## Magnetization

If iron filings are scattered on a piece of paper they will be oriented at random. If a bar magnet is then placed under the paper the iron filings will align themselves so that each filing lies parallel to the magnetic field produced by the magnet. More technically, we can say that iron filings have a susceptibility to be magnetized by a static magnetic field.

Susceptibility refers both to the effect of a magnetic field on an object, and the effect of that object on the field. Paramagnetic materials, like some metals, tend to be attracted by magnets and cause a local increase in magnetic field strength. Diamagnetic materials, like carbon and many organic compounds, tend to be repulsed by magnets and cause a local decrease in field strength.

The brain also has a susceptibility to be magnetized. It is largely composed of water and each molecule of water comprises, of course, two hydrogen atoms and one oxygen atom. The hydrogen nucleus is a single positively charged proton, which has a dynamic property called spin. Like all moving charged particles, spinning protons generate a magnetic field. The axis of the magnetic dipole generated by a spinning proton is sometimes called its magnetic moment, and is drawn as a vector.

When the brain is placed in a strong magnetic field, the spinning protons align themselves with the external field, just as iron filings align themselves to the field of a bar magnet. The angle of alignment between each proton's moment and the (longitudinal) axis of the external magnetic field is a. Protons obey the laws of quantum mechanics, and so two modes of alignment or spin states are possible, one with the magnetic moment in the direction of the field (a = 0°) and one with the moment in the opposite direction (a = 180°). Depending on the strength of the applied field, the spin states have slightly different probabilities, with those protons aligned in the direction of the field in excess by about 5 ppm at an external field strength of 1.5 T. (Magnetic field strength is measured in units of gauss ( G) or tesla (I): 1 T = 10 000 G. The Earth's magnetic field is approximately 0.5 G; a child's toy magnet has a field of around 10 G.)

Thus, if the magnetic moments for all spinning protons are averaged, the net, or bulk, magnetization vector for the brain as a whole will have a = 0°. The length of the net magnetization vector then represents the strength of longitudinal magnetization ( Fig 1).

Fig. 1 Net magnetization vector. (a) In a static magnetic field, the vector is aligned parallel to the longitudinal z axis of the field and a = 0. (b) Immediately after a 90° excitation pulse of radiofrequency energy at Larmor frequency, the angle of alignment a is increased (transverse magnetization) and the phase of precession in the x-y plane is coherent over all protons in the brain. As protons relax following excitation, the angle of the net vector becomes smaller (return of longitudinal magnetization) and the phase of precession becomes more variable from one proton to another (dephasing).

Protons aligned with a static magnetic field are not static themselves. They rotate or precess at very high frequency around the axis of the external field. The precession frequency, or Larmor frequency, is constant for a given type of atomic nucleus and external field strength. For protons, the Larmor frequency at 1.5 T is 63.9 MHz. However, although all hydrogen nuclei in the brain precess at the same frequency in the same field, they will not all precess with the same phase. At any given time, different nuclei have reached a different point in their rotation around the external field axis.

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