Controlling motion prediction errors in radiotherapy with relevance vector machines

Robert Dürichen*, Tobias Wissel, Achim Schweikard

*Corresponding author for this work
2 Citations (Scopus)


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, $$\hbox {HYB}_{\textit{RVM}}$$HYBRVM, can decrease the mean RMSE over all 304 motion traces from $$0.18\,$$0.18mm for a linear RVM to $$0.17\,$$0.17mm.

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 $$\hbox {HYB}_{\textit{RVM}}$$HYBRVM could be translated to clinical practice. It does not require further parameters, can be completely parallelised and easily further extended.

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 ($$\hbox {HYB}_{\textit{RVM}}$$HYBRVM) and the other of a combination between a wavelet-based least mean square algorithm (wLMS) and a RVM ($$\hbox {HYB}_{\textit{wLMS}-\textit{RVM}}$$HYBwLMS-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.

Original languageEnglish
JournalInternational Journal of Computer Assisted Radiology and Surgery
Issue number4
Pages (from-to)363-371
Number of pages9
Publication statusPublished - 01.04.2015


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