A differential equation expresses a relationship between functions and their derivatives. In MRI, the Bloch equation for example is based on this mathematical function.

A compound with respect to whose frequency the chemical shifts of other compounds can be compared. The standard can be either internal or external to the sample. Because of the need for possible corrections due to differential magnetic susceptibility between an external standard and the sample being measured, the use of an internal standard is generally preferred.

(fMRI) Functional magnetic resonance imaging is a technique used to determine the dynamic brain function, often based on echo planar imaging, but can also be performed by using contrast agents and observing their first pass effects through brain tissue. Functional magnetic resonance imaging allows insights in a dysfunctional brain as well as into the basic workings of the brain.
The in functional brain MRI most frequently used effect to assess brain function is the blood oxygenation level dependent contrast (BOLD) effect, in which differential changes in brain perfusion and their resultant effect on the regional distribution of oxy- to deoxyhaemoglobin are observable because of the different 'intrinsic contrast media' effects of the two haemoglobin forms. Increased brain activity causes an increased demand for oxygen, and the vascular system actually overcompensates for this, increasing the amount of oxygenated haemoglobin. Because deoxygenated haemoglobin attenuates the MR signal, the vascular response leads to a signal increase that is related to the neural activity.
Functional imaging relates body function or thought to specific locations where the neural activity is taking place. The brain is scanned at low resolution but at a fast rate (typically once every 2-3 seconds). Structural MRI together with fMRI provides an anatomical baseline and best spatial resolution.
Interactions can also be seen from the motor cortex to the cerebellum or basal ganglia in the case of a movement disorder such as ataxia. For example: by a finger movement the briefly increase in the blood circulation of the appropriate part of the brain controlling that movement, can be measured.

Short name: PLLGd-DTPA, generic name: (Gd-DTPA)n-polylysine, chemical compound: Gd-DTPA poly(L-lysine-Gd-diethylenetriamine-N,N,N',N'',N''-pentaacetic acid), central moiety: Gd2+, relaxivity: r1=13.1, B0=0.23T
A polymeric MRI contrast agent under development (preclin., Bayer Schering Pharma AG, Berlin, Germany) with advantages in both MRA and in the differential diagnosis of tumors, particularly in perfusion studies of the myocardium and potential in MR lung perfusion. Dozens of the relatively small molecule Gd-DTPA is bound covalently to polylysine, a large molecular weight backbone. The stable, highly water-soluble agent does not diffuse through the endothelium of the vascular system; it is subject to renal elimination.

(MRA) Magnetic resonance angiography is a medical imaging technique to visualize blood filled structures, including arteries, veins and the heart chambers. This MRI technique creates soft tissue contrast between blood vessels and surrounding tissues primarily created by flow, rather than displaying the vessel lumen. There are bright blood and black blood MRA techniques, named according to the appearance of the blood vessels. With this different MRA techniques both, the blood flow and the condition of the blood vessel walls can be seen. Flow effects in MRI can produce a range of artifacts. MRA takes advantage of these artifacts to create predictable image contrast due to the nature of flow.
Technical parameters of the MRA sequence greatly affect the sensitivity of the images to flow with different velocities or directions, turbulent flow and vessel size.
This are the three main types of MRA:
All angiographic techniques differentially enhance vascular MR signal. The names of the bright blood techniques TOF and PCA reflect the physical properties of flowing blood that were exploited to make the vessels appear bright. Contrast enhanced magnetic resonance angiography creates the angiographic effect by using an intravenously administered MR contrast agent to selectively shorten the T1 of blood and thereby cause the vessels to appear bright on T1 weighted images.
MRA images optimally display areas of constant blood flow-velocity, but there are many situations where the flow within a voxel has non-uniform speed or direction. In a diseased vessel these patterns are even more complex. Similar loss of streamline flow occurs at all vessel junctions and stenoses, and in regions of mural thrombosis. It results in a loss of signal, due to the loss of phase coherence between spins in the voxel.
This signal loss, usually only noticeable distal to a stenosis, used to be an obvious characteristic of MRA images. It is minimized by using small voxels and the shortest possible TE. Signal loss from disorganized flow is most noticeable in TOF imaging but also affects the PCA images.
Indications to perform a magnetic resonance angiography (MRA):
Conventional angiography or computerized tomography angiography (CT angiography) may be needed after MRA if a problem (such as an aneurysm) is present or if surgery is being considered.

See also Magnetic Resonance Imaging MRI.