Relaxation Mechanisms

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So far the generation of the background field fluctuations has been assumed to derive solely from the field of a tumbling dipole, interacting with other dipole fields (the so-called 'dipole-dipole' interaction). However any process that generates such a random field can induce relaxation and some of the more important mechanisms will be discussed now (Harris, 1986; Gadian, 1982; Callaghan, 1991).

6.4.1 Dipole-Dipole Interaction

For many spin 1/2 nuclei, this is the most important mechanism for inducing relaxation. This is particularly so for the common biological elements 1H, 13C, 23Na and 31P. The dipole-dipole interaction is heavily modulated by r, the internuclear c separation, so that the longitudinal relaxation rate varies as r-6, thus

so the interaction will become diminished if nuclei under consideration become significantly separated. Also note the strong dependence on y so that the dipole-dipole relaxation mechanism is much more effective for 1H than for the previously mentioned nuclei.

6.4.2 Electron Paramagnetism

The magnetic moment of the electron is three orders of magnitude larger than that of its nuclear counterpart. Therefore the unpaired electrons in the outer electronic shells of paramagnetic atoms generate strong relaxation centres, and surrounding material will have substantially increased relaxation rates. This can be devastating to the nuclear signal if impurities contaminate the sample. However it can also be used to advantage whereby T1 contrast is increased by locally reducing T1 and thus enhancing the signal from specific regions. Lanthanide elements and transition metals in particular have been employed, with gadolinium chelates such as Gd DTPA proving especially popular agents (Brasch, 1983).

Iron is also highly paramagnetic and is of considerable interest clinically and neurobiologically (Ordidge et al., 1994; Gillis and Koenig, 1987). It is found predominantly in ferritin, an iron storage protein for mammals. It is roughly spherical in shape with an inner diameter of about 80 A, so that it may contain several thousand iron atoms (Bizzi et al., 1990). In addition to the strong paramagnetic effect, small regions of the ferritin core may become ferromagnetic (Gillis and Koenig, 1987), antiferromagnetic or superparamagnetic (Bizzi et al., 1990). Theory suggests (Gillis and Koenig, 1987) that the ferromagnetic effect should induce relaxation rates greater than that observed from the ferritin core, and it has been suggested that the weaker antifer-romagnetic and superparamagnetic effects compensate for this to some degree. Reversible T2 relaxation occurs when tissue water experiences a range of static magnetic environments (see Section 6.5.2). Further relaxation occurs when slow fluctuations in the magnetization of the ferritin core occur, causing local magnetic field inho-mogeneities and gradients (Drayer et al., 1986b). This T2 shortening causes hypointensity on T2-weighted images (Ordidge et al., 1994; Drayer et al., 1986b; Ogg 1999) and may also be used as a measure of iron concentration in biological tissue (Ordidge et al., 1994; Ogg, 1999; Vymaza et al., 1995).

Also note that the iron in blood haemoglobin has a similar effect. However oxygenated blood produces oxygenated haemoglobin, which is dia-magnetic and has little effect on the local magnetic field, while deoxygenated blood generates deoxy-haemoglobin which has a paramagnetic effect. This fact has demonstrated remarkable utility in neurological fMRI experiments (Chapter 12) whereby increases in oxygenated blood to activated regions of brain result in local signal increases that can be detected to produce brain activation maps.

6.4.3 Scalar Interactions

Nuclear spins can couple indirectly, modulated by an electron bond. The interaction produces a magnetic field that can become time-dependent owing to exchange mechanisms for example. The coupling of the two nuclei also implies that relaxation of one nucleus can induce relaxation at the other. This mechanism usually modulates the field slowly and as such contributes more to T2 relaxation than to T1.

6.4.4 Spin Rotation

Rotating molecules can generate their own magnetic fields. As the molecule moves, so the electrons of the molecule move, which in turn constitutes an electric current. This current is the source of the magnetic field, the magnitude of which is dependent upon the angular momentum of the molecule and will be heavily modulated by Brow-nian motion. The resulting rapid, random time variation in the field contributes to the relaxation process. This mechanism will be most effective for light, rapidly moving molecules, and less so for large (biological) molecules. The 'correlation time' for this interaction is related to the time between collisions of molecules undergoing Brow-nian motion.

6.4.5 Shielding Anisotropy

The chemical shift effect is a result of the variation in the motion of bound electrons owing to an interaction with B0 (Harris, 1986; Dickinson, 1950; Proctor and Yu, 1950). As a result, the magnetic field experienced by the corresponding nucleus changes by a small amount. This chemical shift effect can be determined by the specifics of the chemical bonds involved, and as such can be directionally dependent. For example the annular structure of aromatic hydrocarbons demonstrates little or no shielding with their ring plane parallel to the applied B0 field, but significant shielding is observed if the plane is perpendicular to the applied field (Gadian, 1982). As the molecule orientation changes relative to B0, so does the field at the relevant nuclei. The shielding effect is proportional to the square of the applied field and as such can have significant effects for spectroscopy studies at high field (Brady etal, 1981).

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