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Rephasing
 
The process of returning out of phase magnetic moments back into phase coherence. Caused either by rapidly reversing a magnetic gradient (Field Echo) or by applying a 180° RF pulse (Spin Echo). In the spin echo pulse sequence this action effectively cancels out the spurious T2* information from the signal.

See also Spin Echo Sequence and Gradient Echo Sequence.
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Rephasing Gradient
 
Magnetic field gradient pulse applied to reverse the spatial variation of phase of transverse magnetization caused by a dephasing gradient. For example, in selective excitation, it is a magnetic field gradient applied for a brief period after a selective excitation pulse, in the opposite direction to the gradient used for the selective excitation. The result of the gradient reversal is a rephasing of the spins (which will have gotten out of phase with each other along the direction of the selection gradient), forming a gradient echo and improving the sensitivity of imaging after the selective excitation process.
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Even Echo Rephasing
 
A rephasing or refocusing, which occurs when constant velocity spins return to the same starting phase they had directly after the initial exciting RF pulse, as a result of the application of an even number of gradient pulses. This may also result from the application of multiple gradient echo pulses following the RF pulse. The even echo rephasing phenomenon is one of the flow effects observed in MR imaging.
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Further Reading:
  Basics:
Motion Compensation in MR Imaging
   by ccn.ucla.edu    
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Field Even Echo Rephasing
 
The FEER method was the first clinically useful flow quantification method using phase effects, from which all spin phase related flow quantification techniques currently in use are derived.
In this sequence a gradient echo is measured after a gradient with flow compensation. The measured signal phase should be zero for all pixels. A deviation from gradient symmetry by shifting the gradient ramp slightly away from the symmetry condition will impart a defined phase shift to the magnetization vectors associated with spins from pixels with flow.
Slight stable variations in the magnetic field across the imaging volume will prevent the phase angle from being uniformly zero throughout the volume in the flow-compensated image. The first image (acquired without gradient shift) serves as reference, defining the values of all pixel phase angles in the flow (motion) compensated sequence. Ensuing images with gradient phase shifts imparted in each of the 3 spatial axes will then permit measurement of the 3 components of the velocity vector v = (vx, vy, vz) by calculating the respective phases px, py and pz by simply subtracting the pixel phases measured in the compensated image from the 3 images with a well defined velocity sensitization.
The determination of all 3 components of the velocity vector requires the measurement of 4 images.
The phase quantification requires an imaging time four times longer than the simple measurement of a phase image and associated magnitude image. If only one arbitrary flow direction is of interest, it suffices to acquire the reference image plus one image velocity sensitized in the arbitrary direction of interest.

See also Flow Quantification.
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Gradient Motion Rephasing
 
(GMR) The application of strategic gradient pulses can compensate the objectionable spin phase effects of flow motion. That means the reducing of flow effects, e.g. gradient moment nulling of the first order of flow. The simplest velocity-compensated pulse sequence is the symmetrical second echo of a spin echo pulse sequence.
Gradient field changes can be configured in such a way that during an echo the magnetization signal vectors for all pixels have zero phase angle independent of velocities, accelerations etc. of the measured tissue. E.g. the adjustment to zero at the time TE of the net moments of the amplitude of the waveform of the magnetic field gradients with time. The zeroth moment is the area under the curve, the first moment is the 'center of gravity' etc. The aim is to minimize the phase shifts acquired by the transverse magnetization of excited nuclei moving along the gradients (including the effect of refocusing RF pulses), particularly for the reduction of image artifacts due to motion.
Also called Flow Compensation (FC), Motion Artifact Suppression Technique (MAST), Flow motion compression (STILL), Gradient Rephasing (GR), Shimadzu Motion Artifact Reduction Technique (SMART).
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Further Reading:
  Basics:
Motion Compensation in MR Imaging
   by ccn.ucla.edu    
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