Smoothing of respiratory motion traces for motion-compensated radiotherapy

Purpose: The CyberKnife^® system has been used successfully for several years to radiosurgically treat tumors without the need for stereotactic fixation or sedation of the patient. It has been shown that tumor motion in the lung, liver, and pancreas can be tracked with acceptable accuracy and repeatability. However, highly precise targeting for tumors in the lower abdomen, especially for tumors which exhibit strong motion, remains problematic. Reasons for this are manifold, like the slow tracking system operating at 26.5 Hz, and using the signal from the tracking camera "as is." Since the motion recorded with the camera is used to compensate for system latency by prediction and the predicted signal is subsequently used to infer the tumor position from a correlation model based on x-ray imaging of gold fiducials around the tumor, camera noise directly influences the targeting accuracy. The goal of this work is to establish the suitability of a new smoothing method for respiratory motion traces used in motion-compensated radiotherapy. The authors endeavor to show that better prediction-With a lower rms error of the predicted signal-and/or smoother prediction is possible using this method. Methods: The authors evaluated six commercially available tracking systems (NDI Aurora, PolarisClassic, Polaris Vicra, MicronTracker2 H40, FP5000, and accuTrack compact). The authors first tracked markers both stationary and while in motion to establish the systems' noise characteristics. Then the authors applied a smoothing method based on the ̀ trous wavelet decomposition to reduce the devices' noise level. Additionally, the smoothed signal of the moving target and a motion trace from actual human respiratory motion were subjected to prediction using the MULIN and the nLMS₂ algorithms. Results: The authors established that the noise distribution for a static target is Gaussian and that when the probe is moved such as to mimic human respiration, it remains Gaussian with the exception of the FP5000 and the Aurora systems. The authors also showed that the proposed smoothing method can indeed be used to filter noise. The signal's jitter dropped by as much as 95% depending on the tracking system employed. Subsequently, the 3D prediction error (rms) for a prediction horizon of 150 ms on a synthetic signal dropped by up to 37% when using a normalized LMS prediction algorithm (nLMS₂) and hardly changed when using a MULIN algorithm. When smoothing a real signal obtained in our laboratory, the improvement of prediction was similar: Up to 30% for both the nLMS₂ and the best MULIN algorithm. The authors also found a noticeable increase in smoothness of the predicted signal, the relative jitter dropped by up to 95% on the real signal, and on the simulated signal. Conclusions: In conclusion, the authors can say that preprocessing of marker data is very useful in motion-compensated radiotherapy since the quality of prediction increases. This will result in better performance of the correlation model. As a side effect, since the prediction of a preprocessed signal is also less noisy, the authors expect less robot vibration resulting in better targeting accuracy and less strain on the robot gears.