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Magnetization Value
(Mo) Equilibrium value of the magnetization;; directed along the direction of the static magnetic field. Proportional to spin density (N).
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Gradient Echo SequenceForum -
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Gradient Echo Sequence Timing Diagram (GRE - sequence) A gradient echo is generated by using a pair of bipolar gradient pulses. In the pulse sequence timing diagram, the basic gradient echo sequence is illustrated. There is no refocusing 180° pulse and the data are sampled during a gradient echo, which is achieved by dephasing the spins with a negatively pulsed gradient before they are rephased by an opposite gradient with opposite polarity to generate the echo.
See also the Pulse Sequence Timing Diagram. There you will find a description of the components.
The excitation pulse is termed the alpha pulse a. It tilts the magnetization by a flip angle a, which is typically between 0° and 90°. With a small flip angle there is a reduction in the value of transverse magnetization that will affect subsequent RF pulses. The flip angle can also be slowly increased during data acquisition (variable flip angle: tilt optimized nonsaturation excitation). The data are not acquired in a steady state, where z-magnetization recovery and destruction by ad-pulses are balanced. However, the z-magnetization is used up by tilting a little more of the remaining z-magnetization into the xy-plane for each acquired imaging line.
Gradient echo imaging is typically accomplished by examining the FID, whereas the read gradient is turned on for localization of the signal in the readout direction. T2* is the characteristic decay time constant associated with the FID. The contrast and signal generated by a gradient echo depend on the size of the longitudinal magnetization and the flip angle. When a = 90° the sequence is identical to the so-called partial saturation or saturation recovery pulse sequence. In standard GRE imaging, this basic pulse sequence is repeated as many times as image lines have to be acquired. Additional gradients or radio frequency pulses are introduced with the aim to spoil to refocus the xy-magnetization at the moment when the spin system is subject to the next a pulse.
As a result of the short repetition time, the z-magnetization cannot fully recover and after a few initial a pulses there is an equilibrium established between z-magnetization recovery and z-magnetization reduction due to the a pulses.
Gradient echoes have a lower SAR, are more sensitive to field inhomogeneities and have a reduced crosstalk, so that a small or no slice gap can be used. In or out of phase imaging depending on the selected TE (and field strength of the magnet) is possible. As the flip angle is decreased, T1 weighting can be maintained by reducing the TR. T2* weighting can be minimized by keeping the TE as short as possible, but pure T2 weighting is not possible. By using a reduced flip angle, some of the magnetization value remains longitudinal (less time needed to achieve full recovery) and for a certain T1 and TR, there exist one flip angle that will give the most signal, known as the "Ernst angle".
Contrast values:
PD weighted: Small flip angle (no T1), long TR (no T1) and short TE (no T2*)
T1 weighted: Large flip angle (70°), short TR (less than 50ms) and short TE
T2* weighted: Small flip angle, some longer TR (100 ms) and long TE (20 ms)

Classification of GRE sequences can be made into four categories:
T1 weighted or incoherent/(RF or gradient) spoiled GRE sequences
T1/T2* weighted or coherent//refocused GRE sequences
T2 weighted contrast enhanced GRE sequences
ultrafast GRE sequences
See also Gradient Recalled Echo Sequence, Spoiled Gradient Echo Sequence, Refocused Gradient Echo Sequence, Ultrafast Gradient Echo Sequence.
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Further Reading:
Enhanced Fast GRadient Echo 3-Dimensional (efgre3D) or THRIVE
Imaging strategies for uncooperative patients
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Magnetization Vector
The integration of all the individual nuclear magnetic moments, which have a positive magnetization value at equilibrium versus those in a random state.

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Transverse Relaxation Time
The T2 time constant, which determines the rate at which excited protons reach equilibrium, or go out of phase with each other. A measure of the time taken for spinning protons to lose phase coherence among the nuclei spinning perpendicular to the main field due to interaction between spins, resulting in a reduction in the transverse magnetization. The transverse magnetization value will drop from maximum to a value of about 37% of its original value in a time of T2.
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Balanced Fast Field EchoInfoSheet: - Sequences - 
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(bFFE) A FFE sequence using a balanced gradient waveform. A balanced sequence starts out with a RF pulse of 90° or less and the spins in the steady state. Before the next TR in the slice phase and frequency encoding, gradients are balanced so their net value is zero. Now the spins are prepared to accept the next RF pulse, and their corresponding signal can become part of the new transverse magnetization. Since the balanced gradients maintain the transverse and longitudinal magnetization, the result is, that both T1 and T2 contrast are represented in the image. This pulse sequence produces images with increased signal from fluid, along with retaining T1 weighted tissue contrast. Because this form of sequence is extremely dependent on field homogeneity, it is essential to run a shimming prior the acquisition. A fully balanced (refocused) sequence would yield higher signal, especially for tissues with long T2 relaxation times.
See Steady State Free Precession and Gradient Echo Sequence.

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Further Reading:
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T1rho-prepared balanced gradient echo for rapid 3D T1rho MRI
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