title: Respiratory motion sampling in 4DCT reconstruction for radiotherapy.
abstract: OBJECTIVE
  Phase-based and amplitude-based sorting techniques are commonly used in four-dimensional CT (4DCT) reconstruction. However, effect of these sorting techniques on 4D dose calculation has not been explored. In this study, the authors investigated a candidate 4DCT sorting technique by comparing its 4D dose calculation accuracy with that for phase-based and amplitude-based sorting techniques.
  
  
  METHODS
  An optimization model was formed using organ motion probability density function (PDF) in the 4D dose convolution. The objective function for optimization was defined as the maximum difference between the expected 4D dose in organ of interest and the 4D dose calculated using a 4DCT sorted by a candidate sampling method. Sorting samples, as optimization variables, were selected on the respiratory motion PDF assessed during the CT scanning. Breathing curves obtained from patients' 4DCT scanning, as well as 3D dose distribution from treatment planning, were used in the study. Given the objective function, a residual error analysis was performed, and k-means clustering was found to be an effective sampling scheme to improve the 4D dose calculation accuracy and independent with the patient-specific dose distribution.
  
  
  RESULTS
  Patient data analysis demonstrated that the k-means sampling was superior to the conventional phase-based and amplitude-based sorting and comparable to the optimal sampling results. For phase-based sorting, the residual error in 4D dose calculations may not be further reduced to an acceptable accuracy after a certain number of phases, while for amplitude-based sorting, k-means sampling, and the optimal sampling, the residual error in 4D dose calculations decreased rapidly as the number of 4DCT phases increased to 6.
  
  
  CONCLUSIONS
  An innovative phase sorting method (k-means method) is presented in this study. The method is dependent only on tumor motion PDF. It could provide a way to refine the phase sorting in 4DCT reconstruction and is effective for 4D dose accumulation. Optimized sorting techniques could achieve acceptable residuals (less than 0.5% of the prescription dose) using 6 sorting samples, which is much better than amplitude-based or phase-based sorting. Further increase in sorting phase number exceeding 6 or more may not be necessary when using the k-means sampling or optimal sampling points.
authors.affiliation: Department of Radiation Oncology, Columbia University, New York, NY, USA.
authors.forename: Yuwei
authors.initials: Y
authors.lastname: Chi
authors.forename: Jian
authors.initials: J
authors.lastname: Liang
authors.forename: Xu
authors.initials: X
authors.lastname: Qin
authors.forename: Di
authors.initials: D
authors.lastname: Yan
mesh_terms: D006801:Humans; D021621:Imaging, Three-Dimensional / Q000379:methods*; D008175:Lung Neoplasms / Q000000981:diagnostic imaging* / Q000532:radiotherapy*; D011874:Radiometry / Q000379:methods*; D061089:Radiotherapy, Image-Guided / Q000379:methods*; D015203:Reproducibility of Results; D015656:Respiratory Mechanics; D055425:Respiratory-Gated Imaging Techniques / Q000379:methods*; D012680:Sensitivity and Specificity; D014057:Tomography, X-Ray Computed / Q000379:methods*