The magnitude of MZand MXYafter the applica-tion of a 90˚ RF pulse is shown in Figure 6-4.
They are similar in shape. Much like radioactive decay, they are both exponential in form. The T1 relaxation time is much longer than the T2 relax-ation time. Just as T1 relaxrelax-ation controls MZ, T2 relaxation controls MXY. The constants T1 and T2 control the rate of relaxation of MZand MXY, respectively. Each is a fundamental property of tissue.
Figure 6-3 MZ shrinks with time constant T1 when the patient is removed from an external mag-netic field.
TABLE6-2 Approximate T1 Relaxation Times at a Field Strength of 1.0 T for Various Tissues
T2 relaxation never exceeds T1 relax-ation time for any given tissue.
A large value for T1 or T2 indicates a long, gradual relaxation; a small value indicates a rapid relaxation. For example, the T1 and T2 for water are approximately 2500 ms, indi-cating that the signal would take several seconds to relax. This occurs much like a struck bell, which reverberates for several seconds.
Because the relaxation of MZis independent of MXY, T1 and T2 are also independent. T2 is always less than T1. Because the MR signal received is proportional to MXY, it also relaxes according to T2, and the envelope of the free induction decay (FID) is exponential in T2 (Figure 6-4).
It may seem strange that T1 relaxation is represented by an increasing value with time, whereas T2 relaxation is represented by a decreasing value. This happens because the relaxation of MZto M0is actually a relaxation from the excited state to the equilibrium state, whereas MXYis relaxation to zero.
Analogous to T1, T2 is called the transverse relaxation time. Because T2 relaxation repre-sents a loss of XY magnetization, it reprerepre-sents
the loss of phase coherence in a plane perpen-dicular to or transverse to M0. M0lies along the Z-axis.
T2 relaxation time is the same as trans-verse relaxation time or spin-spin relax-ation time.
T2 relaxation also involves the exchange of energy among the nuclei. The MXY vector shrinks because the nuclei are interacting with each other, and this causes spin dephasing.
In any material above absolute zero in tem-perature, molecules and atoms are in constant motion. At room temperature, this motion is so rapid that the nuclei continually bounce into each other. This continual jostling allows one nucleus to lose energy to other nuclei. This is the principal mechanism for the relaxation of MXY—the transfer of energy from one spin to another.
Pixel intensity in an MR image is also a complicated function of T2 relaxation time.
The pulse sequence that is used determines the T2-related brightness of pixels. Table 6-3 presents approximate values of T2 relaxation times for various tissues.
M0
Figure 6-4 After a 90˚ radiofrequency pulse, MZ relaxes to M0. MXY relaxes to zero more quickly because T2 relaxation times are considerably shorter than T1 relaxation times. T2* relaxation is the envelope of the free induction decay (FID).
TABLE6-3 Approximate T2 Relaxation Times at a Field Strength of 1.0 T for Various Tissues
Generally, with T2W images, tissue with long T2 appears bright; tissue with short T2 appears dark.
Phase Coherence
With the three fundamental MRI parameters known, a simple experiment can be done to see whether the effects of each can be observed. After a 90˚ RF pulse, the net magne-tization is rotated onto the XY plane. A large MXYwill be detected as a signal. As a result of T2 relaxation, MXY shrinks and the signal shrinks, too. Before equilibrium is reached, the signal has relaxed to zero.
The T2 can be calculated directly, because the shrinking of the MR signal follows the relaxation of MXYexactly. However, unexpected results are obtained when the experiment is performed.
After excitation with a 90˚ RF pulse, the FID shrinks more rapidly instead of lasting for sev-eral seconds. The T2 obtained from such a measurement is called T2 star (T2*). T2* is much shorter than T2 (Figure 6-5).
T2 must be determined indirectly. Consider the nuclei in the B0magnetic field of a patient who is approximately 50 cm long. Divide that length into three regions and consider the nuclear spins that lie within each of these three regions (Figure 6-6). After the 90˚ RF pulse at time zero, the net magnetization vec-tors of the three regions are flipped onto the XY plane along the Y-axis (Figure 6-7).
Even though the patient is considered to be divided into three regions, the received MR sig-nals still come from throughout the patient.
Therefore the signal is the vector sum of the net magnetization of the three regions.
Because the magnetization vectors in the three regions all point in the same direction, they add maximally and produce a large signal.
At some later time (time A), the three net magnetization vectors of Figure 6-7 have changed. They are shorter because of T2 relax-ation. They have rotated and now point in a new direction (i.e., they are precessing). The rate of precession is the same for each net
magnetization vector because this is controlled by the magnetic field strength in the three regions and B0is the same in each region.
The net result is that each MXY is smaller and changed direction, but they all still point in the same direction. Their sum is smaller than at time zero because of T2 relaxation.
At some later time (time B), the net magne-tization vectors have continued to decrease because of T2 relaxation. Now they point in another direction as a result of precession, but they still all point in the same direction. Once again, their sum has decreased.
T2 relaxation
T2* relaxation
Figure 6-5 Theoretically, MXY should relax as T2. The actual relaxation is much shorter and is called T2*.
1 2 3
Figure 6-6 To visualize T1 and T2*, consider a patient in a magnet whose trunk is divided into three regions.
The dotted line in Figure 6-8 represents the envelope of the decreasing, precessing signal, which results in an FID. The envelope is reduced with a time constant T2. This condi-tion in which all the spins precess together so that they are always pointing in the same direction is termed in phase. The spins have maintained phase coherence.
Frequency and phase are sometimes confused.
