title: A comparison of phase, amplitude, and velocity binning for cone-beam computed tomographic projection-based motion reconstruction.
abstract: OBJECTIVE
  We previously developed a motion estimation technique based on direct cone-beam projection analysis. It is able to reconstruct the complete motion trajectory of a radio-opaque marker, including cycle-to-cycle variability, using respiratory binning of the projection images. This paper investigates the use of phase, amplitude, and amplitude-velocity binning in the context of projection-based cone-beam motion estimation (CBME).
  
  
  METHODS
  We simulated cone-beam computed tomographic scans of 160 tumor trajectories estimated by a CyberKnife Synchrony System (Accuray, Sunnyvale, CA), and reconstructed the complete trajectory with CBME using phase, amplitude, and amplitude-velocity binning of the projection data. Various numbers of respiratory bins, from 1 (no binning) to 100, were used for phase and amplitude binning, while 1 to 100 amplitude bins with 4 velocity bins were used for amplitude-velocity binning. From this large pool of data, we correlated the reconstruction accuracy with bin type, total number of bins, number of breathing cycles per bin, and the position of the bin within the breathing cycle.
  
  
  RESULTS
  CBME predicted the true motion of the marker with a 3-dimensional (3D) mean root mean square (RMS) error of 0.24 mm for amplitude-velocity binning, 0.31 mm for amplitude binning, and 0.52 mm for phase binning. Reconstruction 3D RMS error increased to over 1 mm when less than 3 breathing cycles contributed to a bin. We found that reconstruction accuracy was optimized when about 20 bins were used. Accuracy also decreased in bins located around the inhale portion of the breath cycle, compared with the mid- and end-exhale positions.
  
  
  CONCLUSIONS
  This study provides a quantitative assessment of phase, amplitude, and amplitude-velocity binning for CBME. A joint binning approach should be used to give both the accuracy of amplitude binning, as well as the robustness of phase binning, in areas of limited motion sampling.
authors.affiliation: Department of Radiation Physics, Princess Margaret Hospital, Toronto, Ontario, Canada. Electronic address: nathan.becker@rmp.uhn.on.ca.
authors.forename: Nathan
authors.initials: N
authors.lastname: Becker
authors.affiliation: Department of Medical Physics, Tom Baker Cancer Centre, Calgary, Alberta, Canada; Department of Physics and Astronomy, University of Calgary, Calgary, Alberta, Canada.
authors.forename: Sarah
authors.initials: S
authors.lastname: Quirk
authors.affiliation: Medical Physics & Bioengineering, Canterbury District Health Board, Christchurch, New Zealand.
authors.forename: Ian
authors.initials: I
authors.lastname: Kay
authors.affiliation: MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts.
authors.forename: Boris
authors.initials: B
authors.lastname: Braverman
authors.affiliation: Department of Medical Physics, Tom Baker Cancer Centre, Calgary, Alberta, Canada; Department of Physics and Astronomy, University of Calgary, Calgary, Alberta, Canada; Department of Oncology, University of Calgary, Calgary, Alberta, Canada.
authors.forename: Wendy L
authors.initials: WL
authors.lastname: Smith