## 3 Results
Increasing the inter-BH variation to 3 mm also resulted in a significant decrease (\(p\) < 0.001) in the \(H_{RMS}\), \(GPR_{3\%/3\text{mm}}\), and \(GPR_{3\%/2\text{mm}}\) to a mean of 93%, 88%, and 79%, respectively. The dose distributions obtained only for the [1 s-1 mm] pattern met the thresholds for the \(H_{RMS}\), \(GPR_{3\%/3\text{mm}}\), and \(GPR_{3\%/2\text{mm}}\) on average (Table 1). The irradiation time was approximately the same as for rescanning, averaging 5 min 40 s for all the irradiation sessions. The dose distributions obtained with gating were similar to the stationary distribution in terms of the \(D_{\text{ROI1}}\) (\(p\) = 0.73), \(D_{\text{ROI2}}\) (\(p\) = 0.42), and \(H_{RMS}\) (\(p\) = 0.18) for both the regular and irregular motion patterns used (Figure 5a vs. Figure 5k,l). However, for the \(GPR_{3\%/3\text{mm}}\) and \(GPR_{3\%/2\text{mm}}\), only the dose distributions for the regular [12 mm-0%] pattern met the \(\geq\)95% and \(\geq\)90% thresholds on average (Table 1). For the irregular [12 mm-10%] pattern, the \(GPR_{3\%/3\text{mm}}\) and \(GPR_{3\%/2\text{mm}}\) were on average a few percent lower than for the regular [12 mm-0%] pattern (\(p\) = 0.02) (Table 1 and Figure 6k vs. Figure 6l). The irradiation time  
Figure 6: An example of the local gamma index distributions (beam’s eye view) with the worst case GPR (3%/2 mm) measured by **(a)** the stationary and moving films irradiated with different perpendicular motion patterns using different beam delivery modalities: **(b–e)** FB irradiation without motion mitigation, **(f–h)** FB irradiation with rescanning, **(i,j)** DIBH irradiation, and **(k,l)** respiratory-gated irradiation. The color maps are labeled as “Modality [Motion pattern]”. The black color indicates out of range. Abbreviations: GPR = gamma passing rate; FB = free breathing; Resc = rescanning; and DIBH = deep inspiration breath-hold. did not depend on the motion pattern (\(p\) = 0.89) and was shorter than for the rescanning and DIBH, averaging 3 min 29 s for all the irradiation sessions. In summary, the \(D_{\text{ROII}}\), which characterized the mean dose within the PTV, decreased with increasing motion amplitude to 0.94-0.96 for FB irradiation without motion mitigation and DIBH and was acceptable for rescanning and gating at 0.99-1.02. The \(D_{\text{ROI2}}\), which characterized the dose outside the PTV, was approximately the same for FB irradiation with and without rescanning up to 0.22-0.28 but was minimized to 0.10-0.12 by the DIBH and gating. The \(H_{\text{RMS}}\), which quantified the dose dispersion within the PTV relative to the \(D_{\text{ROII}}\), systematically decreased as a function of motion amplitude for FB irradiation with and without rescanning, as well as for the DIBH, but was approximately the same as in the stationary case at about 96% for the gating. The GPRs showed a similar trend as the \(H_{\text{RMS}}\) and decreased with increasing motion amplitude for FB irradiation with and without rescanning and DIBH, but also characterized the influence of motion irregularity when gating was used, resulting in a difference of about 4-7%. The use of rescanning and DIBH significantly increased the irradiation time, while gating was more time efficient.