Comparisons of bank A and bank B for the three accelerators
The box plots of the maximum leaf RMS and 95th percentile errors for the three accelerators with IMRT and VMAT techniques are shown in Figure 1. In all three accelerators, no statistical differences were observed between bank A and bank B in the maximum leaf RMS and 95th percentile errors. No statistical differences were observed between bank A and its counterpart bank B for each accelerator in terms of maximum leaf RMS and 95th percentile errors. Correlations were observed between bank A and bank B in the two leafpositionerror evaluation parameters of all accelerators and techniques, and the Pearson correlation coefficients were all greater than 0.5. Figure 2 shows the correlation analysis of bank A and bank B in the maximum leaf RMS and 95th percentile errors of the three accelerators with IMRT and VMAT. Compared to IMRT, VMAT increased the maximum leaf RMS and 95th percentile errors in all accelerators.
Table 1 Evaluation parameters of leaf positioning errors for IMRT and VMAT plans on the three accelerators

95th error (mm)

Max RMS error(mm)

Max leaf speed (mm/s)

Mean leaf speed (mm/s)

Fail leaves number


Trilogy

IMRT

0.66±0.17

0.45±0.10

22.72±2.21

3.37±1.13

4.89±4.97

VMAT

1.11±0.19

0.80±0.07

36.31±2.41

7.92±0.68

23.11±7.69

TrueBeam

IMRT

0.03±0.01

0.03±0.01

22.73±2.21

1.62±1.00

0

VMAT

0.05±0.01

0.03±0.01

23.44±3.04

4.05±1.82

0

Halcyon

IMRT

0.08±0.02

0.06±0.01

56.01±1.38

3.19±1.32

0

VMAT

0.09±0.01

0.07±0.01

59.16±1.00

12.25±3.61

0

IMRT, intensitymodulated radiation therapy; VMAT, volumetricmodulated arc therapy
Comparison between the three accelerators
For the IMRT technique, the mean values of maximum leaf RMS error and 95th percentile error were 0.45±0.1 mm, 0.66±0.17 mm in Trilogy, 0.03± 0.01 mm, 0.03±0.01 mm in TrueBeam, and 0.06±0.013mm, 0.08±0.02 mm in Halcyon respectively. For the VMAT technique, the mean values of maximum leaf RMS error and 95th percentile error were 0.80±0.07 mm, 1.11±0.19 mm in Trilogy, 0.03±0.01 mm, 0.05±0.01 mm in TrueBeam, and 0.07±0.01 mm, 0.09±0.01 mm in Halcyon, respectively. The data are shown in Table 1. The maximum leaf RMS and 95th percentile errors in Trilogy were significantly higher than in the other two accelerators. Halcyon significantly increased the values of the two parameters compared to TrueBeam. The differences in the pairwise comparison of the three accelerators were statistically significant (p<0.05). Supplementary Fig. 1 shows the comparison of maximum leaf RMS error and 95th percentile error among the three accelerators with IMRT and VMAT technique.
Separate analysis for each accelerator
 Trilogy
In IMRT plans, the maximum leaf RMS and 95th percentile error showed strong correlation with the mean leaf speed, with R values of 0.71 (p=0.00) and 0.61 (p=0.00), respectively. The maximum leaf RMS error also showed a correlation with the maximum leaf speed (R=0.76, p=0.00). There was no correlation between the 95th percentile error and the maximum leaf speed (R= 0.36, p=0.00). Figure 3 showed the density plot which displayed the maximum leaf RMS and 95th percentile error as a function of the maximum and mean leaf speed in IMRT plans.
In VMAT plans, a strong correlation was observed between the maximum leaf RMS error and the maximum leaf speed (R= 0.85, p<0.05) and mean leaf speed (R= 0.75, p<0.05). The 95th percentile error was also correlated with the maximum leaf speed (R= 0.76, p<0.05) and mean leaf speed (R= 0.60, p<0.05). The density plots in Supplementary Fig. 2 shows the maximum leaf RMS and 95th percentile error as a function of the maximum and mean leaf speed in VMAT plans.
