The phase angle f is in turn affected by resonance offsets due to magnetic field inhomogeneity. If f varies throughout the image, the result will be inhomogeneous signal intensity (shading).

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.

Quantification relies on inflow effects or on spin phase effects and therefore on quantifying the phase shifts of moving tissues relative to stationary tissues.
With properly designed pulse sequences (see phase contrast sequence) the pixel by pixel phase represents a map of the velocities measured in the imaging plane. Spin phase effect-based flow quantification schemes use pulse sequences specifically designed so that the phase angle in a pixel obtained upon measuring the signal is proportional to the velocity. As the relation of the phase angle to the velocity is defined by the gradient amplitudes and the gradient switch-on times, which are known, velocity can be determined quantitatively on a pixel-by-pixel basis. Once, this velocity is known, the flow in a vessel can be determined by multiplying the pixel area with the pixel velocity. Summing this quantity for all pixels inside a vessel results in a flow volume, which is measured, e.g. in ml/sec.
Flow related enhancement-based flow quantification techniques (entry phenomena) work because spins in a section perpendicular to the vessel of interest are labeled with some radio frequency RF pulse. Positional readout of the tagged spins some time T later will show the distance D they have traveled.
For constant flow, the velocity v is obtained by dividing the distance D by the time T : v = D/T. Variations of this basic principle have been proposed to measure flow, but the standard methods to measure velocity and flow use the spin phase effect.
Cardiac MRI sequences are used to encode images with velocity information. These pulse sequences permit quantification of flow-related physiologic data, such as blood flow in the aorta or pulmonary arteries and the peak velocity across stenotic valves.

Flow compensation is based on the principle of even echo rephasing and a function of specific pulse sequences, wherein the application of strategic gradient pulses can compensate for the objectionable spin phase effects of flow motion. Gradient moment nulling of the first order of flow is another adjustment for the reduction of flow artifacts.
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. The simplest velocity-compensated pulse sequence is the symmetrical second echo of a spin echo pulse sequence.
Strategic gradient pulses are integrated in special sequences (e.g. CRISP, Complex Rephasing Integrated with Surface Probes) and for the most sequences flow compensation is an optional parameter.

(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).