Biomedical Engineering Reference
In-Depth Information
TABLE 16.3
T
1
and T
2
Values for Common Tissue Types
Tissue
T
1
(ms)
T
2
(ms)
Cerebrospinal fluid
2,000
1,000
Fat
160
100
Gray matter
520
95
Malignant tumor
800
200
Typical edema or infarction
600
150
White matter
380
85
EXAMPLE PROBLEM 16.14
After a
/2 rotation, determine the percentage of recovery of the magnetization vertical compo-
nent associated with
p
T
1
in fat when the horizontal magnetization vector component has decayed
to a 1/
e
value.
Solution
From Table 16.3,
100 ms, which would be the time required for the horizontal magnetiza-
tion component to decay to a value of 1/
T
2
¼
e
value. With the value of
T
1
¼
160 ms and Eq. (16.62), the
relative recovery value is
1
exp
ð
T
2
=
T
1
Þ¼
0
:
465
Detected Response Waveforms
Because sufficient background information has been given to describe the excitation and
decay of a nuclear resonance, it is now possible to describe the kinds of signals detected. A
setup like that of Figure 16.33a is used with a detection loop in a plane perpendicular to the
x
/2 rf excitation pulse for tipping the field 90
consists of a tone burst
long at the
Larmor frequency according to Eq. (16.61). Since the duration of the pulse is much longer
than any of the recovery and decay time constants, a sinusoidal excitation in an exponential
form will be used to simplify analysis. The resulting transverse magnetization vector in the
x
-axis. A
p
t
p
-
y
plane is
M
xy
ð
t
Þ¼
M
0
xy
e
j
t
j=
T
2
e
j
o
t
ð
x
þ
y
Þ
t
<
t
p
ð
16
:
67
Þ
The effect of this excitation is to cause a resonance and a change in the spin states of
hydrogen electrons. Faraday's law can be applied to the detection of the overall net magne-
tization response from Section 16.3.2, case 3. The area
S
of a loop of diameter
d
can be
rewritten in terms of magnetization
M
and an equivalent current
I:
S
¼
M
I
ð
16
:
68
Þ
