Estimation of lung tumor position from multiple anatomical features on 4D‐CT using multiple regression analysis

Abstract To estimate the lung tumor position from multiple anatomical features on four‐dimensional computed tomography (4D‐CT) data sets using single regression analysis (SRA) and multiple regression analysis (MRA) approach and evaluate an impact of the approach on internal target volume (ITV) for stereotactic body radiotherapy (SBRT) of the lung. Eleven consecutive lung cancer patients (12 cases) underwent 4D‐CT scanning. The three‐dimensional (3D) lung tumor motion exceeded 5 mm. The 3D tumor position and anatomical features, including lung volume, diaphragm, abdominal wall, and chest wall positions, were measured on 4D‐CT images. The tumor position was estimated by SRA using each anatomical feature and MRA using all anatomical features. The difference between the actual and estimated tumor positions was defined as the root‐mean‐square error (RMSE). A standard partial regression coefficient for the MRA was evaluated. The 3D lung tumor position showed a high correlation with the lung volume (R = 0.92 ± 0.10). Additionally, ITVs derived from SRA and MRA approaches were compared with ITV derived from contouring gross tumor volumes on all 10 phases of the 4D‐CT (conventional ITV). The RMSE of the SRA was within 3.7 mm in all directions. Also, the RMSE of the MRA was within 1.6 mm in all directions. The standard partial regression coefficient for the lung volume was the largest and had the most influence on the estimated tumor position. Compared with conventional ITV, average percentage decrease of ITV were 31.9% and 38.3% using SRA and MRA approaches, respectively. The estimation accuracy of lung tumor position was improved by the MRA approach, which provided smaller ITV than conventional ITV.

When treating lung cancer with radiotherapy, respiratory motion is one of the factors causing uncertainties during treatment planning and beam delivery. Without respiratory motion management, larger margins would be needed to account for respiratory motion, leading to a larger planning target volume (PTV) size, which, in turn, includes a larger organ at risk volume. Matsuo et al. examined the relationship between frequency of normal tissue toxicity and PTV size 3 showing that the frequency of symptomatic radiation pneumonitis was significantly lower with a PTV size of <37.7 mL than with a PTV size of ≥37.7 mL (11.1% vs. 34.5%) for nonsmall cell lung cancer with stereotactic body radiotherapy (SBRT). Thus, to reduce the dose to the normal lung is of clinical importance in terms of toxicity.
The American Association of Physicists in Medicine Task Group 76 has advocated an emphasis on respiratory motion management 4 Four-dimensional computed tomography (4D-CT) and 4D radiotherapy (4D-RT) provide patient-specific radiation treatment, taking respiratory-induced anatomical motion into account. Both approaches frequently require internal and/or external respiratory motion signals.
Generally, image quality of 4D-CT and the advisability of 4D-RT are dependent on correlations with respiratory motion signals (surrogate signals) 5,6 That is, whether the surrogate signals represent the target well is very important in 4D-CT and 4D-RT.
A high correlation between tumor motion and a surrogate signal such as ventilation volume and abdominal displacement has been reported from several facilities 7, 8 Gianoli et al. used one of multiple infrared markers placed on the thoracoabdominal surface to obtain high-quality 4D-CT images and showed that the 4D-CT image quality was improved, using a multidimensional K-means clustering method. 9 Thus, one surrogate signal acquired from one anatomical feature is frequently used in 4D-CT and 4D-RT. However, no correlation between tumor motion and a surrogate signal for one anatomical feature would cause a decrease in 4D-CT image quality or erroneous irradiation. Therefore, the use of multiple surrogate signals for several anatomical features could reduce such risks.
In the current study, we estimated lung tumor position from multiple anatomical features acquired from 4D-CT image sets, including the lung volume, the displacement of diaphragm position, abdominal wall position, and chest wall position, using multiple regression analysis (MRA) and single regression analysis (SRA) approaches. In addition, we assessed an impact of these approaches on internal target volume (ITV) for SBRT of the lung.

