Fundamentals of magnetic resonance imaging - Biomedical Engineering Desk Reference - page 516

where n denotes the number of protons per unit volume.
Notice that as the temperature increases the magneti-
zation is destroyed. Since D E is linearly dependent on B 0 ,
the net magnetization is proportional to the magnetic
field. In NMR the observation of the precession of this
magnetic moment is of great importance.
The effects of RF radiation on the magnetization of
the body sample in a uniformly applied B 0 field needs to
be addressed. Under the influence of an RF magnetic
field, directed on a given processes coordinate, the
magnetization can be rotated away from its equilibrium
position and the angle q is given by

Z

Y

q ¼ VB eff T (6.1.19)

X

where B eff is the value of the effective magnetic field in
the rotating frame. The rotation of M will have an angular
frequency

Figure 6.1-9 Relaxation signal and equilibrium.

u ¼ g B eff

(6.1.20)

When a magnetic field B 0 is applied in the z direction,
the nuclei precess about the z axis at the Larmor fre-
quency and with a precessional angle q. Some of the
nuclei precess around the þz axis protons and others
precess around the z direction and this results in a bulk
magnetization, as shown in Figure 6.1-10 .
Upon the application of an RF pulse phase coherence
is accomplished in both the þz and z precession. The
RF pulse is at the resonant frequency and it stimulates
the flipping between the two sections in the þz and z
precession. This allows energy to be imparted into the
protons and nuclei migrate to the z precession. Once
the population of nuclei in each þz and z precession
sections is the same, there will be no net axial magneti-
zation. After a 90 pulse, as the magnetization precesses

We can notice that a large gyromagnetic ratio provides
a quicker perturbation of the magnetization vector. In
practice it rotates M by 90 and 180 . The durations of
these rotations are given by

p
2g B eff

T 90 ¼ (6.1.21a)

M
g B eff

T 180 ¼

(6.1.21b)

After the initial 90 rotation, the magnetization vector
M processes in the transverse plane. The relaxation
process is better explained by the Block equations de-
scribed next.

dM x;y
dt

¼ g ð ! ! Þ x;y M x;y

T 2

B 0

(6.1.22)

dM z
dt

¼ g ð ! ! Þ z þ M 0 M z

+Z

T 1

where T 2 and T 1 are the transverse and longitudinal re-
laxation times, respectively, and M 0 denotes the equi-
librium value of magnetization, which is assumed to lie in
the z direction. The solution of Eqs. (6.1.22) is given by
M x ðtÞ¼M 0 exp t
T 2

θ

cos ð g B 0 tÞ
M y ðtÞ¼M 0 exp t

Z=0

sin ð g B 0 tÞ
M z ðtÞ¼M 0 1 exp t
T 1

(6.1.23)

T 2

-Z

The relaxation signal as it returns to equilibrium is shown
in Figure 6.1-9 . Figure 6.1-10 Bulk magnetization illustration.