A coordinate system, which uses the distance from the coordinate system center and positional angles to identify points in space rather than orthogonal independent unit vectors as in the Cartesian coordinate system. Polar and partly polar (cylindrical) coordinate systems are widely used to describe spin motion in NMR experiments.
It is important to know how to compute the coordinates of a point in the polar coordinate system when they are given in a Cartesian system and vice versa. The length of the vector r pointing from the coordinate origin to a point in 2D space is given as
r = √(x² + y²).
while the polar or phase angle f is obtained by performing the operation
f = arctan (y/x),
where the arctan function is the inverse of the tangent function.

A 'Rotating Frame of Reference' is a concept to simplify the complex motions of a magnetization vector. The frame of reference rotates about the axis of the external magnetic field B0 (z-axis) at the Larmor frequency of the applied RF magnetic field B1. In this simplified concept the rotating vector B1 appears stationary.

(AFP) Adiabatic fast passage is a NMR technique of producing rotation of the macroscopic magnetization vector by shifting the frequency of RF energy pulses (or the strength of the magnetic field) through resonance (the Larmor frequency) in a time short compared to the relaxation times. Particularly used for inversion of the spins between high and low energy states with an excess of spins in the higher energy level. A continuous wave NMR technique used in e.g., MR spectroscopy.

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.

Contrast agents are chemical substances introduced to the anatomical or functional region being imaged, to increase the differences between different tissues or between normal and abnormal tissue, by altering the relaxation times. MRI contrast agents are classified by the different changes in relaxation times after their injection.
The design objectives for the next generation of MR contrast agents will likely focus on prolonging intravascular retention, improving tissue targeting, and accessing new contrast mechanisms. Macromolecular paramagnetic contrast agents are being tested worldwide. Preclinical data shows that these agents demonstrate great promise for improving the quality of MR angiography, and in quantificating capillary permeability and myocardial perfusion.
Ultrasmall superparamagnetic iron oxide (USPIO) particles have been evaluated in multicenter clinical trials for lymph node MR imaging and MR angiography, with the clinical impact under discussion. In addition, a wide variety of vector and carrier molecules, including antibodies, peptides, proteins, polysaccharides, liposomes, and cells have been developed to deliver magnetic labels to specific sites. Technical advances in MR imaging will further increase the efficacy and necessity of tissue-specific MRI contrast agents.

See also Adverse Reaction and Nephrogenic Systemic Fibrosis.

See also the related poll result: 'The development of contrast agents in MRI is'