Evaluation of a wavelet-based least mean square motion prediction algorithm for lung and liver patients

Objectives: Accurate radiation therapy and radiosurgery treatment of lung and liver tumors are challenging problems due to continuous target motion due to the patients breathing. Motion compensation systems are often needed such as CyberKnife™ Synchrony™ tracking (Accuray Inc, USA), where internal tumor motion is estimated on stereo x-ray images and correlated with external optical markers attached to the patients’ chest. During treatment the system compensates the target motion based on time series prediction of the optical marker movements. Errors for this method mainly come from delays, which arise from data acquisition, signal processing, kinematical limitations of the system and the quality of the predication. We analyzed a new wavelet-based least mean square algorithm (wLMS) and compared the results to the CyberKnife prediction algorithm and a multi-step linear method (MULIN). [2] Materials / Methods: The algorithms were evaluated on 7 lung and 17 liver patients treated with the CyberKnife in 3-5 fractions, a total of 103 fractions. The prediction horizon was set to 115 ms, which is in line with the latency of the CyberKnife. The wLMS prediction algorithm is based on the á trous wavelet decomposition. The signal is decomposed into J wavelet scales and a residual. With this decomposition it is possible to perform prediction on each individual scale [1]. The algorithms are evaluated with respect to the relative root mean square error (RMS) and the relative jitter of the predicted signal. The rel. RMS error is defined as the RMS error between the predicted signal and the real signal divided by the RMS error between the real signal and the real signal delayed by 4 samples. The jitter is defined as the sum of the differences between the data points divided by the time steps. Results: Figure 1 and table 1 show the averaged rel. RMS error and rel. jitter with standard deviation. In general the rel. RMS errors are higher for lung as for liver patients. The current CyberKnife algorithm was found to have the highest error for both patient categories whereas the wLMS algorithm was found to have the lowest rel. RMS error (fig. 1a,b). Also the averaged rel. jitter of the wLMS algorithm and MULIN algorithm is lower compared to the Cyberknife algorithm (fig 1c,d). Conclusion: In summary all algorithms predict the respiratory movement with high accuracy and lead to a significant improvement compared to no prediction. However the evaluation clearly shows that the wLMS algorithm is superior for both patient categories compared to the MULIN and the currently implemented CyberKnife algorithm. With the new wLMS algorithm the treatment accuracy and the smoothness of the robot motion control can be increased.