Las gabardinas de Deneuve, Los paraguas de Cherburgo

4.1.1 Atomic nuclei and moments

All particles within an atom, protons (p+), neutrons and, electrons (e-) exhibit quantum motion; electrons spin about their axes whilst orbiting around the nucleus, and protons and neutrons spin within the nucleus. Such spins can be described by the spin quantum number I. In, for example, the deuterium atom (^H),

which has one unpaired electron, one proton, and one neutron, the total electron spin = Vi and the total nuclear spin =1. In MR, nuclei with an odd number of protons or neutrons (e.g. one neutron, two protons) are used because the overall nuclear charge generates a magnetic field, known as the magnetic dipole moment, normal to the plane of spin rotation. Such nuclei, also referred to as MR active nuclei, include (unpaired protons = 0; impaired neutrons = 1; total nuclear spin = Vi), (0;1;V^),

(0;1;V2), and more importantly (1;0; !6). Of these, hydrogen protons are the most widely studied in MRI because: (a) hydrogen protons are abundant in soft tissues, and (b) the single proton (nuclear I=!4) provides a large magnetic moment.

Normally, spin Vi moments are distributed randomly such that there is no net or bulk magnetic moment in any particular direction. However, in the presence of a strong magnetic field, with flux density B o , the moments assume either a parallel or anti-parallel state relative to Bq , also known as spin-up and spin-down respectively. The proportion of moments in either state depends on the magnetic flux density of the field and the thermal energy of the system, since the parallel state corresponds to a lower energy level than the antiparallel state. In other words, moments from nuclei with high thermal energy occupy the more energetic antiparallel state, whereas moments from nuclei with less than the required quanta of energy yield to Bq and align in the lower energy parallel state. Thus, samples that are thermally equilibrated at room temperature and subject to a strong magnetic field have an excess of

moments in the parallel state. The effective number of parallel moments is given by the equation,

Where Ny is the total number of moments in the sample, h is Planck’s constant (6.626x10'^"^ J s), / i s the frequency of energy required for transition from the

parallel to antiparallel state, k is Boltzmann’s constant (1.3805x10'^^ J K‘^),and T is the absolute temperature of the sample. The result is a net magnetisation vector (NMV: see Westbrook and Kaut, 1993 for a description of the NMV), which is the sum of the effective moments (Ne%ctive) times the magnetic moments, in the direction of Bo (Figure 4.1).

B, Macro view of system

^ a n ti-p a r a lle l 1 9 N p a ra lle l = I 8 ^ a n ti-p a r a lle l I ^ ^ p a r a ll e l 1 9 ^ a n ti-p a r a lle l t N parallel " 1 4 Bo NMV 4 M, x.y

z

Figure 4.1. Diagrammatic representation o f magnetic resonance. As the system is irradiated by RF energy (B ,) some o f the excess moments in parallel alignment with Bo, which create the net magnetic vector (NM V) in the direction o f Bq, gradually gain sufficient energy to move to the antiparallel state. In doing so, the position o f the NM V gradually changes relative to Bo.

4.1.2 Precession

Parallel moments, which are already spinning about their own axes, also spin about the longitudinal axis of Bq. Hence, moments are often referred to as spins, though the former term is used here to differentiate it from other spin terminology. For the sake of simplicity, it can be imagined that the NMV is a large moment that also processes about Bq with a processional path and frequency that is the same its constituent moments. The processional frequency, known as the Larmor frequency (cOo), is proportional to the frequency of energy required (j) for one moment

contributing to the NMV to gain AE and move to the antiparallel state. It can be determined by,

fOo=Boy

From this it is possible to see that the processional frequency of the moments, and hence the processional frequency of the NMV, is proportional to the strength of the external magnetic field (cOoQC B q ).

4.1.3 Resonance

Irradiating moments with frequencies that are similar to their Larmor frequency will, provided the energy is delivered perpendicular to NMV and B q, increase the oscillatory amplitude of their spins i.e. the NMV begins to resonate. For a typical scanner (1-2 Tesla), frequencies in the radiofrequency (RF) range (42-84 MHz) are necessary to generate a state of ‘excitation’. This state arises as some of the parallel moments gain sufficient energy (AE) to move into the antiparallel state, thereby causing the NMV to gradually move out of alignment with Bq (Figure 4.1).

by the magnetic flux density produced by the RF pulse (B J and the duration of the pulse (tp),

e -y B itp

For MRI measurements Bi and tp are typically adjusted so that NMV moves into a plane perpendicular to Bq and continues to processes about Bq at the Larmor frequency of its moments (N.B. other flip angles are often used during more complex procedures e.g. gradient echo sequences: see Hendrick and Osborn, 1988). In effect, there is now a larger component of moment magnetisation in a transverse plane (x,y) perpendicular to Bq than in the longitudinal plane (z) parallel to Bq. An additional effect of excitation is that individual moments become displaced to the same location in their precessional paths and are said to be in phase. If a receiver coil is positioned across the transverse plane of coherent magnetisation (phased moments), a voltage will be induced in the coil with a similar frequency to that of the Larmor frequency of the moments.

4.1.4 Relaxation: T1 recovery and T2 decay

When the RF pulse ceases, the moments no longer gain energy and the transverse component of magnetisation (Mx,y) is gradually lost as excited moments relax back to their original parallel state. The recovery of the longitudinal

component of magnetisation (M%), i.e. moments re-aligning with Bo, is known as T] recovery or spin-lattice relaxation and is caused by moments losing energy to their surrounding environment or ’lattice'. Conversely, the reduction in the transverse component of magnetisation, known as T2 decay or spin-spin relaxation, is due to

As the voltage in the coil decreases with the loss of coherent

magnetisation in the transverse plane, a characteristic Free Induction Decay (FID) signal is produced. The intensity and frequency of this signal describes the

concentration and type of nuclei and its duration depends on the chemical environment of the moments. The rates of Ti recovery and T% decay are

exponential and the time taken for 1/exp. of the longitudinal magnetisation to be recovered and 1/exp. of the transverse component to be lost are known as the recovery time constant Ti and decay time constant T2, respectively.

In addition to Ti and T% relaxation, there is a third relaxation process called T2* decay. This is a combination of T2 decay and dephasing caused by

inhomogeneities in the magnetic field. Since the Larmor frequency is dependent on the size of the field (ooooc B q ), moments in regions of negative field inhomogeneity have lower precessional (Larmor) frequencies, whilst those in positive regions have higher precessional frequencies. This results in a loss of phase coherence across the field that also has an exponential decay rate denoted by T2*.