Z

Fig. 4. (A) Magnetization vector M precesses toward the transverse (x-y) plane after RF pulse that generates a field of B1 that is perpendicular to B0. (B) View of the M vector after a 90° RF pulse with the observer within the rotating frame. (C) As the spin magnetization returns to equilibrium, the M vector can be split and viewed as two components whereby, if not for signal loss from phase coherence, the two components will return at the same rate.

Fig. 4. (A) Magnetization vector M precesses toward the transverse (x-y) plane after RF pulse that generates a field of B1 that is perpendicular to B0. (B) View of the M vector after a 90° RF pulse with the observer within the rotating frame. (C) As the spin magnetization returns to equilibrium, the M vector can be split and viewed as two components whereby, if not for signal loss from phase coherence, the two components will return at the same rate.

Any atomic nucleus that consists of an odd number of protons or neutrons such as 13C, 23Na, 19F, and 31P will have a net nuclear spin that acts like a small bar magnet aligned along the axis of the spinning nucleus. In the steady state the proton can only be in two equivalent energy states, either "up" or "down." As these protons randomly distribute themselves in the absence of an external magnetic field, these spins cancel each other out, leaving no net magnetism. If an external magnetic field (B0) is present, a very small percentage of the protons will favor lining up with this external field, the sum of which generates a small net magnetization or vector M. It is this vector that is perturbed by a second RF field B1 (applied perpendicular to B0) that causes the spins to precess around this axis (Fig. 4A,B). The RF field is time varying in a sinusoidal pattern, and the frequency needs to be identical to the Larmor frequency of the spins in order to excite them. The Larmor frequency of the spins, as described before, is dependent on the gyromagnetic ratio and magnetic field strength. The rate and angle of precession of M is determined by the strength of B1 and length of the pulse as Bi is turned on and off. One often comes across an RF pulse represented by the precession angle that it causes, such as 90° and 180° in the classic spin-echo pulse sequence.

After the RF pulse or B1 field has been turned off, the M vector or cumulative spins will again try to align back along B0 axis, and it is this precession of magnetization to return to the equilibrium state that forms the MR signal. It is important to point out that it is best to view the M vector as having two components: the longitudinal (parallel to B0 or z-axis) and the transverse (perpendicular to Bo or in the x-y plane), with the latter being the only component that contributes to the measured MR signal (Fig. 4C).

The T1 contrast in tissues is caused by the different local environment that the spins experience, whereas the transverse decay is slightly more complex: its decay is comprised of three components. The first is owing to T1 relaxation: the transverse portion decreases at the same time as the longitudinal vector returns to its original position. The other two causes of transverse magnetization decay are owing to both static and nonstatic magnetic field inhomo-geneities; the former is caused by magnet design or materials used that cause different magnetic susceptibilities. This slight difference in local fields causes the nuclear spins to precess at a slightly different rate (though constant frequency as the inhomogeneity is constant) and thus lose phase coherence, (dephasing)/or fanning out to cancel each other. This form of signal loss also known as T2* decay; it can be reversed by applying a second refocusing RF pulse (180°) in the transverse plane to rephase such spins (Fig. 5). An analogy would be if different runners at constant but variable speeds set off say for 5 min; they then reverse direction and after another 5 min they will all end up back at the starting line at the same time. This is exactly what a spin-echo or spin-warp pulse sequence does consisting of a 90° RF pulse followed by 180° pulse just before the echo is recorded. Unlike those previously mentioned, the nonstatic inhomogeneities are microscopic and irreversible owing to the neighboring molecules that are in constant and variable motion, causing the spins to experience random frequency and changing fields over time. This and the reduction of transverse component owing to the T1 relaxation process are exponential and are described by T2, whereas the reversible loss as mentioned before is represented by T2* (Fig. 6).

The precessing vector M thus creates a time-varying magnetic field that will induce a voltage across a closed-looped wire according to Faraday's law. The intensity of the voltage (which is also the MR signal) is proportional to the magnitude of the net transverse magnetization vector and will be sinusoidal and also at Larmor frequency. It is appropriate here to illustrate again a classic pulse sequence called the spin echo or 90-180° or Carr-Purcell pulse. The terms TR and TE are also introduced: in a conventional spin-echo pulse sequence, TR is the repetition time or the time between two 90° pulses, whereas TE is the time during which the echo or data is collected after the 180° pulse. This acquisition of data is often represented by five lines, three for each of the x', y', and z-gradients, one for the RF pulse, and the last for readout of data (Fig. 7). The z-gradient (parallel to B0) is also the slice-select gradient and is turned on at the same time as the 90° RF pulse. The z-gradient goes from the negative and then passes through zero and onto a positive slope where only the protons at a certain location along the z-axis with a local Lar-

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