Chemical shift depends on the nucleus and its environment and is defined as nuclear shielding / applied magnetic field. Nuclei are shielded by a small magnetic field caused by circulating electrons, termed nuclear shielding. The strength of the shield depends on the different molecular environment in that the nucleus is embedded. Nuclear shielding is the difference between the magnetic field at the nucleus and the applied magnetic field.
Chemical shift is measured in parts per million (ppm) of the resonance frequency relative to another or a standard resonance frequency.
The major part of the MR signal comes from hydrogen protons; lipid protons contribute a minor part. The chemical shift between water and fat nuclei is about 3.5 ppm (~220 Hz; 1.5T). Through this difference in resonance frequency between water and fat protons at the same location, a misregistration (dislocation) by the Fourier Transformation take place, when converting MR signals from frequency to spatial domain. This effect is called chemical shift artifact or chemical shift misregistration artifact.

The Larmor precession frequency is the rate of precession of a spin packet under the influence of a magnetic field. The frequency of an RF signal, which will cause a change in the nucleus spin energy level, is given by the Larmor equation. The frequency is determined by the gyro magnetic ratio of atoms and the strength of the magnetic field. The gyromagnetic ratio is different for each nucleus of different atoms.
The stronger the magnetic field, the higher the precessional frequency. If an RF pulse at the Larmor frequency is applied to the nucleus of an atom, the protons will alter their alignment from the direction of the main magnetic field to the direction opposite the main magnetic field. As the proton tries to realign with the main magnetic field, it will emit energy at the Larmor frequency. By varying the magnetic field across the body with a magnetic field gradient, the corresponding variation of the Larmor frequency can be used to encode the position. For protons (hydrogen nuclei), the Larmor frequency is 42.58 MHz/Tesla.

See also Larmor Equation.

Signal intensity interpretation in MR imaging has a major problem.
Often there is no intuitive approach to signal behavior as signal intensity is a very complicated function of the contrast-determining tissue parameter, proton density, T1 and T2, and the machine parameters TR and TE. For this reason, the terms T1 weighted image, T2 weighted image and proton density weighted image were introduced into clinical MR imaging.
Air and bone produce low-intensity, weaker signals with darker images. Fat and marrow produce high-intensity signals with brighter images.
The signal intensity measured is related to the square of the xy-magnetization, which in a SE pulse sequence is given by
Mxy = Mxy0(1-exp(-TR/T1)) exp(-TE/T2) (1)
where Mxy0 = Mz0 is proportional to the proton or spin density, and corresponds to the z-magnetization present at zero time of the experiment when it is tilted into the xy-plane.

See also T2 Weighted Image and Ernst Angle.

The dephasing of the protons is named the T2, spin-spin or transverse relaxation. The T2 time constant is the time taken for spinning protons to lose phase coherence among the nuclei spinning perpendicular to the main field. This interaction between spins results in a reduction in the transverse magnetization. The value of T2 depends on the mobility of the protons. A large mobility results in an average magnetic field variation of zero, resulting in a long T2 period of this tissue.

See also T2 Time.

(ADC) A diffusion coefficient to differentiate T2 shine through effects or artifacts from real ischemic lesions. In the human brain, water diffusion is a three-dimensional process that is not truly random because the diffusional motion of water is impeded by natural barriers. These barriers are cell membranes, myelin sheaths, white matter fiber tracts, and protein molecules.
The apparent water diffusion coefficients can be calculated by acquiring two or more images with a different gradient duration and amplitude (b-values). The contrast in the ADC map depends on the spatially distributed diffusion coefficient of the acquired tissues and does not contain T1 and T2* values.
The increased sensitivity of diffusion-weighted MRI in detecting acute ischemia is thought to be the result of the water shift intracellularly restricting motion of water protons (cytotoxic edema), whereas the conventional T2 weighted images show signal alteration mostly as a result of vasogenic edema.
The reduced ADC value also could be the result of decreased temperature in the nonperfused tissues, loss of brain pulsations leading to a decrease in apparent proton motion, increased tissue osmolality associated with ischemia, or a combination of these factors. The lower ADC measurements seen with early ischemia, have not been fully established, however, a lower apparent ADC is a sensitive indicator of early ischemic brain at a stage when ischemic tissue remains potentially salvageable.

See also Diffusion Weighted Imaging and Diffusion Tensor Tractography.