title: Three-dimensional quantification of vorticity and helicity from 3D cine PC-MRI using finite-element interpolations.
abstract: OBJECTIVE
  We propose a 3D finite-element method for the quantification of vorticity and helicity density from 3D cine phase-contrast (PC) MRI.
  
  
  METHODS
  By using a 3D finite-element method, we seamlessly estimate velocity gradients in 3D. The robustness and convergence were analyzed using a combined Poiseuille and Lamb-Ossen equation. A computational fluid dynamics simulation was used to compared our method with others available in the literature. Additionally, we computed 3D maps for different 3D cine PC-MRI data sets: phantom without and with coarctation (18 healthy volunteers and 3 patients).
  
  
  RESULTS
  We found a good agreement between our method and both the analytical solution of the combined Poiseuille and Lamb-Ossen. The computational fluid dynamics results showed that our method outperforms current approaches to estimate vorticity and helicity values. In the in silico model, we observed that for a tetrahedral element of 2 mm of characteristic length, we underestimated the vorticity in less than 5% with respect to the analytical solution. In patients, we found higher values of helicity density in comparison to healthy volunteers, associated with vortices in the lumen of the vessels.
  
  
  CONCLUSIONS
  We proposed a novel method that provides entire 3D vorticity and helicity density maps, avoiding the used of reformatted 2D planes from 3D cine PC-MRI. Magn Reson Med 79:541-553, 2018. © 2017 International Society for Magnetic Resonance in Medicine.
authors.affiliation: Biomedical Imaging Center, Pontificia Universidad Católica de Chile, Santiago, Chile.|Department of Electrical Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile.|Department of Structural and Geotechnical Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile.
authors.forename: Julio
authors.initials: J
authors.lastname: Sotelo
authors.affiliation: Biomedical Imaging Center, Pontificia Universidad Católica de Chile, Santiago, Chile.|Department of Radiology, School of Medicine, Pontificia Universidad Católica de Chile, Santiago, Chile.
authors.forename: Jesús
authors.initials: J
authors.lastname: Urbina
authors.affiliation: Pediatric Cardiology Unit, Hospital Virgen del Rocio, Sevilla, Spain.|Cardiovascular Pathology Unit, Institute of Biomedicine of Seville (IBIS), Hospital Virgen del Rocio, Sevilla, Spain.
authors.forename: Israel
authors.initials: I
authors.lastname: Valverde
authors.affiliation: Biomedical Imaging Center, Pontificia Universidad Católica de Chile, Santiago, Chile.
authors.forename: Joaquín
authors.initials: J
authors.lastname: Mura
authors.affiliation: Biomedical Imaging Center, Pontificia Universidad Católica de Chile, Santiago, Chile.|Department of Electrical Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile.|Institute for Biological and Medical Engineering, Schools of Engineering, Medicine and Biological Sciences, Pontificia Universidad Católica de Chile, Santaigo, Chile.
authors.forename: Cristián
authors.initials: C
authors.lastname: Tejos
authors.affiliation: Biomedical Imaging Center, Pontificia Universidad Católica de Chile, Santiago, Chile.|Department of Electrical Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile.|Institute for Biological and Medical Engineering, Schools of Engineering, Medicine and Biological Sciences, Pontificia Universidad Católica de Chile, Santaigo, Chile.
authors.forename: Pablo
authors.initials: P
authors.lastname: Irarrazaval
authors.affiliation: Biomedical Imaging Center, Pontificia Universidad Católica de Chile, Santiago, Chile.|Department of Radiology, School of Medicine, Pontificia Universidad Católica de Chile, Santiago, Chile.|Institute for Biological and Medical Engineering, Schools of Engineering, Medicine and Biological Sciences, Pontificia Universidad Católica de Chile, Santaigo, Chile.
authors.forename: Marcelo E
authors.initials: ME
authors.lastname: Andia
authors.affiliation: Department of Structural and Geotechnical Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile.|Institute for Biological and Medical Engineering, Schools of Engineering, Medicine and Biological Sciences, Pontificia Universidad Católica de Chile, Santaigo, Chile.
authors.forename: Daniel E
authors.initials: DE
authors.lastname: Hurtado
authors.affiliation: Biomedical Imaging Center, Pontificia Universidad Católica de Chile, Santiago, Chile.|Department of Radiology, School of Medicine, Pontificia Universidad Católica de Chile, Santiago, Chile.|Institute for Biological and Medical Engineering, Schools of Engineering, Medicine and Biological Sciences, Pontificia Universidad Católica de Chile, Santaigo, Chile.
authors.forename: Sergio
authors.initials: S
authors.lastname: Uribe
mesh_terms: D000328:Adult; D000465:Algorithms; D001011:Aorta / Q000000981:diagnostic imaging; D003198:Computer Simulation; D005260:Female; D020342:Finite Element Analysis; D064368:Healthy Volunteers; D006801:Humans; D057446:Hydrodynamics; D007091:Image Processing, Computer-Assisted; D021621:Imaging, Three-Dimensional; D008279:Magnetic Resonance Imaging; D019028:Magnetic Resonance Imaging, Cine; D008297:Male; D015233:Models, Statistical; D019047:Phantoms, Imaging; D012984:Software; D014783:Viscosity; D055815:Young Adult
keywords: 3D cine PC-MRI; finite elements; flow quantification; helicity; vorticity