Evaluation of a wavelet-based least mean square algorithm for prediction of respiratory movements

Objectives: To successfully ablate a tumor in robotic radiotherapy, it is necessary to compensate the motion of inner organs caused by respiration. This can be achieved by tracking the body surface and correlation of the external movement to the tumor position, as it is implemented in Cyberknife Synchrony. A systematic error is produced from the delays, which arise from the data acquisition, signal processing and kinematical limitations of the system. The error can be decreased by predicting the time series of human respiration. A wavelet-based least mean square algorithm (wLMS) is evaluated on 17 patients and compared to the results of the Cyberknife Synchrony prediction algorithm and a multi-step linear method (MULIN).

Methods: The algorithms were evaluated on 17 patients of the Cyberknife Center North Germany. The patients were treated with up to 5 fractions, in total 62 fractions. The fractions have a mean duration of 51 minutes. During the treatment, 3 markers were recorded at a frequency of 26 Hz. Besides respiratory movements, the data also contains movements due to the alignment of the patient. These periods have been cut out of the data. The prediction horizon was set to 4 samples (approx. 150 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. At each time step, a new weight vector is calculated depending on the past observations and is used to calculate the next prediction. The wavelet scale J was set to 3 according to previous experiments. The basic idea behind the MULIN algorithm is to compute the predicted signal from an expansion of the error signal. This linear prediction algorithm can be extended to the MULIN algorithm by taking higher derivatives into account. 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 a measure of the accuracy of the prediction and 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 a measure of the stability and smoothness of the predicted signal. It is defined as the sum of the differences between the data points divided by the time steps.

Results: Evaluating the data, the Cyberknife algorithm has the highest averaged rel. RMS error over all fractions. The mean averaged rel. RMS error for all fractions and the directions is 64.6 The averaged rel. RMS error for the wLMS prediction algorithm is in average 13 % better (51.3. Compared with the MULIN algorithm, the wLMS algorithm is in average 6 % better (57.2. The standard deviation of the relative RMS error is also the highest for the Cyberknife algorithm. The standard deviation averaged over all 3 directions and all fractions is 25.5% for the Cyberknife, 17.7% for wLMS and 21.1% for the MULIN algorithm. In terms of the rel. Jitter, the results are very similar. The wLMS algorithm outperforms the Cyberknife algorithm. The mean average rel. Jitter over all fractions and direction is 141.6% for the Cyberknife, 114.5% wLMS and 125.1% for MULIN. In general all rel. Jitter values are above 100% for the 3 predictors above 100 This means that the delayed signal without prediction is smoother as the predicted signals.

Conclusion: The evaluation clearly shows that the wLMS algorithm is superior compared to the MULIN algorithm and the Cyberknife. The wLMS algorithm has lowest rel. RMS error, standard deviation of the rel. RMS error and rel. Jitter. This means that the accuracy of the treatments and the smoothness of the robot control are increased.