Accuracy of four models and update strategies to estimate liver tumor motion from external respiratory motion.

Background: This study investigates different strategies for estimating internal liver tumor motion during radiotherapy based on continuous monitoring of external respiratory motion combined with sparse internal imaging. Methods: Fifteen patients underwent three-fraction stereotactic liver radiotherapy. The 3D internal tumor motion (INT) was monitored by electromagnetic transponders while a camera monitored the external marker block motion (EXT). The ability of four external-internal correlation models (ECM) to estimate INT as function of EXT was investigated: a simple linear model (ECM1), an augmented linear model (ECM2), an augmented quadratic model (ECM3), and an extended quadratic model (ECM4). Each ECM was constructed by fitting INT and EXT during the first 60s of each fraction. The fit accuracy was calculated as the root-mean-square error (RMSE) between ECM-estimated and actual tumor motion. Next, the RMSE of the ECM-estimated tumor motion throughout the fractions was calculated for four simulated ECM update strategies: (A) no update, 0.33Hz internal sampling with continuous update of either (B) all ECM parameters based on the last 2 minutes samples or (C) only the baseline term based on the last 5 samples, (D) full ECM update every minute using 20s continuous internal sampling. Results: The augmented quadratic ECM3 had best fit accuracy with mean (± SD)) RMSEs of 0.32 ± 0.11mm (left-right, LR), 0.79 ± 0.30mm (cranio-caudal, CC) and 0.56 ± 0.31mm (anterior-posterior, AP). However, the simpler augmented linear ECM2 combined with frequent baseline updates (update strategy C) gave best motion estimations with mean RMSEs of 0.41 ± 0.14mm (LR), 1.02 ± 0.33mm (CC) and 0.78 ± 0.48mm (AP). This was significantly better than all other ECM-update strategy combinations for CC motion (Wilcoxon signed rank p<0.05). Conclusion: The augmented linear ECM2 combined with frequent baseline updates provided the best compromise between fit accuracy and robustness towards irregular motion. It allows accurate internal motion monitoring by combining external motioning with sparse 0.33Hz kV imaging, which is available at conventional linacs.