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02-02 Magnetic Properties of Nuclei

mong all nuclei in the periodic table, ¹H, ¹³C, ¹⁹F, ²³Na, and ³¹P are among the most interesting for magnetic resonance imaging. All of these nuclei occur naturally in the body. The proton (¹H) is the most com­mon­ly used because the two major components of the hu­man body are water and fat, both of which contain hydrogen. They all have mag­ne­tic properties which dis­tin­gu­ish them from nonmagnetic isotopes.

Nuclei such as ¹²C and ¹⁶O which have even numbers of protons and neutrons do not pro­duce magnetic resonance signals.

The hydrogen atom (¹H) consists of a single positively charged proton which spins around its axis. Spinning charged particles create an electromagnetic field, analogous to that from a bar magnet (Figure 02-02).

Figure 02-02:
A spinning charged particle possesses a characteristic magnetic moment μ and can be described as a magnetic dipole creating a magnetic field similar to a bar magnet (N = north, S = south).

When atomic nuclei with magnetic properties are placed in a magnetic field, they can absorb elec­tro­mag­ne­tic waves of characteristic frequencies. The exact frequency de­pends on the type of nucleus, the field strength, and the physical and chemical en­vi­ron­ment of the nucleus (Figure 02-03).

Figure 02-03:
The nuclei are able to absorb elec­tro­mag­ne­tic waves in both strong and weak mag­ne­tic fields. However, the absorption oc­curs at a field-strength-dependent fre­quen­cy, which is higher in the strong mag­ne­tic field than in the weak mag­ne­tic field.

The absorption and re-emission of such radiowaves is the basic phenomenon utilized in MR imaging and MR spectroscopy. To understand the magnetic re­so­nan­ce phe­no­me­non, two simple macroscopic parallels can be drawn:

First, let us consider a small magnetic needle placed in a magnetic field (Fi­gu­re 02-04). If the needle is capable of rotating freely, it will orientate itself in the field in such a way that an equilibrium situation is attained. This equilibrium can be main­tai­ned in­de­fi­ni­te­ly if no external forces influence the system.

Figure 02-04:
The compass needle will seek the stable equilibrium state.
(Top) When it is turned around with a finger, energy is brought in and it will be in an un­stab­le energy-rich position.
(Bottom) As soon as the finger is taken away, the needle will return to its stable state.

A second example illustrates the influence of the external strain on the fre­quen­cy of the wave absorbed or re-emitted by the system. Imagine three iden­ti­cal guitar strings ex­po­sed to different tensions; the uppermost string of this in­stru­ment has no tension at all, the middle string weak tension, and the lower­most high tension. If we excite the strings, the resultant vibration is dependent on the tension of the strings (Figure 02-05).

Figure 02-05:
A string (the nucleus) cannot vibrate with­out being exposed to tension (the external magnetic field). The higher the tension, the higher will be the frequency of the vi­bra­tion.

In both examples, we have made comparisons between a macroscopic and the mi­cro­sco­pic nuclear system. In the first example, we compared the nuclei with small magnet needles and in the second, with strings.

Such parallels provide a mental picture of the phenomenon, but have their short­co­mings. One limitation of the models is that all physical phenomena on the molecular scale are quantified. For example, whereas an infinity of different orientations is pos­si­ble for the magnetic needle, no smooth continuous tran­si­tions between the equilibrium state and the unstable, energy-rich state exist for the magnetic nucleus; instead, quan­tum mechanics predicts that only jumps bet­ween these two states are pos­si­ble for nuc­lei with a spin of ½, such as protons (Figure 02-06) [spin of ½: ⇒ Holland 1993].

Figure 02-06:
(a) Protons outside a magnetic field, and
(b) pro­tons in a magnetic field.
In the pre­sence of a magnetic field, nuclei populate two distinct energy levels. The se­pa­ra­tion bet­ween these levels increases li­ne­ar­ly with magnetic field strength, as does the population dif­fe­rence.

At equilibrium, we have a slightly larger population in the lower energy level, giving a net magnetization. To observe this population difference we have to pro­vide an amount of energy equal to ΔE (the energy difference between the two levels).