TwinTree Insert

06-03 Excitation of Selected Spins

ith the implementation of gradients, we can locate the nuclei in our sam­ple, but we also have added a problem. If we switch on a gra­dient after the RF pulse, the mere act of switching on the gradient significantly re­duces the magnitude of the magnetic reso­nance signal from a sample (Figure 06-07).

Figure 06-07:
Dephasing produced by the application of a gradient.
(a) The signal is initially aligned along the y'-axis and decays at a rate determined by T2.
(b) If we turn on a magnetic field gradient, we observe an acceler­ated spreading of the spins.
(c) Increasing the time delay increases the fanning out of the signal.
The solid arrows represent the net signal. The dotted lines in (b) and (c) are the signal that would be mea­­sur­ed in the absence of the gradient.

Ideally, the signal will remain aligned along the y'-axis and decay at a rate de­ter­­min­ed by T2. However, even small imper­fections in the magnetic field cause a spread­ing out (de­phas­ing) of the magnetiza­tion.

The dephasing of the spins is amplified by the field gradients we want to use to lo­­ca­lize the spins. Thus, by the time we have a stable gradient and can measure the sig­nal in the presence of the gradient, we will have little or no net signal.

To avoid this problem, we have to re­form the signal in the presence of the mag­­ne­tic field gradient. This can be achieved using either a spin-echo or a gradient-echo pul­se sequence, thus restoring the original signal in the presence of the gradient, al­low­ing its detec­tion and spatial encoding.

06-03-01 The Spin-Echo Imaging Ex­periment

As we have already seen in Chapter 4, a spin echo is formed by applying a 180° pulse at a time τ after a 90° pulse. Follow­ing the 90° pulse, the magnetization vectors spread out because of the variations in reso­nance frequency caused by field in­ho­mo­­ge­ne­i­ties (ΔB₀).

Applying the 180° pulse reverses the de­phasing, so that at a time τ after the 180° pul­se, these effects are cancelled out and an echo is formed: only T2 decay reduces the intensity of the echo.

Complete rephasing only occurs at the center of the spin echo. With increasing dis­­tan­ce from the center the effects of field in­homogeneities grow.

The spin-echo se­quence also refocuses chemical-shift effects at the center of the spin echo.

Therefore, the water and fat signals will be in phase at the echo center. In a non-imaging spin-echo ex­periment, the dephasing effects in the two halves of the ex­pe­ri­ment before and after the 180° pulse are equal.

In an imaging experiment, we can control both the duration and the amplitude of the imaging field gradients and arrange for the gradient areas to be equal (Figure 06-08).

Figure 06-08:
Spin-echo experiment with balanced gradients during the sequence. The (green) gradient pulse bet­ween the 90° and 180° pulses equals the green area of the gra­dient after the 180° pulse. Since the 180° pulse in­duces a phase reversal, the effects of the two gradi­ents cancel at the center of the spin echo. Therefore, a spin echo forms in the presence of a gradient.

06-03-02 The Gradient-Echo Imaging Ex­periment

We do not necessarily need a 180° pulse To create an echo. Another pos­si­bi­li­ty is us­ing field gra­dients. This leads to gradient echoes, which are widely used in so-called rapid (or fast) imaging sequences.

Following an RF pulse, the signal decays due to the combined action of T2 decay and local field inhomogeneities. This effect is described by T2*. By altering the po­la­ri­ty of the gradient, we change the direction of the induced precession, the spins start rephasing, and at the echo time TE grow into a gradient echo (Figures 06-09, 06-10, and 06-11). To create such an echo, the areas of the gradients with dif­fe­rent po­la­ri­ties must be equal [⇒ Hutchison 1980].

A gradient-echo (GRE) experiment measures a delayed reformed version of the FID. This is necessary due to the gradient switching. Unlike spin echoes, with gra­dient echoes the effects of field inhomogeneities are not cancelled out. The sig­nal decays faster; therefore, GRE experiments require a relatively short echo time.

Figure 06-09:
Formation of a gradient echo using the example of the runners we have already used to demonstrate the creation of a spin echo (cf. Figure 04-18).
 All participants start together; they begin to separate from each other, ac­celerated by the gradient. By the reversal of the gra­dient, they are recalled: they turn around at their present position and run back to the starting line.
 Un­like in the spin-echo experiment, they return on their own track to form a gradient echo.

Figure 06-10:
Formation of a gradient echo in the absence of local field inhomogeneities. The presentation is counter clockwise !
(a) Immediately after the RF pulse the transverse magnetization is strong; the spins are in phase.
(b) The spins begin to dephase; the application of a field gradient accelerates this process. The net mag­­ne­ti­za­tion vanishes.
(c) The gradient is switched to the opposite polariza­tion and the spins begin to rephase, until
(d) a gradient echo is formed.

Figure 06-11:
Formation of a gradient echo.
 Instead of the 180° pulse, a gradient pulse (-G) is used followed by a second gradient pulse of op­po­site polarity (+G).
 For spin echoes, the signal decay is determined by T2, since the effects of local field in­ho­mo­ge­ne­i­ties are cancelled out. With gradient echoes the signal de­cay is determined by T2*; it is always less than T2. More about T2* can be found in Chapter 4 at Table 04-01 and T2*.