Part 2 – T2 relaxation: definition, measurement and practical implications!

In NMR the net magnetization is detected in the xy plane, giving rise to the FID (Free Induction Decay). The process by which the magnetization in the xy plane decays to its equilibrium value of zero is known as T₂ relaxation, transversal relaxation, relaxation in the xy plane, or spin-spin relaxation. However, in practice, the transversal magnetization (M_xy) usually decays to zero quicker than is expected. T₂* is used to explain such observed decay, as it considers both the natural T₂ relaxation (spin-spin interaction) and the relaxation due to magnetic field inhomogeneity (T₂’), as described in Equation 1.

So, T₂ * is always shorter than or equal to T₂. Considering the most straightforward pulse sequence, a 90° rf pulse followed by detection, the NMR signal will hit the detector with a sine dependence that should oscillate with the same intensity for a long time if no relaxation takes place (Figure 1a). In practice this never happens, and a decay in signal intensity over time is always observed (Figure 1b), which is represented by Equation 2.

Figure 1. a) Sine dependence of NMR signal; b) Signal decay rate without accounting for the field inhomogeneity (T₂) and real signal decay rate (T₂*).

With the net magnetization in the xy plane, we always have two relaxation mechanisms playing at the same time; while T₁ relaxation recovers the z magnetization, T₂ relaxation represents the loss of coherence in the xy plane (magnetization is being diphased over time), as demonstrated in Figure 2. For a visual and sonic representation of this phenomenon, listen to the music from Science Grove here!

Figure 2. Schematic representation of signal decrease due to coherence loss over time.

One of the methods used to determine pure T₂ is the CPMG (Carr-Purcell-Meiboom-Gill) experiment because in this sequence we can refocus the field inhomogeneity effect. In CPMG experiments, a 90° pulse is first applied, so the magnetization goes from z to xy plane, followed by a loop of echoes (delay-180°-delay) that locks the magnetization in the xy plane for a specific time (Figure 3a). By repeating the same procedure with different values of time (t), an exponential decay of the signal over time will be observed (Figure 3b). The fitting of this decay will provide the T₂ value.

Figure 3. a) Pulse sequence diagram for the CPMG experiment and b) Graph of the relative intensity of the transversal magnetization (M_xy) versus time (t) for a sample of 40% H₂O in D₂O. The CPMG experiment displayed was acquired using the Benchtop NMR 60.

While T₂* value will be reflected in the signal line-width observed in the spectrum (field homogeneity dependent), the real T₂ value is of high importance for many applications such as in MRI, petrophysics, proteins dynamic studies, among others, as it is a property of each spin and its surrounding.

References :
* Chapter 9 from J. Keeler, Understanding NMR Spectroscopy (2nd edition, John Wiley & Sons, Ltd, 2010.)
* S. Meiboom and D. Gill, Rev. Sci. Instrum., 1958, 29, 688-691.