Controlling motion prediction errors in radiotherapy with relevance vector machines

Abstract

Purpose

Robotic radiotherapy can precisely ablate moving tumors when time latencies have been compensated. Recently, relevance vector machines (RVM), a probabilistic regression technique, outperformed six other prediction algorithms for respiratory compensation. The method has the distinct advantage that each predicted point is assumed to be drawn from a normal distribution. Second-order statistics, the predicted variance, were used to control RVM prediction error during a treatment and to construct hybrid prediction algorithms.

Methods

First, the duty cycle and the precision were correlated to the variance by interrupting the treatment if the variance exceeds a threshold. Second, two hybrid algorithms based on the variance were developed, one consisting of multiple RVMs ($\hbox {HYB}_{\textit{RVM}}$) and the other of a combination between a wavelet-based least mean square algorithm (wLMS) and a RVM ($\hbox {HYB}_{\textit{wLMS}-\textit{RVM}}$). The variance for different motion traces was analyzed to reveal a characteristic variance pattern which gives insight in what kind of prediction errors can be controlled by the variance.

Results

Limiting the variance by a threshold resulted in an increased precision with a decreased duty cycle. All hybrid algorithms showed an increased prediction accuracy compared to using only their individual algorithms. The best hybrid algorithm, $\hbox {HYB}_{\textit{RVM}}$, can decrease the mean RMSE over all 304 motion traces from $0.18\,$mm for a linear RVM to $0.17\,$mm.

Conclusions

The predicted variance was shown to be an efficient metric to control prediction errors, resulting in a more robust radiotherapy treatment. The hybrid algorithm $\hbox {HYB}_{\textit{RVM}}$ could be translated to clinical practice. It does not require further parameters, can be completely parallelised and easily further extended.