Basic Physics of MR Signal and Image Generation - Advance Image Processing in Magnetic Resonance Imaging - page 10

where µ i is the magnetic moment of the i -th nuclear spin, and N s is the total
number of spins.
Although there is a microscopic transverse component for each magnetic
moment vector, the transverse component of M is zero at equilibrium because
the precessing magnetic moments have random phases. The macroscopic effect
of an external magnetic field B 0 on an ensemble of nuclei with nonzero spins is
the generation of an observable bulk magnetization vector M pointing along the
direction of B 0 .
The magnitude of the equilibrium magnetization M is equal to that of the spin
excess predicted by the quantum model. M itself behaves like a large magnetic
dipole moment, and if perturbed from its equilibrium state, it will precess at ω 0

about B 0 . By analogy with Equation 1.5, we can write:

ω 0

d M /dt = × M = γ M × B 0 (1.12)

1.4 RF EXCITATION FOR THE RESONANCE

PHENOMENON GENERATION

It is the precessing bulk magnetization that we detect in an MR experiment. In
order to detect it, we must somehow perturb the system from its equilibrium state,
and get M to precess about B 0 . This is done by applying a second magnetic field
B 1 , perpendicular to B 0 , rotating about B 0 at ω 0 in synchronism with the precessing

nuclear magnetic moments.
The B 1 field causes M to tilt away from B 0 and to execute a spiral path, as

schematically described in Figure 1.4 .
The term RF pulse is a synonym of the B field generation, so called because

1

ω 0 /2 is normally between 1MHz and 500 MHz, corresponding to radio waves.

The field is usually turned on for a few microseconds or milliseconds. Also, in
contrast to the static magnetic field B 0 , the B 1 field is much weaker (i.e., B 1

π

=

50 mT while B 0 1.5 T).

A typical B 1 field takes the following form:

=

BB () t = () t + i B B () t = () t e

− i ( ωϕ t )

(1.13)

0

1 1 , x 1 , y 1

where B 1 ( t ) is the envelope function, ω 0 is the excitation carrier frequency, and

ϕ is the initial phase angle.

Equation 1.13 describes a circularly polarized RF pulse, perpendicular to the
z axis, and hence to the B 0 field. The initial phase angle , if it is a constant, has

no significant effect on the excitation result so that we assume it is equal to zero.
The excitation frequency

ϕ

ω 0 can be considered as a constant for almost all RF
pulses, and it is determined by the resonance conditions. The envelope function
B 1 ( t ) is the heart of an RF pulse. It uniquely specifies the shape and duration of
an RF pulse and thus its excitation property. In fact, many RF pulses are named