Biomedical Engineering Reference
In-Depth Information
1
0.8
0.6
0.4
0.2
0
pi/2 angle
pi angle
t=T1
t=T1
0.2
0.4
0.6
0.8
1
0
500
1000
1500
2000
2500
Time (ms)
FIGURE 16.36
Plots of the recovery of a magnetization vector component along the
z
0
-axis for a relaxation time
T
1
,
versus time for a
p
/2 rotation, and a
p
rotation for gray matter of the brain.
s
This change is illustrated by Figure 16.35b. A generalization of these equations to an
arbitrary value of the z- component of magnetization following the rf pulse,
0
z
M
,is
"
!
exp
#
0
z
0
M
0
M
M
z
0
ð
t
Þ¼
M
0
1
1
Þ
ð
16
:
64
Þ
ð
t
=
T
1
To determine the magnetization components in the
x
-
y
plane, refer back to the situation
y
0
-axis at time
of the
p
/2 flip angle where the magnetization is rotated to the
t
¼
t
p/2
.In
0
x
0
y
0
order for equilibrium to be restored, the initial
beginning after
the rf pulse must decay back to a zero value so the original value of the purely vertical M
0
can be recovered,
M
component at a time
t
0
M
x
0
y
0
ðy ¼ p=
2
Þ¼
M
x
0
y
0
½
exp
ð
t
=
T
Þ
ð
16
:
65
Þ
2
in which
T
2
is the spin-spin relaxation time as plotted in Figure 16.37.Becauseofthe
motion and orientation of this component, its interaction with the material or tissue
is different from that of
T
1
.AsFigure 16.38 shows, a dephasing process occurs as vectors
sweep over an increasing sector over time so the net sum of vectors gradually goes
to zero.
