(TFE) Turbo field echo is a gradient echo pulse sequence with data acquisition after an initial 180° (similar to IR) preparation pulse for contrast enhancement. The difference between a FFE and TFE other than the speed of the sequence is that the image is acquired while approaching steady state (the echoes are collected during the time in which the tissues are experiencing T1 relaxation).
The contrast is prepared one time, which means the contrast is changing while the echoes are collected and can be manipulated by selecting the type and timing of the prepulse. A delay time is given before the actual image acquisition. To achieve T1 contrast the 180° prepulse is followed by an operator selected delay time, that results in no signal from the targeted tissue. So when the echoes are acquired, no signal is present, additional RF spoiling is performed to optimize for T1 contrast. The delay chosen corresponds to when T1 relaxation reaches and suppresses T1 signal or optimizes the difference between tissues. Contrast for these sequences are enhanced when K-space is filled using a centric or low-high ordering. A TFE can be acquired with a 2D or 3D technique and with or without T1, T2 weighting.
See Ultrafast Gradient Echo Sequence, TurboFLASH and Magnetization Prepared Rapid Gradient Echo (MPRAGE).

(BOLD) In MRI the changes in blood oxygenation level are visible. Oxyhaemoglobin (the principal haemoglobin in arterial blood) has no substantial magnetic properties, but deoxyhaemoglobin (present in the draining veins after the oxygen has been unloaded in the tissues) is strongly paramagnetic. It can thus serve as an intrinsic paramagnetic contrast agent in appropriately performed brain MRI. The concentration and relaxation properties of deoxyhaemoglobin make it a susceptibility , e.g. T2 relaxation effective contrast agent with little effect on T1 relaxation.
During activation of the brain, the oxygen consumption of the local tissue increase by approximately 5% with that the oxygen tension will decrease. As a consequence, after a short period of time vasodilatation occurs, resulting in a local increase of blood volume and flow by 20 - 40%. The incommensurate change in local blood flow and oxygen extraction increases the local oxygen level.
By using T2 weighted gradient echo EPI sequences, which are highly susceptibility sensitive and fast enough to capture the three-dimensional nature of activated brain areas will show an increase in signal intensity as oxyhaemoglobin is diamagnetic and deoxyhaemoglobin is paramagnetic. Other MR pulse sequences, such as spoiled gradient echo pulse sequences are also used.
As the effects are subtle and of the order of 2% in 1.5 T MR imaging, sophisticated methodology, paradigms and data analysis techniques have to be used to consistently demonstrate the effect.
As the BOLD effect is due to the deoxygenated blood in the draining veins, the spatial localization of the region where there is increased blood flow resulting in decreased oxygen extraction is not as precisely defined as the morphological features in MRI. Rather there is a physiological blurring, and is estimated that the linear dimensions of the physiological spatial resolution of the BOLD phenomenon are around 3 mm at best.

The characteristic time between significant fluctuations in the local magnetic field experienced by a spin due to molecular motions. For values of the correlation time such that the magnetic field as a function of time has large Fourier components near the resonance frequency, the T1 relaxation time will be shortened.

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.

(DE FGR) A gradient echo sequence using a pulse, which sensitizes the sequence to variations in T2, rather than waiting for T1 relaxation.
See Driven Equilibrium, Gradient Recalled Echo Sequence and Steady State Free Precession.