(GRAPPA) GRAPPA is a parallel imaging technique to speed up MRI pulse sequences. The Fourier plane of the image is reconstructed from the frequency signals of each coil (reconstruction in the frequency domain).
Parallel imaging techniques like GRAPPA, auto-SMASH and VD-AUTO-SMASH are second and third generation algorithms using k-space undersampling. A model from a part of the center of k-space is acquired, to find the coefficients of the signals from each coil element, and to reconstruct the missing intermediary lines. The acquisition of these additional lines is a form of self-calibration, which lengthens the overall short scan time. The acquisition of these k-space lines provides mapping of the whole field as well as data for the image contrast.
Algorithms of the GRAPPA type work better than the SENSE type in heterogeneous body parts like thoracic or abdominal imaging, or in pulse sequences like echo planar imaging. This is caused by differences between the sensitivity map and the pulse sequence (e.g. artifacts) or an unreliable sensitivity map.

The gradient recalled echo MRI sequence generates gradient echoes as a consequence of echo refocusing. The initial slice selective RF pulse applied to the tissue is less than 90° (typically rotation angles are between 10° and 90°). Immediately after this RF pulse, the spins begin to dephase.
Instead of a refocusing 180° RF pulse, reversing the gradient polarity produces a gradient echo. A negative phase encoding gradient and a dephasing frequency encoding gradient are used simultaneous. The switch on of the frequency encoding gradient produces an echo caused by refocusing of the dephasing, which is caused by the dephasing gradient.
TR and flip angle together control the T1, and TE control T2* weighting.

A constant for any given nucleus that relates the nuclear MR frequency and the strength of the external magnetic field.
Definition: The ratio of the magnetic moment (field strength = T) to the angular momentum (frequency = ν) of a particle.
The gyromagnetic effect happens if a magnetic substance is subjected to a magnetic field. Upon a change in direction of the magnetic field, the magnetization of the substance must change. In order for this to happen, the atoms must change their angular momentum. Since there are no external torques acting on the system, the total angular momentum must remain constant. This mass rotation may be measured. The gyromagnetic ratio is different for each nucleus of different atoms. The value of the gyromagnetic ratio for hydrogen (1H) is 4,258 (Hz/G) (42.58 MHz/T).

Form of the Fourier transformation that reverses the process, e.g. if the Fourier transformation is used to analyze a function of time into its equivalent frequency components, the inverse Fourier transformation will synthesize that function of time from these frequency components.

(IR) The inversion recovery pulse sequence produces signals, which represent the longitudinal magnetization existing after the application of a 180° radio frequency pulse that rotates the magnetization Mz into the negative plane. After an inversion time (TI - time between the starting 180° pulse and the following 90° pulse), a further 90° RF pulse tilts some or all of the z-magnetization into the xy-plane, where the signal is usually rephased with a 180° pulse as in the spin echo sequence. During the initial time period, various tissues relax with their intrinsic T1 relaxation time.
In the pulse sequence timing diagram, the basic inversion recovery sequence is illustrated. The 180° inversion pulse is attached prior to the 90° excitation pulse of a spin echo acquisition. See also the Pulse Sequence Timing Diagram. There you will find a description of the components.
The inversion recovery sequence has the advantage, that it can provide very strong contrast between tissues having different T1 relaxation times or to suppress tissues like fluid or fat. But the disadvantage is, that the additional inversion radio frequency RF pulse makes this sequence less time efficient than the other pulse sequences.

Contrast values:
PD weighted: TE: 10-20 ms, TR: 2000 ms, TI: 1800 ms
T1 weighted: TE: 10-20 ms, TR: 2000 ms, TI: 400-800 ms
T2 weighted: TE: 70 ms, TR: 2000 ms, TI: 400-800 ms

See also Inversion Recovery, Short T1 Inversion Recovery, Fluid Attenuation Inversion Recovery, and Acronyms for 'Inversion Recovery Sequence' from different manufacturers.