Improving 3D MR Velocity-Vector Field Mapping by Divergence-Free Image Reconstruction
نویسندگان
چکیده
Introduction Phase-contrast magnetic resonance imaging (PC-MRI) provides time-resolved 3D information of velocity fields of flowing blood in vessels. It has however been noted that system imperfections including eddy current related phase offsets, sample noise, displacement and partial volume effects can compromise the accuracy of velocity data derived from phase-contrast measurements [1]. If only noise as a source of inaccuracy is considered, statistical methods of streamline generation may be used to improve overall confidence in the vector field visualization [2]. Eddy-current related phase offsets may be measured and corrected for to a certain extent [3], but residual phase errors remain. In contrast to single-slice phase-contrast measurements, three-directional 3D phase-contrast mapping permits incorporation of the physical constraint of approximate incompressibility of blood flow. The present work introduces divergence-free image reconstruction for 3D phase-contrast vector field mapping based on a synergistic combination of normalized convolution and divergence-free radial basis functions. Using computer simulations and in-vivo data it is demonstrated that vector field divergence arising from measurement imperfections can be significantly reduced resulting in improved vector field representations. Theory Velocity vector fields of incompressible fluid flow can be locally approximated by divergence-free radial basis functions [4, 5] according to:
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