Relaxation

As we have seen, perturbation of the magnetization by application of a short RF pulse tips it away from the longitudinal axis and generates a transverse component. If this magnetization is allowed to precess freely, there is a regrowth of the longitudinal magnetization called longitudinal relaxation, and destruction of the transverse magnetization called transverse relaxation. Relaxation is described by exponential time constants: T1 for longitudinal and T2 for transverse relaxation. Exponential processes are those whose rate of change depends on how far they have left to go; the closer they get to their final value, the more slowly they approach it. T1 is defined as the time taken for the longitudinal magnetization to relax from 0 to 63% of the equilibrium magnitude. T2, or the transverse relaxation time constant, is the measure of the time that the transverse magnetization takes to relax (decay) to 37% of its initial magnitude. T2 decay occurs because individual spins (usually referred to as isochromats) rotate at slightly different rates due to their chemical environment, and eventually they get out of sync and begin to point in random directions and cancel each other. This process is referred to as "dephasing," because the spins acquire different phases in the range 0 to 360°. In practice, field inhomogeneities can be another source of transverse relaxation, other than the chemical environment. The dephasing due to this process is accounted for by another time constant, T2'. The total transverse relaxation time constant (T2*) then is the reciprocal sum of T2 and T2' and is given by:


Both the longitudinal and transverse relaxations are modeled by exponential functions (Fig. 5-3) given by the Bloch equations, which are stated without further justification:


Mz
longitudinal magnetization
Mz0
longitudinal magnetization at t = 0+, i.e., immediately after the RF pulse
M0
equilibrium magnetization
Mxy
transverse magnetization.
Different tissues have different relaxation time constants, and these form the basis of some of the contrast mechanisms in MRI.