Image Processing Reference
In-Depth Information
using guide-point modeling [27]. The intersections of the model tags could then
be superimposed on the images (giving a set of “model stripes”), allowing direct
comparison between image stripes and model stripes. Image-derived forces were
then calculated to pull the model stripes toward the image stripes. A Leven-
burg-Marquardt nonlinear least-squares algorithm was used to minimize Equation
9, updating the material (element) positions of the image stripe points at each
iteration. By interactively modeling the deformation in all slices simultaneously,
without the need to stripe tracking on each image, the time required for image
analysis was decreased by a factor of 10.
10.3.5
S LICE F OLLOWING
CSPAMM can also be used in conjunction with slice following [28] to give tagged
images in which the effects of through-plane motion are eliminated. By making
the first RF pulse slice selective, only a thin slice of tissue is excited and tagged
by the SPAMM sequence. A thick slice encompassing the tagged slice (and the
range of possible through-plane motions) is then imaged by the subsequent imaging
pulse sequence. Subtraction of the complementary tagged images cancels the signal
in the thick slice which is not tagged, leaving an image of the tagged myocardium
only. This simplifies the motion tracking and strain analysis procedure, in that
material points imaged at ED are also imaged in each subsequent frame. Note that
slice following is not necessary for the evaluation of 2-D or 3-D motion and strain,
but does allow a simplified 3-D analysis.
10.4
HARP
10.4.1
T HEORY
In 1998, Osman et al. [29] introduced a fast analysis for MR tagged images using
harmonic phase, or HARP. Noting that the tagged image is spatially modulated by
a cosine (in the case of a 1-1 tag pulse sequence; a sum of cosines for a DANTE
type tag pulse sequence), at point c in Figure 10.1 the longitudinal component of
the magnetization is
MM
z
()
X
=
()co (
X
k
X
)
(10.10)
0
e
where k is given by the strength and duration of the tagging gradient and X is
e
the initial position of the material point at the time point c. The Euler equations
give the exponential form:
M
() (exp(
X
0
2
M
()
X
=
j
kX
)
+
exp(
j
kX
))
(10.11)
z
e
e
This expresses the cosine modulation as the sum of two complex phasors
rotating in opposite directions, as in Figure 10.7 .
Search WWH ::




Custom Search