TwinTree Insert

06-02 Localization of Spins with Field Gradients

n MR spectroscopy experiments a sam­ple is placed in a shimmed magnetic field to make it as uniform as possible. Now a particular molecule will give a sig­nal of the same frequency at any point in the sample. Any fre­que­ncy changes ob­served in the Fourier-transformed signal re­flect chemical shifts within the sample which can be used to create analytical spec­tra.

In imaging experiments we are not con­cerned with chemical shift information; che­mi­cal shift might even be counterproductive and considered artifact. To create an image from a patient, the magnetic resonance signal from the nuclei has to con­tain information about where the nuclei are positioned in the patient.

The MR equipment, as we have described it so far, does not provide us with any such informa­tion.

In Figure 06-03 we examine three small samples of water placed at different po­si­­tions along the x-axis. Without the mag­netic field gradient, applying an RF pulse pro­duces a signal consisting of a single fre­quency; Fourier-transforming this signal gives a spectrum with a single peak.

Figure 06-03:
The signals and spectra from three water samples at different positions along the x-axis with and with­out the application of a magnetic field gradient along the x-axis. In the presence of the gradient, the signals from the three samples are resolved, with the separa­tion of the sig­nals being dependent on their spatial separation in the x-direction and on the strength of the magnetic field gradient.
(FT = Fourier transform).

If a magnetic field gradient is imposed when we measure the signal, the signal con­sists of three different frequencies cor­responding to the three different po­si­tions.

As stated before, the Larmor frequency is proportional to the magnetic field strength. If one varies the frequency of the signal by changing the magnetic field li­ne­ar­ly across the sample, the frequencies at different lo­cations will also vary li­ne­ar­ly.

In our example, Fourier-transforming the signal gives a spectrum of three peaks cor­res­pond­ing to the three different sample positions. The frequency differences be­t­ween the samples depend on their physical separation and the strength of the mag­ne­tic field gra­di­ent.

Today, all MR imaging methods utilize such magnetic field gradi­ents for spatial en­­cod­ing (Figure 06-04).

Figure 06-04:
Effect of field gradients: the frequency range is spread out.
In this case, the gradient follows the x-direction. The frequency in the center is the 'exact' resonance frequency.

The (magnetic) field gradients are gen­erated by a set of coils positioned within the mag­net. They can produce fields which vary uniformly along each of the three main axes (x, y, z).

At the center of the magnet, the reso­nance frequency is unchanged since the gra­dient has no effect at the center. On ei­ther side, the resonance frequency will be either higher or lower depending on the po­larity of the gradient (Figure 06-05).

Figure 06-05:
Magnetic gradient fields are superimposed upon the static magnetic field. Different parts of the sam­ple experience different magnetic field strengths. Only in the center of the sam­ple is there no change of the static magnetic field, and thus of the resonance fre­quency ν₀.

These linear field gradients have a strength of up to 30 milli-Tesla per meter (mT/m) in standard 1.5 Tesla clinical systems, but much stronger gradients can be ob­tain­ed by using smaller gradient coils, for specialized imaging methods, or at ultra­high fields to avoid chemical shift artifacts.

Although the frequency variations produced by the gradients are very small com­par­ed to the resonance frequency, the range of resonance frequencies created is suf­fi­cient for high-resolution MR imaging. For example, to produce a frequency dis­tri­bu­tion of 25 kHz over a distance of 30 cm requires a gradient of only 2 mT/m.

The principle of the generation of a field gradient and the shape of gradient coils in a whole-body imaging system have been explained in Figure 01-04 and Figure 03-10.

Figure 06-06 shows how a pulsed magnetic field gradient is usually depicted in pulse sequence diagrams. In this case the gradient pulse is positive. Because there are three gradient directions x, y, and z, one can find gradients depicted in three 'elec­tro­nic channels' in pulse sequence diagrams. Gradient pulses can consist of se­ve­ral dif­fe­rent components.

The amplitude of the gradient is determined by the current flowing in the gra­dient coils. Shortening the rise time requires a faster rate of change of the voltage in the gradient coils.

Figure 06-06:
Schematic representation of a pulsed field gradient used for pulse sequence diagrams.