Biomedical Engineering Reference
In-Depth Information
where
M
0
x
,
M
0
y
, and
M
0
z
are the values of
M
x
,
M
y
, and
M
z
at
t
=
0, and
M
0
is the
steady-state magnetization in the
z
direction. This condition is good for spins
rotating in the transverse plane aligning through the
x
axis at
M
0
y
=
0
.
For fundamental understanding for the signal generation, we describe dif-
ferent signal intensities of main pulse sequences as follows:
90
◦
selective
−
TE
/
2
−
180
◦
:
S
=
M
0
exp(
−
TE
/
T2)
180
◦
−
(TR
−
TE
/
2)
−
90
◦
−
TE
/
2
−
180
◦
:
S
=
M
0
{
1
−
2exp[
−
(TR
−
TE
/
2)
/
T1]
}
exp(
−
TE
/
T2)
90
◦
−
TE
/
2
−
180
◦
−
(TR
−
TE
/
2)
−
90
◦
−
TE
/
2
−
180
◦
:
S
=
M
0
{
1
−
2exp[
−
(TR
−
TE
/
2)
/
T1]
+
exp(
−
TR
/
T1)
}
exp(
−
TE
/
2)
The complete expression for the echo signal has four separate velocity boundary
conditions:
Plug flow signal will be:
SV
(TR
−
TE
/
2)
/
D
+
SVTE
/
(2D)
+
S
[1
−
V
(TR
+
TE
/
2)D]
if 0
<
V
<
D
/
(TR
+
TE
/
2)
SV
(TR
−
TE
/
2)
/
D
+
S
(1
−
VTR
/
D
) f
D
/
TR
+
TE
/
2)
<
V
<
(TR
S
[1
−
V
TE
/
(2
D
) f
D
/
TR
<
V
<
D
/
(TE
/
2)
0 f
V
>
D
/
(TE
/
2)
Laminar flow signal will be:
S
a
[
V
m
(TR
−
TE
/
2)
/
(2
D
)]
+
S
b
V
m
TE
/
(4
D
)
+
S
c
[1
−
V
m
(TR
+
TE
/
2)
/
2
D
)]
if 0
<
V
m
<
D
/
(TR
+
TE
/
2)
S
a
[
V
m
(TR
−
TE
/
2)
/
(2
D
)]
+
S
b
{
1
−
D
/
2
V
m
(TR
+
TE
/
2)]
−
V
m
TR
/
(2
D
)
}
+
S
c
D
/
[2
V
m
(TR
+
TE
/
2)] if
D
/
(TR
+
TE
/
2)
<
V
m
<
D
/
TR
S
a
[1
−
D
/
(2
V
m
TR)
−
V
m
TE
/
4
D
)]
+
S
b
{
D
/
(2
V
m
TR)
−
D
/
[2
V
m
(TR
+
TE
/
2)]
}
+
S
c
D
/
[2
V
m
(TR
+
TE
/
2)] if
D
/
(TR)
<
V
m
<
D
/
(TE
/
2)
S
a
[
D
/
V
m
TE)
−
D
/
2
V
m
(TR)]
+
S
b
{
D
/
(2
V
m
TR)
−
D
/
[2
V
m
(TR
+
TE
/
2)]
}
+
S
c
D
/
[2
V
m
(TR
+
TE
/
2)]
if
V
m
>
D
/
(TE
/
2)
90
◦
selective
−
TI
−
90
◦
selective
−
TE/2
−
180
◦
selective pulse:
a. 90
◦
−
TE/2
−
180
◦
:
S
a
=
M
0
exp (TE/T2)
b. 90
◦
−
TI
−
90
◦
−
TE/2
−
180
◦
:
S
b
=
M
0
[1
−
exp(
−
TI
/
T1] exp(
−
TE
/
T2)
