Biomedical Engineering Reference
In-Depth Information
(x
n
, y
m
)
origin
slice at z
FIGURE 16.43
Depiction of an
x-y
slice plane of thickness
D
z
at a distance
z
, like the positions shown in
Figure 16.41.
w
G
x
w
2
B-B
0
w
1
w
0
0
x
1
x
2
x
FIGURE 16.44
Frequency encoding method for
x-
axis with two locations,
x
1
and
x
2
, shown.
frequency varies with distance
, a consequence of the linear magnetic field gradient, as
shown in Figure 16.44. A number of excited resonances positioned along the scan line
x
x
can contribute to the overall detected signal and are encoded in the received signal as
different frequencies.
Unlike diagnostic ultrasound imaging in which specific echo delays in time are associated
with reflectors at different round-trip distances, MRI signals for different spatial locations are
frequency encoded and added together in the same time signal position. In this case,
X
V
ð
f
Þ¼
S
ð
f
f
n
Þ
ð
16
:
75
Þ
n
The means of decoding these positions will be explained in a later section. Although MRI
systems have employed yet another linear magnetic gradient along the
-axis to provide
localization for this coordinate, a different phase-encoding scheme is now more common.
The mechanism employed is that of the flip angle, Eq. (16.61), with a different twist
y
jð
y
Þ¼o
t
¼ðg
B
0
t
þ g
G
y
t
p
y
Þ
ð
16
:
76
Þ
y
¼
y
0
þ
y
0
,where
in which
y
0
is the value at the center. In the previous discussion of the flip
angle, an rf magnetic field with an appropriate pulse width,
, was applied to the spins to
rotate a magnetization vector through a desired angle. In this context, Eq. (16.76) shows that
either the pulse length,
t
p
, can be used to change the phase.
The preferred method, as shown in Figure 16.45, is not to change pulse widths but rather
to alter amplitudes and signs of the gradient slope, which can be changed by voltage ampli-
tudes applied to the
t
p
, or the pulse gradient slope,
G
y
y
-axis gradient coil. In order to fill out the
x
-
y
plane, a means of
