POTHIER

The radiofrequency (RF) pulse sequence shown in Figure 7-1 results in a magnetic resonance (MR) signal, the free induction decay (FID).

The dotted line indicates the FID in a perfect magnet. A more realistic, shorter FID is also shown.

If, in real-world magnets, the FID does not relax according to the T2 of the sample because of B₀ inhomogeneity, how can the true T2 be measured? Several methods have been devel-oped, all of which use additional pulses after the initial 90˚ RF pulse. The most common of

these is the spin echo pulse sequence (see Chapter 4).

In Figure 7-2, the net magnetization in the three regions of the patient is represented by three runners on an oval track. At time zero, they all leave the starting line together. A per-Figure 7-1 After a 90˚ RF pulse, T2*, rather than T2, relaxation is observed.

RF_t pulse

RF_s signal

90

T2

T2*

FID

Figure 7-2 Immediately after a 90˚ radiofrequency pulse, all spins begin at the same starting line, just like runners in a race.

fect magnet system is represented by runners moving at exactly the same speed, so that at some later time the runners are still exactly together and in step (Figure 7-3).

However, in a real magnet the net magneti-zation in the three regions dephases because spins are precessing at slightly different rates (Figure 7-4). The runners start together but now each runs at a slightly different speed, so that after some point in time, they are no longer together.

Is there some way to cause the runners to come back together even though they each run at a different speed? It is possible if a new rule is introduced to the race. For example, at the time in Figure 7-4, a whistle is blown, and all the runners immediately have to turn around, reversing their direction and run back toward the starting line.

If the race is now run making use of this rule, the scene will change. The runners start out together but soon begin to separate, that is,

dephase. Now at time A, the whistle is blown, and all the runners reverse and start running back toward the starting line. Suddenly the fastest runner, who was far ahead, is behind, and the slowest runner, who was behind, is in the lead. Even though they have changed direc-tions, they have not changed speed. Therefore even though the faster runner is now behind, he will catch up with the others.

A 180˚ RF pulse causes spins to rephase and form a spin echo.

Running toward the starting line is exactly the reverse of the start, when the runners ran from the starting line. This means that as the run-ners cross the starting line (Figure 7-5), they will again be precisely together; they are in phase again. They will cross the starting line at a time exactly twice that when the whistle was blown. For example, if the whistle was blown at 20 seconds, “rephasing” of the runners occurs at 40 seconds.

Figure 7-3 A perfect magnet is analogous to a perfect race. In a perfect magnet, M_XY remains in phase. In a perfect race, the runners remain in step.

If the race continues, the runners again dephase (Figure 7-6). However, they can then be forced to rephase by blowing the whistle at a later time, which will cause them to reverse direction again and come together at the start-ing line.

This process can be repeated any number of times. Each time the runners will rephase, and the information lost because of the difference in runners’ speeds is recovered. The difference in the runners’ speeds is analogous to the dephasing that occurs as a result of magnetic field inhomogeneities.

In a magnet, these reversals of the runners are accomplished with a 180˚ RF pulse. Such a pulse causes all the net magnetization vectors to flip 180˚, in essence, reversing their direc-tion. The spins then begin to rephase, and as they do, a signal is generated. The maximum signal occurs at the point where they are again in phase. If the 180˚ RF pulse were at time t, the maximum rephasing would occur at time 2t.

Figure 7-4 In an imaging magnet, M_XYdephases rapidly. In a real race, competitors run at different speeds.

Figure 7-5 If the runners in Figure 7-4 reverse direction, they will cross the starting line at pre-cisely the same time. They are back in phase.

During imaging, the spin ensemble begins at equilibrium. A 90˚ RF pulse rotates the net magnetization onto the XY plane, that is, the starting line (Figure 7-7). The spins precess at the Larmor frequency, but because this is illus-trated in the rotating frame, the precession is not shown. The dephasing (varying speed of the runners) is illustrated by the shrinking and spreading arrows. Figure 7-7 also has vector diagrams showing the relaxation of the MR sig-nal during this time. The dephasing results in a decreasing signal intensity until there is no signal. This is the FID.

Now a 180˚ RF pulse is applied, and the result flips all spins, which then rephase to form a spin echo with a maximum amplitude at exactly the time the spins rephase (runners cross the starting line). Additional 180˚ RF pulses can be applied to the spin ensemble to produce additional spin echoes. Each additional spin echo will be reduced in amplitude.

The spin echo first increases in intensity to a maximum and then relaxes back to zero (Figure 7-8). The first half of the spin echo is a mirror image of the second half.

The second half of the spin echo is an FID, and the first half is a mirror image of an FID.

The key point that allows rephasing of the run-ners is that even though the runrun-ners’ speeds are different, the speed of each runner is constant.

There is a systematic difference among the runners, and the effect of this difference can be detected by reversing direction. In the same way, the loss of signal due to magnetic field inhomogeneities can be recovered because the inhomogeneities are constant. A region of the magnetic field that is slightly lower in field strength will remain so throughout an imaging sequence.

However, any random changes cannot be recovered in this manner. For example, if the

Figure 7-6 After additional time, the runners are again out of phase but not running quite so fast. A whistle blown at this time causes the runners to reverse direction again and rephase at the starting line.

runners bump into each other momentarily on the track, the distance lost is not recoverable by reversing directions; the runner still ends up a little behind or “out of phase” when the run-ners “rephase.”

In a similar manner, the effects of true T2 relaxation are not recovered by the 180˚ pulses.

Thus the spin echoes reflect a removal of mag-net inhomogeneity but not the removal of true T2 relaxation. Subsequent amplitudes of the

equilibrium dephasing

spin echo

dephase again 90
RF

180
RF

repeat M_XY

time X

Z

Y

spin echo FID

Figure 7-7 Vector diagram showing the formation of multiple spin echoes and the associ-ated graph of transverse relaxation.

Spin echo

Mirror image FID

FID

Figure 7-8 The spin echo consists of a free induc-tion delay (FID) and its mirror image.

spin echoes are smaller because of true T2 alone, and this leads to a method to calculate true T2 (Figure 7-9).

If the maximum amplitude of multiple spin echoes are plotted over time (Figure 7-10), the result is a curve that reflects true T2 relaxation (see Appendix A). Each time a 180˚ RF pulse is used a spin echo results, and each spin echo is smaller than the previous one and reversed in polarity. The time from the 180˚ RF pulse to the echo is always equal to the time from the 90˚ RF pulse to the 180˚ RF pulse.

The envelope of the amplitude of multi-ple spin echoes describes the true T2 relaxation time.