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Objectives: To establish and validate a linear model utilizing diaphragm motion (DM) to predict the displacement of liver tumors (DLTs) for patients who underwent carbon ion radiotherapy (CIRT). A total of 60 pairs of planning and reviewing four-dimensional computed tomography (4DCT) sets over 23 patients were used. Method: We constructed an averaged computed tomography (CT) set for each either planning or reviewing 4DCT within respiratory phases between 20% of exhale and inhale. A rigid image registration to align bony structures was performed between planning and reviewing 4DCT. The position changes on top of diaphragm in superior–inferior (SI) direction between 2 CTs to present DM were obtained. The translational vectors in SI from matching to present DLT were obtained. The linear model was built by training data for 23 imaging pairs. A distance model utilized the cumulative probability distribution (CPD) of DM or DLT and was compared with the linear model. We conducted the statistical regression analysis with receiver operating characteristic (ROC) testing data of 37 imaging pairs to validate the performance of our linear model. Results: The DM within 0.5 mm was true positive (TP) with an area under the ROC curve (AUC) of 0.983 to predict DLT. The error of predicted DLT within half of its mean value indicated the reliability of prediction method. The 23 pairs of data showed (4.5 ± 3.3) mm for trend of DM and (2.2 ± 1.6) mm for DLT. A linear model of DLT = 0.46*DM + 0.12 was established. The predicted DLT was (2.2 ± 1.5) mm with a prediction error of (0.3 ± 0.3) mm. The accumulated probability of observed and predicted DLT with < 5.0 mm magnitude was 93.2% and 94.5%, respectively. Conclusion: We utilized the linear model to set the proper beam gating for predicting DLT within 5.0 mm to treat patients. We will investigate a proper process on x-ray fluoroscopy images to establish a reliable model predicting DLT for DM observed in x-ray fluoroscopy in the following two years.

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