Biomedical Engineering Reference
In-Depth Information
z
z'
B
0
B
0
M
0
t = 0
0
M
z'
M
0
t > t
p
f
y
y'
B
1
M
0
x'y'
cos
q
q
M
0
x'y'
sin
M
0
x'y'
q
x
x'
(a)
(b)
FIGURE 16.34
(a) Initial alignment of magnetization at
t
¼ 0. (b) Tipping of the net magnetization from the
z
-
axis through an angle
f
by the application of rf
B
1
field at the Larmor frequency aligned along
x
0
-axis in rotated
coordinates. The projections of the net magnetization onto the axes are shown.
z'
z'
z'
B
0
B
0
B
0
t > t
p
t > t
p
t = t
/2
+t
t > t
p
π
π
t = t
π
/2
t = t
π
f
=
π
/2
f
=
π
f
1
=
π
/2
y'
−
y'
y'
y'
M
0
B
1
B
1
B
1
M
0
f
2
=
π
x'
x'
x'
M
0
−
z'
(a)
(b)
(c)
FIGURE 16.35
y
0
-axis. (b) Tipping through an angle of
(a) Tipping through an angle of
p
/2 radians to the
p
z
0
-axis. (c) Tipping sequence: first tip through an angle of
y
0
-axis and then tip
radians to the -
p
/2 radians to the
y
0
-axis.
through an angle of
p
radians to the -
Iftheflipangleischosentobe90
or
p
/2 radians, the magnetization is rotated
y
0
-axis,
as shown in Figure 16.35a. The vertical component is brought a value of zero in
the
z
0
-axis to a position lying along the
from an initial value of M
0
along the
x
0
-
y
0
M
0
over a
period of time. This recovery can be described by the following equation and
Figure 16.36.
plane and then rebounds back to its original initial value of
M
z
0
ðy ¼ p=
2
Þ¼
M
0
½
1
exp
ð
t
=
T
1
Þ
ð
16
:
62
Þ
where
starts after the rf pulse. It is also called the
longitudinal time constant because of its association with the vertical direction. This relaxa-
tion time is affected by temperature and the viscosity of the tissue or material (it is longer as
viscosity increases).
If the flip angle is chosen to be 180
or
T
1
is the spin lattice recovery time and
t
p
radians, the magnetization is rotated from an
z
0
-axis to a position lying along the -
z
0
-axis. In this antiparallel
initial value of
M
0
along the
orientation, the appropriate relaxation equation is
M
z
0
ðy ¼ pÞ¼
M
0
½
1
2 exp
ð
t
=
T
1
Þ
ð
16
:
63
Þ
