## 3 Results
### Tumor Volume  
For patient number 10, we compared the 3D-PET, 4D-PET (T55%), MF-PET (T55%) images, and the vertical image profiles drawn across the SUV\({}_{\text{max}}\) voxel of the lesion on MF-PET image and the same location in 3D-PET and 4D-PET images in Figure 1. Compared with 3D-PET and 4D-PET, the lesion was substantially improved in MF-PET. Further, the ITV (SUV over 40% of the SUV\({}_{\text{max}}\)), the solid line area on the profile, of MF-PET was smaller than other images. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Waveform** & **PET\({}_{\text{MF}}\)** & **PET\({}_{\text{4D-T50\%}}\)** & **PET\({}_{\text{3D}}\)** & **PET\({}_{\text{Static}}\)** \\ \hline Cos6 & 8.09 & 8.29 & 9.17 & 8.12 \\ (\% of difference) & 1\% & 3\% & 13\% & 1\% \\ Sin & 8.34 & 8.51 & 9.02 & 8.19 \\ Percentage Difference (P.D.) & 4\% & 6\% & 11\% & 2\% \\ Sharkfin & 8.19 & 8.34 & 9.39 & 8.04 \\ P.D. & 2\% & 4\% & 15\% & 0\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Target volumes delineated by different positron emission tomography (PET) images taken from the CIRS dynamic thorax phantom under various waveforms. The percentage of difference was calculated from volume contour and gold standard volume (8 cm\({}^{3}\)). MF-Motion Freeze. Figure 1: The coronal views of the positron emission tomography (PET) images from (**a**) 3D, (**b**) 4D (T55%), (**c**) Motion Freeze technology (T55%-based) for patient number 10, and (**d**) vertical image profiles drawn across the standardized uptake value (SUV)\({}_{\text{max}}\) voxel of the lesion on Motion Freeze (MF)-PET image and the profiles of 3D-PET and 4D-PET were both drawn on the same location. The solid line indicated the area over the threshold of 40% SUV\({}_{\text{max}}\). The SUV\({}_{\text{max}}\) value of each patient were as shown in Table 3. The SUV\({}_{\text{max}}\) of 4D-PET\({}_{\text{MIP}}\) and MF-PET\({}_{\text{MIP}}\) was close and the maximum percentage difference was 2%. When comparing MF-PET\({}_{\text{MIP}}\) with 3D-PET\({}_{\text{MIP}}\), there were five patients' SUV\({}_{\text{max}}\) that were smaller than 3D-PET\({}_{\text{MIP}}\). The tumor volumes delineated in the radiotherapy plans were as shown in Table 4. The results demonstrated that the PTV obtained from 3D-PET imaging (PTV3D) was the largest (range, 732.9-54.4 cm\({}^{3}\)), followed by PTV\({}_{\text{4D}}\) defined by PET\({}_{\text{MIP}}\) (range, 509.7-24.7 cm\({}^{3}\)), with PTV\({}_{\text{MF}}\) defined by MF-PET\({}_{\text{MIP}}\) being the smallest (range, 499.4-14.1 cm\({}^{3}\)). Comparison of the PTVs obtained using the three methods showed that PTV\({}_{\text{3D}}\) versus PTV\({}_{\text{4D}}\), PTV\({}_{\text{3D}}\) versus PTV\({}_{\text{MF}}\), and PTV\({}_{\text{4D}}\) versus PTV\({}_{\text{MF}}\) were significantly different, with \(p\) values of 0.001, 0.001, and 0.002, respectively. We next compared the percentage difference in PTVs between the treatment plans (Table 5). Between PTV\({}_{\text{3D}}\) and PTV\({}_{\text{4D}}\), a maximum percentage difference of 55.3% was observed, with a median value of 35.6%; between PTV\({}_{\text{3D}}\) and PTV\({}_{\text{MF}}\), the maximum percentage difference and the median were 74.1% and 40.6%, respectively; and between PTV\({}_{\text{4D}}\) and PTV\({}_{\text{MF}}\), the maximum percentage difference and the median were 44.7% and 5.6%, respectively. Delineation of PTVs on CT images in the three treatment plans and their differences are shown in Figure 2.