Through the analysis of the number of failed leaves with a position error of more than 1mm, it was found that the number of failed leaves was correlated with the 95th percentile error both in IMRT (R=0.51, p=0.00) and VMAT (R=0.57, p=0.00). The number of failed leaves in VMAT was also correlated with the mean leaf speed (R=0.53, P=0.00), and the number of failed leaves increased with the increase of leaf speed. The data are shown in Supplementary Fig. 3. There was no correlation between the number of failed leaves and the maximum leaf speed, and the correlation coefficients were 0.45 and 0.41 in IMRT and VMAT, respectively. Supplementary Fig. 4 showed the specific values of the correlation coefficients among the evaluation parameters.
 TrueBeam
In IMRT plans, the 95th percentile error was correlated with maximum and mean leaf speed (R= 0.59, 0.60, respectively). No correlation was observed between the maximum leaf RMS error and the maximum and mean leaf speed (R=0.41 and 0.45, respectively).
In VMAT plans, both the maximum leaf RMS and the 95th percentile error were correlated with the mean leaf speed (R= 0.70 and 0.55, p<0.05). No correlation was observed between the maximum leaf RMS and 95th percentile error and the maximum leaf speed (R=0.28 and 0.22, respectively). Supplementary Fig. 5 shows the correlation between the maximum leaf RMS and 95th percentile error and leaf speed in TrueBeam.
In TrueBeam, leaf position error above the threshold (1 mm) were not found in IMRT and VMAT plans. The specific percentages of different leaf position errors are shown in the subsequent analysis.
 Halcyon
No correlation was observed between the maximum leaf RMS and 95th percentile error and the maximum leaf speed in IMRT and VMAT plans. The maximum leaf RMS error had no correlation with the mean leaf speed in IMRT and VMAT plans (R= 0.18, 0.36). Only 95th percentile error was found to be correlated with the mean leaf speed (R=0.59 and 0.52 in IMRT and VMAT, p<0.05). Supplementary Fig. 6 shows the correlation between the 95th percentile error and mean leaf speed in IMRT and VMAT plans of Halcyon.
Like TrueBeam, leaf positioning error exceeding 1mm was not found in IMRT and VMAT plans in Halcyon.
Percentages of leaf positioning errors
The percentages of different leaf positioning errors are shown in Figure 4. Almost all leaf positioning errors occured within ±0.05mm in TrueBeam. The data dispersion between 0 and ±0.05mm of the leaf positioning error in Halcyon was higher than that in TrueBeam, indicating that the leaf positioning accuracy of TrueBeam was better than that of Halcyon.
As can be seen in Table 1, some of the leaf positioning deviations for the Trilogy accelerator showed exceeding the threshold (1 mm), and the leaf positioning deviations data within the threshold also appeared discrete (Figure 4). The Trilogy VMAT chart in Figure 4 showed the worst results for percentages of different leaf positioning errors. The leaf positioning errors in VMAT were higher than those in IMRT for all accelerators.
Correlation between leaf positioning error evaluation parameters and gantry or arc angles
In IMRT plans, no correlation was found between the two leafpositioningerror evaluation parameters and the gantry angles, and the number of failed leaves was not correlated with the gantry angles as well. As shown in the radar plot in figure 5, this plot is composed of IMRT data from the Trilogy. No significant aggregation bias was seen for the maximum leaf RMS and 95th percentile error at different gantry angles, and angles with small values of the evaluation parameters do not necessarily represent small leaf errors, possibly due to the fact that these angles were set less in the treatment plan, as the number and angles of the fields in all plans were inconsistent. In TrueBeam and Halcyon, the data distributions of the two leafpositioningerror evaluation parameters and the gantry angles were similar to that in Trilogy. Similar results were also generated between the degrees of arc and the evaluation parameters in the VMAT plans, showing that the leaf positioning errors of all three accelerators were independent of the gantry and arc angles for IMRT and VMAT techniques.