TwinTree Insert

04-04 T2: The Spin-Spin Relaxation Time

fter a spin system has been excited by an RF pulse, it initially behaves like a coherent system; i.e., all microscopic components of the ma­cro­scopic mag­­ne­­ti­­za­tion precess in phase (all together) around the direction of the ex­ter­nal field. However, as time passes, the observed signal starts to decrease as the spins begin to dephase (Figure 04-14).

Figure 04-14:
Transverse relaxation phenomena induce an increase in dephasing of individual spins, so a progressive de­crease of the macroscopic magnetization is observed.

The decay of the signal in the x'-y' plane is faster than the decay of the mag­ne­ti­za­tion along the z-axis. This additional decay of the net mag­ne­ti­zation in the x'-y' plane is due to a loss of phase coherence of the mi­cro­sco­pic components, which part­ly results from the slightly different Lar­mor fre­quen­cies induced by small dif­fe­ren­ces in the static mag­ne­tic fields at different locations of the samples.

This process is characterized by T2, the spin-spin or transverse re­la­xa­tion. T2 is dependent on a number of parameters:

spaceholder darkblueresonance frequency (field strength), although for T2 this is less crucial than for T1 at low, medium, and high (but seemingly not ultrahigh) fields;

spaceholder darkbluetemperature;

spaceholder darkbluemobility of the observed spin (microviscosity);

spaceholder darkbluepresence of large molecules, paramagnetic ions and molecules, or other outside interference.

In mobile fluids, T2 is nearly equal to T1, whereas in solids or in slowly tumb­ling sys­tems (i.e., high-viscocity sys­tems), static-field components induced by neigh­bor­ing nuclei are operative and T2 becomes significantly shorter than T1.

In solids T2 is usually so short that the signal has died out within the first milli­second, whereas in fluids the magnetic resonance signal may last for several se­conds. To a large extent, this is the cause of the low or absent signal from solid struc­tu­res such as compact bone or tendons in medical magnetic resonance imag­ing.

With increasing field strength, T2 first in­crea­ses as does T1. Then, while T1 still in­crea­ses, T2 stays constant (on a plateau) but it might also appear to decrease. This could be due to microscopic susceptibility differences which can induce a T2* ef­fect.

So, if we represent T1 and T2 versus the microscopic mobility of the spin system, we will obtain for T1 a curve passing through a minimum, corresponding to the Lar­mor frequency, and a continuously decreasing curve for T2 (Figure 04-15).

Figure 04-15:
Zone 1: high mobility with fast molecular motion; usually small molecules and ‘free’ water.
Zone 2: low mobility with slow molecular motion; usually large molecules and ‘bound’ water.

At low and medium fields, the T2 value is approximately 3 seconds and the T1/T2 ratio is 1 for pure water. The T1 value of tissues is usually under 1 second. Here, the T1/T2 ratio increases rapidly with values of 5-10 covering most tissue types. It is about 5 for muscle tissue at 0.1 T.

In practice, it is observed that the same sample can show two different T2 re­la­xa­tion times at the same field strength. This is because two phenomena contribute to the local inhomogeneity experienced by the nuclei:

spaceholder darkbluestatic and oscillating fields locally induced by neighboring magnetic moments (from other nuclei or unpaired electrons), and

spaceholder darkblueimperfections of the main static magnetic field B₀ (field inhomogeneities).

This leads to a decay of the observed signal which is faster than T2. It is called T2* (T-two-star) (Figure 04-16). T2 has an irrecoverable decay whereas T2* has a re­co­ver­able decay and is always shorter than T2.

Figure 04-16:
T2 and T2*. The signal decay of T2* is faster than that of T2, because of field inhomogeneities and che­mi­cal shifts. However, the T2* can be made reap­pear by applying a second RF pulse.

It is important to understand that T2* is not a constant or pure relaxation process. T2* is not a real relaxation pa­ra­me­ter of the nucleus, it is a capricious global parameter. It should not be used for quantitative diagnostic purposes because it is a fluctuant time (or time range) for loss of phase co­he­rence among spins ori­ented at an angle to the static mag­netic field and depends on the location of the molecule in the magnet. These inhomog­eneities can easily change, in MR imaging for instance if the patient moves or turns.

Let's use a comparison: each of one thousand tuning forks of the same type (fre­quen­cy) vibrat­ing while dephasing have their sound de­caying slower than the global sound per­ceived. The main parameters contributing to T2* are spin-spin in­ter­­ac­tions, magnetic field inhomogeneities, magnetic suscepti­bility, and chemical shift effects.

spaceholder redFor a given experiment (a single exami­nation) T2* can be calculated in a similar way as T1 of complex systems (see the con­tainer example, Figure 04-06) by adding the R2 relaxation rates.

The observed decay rate R2* (R2* = 1/T2*) thus is related to the true spin-spin re­la­xa­tion rate R2 (R2 = 1/T2) and to that induced by the field inhom­ogeneities R2inh or R2’ (R2inh = 1/T2inh):

R2* = R2 + R2inh or

R2* = R2 + R2’ or

R2* = R2 + γΔB₀

where γ is the gyromagnetic ratio (unit: MHz/T), ΔB₀ the difference in strength of the locally varying field (unit: T).

In case the signal is influenced by flow or perfusion, this has to be taken into ac­­count ad­di­ti­o­nal­ly, leading to an apparent T2 value: T2app.

To remove the effect of field inhomo­geneities, a spin echo (SE) can be used; its am­pli­tu­de depends on the time, TE, which has elapsed since the initial ex­ci­tat­ion. This is done in one of the formerly most common imaging sequences, the spin-echo pulse sequence, which was the standard pulse sequence in mag­ne­tic re­so­nance imaging and the mainstay of clinical diag­nosis. Even after the in­tro­duc­tion of spe­­ci­a­li­zed pulse sequences for distinct diag­nostic questions, SE re­mains the pulse se­­quen­ce of preferred use if any doubt exists.