2.A | Patients and data acquisition
Of the patients who underwent SBRT at Osaka Red Cross Hospital between November 2011 and April 2015, 11 consecutive lung cancer patients (12 cases) with three-dimensional (3D) motion ranges greater than 5 mm were enrolled in this study. There were seven men and four women with a median age of 76 (range, 67-98) yr. Lung tumors were located in the right upper lobe (two patients), in the right middle lobe (two patients), in the right lower lobe (six patients), and in the left lower lobe (two patients). 4D-CT data were acquired using the Discovery CT750HD (GE Medical Systems, Waukesha, WI, USA) and the Real-time Positioning Management (RPM) system (Varian Medical Systems, Palo Alto, CA, USA) in axial cine mode for all patients. 4D-CT was performed under free breathing without audio/visual coaching. The CT slice thickness was 2.5 mm. Cine duration time of the scan at each couch position was set to 0.5 s, which was more than the maximum observed respiratory period. The cine interval between images was 1.3 s. CT data were reconstructed in a field of view of 500 mm on a 512 9 512 grid for the 4D-CT scan. The RPM system illuminated and tracked an infrared reflective marker placed on the patient's abdomen. The RPM software was used to calculate the respiratory phase at each instant in time based on modeling the abdominal motion amplitude. The RPM system was used to calculate a phase at each point of a respiratory trace, where 0% corresponded to the inhalation peak and 50% to the midpoint between consecutive inhalation peaks. All CT slices and the RPM respiratory data file were transferred to an Advantage 4D workstation (GE). The Advantage 4D software was used to read all CT slices as well as the corresponding RPM respiratory data file, to assign a phase to each CT slice, according to the temporal correlation between the RPM trace and CT data acquisition, and to export 10 respiratory phase volumes, evenly distributed over a respiratory cycle. | 37 approach estimates one objective variable from multiple explanatory variables. In this study, the lung tumor position was defined as the objective variable, and lung volume and displacements of the diaphragm, abdominal wall, and chest wall were defined as the explanatory variables. The estimated lung tumor position (X E , Y E , Z E ) was calculated from the following equation: Standard partial regression coefficient = Partial regression coefficient

2.B | Lung tumor position and anatomical features
where SD obj is the standard deviation (SD) of the objective variable, and SD exp is the standard deviation of the explanatory variable. The standard partial regression coefficient refers to a to d obtained from eq. (1). In this study, the standard partial regression coefficient was evaluated for four explanatory variables, which were the lung volume, the displacement of diaphragm, abdominal wall, and chest wall.
Additionally, Student's t-test was performed to explore the impact of the standard partial regression coefficient for each anatomical feature. A difference was considered statistically significant at the P < 0.05 level.    Fig. 2(a) and a relative manner in Fig. 2(b). In Fig. 2(a)      it was found that the MRA approach improved estimating accuracy compared with the SRA approach (Fig. 2). Using the MRA approach, the RMSE of the lung tumor position was within 1.6 mm, which enables reducing the internal margin size when applying respiratory motion management techniques (see Fig. 2(a)). However, note that overestimating or underestimating tumor motion is possible using 4D-CT. 5,13 In an absolute manner, the RMSEs in the SI and 3D

3.C | Comparison of internal target volumes
directions were larger than those in the LR and AP directions because the average displacements of lung tumor positions were larger in the SI and 3D directions than in the LR and AP directions.
In the relative evaluation, the RMSEs in the SI and 3D directions were smaller than those in the LR and AP directions. This implies that the estimated lung tumor position had a high correlation with the actual position in the SI and 3D directions. In the explanatory variables of the MRA approach, the lung volume had a high standard partial regression coefficient (see Fig. 3). The results in Table 2 show that the explanatory variable of the lung volume had a signifi-  [15][16][17] respectively. In addition, correspondence models have been used to improve image quality in 4D-CT image reconstruction. 18,19 From these findings and our results, if the MRA approach is available, using multiple tools including a spirometer or infrared camera, the correspondence model will be improved, which would provide higher accuracy for 4D-RT and higher image quality for 4D-CT.
Matsuo et al. conducted RTTT using a gimbal mounted linac for lung cancer and reported that PTV size was reduced by 30.1% compared with conventional PTV. 20 The intrafractional variation between the centroid of tumor and the centroid of fiducial markers was included in their PTV. 10 We also found that MRA approach had a potential to reduce internal margin in RTTT without fiducial markers. images. 25 Applying the MRA approach to the MR-guided system, highly accurate predictions of the position of a lung tumor (even those with low density) should be possible from anatomical features.

| CONCLUSIONS
Lung tumor position was estimated from anatomical features using SRA and MRA approaches and the impact of these approaches on ITVs were assessed. We confirmed that the variance in lung volume had an influence on the estimated lung tumor position. Moreover, multiple anatomical features improved the estimation accuracy of lung tumor position and reduced the ITV by using MRA and SRA approaches, compared with the ITV conv .