title: Phase unwrapping in 4D MR flow with a 4D single-step laplacian algorithm.
abstract: OBJECTIVE
  To introduce and demonstrate a method for unwrapping 4D flow data by utilizing continuity constraints in all four available dimensions.
  
  
  METHODS
  A Laplacian-based algorithm for unwrapping phase data was expanded to unwrap along the temporal dimension in addition to all three spatial dimensions. The method was tested on simulated blood flow under varying vessel diameters and velocity encoding (Venc ) values. The algorithm was also tested in the aorta of five volunteers, with wrapped data acquired with Venc  = 80 cm/s and 40 cm/s. Unwrapping performance was measured visually and in comparison to a high Venc reference free of phase wrapping. Ten patients with aortic coarctations with clinical Venc values and lower-Venc reconstructions were corrected and scored by blinded reviewers on a 0-3 scale.
  
  
  RESULTS
  Simulated data were completely unwrapped for most clinically relevant levels of velocity aliasing using the proposed method. In vivo data in the aorta were completely unwrapped for cases of moderate wrapping (Venc  = 80 cm/s, peak velocities = ∼160 cm/s), while residual aliasing remained for the more considerably aliased datasets (Venc  = 40 cm/s). Improvements were seen in scoring (mean score improved by 1.1 and 2.2 for clinical and low-Venc datasets, respectively) by the blinded reviewers in the patient cohort for both standard and low-Venc reconstructions.
  
  
  CONCLUSIONS
  A computationally fast, fully automated, easy to use, and parameter-free single-step method for unwrapping 4D flow data is shown to be effective for use in most common clinical occurrences of velocity aliasing.
authors.affiliation: Department of Medical Physics, University of Wisconsin-Madison, Madison, Wisconsin, USA.
authors.forename: Michael
authors.initials: M
authors.lastname: Loecher
authors.affiliation: Department of Medical Physics, University of Wisconsin-Madison, Madison, Wisconsin, USA.
authors.forename: Eric
authors.initials: E
authors.lastname: Schrauben
authors.affiliation: Department of Medical Physics, University of Wisconsin-Madison, Madison, Wisconsin, USA.
authors.forename: Kevin M
authors.initials: KM
authors.lastname: Johnson
authors.affiliation: Department of Medical Physics, University of Wisconsin-Madison, Madison, Wisconsin, USA.|Department of Radiology, University of Wisconsin-Madison, Madison, Wisconsin, USA.
authors.forename: Oliver
authors.initials: O
authors.lastname: Wieben
mesh_terms: D000328:Adult; D000465:Algorithms; D001011:Aorta / Q000000981:diagnostic imaging / Q000473:pathology; D001017:Aortic Coarctation / Q000000981:diagnostic imaging*; D001331:Automation; D001783:Blood Flow Velocity; D015331:Cohort Studies; D003198:Computer Simulation; D005260:Female; D005583:Fourier Analysis; D064368:Healthy Volunteers; D006801:Humans; D007090:Image Interpretation, Computer-Assisted / Q000379:methods; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D008279:Magnetic Resonance Imaging; D008297:Male; D008962:Models, Theoretical; D019047:Phantoms, Imaging; D059629:Signal-To-Noise Ratio; D012984:Software; D055815:Young Adult
keywords: 4D flow; phase contrast MRI; phase unwrapping; velocity aliasing