Biomedical Engineering Reference
In-Depth Information
d
G
M
dt
¼
cM
B
eff
1
T
1
ð
M
z
M
0
Þ
e
z
1
T
2
M
?
þ
M
0
M
z
T
1
¼
c
ð
M
r
e
r
þ
M
u
e
u
þ
M
z
e
z
Þ
x
1
c
e
r
þ
1
e
z
M
r
e
r
þ
M
u
e
u
T
2
c
ð
x
L
x
Þ
e
z
e
r
þð
x
x
L
Þ
M
r
þ
x
1
M
z
M
u
T
2
e
u
þ
M
0
M
z
T
1
e
z
:
¼
x
L
x
Þ
M
u
M
r
T
2
x
1
M
u
ð
3
:
33
Þ
From (
3.33
) the changes of magnetization of the single coordinates of the
magnetization vector M, with respect to time and with respect to the rotating
coordinate axes thus read
d
G
M
r
dt
¼
M
r
þð
x
L
x
Þ
M
u
T
2
d
G
M
u
dt
¼ð
x
x
L
Þ
M
r
M
u
þ
x
1
M
z
ð
3
:
34
Þ
T
2
d
G
M
z
dt
¼
ð
M
0
M
z
Þ
x
1
M
u
:
T
1
3.1.5 Signal Detection
Due to the rf-field, the magnetic dipole moments are rotated into the x-y-plane.
The resulting motion is a spiral motion (nutation) in a downward z-direction, due
to the still ongoing precession about the static field z-axis. In this process the
transverse magnetization component increases until it reaches its maximum, when
it is completely tipped into the x-y-plane. After the rf-field has been switched off,
the magnetization returns to its equilibrium state (longitudinal magnetization in
time T
1
and transverse magnetization in time T
2
) and the magnetic dipole moments
again align along with the external B
0
-field. In both processes, the magnetic field
and the net magnetization (vector) respectively, of the moving magnetic dipoles
change accordingly during the downward and upward movement. These field
changes cause electromotive forces to be induced in nearby rf-coil elements (MR-
signal). The resulting generated currents (following Faraday's induction law)
provide the information that is finally transformed into the MR-image. Electrical
power production using spinning electromagnets near conducting coils may serve
as an analog to the induction process on the macroscopic scale.
The currents generated in the coil wires follow decay with the revised decay time
T
2
due to dephasing of the transverse magnetization. The corresponding signal in
the time domain is called free induction decay (FID). Controlled on-off switching
of the rf-fields is referred to as pulsing, and a set of rf-pulses is termed pulse
sequence.A90 FID pulse sequence rotates the magnetization by 90 into the x-y-
plane, whereas the spin-echo sequence combines a 90 and a 180 rotation: after a