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Improving computation of cardiovascular relative pressure fields from velocity MRI
Author(s) -
Ebbers Tino,
Farnebäck Gunnar
Publication year - 2009
Publication title -
journal of magnetic resonance imaging
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.563
H-Index - 160
eISSN - 1522-2586
pISSN - 1053-1807
DOI - 10.1002/jmri.21775
Subject(s) - solver , multigrid method , computation , galerkin method , domain (mathematical analysis) , computer science , mathematics , poisson distribution , algorithm , mathematical optimization , mathematical analysis , finite element method , physics , partial differential equation , statistics , thermodynamics
Purpose 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. Materials and 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. Conclusion 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. J. Magn. Reson. Imaging 2009;30:54–61. © 2009 Wiley‐Liss, Inc.