Biomedical Engineering Reference
In-Depth Information
in which
f
n
¼
f
L
for this case. In general, the index
n
can be associated with the excitation
Larmor frequency at a location
x
n
. How this mapping is carried out is the subject of the next
section.
16.3.5 Setup for Imaging
To create images from detected signals, a means of spatially localizing the detected
waveforms must be used. Three methods are used to encode the waveform data and posi-
tion, one for each Cartesian coordinate. The three-dimensional image is discretized into tiny
cubes called voxels, each with a volume
.
The first step in setting up the image is to fix the desired location of the slice plane, one
voxel thick, along the
V
oxel
¼ D
x
D
y
D
z
-axis, as shown in Figure 16.41. The person to be imaged is slid into a
large superconducting magnet that creates a strong static field,
z
B
0
. Recall from cases 1 and
2 from Section 16.3.2 that a current in a wire or loop can generate a magnetic field. Electrical
coils are arranged within the magnet to create an electrically controlled linear magnetic
field gradient along the
z
-axis
!
B
z
¼
z
ð
B
0
þ
G
z
z
Þ
ð
16
:
72a
Þ
where
G
z
is a gradient constant in
T
/
m
. From Eq. (16.56), a unique Larmor frequency is
associated with each spatial location
z
,
o ¼ g
B
z
¼ g
B
0
þ g
G
z
z
ð
16
:
72b
Þ
The relative position
z
¼
0 is called the isocenter. The reference frequency associated with
this center is
by electronic mixing.
By applying a time excitation pulse with an appropriate center frequency as shown in
Figure 16.41, a specific location is selected. The envelope of the sinusoid used for time
o
0
¼ g
B
0
, which can be subtracted from
o
Δ
z
Δ
z
(a)
z
1
z
2
w
G
z
w
2
B-B
0
w
1
w
0
z
isocenter
(b)
FIGURE 16.41
(a) Side view of selected axial image plane locations. (b) Two regions corresponding to selected
locations on the
-axis magnetic field gradient. On the right vertical axis are regional gradient spectra from rf exci-
tation pulses whose Larmor center frequencies are selected for
z
z
-axis positions. Scale is exaggerated for clarity.
