## 4 Discussion  
Radiation therapy plays an important role in the treatment of patients with lung tumors, and is usually used alone or in combination with chemotherapy or surgery. The purpose of radiation therapy is to deliver radiation to the tumor in the patient's body. As technology develops further, it will be possible to emit radiation more precisely into the tumor [5; 6; 37; 38], but such accuracy remains very difficult to achieve. The method presented in this study has demonstrated the feasibility of tracking the respiratory phase and 3D tumor position in real time during treatment using a kV image mounted on the treatment system. The proposed method works well even under poor conditions in which the shape of the diaphragm is not clear, and regardless of the irradiation angle, that is, the gantry angle, the method shows a good level of performance, i.e., a respiration phase tracking accuracy of (n = 6) = 97.2 \(\pm\) 2.5%, and tumor tracking error in 3D of (n = 4) = 0.9 \(\pm\) 0.4 mm. To the best of our knowledge, previous imaging-based tumor tracking methods have been applied only at certain angles (e.g., the anterior-posterior direction) where the tumor is relatively well visible [5; 6; 24; 25; 26]; however, the proposed method tracked the tumor's 3D location successfully at any angle of the gantry with sub-millimeter accuracy using a gantry-mounted on-board X-ray imaging system. Other tracking systems such as implanted fiducials [17; 18] or electromagnetic beacons (i.e., Calypso system) [39; 40] can track the tumor's 3D position at any gantry angle because they are not limited by the gantry's position at any given point in the treatment. However, the patient may become uncomfortable with such an invasive procedure, which also poses a risk of complications clinically, such as the occurrence of a pneumothorax [41; 42; 43]. A variety of potential advantages are expected to be achieved when high-precision radiation therapy is eventually enabled using this method. In addition to improving the success rate of radiation therapy, the quality of life of the patient can be improved by reducing the risk of complications of radiation therapy. Radiation therapies, which are difficult to \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Amplitude (mm)**} & \multicolumn{3}{c}{**SD (mm)**} & \multicolumn{3}{c}{**Tumor Tracking Error in**} \\  & & & & & & & & **3D (mm)** \\ \cline{2-9}  & **L-R \({}^{\ast}\)** & **A-P \({}^{\ast}\)** & **C-C \({}^{\ast}\)** & **L-R** & **A-P** & **C-C** & **Surface** & **Center of Mass** \\  & & & & & & & & **Distance** & **Distance** \\ \hline Patient 1 & 1.7 & 3.8 & 13.0 & 0.5 & 1.3 & 4.1 & 0.9 (\(\pm\) 0.4) & 0.6 (\(\pm\) 0.5) \\ Patient 2 & 7.0 & 4.1 & 6.6 & 1.8 & 1.2 & 1.9 & 0.7 (\(\pm\) 0.3) & 0.7 (\(\pm\) 0.4) \\ Patient 3 & 1.9 & 1.5 & 12.0 & 0.5 & 0.4 & 3.8 & 0.8 (\(\pm\) 0.4) & 0.8 (\(\pm\) 0.2) \\ Patient 4 & 5.5 & 10.4 & 30.5 & 1.8 & 3.8 & 10.2 & 1.0 (\(\pm\) 0.5) & 1.0 (\(\pm\) 0.4) \\ \hline \hline \end{tabular} \({}^{\ast}\) L–R = left to right, A–P = anterior to posterior, C–C = cranial to caudal.  
\end{table} 
Table 2: Tumor motion during the entire respiratory cycle along the L–R, A–P, and C–C directions for patients 1 through 4. The tumor motion is reported in terms of the maximum amplitude (max-min) and standard deviation (SD) of the centroid of mass of the tumors. The patients (patients 5 and 6) with little tumor motion (amplitude of \(<\) 1 mm) are not reported. perform owing to the presence of important structures near the tumor, including the spinal cord, may become applicable if accurate targeting is made possible. The performance of an elevation-based method (40.3 \(\pm\) 17.0%) is much lower than that of the method proposed herein (97.2 \(\pm\) 2.5%). Given the fact that the inhale/exhale identification accuracy (48.3%) is close to the accuracy achieved through a diaphragm elevation-based method (40.3%), most identification errors are due to a failure of inhale/exhale identification.