T1 relaxation

process by which the longitudinal magnetization Mz attains its equilibrium value Mz0. If at any time the longitudinal magnetization is not equal to Mz0, it will exponentially approach the equilibrium value. The time constant for this exponential approach toward Mz0 is T1. Thus, if at time t=0 the longitudinal magnetization is Mz(0), <> the magnetization at time t will be

M_z(t) = M₀+(M_z(0) - M_z0) exp(-t/T1)

As a special case, if at time t=0 the longitudinal magnetization is zero (e.g. due to the action of a 90 pulse), a time TR later Mz will be equal to Mz0 (1-exp(-TR/T1)), which is the well known T1 dependence of the signal intensity in MR imaging with 90 radiofrequency RF pulses. The exponential recovery of longitudinal magnetization can also be characterized by the relaxation rate R1 which is the inverse of T1, R1=1/T1.

The above description describes the behaviour of the macroscopic magnetization produced by a large number of spins. At the level of an individual nucleus, the magnetic moment can be parallel to the applied field (the lower energy or ground state), or antiparallel to the external field (excited state). The transition from the ground state to the excited state requires the absorption of energy at the Larmor frequency. Similarly, relaxation, the transition from the excited state to the ground state, requires a stimulating radiofrequency field. This can be provided by the randomly fluctuating fields within the environment that the nucleus experiences. This environment is called the lattice, and so longitudinal relaxation is sometimes referred to as spin-lattice relaxation. The randomly fluctuating fields experienced by the nucleus are caused by tumbling and other motions of the nucleus itself (or more precisely the molecule which contains the nucleus) or of other molecules containing magnetic moments, such as other protons. The fields that happen to be at the Larmor frequency contribute to longitudinal relaxation. Thus, the rate of tumbling of the spins or surrounding molecules is a critical component of T1. In macromolecular solutions encountered in MR imaging there are large, medium and small molecules representing the lattice (Fig.1). Very small molecules rotate too quickly (small correlation time tc zone 1 in Fig. 1) and there is only a small number of potential resonant frequencies, while for very large macromolecules, the rotations are so slow that no frequencies comparable to the Larmor frequency exist (large correlation time tc; zone 2 in Fig. 1). Hence, intermediate-sized molecules are the best relaxation agents and therefore tissues with such molecules exhibit the smallest T1 relaxation (fat, mucous fluids and relatively ordered structures).

A higher lattice field at the Larmor frequency leads to a higher relaxation rate and therefore shorter T1. Paramagnetic ions generate very large lattice fields in the immediate neighborhood of the ion, and can therefore greatly shorten the T1 of water if the water protons can approach the paramagnetic centre. This is the mechanism of action of T1-shortening MR contrast medium. The efficiency with which a contrast medium can shorten T1 is determined by its relaxivity. Because the Larmor frequency depends on the strength of the external magnetic field, T1 is field-strength dependent. Generally, T1 lengthens with increasing field strength.

NP