## 2 Materials and Methods
### Data Analysis  
The irradiation session and dose measurement were repeated 3 times for all the beam delivery modalities and motion patterns to calculate the statistical variance. The 2D dose matrices obtained were analyzed using an in-house software developed in Lab-Windows/CVI v.17.0.0 (295) (National Instruments, Austin, TX, USA). Two rectangular regions of interest (ROIs) (Figure 3c) were delineated for a quantitative analysis. ROI1 was 50 mm \(\times\) 50 mm and followed the PTV contour, allowing for a dose evaluation in the central thin slice of the PTV. ROI2 consisted of two areas of 50 mm \(\times\) 15 mm, symmetrically adjacent to ROI1 on either side, and allowed for an evaluation of the dose distribution beyond the PTV. Both ROIs were outlined in the same coordinates for all the dose distributions because the film in the holder was placed in approximately the same position relative to the nozzle for each measurement. All the dose distributions measured in the moving film were normalized to the mean ROI1 dose in the stationary film. Several metrics, including the mean dose in ROI1 and ROI2 (\(D_{\text{ROI1}}\) and \(D_{\text{ROI2}}\)), root mean square dose homogeneity in ROI1 (\(H_{RMS}\)), and gamma passing rate (\(GPR_{3\%/3\text{mm}}\) and \(GPR_{3\%/2\text{mm}}\)) in the gamma index analysis, were used to analyze the dose distributions [11]. The gamma index analysis allowed us to quantify the difference between the stationary dose distribution and the measured distribution distorted by motion effects, taking into account both the dose and spatial errors. The 95% threshold was accepted for \(H_{RMS}\). The gamma index analysis included two acceptance criteria of 3%/3 mm and 3%/2 mm [40] with thresholds of 95% and 90%, respectively. The local gamma index was calculated for both criteria to highlight failures in the regions with gradients and a low dose [41]. A low dose threshold (LDT) was set at 10% relative to the mean stationary dose in ROI1. It determined the pixels in the 2D dose matrix that were included in the GPR calculation. The GPRs were calculated as the percentage of pixels in the 2D dose matrix that met the acceptance criteria relative to the total number of pixels that met the LDT. In addition to the quantitative analysis, a one-way analysis of variance (ANOVA) with a significance level of \(p<0.05\) was used to statistically compare the dose distributions obtained for the different beam delivery modalities and motion patterns. In the gamma index analysis, the stationary dose distribution measured by the film was used as the reference for calculating the gamma index for the dose distribution measured by the moving film, rather than the planned distribution, which is the most commonly used [41]. This approach allowed for a relative comparison of the motion-distorted dose distribution and the planned distribution, thus reducing the uncertainty associated with the measurement of the absolute dose using the EBT3 films [42]. Thus, the gamma index is used in our study as a metric of dose distortion caused by the interplay effect. At the same time, the stationary dose distributions obtained from repeated measurements were compared with each other. A total uncertainty for \(D_{\text{ROI1}}\) and \(D_{\text{ROI2}}\) included the calibration error, the statistical variance in three repeated measurements, and the film positioning error associated with outlining the ROIs. Although the holder had a side stop that allowed for each film to be placed in the rigid position, the film positioning error was estimated to be up to \(\pm\)1 mm. This error was caused by the offsetting of the film in the holder slot and uneven film edges during cutting. It cannot be compensated by alignment procedures that refer to the phantom rather than the film. To evaluate this error, \(D_{\text{ROI1}}\) and \(D_{\text{ROI2}}\) were calculated using five options for the ROI outline: a central position of the ROIs and when the ROIs were offset by 1 mm in four directions.