In fast imaging sequences driven equilibrium sensitizes the sequence to variations in T2. This MRI technique turns transverse magnetization Mxy to the longitudinal axis using a pulse rather than waiting for T1 relaxation.
The first two pulses form a spin echo and, at the peak of the echo, a second 90° pulse returns the magnetization to the z-axis in preparation for a fresh sequence. In the absence of T2 relaxation, then all the magnetization can be returned to the z-axis. Otherwise, T2 signal loss during the sequence will reduce the final z-magnetization.
The advantage of this sequence type is, that both longitudinal and also transverse magnetization are back to equilibrium in a shorter amount of time. Therefore, contrast and signal can be increased while using a shorter TR. This pulse type can be applied to other sequences like FSE, GE or IR.

Sequences with driven equilibrium:
Driven Equilibrium Fast Gradient Recalled acquisition in the steady state - DE FGR,
Driven Equilibrium Fourier Transformation - DEFT,
Driven Equilibrium magnetization preparation - DE prep,
Driven Equilibrium Fast Spin Echo - DE FSE.

(FISP) A fast imaging sequence, which attempts to combine the signals observed separately in the FADE sequence, generally sensitive about magnetic susceptibility artifacts and imperfections in the gradient waveforms. Confusingly now often used to refer to a refocused FLASH type sequence.
This sequence is very similar to FLASH, except that the spoiler pulse is eliminated. As a result, any transverse magnetization still present at the time of the next RF pulse is incorporated into the steady state. FISP uses a RF pulse that alternates in sign. Because there is still some remaining transverse magnetization at the time of the RF pulse, a RF pulse of a degree flips the spins less than a degree from the longitudinal axis. With small flip angles, very little longitudinal magnetization is lost and the image contrast becomes almost independent of T1. Using a very short TE (with TR 20-50 ms, flip angle 30-45°) eliminates T2* effects, so that the images become proton density weighted. As the flip angle is increased, the contrast becomes increasingly dependent on T1 and T2*. It is in the domain of large flip angles and short TR that FISP exhibits vastly different contrast to FLASH type sequences. Used for T1 orthopedic imaging, 3D MPR, cardiography and angiography.

(GRASS) This sequence is very similar to FLASH, except that the spoiler pulse is eliminated. As a result, any transverse magnetization still present at the time of the next RF pulse is incorporated into the steady state. GRASS uses a RF pulse that alternates in sign. Because there is still some remaining transverse magnetization at the time of the RF pulse, a RF pulse of a degree flips the spins less than a degree from the longitudinal axis. With small flip angles, very little longitudinal magnetization is lost and the image contrast becomes almost independent of T1. Using a very short TE eliminates T2* effects, so that the images become proton density weighted. As the flip angle is increased, the contrast becomes increasingly dependent on T1 and T2*. It is in the domain of large flip angles and short TR that GRASS exhibits vastly different contrast to FLASH type sequences.

The incoherent gradient echo (gradient spoiled) type of sequence uses a continuous shifting of the RF pulse to spoil the remaining transverse magnetization. The transverse magnetization is destroyed by a magnetic field gradient. This results in a T1 weighted image. Spoiling can be accomplished by RF or a gradient.
Gradient spoiling occurs after each echo by using strong gradients in the slice-select direction after the frequency encoding and before the next RF pulse. Because spins in different locations in the magnet thereby experience a variety of magnetic field strengths, they will precess at differing frequencies; as a consequence they will quickly become dephased. Magnetic field gradients are not very efficient at spoiling the transverse steady state. To be effective, the spins must be forced to precess far enough to become phased randomly with respect to the RF excitation pulse. In clinical MRI machines, the field gradients are set up in such a way that they increase and decrease relative to the center of the magnet; the magnetic field at the magnet 'isocenter' does not change.
The T1 weighting increases with the flip angle and the T2* weighting increases with echo time (TE). Typical repetition time (TR) are 30-500 ms and TE less than 15 ms.

See also Ernst Angle.

After RF excitation the spins will tend to return to their equilibrium distribution in which there is no transverse magnetization and the longitudinal magnetization is at its maximum value and oriented in the direction of the static magnetic field. The transverse magnetization decays toward zero with a characteristic time constant T2, and the longitudinal magnetization returns toward equilibrium with a characteristic time constant T1.