MR imaging techniques capable to provide maps of cerebral activity. All these techniques are based on indirect assessment of local cerebral haemodynamics that have been demonstrated to be closely related to cerebral activity.
Two kinds of techniques have been developed:

Velocity of flowing blood, usually measured in cm/s. It is always zero at the vessel wall and the velocity profile across a vessel can have various shapes depending upon the type of flow being observed. Laminar flow giving rise to a laminar velocity profile, plug flow giving rise to a flat velocity profile and disturbed flow can be distinguished.

Quick Overview
Please note that there are different common names for this artifact.

Flow effects in MRI produce a range of artifacts, e.g. intravascular signal void by time of flight effects; turbulent dephasing and first echo dephasing, caused by flowing blood.
Through movement of the hydrogen nuclei (e.g. blood flow), there is a location change between the time these nuclei experience a radio frequency pulse and the time the emitted signal is received (because the repetition time is asynchronous with the pulsatile flow).
The blood flow occasionally produces intravascular high signal intensities due to flow related enhancement, even echo rephasing and diastolic pseudogating. The pulsatile laminar flow within vessels often produces a complex multilayered band that usually propagates outside the head in the phase encoded direction. Blood flow artifacts should be considered as a special subgroup of motion artifacts.

Artifacts can be reduced by reduction of phase shifts with flow compensation (gradient moment nulling), suppression of the blood signal with saturation pulses parallel to the slices, synchronization of the imaging sequence with the heart cycle (cardiac triggering) or can be flipped 90° by swapping the phase//frequency encoding directions.

See also Flow Related Enhancement and Flow Effects.

(FRE) Flow related enhancement could be seen most for blood flow, but also for other liquids with some MR imaging techniques, as an increase in intensity due to the washout of saturated spins. FRE provides positive contrast ("bright blood") of vascular details in time of flight MRA as well as the physiologic characterization of blood flow.
If stationary spins within the scanned region experience only an incomplete T1 relaxation between the repeated radio frequency (RF) excitations, this results in fewer signal of the stationary tissue (compared to inflowing blood with completely relaxed spins). The degree of the flow related enhancement is proportional to the blood flow velocity and the used repetition time. The use of flow compensation (gradient moment nulling) improves the FRE especially in gradient echo sequences.

(ASL) A MR image can be sensitized to the effect of inflowing blood spins if those spins are in a different magnetic state to that of the static tissue. Techniques known as ASL techniques uses this idea by magnetically labeling blood flowing into the slices of interest. Contrast agents are not required for these techniques. This perfusion measurement is completely noninvasive.
Blood flowing into the imaging slice exchanges with tissue water, altering the tissue magnetization. A perfusion-weighted image can be generated by the subtraction of an image in which inflowing spins have been labeled from an image in which spin labeling has not been performed. Quantitative perfusion maps can be calculated if other parameters (such as tissue T1 and the efficiency of spin labeling) also are measured.