Reference respiratory waveforms by minimum jerk model analysis

Yusuke Anetai, Iori Sumida, Yutaka Takahashi, Hirokazu Mizuno, Masashi Yagi, Kazuhiko Ogawa, Seiichi Ota

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Purpose: CyberKnife® robotic surgery system has the ability to deliver radiation to a tumor subject to respiratory movements using Synchrony® mode with less than 2 mm tracking accuracy. However, rapid and rough motion tracking causes mechanical tracking errors and puts mechanical stress on the robotic joint, leading to unexpected radiation delivery errors. During clinical treatment, patient respiratory motions are much more complicated, suggesting the need for patient-specific modeling of respiratory motion. The purpose of this study was to propose a novel method that provides a reference respiratory wave to enable smooth tracking for each patient. Methods: The minimum jerk model, which mathematically derives smoothness by means of jerk, or the third derivative of position and the derivative of acceleration with respect to time that is proportional to the time rate of force changed was introduced to model a patient-specific respiratory motion wave to provide smooth motion tracking using CyberKnife®. To verify that patient-specific minimum jerk respiratory waves were being tracked smoothly by Synchrony® mode, a tracking laser projection from CyberKnifeR was optically analyzed every 0.1 s using a webcam and a calibrated grid on a motion phantom whose motion was in accordance with three pattern waves (cosine, typical free-breathing, and minimum jerk theoretical wave models) for the clinically relevant superiorinferior directions from six volunteers assessed on the same node of the same isocentricplan. Results: Tracking discrepancy from the center of the grid to the beam projection was evaluated. The minimum jerk theoretical wave reduced the maximum-peak amplitude of radial tracking discrepancy compared with that of the waveformsmodeled by cosine and typical free-breathing model by 22% and 35%, respectively, and provided smooth tracking for radial direction. Motion tracking constancy as indicated by radial tracking discrepancy affected by respiratory phase was improved in the minimum jerk theoretical model by 7.0% and 13% compared with that of the waveforms modeled by cosine and free-breathing model, respectively. Conclusions: The minimum jerk theoretical respiratory wave can achieve smooth tracking by CyberKnifeR and may provide patient-specific respiratory modeling, which may be useful for respiratory training and coaching, as well as quality assurance of the mechanical CyberKnife® robotic trajector.

Original languageEnglish (US)
Pages (from-to)5066-5074
Number of pages9
JournalMedical Physics
Issue number9
StatePublished - Sep 1 2015

Bibliographical note

Publisher Copyright:
© 2015 Am. Assoc. Phys. Med.


  • CyberKnife
  • Synchrony
  • gated radiotherapy
  • respiratory coaching
  • respiratory monitoring
  • respiratory tracking
  • respiratory training


Dive into the research topics of 'Reference respiratory waveforms by minimum jerk model analysis'. Together they form a unique fingerprint.

Cite this