# The Physics of Magnetic Resonance Imaging

Atoms which have an unequal number of neutrons and protons in their nucleus, spin.
Because the nuclei are charged, and moving charges produce a magnetic field, they also act like tiny magnets.

If these spinning nuclei are subjected to an external magnetic field they will align themselves with the filed, just like iron filings do on a larger scale. Most will be parallel to the field (low energy state) but a few will be anti-parallel (high energy state).

However this alignment is not static and the nuclei rotate around the direction of the field, while spinning. This motion is called precession, and it is exactly the same as the motion of a top spinning in gravity and the Earth in its motion in space (with a period of 23 000 years).

The frequency of the precession depends on the magnetic field and on the nature of the nucleus. It is called the Larmor frequency and is found to be in the radio-frequency part of the electromagnetic spectrum.

The frequency of the precession is given by the equation:

Precession frequency (f) = gB/2π

where g is the gyromagnetic ratio ( 42.57 MHz/T) and B is the external field. For B = 2T the precession (Larmor) frequency is about 50 MHz.

If you apply a pulse of radiation of the same frequency of precession resonance will occur, the nucleus will flip into the high energy state (b) and the spin axis of the nucleus will reverse so taking energy from the applied radiation field.

This results in an increase in the energy of the nucleus can be shown in an energy level diagram similar to those for electrons in an atom (Figure 5).

When the pulse ends the nuclei return to their equilibrium state with the emission of radio frequency (RF) radiation. This occurs over a short period of time, called the relaxation time.

There are in fact two different relaxation processes the times of which can be measured. It is these which form the basis of magnetic resonance image formation.

Examples of nuclei able to resonate in this way are hydrogen, phosphorus and carbon. Because of its abundance, in body fluids in particular, hydrogen is the nucleus used in imaging.

The external magnetic field is usually provided by large super conducting magnets operating at –269 oC and giving a field of 2T.

The change in the remitted signal depends on the number of hydrogen nuclei present in the volume of the body examined.

Magnetic resonance imaging (MRI) was first used in Britain in the early 1990s.

Pulses of radiation of the Larmor frequency are sent through the patient each pulse lasting between usually between 50 and 100 microseconds. One of the advantages of this method of imaging is that the energy of pulses of the RF signals used are around 10-7 eV and since the molecular bond strengths are about 1 eV little cellular damage results. Compare this with the energies of X or gamma radiation photons which are of the order of 104 to 106 eV.

Study of the behaviour of the body molecules in a magnetic field. Nuclear magnetic resonance in which protons interact with a strong magnetic field and radio waves to generated pulses that can be analysed in the same way as X rays without the harmful side effects.

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