Phenomenological (classical) equations of motion for the macroscopic magnetization vector. They include the effects of precession about the magnetic field (static and RF) and the T1 and T2 relaxation times.

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.

A nonequilibrium state in which the macroscopic magnetization vector is oriented opposite to the magnetic field; usually produced by adiabatic fast passage or 180° RF pulses.

A microscopic group of spins, which resonate at the same frequency. The spin precesses around a circle in the xy-plane and the net magnetization is the length, amplitude or magnitude of the magnetization vector Mxy: the quantity normally represented on a pixel-by-pixel basis in a MR image (thus amplitude or magnitude image).

(Mz) The component of the net magnetization vector in the direction of the static magnetic field (z). After RF excitation, this vector returns to its equilibrium value at a rate characterized by the time constant T1.