Image Processing Reference
In-Depth Information
Signal
rf
g
FIGURE 10.10 Gradient echo version of the velocity-encoding sequence.
different velocity-encoding gradient strengths, to allow subtraction of phase off-
sets arising from sources other than motion (e.g., eddy currents). The velocity is
typically calculated from the phase difference as
v
=
(v enc /
π
)
∆φ
(10.18)
where v enc is the velocity that produces a phase shift of
radians. Note that the act
of encoding the velocity as a phase angle implies that velocities outside a certain
range are aliased into a 2
π
range, so velocities greater than or equal to v enc or less
than -v enc are wrapped to the range [
π
v enc , v enc ). Separate acquisitions with velocity-
encoding gradients in the x, y, and z directions allow the calculation of all compo-
nents of the velocity vector.
An advantage of velocity-encoded images (compared with the displacement
encoding of tagging techniques such as SPAMM) is improved spatial resolution,
because the velocity is measured at every pixel in the image (~1 mm, compared
with a typical stripe spacing of 5-8 mm). Also, velocity images allow the simple
calculation of instantaneous strain rate. The Cartesian rate of deformation tensor
V is derived from the spatial derivative of velocity:
1
2 (
=
v
x
VDDD
=
+
T
);
(10.19)
The rate of deformation tensor is related to the material derivative of E by
[23, p. 446]
DE
Dt
=
FVF
T
(10.20)
A disadvantage of velocity encoding is that motion through the cardiac cycle
must be reconstructed by the integration of myocardial velocities over time. A
nonrigid motion tracking procedure is described by Zhu et al. [33]. Due to
through-plane motion, material points are not imaged through time, leading to
difficulties in the calculation of 3-D displacement.
A stimulated echo variant of the velocity-encoding pulse sequence was pro-
posed by Wedeen et al. [34] to give velocity-encoded images in which the effects
of through-plane motion are eliminated. Unlike the slice following CSPAMM
Search WWH ::




Custom Search