## 4 Discussion
At the same time, the relative improvement in the GPR (3%/2 mm) with rescanning compared to irradiation without rescanning was found to be 3-15% for 6-12 mm pk-pk motion in our study as opposed to 2-4% for 6-14 mm pk-pk motion in [PERSON]'s study [40]. This difference may be due to the use of layered rescanning for the high-energy layer in our study, which may also improve homogeneity in the central layer where the EBT3 film was located. In addition, the large beam size delivery system is less susceptible to the interplay effect [10], so the mitigation by rescanning may also be weaker compared to the small beam size system used in our study. In this study, rescanning provided at least 95% dose homogeneity for pk-pk motion up to 12 mm, but the irradiation time doubled from 3 to 6 min compared to FB irradiation without rescanning for the 125-cubic-centimeter (cc) PTV and 1.5 s energy switch time. This is consistent with the results of [PERSON] et al. [17], who showed an average 2-fold increase in irradiation time for volumetric rescanning with five rescans. Reducing the number of rescans may reduce the irradiation time [17] with acceptable dose coverage when the motion amplitude is less than 12 mm. However, dose homogeneity may be difficult to predict because it is an unsystematically fluctuating function of the number of rescans due  
Figure 7: An example of the lateral dose profiles along the magenta line in Figure 4c obtained for the different beam delivery modalities (except DIBH) for the 12 mm pk-pk amplitude of FB motion. Abbreviations: FB = free breathing; DIBH = deep inspiration breath-hold; and pk-pk = peak to peak. to the interference effect between the target motion and the scan pattern when the target motion is very regular [12; 13; 14]. Although our study used the asymmetric motion patterns with 10% random fluctuations in the period and randomization of the start phase, which could potentially minimize the interference effect, the dose coverage for specific motion and the number of rescans should be investigated. Eventually, the implementation of layered [45] or phase-controlled [18] rescanning may be more preferable for the Prometheus facility than volumetric rescanning because these approaches were more effective in terms of treatment time for the slow energy change systems [13]. In contrast to rescanning, which does not require the patient's breathing to be modified, the DIBH technique requires a specific breathing pattern with breath holding, where the target is in approximately the same position and nearly immobile. We simulated the variation in the film position between BHs to evaluate the potential interplay effect associated with the repeatability of the target position between individual BHs. These variations caused dose distortions similar to those of systematic regular FB motion, resulting in an average 3% decrease in homogeneity and 16% decrease in the GPR (3%/2 mm) for 3 mm (SD) position variations relative to the stationary case. This was about the same as for 6 mm FB motion (without rescanning), which was 3% and 12% for homogeneity and the GPR (3%/2 mm), respectively. However, the uncertainty of the GPR (3%/2 mm) was greater for the DIBH than for FB (8% vs. 1%). This may be related to the randomized nature of the inter-BH variations simulated with the Gaussian function compared to the regular FB motion without random variations in period and amplitude. The DIBH distortion also manifested as hot and cold spots and dose blurring along the direction of motion but appeared less symmetrical (Figure 6) compared to the FB distortion (Figure 6e). This asymmetry may be related to differences in the motion patterns of FB and the DIBH. When FB was applied, the target moved continuously and regularly with a period of 4 s and an equal offset to both sides of the relative center position. When the DIBH was applied, the target position changed discretely and randomly around the center position every 40 s, allowing for the film to remain on one side of the center position for long periods of time.