title: Improving computation of cardiovascular relative pressure fields from velocity MRI.
abstract: OBJECTIVE
  To evaluate a multigrid-based solver for the pressure Poisson equation (PPE) with Galerkin coarsening, which works directly on the specified domain, for the computation of relative pressure fields from velocity MRI data.
  
  
  METHODS
  We compared the proposed structure-defined Poisson solver to other popular Poisson solvers working on unmodified rectangular and modified quasirectangular domains using synthetic and in vitro phantoms in which the mathematical solution of the pressure field is known, as well as on in vivo MRI velocity measurements of aortic blood flow dynamics.
  
  
  RESULTS
  All three PPE solvers gave accurate results for convex computational domains. Using a rectangular or quasirectangular domain on a more complicated domain, like a c-shape, revealed a systematic underestimation of the pressure amplitudes, while the proposed PPE solver, working directly on the specified domain, provided accurate estimates of the relative pressure fields.
  
  
  CONCLUSIONS
  Popular iterative approaches with quasirectangular computational domains can lead to significant systematic underestimation of the pressure amplitude. We suggest using a multigrid-based PPE solver with Galerkin coarsening, which works directly on the structure-defined computational domain. This solver provides accurate estimates of the relative pressure fields for both simple and complex geometries with additional significant improvements with respect to execution speed.
authors: Division of Cardiovascular Medicine, Department of Medical and Health Sciences, Linköping University, Linköping, Sweden. tino.ebbers@liu.se
authors: Tino
authors: T
authors: Ebbers
authors: Gunnar
authors: G
authors: Farnebäck
mesh_terms: D000328:Adult; D001783:Blood Flow Velocity / Q000502:physiology; D006321:Heart / Q000502:physiology*; D018056:Hemorheology / Q000502:physiology; D006801:Humans; D021621:Imaging, Three-Dimensional / Q000379:methods; D008279:Magnetic Resonance Imaging / Q000379:methods*; D008955:Models, Cardiovascular; D019047:Phantoms, Imaging; D016012:Poisson Distribution; D012016:Reference Values; D015203:Reproducibility of Results; D017725:Ventricular Pressure / Q000502:physiology*