## 4 Discussion  
In this study, we demonstrated the effect of application of the MF technique on the dose distribution in respiratory-gated radiation therapy. In comparison with the conventional 3D-Plan or respiratory-gated 4D-Plan, the MF-Plan using a MF reconstruction approach showed a better efficacy in terms of delineation of the target volume and reduced the radiation dose received by the surrounding normal tissues. Our findings suggested that the MF technique is of clinical value for use in radiotherapy planning for the treatment of lung cancer. In the past, respiration-caused motion and deformation of the tumor have represented an extensive problem during radiotherapy for lung cancer. Conventional treatment increased treatment volumes by adding additional margins to the extent of the tumor. In this way, it is ensured that the radiation covers the possible path of the tumor due to target motion under respiration. However, although a better killing effect on the tumor may be obtained, this method also increases the radiation dose received by the surrounding normal tissues, which often lowers the quality of life for patients. Therefore, in order to obtain a balance between killing cancer cells and reducing normal tissue complications, a better method for the definition of tumor volumes is required [5; 13]. Following the development of respiratory-gated imaging or real-time tumor tracking, diagnosis of and radiotherapy for lung tumors have become more accurate. The results of our current study demonstrated that the 4D-Plan and MF-Plan for respiratory-gated radiotherapy maintained a high radiation dose on the target volume, achieving the same treatment effect as that obtained by conventional treatment while reducing the dose received by OARs. Figure 8: (**a**) Correlation between the percentage difference in the PTV and the percentage difference in the V\({}_{20}\) (the relative volume of the lung receiving a dose above 20 Gy); (**b**) correlation between the percentage difference in the PTV and the percentage difference in the mean dose of the lung. The red lines indicate the 3D-Plan vs. 4D Plan; the blue lines indicate the 3D-Plan vs. MF-Plan; and the yellow lines indicate the 4D-Plan vs. MF plan. For definition of a tumor, unlike traditional 3D-PET imaging, 4D-PET can only collect images at certain respiratory phases, which limits the application of 4D PET/CT for the diagnosis and treatment of cancer. [PERSON] and coworkers concluded that when 4D-PET uses a higher frame rate to collect fast dynamic images, noise in the images during most respiratory phases is increased. In order to increase the temporal resolution, complex image reconstruction needs to be introduced to divide the images into more respiratory phases, but the process also separates the original data collected into sequences and is time-consuming [13]. The differences in the signal level of the 4D-PET images among the respiratory phases directly affects the accuracy of volume definition of a tumor, and may even affect the outcome of the radiation treatment [5]. Although the currently-used respiratory-gated radiotherapy technique enables administration of radiation at the correct time and location, the question of how to make better use of clinical imaging technology to define the extent of a tumor remains an important issue in this field [6; 14]. Studies have shown that PET/CT in combination with \({}^{18}\)F-FDG can define smaller tumor volumes than those defined by CT alone [15]. Respiratory-gated \({}^{18}\)F-FDG PET imaging has a significantly higher SUV\({}_{\text{max}}\) than 3D-PET and 4D-PET [16], which can provide more accurate image quantification in cases of lung cancer. Therefore, in the present study, we applied the MF technique to reconstruct PET\({}_{\text{MF}}\) images for delineation of the tumor volume. In comparison with 3D and 4F PET, we found that the PTV\({}_{\text{MF}}\) delineated by PET\({}_{\text{MF}}\) was significantly smaller than that defined by PTV\({}_{\text{3D}}\) or PTV\({}_{\text{4D}}\).