Biomedical Engineering Reference
In-Depth Information
Alternatively, the gradient field-recalled echo or gradient inversion method
inverts the precession direction of spin isochromats. Interestingly, slice-
selection gradient is not needed after initial phase in this process. So, refo-
cusing is achieved by using a negative read-out gradient for the first echo, a
positive one for the second echo, and so on. In both methods, all the precessing
isochromats point along the
x
direction after time TE. It results in first spin echo
generation.
3.1.1.1 Spin Isochromats in Motion
Let us consider the case of time-dependent position
x
(
t
) of a spin isochromat
in motion. The position may be represented as Taylor series expansion in the
x
direction:
x
(
t
)
=
S
+
V
t
+
A
x
t
2
+
higher order terms
where
S
is initial position of spin isochromat,
V
is velocity, and
A
is acceleration
in time
t
.
For simplicity, assume a spin isochromat moves along the
x
axis (
y
axis
and
z
axis assumed zero) and read-out occurs along the
x
axis. In that case,
according to Eq. (3.1),
G
x
gradient will have an effect on spin isochromat to
generate precession phase of moving spin isochromat relative to stationary
spin isochromat (see Fig. 3.2). This precession phase can be represented as
Figure 3.2:
Precessing isochromats are shown in motion to result nonzero
phase angle at odd echoes (arrows with lebel “0”). The isochromat magneti-
zation vectors within a voxel add up to a small resultant vector (short thick
arrow) if the isochromats within the voxel have different velocities. On even
echoes, all isochromat magnetization vectors point in the 0
◦
direction (along
the
x
-axis) independent of velocity (arrows lebeled “e”).
