title: Computational fluid dynamics simulations of blood flow regularized by 3D phase contrast MRI.
abstract: BACKGROUND
  Phase contrast magnetic resonance imaging (PC-MRI) is used clinically for quantitative assessment of cardiovascular flow and function, as it is capable of providing directly-measured 3D velocity maps. Alternatively, vascular flow can be estimated from model-based computation fluid dynamics (CFD) calculations. CFD provides arbitrarily high resolution, but its accuracy hinges on model assumptions, while velocity fields measured with PC-MRI generally do not satisfy the equations of fluid dynamics, provide limited resolution, and suffer from partial volume effects. The purpose of this study is to develop a proof-of-concept numerical procedure for constructing a simulated flow field that is influenced by both direct PC-MRI measurements and a fluid physics model, thereby taking advantage of both the accuracy of PC-MRI and the high spatial resolution of CFD. The use of the proposed approach in regularizing 3D flow fields is evaluated.
  
  
  METHODS
  The proposed algorithm incorporates both a Newtonian fluid physics model and a linear PC-MRI signal model. The model equations are solved numerically using a modified CFD algorithm. The numerical solution corresponds to the optimal solution of a generalized Tikhonov regularization, which provides a flow field that satisfies the flow physics equations, while being close enough to the measured PC-MRI velocity profile. The feasibility of the proposed approach is demonstrated on data from the carotid bifurcation of one healthy volunteer, and also from a pulsatile carotid flow phantom.
  
  
  RESULTS
  The proposed solver produces flow fields that are in better agreement with direct PC-MRI measurements than CFD alone, and converges faster, while closely satisfying the fluid dynamics equations. For the implementation that provided the best results, the signal-to-error ratio (with respect to the PC-MRI measurements) in the phantom experiment was 6.56 dB higher than that of conventional CFD; in the in vivo experiment, it was 2.15 dB higher.
  
  
  CONCLUSIONS
  The proposed approach allows partial or complete measurements to be incorporated into a modified CFD solver, for improving the accuracy of the resulting flow fields estimates. This can be used for reducing scan time, increasing the spatial resolution, and/or denoising the PC-MRI measurements.
authors.affiliation: Department of Electrical Engineering, University of Brasilia, Brasília, Brazil. vrispoli@pgea.unb.br.|UnB Gama College, University of Brasilia, Brasília, Brazil. vrispoli@pgea.unb.br.
authors.forename: Vinicius C
authors.initials: VC
authors.lastname: Rispoli
authors.affiliation: fMRI Laboratory, Biomedical Engineering Department, University of Michigan, Ann Arbor, USA. jfnielse@umich.edu.
authors.forename: Jon F
authors.initials: JF
authors.lastname: Nielsen
authors.affiliation: Magnetic Resonance Engineering Laboratory, Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, USA. knayak@usc.edu.
authors.forename: Krishna S
authors.initials: KS
authors.lastname: Nayak
authors.affiliation: Department of Electrical Engineering, University of Brasilia, Brasília, Brazil. joaoluiz@pgea.unb.br.
authors.forename: Joao L A
authors.initials: JL
authors.lastname: Carvalho
mesh_terms: D000465:Algorithms; D001775:Blood Circulation; D003198:Computer Simulation; D006801:Humans; D057446:Hydrodynamics; D021621:Imaging, Three-Dimensional; D008279:Magnetic Resonance Imaging; D008954:Models, Biological; D019047:Phantoms, Imaging