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Encyclopedia of Physical Science and Technology EN008M-395 June 29, 2001 15:52

Magnetic Resonance in Medicine 965

D. Comparison to Other Forms of Magnetism Furthermore, unlike ferromagnetism, nuclear magnetism
is present only when an external field is applied.
As already mentioned, individual atoms can create mag-
netic fields by three general mechanisms: the orbital mo-
tion of their electrons and the spin motions of their elec- E. Bloch Equations
trons and nuclei. In most cases, for any large collection
The magnetic energy associated with the spin of an indi-
of atoms, there is a very strong cancellation of magnetic
vidual nucleus is far too weak to produce detectable effect
properties so that on a macroscopic scale most materials
under any circumstances. In practice, we are always con-
appear to be nonmagnetic. The most important exceptions
cerned with the signals arising from the additive effects of
are the ferromagnetic materials, of which iron is the most 3
enormous numbers of nuclei (e.g., 1 mm of water con-
familiar. In this case, internal quantum effects force many 19
tains 6.62 × 10 protons). It is desirable, therefore, to
of the electron spins to be in alignment with one another,
turn from the properties of individual nuclei governed by
and an intense and easily observable spontaneous magne-
quantum mechanics to the behavior in space and time of
tization results, even when no external field is applied.
a statistically averaged quantity (i.e., M), the bulk nuclear
Nonferromagnetic materials, such as human tissues,
magnetization. Strictly speaking we should use a more
have no net magnetization until placed in an external mag-
qualified notation, such as M n , to indicate that we are now
netic field and even then the resultant magnetization is so
concerned only with the nuclear component of the magne-
weak that it cannot be detected except by use of very sen-
tization. Instead, however, we will follow convention, use
sitive equipment. Alignment processes, which cause M to
M,andassumethattherestrictionisclearfromthecontext.
oppose the applied field, give negative contributions to the
Once the statistical averaging is carried out, the peculiari-
susceptibility and are called diamagnetic. Processes with
ties associated with the quantum behavior of the individual
the opposite behavior are called paramagnetic. Generally
nuclei are no longer evident. For example, unlike the mag-
speaking, diamagnetism results from a field-induced al-
netic moment of a single nucleus, the component of the
teration of the electron orbits. This produces an induced
magnetization in a given direction can take on a continu-
field that tends to oppose the applied field. Paramagnetism
ous range of values without restrictions. It is found that the
results from the tendency of spinning particles (electrons
nuclear magnetization can exhibit an elaborate behavior
or nuclei) to align with the applied field. The electron spin
as a function of time that is driven by two factors. First,
paramagnetism tends to be small or absent because in most
there are the externally applied fields that act on all of the
materials these electron spins tend to cancel in pairs. The
nuclei equally and simultaneously to produce a gyroscopic
orbital motion of the electrons in the H 2 O molecule give motion of the magnetization vector. Second, there is the
−6
bulk water a diamagnetic susceptibility of −9.05 × 10 .
effect of all the internal magnetic fields that are derived
From Eq. (3) the paramagnetic nuclear susceptibility of
from the electrons and other nuclei in the vicinity of each
the protons in water at body temperature was calculated individual nucleus to produce relaxation processes. These
−9
as 3.86 × 10 . The total magnetic susceptibility of water
relaxation processes continually drive the magnetization
is the sum of these two values. Even though water has
toward its equilibrium value. The effects of the externally
one of the highest nuclear magnetic susceptibilities due
applied fields, considered for a moment to be acting alone,
to the large magnetic moment of the proton and the large
are to provide a torque acting on the magnetization such
number of protons in a sample of water, the nuclear para-
that
magnetism of water is completed swamped by the orbital
dM
diamagnetism of the electrons even though that itself is a = γ (M × B). (4)
very weak effect. dt
It is useful to compare the relative strengths of the This equation does not yet include the effects of the
various forms of magnetism. The spontaneous magne- interaction of the spins with their internal surroundings,
6
tization of iron is about 1.7 × 10 A/m. In a rather in- the “lattice.” However, it contains many of the physical
tense applied field of 1 T, the bulk magnetization of water concepts that explain how the nuclear magnetization can
would be −7.0 A/m due to the orbital diamagnetism and be detected despite its weak strength. Equation (4) will
3.1 × 10 −3 A/m due to the nuclei. These comparative fig- describe the evolution of M for short times (i.e., for times
ures explain why it is not possible to detect nuclear mag- much shorter than T 1 and T 2 described in the following).
netization by direct effects such as the orientation of iron In human imaging studies this means that Eq. (4) by itself
filings or the deflection of a compass needle, even though is enough to describe processes that require a few mil-
these effects can be easily demonstrated with ferromag- liseconds or less to complete. This includes the Larmor
netic materials. The nuclear magnetization is too weak, precession, which completes each cycle in a fraction of
by several orders of magnitude, to produce these effects. a microsecond. It also includes the B 1 excitation pulses,