Controlling motion prediction errors in radiotherapy with relevance vector machines

  • Robert Dürichen
  • Tobias Wissel
  • Achim Schweikard
Original Article



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.


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.


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.


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.


Computer-assisted radiation therapy  Respiratory motion compensation Uncertainty measures Relevance vector machines 


Conflict of interest

Robert Dürichen, Tobias Wissel and Achim Schweikard declare that they have no conflict of interest.


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Copyright information

© CARS 2014

Authors and Affiliations

  • Robert Dürichen
    • 1
  • Tobias Wissel
    • 1
  • Achim Schweikard
    • 1
  1. 1.Institute for Robotics and Cognitive SystemsUniversity of LuebeckLübeckGermany

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