Basic Physics of MR Signal and Image Generation - Advance Image Processing in Magnetic Resonance Imaging - page 13

More generally, if we allow the amplitude of the applied RF to vary with
time, the FA α is given by:

τ

∫

αγ = Btdt

1

() (1.17)

0

1.5 MR SIGNAL GENERATION AND ACQUISITION

Once displaced from the z axis by the RF pulse, the net magnetization M is
no longer at equilibrium. We denote this nonequilibrium magnetization vector
by M , and the magnitudes of its components along the x, y, and z axes will
be denoted by M x , M y , and M z , respectively. The magnitude of the component
of M in the transverse xy plane (i.e., the resultant of M x and M y ) will be
denoted as M xy . The equilibrium magnetization M 0 represents the situation in
which M is aligned along the z axis corresponding to the case of M z

= M 0 and

M xy 0.

During the period following the pulse, M experiences a torque due to the B 0
field and thus precesses about the B 0 field at the Larmor frequency. The effect of
the precessing magnetization is similar to that of a rotating bar magnet and hence
is equivalent to producing a periodically changing magnetic field in the transverse
plane. If the sample investigated is surrounded by a suitable oriented coil of wire,
an alternating voltage will be induced in the coil according to Faraday's law of
induction. The coil used to receive the signal can be the same as or different from
that used to produce the B 1 field so that precession of M corresponds to reorien-
tation of M xy in the xy plane at a rate equal to the Larmor frequency (i.e., M x
and M y are oscillatory with time at a frequency equal to the Larmor frequency)
while M z is unchanged.
It can be shown that the amplitude of the alternating voltage induced in the
receiver coil is proportional to the transverse magnetization component M xy .
Hence, a maximum amplitude voltage signal is obtained following a

=

/2 pulse
because such a pulse creates a maximum M xy component equal to M 0 . In general,
for RF pulse of flip angle

π

α , the amplitude of the alternating voltage is propor-

tional to M 0 sin( .

As a result of relaxation (such phenomena will be described later), M xy (i.e.,
the amplitudes of oscillation of M x and M y ) decays to zero exponentially; thus,
the voltage signal observed in practice corresponds to an oscillating signal at the
Larmor frequency, with exponentially decaying signal amplitude. This type of
decaying signal, obtained in the absence of B 1 , is called a free induction signal
or free induction decay (FID).

α)

1.5.1 F REE I NDUCTION D ECAY AND THE F OURIER T RANSFORM

The FID induced in the receiver coil is extremely weak and has a frequency in
the RF range: very-high-frequency signal information cannot easily be stored in