A large network of interconnecting blood vessels at the base of the brain that when visualized resembles a circle, the arteries effectively act as anastomoses for each other. This means that if any one of the communicating arteries becomes blocked, blood can flow from another part of the circle to ensure that blood flow is not compromised.
The circle of Willis is formed by both the internal carotid arteries, entering the brain from each side and the basilar artery, entering posteriorly. The connection of the vertebral arteries forms the basilar artery. The basilar artery divides into the right and left posterior cerebral arteries. The internal carotid arteries trifurcate into the anterior cerebral artery, middle cerebral artery, and posterior communicating artery. The two anterior cerebral arteries are joined together anteriorly by the anterior communicating artery. The posterior communicating arteries join the posterior cerebral arteries, completing the circle of Willis.
The time of flight angiography MRI technique allows imaging of the circle of Willis without the need of a contrast medium (best results with high field MRI). A cerebrovasular contrast enhanced magnetic resonance angiography (MRA) depicts the circle of Willis in addition to the vessels of the neck (carotid and vertebral arteries) with one bolus injection of a contrast agent.

For Ultrasound Imaging (USI) see Cerebrovascular Ultrasonography at Medical-Ultrasound-Imaging.com.

(3D MRA) The 3D angiography technique can be applied to focus on fast flowing (arterial) blood and to visualize small tortuous vessels. 3D TOF images are less sensitive to turbulent flow artifacts. The advantage of this approach is that the signal, acquired from the entire volume has an increased signal to noise ratio. Slices are defined by a second phase encoded axis, which divides the volume into 'partitions'. 3D TOF MRA is acquired with 3D FT slabs or multiple overlapping thin 3D FT slabs (MOTSA) depending on the coverage required and the range of flow-velocities under examination.
Such 3D techniques can provide equal spatial resolution along all three axes, i.e. be 'isotropic', or the partition thickness can be greater or less than the in plane spatial resolution in which case can be said to be 'anisotropic'. The circle of Willis, anatomy as well as its fast arterial flow, lends itself well to both 3D TOF and 2D or 3D phase contrast angiography.

From Siemens Medical Systems;
with the introduction of this system, it is possible to perform contrast MR angiography for abdominal, thoracic and neck vessels from the origins to the circle of Willis. The system also has many newer features including functional imaging, spectroscopy, advanced body, ortho- and neuroimaging.

(MOTSA) This technique combines the best features of 2D time of flight angiography (2D TOF) and 3D TOF MRA. The MOTSA technique consists of multiple 2 cm thick 3D TOF slabs (which minimize saturation effects for through plane flow) combine to provide unlimited coverage similar to multiple 2D TOF slices. High resolution imaging of the carotid arteries is possible when image quality is of greater concern than acquisition time. Images with 1 mm (or less) spatial resolution in all three planes are required. The slabs typically overlap 25-40 to minimize the venetian blind artifact venetian blind artifact due to minimal saturation effects. MOTSA is an useful technique for the evaluation of vertebrobasilar ischemia and aneurysm scanning from the foramen magnum through the circle of Willis.

(TOF) The time of flight angiography is used for the imaging of vessels. Usually the sequence type is a gradient echo sequences with short TR, acquired with slices perpendicular to the direction of blood flow.
The source of diverse flow effects is the difference between the unsaturated and presaturated spins and creates a bright vascular image without the invasive use of contrast media. Flowing blood moves unsaturated spins from outside the slice into the imaging plane. These completely relaxed spins have full equilibrium magnetization and produce (when entering the imaging plane) a much higher signal than stationary spins if a gradient echo sequence is generated. This flow related enhancement is also referred to as entry slice phenomenon, or inflow enhancement.
Performing a presaturation slab on one side parallel to the slice can selectively destroy the MR signal from the in-flowing blood from this side of the slice. This allows the technique to be flow direction sensitive and to separate arteriograms or venograms. When the local magnetization of moving blood is selectively altered in a region, e.g. by selective excitation, it carries the altered magnetization with it when it moves, thus tagging the selected region for times on the order of the relaxation times.
For maximum flow signal, a complete new part of blood has to enter the slice every repetition (TR) period, which makes time of flight angiography sensitive to flow-velocity. The choice of TR and slice thickness should be appropriate to the expected flow-velocities because even small changes in slice thickness influences the performance of the TOF sequence. The use of sequential 2 dimensional Fourier transformation (2DFT) slices, 3DFT slabs, or multiple 3D slabs (chunks) are depending on the coverage required and the range of flow-velocities.
3D TOF MRA is routinely used for evaluating the Circle of Willis.

See also Magnetic Resonance Angiography and Contrast Enhanced Magnetic Resonance Angiography.