For example, a saloon in Houston has five clocks above the bar (Figure 6-9). Each indicates the same time. They each have the same frequency (i.e., one revolution per hour for the minute hand) and the same phase, because all hands
point in the same direction. A reception desk in a fancy San Francisco hotel also has five clocks (Figure 6-10). These clocks indicate the time in various cities around the world. The clocks have the same frequency, but they are out of phase.
In xy plane IN PHASE
Region Region Region
1 2 3
Total magnetization
X
Y Y
Time 0
Time A
Time B
X X
X
X
X
X X X
X X X
Y Y Y
Y Y
Y
Y Y Y Y
Figure 6-7 In a perfect magnet, loss of MXYis the same throughout a homogeneous tissue.
A B
C 0
T2 relaxation
Signal
Figure 6-8 The envelope of the free induction decay obtained from a perfect magnet describes T2 relaxation. Times 0 (zero), A, B, and C refer to Figure 6-7.
Figure 6-9 The five clocks above the bar in a Houston saloon have the same frequency. They are also in phase.
The key assumption in the earlier descrip-tion is that the magnetic field in the three regions of the patient is the same. Such B0field
uniformity causes all net magnetization vec-tors to rotate at precisely the same frequency and remain in phase.
It is impossible to build such a perfect mag-net in real life. Although the magmag-nets used in MRI are high quality, the magnetic fields are not perfectly uniform. The field strength varies slightly from place to place in the imaging aperture. Even this small nonuniformity in magnetic field intensity greatly affects the MR signal.
T2* Relaxation
A different FID results if the earlier MRI exper-iment is repeated with a less-than-perfect mag-net. Once again, a 90˚ RF pulse is transmitted into the patient, and the net magnetization vectors in the three regions flip together onto the XY plane along the Y-axis, as shown at time zero in Figure 6-11. At this point, the magnetization vectors are all parallel and add maximally as before. However, as time pro-gresses, something different occurs. The mag-netization vectors will be different at time A.
Figure 6-10 The five clocks above the reception desk of a fancy San Francisco hotel have the same frequency, but they are out of phase.
In xy plane DEPHASED
Region Region Region
1 2 3
Total magnetization
X
Y Y Y
X
X X X
Time 0
Time A
Time B
X X X
X
X X X
Y
Y
Y
Y
Y
Y
Y
Y
Y
Figure 6-11 In a magnetic resonance imaging system, inhomogeneity of the magnetic field causes MXYto relax more rapidly than expected. The result is T2* relaxation.
Each vector shrinks by the same amount as a result of T2 relaxation, so they remain at equal but reduced length. Each has also precessed in the magnetic field. However, because the mag-netic field is slightly different in the three regions, each vector rotates differently so that they now point in slightly different directions.
For example, the magnetization vector in region 1 is in a slightly higher field and precesses at a slightly faster rate; therefore, at time A, it has rotated a little further than its neighbor in region 2. In contrast, the magnetization vector in region 3 is in a slightly lower magnetic field and therefore has precessed more slowly. It points in yet another direction.
When these three magnetization vectors are added together, the total net magnetization vector is smaller for two reasons. First, T2 has shortened all three magnetization vectors equally. Second, the vectors no longer point in the same direction because of inhomogeneities in the B0magnetic field. Therefore the total net magnetization vector is shorter than that for the perfect magnetic field.
At time B, the effect of the variations in the magnetic field on the direction of the magneti-zation vectors is even more pronounced. The higher-field magnetization vector on the left is farther ahead, and the lower-field magnetiza-tion vector on the right falls farther behind.
The sum is almost zero.
The resulting MR signal relaxes more rapidly than that caused by T2 alone (Figure 6-12). The small variations in the magnetic field cause the
magnetization vectors in different regions to precess at different frequencies; that is, the spins in different regions rapidly lose their phase coherence—they dephase.
Although this discussion has used a three-compartment model, the actual situation involves a multicompartment model. The scale of the magnetic field inhomogeneity is not regional but intravoxel.
The inhomogeneity in the magnetic field causes each spin to precess differently so that T2* is significantly shorter than T2.
The T2* measured in such an MRI experiment combines two factors: the real T2 of tissue and the magnetic field inhomogeneities.
Unfortunately, in practical magnets, the effect of magnetic field inhomogeneities outweighs that of relaxation. The imperfections of the magnet, rather than the T2 of the tissue, end up being measured.
CHALLENGE QUESTIONS
1. Name the three principal MRI parameters characteristic of each tissue.
2. Arrange the three MRI relaxation times, T1, T2, and T2*, from shortest to longest for soft tissue.
3. Which MRI characteristic of tissue principally determines the intensity of the MR signal?
4. What is the principal reason that the T2*
is always shorter than T2?
5. How much longitudinal relaxation occurs during one T1, and approximately how many relaxation times are needed for complete relaxation to reach equilibrium?
6. Distinguish between frequency and phase.
7. T1 relaxation is spin-lattice relaxation. To what does lattice refer?
8. What does the envelope of an FID represent?
9. In a T1W image, which tissues appear bright and which dark?
10. When a T2W image is presented, what tissues will appear bright?
0 T2* relaxation
Figure 6-12 The envelope of the free induction delay obtained from an imaging magnet describes T2* relaxation. T2* is considerably less than T2 because of magnetic field inhomogeneities.
73
Chapter 7
OBJECTIVES
At the completion of this chapter, the student should be able to do the following:
1. Identify the radiofrequency (RF) pulse sequence required to measure T2.
2. Plot T2 relaxation and its relation to T2* relaxation.
3. Identify the RF pulse sequence required to measure T1.
4. Draw and discuss the relationships between net magnetization vector diagrams and relax-ation curves.
OUTLINE
HOW TO MEASURE T2 HOW TO MEASURE T1
T1 VERSUS T2 MEASUREMENTS