Online model checking for monitoring surrogate-based respiratory motion tracking in radiation therapy

  • Sven-Thomas Antoni
  • Jonas Rinast
  • Xintao Ma
  • Sibylle Schupp
  • Alexander Schlaefer
Original Article



Correlation between internal and external motion is critical for respiratory motion compensation in radiosurgery. Artifacts like coughing, sneezing or yawning or changes in the breathing pattern can lead to misalignment between beam and tumor and need to be detected to interrupt the treatment. We propose online model checking (OMC), a model-based verification approach from the field of formal methods, to verify that the breathing motion is regular and the correlation holds. We demonstrate that OMC may be more suitable for artifact detection than the prediction error.

Materials and methods

We established a sinusoidal model to apply OMC to the verification of respiratory motion. The method was parameterized to detect deviations from typical breathing motion. We analyzed the performance on synthetic data and on clinical episodes showing large correlation error. In comparison, we considered the prediction error of different state-of-the-art methods based on least mean squares (LMS; normalized LMS, nLMS; wavelet-based multiscale autoregression, wLMS), recursive least squares (RLSpred) and support vector regression (SVRpred).


On synthetic data, OMC outperformed wLMS by at least 30 % and SVRpred by at least 141 %, detecting 70 % of transitions. No artifacts were detected by nLMS and RLSpred. On patient data, OMC detected 23–49 % of the episodes correctly, outperforming nLMS, wLMS, RLSpred and SVRpred by up to 544, 491, 408 and 258 %, respectively. On selected episodes, OMC detected up to 94 % of all events.


OMC is able to detect changes in breathing as well as artifacts which previously would have gone undetected, outperforming prediction error-based detection. Synthetic data analysis supports the assumption that prediction is very insensitive to specific changes in breathing. We suggest using OMC as an additional safety measure ensuring reliable and fast stopping of irradiation.


Respiration Radiosurgery Prediction Model checking Internal–external correlation 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© CARS 2016

Authors and Affiliations

  • Sven-Thomas Antoni
    • 1
  • Jonas Rinast
    • 2
  • Xintao Ma
    • 2
  • Sibylle Schupp
    • 2
  • Alexander Schlaefer
    • 1
  1. 1.Institute of Medical TechnologyHamburg University of TechnologyHamburgGermany
  2. 2.Institute for Software SystemsHamburg University of TechnologyHamburgGermany

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