Magnetic Resonance Imaging the Velocity Vector Components of Fluid Flow

Abstract

Encoding the precession phase angle of proton nuclei for Fourier analysis has produced accurate measurement of fluid velocity vector components by MRI. A pair of identical gradient pulses separated in time by exactly 1/2 TE, are used to linearly encode the phase of flow velocity vector components without changing the phase of stationary nuclei. Two-dimensional Fourier transformation of signals gave velocity density images of laminar flow in angled tubes which were in agreement with the laws of vector addition. These velocity profile images provide a quantitative method for the investigation of fluid dynamics and hemodynamics.

Rapid Quantitation of Aortic Valve Flow Using Spiral Fourier Velocity Encoded MRI

“…Other problems include the large voxel size and low temporal resolution. FVE has also been accelerated by simply neglecting spatial encoding along one of the spatial dimensions (Feinberg et al, 1985;Hennig et al, 1988), or by acquiring velocity images with no spatial encoding other than slice selection (Galea et al, 2002). In these techniques, the velocity measurement is a projection of all signal along a line or a plane in 3D space, respectively.…”

Flow quantification using low-spatial-resolution and low-velocity-resolution velocity images

“…In contrast to PC, which requires higher spatial resolution to compensate for the lack of velocity resolution, Fourier velocity encoding (FVE) (2,(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18) acquires multiple images with different velocity sensitivities and therefore can resolve spins along the velocity domain in addition to the spatial domain. PC image acquisition can be regarded as a special case of FVE in which the number of velocity encodings is two, but the postprocessing methods of PC and FVE are different.…”

“…Consequently, restrictions on the pixel size are alleviated, and a pixel size greater than the vessel size becomes possible. For the special case of parabolic laminar flow in a circular cross section, Feinberg et al (8) and Dumoulin et al (12) used one-dimensional spatial encoding in conjunction with FVE to measure the flow rate. The flow rate is equal to the product of the mean velocity, which is half of the maximum velocity for parabolic laminar flow, and the crosssectional area of the vessel, which can be derived from the vessel diameter.…”

Pencil excitation with interleaved fourier velocity encoding: NMR measurement of aortic distensibility

“…An NMR pencil-excitation pulse is again used, with a bipolar velocityencoding gradient and then a readout gradient applied along the pencil axis, and with data interleaving employed to improve the effective time resolution so that rapid propagation of wavefronts can be followed. In this method, however, the bipolar gradient is stepped through a range of values, with a Fourier transform applied to produce velocity distribution profiles for different phases of the heart cycle (16,17). If a sinusoidal bipolar gradient is employed which has maximum amplitude G and separation between lobe centers of T, then the velocity resolution V res obtained with this method is [1] where γ is the gyromagnetic ratio.…”