. The spot irradiation time was set to 5 ms per spot for the maximum dose weight. Then, the irradiation time for each spot was evaluated according to the spot weight.

2.C.2 | Gating efficiency
In respiratory-gated radiation therapy, treatment time is one of the main concerns because the treatment time can be prolonged if the gating efficiency is low. It is difficult to evaluate irradiation time quantitatively in respiratory-gated spot-scanning particle therapy because it depends on the specifications of the treatment system such as dose rate and particle accelerator used. Thus, in this study, the gating efficiency was evaluated as an index of irradiation time.
The gating efficiency was determined as a ratio of the accumulated time of gate-on to the total time required to finish irradiation. In other words, it was equal to the ratio of the time when the fiducial marker was within the gating window to the time required to finish the irradiation. In this study, the gating efficiency for each irradiation layer was evaluated as a ratio of the gate-on time to the required time for the irradiation of each layer. The gating efficiency for each layer was averaged for 34 cases. The overall gating efficiency was evaluated as a ratio of the accumulated gate-on time to the required irradiation time through all the layers. The overall gating efficiency of 34 cases was compared by using box plot.

3.A | Dosimetric characteristics
The sizes of the gating window in X G , Y G , and Z G directions for the spots in each layer are shown in Fig. 3. In this evaluation, the same size of the gating window was used for the spots in each layer because a simple cubic target was assumed. Regarding the gate size in the beam  shown in Figs. 4(a) and 4(b), respectively. Higher dose than prescribed dose was delivered and shifted laterally overall in fixed gate compared with dynamic gate. The dose profile along the beam direction at the field center is shown in Fig. 4(c). In the fixed gate approach, a large dosimetric error was observed compared with that of the dynamic gate especially in the distal region. In the dynamic gate approach, the dosimetric error was reduced because the smaller size of the gating window was used for the spots with high weight, as shown in Fig. 3. The box plots of D max , D min , HI, and SD in the CTV and the TV, which were evaluated for 34 cases, are shown in The dosimetric accuracy in CTVs was improved by applying the dynamic gate, although the improvement was moderate compared with TVs. The results in this study suggest that dose deterioration within the target owing to the interplay effect can be reduced, and the dose to the adjacent organ-at-risk can be reduced compared with that of the fixed gate. The variation of dosimetric characteristics as a function of the target depth was small in dynamic gate compared with fixed gate. These results suggested that the dynamic gating window technique can maintain an acceptable dose distribution regardless of the target depth.

3.B | Gating efficiency
Gating efficiency was averaged for each irradiation layer, and the irradiation volumes for 34 cases are shown in Fig. 7. As shown in as the target depth becomes shallower, the gating efficiency is reduced, although the dosimetric characteristics will be maintained regardless of the target depth.

| DISCUSSION
The repaint technique is also effective for treating a mobile target during spot-scanning. 23 although it was assumed that the displacement of the target position along the beam direction was identical to the WEL variation, it cannot be established in actual clinical practice. The WEL variation owing to respiration in the chest was investigated using 4DCT. 27,28 It has been reported that the mean intra-fractional WEL variation for chest wall was less than 4.1 mm for the ITV region. More precisely, the size of the gating window can be optimized by considering the possible dosimetric error using CT images. Currently, it is difficult to evaluate the possible dosimetric error in advance of the treatment with enough temporal and spatial resolution. A novel technique to reconstruct cine-4DCT[ [29][30][31][32] with high-temporal resolution may be applied to determine the gate size by evaluating the actual WEL variation according to the target location.

| CONCLUSION
In this study, the dynamic gating window technique was proposed to improve the dose distribution to treat mobile targets in spot-scanning particle therapy. The effectiveness of the dynamic gating window technique was validated using a simulation study with a simple phantom geometry because the treatment system that has this function was not available in the current situation. Although a simple cubic target was assumed in the simulation, the results in this study suggest that the proposed gating technique was potentially applicable to improve the dose distribution. The possible solution to implement the dynamic gate function in the treatment system was discussed. When the treatment system with the dynamic gate function is realized, additional evaluations for possible clinical application should be undertaken in the future by accounting for the specifications of the treatment system and clinical situation.

CONFLI CT OF INTEREST
The authors have no conflict of interest to disclose.