## Nuclear magnetic resonance

When a wineglass is tapped by a knife, it produces a high-pitched sound of characteristic frequency. If a singer can exactly match that frequency with her voice then the glass will resonate and may break. The basic idea is that if an object has a characteristic frequency of oscillation, exposing it to energy precisely at that frequency will cause a change in physical state.

Analogously, if we supply a pulse of radiofrequency energy at (and only at) the Larmor frequency to a brain located in a magnetic field, the protons within the brain will absorb the energy and resonate. Their angle of alignment a with the external field increases. If sufficient energy is supplied to cause a = 90°, the radiofrequency pulse is called a '90° pulse'. If the net magnetization vector is flipped to an angle a = 180°, the radiofrequency pulse is called a '180° pulse'. At the same time as the angle of alignment is increased by radiofrequency irradiation, the phase of precession becomes coherent over all protons. In other words, in place of the random variation in the phase of precession that existed before the radiofrequency pulse, protons are now 'marching in step' with each other around the axis of the external field.

After the radiofrequency pulse has ceased, the resonating nuclei gradually relax back to the equilibrium state of random precession in alignment with the external field. The two components of this relaxation process are characterized by relaxation times. The first relaxation time ( T1), also called the spin-lattice relaxation time, describes the time taken for the strength of longitudinal magnetization to return to 63 per cent of its value before radiofrequency irradiation. This is a measure of the time taken for a to return to zero having been flipped to 90° or 180°. T, is determined by interactions between protons and their long-range (molecular) environment or lattice. The second relaxation time (T2), also called the spin-spin relaxation time, describes the time taken for the flipped nuclei to stop 'marching in step' around the axis of the field. This process of dephasing begins as soon as the radiofrequency pulse stops, but its rate is determined by the immediate (atomic) environment of the protons. Small variations in the applied magnetic field accentuate spin-spin relaxation, resulting in an observed relaxation time T2* which is somewhat faster than the 'true' relaxation time T2 that would have been observed in an ideally homogeneous field.

As protons relax, they release the energy absorbed from the radiofrequency pulse in the form of a weak radiofrequency signal, which decays at a rate normally determined by T2*. This process is called free induction decay, and the emitted signal forms the data from which magnetic resonance images are ultimately constructed.

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