title: 4D Cone-beam CT reconstruction using a motion model based on principal component analysis.
abstract: OBJECTIVE
  To provide a proof of concept validation of a novel 4D cone-beam CT (4DCBCT) reconstruction algorithm and to determine the best methods to train and optimize the algorithm.
  
  
  METHODS
  The algorithm animates a patient fan-beam CT (FBCT) with a patient specific parametric motion model in order to generate a time series of deformed CTs (the reconstructed 4DCBCT) that track the motion of the patient anatomy on a voxel by voxel scale. The motion model is constrained by requiring that projections cast through the deformed CT time series match the projections of the raw patient 4DCBCT. The motion model uses a basis of eigenvectors that are generated via principal component analysis (PCA) of a training set of displacement vector fields (DVFs) that approximate patient motion. The eigenvectors are weighted by a parameterized function of the patient breathing trace recorded during 4DCBCT. The algorithm is demonstrated and tested via numerical simulation.
  
  
  RESULTS
  The algorithm is shown to produce accurate reconstruction results for the most complicated simulated motion, in which voxels move with a pseudo-periodic pattern and relative phase shifts exist between voxels. The tests show that principal component eigenvectors trained on DVFs from a novel 2D/3D registration method give substantially better results than eigenvectors trained on DVFs obtained by conventionally registering 4DCBCT phases reconstructed via filtered backprojection.
  
  
  CONCLUSIONS
  Proof of concept testing has validated the 4DCBCT reconstruction approach for the types of simulated data considered. In addition, the authors found the 2D/3D registration approach to be our best choice for generating the DVF training set, and the Nelder-Mead simplex algorithm the most robust optimization routine.
authors.affiliation: Department of Radiation Oncology, Virignia Commonwealth University, Richmond, Virginia 23298, USA. david.staub32@gmail.com
authors.forename: David
authors.initials: D
authors.lastname: Staub
authors.forename: Alen
authors.initials: A
authors.lastname: Docef
authors.forename: Robert S
authors.initials: RS
authors.lastname: Brock
authors.forename: Constantin
authors.initials: C
authors.lastname: Vaman
authors.forename: Martin J
authors.initials: MJ
authors.lastname: Murphy
mesh_terms: D000465:Algorithms; D016477:Artifacts; D054893:Cone-Beam Computed Tomography / Q000295:instrumentation / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D009038:Motion; D019047:Phantoms, Imaging; D025341:Principal Component Analysis; D011856:Radiographic Image Enhancement / Q000379:methods*; D011857:Radiographic Image Interpretation, Computer-Assisted / Q000379:methods*; D015203:Reproducibility of Results; D055425:Respiratory-Gated Imaging Techniques / Q000379:methods*; D012680:Sensitivity and Specificity